\\over \\sim \\;$}\n\\def\\rfe{R$_{\\rm FeII}$}\n\\def\\ai{A.I.($\\frac{1}{4}$)\\/}\n\\def\\aox{$\\alpha_{ox}$\\/}\n\\def\\gs{$\\Gamma_{\\rm soft}$}\n\\def\\gh{$\\Gamma_{\\rm hard}$}\n\\def\\G{$\\Gamma$}\n\\def\\ne{n$_{\\rm e}$\\/}\n\\def\\ergss{ergs s$^{-1}$}\n\\def\\simgt{\\lower.5ex\\hbox{\\gtsima}} % > over MMM\n\\def\\bv{{\\bf $\\bigvee$}\\/}\n\\def\\qu{{$\\lambda$ 1400}}\n\\def\\h{$h^{-1}$}\n\\def\\hii{{\\sc Hii\\/}}\n\\def\\hi{{\\sc Hi\\/}}\n\\def\\a{$\\alpha$}\n\\def\\ha{{\\sc H}$\\alpha$}\n\\def\\nv{{\\sc Nv}$\\lambda$1240}\n\\def\\civ{{\\sc{Civ}}$\\lambda$1549\\/}\n\\def\\civnc{{\\sc{Civ}}$\\lambda$1549$_{\\rm NC}$\\/}\n\\def\\civbc{{\\sc{Civ}}$\\lambda$1549$_{\\rm BC}$\\/}\n\\def\\cmsq{cm$^{-2}$\\/}\n\\def\\cm3{cm$^{-3}$\\/}\n\\def\\md{$\\dot{\\rm M}$}\n\\def\\rg{$\\rm R_{\\rm g}$}\n\\def\\hb{{\\sc{H}}$\\beta$\\/}\n\\def\\hg{{\\sc{H}}$\\gamma$\\/}\n\\def\\hbbc{{\\sc{H}}$\\beta_{\\rm BC}$\\/}\n\\begin{document}\n\\maketitle\n\\section{Introduction \\label{sec:intro}}\n\nThe Broad Line Region (BLR) in Active Galactic Nuclei (AGN) is unresolved with present\nday imaging detectors and it will remain so for the foreseeable future. This is why\n``one quasar spectrum is really worth a thousand images'' as stressed by Gary Ferland\nat this meeting. In response we would add that {\\em a thousand spectra are better than\none average spectrum}. Understanding the diversity in optical spectroscopic properties\nof AGN is the key to any realistic AGN modeling \\cite{bg92,smd}. The ideal to\nreconstruct the BLR velocity field from a single profile is not realistic \\cite{pen90}.\n\nDetermination of BLR structure and kinematics can be approached in two ways. It has\nbeen recognized for a long time that strong broad and narrow emission lines coming from\nboth high and low ionization species are present in Seyfert galaxies and quasars. This\nis considered a defining spectroscopic property of AGN. Restricting attention to broad\nlines: a) typical (i.e., strongest and most frequently observed) high ionization lines\n(HIL: ionization potential $\\simgt$ 50 eV) are \\civ\\ \\heii\\ and \\heiiuv\\ lines; while\nb) observed low ionization lines (LIL: ionization potential $\\simlt $ 20 eV) include\n\\hi\\ Balmer lines, \\feii\\ multiplets, \\mgii, and the Ca{\\sc ii}\\ IR triplet.\n\nThe first approach involves the study of line variability in response to continuum\nchanges. This approach has been pursued through a number of successful monitoring\ncampaigns using Reverberation Mapping (RM) techniques. RM requires a large amount of\ntelescope time and, consequently, has been achieved only for a handful of sources. RM\nconfirms that photoionization is the main heating process in the BLR and that a large\npart of the BLR is optically thick to the ionizing continuum (e. g. \\pcite{baldwin97}).\nRM studies have quantified a main difference between HIL and LIL; HIL respond to\ncontinuum changes with a time delay of a few days while the LIL respond with a delay of\ntens of days. This implies that the LIL are emitted at larger distance from the\ncontinuum source (\\pcite{ulr,kor95}. An exhaustive list of reference can be found in\n\\pcite{smd}). RM applied to line profiles suffers from uncertainty in our knowledge\nabout the physics of continuum and broad line formation, so that conflicting models can\nstill describe the same lag times \\cite{pen91,wanpet96}.\n\nThe second approach involves statistical analysis of large samples of line profiles\nwhich differ because of properties that may affect the BLR structure, for example\nsamples of radio quiet (RQ) and radio loud (RL) AGN. Statistical studies can be done\nfor a single line or by comparing lines sensible to different physical parameters (e.g.,\nstrongest LIL and HIL). The statistical approach, on which we will focus here, is more\nempirical and therefore requires a conceptual framework for interpretation. This\napproach is often criticized as relying on several assumptions including that the\nprofile variability does not influence profile shapes and that the non-simultaneity of\nthe observations of LIL and HIL are unimportant. Actually as the size of high quality\ndata samples grow these effects become less and less important.\n\n\\section{Baring the Broad Profiles \\label{bare}}\n\nThe collection of moderate resolution (\\l/$\\Delta$\\l $\\sim 10^3$) optical and UV\nspectra of good quality (S/N $\\simgt$ 20 in the continuum) has become possible only in\nrecent years thanks to the widespread use of CCD detectors and the unprecedented\nsensitivity and resolution of the UV spectrographs on board HST. For practical\npurposes, \\hi\\ \\hb\\ and \\civ can be considered representative of HIL and LIL\nrespectively. They are also the best lines for statistical studies because they permit\ncomparison in the same sources out to z=1.0. The linearity of response of the\ncurrently employed detectors has made possible a reliable correction for emission\nfeatures contaminating \\hb\\ and \\civ, which are: (1) \\feii\\ emission; significant\n\\feiiuv\\ emission contaminates the red wing of \\civ, and has been identified in I Zw 1\nby \\pcite{m96} and later confirmed by \\pcite{lao97}; (2) \\heii\\ emission for \\hb, and\n\\heiiuv\\ + \\oiiiuv\\ for \\civ; (3) \\oiii\\ for \\hb; (4) narrow component, present in\nseveral cases in both \\hb\\ and \\civ.\n\n\n\\civ\\ often shows a narrow core with FWHM $\\sim$ 1000-2000 \\kms, which is\nsystematically broader than the narrow component of \\hb\\ (\\hbnc). The separation\nbetween the broad component \\civbc\\ and the core component is often ambiguous. This\ncore however shows no shift with respect to the AGN rest frame \\cite{brot94}, no\nvariations \\cite{turla}, and correlates with \\oiii\\ prominence \\cite{franc92}. It can\ntherefore be ascribed to the NLR and considered as the narrow line component of \\civ\\\n(\\civnc). The different width between \\civnc\\ and \\hbbc\\ can be understood in terms of\ndensity stratification \\cite{sm99} without invoking an additional emitting region such\nas the so-called ``intermediate line region''. Even if \\civnc\\ fractional intensity is\nsmall ($\\sim$ 10\\%), and in some cases obviously absent, failure to account for \\civnc\\\nhas led to the erroneous conclusions that FWHM \\civbc\\ $>$ FWHM \\hbbc\\ and that the\n\\civ\\ peak shows no shift with respect to \\hb\\ \\cite{cb96}.\n\n\\section{A DIFFERENT BLR STRUCTURE IN RADIO LOUD AND RADIO QUIET AGN? \\label{struct}}\n\n\\scite{m96} made a comparison between \\civbc\\ and \\hbbc\\ for a sample of 52 AGN (31\nRL). They presented measures of radial velocity for the blue and red sides of \\hbbc\\\nand \\civbc\\ at 5 different values of fractional intensity which provide a quantitative\ndescription of the profiles. The reference frame was set by the measured velocity of\n\\oiii$\\lambda$5007$\\rm{\\AA}$ (IZw1 was the only exception). Standard profile parameters\nlike peak shift, FWHM, asymmetry index and curtosis can be extracted from these\nmeasures. Representative profiles constructed from the {\\em median values} of \\civbc\\\nand \\hbbc\\ $v_r$\\ are reproduced in the left panels of Fig. \\ref{fig:rq} and\n\\ref{fig:rl} for the radio quiet (RQ) and radio loud (RL) samples respectively.\n\\begin{figure}\n %\\begin{center}\n \\leavevmode\n \\includegraphics[width=\\columnwidth, height=8cm]{fig01.eps}\n% \\includegraphics[width=\\textwidth, height=10cm]{Fig01dd.eps}\n\\caption[]{Profiles of \\civbc\\ (solid lines) and \\hbbc\\ normalized to the same peak\nintensity and constructed from median values of the radial velocities measured on the\nblue and red sides of the profiles for the 21 RQ AGN of \\scite{m96} (left panel).\nEmission line profiles of \\civ\\ (middle panel) and \\hb\\ (right panel) of the prototype\nNLSy1 galaxy I Zw 1, adapted from \\scite{m96}. The thick and the dotted lines trace \\hb\\\nand \\oiii\\ after \\feiiopt\\ (dashed line) subtraction. \\label{fig:rq}}\n %\\end{center}\n\\end{figure}\n\n\\civbc\\ is broader than \\hbbc in both RQ and RL samples and it is {\\em almost always}\nblueshifted relative to \\hbbc. However Fig. \\ref{fig:rq} and Fig. \\ref{fig:rl} show\nsignificant differences between RQ and RL AGN. In RQ AGN, \\civbc\\ is significantly\nblueshifted with respect to the source rest frame while \\hbbc\\ is symmetric and\nunshifted. Contrarily in RL AGN \\civbc\\ is more symmetric, while \\hbbc\\ is shifted to\nthe red at peak intensity and redward asymmetric as well (the median profile\ncorresponds to the type AR,R according to \\pcite{sul89}). There are two important\nresults which are not displayed in the Figures: (i) in RQ AGN, \\civbc\\ blueshifts are\napparently uncorrelated with respect to any \\hbbc\\ line profile parameter and the\nlargest \\civ\\ blueshifts are associated with the lowest W(\\civ); (ii) in RL AGN, on the\ncontrary, \\civbc\\ and \\hbbc\\ line profile parameters (FWHM and peak shift) appear to be\ncorrelated. Asymmetry index of \\civbc\\ and \\hbbc, even if not correlated, shows a clear\ntrend toward asymmetries of the same kind (symmetric or redward asymmetric). These\nfindings on \\civbc\\ have been confirmed by other authors (\\pcite{wills95}, save the\ndifference in terminology and line profile decomposition) and especially by an analysis\nof archival HST/FOS observations which have become publicly available after 1995\n\\cite{sul20}.\n\nThe LIL and HIL emitting regions are apparently de-coupled in at least some RQ\nsources. The ``de-coupling'' is well seen in I Zw 1, the prototype Narrow Line Seyfert\n1 Galaxy (NLSy1; see Fig. \\ref{fig:rq}). The \\hb\\ profile is very narrow, slightly\nblueward asymmetric and unshifted with respect to the rest frame defined by 21 cm\nobservations, while the \\civ\\ profile is almost totally blueshifted. At least in the\ncase of I Zw 1 the distinction between LIL and HIL emitting regions appears to be\nobservationally established (it was actually suggested because of the difficulty to\nexplain the relative strengths of LIL and HIL emission using a photoionized ``single\ncloud;'' \\pcite{cs88}). There is a very important zeroth-order result here: since I Zw\n1 is a strong \\feiiuv\\ emitter, we have HIL \\civ\\ and LIL \\feiiuv\\ in the same\nrest-frame wavelength range. We see that \\feiiuv\\ is obviously unshifted (this can be\nvery well seen by shifting an \\feiiuv\\ template to the peak radial velocity of \\civ).\nThis result disproves models that see an (unknown) wavelength dependent mechanism\naccounting for the quasar broad line shifts relative to the quasar rest frame.\n\nRL AGN apparently mirror RQ AGN in a curious way: \\civbc\\ is more symmetric, while\n\\hbbc\\ shows preferentially redshifted profiles and increasingly redward asymmetries.\nLarge peak redshifts ($v_r \\simgt 1000$ \\kms, as in the case of OQ 208, Fig.\n\\ref{fig:rl}) are rarely observed; \\hbbc\\ peak shifts are usually small ($\\Delta\nv_r$/FWHM $\\ll$ 1, median profile of Fig. \\ref{fig:rl}). RL \\civbc\\ and \\hbbc\\ data\nleave open the possibility that both lines are emitted in the same region. \\civbc\\\nshows a red-wing (very evident in the latest, higher S/N spectra analyzed by\n\\scite{sul20}), which cannot be entirely accounted for by \\feiiuv emission. It is\ninteresting to note that superluminal sources with apparent radial velocity $\\beta_{\\rm\napp} \\sim 5-10$~ (whose radio axis is probably oriented close to the line of sight in\nthe sample of \\scite{m96} show very strong \\civ\\ redward asymmetries, low W(\\civ) and\nW(\\hbbc). This result suggests that redshifts are maximized in RL objects at\n``face-on'' orientation (we assume that any disk is perpendicular to the radio axis).\n\n\\section{NLSy1 NUCLEI ARE NOT A DISJOINT RQ POPULATION}\n\nNLSy1 are neither peculiar nor rare. The 8$^{th}$\\ edition of the \\scite{veron98}\ncatalogue includes 119 NLSy1 satisfying the defining criterion FWHM Balmer $\\simlt$\n2000 \\kms. They account for $\\approx 10$\\%\\ of all AGN in the same redshift and\nabsolute magnitude range. Attention toward NLSy1 remained dormant after their\nidentification as a particular class \\cite{op85} until it was discovered that they may\nrepresent $\\approx$1/3--1/2 of all soft X-ray selected Seyfert 1 sources (e. g.,\n\\pcite{grupe98}). NLSy1 are also apparently favored in AGN samples selected on the\nbasis of color. They account for 27\\%\\ of the RQ \\scite{bg92} sample, probably because\nof an optical continuum that is steeply rising toward the near UV. NLSy1 do not occupy\na disjoint region in parameter space. They are at an extremum in the FWHM(\\hb) vs.\n\\rfe\\ (=I(\\feii \\l 4570/I(\\hbbc)) and in the ``Eigenvector 1'' parameter spaces\n\\cite{bg92,bf99,smd}. Also, the soft X-ray spectral index \\gs\\ shows a continuous\ndistribution which includes NLSy1 at the high end \\cite{wang96,smd,sul20}.\n\n\\begin{figure}\n %\\begin{center}\n \\leavevmode\n \\includegraphics[width=\\columnwidth, height=8cm]{fig02.eps}\n% \\includegraphics[width=\\textwidth, height=10cm]{Fig01dd.eps}\n \\caption[]{Left panel: Profiles of \\civbc\\ (solid lines) and \\hbbc\\ normalized to the same\n peak intensity and constructed from median values of the radial velocities measured on\n the blue and red sides of the profiles for the 31 RL AGN of \\scite{m96}.\n Middle panel: \\hb\\ spectrum of OQ 208, showing a single, widely displaced \\hbbc\\ peak (adapted from \\pcite{m93}).\n Right panel: \\ha\\ profile of the prototype of ``wide-separation double peakers'' Arp 102B.\n Unpublished spectrum obtained at the 1.82 m telescope of the Asiago observatory on March 25, 1989.\n The thick solid line traces \\hbbc.}\n \\label{fig:rl}\n %\\end{center}\n\\end{figure}\n\nOrientation can easily explain much of the RQ phenomenology observed by \\scite{m96}. I\nZw 1 can be considered as an extremum with an accretion disk seen face-on\n(i$=0^\\circ$), and an outflowing wind observed along the disk axis. We can infer that\nthe opening angle of any \\civ\\ outflow is probably large (i. e., the wind is quasi\nspherical) because \\civ\\ profiles like I Zw 1 are rare. Other NLSy1 show low W(\\civ),\nand strong \\feiiopt, but do not always show large \\civ\\ blueshifts \\cite{rp97}.\nNonetheless, it is still possible that NLSy1 may be structurally different from other\nRQ AGN. If the soft X-ray excess of NLSy1 is due to high accretion rate, then a slim\naccretion disk is expected to form \\cite{abram88}. Line correlations presented in\n\\cite{sul20} appear to hold until FWHM(\\hb)$\\simlt$ 4000 \\kms. For FWHM$\\simgt$ 4000\n\\kms line parameters appear to be uncorrelated however it is still unclear it is at\npresent unclear because of the difficulty in measuring weak and broad \\feiiopt sources\nand/or because of a BLR structural difference. This limit may be related to the\npossibility of sustaining a particular disk structure and an HIL outflow. A second\nparameter, independent from orientation is needed to account for the FWHM(\\hbbc) vs\n\\rfe\\ vs \\gs\\ sequences (see \\pcite{smd,sul20} for a detailed discussion).\n\n\n\\section{Inferences on BLR Models for RQ AGN}\n\nModels developed almost independently of the data through the 80's and early 90's.\nThe situation has now changed because of three main developments: (1) the ``Eigenvector\n1'' correlations allow a systematic view of the change in optical emission line\nproperties for different classes of AGN \\cite{bg92,bf99,smd}; (2) the \\civ\\ - \\hb\\\ncomparison has yielded direct clues about the structure of the BLR \\cite{m96,sul20} and\n(3) data collected for RM projects provide a high-sampling description of line\nvariations. For instance, binary black hole scenarios \\cite{gask96} were recently\nchallenged by the failure to detect the radial velocity variations expected from\nprevious observations and model predictions \\cite{eracl97}.\n\nA model in which \\civ\\ is emitted by outflowing gas (e.g. a spherical wind) while\n\\hbbc\\ is emitted in a flattened distribution of gas (observed in a direction that\nminimizes velocity dispersion) such as an optically thick disk (obscuring the receding\nhalf of the \\civ\\ flow, \\pcite{liv97}) or at the wind base is immediately consistent\nwith the I Zw 1 data. The big question is whether the results for I Zw 1 can be\nstraightforwardly extended to other RQ AGN.\n\nAn accretion disk (AD) provides a high density and high column density medium for\n\\feii\\ production (e. g. \\pcite{dj92}), and possibly other low ionization lines such as\nCaII (e. g. \\pcite{dd99}). AD avoid conflict with the stringent restrictions on line\nprofile smoothness imposed by the first extremely high s/n Balmer line observations\n(\\pcite{arav97,arav98}) of -incidentally- two NLSy1. They place a lower limit of\n(10$^{7-8}$) on the number of discrete emitters needed to explain the observed profiles.\n\nWinds arise as a natural component of an AD model when the effects of radiative\nacceleration are properly taken into account \\cite{murray95,mc98} or when a\nhydromagnetic or hydrodynamic treatment is performed \\cite{bottorff97,williams99}. A\nsignature of radiative acceleration is provided by observations of ``double troughs'' in\n$\\approx \\frac{1}{5}$ of BAL QSOs i. e., of a hump in the absorption profiles of \\nv\\\nand \\civ\\ at the radial velocity difference between \\lya\\ and \\nv, 5900 \\kms. Such a\nfeature indicates that \\lya\\ photons are accelerating the BAL clouds (\\pcite{arav94},\nand references therein). Additional evidence is provided by the radial velocity\nseparation in the narrow absortion components of \\lya\\ and \\nv\\ which show the same\n$\\Delta v_r$\\ of the two doublet components of \\civ\\ (e. g. \\pcite{wampler91}).\n\n\\section{The Trouble With Bare Accretion Disks and Bipolar Flows}\n\nRelativistic Keplerian disks \\cite{ch89,sb93} may explain unusual profile shapes (e.g.\ndouble-peaked profiles of Balmer emission lines; \\pcite{eh94,sul95}). Uniform\naxisymmetric disk models produce double-peaked line profiles with the blue peak\nstronger than the red peak because of Doppler boosting, a feature that is not always\nobserved in these already rare profiles. To solve this problem, \\scite{sb95} and\n\\scite{eracl95}, proposed that the lines can originate in an eccentric (i.e.\nelliptical) disk. Simple disk illumination models can also produce single peaked LIL,\nprovided they are produced at large radii ($\\simgt 10^3$\\ gravitational radii) or that\nthe disk is observed at small inclination \\cite{dc90,rokaki92,sul98}. The first of these\nconditions may be met in all NLSy1 galaxies; both of them seem to be met in I Zw 1.\n\nAside from NLSy1 sources, there is general disagreement between observations and model\npredictions for externally illuminated Keplerian disks in a line shift-- asymmetry\nparameter space \\cite{sul90}. Only a minority ($\\simlt$ 10 \\%) of RL and a handful of\nRQ AGN show double peaked Balmer lines suggestive of a Keplerian velocity field\n\\cite{eh94,sul99}. Double-peakers (e. g. Arp 102B in Fig. \\ref{fig:rl},\nFWHM(\\hbbc)$\\simgt$10000 \\kms) cannot be like the classical cases because the line\nwidths are much smaller. The peaks often vary out of phase (Arp 102B: \\pcite{mp90}, 3C\n390.3: \\pcite{zheng91}). Double peaks (NGC 1097) \\cite{sb93,sb95} or one of the peaks\n(Pictor A) \\cite{sul95} sometimes appear quite suddenly. Profile variability studies of\nBalmer lines force us to introduce second order modifications to the basic scheme, such\nas: eccentric rings and precession \\cite{eracl95,sb97}, inhomogeneities such as\norbiting hot spots \\cite{zheng91}, and warps \\cite{bachev99}. Not even these {\\em\nepicycles} are always capable of explaining the observed variability patterns. Even if\nelliptical AD models do well in explaining the integrated profiles, they face important\ndifficulties in explaining variability patterns.\n\nA serious problem for AD models of emission lines is emerging from spectropolarimetric\nobservations. If profile broad line shapes are orientation dependent then, in\nprinciple, the profile shape in polarized light will depend on the distribution of the\nscatterers relative to the principal axis and to our line of sight. Early\nspectropolarimetric results showed a discrepancy with the simple disk +\nelectron-scattering-dominated atmosphere models, which predicted polarization\nperpendicular to the radio axis. The observed polarization is low, parallel to the disk\naxis, and shows no statistically significant wavelength dependence \\cite{anton88}.\nRecently \\scite{anton96} and \\scite{corbett98} included double-peakers in their\nsamples, and obtained troublesome results for disk emission models because the\npolarized \\ha\\ profiles are centrally peaked \\cite{corbett98}. They investigated the\ncase of disk emission where the scattering particles are located above and below an\nobscuring torus, along its poles. This ``polar scattering model'' is successful in\nexplaining the polarized profiles {\\em but not the position angle of the polarization\nvector}.\n\nThe same polarization studies indicate that the {\\em only} scenario that can account\nfor both the shapes of the scattered line profiles and the alignment of the optical\npolarization with the radio jet in wide separation double peakers like Arp 102B (Fig.\n\\ref{fig:rl}) involves a {\\em biconical} BLR within an obscuring torus. \\ha\\ photons\nemitted by clouds participating in a biconical flow are scattered towards the observer\nby dust or electrons in the inner wall of the surrounding torus. The particular case of\nbiconical outflow was first developed to reproduce observed profiles by\n\\scite{zheng90}. This model has been successfully applied to fit observed profiles in\ndouble-peaked objects \\cite{zheng91,sul95}.\n\nDouble peaked or single blueshifted peak LIL profiles fitted with bi-cone outflow\nmodels require that the receding part of the flow is also seen. Self-gravity may be\nimportant beyond $\\sim 1$ pc, and the disk may be advection-dominated and optically\nthin \\cite{liv96}. Recent work by \\scite{sh99} models the vertical structure of AD and\nthe origin of thermal winds above AD. They not only find that a wind powered by a\nthermal instability develops in all disks with certain opacity laws but also that in\ndisks dominated by bremsstrahlung radiation, a time-dependent inner hole develops below\na critical accretion rate. This scenario provides a natural explanation for transient\ndouble-peakers, such as NGC1097 \\cite{sb95,sb97}, but low accretion rate is a\nrequirement for {\\em both} advection dominated disks and hole formation.\n\n\\scite{sul95} explored the idea that the double-peaked emitters represent a\ngeometrical extremum where an outflow is viewed close to pole-on. However,\ndouble-peakers are associated with double-lobe radio-sources suggesting that the line\nof sight has a considerable inclination to the axis of the jets. The problem arises\n{\\em only} if the core (pc scale) jets is related to the much larger (100 kpc scale)\njets. There is both theoretical (e. g. \\pcite{valtonen99}) and observational evidence\nagainst this assumption.\n\n\\section{Emission from Clouds Illuminated by an Anisotropic Continuum}\n\nModels based on radiative acceleration of optically thick clouds with small volume\nfilling factor gained wide acceptance in the Eighties (\\pcite{om86} and references\ntherein; see also \\pcite{binette96}). However, problems with cloud confinements and\nstability \\cite{mathews90} have made them increasingly less frequently invoked to\nexplain observations.\n\nFirst RM studies on Balmer lines excluded radial, and favored orbital or chaotic\nmotions (e.g. \\pcite{kg91,kor95}). \\scite{goadw96} applied RM techniques to one of the\nmost extensively monitored objects: NGC 5548. They ruled out radial motions, and found\nthat the \\civ\\ line variations are broadly consistent with a spherical BLR geometry, in\nwhich clouds following randomly inclined circularly Keplerian orbits are illuminated by\nan anisotropic source of ionizing continuum. A RM result favoring Keplerian motion may\nbe approximately correct also for models in which the emitting gas is not bound, such\nas a wind, since most of the emission occurs near the base of the flow, when the\nvelocity is still close to the escape velocity which is similar to the Keplerian\nvelocity \\cite{mc98}.\n\n\\section{Is the disk + wind model applicable to all AGN?}\n\nEmission from a terminal flow can explain the recent observations of Goad et al. 1999\nwho reported that LIL (\\mgii + \\feiiuv) in NGC 3516 do not respond to continuum\nvariations which did induce detectable variability in the HIL (\\lya\\ and \\civ) lines.\nHydromagnetic wind models such as those developed by \\scite{emmering92} and\n\\scite{bottorff97} exhibit these basic properties. A two-zone wind provides another\nscenario for the different origins of LIL and HIL.\n\nTurning to the general population of RL AGN, the predominance of redshifts and redward\nasymmetric profiles is difficult to explain. Several lines of evidence suggest a\nsignificant role of gravitational redshift in RL AGN \\cite{corbin97} possibly related\nto a lower distance (in units of gravitational radii) between BLR and central black\nhole, which may be systematically more massive in RL than in RQ AGN. If this is the\ncase, then a double zone wind may be present also in RL AGN, since \\civbc\\ is still\nsystematically blueshifted with respect to \\hbbc. The ``correlation'' between \\civbc\\\nand \\hbbc\\ parameters could be due to the impossibility of maintaining a radial flow\nalong the disk axis, where a relativistic jet is instead propagating. This will make\nany HIL outflow possible only at lower latitudes over the disk plane, and therefore\nwill produce more similar \\hbbc\\ and \\civbc\\ profiles.\n\n\n\\section{CONCLUSION}\n\nWhile observations support emission from an accretion disk and an associated spherical\nwind in RQ AGN with FWHM(\\hbbc) $\\simlt$ 4000 \\kms, there is not enough observational\nsupport to warrant the same conclusion for RL AGN (and possibly RQ with FWHM$>$4000\n\\kms), although a disk + wind model is a viable possibility also in this case. Wide\nseparation double peakers (mostly RL) do not provide conclusive evidence in favor of\nLIL disk emission; rather, there is evidence against disk emission as well as against\nevery other reasonably simple scenario.\n\n\\acknowledgements DD-H acknowledges support through grant IN109698 from PAPIIT-UNAM. PM\nacknowledges financial support from MURST through grant Cofin 98-02-32, as well as\nhospitality and support from IA-UNAM. We also acknowledge consistent (cycles5-9 AR and\nGO) rejection of proposals to continue this work.\n\n%There are conflicting lines of evidences. It is unclear whether\n%wide separation double-peaks in Balmer lines are due to rotation\n%or to outflow. Their rarity and abnormal line width suggest that\n%they may be a peculiar class in a short-lived phase of their\n%evolution.\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format:\n%%\n%% \\bibitem[AUTHOR]{KEY}\n%%\n%% so that the \\cite{KEY}, etc. commands will work properly.\n%%\n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%%\n\\begin{thebibliography}{}\n%\\bibitem[Aretxaga et al.<1999>]{arex} Aretxaga, I., Joguet, B., Kunth, D., Melnick, J. \\& Terlevich, R. 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A. 1991. \\apj, 381, 418\n\\end{thebibliography}\n%\\bibitem[Bally et al.{}<1995>]{p:Bal95}\n% Bally, J., Devine, D. \\& Sutherland, R. 1995, In: S. Lizano \\&\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\n\n\n\n\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"dd_submitted.tex\",\n \"string\": \"%%% Sample proceedings article for rmaa.cls\\n%%%\\n%%% Converted to RMAA(SC) style and annotated by Will Henney\\n%%% (04 Oct1999)\\n%% This file contains examples of many of the commands in the LaTeX\\n%% document class rmaa.cls, such as the commands for specifying data\\n%% for the title page and the commands for including postscript\\n%% figures. For more details, you should consult the accompanying\\n%% Author Guide (`rmuser.tex'). A further sample document\\n%% (`rmtest.tex') contains examples of some commands not used in this\\n%% file, eg. for marking up tables. You may also want to use this file\\n%% as a template for your own article.\\n%% Note: This article was originally published in `IAU Symposium 182:\\n%% Herbig-Haro Objects and the Birth of Low-mass Stars',\\n%% ed. B. Reipurth & C. Bertout (Dordrecht: Kluwer). Hopefully, I've\\n%% changed it enough to avoid copyright violation!\\n%% All proceedings articles must begin with the following line\\n\\\\documentclass[proceedings,onecolumn]{rmaa}\\n%%\\n%% The file `rmaa.cls' should be somewhere in your TeX search path\\n%% (e.g, in the current directory, or in a personal or system-wide\\n%% directory of LaTeX packages.\\n%%\\n%% This will not work with old versions of LaTeX: any version\\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\\n%% complains that it doesn't recognise the command `\\\\documentclass'\\n%% then your LaTeX installation needs updating!\\n%% The following package allows one to do the citations\\n%% semi-automatically. It defines the commands \\\\cite{KEY},\\n%% \\\\scite{KEY}, and \\\\pcite{KEY} which respectively produce citations\\n%% in the following styles:\\n%% (AUTHOR YEAR)\\n%% AUTHOR (YEAR)\\n%% AUTHOR YEAR\\n%% For this to work, you need to pay attention to the formatting of\\n%% the `\\\\bibitem's in your `thebibliography ' environment, qv.\\n\\\\usepackage{rmaacite}\\n%% If you would rather do your citations by hand, then comment out the\\n%% above line\\n\\n%% Here, you can put the definitions of your own personal macros.\\n%% All the special commands defined in AASTEX 4.0 (e.g. \\\\ion{}{},\\n%% \\\\gtrsim, \\\\arcsec, \\\\apj, etc) are already defined. I haven't checked\\n%% if there are any new ones in AASTEX 5.0 yet.\\n\\\\newcommand{\\\\thOr}{$\\\\theta^1\\\\,$C~Ori}\\n\\\\newcommand{\\\\zero}{_0}\\n\\\\newcommand{\\\\kms}{\\\\,\\\\mbox{km s$^{-1}$}}\\n\\\\newcommand{\\\\Othree}{[\\\\ion{O}{3}]~5007\\\\AA}\\n\\\\renewcommand{\\\\P}[1]{%\\n\\\\ifnum#1=1\\\\hbox{OW~168--326E}\\\\fi \\\\ifnum#1=2\\\\hbox{OW~167--317}\\\\fi\\n\\\\ifnum#1=3\\\\hbox{OW~163--317}\\\\fi \\\\ifnum#1=5\\\\hbox{OW~158--323}\\\\fi\\n\\\\ifnum#1=0\\\\hbox{OW~171--334}\\\\fi}\\n\\n%%\\n%% The following commands specify the title, authors etc\\n%%\\n\\\\title{The Broad Line Region in Active Galactic Nuclei}\\n\\\\author{D. Dultzin-Hacyan\\\\altaffilmark{1},\\nP. Marziani\\\\altaffilmark{2}, J.W. Sulentic\\\\altaffilmark{3}} \\\\altaffiltext{1}{Instituto\\nde Astronom\\\\'{\\\\i}a, UNAM, M\\\\'exico} \\\\altaffiltext{2}{Osservatorio Astronomico, Padova,\\nItalia} \\\\altaffiltext{3}{Dept. Physics and Astronomy, University of Alabama,\\nTuscaloosa, USA}\\n\\n\\n%%\\\\altaffiltext{1}{Just to see that the affiliation subscripts work OK}\\n%% Note that the \\\\affil{} command is inside the argument of the\\n%% \\\\author{} command and that a short version of the address should go\\n%% here. More complicated author/address examples are discussed in the\\n%% Author Guide (`rmuser.tex') and illustrated in the example document\\n%% `rmtest.tex'\\n%% The full postal addresses are specified here - they will be typeset\\n%% at the end of the article. Here is also the place to put email\\n%% addresses.\\n%\\\\fulladdresses{\\\\item}\\n%\\\\item D. Dultzin-Hacyan: Instituto de Astronom\\\\'\\\\i a,\\n% UNAM, Ap.do Postal 70-264, M\\\\'exico D. F. 04510, M\\\\'exico (deborah@astroscu.unam.mx)\\n%\\\\item P. Marziani: Osservatorio Astronomico di Padova,\\n%Vicolo dell' Osservatorio 5, I--35122 Padova, Italia (marziani@pd.astro.it)\\n% \\\\item J.W. Sulentic: Dept of Physics And Atronomy, Univesity of Alabama,\\n%Tuscaloosa, AL 35487 (giacomo@merlot.astr.ua.edu) }\\n%% Note that the `\\\\fulladdresses' command defines a list-like\\n%% environment, so each separate address must be preceded by the\\n%% `\\\\item' command (here there is only one, since the authors share the\\n%% same address).\\n\\n%% Title/author for running headers\\n\\\\shortauthor{Dultzin-Hacyan et al.} \\\\shorttitle{BLR in AGN}\\n%% These will automatically be converted to upper case in the current\\n%% style.\\n\\n%% No more than 5 keywords, chosen from the standard list\\n\\\\keywords{galaxies: active --- lines: profiles --- quasars: emission lines}\\n\\n\\\\abstract{We review constraints on models of the broad line region that are imposed by\\nobservations of the emission lines in Active Galactic Nuclei. Comparison of high and\\nlow ionization lines in sources with FWHM H$\\\\beta\\\\leq$4000 km s$^{-1}$ points toward low\\nionization line emission produced in a flattened geometry (the accretion disk?) with an\\nassociated high ionization wind. It remains unclear whether these results can be\\nextended to all radio quiet AGN and particularly to radio loud AGN.}\\n\\n\\\\resumen{Revisamos las limitaciones que se pueden imponer a partir de las\\nobservaciones, sobre los modelos de la estructura de las regiones que emiten las lineas\\nanchas en los N\\\\'ucleos Activos de Galaxias. La comparaci\\\\'on entre las lineas de\\nbaja- y alta ionizaci\\\\'on, sugiere que la emisi\\\\'on proviene, en parte, de una\\ngeometr\\\\'{\\\\i}a fuertemente aplanada (el disco de acreci\\\\'on?) y, en parte, de un viento\\nasociado, para una fracci\\\\'on importante de objetos radio callados que incluye a los\\nnucleos Seyfert 1 de lineas angostas (NLSy1). Sin embargo, es incierto si estos\\nresultados pueden extenderse a todos los Nucleos Activos radio callados y, sobre todo,\\na los radio fuertes.}\\n\\n\\n%% This command is so LaTeX won't stop on errors. I've put it in so\\n%% you will still be able to compile the file even if you have lost\\n%% the associated PS files of the figures.\\n\\\\nonstopmode\\n\\\\def\\\\habc{{\\\\sc{H}}$\\\\alpha_{\\\\rm BC}$\\\\/}\\n\\\\def\\\\hbnc{{\\\\sc{H}}$\\\\beta_{\\\\rm NC}$\\\\/}\\n\\\\def\\\\lya{{\\\\sc L}{\\\\rm y}$\\\\alpha$\\\\/}\\n\\\\def\\\\fevii{{\\\\sc{Fe vii}}$\\\\lambda$6087\\\\/}\\n\\\\def\\\\ovi{{\\\\sc{Ovi}}$\\\\lambda$1034\\\\/}\\n\\\\def\\\\mgii{{\\\\rm Mg\\\\sc{ii}}$\\\\lambda$2800\\\\/}\\n\\\\def\\\\niv{{\\\\sc{Niv]}}$\\\\lambda$1486\\\\/}\\n\\\\def\\\\ciii{{\\\\sc{Ciii}]}$\\\\lambda$1909\\\\/}\\n\\\\def\\\\oiiiopt{{\\\\sc{[Oiii]}}$\\\\lambda$4959,5007\\\\/}\\n\\\\def\\\\o4363{{\\\\sc{[Oiii]}}$\\\\lambda$4363\\\\/}\\n\\\\def\\\\oiiiuv{{\\\\sc{Oiii]}}$\\\\lambda$1663\\\\/}\\n\\\\def\\\\heiiuv{{\\\\rm He\\\\sc{ii}}$\\\\lambda$1640}\\n\\\\def\\\\heiiuvnc{He{\\\\sc{ii}}$\\\\lambda$1640$_{\\\\rm NC}$\\\\/}\\n\\\\def\\\\feiiuv{\\\\rm Fe{\\\\sc ii}$_{\\\\rm UV}$\\\\/}\\n\\\\def\\\\fei{\\\\rm Fe{\\\\sc i}}\\n\\\\def\\\\feii{\\\\rm Fe{\\\\sc ii}}\\n\\\\def\\\\feiii{\\\\rm Fe{\\\\sc iii}}\\n\\\\def\\\\feiiopt{\\\\rm Fe{\\\\sc ii}$_{\\\\rm opt}$\\\\/}\\n\\\\def\\\\feiiq{\\\\rm Fe{\\\\sc ii }$\\\\lambda$4570\\\\/}\\n\\\\def\\\\heiiopt{\\\\rm He{\\\\sc{ii}$\\\\lambda$4686}\\\\/}\\n\\\\def\\\\heii{He{\\\\sc{ii}}$\\\\lambda$4686\\\\/}\\n\\\\def\\\\oiii{{\\\\sc [Oiii]}$\\\\lambda\\\\lambda$4959,5007}\\n\\\\def\\\\oii{{\\\\sc [Oii]}$\\\\lambda$3727}\\n\\\\def\\\\oiir{{\\\\sc Oi}$\\\\lambda$8442}\\n\\\\def\\\\aliii{Al{\\\\sc iii}$\\\\lambda$1860}\\n\\\\def\\\\siiii{Si{\\\\sc iii]}$\\\\lambda$1892}\\n\\\\def\\\\iron{{[Fe/H]\\\\/}}\\n\\\\def\\\\ironsol{{ [Fe/H]}$_{\\\\odot}$\\\\/}\\n\\\\def\\\\feka{Fe~{\\\\sc K$\\\\alpha$\\\\/}}\\n\\\\def\\\\apj{{\\\\it Ap. J.}}\\n\\\\def\\\\aap{{\\\\it Astr. Astroph.}}\\n\\\\def\\\\apjs{{\\\\em Ap. J. Suppl.}}\\n\\\\def\\\\nat{{\\\\it Nature}}\\n\\\\def\\\\b{$\\\\beta$}\\n\\\\def\\\\kms{km~s$^{-1}$}\\n\\\\def\\\\l{$\\\\lambda$}\\n\\\\def\\\\araa{{\\\\it Annu. Rev. Astron. Astrophys. }}\\n\\\\def\\\\aj{{\\\\it Astron. J. }}\\n\\\\def\\\\mnras{{\\\\it MNRAS}}\\n\\\\def\\\\aap{{\\\\it Astron. Astrophys.}}\\n\\\\def\\\\apjl{{\\\\it Ap. J. Lett. }}\\n\\\\def\\\\aaps{{\\\\it Astron. Astrophys. Suppl. }}\\n\\\\def\\\\REF{\\\\par\\\\noindent\\\\hangindent 20pt}\\n\\\\def\\\\ab{{\\\\sc Z}}\\n\\\\def\\\\absol{{\\\\sc Z$_{\\\\odot}$\\\\/}}\\n\\\\def\\\\msol{$\\\\rm M_\\\\odot$}\\n\\\\def\\\\msoly{$ M_\\\\odot~yr^{-1}$}\\n\\\\def\\\\ltsima{$\\\\; \\\\buildrel < \\\\over \\\\sim \\\\;$}\\n\\\\def\\\\simlt{\\\\lower.5ex\\\\hbox{\\\\ltsima}}\\n\\\\def\\\\gtsima{$\\\\; \\\\buildrel > \\\\over \\\\sim \\\\;$}\\n\\\\def\\\\rfe{R$_{\\\\rm FeII}$}\\n\\\\def\\\\ai{A.I.($\\\\frac{1}{4}$)\\\\/}\\n\\\\def\\\\aox{$\\\\alpha_{ox}$\\\\/}\\n\\\\def\\\\gs{$\\\\Gamma_{\\\\rm soft}$}\\n\\\\def\\\\gh{$\\\\Gamma_{\\\\rm hard}$}\\n\\\\def\\\\G{$\\\\Gamma$}\\n\\\\def\\\\ne{n$_{\\\\rm e}$\\\\/}\\n\\\\def\\\\ergss{ergs s$^{-1}$}\\n\\\\def\\\\simgt{\\\\lower.5ex\\\\hbox{\\\\gtsima}} % > over MMM\\n\\\\def\\\\bv{{\\\\bf $\\\\bigvee$}\\\\/}\\n\\\\def\\\\qu{{$\\\\lambda$ 1400}}\\n\\\\def\\\\h{$h^{-1}$}\\n\\\\def\\\\hii{{\\\\sc Hii\\\\/}}\\n\\\\def\\\\hi{{\\\\sc Hi\\\\/}}\\n\\\\def\\\\a{$\\\\alpha$}\\n\\\\def\\\\ha{{\\\\sc H}$\\\\alpha$}\\n\\\\def\\\\nv{{\\\\sc Nv}$\\\\lambda$1240}\\n\\\\def\\\\civ{{\\\\sc{Civ}}$\\\\lambda$1549\\\\/}\\n\\\\def\\\\civnc{{\\\\sc{Civ}}$\\\\lambda$1549$_{\\\\rm NC}$\\\\/}\\n\\\\def\\\\civbc{{\\\\sc{Civ}}$\\\\lambda$1549$_{\\\\rm BC}$\\\\/}\\n\\\\def\\\\cmsq{cm$^{-2}$\\\\/}\\n\\\\def\\\\cm3{cm$^{-3}$\\\\/}\\n\\\\def\\\\md{$\\\\dot{\\\\rm M}$}\\n\\\\def\\\\rg{$\\\\rm R_{\\\\rm g}$}\\n\\\\def\\\\hb{{\\\\sc{H}}$\\\\beta$\\\\/}\\n\\\\def\\\\hg{{\\\\sc{H}}$\\\\gamma$\\\\/}\\n\\\\def\\\\hbbc{{\\\\sc{H}}$\\\\beta_{\\\\rm BC}$\\\\/}\\n\\\\begin{document}\\n\\\\maketitle\\n\\\\section{Introduction \\\\label{sec:intro}}\\n\\nThe Broad Line Region (BLR) in Active Galactic Nuclei (AGN) is unresolved with present\\nday imaging detectors and it will remain so for the foreseeable future. This is why\\n``one quasar spectrum is really worth a thousand images'' as stressed by Gary Ferland\\nat this meeting. In response we would add that {\\\\em a thousand spectra are better than\\none average spectrum}. Understanding the diversity in optical spectroscopic properties\\nof AGN is the key to any realistic AGN modeling \\\\cite{bg92,smd}. The ideal to\\nreconstruct the BLR velocity field from a single profile is not realistic \\\\cite{pen90}.\\n\\nDetermination of BLR structure and kinematics can be approached in two ways. It has\\nbeen recognized for a long time that strong broad and narrow emission lines coming from\\nboth high and low ionization species are present in Seyfert galaxies and quasars. This\\nis considered a defining spectroscopic property of AGN. Restricting attention to broad\\nlines: a) typical (i.e., strongest and most frequently observed) high ionization lines\\n(HIL: ionization potential $\\\\simgt$ 50 eV) are \\\\civ\\\\ \\\\heii\\\\ and \\\\heiiuv\\\\ lines; while\\nb) observed low ionization lines (LIL: ionization potential $\\\\simlt $ 20 eV) include\\n\\\\hi\\\\ Balmer lines, \\\\feii\\\\ multiplets, \\\\mgii, and the Ca{\\\\sc ii}\\\\ IR triplet.\\n\\nThe first approach involves the study of line variability in response to continuum\\nchanges. This approach has been pursued through a number of successful monitoring\\ncampaigns using Reverberation Mapping (RM) techniques. RM requires a large amount of\\ntelescope time and, consequently, has been achieved only for a handful of sources. RM\\nconfirms that photoionization is the main heating process in the BLR and that a large\\npart of the BLR is optically thick to the ionizing continuum (e. g. \\\\pcite{baldwin97}).\\nRM studies have quantified a main difference between HIL and LIL; HIL respond to\\ncontinuum changes with a time delay of a few days while the LIL respond with a delay of\\ntens of days. This implies that the LIL are emitted at larger distance from the\\ncontinuum source (\\\\pcite{ulr,kor95}. An exhaustive list of reference can be found in\\n\\\\pcite{smd}). RM applied to line profiles suffers from uncertainty in our knowledge\\nabout the physics of continuum and broad line formation, so that conflicting models can\\nstill describe the same lag times \\\\cite{pen91,wanpet96}.\\n\\nThe second approach involves statistical analysis of large samples of line profiles\\nwhich differ because of properties that may affect the BLR structure, for example\\nsamples of radio quiet (RQ) and radio loud (RL) AGN. Statistical studies can be done\\nfor a single line or by comparing lines sensible to different physical parameters (e.g.,\\nstrongest LIL and HIL). The statistical approach, on which we will focus here, is more\\nempirical and therefore requires a conceptual framework for interpretation. This\\napproach is often criticized as relying on several assumptions including that the\\nprofile variability does not influence profile shapes and that the non-simultaneity of\\nthe observations of LIL and HIL are unimportant. Actually as the size of high quality\\ndata samples grow these effects become less and less important.\\n\\n\\\\section{Baring the Broad Profiles \\\\label{bare}}\\n\\nThe collection of moderate resolution (\\\\l/$\\\\Delta$\\\\l $\\\\sim 10^3$) optical and UV\\nspectra of good quality (S/N $\\\\simgt$ 20 in the continuum) has become possible only in\\nrecent years thanks to the widespread use of CCD detectors and the unprecedented\\nsensitivity and resolution of the UV spectrographs on board HST. For practical\\npurposes, \\\\hi\\\\ \\\\hb\\\\ and \\\\civ can be considered representative of HIL and LIL\\nrespectively. They are also the best lines for statistical studies because they permit\\ncomparison in the same sources out to z=1.0. The linearity of response of the\\ncurrently employed detectors has made possible a reliable correction for emission\\nfeatures contaminating \\\\hb\\\\ and \\\\civ, which are: (1) \\\\feii\\\\ emission; significant\\n\\\\feiiuv\\\\ emission contaminates the red wing of \\\\civ, and has been identified in I Zw 1\\nby \\\\pcite{m96} and later confirmed by \\\\pcite{lao97}; (2) \\\\heii\\\\ emission for \\\\hb, and\\n\\\\heiiuv\\\\ + \\\\oiiiuv\\\\ for \\\\civ; (3) \\\\oiii\\\\ for \\\\hb; (4) narrow component, present in\\nseveral cases in both \\\\hb\\\\ and \\\\civ.\\n\\n\\n\\\\civ\\\\ often shows a narrow core with FWHM $\\\\sim$ 1000-2000 \\\\kms, which is\\nsystematically broader than the narrow component of \\\\hb\\\\ (\\\\hbnc). The separation\\nbetween the broad component \\\\civbc\\\\ and the core component is often ambiguous. This\\ncore however shows no shift with respect to the AGN rest frame \\\\cite{brot94}, no\\nvariations \\\\cite{turla}, and correlates with \\\\oiii\\\\ prominence \\\\cite{franc92}. It can\\ntherefore be ascribed to the NLR and considered as the narrow line component of \\\\civ\\\\\\n(\\\\civnc). The different width between \\\\civnc\\\\ and \\\\hbbc\\\\ can be understood in terms of\\ndensity stratification \\\\cite{sm99} without invoking an additional emitting region such\\nas the so-called ``intermediate line region''. Even if \\\\civnc\\\\ fractional intensity is\\nsmall ($\\\\sim$ 10\\\\%), and in some cases obviously absent, failure to account for \\\\civnc\\\\\\nhas led to the erroneous conclusions that FWHM \\\\civbc\\\\ $>$ FWHM \\\\hbbc\\\\ and that the\\n\\\\civ\\\\ peak shows no shift with respect to \\\\hb\\\\ \\\\cite{cb96}.\\n\\n\\\\section{A DIFFERENT BLR STRUCTURE IN RADIO LOUD AND RADIO QUIET AGN? \\\\label{struct}}\\n\\n\\\\scite{m96} made a comparison between \\\\civbc\\\\ and \\\\hbbc\\\\ for a sample of 52 AGN (31\\nRL). They presented measures of radial velocity for the blue and red sides of \\\\hbbc\\\\\\nand \\\\civbc\\\\ at 5 different values of fractional intensity which provide a quantitative\\ndescription of the profiles. The reference frame was set by the measured velocity of\\n\\\\oiii$\\\\lambda$5007$\\\\rm{\\\\AA}$ (IZw1 was the only exception). Standard profile parameters\\nlike peak shift, FWHM, asymmetry index and curtosis can be extracted from these\\nmeasures. Representative profiles constructed from the {\\\\em median values} of \\\\civbc\\\\\\nand \\\\hbbc\\\\ $v_r$\\\\ are reproduced in the left panels of Fig. \\\\ref{fig:rq} and\\n\\\\ref{fig:rl} for the radio quiet (RQ) and radio loud (RL) samples respectively.\\n\\\\begin{figure}\\n %\\\\begin{center}\\n \\\\leavevmode\\n \\\\includegraphics[width=\\\\columnwidth, height=8cm]{fig01.eps}\\n% \\\\includegraphics[width=\\\\textwidth, height=10cm]{Fig01dd.eps}\\n\\\\caption[]{Profiles of \\\\civbc\\\\ (solid lines) and \\\\hbbc\\\\ normalized to the same peak\\nintensity and constructed from median values of the radial velocities measured on the\\nblue and red sides of the profiles for the 21 RQ AGN of \\\\scite{m96} (left panel).\\nEmission line profiles of \\\\civ\\\\ (middle panel) and \\\\hb\\\\ (right panel) of the prototype\\nNLSy1 galaxy I Zw 1, adapted from \\\\scite{m96}. The thick and the dotted lines trace \\\\hb\\\\\\nand \\\\oiii\\\\ after \\\\feiiopt\\\\ (dashed line) subtraction. \\\\label{fig:rq}}\\n %\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\civbc\\\\ is broader than \\\\hbbc in both RQ and RL samples and it is {\\\\em almost always}\\nblueshifted relative to \\\\hbbc. However Fig. \\\\ref{fig:rq} and Fig. \\\\ref{fig:rl} show\\nsignificant differences between RQ and RL AGN. In RQ AGN, \\\\civbc\\\\ is significantly\\nblueshifted with respect to the source rest frame while \\\\hbbc\\\\ is symmetric and\\nunshifted. Contrarily in RL AGN \\\\civbc\\\\ is more symmetric, while \\\\hbbc\\\\ is shifted to\\nthe red at peak intensity and redward asymmetric as well (the median profile\\ncorresponds to the type AR,R according to \\\\pcite{sul89}). There are two important\\nresults which are not displayed in the Figures: (i) in RQ AGN, \\\\civbc\\\\ blueshifts are\\napparently uncorrelated with respect to any \\\\hbbc\\\\ line profile parameter and the\\nlargest \\\\civ\\\\ blueshifts are associated with the lowest W(\\\\civ); (ii) in RL AGN, on the\\ncontrary, \\\\civbc\\\\ and \\\\hbbc\\\\ line profile parameters (FWHM and peak shift) appear to be\\ncorrelated. Asymmetry index of \\\\civbc\\\\ and \\\\hbbc, even if not correlated, shows a clear\\ntrend toward asymmetries of the same kind (symmetric or redward asymmetric). These\\nfindings on \\\\civbc\\\\ have been confirmed by other authors (\\\\pcite{wills95}, save the\\ndifference in terminology and line profile decomposition) and especially by an analysis\\nof archival HST/FOS observations which have become publicly available after 1995\\n\\\\cite{sul20}.\\n\\nThe LIL and HIL emitting regions are apparently de-coupled in at least some RQ\\nsources. The ``de-coupling'' is well seen in I Zw 1, the prototype Narrow Line Seyfert\\n1 Galaxy (NLSy1; see Fig. \\\\ref{fig:rq}). The \\\\hb\\\\ profile is very narrow, slightly\\nblueward asymmetric and unshifted with respect to the rest frame defined by 21 cm\\nobservations, while the \\\\civ\\\\ profile is almost totally blueshifted. At least in the\\ncase of I Zw 1 the distinction between LIL and HIL emitting regions appears to be\\nobservationally established (it was actually suggested because of the difficulty to\\nexplain the relative strengths of LIL and HIL emission using a photoionized ``single\\ncloud;'' \\\\pcite{cs88}). There is a very important zeroth-order result here: since I Zw\\n1 is a strong \\\\feiiuv\\\\ emitter, we have HIL \\\\civ\\\\ and LIL \\\\feiiuv\\\\ in the same\\nrest-frame wavelength range. We see that \\\\feiiuv\\\\ is obviously unshifted (this can be\\nvery well seen by shifting an \\\\feiiuv\\\\ template to the peak radial velocity of \\\\civ).\\nThis result disproves models that see an (unknown) wavelength dependent mechanism\\naccounting for the quasar broad line shifts relative to the quasar rest frame.\\n\\nRL AGN apparently mirror RQ AGN in a curious way: \\\\civbc\\\\ is more symmetric, while\\n\\\\hbbc\\\\ shows preferentially redshifted profiles and increasingly redward asymmetries.\\nLarge peak redshifts ($v_r \\\\simgt 1000$ \\\\kms, as in the case of OQ 208, Fig.\\n\\\\ref{fig:rl}) are rarely observed; \\\\hbbc\\\\ peak shifts are usually small ($\\\\Delta\\nv_r$/FWHM $\\\\ll$ 1, median profile of Fig. \\\\ref{fig:rl}). RL \\\\civbc\\\\ and \\\\hbbc\\\\ data\\nleave open the possibility that both lines are emitted in the same region. \\\\civbc\\\\\\nshows a red-wing (very evident in the latest, higher S/N spectra analyzed by\\n\\\\scite{sul20}), which cannot be entirely accounted for by \\\\feiiuv emission. It is\\ninteresting to note that superluminal sources with apparent radial velocity $\\\\beta_{\\\\rm\\napp} \\\\sim 5-10$~ (whose radio axis is probably oriented close to the line of sight in\\nthe sample of \\\\scite{m96} show very strong \\\\civ\\\\ redward asymmetries, low W(\\\\civ) and\\nW(\\\\hbbc). This result suggests that redshifts are maximized in RL objects at\\n``face-on'' orientation (we assume that any disk is perpendicular to the radio axis).\\n\\n\\\\section{NLSy1 NUCLEI ARE NOT A DISJOINT RQ POPULATION}\\n\\nNLSy1 are neither peculiar nor rare. The 8$^{th}$\\\\ edition of the \\\\scite{veron98}\\ncatalogue includes 119 NLSy1 satisfying the defining criterion FWHM Balmer $\\\\simlt$\\n2000 \\\\kms. They account for $\\\\approx 10$\\\\%\\\\ of all AGN in the same redshift and\\nabsolute magnitude range. Attention toward NLSy1 remained dormant after their\\nidentification as a particular class \\\\cite{op85} until it was discovered that they may\\nrepresent $\\\\approx$1/3--1/2 of all soft X-ray selected Seyfert 1 sources (e. g.,\\n\\\\pcite{grupe98}). NLSy1 are also apparently favored in AGN samples selected on the\\nbasis of color. They account for 27\\\\%\\\\ of the RQ \\\\scite{bg92} sample, probably because\\nof an optical continuum that is steeply rising toward the near UV. NLSy1 do not occupy\\na disjoint region in parameter space. They are at an extremum in the FWHM(\\\\hb) vs.\\n\\\\rfe\\\\ (=I(\\\\feii \\\\l 4570/I(\\\\hbbc)) and in the ``Eigenvector 1'' parameter spaces\\n\\\\cite{bg92,bf99,smd}. Also, the soft X-ray spectral index \\\\gs\\\\ shows a continuous\\ndistribution which includes NLSy1 at the high end \\\\cite{wang96,smd,sul20}.\\n\\n\\\\begin{figure}\\n %\\\\begin{center}\\n \\\\leavevmode\\n \\\\includegraphics[width=\\\\columnwidth, height=8cm]{fig02.eps}\\n% \\\\includegraphics[width=\\\\textwidth, height=10cm]{Fig01dd.eps}\\n \\\\caption[]{Left panel: Profiles of \\\\civbc\\\\ (solid lines) and \\\\hbbc\\\\ normalized to the same\\n peak intensity and constructed from median values of the radial velocities measured on\\n the blue and red sides of the profiles for the 31 RL AGN of \\\\scite{m96}.\\n Middle panel: \\\\hb\\\\ spectrum of OQ 208, showing a single, widely displaced \\\\hbbc\\\\ peak (adapted from \\\\pcite{m93}).\\n Right panel: \\\\ha\\\\ profile of the prototype of ``wide-separation double peakers'' Arp 102B.\\n Unpublished spectrum obtained at the 1.82 m telescope of the Asiago observatory on March 25, 1989.\\n The thick solid line traces \\\\hbbc.}\\n \\\\label{fig:rl}\\n %\\\\end{center}\\n\\\\end{figure}\\n\\nOrientation can easily explain much of the RQ phenomenology observed by \\\\scite{m96}. I\\nZw 1 can be considered as an extremum with an accretion disk seen face-on\\n(i$=0^\\\\circ$), and an outflowing wind observed along the disk axis. We can infer that\\nthe opening angle of any \\\\civ\\\\ outflow is probably large (i. e., the wind is quasi\\nspherical) because \\\\civ\\\\ profiles like I Zw 1 are rare. Other NLSy1 show low W(\\\\civ),\\nand strong \\\\feiiopt, but do not always show large \\\\civ\\\\ blueshifts \\\\cite{rp97}.\\nNonetheless, it is still possible that NLSy1 may be structurally different from other\\nRQ AGN. If the soft X-ray excess of NLSy1 is due to high accretion rate, then a slim\\naccretion disk is expected to form \\\\cite{abram88}. Line correlations presented in\\n\\\\cite{sul20} appear to hold until FWHM(\\\\hb)$\\\\simlt$ 4000 \\\\kms. For FWHM$\\\\simgt$ 4000\\n\\\\kms line parameters appear to be uncorrelated however it is still unclear it is at\\npresent unclear because of the difficulty in measuring weak and broad \\\\feiiopt sources\\nand/or because of a BLR structural difference. This limit may be related to the\\npossibility of sustaining a particular disk structure and an HIL outflow. A second\\nparameter, independent from orientation is needed to account for the FWHM(\\\\hbbc) vs\\n\\\\rfe\\\\ vs \\\\gs\\\\ sequences (see \\\\pcite{smd,sul20} for a detailed discussion).\\n\\n\\n\\\\section{Inferences on BLR Models for RQ AGN}\\n\\nModels developed almost independently of the data through the 80's and early 90's.\\nThe situation has now changed because of three main developments: (1) the ``Eigenvector\\n1'' correlations allow a systematic view of the change in optical emission line\\nproperties for different classes of AGN \\\\cite{bg92,bf99,smd}; (2) the \\\\civ\\\\ - \\\\hb\\\\\\ncomparison has yielded direct clues about the structure of the BLR \\\\cite{m96,sul20} and\\n(3) data collected for RM projects provide a high-sampling description of line\\nvariations. For instance, binary black hole scenarios \\\\cite{gask96} were recently\\nchallenged by the failure to detect the radial velocity variations expected from\\nprevious observations and model predictions \\\\cite{eracl97}.\\n\\nA model in which \\\\civ\\\\ is emitted by outflowing gas (e.g. a spherical wind) while\\n\\\\hbbc\\\\ is emitted in a flattened distribution of gas (observed in a direction that\\nminimizes velocity dispersion) such as an optically thick disk (obscuring the receding\\nhalf of the \\\\civ\\\\ flow, \\\\pcite{liv97}) or at the wind base is immediately consistent\\nwith the I Zw 1 data. The big question is whether the results for I Zw 1 can be\\nstraightforwardly extended to other RQ AGN.\\n\\nAn accretion disk (AD) provides a high density and high column density medium for\\n\\\\feii\\\\ production (e. g. \\\\pcite{dj92}), and possibly other low ionization lines such as\\nCaII (e. g. \\\\pcite{dd99}). AD avoid conflict with the stringent restrictions on line\\nprofile smoothness imposed by the first extremely high s/n Balmer line observations\\n(\\\\pcite{arav97,arav98}) of -incidentally- two NLSy1. They place a lower limit of\\n(10$^{7-8}$) on the number of discrete emitters needed to explain the observed profiles.\\n\\nWinds arise as a natural component of an AD model when the effects of radiative\\nacceleration are properly taken into account \\\\cite{murray95,mc98} or when a\\nhydromagnetic or hydrodynamic treatment is performed \\\\cite{bottorff97,williams99}. A\\nsignature of radiative acceleration is provided by observations of ``double troughs'' in\\n$\\\\approx \\\\frac{1}{5}$ of BAL QSOs i. e., of a hump in the absorption profiles of \\\\nv\\\\\\nand \\\\civ\\\\ at the radial velocity difference between \\\\lya\\\\ and \\\\nv, 5900 \\\\kms. Such a\\nfeature indicates that \\\\lya\\\\ photons are accelerating the BAL clouds (\\\\pcite{arav94},\\nand references therein). Additional evidence is provided by the radial velocity\\nseparation in the narrow absortion components of \\\\lya\\\\ and \\\\nv\\\\ which show the same\\n$\\\\Delta v_r$\\\\ of the two doublet components of \\\\civ\\\\ (e. g. \\\\pcite{wampler91}).\\n\\n\\\\section{The Trouble With Bare Accretion Disks and Bipolar Flows}\\n\\nRelativistic Keplerian disks \\\\cite{ch89,sb93} may explain unusual profile shapes (e.g.\\ndouble-peaked profiles of Balmer emission lines; \\\\pcite{eh94,sul95}). Uniform\\naxisymmetric disk models produce double-peaked line profiles with the blue peak\\nstronger than the red peak because of Doppler boosting, a feature that is not always\\nobserved in these already rare profiles. To solve this problem, \\\\scite{sb95} and\\n\\\\scite{eracl95}, proposed that the lines can originate in an eccentric (i.e.\\nelliptical) disk. Simple disk illumination models can also produce single peaked LIL,\\nprovided they are produced at large radii ($\\\\simgt 10^3$\\\\ gravitational radii) or that\\nthe disk is observed at small inclination \\\\cite{dc90,rokaki92,sul98}. The first of these\\nconditions may be met in all NLSy1 galaxies; both of them seem to be met in I Zw 1.\\n\\nAside from NLSy1 sources, there is general disagreement between observations and model\\npredictions for externally illuminated Keplerian disks in a line shift-- asymmetry\\nparameter space \\\\cite{sul90}. Only a minority ($\\\\simlt$ 10 \\\\%) of RL and a handful of\\nRQ AGN show double peaked Balmer lines suggestive of a Keplerian velocity field\\n\\\\cite{eh94,sul99}. Double-peakers (e. g. Arp 102B in Fig. \\\\ref{fig:rl},\\nFWHM(\\\\hbbc)$\\\\simgt$10000 \\\\kms) cannot be like the classical cases because the line\\nwidths are much smaller. The peaks often vary out of phase (Arp 102B: \\\\pcite{mp90}, 3C\\n390.3: \\\\pcite{zheng91}). Double peaks (NGC 1097) \\\\cite{sb93,sb95} or one of the peaks\\n(Pictor A) \\\\cite{sul95} sometimes appear quite suddenly. Profile variability studies of\\nBalmer lines force us to introduce second order modifications to the basic scheme, such\\nas: eccentric rings and precession \\\\cite{eracl95,sb97}, inhomogeneities such as\\norbiting hot spots \\\\cite{zheng91}, and warps \\\\cite{bachev99}. Not even these {\\\\em\\nepicycles} are always capable of explaining the observed variability patterns. Even if\\nelliptical AD models do well in explaining the integrated profiles, they face important\\ndifficulties in explaining variability patterns.\\n\\nA serious problem for AD models of emission lines is emerging from spectropolarimetric\\nobservations. If profile broad line shapes are orientation dependent then, in\\nprinciple, the profile shape in polarized light will depend on the distribution of the\\nscatterers relative to the principal axis and to our line of sight. Early\\nspectropolarimetric results showed a discrepancy with the simple disk +\\nelectron-scattering-dominated atmosphere models, which predicted polarization\\nperpendicular to the radio axis. The observed polarization is low, parallel to the disk\\naxis, and shows no statistically significant wavelength dependence \\\\cite{anton88}.\\nRecently \\\\scite{anton96} and \\\\scite{corbett98} included double-peakers in their\\nsamples, and obtained troublesome results for disk emission models because the\\npolarized \\\\ha\\\\ profiles are centrally peaked \\\\cite{corbett98}. They investigated the\\ncase of disk emission where the scattering particles are located above and below an\\nobscuring torus, along its poles. This ``polar scattering model'' is successful in\\nexplaining the polarized profiles {\\\\em but not the position angle of the polarization\\nvector}.\\n\\nThe same polarization studies indicate that the {\\\\em only} scenario that can account\\nfor both the shapes of the scattered line profiles and the alignment of the optical\\npolarization with the radio jet in wide separation double peakers like Arp 102B (Fig.\\n\\\\ref{fig:rl}) involves a {\\\\em biconical} BLR within an obscuring torus. \\\\ha\\\\ photons\\nemitted by clouds participating in a biconical flow are scattered towards the observer\\nby dust or electrons in the inner wall of the surrounding torus. The particular case of\\nbiconical outflow was first developed to reproduce observed profiles by\\n\\\\scite{zheng90}. This model has been successfully applied to fit observed profiles in\\ndouble-peaked objects \\\\cite{zheng91,sul95}.\\n\\nDouble peaked or single blueshifted peak LIL profiles fitted with bi-cone outflow\\nmodels require that the receding part of the flow is also seen. Self-gravity may be\\nimportant beyond $\\\\sim 1$ pc, and the disk may be advection-dominated and optically\\nthin \\\\cite{liv96}. Recent work by \\\\scite{sh99} models the vertical structure of AD and\\nthe origin of thermal winds above AD. They not only find that a wind powered by a\\nthermal instability develops in all disks with certain opacity laws but also that in\\ndisks dominated by bremsstrahlung radiation, a time-dependent inner hole develops below\\na critical accretion rate. This scenario provides a natural explanation for transient\\ndouble-peakers, such as NGC1097 \\\\cite{sb95,sb97}, but low accretion rate is a\\nrequirement for {\\\\em both} advection dominated disks and hole formation.\\n\\n\\\\scite{sul95} explored the idea that the double-peaked emitters represent a\\ngeometrical extremum where an outflow is viewed close to pole-on. However,\\ndouble-peakers are associated with double-lobe radio-sources suggesting that the line\\nof sight has a considerable inclination to the axis of the jets. The problem arises\\n{\\\\em only} if the core (pc scale) jets is related to the much larger (100 kpc scale)\\njets. There is both theoretical (e. g. \\\\pcite{valtonen99}) and observational evidence\\nagainst this assumption.\\n\\n\\\\section{Emission from Clouds Illuminated by an Anisotropic Continuum}\\n\\nModels based on radiative acceleration of optically thick clouds with small volume\\nfilling factor gained wide acceptance in the Eighties (\\\\pcite{om86} and references\\ntherein; see also \\\\pcite{binette96}). However, problems with cloud confinements and\\nstability \\\\cite{mathews90} have made them increasingly less frequently invoked to\\nexplain observations.\\n\\nFirst RM studies on Balmer lines excluded radial, and favored orbital or chaotic\\nmotions (e.g. \\\\pcite{kg91,kor95}). \\\\scite{goadw96} applied RM techniques to one of the\\nmost extensively monitored objects: NGC 5548. They ruled out radial motions, and found\\nthat the \\\\civ\\\\ line variations are broadly consistent with a spherical BLR geometry, in\\nwhich clouds following randomly inclined circularly Keplerian orbits are illuminated by\\nan anisotropic source of ionizing continuum. A RM result favoring Keplerian motion may\\nbe approximately correct also for models in which the emitting gas is not bound, such\\nas a wind, since most of the emission occurs near the base of the flow, when the\\nvelocity is still close to the escape velocity which is similar to the Keplerian\\nvelocity \\\\cite{mc98}.\\n\\n\\\\section{Is the disk + wind model applicable to all AGN?}\\n\\nEmission from a terminal flow can explain the recent observations of Goad et al. 1999\\nwho reported that LIL (\\\\mgii + \\\\feiiuv) in NGC 3516 do not respond to continuum\\nvariations which did induce detectable variability in the HIL (\\\\lya\\\\ and \\\\civ) lines.\\nHydromagnetic wind models such as those developed by \\\\scite{emmering92} and\\n\\\\scite{bottorff97} exhibit these basic properties. A two-zone wind provides another\\nscenario for the different origins of LIL and HIL.\\n\\nTurning to the general population of RL AGN, the predominance of redshifts and redward\\nasymmetric profiles is difficult to explain. Several lines of evidence suggest a\\nsignificant role of gravitational redshift in RL AGN \\\\cite{corbin97} possibly related\\nto a lower distance (in units of gravitational radii) between BLR and central black\\nhole, which may be systematically more massive in RL than in RQ AGN. If this is the\\ncase, then a double zone wind may be present also in RL AGN, since \\\\civbc\\\\ is still\\nsystematically blueshifted with respect to \\\\hbbc. The ``correlation'' between \\\\civbc\\\\\\nand \\\\hbbc\\\\ parameters could be due to the impossibility of maintaining a radial flow\\nalong the disk axis, where a relativistic jet is instead propagating. This will make\\nany HIL outflow possible only at lower latitudes over the disk plane, and therefore\\nwill produce more similar \\\\hbbc\\\\ and \\\\civbc\\\\ profiles.\\n\\n\\n\\\\section{CONCLUSION}\\n\\nWhile observations support emission from an accretion disk and an associated spherical\\nwind in RQ AGN with FWHM(\\\\hbbc) $\\\\simlt$ 4000 \\\\kms, there is not enough observational\\nsupport to warrant the same conclusion for RL AGN (and possibly RQ with FWHM$>$4000\\n\\\\kms), although a disk + wind model is a viable possibility also in this case. Wide\\nseparation double peakers (mostly RL) do not provide conclusive evidence in favor of\\nLIL disk emission; rather, there is evidence against disk emission as well as against\\nevery other reasonably simple scenario.\\n\\n\\\\acknowledgements DD-H acknowledges support through grant IN109698 from PAPIIT-UNAM. PM\\nacknowledges financial support from MURST through grant Cofin 98-02-32, as well as\\nhospitality and support from IA-UNAM. We also acknowledge consistent (cycles5-9 AR and\\nGO) rejection of proposals to continue this work.\\n\\n%There are conflicting lines of evidences. It is unclear whether\\n%wide separation double-peaks in Balmer lines are due to rotation\\n%or to outflow. Their rarity and abnormal line width suggest that\\n%they may be a peculiar class in a short-lived phase of their\\n%evolution.\\n%% When using the rmaacite package, the \\\\bibitem command should be of\\n%% the format:\\n%%\\n%% \\\\bibitem[AUTHOR]{KEY}\\n%%\\n%% so that the \\\\cite{KEY}, etc. commands will work properly.\\n%%\\n%% If you are doing the citations manually, then you can just use\\n%% `\\\\bibitem{}' instead. 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A. 1991. \\\\apj, 381, 418\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":96,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002097"},"title":{"kind":"string","value":"A phase-reference study of the quasar pair 1038+528A,B"},"authors":{"kind":"list like","value":[{"author":"Mar\\'{\\i}a J. Rioja \\inst{1} \\inst{2}"},{"author":"Richard W. Porcas\\inst{3} % \\fnmsep\\thanks{Just to show the usage % of the elements in the author field}"}],"string":"[\n {\n \"author\": \"Mar\\\\'{\\\\i}a J. Rioja \\\\inst{1} \\\\inst{2}\"\n },\n {\n \"author\": \"Richard W. Porcas\\\\inst{3} % \\\\fnmsep\\\\thanks{Just to show the usage % of the elements in the author field}\"\n }\n]"},"abstract":{"kind":"string","value":"We present results from $\\lambda$ 3.6~cm observations of the quasar pair \\object{1038+528} A and B, made in 1995 using the VLBA together with the Effelsberg 100m telescope. We describe the use of a phase-referencing technique to measure the astrometric separation between the quasars. We also introduce a new data analysis method - \"hybrid double mapping\" - which preserves the relative astrometric information in a single VLBI hybrid map for close source pairs. We combine our measurements with those from three previous epochs, the earliest in 1981. Our new observations confirm the evolution within the structure of quasar B, previously proposed to explain the measured change in the relative separation of the pair. Our upper bound for any systematic proper motion between the mass centres of quasars A and B is 10~$\\mu$as~yr$^{-1}$. This is set by the limited precision in defining the reference points in the quasars at different epochs and by possible instabilities of the source \"core\" locations. A separate analysis enables us to put more stringent upper limits to any core motions along the two source axes. \\keywords{Instrumentation: interferometers -- Techniques: interferometric -- Astrometry -- Radio continuum: general }"},"latex":{"kind":"list like","value":[{"name":"rioja_17jan2000.tex","string":"% aa.dem\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% demonstration file\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n%\n\\usepackage{psfig}\n\n\\begin{document}\n\n \\thesaurus{03 % A&A Section 3: Extragalactic astronomy\n (03.09.2; % Instrumentation: interferometers,\n 03.20.2; % Techniques: interferometric, \n 05.01.1; % Astrometry,\n 13.18.2)} % Radio continuum: general.\n%\n \\title{A phase-reference study of the quasar pair 1038+528A,B }\n% \\title{A phase-reference study of the}\n% \\subtitle{quasar pair 1038+528A,B }\n\n% \\subtitle{I. Overviewing the $\\kappa$-mechanism}\n\n \\author{Mar\\'{\\i}a J. Rioja \n \\inst{1}\n \\inst{2}\n \\and\n Richard W. Porcas\\inst{3}\n% \\fnmsep\\thanks{Just to show the usage\n% of the elements in the author field}\n }\n\n \\offprints{Mar\\'{\\i}a J. Rioja}\n\n \\institute{Observatorio Astron\\'omico Nacional (OAN), Apdo. 1143, \n E-28800 Alcal\\'a de Henares, Spain \\\\\n email: rioja@oan.es\n \\and\n Joint Institute for VLBI in Europe (JIVE), \n NL-7990 AA Dwingeloo, The Netherlands \\\\\n \\and\n Max-Planck Institut f\\\"ur Radioastronomie, Auf dem H\\\"ugel 69,\n D-53121 Bonn, Germany \\\\\n email: porcas@mpifr-bonn.mpg.de \n% \\thanks{The university of heaven temporarily does not\n% accept e-mails}\n }\n\n \\date{Received 5 October, 1999; accepted XX }\n\n \\titlerunning{Relative Astrometry of 1038+528AB}\n \\authorrunning{Rioja \\& Porcas}\n\n \\maketitle\n \n \\begin{abstract}\n\nWe present results from $\\lambda$ 3.6~cm observations of the quasar pair \n\\object{1038+528} A and B, made in 1995 using the VLBA together with the \nEffelsberg 100m telescope. We describe the use of a phase-referencing \ntechnique to measure the astrometric separation between the quasars.\nWe also introduce a new data analysis method - \"hybrid double mapping\" - \nwhich preserves the relative astrometric information in a single VLBI \nhybrid map for close source pairs. We combine our measurements with those \nfrom three previous epochs, the earliest in 1981. \nOur new observations confirm the evolution within the structure of quasar B, \npreviously proposed to explain the measured change in the relative separation \nof the pair. Our upper bound for any systematic proper motion between the \nmass centres of quasars A and B is 10~$\\mu$as~yr$^{-1}$. This is set by the \nlimited precision in defining the reference points in the quasars at \ndifferent epochs and by possible instabilities of the source \"core\" locations.\nA separate analysis enables us to put more stringent upper limits to any \ncore motions along the two source axes.\n\n \\keywords{Instrumentation: interferometers --\n Techniques: interferometric --\n Astrometry --\n Radio continuum: general\n }\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\nThe quasar pair 1038+528~A,B (Owen et al. \\cite{owen78}) \nconsists of two\nflat-spectrum radio sources, with redshifts 0.678 and 2.296 (Owen et\nal. \\cite{owen80}), separated on the sky by only 33\\arcsec. \nThis system provides a unique opportunity to carry out high precision, relative\nastrometric studies using the full\nprecision of VLBI relative phase measurements, \nsince most sources of phase errors are common for the 2 sources\n(Marcaide \\& Shapiro \\cite{marca83}).\n\n VLBI studies of the mas-scale structure of flat-spectrum quasars\nshow that they typically have ``core-jet'' morphologies, consisting of a highly\ncompact feature (the ``core'') located at the base of an extended linear feature \nor line of lower brightness components (the ``jet'').\nBoth 1038+528 A and B exhibit such structures.\nIn standard models of extragalactic radio sources, these radio-emitting \nfeatures\narise from a collimated beam of plasma which is ejected with a highly \nrelativistic bulk velocity from a region close to a central massive object \nsuch as a black hole (see eg. Blandford \\& K\\\"onigl \\cite{blandford86}).\nWhilst jet features may correspond to shocks in the moving plasma, and \ncan give rise to the observed ``superluminal'' component motions in some \nsources (Porcas \\cite{porcas87}),\nthe ``core'' emission is thought to arise from a more-or-less permanent location close to\nthe origin of the beam, where the ambient conditions correspond to a transition\nfrom optically thick to optically thin emission at the observed frequency.\nAlthough the ``core'' position may thus be frequency-dependent, for a fixed\nobserving frequency\nthe core should provide a stable marker, anchored to the central mass of\nthe quasar, whose location can be used to define a precise position for\nthe object as a whole.\nAlthough short time-scale variations in physical conditions may cause\nsmall changes in the ``core'' location, over long time-scales it may be\nused to track any systematic proper motion of the quasar.\n\nThe results from a near decade-long VLBI monitoring program on 1038+52A,B at\n$\\lambda$ 3.6 and 13~cm (from 1981.2 to 1990.5) \nare reported by Rioja et al. (\\cite{rioja97}), whose main conclusions \ncan be summarized as follows:\n\n\\begin{enumerate}\n\n\\item There is no evidence of any relative proper motion between the \n quasars A and B. The uncertainties in the astrometric parameters \n result in an upper bound to any systematic relative \n motion between the cores of 10~$\\mu$as~yr$^{-1}$, consistent\n with zero.\n\n\\item A compact feature within the jet of quasar B, chosen as the \n reference point for the structure, expands away from the core at \n a steady, slow rate of $\\sim~18~\\pm~5~\\mu$as~yr$^{-1}$, corresponding \n to v=$(0.8~\\pm~0.2)~h^{-1}$~c for a Hubble constant,\n H$_0$ = 100~h~km~s$^{-1}$~Mpc$^{-1}$; q$_0=0.5$. These values are used \n here throughout.\n\n\\item The accuracy of the relative separation measurement is limited by \n noise and source structure, with estimated precisions of about \n $50~\\mu$as at $\\lambda$ 3.6~cm at any epoch.\n\n\\item Confirmation of the consistently large offset (about 0.7 mas) between\n the positions of the peak of brightness (``core'') at $\\lambda$ 3.6 \n and 13~cm in quasar A.\n\n\\end{enumerate}\n\nNew VLBI observations of this pair were made in November 1995 (1995.9) \nat $\\lambda$ 2, 3.6 and 13~cm. In this paper we report on results from \nour analysis of the 3.6~cm observations and investigate the temporal \nevolution of the source structures and relative separation from all \nfour epochs spanning $\\sim 15$ years. \nInvestigations of frequency-dependent source structure have also been made \nfrom a comparison of the astrometric measurements\nof the separations between A and B at all 3 wavelengths observed in 1995;\nthese will be presented elsewhere (Rioja \\& Porcas in preparation).\n\nOur new observations are described in Sect. 2. In Sect. 3 we describe\nthe data reduction and mapping techniques used, and in Sect. 4 an analysis\nof the measurements in the maps.\nIn Sect. 5 we compare the astrometric results from these observations\nwith those from previous epochs and analyse the changes in \nseparation. Conclusions are presented in Sect. 6.\n\n%__________________________________________________________________\n\n\\section{Observations}\n\nThe pair of radio sources 1038+528 A and B was observed with the\nNRAO Very Long Baseline Array (VLBA) on November 10, 1995,\nfor a total of 13 hours, alternating every 13 minutes between\nobservations in dual 3.6/13~cm mode and observations at 2~cm. The\n100m telescope at Effelsberg was also included in the array for the\n3.6/13~cm scans. The primary beamwidths of all the antennas were\nsufficiently large that both sources could be observed simultaneously\nat all wavelengths. Each 10 minute observation of 1038+52A,B was\npreceded by a 3 minute observation of the compact calibration source\n\\object{0917+624}, to monitor the behaviour of the array.\n\nAll stations used VLBA terminals to record an aggregate \nof 64 MHz bandwidth for each scan, using 1-bit sampling, subdivided into\n8 channels (mode 128-8-1). For the dual 3.6/13~cm scans, four 8-MHz channels\nwere recorded for each band (2254.5--2286.5 MHz; 8404.5--8436.5 MHz), \nusing \nRHC polarisation. At 2~cm, eight 8-MHz channels (15\\,331.5--15\\,395.5 MHz)\nwere recorded in LHC polarisation.\n\nThe correlation was made at the VLBA correlator in Socorro (New Mexico).\nAs for previous epochs, two separate ``passes'' were needed, using different \nfield centres for the two sources, to recover data\nfor both the A and B quasars from the single observation. \nOutput data sets were generated for the two sources, consisting of the\nvisibility functions averaged to 2 s, with samples every 1 MHz in frequency\nacross the bands. \n\n\\section{Data reduction} \n\nWe used the NRAO AIPS package for the data reduction. \nWe applied standard fringe-fitting, amplitude and phase (self-) calibration \ntechniques and produced hybrid maps of each quasar. \nThe astrometric analysis was done using two different mapping methods: \na ``standard'' phase-referencing approach, transferring phase solutions\nfrom one quasar to the other\n(see e.g. Alef \\cite{alef88}; Beasley \\& Conway \\cite{beasley95}) and a \nnovel mapping method for astrometry of close pairs\nof sources, hybrid double mapping (HDM) (Porcas \\& Rioja \\cite{porcas96}). \nBoth routes preserve the signature of the relative separation of the source \npair present in the calibrated phases. These analysis paths are described \nin Sects. 3.1 to 3.3 below. \n\n\\subsection{Hybrid mapping in AIPS} \n\nWe applied standard VLBI hybrid mapping\ntechniques in AIPS for the analysis of the observations of both\nquasars A and B. We used the\ninformation on system temperature, gain curves and telescope gains measured at\nthe individual array elements, to calibrate the raw correlation\ncoefficients. \nWe used the AIPS task FRING to estimate residual antenna-based phases\nand phase derivatives (delay and rate) at intervals of a few minutes.\nIt is important to realise that FRING is a global self-calibration\nalgorithm, and performs an initial phase self-calibration also. We ran\nFRING on the A quasar data set, with a point-source input model.\n\nAnticipating our phase-referencing scheme (Sect. 3.2) we applied the antenna\nphase, delay and rate solutions from A to both the A and B data sets, and\naveraged them in time to 60 s, and over the total observed bandwidth of 32 MHz.\nAfter suitable editing of the data, we made hybrid maps of both quasars,\nusing a number of iterations of a cycle including the mapping task MX and\nfurther phase self-calibration with CALIB.\n\nFig.~\\ref{fig1}a and b show the hybrid maps for both sources at 3.6~cm \nin 1995.9. \nThe maps are made using uniform weighting of the visibilities, a map\ncell size of 0.15 mas and a circular CLEAN restoring beam of 0.5 mas\n(these same mapping parameters are used throughout this work).\nThe ``dirty'' beam has a central peak of 0.57 x 0.47 mas in PA -29\\degr\n(PA = position angle, defined starting at North, increasing through East).\nThe root-mean-square (rms) levels in the A and B maps, in regions away \nfrom the source structures (estimated using AIPS task IMSTAT) are 1.0 and \n0.12 mJy/beam respectively, an indication that dynamic range considerations \ndominate over thermal noise in determining the map noise levels. \n\n%%% FIGURE 1\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig1a.ps,width=6.cm}}\n\\put (-150,150) {\\bf {a)}}\n{\\psfig{figure=fig1b.ps,width=6.cm}}\n\\put (-150,150) {\\bf {b)}}\n}\n\\caption{VLBI hybrid maps of 1038+528 at 3.6~cm. Uniform weighting, \nCLEAN beam 0.5 x 0.5 mas, pixel size 0.15 mas, tick interval 1 mas.\n{\\bf a} Quasar A. Contours at 3,6,12,24... mJy/beam.\n{\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy/beam.\n\\label{fig1}} \n\\end{figure*}\n\n\\subsection{Phase referencing in AIPS}\n\nIn order to make an astrometric estimate of the separation between\nquasars A and B at this 4th epoch, we first used a \"conventional\" \nphase-reference\ntechnique to make maps of the quasars which preserve the relative phase\ninformation.\nIn practice this consists of using the antenna-based residual terms \nderived from the analysis of the data of one ``reference'' source (A), \nto calibrate the data from simultaneous observations of the other \"target\" \nsource (B).\nThe reference quasar source structure must first \nbe estimated from a hybrid map, and then fed back into\nthe phase self-calibration process to produce estimates of the antenna-based \nresiduals, free from contamination by source structure. \n\nPhase referencing techniques work under the assumption that the\nangular separation between the reference and target sources is smaller\nthan the isoplanatic patch size (i.e. the effects of unmodelled perturbations,\nintroduced by the propagation medium,\non the observed phases of both sources are not very different) and that \nany instrumental terms are common. Geometric errors in the correlator model\nmust also be negligible.\n\nAssuming that the antenna residuals have been ``cleanly'' estimated using the\nreference source data, the calibrated phases of the target \nsource should be free from the errors mentioned above, but still retain the\ndesired signature of the source structure and relative position\ncontributions. The Fourier Transformation of the calibrated visibility\nfunction of the target source produces a ``phase referenced'' map. The\noffset of the brightness distribution from the centre of this map reflects\nany error in the assumed relative separation in the correlator model.\nIf the reference source has a true ``point'' structure and is at the\ncentre of its hybrid map, this offset will be equal to the error;\nmore generally, one should also measure the offset of a\nreference point in the reference source map, and estimate the\nerror in the source separation used in the correlator model from the difference\nbetween the target and reference source offsets.\n\nIn general, the success of the phase-referencing technique is critically\ndependent on the angular separation of the target and reference sources.\nSimultaneous observation of the sources, as was possible here, significantly \nsimplifies the procedure, eliminates the need for temporal interpolation,\nand reduces the propagation of errors introduced in the\nanalysis. While random errors increase the noise level in the phase\nreferenced map, systematic errors may bias the estimated angular\nseparation.\n\nFor our implementation of phase-referencing using AIPS, we chose\nto re-FRING the (calibrated) A data set, using our hybrid map of quasar \nA as an input model, and applied the adjustments to the antenna phase, \ndelay and rate solutions to both the A and B data sets before re-averaging. \nWe then made maps of both A and B using MX, performing no further phase \nself-calibration. These are our ``phase-reference astrometry'' (PRA) \nmaps (shown in Fig.~\\ref{fig2}a and b) on which we performed\nastrometric measurements (see Sect. 4.2). Although the rms noise levels \nin the PRA maps are slightly higher than in the corresponding hybrid maps \n(2.0~mJy~beam$^{-1}$ for A and 0.24~mJy~beam$^{-1}$ for B),\nour procedure ensures that the A and B\nvisibility functions from which they are derived have been calibrated \nidentically. \n\n%%% FIGURE 2\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig2a.ps,width=6.cm}}\n\\put (-150,150) {\\bf {a)}}\n\\put (-84.5,88.5) {\\bf {+}}\n{\\psfig{figure=fig2b.ps,width=6.cm}}\n\\put (-150,150) {\\bf {b)}}\n\\put (-85,88) {\\bf {+}}\n}\n\\caption{VLBI phase-reference astrometry maps. Map parameters as in Fig. 1.\nAstrometry reference points are indicated with a cross.\n{\\bf a} Quasar A. Contours at 3.5,7,14,28... mJy~beam$^{-1}$.\n{\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy~beam$^{-1}$.\n\\label{fig2}} \n\\end{figure*}\n\n\n\\subsection{New mapping method for astrometry of close source pairs} \n\nWhile the conventional phase-referencing approach worked well for our\nNovember 1995 observations of 1038+52A and B, the method relies on\nmaking a good estimate of the antenna residuals from just one of the \nsources - the reference. We have devised an alternative method which\nextends the standard VLBI self-calibration procedure to work on both\nsources together, for cases where they have been observed simultaneously,\nand when either could be used as the reference (see Appendix A).\n\nThe basis of the new method is to recognise that, since the visibility \nfunctions for both sources are corrupted by the same (antenna-based) \nphase and phase derivative errors, the sum of the two visibilities also \nsuffers the same errors. We form the point-by-point sum of the two data \nsets, creating a new one which represents the visibility function of a \n``compound source'' consisting of a superposition of the two structures, \ncorrupted by the common antenna phase errors.\nIf the source separation is close enough, the (summed) data as\na function of the (averaged) uv-coordinates can be\nFourier Transformed to form a map of the\ncompound source structure, and (iterative) self-calibration in FRING or CALIB\nyields the antenna-based residuals. The advantage of this approach is that\nthe antenna-based residuals are determined using both source structures\nsimultaneously, and may thus reduce the chance that reference source structural\nphase terms contaminate the residuals. We term this process ``Hybrid Double\nMapping'' (HDM); a detailed description is given in Porcas \\& Rioja \n(\\cite{porcas96}).\n\nIt is convenient to shift the source position in one of the data\nsets (by introducing artificial phase corrections)\nprior to the combination into a compound-source data set, to avoid \nsuperposition of the images in the map. The phase self-calibration \nsteps which are then applied to the combined data set are \nidentical to the case of a single source. In HDM the information\non the angular separation between the sources is preserved in the \nprocess of self-calibration of the combined visibilities, and can be measured\ndirectly from the compound-image map;\nthe relative positions between the individual source images in the \ncompound map, taken together with any artificial position shift introduced,\ngive the error in the assumed angular separation in the correlator model. \nIn this approach one must be careful to use the same number of visibility\nmeasurements in each time interval from the two data sets, in order to avoid\nthe predominance of data from a particular source. \n\nFig.~\\ref{fig3} shows the HDM map of quasars A and B in 1995.9 at \n$\\lambda$ 3.6~cm; \nthe B source is artificially offset by -4 mas in declination.\nThe rms noise in the map is 0.82~mJy~beam$^{-1}$ - higher than that in \nthe hybrid map of B but lower than in that of A.\n\n\n%%%FIGURE 3\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig3.ps,width=6.cm}}\n}\n\\caption{HDM map of 1038+52 (A+B). Map parameters as in Fig. 1. \nQuasar B has been offset by -4.0 mas in\ndeclination. Contours at 3,6,12,24... mJy~beam$^{-1}$. \n\\label{fig3}} \n\\end{figure}\n\n\n\n\\section{Analysis of the maps} \n\n\\subsection{Source structures} \n\nThe 1995.9 hybrid maps of quasars A and B at $\\lambda$ 3.6~cm \n(Fig.~\\ref{fig1}) show the core-jet structures typical of quasars at \nmas scales. They may be compared with maps from previous epochs given \nin Rioja et al. (\\cite{rioja97}). \nThe structure of A in the new map shows no major changes with respect \nto previous epochs. There is a prominent peak at the SW end of the\nstructure (the ``core'') and a jet extending in PA 15--25\\degr\n~containing at least two ``knot'' components (k1 and k2).\n\nThe new map of B at 3.6~cm is qualitatively similar to\nthose from previous epochs. It shows 2 point-like components separated\nby just under 2 mas in PA 127\\degr.\nSpectral arguments support the identification of\nthe NW component as a ``core'' (Marcaide \\& Shapiro \\cite{marca84}); \nthe SE component, corresponding to a knot in the jet, has been used as \na reference component in previous astrometric studies.\nThe separation between these 2 components in 1995.9 has increased, \ncontinuing the expansion along the axis of the source, as discovered \nfrom previous epochs of observations at this wavelength (Rioja et al. \n\\cite{rioja97}).\nThere is no trace of the third, extreme SE component, seen in maps\nof this source at 13~cm. This feature is evidently of lower surface\nbrightness at 3.6~cm and is resolved out at the resolution of these \nobservations.\n\nWe used AIPS task IMSTAT to estimate total flux densities for quasars A and\nB (within windows surrounding the sources in the hybrid maps). The values \nare given in Table~\\ref{tab1}.\nTable~\\ref{tab1} also lists the fluxes and relative positions of the \nmost prominent features in the maps of A and B, obtained using task JMFIT to\nfind parameters of elliptical Gaussian functions which best\nfit the various source sub-components. The formal errors from the fits,\nhowever, do not give realisitic values for the parameter uncertainties.\nThe distribution of flux between the core and k1 in quasar A, and their\nrelative separation, are quite uncertain, for example. \n\n%%%TABLE 1\n\\begin{table*}\n\\caption {Parameters derived from the Hybrid Maps of 1038+528 A and B.} \n\n\\vspace*{0.25cm}\n\n\\begin{center}\n\\begin{tabular} {|c|c|c|c|c|c|c|c|c|c|} \\hline\n & S-tot & & S-pk & S-int & maj.& min. & PA & sep. & PA \\\\\n & (mJy) & &(mJy/b) & (mJy) & (mas) & (mas) & (deg) & (mas) & (deg) \\\\\n\\hline\n1038+528 A & 603.0 & core & 301.6 & 355.3 & 0.28 & 0.12 & 3 & - & - \\\\\n & & k1 & 171.8 & 235.5 & 0.42 & 0.16 & 13 & 0.639 & 15.1 \\\\\n & & k2 & 9.3 & 14.0 & - & - & - & 1.796 & 24.8 \\\\\n&&&&&&&&& \\\\\n1038+528 B & 86.5 & core & 33.5 & 40.9 & 0.32 & 0.11 & 132 & - & - \\\\\n & & ref & 24.6 & 34.4 & 0.39 & 0.24 & 123 & 1.869 & 127.1 \\\\ \n\\hline \\hline\n\\end{tabular}\n\\end {center}\n\\label{tab1}\n\\end{table*}\n\n\n\\subsection{Estimating positions of reference features} \n\nThe astrometric measurement of a separation between two non-point sources\nmust always refer to the measured positions of reference points within \nmaps (or other representations) of the source structures. \nThe selection of suitable reference points is crucial in monitoring\nprograms, where the results from the analysis of a multi-epoch \nseries of observations are compared. \nIdeally, a reference point should correspond to the peak of\na strong, unresolved component, which is well separated from\nother radio emission within the source structure.\n\nFor the 1995.9 epoch observations of 1038+528 A,B we selected the same \nreference features as those used for the analyses of previous observing \nepochs. These are the ''core'' component for quasar A, and the prominent \nSE component for quasar B.\nThese features are labelled with a cross in Fig.~\\ref{fig2}a and b.\nThe core of A is indeed strong and compact, but has the disadvantage\nthat it merges with knot k1.\nAlthough the SE component of B is no longer the strongest feature at 3.6~cm,\nit has always been strong at both 3.6 and 13~cm wavelengths,\nis reasonably compact and is easily distinguishable\nin maps made at longer wavelengths, thus facilitating spectral studies.\nOur astrometric analysis refers to the measured positions of the peaks\nof these components in A and B. We used the AIPS task MAXFIT to measure \nthe position of these peaks in the PRA and HDM maps.\nMAXFIT defines the location of a peak in a given map region by fitting \na quadratic function to the peak pixel value and those of the adjacent pixels.\nA comparison of this method of defining the peak position with that used\nfor earlier epochs is described in the next section. \n\n\\subsection{Position error analysis} \n\nAn analysis of errors presented in Rioja et al. (\\cite{rioja97}) shows \nthat the dominant uncertainty in the astrometric measurements of the \nseparation between this close pair of quasars comes from the limited \nreproducibility of the reference point positions in the VLBI maps, \nfrom epoch to epoch. The magnitude of this effect\nis hard to quantify, however, since it depends on the nature of the\nsource brightness distribution surrounding the reference point, and\nthe method used to define the position of the peak, in addition\nto the resolution of the array and the signal-to-noise\nratio of the peak in the map.\n\nA rough estimate of the error due solely to finite signal-to-noise in\nthe maps is given by dividing the beam size by the ratio of the\ncomponent peak to the rms noise level in the maps (see e.g. \nThompson et al. \\cite{thompson86}). \nThis yields values of 3.3, 3.5 and 1.4~$\\mu$as for the A and B PRA \nmaps and the HDM map. These may be taken to represent lower limits to \nthe reference point position errors; realistic errors will be larger,\nand will depend on the nature of the reference features \nand the manner in which the position is estimated.\n\nIt is important to choose a definition of the reference point position \nsuch that it can be reproduced reliably from epoch to epoch, and is as \nindependent as possible from the parameters used in making the map \n(e.g. cell size and beam width).\nThe AIPS task JMFIT can be used to fit an elliptical Gaussian to a component\nin a CLEAN map, for example. However, the position of the peak of the \nGaussian depends on how asymmetric the component brightness distribution \nis, and the area of the map to which the fit is restricted. MAXFIT fits \njust to the local maximum around the peak map value, and is thus less \nsensitive to the rest of the distribution.\n\nWe have attempted to quantify some limits to reproducibility arising from \nthe use of MAXFIT for defining the peak position in CLEAN maps.\nWe investigated the effect of changing the true position of a point-like\nsource with respect to the pixel sampling (here 3.3 pixels per beam) \nby offsetting the source position in 10 increments of 1/10 of a pixel \nin the visibility domain, mapping and CLEANing the new data sets, and \nestimating the new positions in the CLEAN maps using MAXFIT. The\nmaximum discrepancy found between the values of the artificial offset\nand the shift derived by MAXFIT was 1/20 of a pixel.\nThis corresponds to 8~$\\mu$as in our 3.6~cm maps.\n\nFor the analysis of previous observing epochs, the reference points\nwere defined to be the centroid of the most prominent delta functions \nfrom which the CLEAN source map was derived (Rioja et al. \\cite{rioja97}).\nWe examined possible systematic differences resulting from these\ndifferent definitions of reference points.\nOne might expect the largest discrepancies to arise when the underlying\nsource structure near the reference point is asymmetric, as in quasar A.\nWe investigated such differences by determining ``centroid'' positions for\nboth A and B reference components, using various criteria for excluding\nclean components from the calculation; this included the ``25 percent\nof the value at the peak'' threshold used for earlier epochs.\nFor A the difference between this centroid position and the MAXFIT\nvalue was 0.12 pixel (18~$\\mu$as). For B the difference was less\nthan 0.1 pixel.\nThese are probably the largest potential sources of error arising from using\ndifferent methodologies at different epochs.\n\nOur use of two different mapping procedures - phase-reference mapping\nand HDM - also gives some insight into the size of position errors resulting\nfrom standard CLEAN + phase self-cal mapping algorithms.\nThe differences between the separation estimates from the PRA maps and the\nHDM map are 27 and 28~$\\mu$as in RA and Dec respectively.\nThis would suggest that differences in the positions of peaks in \nmaps reconstructed in different ways may vary at the 14~$\\mu$as level.\n\nAfter considering the various possible effects which can limit the\naccuracy of postion estimates, we adopt a ``conservative'' value for \nthe error in estimating the peak position in our $\\lambda$ 3.6~cm maps,\nembracing all the effects detailed above, of $18~\\mu$as\n(this corresponds to a thirtieth of the CLEAN beam).\nThe associated estimated error for a separation measurement between\nthe two sources is $25~\\mu$as.\n\n\n\\subsection{Astrometry results} \n\nTable~\\ref{tab2} lists the results of our astrometric measurements of \nreference point positions in the maps.\nThey are presented as changes in measured separation between the \nreference points in A and B in 1995.9, with respect to their separation \nin 1981.3. \nThe values given from the phase-reference technique correspond to the \ndifference between the A and B reference feature position offsets in \ntheir respective PRA map. The values derived from HDM have been corrected \nfor the artificial offset introduced before adding the A and B source \nvisibilities.\n\n%%%TABLE 2\n\n\\begin{table}\n\\caption{Change in the separation between quasars A and B in 1995.9\nwith respect to 1981.2, estimated using standard phase referencing \n(PRA) and hybrid double mapping (HDM) techniques.}\n\\begin{center}\n\n\\vspace*{0.25cm}\n\n\\begin{tabular} {|c| c| c|} \\hline \n$\\Delta(\\Delta \\alpha)$ $\\cos \\delta_A$ & $\\Delta(\\Delta \\delta)$ & Method \\\\ \n$[\\mu$as$]$ & $[\\mu$as$]$ & \\\\ \\hline \\hline\n% (%) = Without Correlator position offset: RA -159muas; DEC 74 muas\n% 11 & 175 & Phase Referencing \\\\\n -148 & 249 & PRA \\\\\n% -16 & 203 & HDM$^1$ \\\\\n% -175 & 277 & HDM$^1$ \\\\ \\hline \\hline\n -175 & 277 & HDM \\\\ \\hline \\hline\n% -7.5 & 204 & HDM$^2$ \\\\\n% -167 & 278 & HDM$^2$ \\\\\n% -9 & 180 & HDM$^3$ \\\\ \\hline\n% -168 & 254 & HDM$^3$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab2}\n\\end{table}\n\n\nAll these values have been corrected for a small error in the AIPS calculation\nof the u,v coordinates in the frequency-averaged data set.\n(Distances measured within the maps must be adjusted\nby a small correction factor of\n$1 - \\Delta \\nu \\ast (2~\\nu)^{-1} = 0.998$.) \n \\\\\n\nTable~\\ref{tab3} lists the coordinates of the reference source (A) adopted in\nthe analysis and the measured coordinate separation between quasars A\nand B in 1995.9.\n\n%%%TABLE 3\n\n\\begin{table*}\n\\caption{{\\it Fixed} source coordinates used for quasar A\nin the astrometric analysis (these coordinates correspond to GSFC global\nsolution GLB831 (Chopo Ma, priv. comm.)), and\nseparation between quasars A and B measured in 1995.9.}\n\n\\begin{center}\n\n\\vspace*{0.25cm}\n\n\\begin{tabular} { |l| r| r|} \\hline\n{\\bf Coordinates} & {\\bf RA} (J2000) \\hspace*{0.5cm} & {\\bf DEC} (J2000) \\hspace*{0.5cm}\n \\\\ \\hline \\hline\n{\\it Reference Source {\\bf (A)}} & 10$^h$ 41$^m$ 46\\fs781613 \n\\hspace*{0.05cm} & 52$^0$ 33\\arcmin 28\\farcs23373 \\hspace*{0.05cm} \\\\ \\hline \n{\\it Relative Sep. {\\bf (B-A)}} & $2\\fs1160588 $ \n& $27\\farcs376325$ \\\\\n{\\it Estimated error {\\bf (B-A)}} & $\\pm 0\\fs0000027$ & $ \\pm 0\\farcs000025$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab3}\n\\end{table*}\n\n\n\\section{Comparison of astrometry at all 4 epochs} \n\nIn this section we make a comparison of the astrometric\nmeasurements from the series of 4 epochs of observations.\nAny increase of the temporal baseline in the program of monitoring the \nseparation between A and B should result in a more precise \nidentification of any systematic trends,\nwith an improved elimination of random contributions.\nIn Sect. 5.1 we justify comparing\nthe astrometric values measured at the various epochs, even\nthough non-identical observing, post-processing and analysis\nprocedures were involved.\nIn Sect. 5.2 we present the astrometric results from the 4 epochs.\nIn Sects. 5.3, 5.4, 5.5 and 5.6 we present various analyses of these\nresults, and attempt to quantify, or put upper-limits to,\nproper motions within and between the A and B quasars.\n\n\n\\subsection{Comparison between the techniques used at different epochs}\n\nBefore attempting a comparison of the astrometric results from \nthe 4 observing epochs, we need to\nshow that any bias in the astrometric estimates introduced by the\nuse of different procedures is small compared with other errors in\nthe measurements for the individual epochs.\nThe consistency between the results from previous epochs of observations \nhas been exhaustively tested (Marcaide et al. \\cite{marca94}; \nRioja et al. \\cite{rioja97}).\nWe outline here the largest changes involved in the fourth epoch, 1995.9,\nwith respect to previous ones:\n\n\\begin{enumerate}\n\n\\item The observing array and frequency set-up used in the fourth epoch\nwas different from previous epochs of observations \n(frequency range 8404.5 to 8436.5 MHz instead of 8402.99 to 8430.99 MHz\nat first 3 epochs). This results in a different coverage of the {\\it UV} \nplane, leading to changes in the reconstruction of the source images. \nInvestigations of such effects by Marcaide et al. (\\cite{marca94}) show that\nthe effect on the astrometric anaylsis is only a few $\\mu$as. \nIt is important to note that the observations at all 4 epochs have\ncomparable resolutions and sample the same range of structural scales\nin the sources.\n\n\\item The processing of the fourth epoch was done using the VLBA correlator,\nwhich uses a theoretical model derived from CALC 8.2; we used AIPS to\nanalyse the data with visibility phases residual to that model.\nFor previous epochs the correlation was done at the MPIfR (Bonn) MK3\ncorrelator, and an analysis of the data using total phases was made\nwith VLBI3 (Robertson \\cite{robertson75}).\nThe differences between CALC 8.2 and the one implemented in VLBI3 \npropagate into changes of only 1-2~$\\mu$as in the astrometric analysis\nof the 1038+528 A-B separation (Rioja \\cite{rioja93}, Rioja et al. \n\\cite{rioja97}). \nThis is because any such differences are ``diluted'' by the source \nseparation expressed in radians - \n$10^{-4}$ in the case of this very close source pair.\n\n\\item The values used in the analysis of previous epochs for\nEarth Orientation Parameters (EOP), stations and reference source coordinates\nwere consistently derived from a single global solution provided by Goddard \nSpace Flight Center (GSFC). \nFor the correlation of the fourth epoch, the values used for \nEOP were derived from IERS solutions, and the station coordinates from \nUSNO catalogs.\nWe have made a comparison of the values derived for all the parameters at\nthe 4 epochs from a single global solution from IERS (namely IERS eopc04),\nwith the actual values\nused in the individual epoch analysis. The difference between the corresponding\nEOP values is always less than 4 mas. Such discrepancies propagate into \nerrors in the relative position estimates at each epoch of only a few \n$\\mu$as.\n\n\\item Our astrometric analysis in AIPS using a phase-referencing approach and\nHDM differs from the phase difference method used in VLBI3 analysis.\nComparisons show that these procedures are equivalent \n(Porcas \\& Rioja \\cite{porcas96}; Thompson et al. \\cite{thompson86}).\nBoth involve the definition of reference points in source maps;\nuncertainties in the reference point positions \n(as described in Sect. 4.3) arise in the same way.\n\n\\item Finally, a minor VLBA correlator error (Romney priv. comm.) caused\nincorrect time labels to be attached to the visibility records, resulting in\nincorrect ({\\it u,v}) values. \nThe effect on the relative visibility phases for our source pair is small\n($\\sim 0.004$\\degr) and can be neglected.\n\n\\end{enumerate}\n\n The magnitudes of all of the effects reported in this section are\nmuch smaller than our estimate in Sect. 4.3 of the uncertainity in reproducing\nthe reference point in the source, from epoch to epoch, and we are thus\njustified in comparing the astrometric results from all 4 epochs.\n\n\n\\subsection{Astrometric separations at the 4 epochs} \n\nThe astrometric measurements of the separations between the reference \npoints in A and B at $\\lambda$ 3.6~cm from 4 epochs are presented in \nFig.~\\ref{fig4}.\nIt includes our new 1995.9 measurement and those from three earlier epochs, \nin 1981.3, 1983.4 and 1990.5, reported in Marcaide \\& Shapiro \n(\\cite{marca84}), Marcaide et al. (1994) and Rioja et al. (\\cite{rioja97}), \nrespectively. The origin of the plot represents the separation at epoch 1.\n\n%%% FIGURE 4\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig4.ps,width=6.cm}}\n}\n\\caption{Measured separations between the A and B reference points at epochs\n2 (1983.4), 3 (1990.5) and 4 (1995.9), with respect to epoch 1 (1981.2).\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig4}} \n\\end{figure}\n\n\nChanges with time in Fig.~\\ref{fig4} represent the vector difference between\nany motions of the reference points in quasars A and B.\nThe near-orthogonal nature of the source axes in 1038+52 A,B (along\nwhich one might expect any motion to occur) simplifies the\ninterpretation of any trends seen. The new 1995.9 value follows the\nsame steady trend towards the NW shown by the three previous epochs.\nRioja et al. (\\cite{rioja97}) interpreted this as an outward expansion of the\nreference component in quasar B at a rate of $18~\\pm~5~\\mu$as~yr$^{-1}$, \nand quoted an upper bound on any proper motion of quasar A of \n$10~\\mu$as~yr$^{-1}$.\n\n\\subsection{Vector decomposition} \n\nIn this section we attempt to separate the individual contributions from \nthe 2 quasars in the astrometric separation measurements presented in \nFig.~\\ref{fig4}. We make no assumption about the stability of either \ncomponent, but\nassume that any displacements of the A or B reference points from their \npositions at epoch 1 are along the corresponding source axis directions.\nThis is a plausible assumption if the reference point coincides \nwith a non-stationary component moving along a ballistic trajectory, \nor with the location of the peak of brightness within an active core \nor near the base of jet, where changes during episodes of activity are \nlikely to occur along the jet direction.\nThis approach is closely related to that used previously \nby Rioja et al. (\\cite{rioja97}). For fixed assumed source axes for A and B,\nit results in a unique decomposition of the changes in the A-B separation\ninto separate A and B displacements, from 1981 to 1995.\n\nIt is clear that the dominant contribution to the separation changes\nseen in Fig.~\\ref{fig4} comes from quasar B, \nin which the source axis is well defined by the 127\\degr PA of\nthe separation between core and reference components.\nFor quasar A the source axis bends, from the inner ``core'' region \n(PA = 15\\degr) to the outer jet components, and it is not so clear which \ndirection should be chosen.\n\nIn our analysis we tried a range of values for fixing the A source axis \n(0 to 45\\degr ~in steps of 5\\degr).\nFor each, we calculated A and B reference-point displacements at epochs 2, \n3 and 4 with respect to epoch 1.\nThen we performed a least-squares fit to the B displacements with time to\nestimate a linear expansion rate for the B reference feature along \nPA 127\\degr. In Fig.~\\ref{fig5} we plot the deconvolved B reference point \ndisplacements from the analysis with the A source axis fixed at \nPA 25\\degr (the value adopted by Rioja et al. \\cite{rioja97}).\nThe fitted expansion rate is $16.9~\\pm~0.6~\\mu$as~yr$^{-1}$;\nthe error and associated rms values take account of the small number \nof points and 2 degrees of freedom. This rate agrees well with the value\nof $18~\\pm~5~\\mu$as~yr$^{-1}$ deduced by Rioja et al. (\\cite{rioja97}).\nThe rms residual from the fit (7~$\\mu$as) is low, and vindicates\nour use of measurements derived from differing techniques for\ninvestigating the relative proper motion between A and B. \n\n%%% FIGURE 5\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig5.ps,width=6.cm}}\n}\n\\caption{Changes in position of reference component in B along PA 127\\degr,\ndeduced from deconvolution of the A-B separation measurements. Assumed source\naxis for A is 25\\degr.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig5}} \n\\end{figure}\n\n\n\\subsection{Structural evolution within 1038+528 B} \n\nOur deconvolution analysis of the changes in separation measured between \nall 4 epochs supports the finding, previously proposed, that the B reference\ncomponent moves along the source axis, away from the B core.\nIn this section we make an independent determination of the separation \nrate between the core and reference component in B from measurements \nwithin the maps at the 4 epochs.\n\nFig.~\\ref{fig6} shows the separation between the core and reference \ncomponent in B at the four epochs plotted against time. For epochs 1--3 \nwe used the values given in Rioja et al. (\\cite{rioja97}). For 1995.9 we \nused AIPS task UVFIT to estimate a separation from the B visibility data \ndirectly, in order to follow the methodology used for the other epochs as \nclosely as possible; the value obtained was 1.895 mas.\nThe slope from a least-squares fit corresponds to an expansion rate \nof $13.0~\\pm~0.7~\\mu$as~yr$^{-1}$.\nIn the standard picture of extragalactic radio sources, the ``core'' is\nstationary, so this corresponds to an outward expansion of the\nreference component along PA 127\\degr.\n\n%%% FIGURE 6\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig6.ps,width=6.cm}}\n}\n\\caption{Changes in the position of the reference component in B \nalong PA 127\\degr, from measurements of its separation from the core\nin hybrid maps of B.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig6}} \n\\end{figure}\n\n\nThe rms of the fit (8~$\\mu$as) is again surprisingly low, implying\ntypical errors in the separation measurements at each epoch \n(both within the B structure and between the reference points)\nof only about 10--12$~\\mu$as along the direction of the B source axis.\nThis is considerably less than the estimate of position separation \nerrors given in Sect. 4.3. \n\n\\subsection{Relative proper motion }\n\nThe analysis presented in the previous sections demonstrate\nclearly that the chosen reference component within quasar B is\nunsuitable for use as a marker for tracing any relative proper motion\nbetween quasars A and B. The value of its expansion velocity derived \nin Sect. 5.4 appears to differ significantly from that deduced by \nvector-decomposition in Sect. 5.3. Although the difference between \nthese estimates, if real, could be interpreted as motion of the core of B \nat a rate of $\\sim 4~\\mu$as~yr$^{-1}$, this is not a conclusive result\nsince differences of this order arise from choosing different values of \nPA for the motion in A in the vector decomposition method.\n\nA more suitable tracer of relative proper motion between the quasars is \nthe variation of the separation between the cores of A and B.\nWe have used the separations between the core and reference component\nmeasured in the B map at each epoch, and the astrometric\nseparations between A and B, to calculate the separations between the\nA and B cores at each epoch; these are plotted in Fig.~\\ref{fig7}.\nThe area occupied by the points defines an upper limit of \n$\\sim 10~\\mu$as~yr$^{-1}$ for any relative proper motion between \nthe A and B cores, and hence between the quasars themselves, during\nthe period of nearly 15 years for which the separation has been\nmonitored with VLBI.\nThe limit seems to be set by the relatively large deviation of the\n1995.9 epoch point in the direction of the A source axis, presumably\narising from the difficulty in defining the reference point at the\nA ``core'' from epoch to epoch. \n\n%%% FIGURE 7\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig7.ps,width=6.cm}}\n}\n\\caption{Separation between the cores of A and B (with respect to epoch 1),\nderived by correcting the A-B reference point separation measurements with the\ncore-reference separations measured in the B hybrid maps.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig7}} \n\\end{figure}\n\n\n\\subsection{Possible ``core'' motions ? } \n\nFinally, we investigate any possible residual motions of the ``cores'' \nin A and B. The most likely causes of any such apparent motions are \nchanges in the relative brightness or positions of features in the \nsource structures at a resolution below that of the maps.\nOne might expect that these, too, would produce effects predominantly\nalong the source axis directions.\nWe therefore used the vector deconvolution method on the plot of\ncore-core separation with time to study displacements of the cores\nalong their source axis directions.\nFig.~\\ref{fig8}a and b show plots of the separated contributions from \nB and A, for an assumed A source axis PA 25\\degr.\nThe displacements for the B core seem to increase systematically.\nThe fitted rate is $3.8~\\pm~0.3~\\mu$as~yr$^{-1}$, indicating a possible \nslow outward motion. The displacements for the A core do not seem to \nvary systematically - the fitted slope is $5.5~\\pm~3.6~\\mu$as~yr$^{-1}$.\nHere the scatter is considerably larger, reflecting both the difficulties of\ndefining the reference point along the A core-jet axis, and\nalso, perhaps, real ``jitter'' of the position of the peak due to variations \nin the ``core'' substructure. These plots indicate the level of stability \nof the individual core positions; the fits represent realistic upper limits \nto any possible systematic core motion in the A and B quasars along their \nsource axis directions.\n\n%%% FIGURE 8\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig8a.ps,width=6.cm}}\n\\put (-140,140) {\\bf {a)}}\n{\\psfig{figure=fig8b.ps,width=6.cm}}\n\\put (-130,140) {\\bf {b)}}\n}\n\\caption{Residual motions of the cores using the deconvolution approach.\n {\\bf a} Displacements of B core along PA 127\\degr; \n{\\bf b} Displacements of A core along PA 25\\degr. \nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig8}} \n\\end{figure*}\n\n\n\\section{Conclusions} \n\nThe series of astrometric VLBI measurements of the separation between \nthe quasar pair 1038+528 A and B, spanning\nnearly 15 years, provides excellent material for investigating \nthe relative proper motion of two extragalactic radio sources and\nthe positional stability of their cores.\nThe changes measured in the separations between quasars A and B \nat 3.6~cm are dominated by the motion of the reference feature in quasar B. \nThese astrometric results, and measurements in the hybrid maps of B are\ncompatible with an expansion rate for the B reference component of \n13--17$~\\mu$as~yr$^{-1}$.\nAt a redshift of 2.296 this translates to an apparent\ntransverse velocity of 0.55--0.70~c~h$^{-1}$.\nWe note that this is an order of magnitude smaller than the more\ntypical superluminal velocities seen in many quasars; it is a \nrare example of a subluminal velocity measured for a knot in a quasar jet.\n\nAfter correcting for the motion of the reference component in B,\nwe can put a conservative upper bound to any relative proper\nmotion between the quasars of $10~\\mu$as~yr$^{-1}$.\nDespite the increase in temporal baseline, this upper bound is no\nbetter than that given by Rioja et al. (\\cite{rioja97}).\nIts value is related to the difficulty in reproducing a stable reference\nposition along the A source axis near its ``core''.\n\nTheories in which the redshifts of quasars do not indicate cosmological\ndistances, and in which quasars are ``local'' and have high Doppler\nredshifts (e.g. Narlikar \\& Subramanian \\cite{narlikar83}) are incompatible \nwith our measured upper-limit to relative proper motion. Quasars at \n100 Mpc distance moving at relativistic speeds would have proper motions \nof the order of $600~\\mu$as~yr$^{-1}$, nearly 2 orders of magnitude \ngreater than our limit. Assuming cosmological distances,\nour limit corresponds to apparent transverse velocities of \n0.43~c~h$^{-1}$ and 0.22~c~h$^{-1}$ at the redshifts of the B and A\nquasars, respectively.\n\nWe have investigated the way in which the definition of \nreference points in a map may be only loosely ``fixed'' to the radio\nsource structure, especially when the latter is strongly asymmetric.\nWe have also developed an alternative analysis route - Hybrid Double\nMapping - for imaging both sources of a close pair simultaneously, and\nat the same time preserving their relative astrometric information\nin a single map.\n\nThe surprisingly low rms from the fits of linear expansion in quasar B,\nand the discrepancy between the two estimates \n($16.9~\\pm~0.6~\\mu$as~yr$^{-1}$ from the astrometric measurements and\n $ 13.0~\\pm~0.7~\\mu$as~yr$^{-1}$ from the hybrid maps)\nare suggestive of (but do not prove) a residual motion of the core \nin quasar B; our decomposition along the source axis direction gives a fit\nof $3.8~\\pm~0.3~\\mu$as~yr$^{-1}$, corresponding to an apparent transverse \nvelocity of 0.17~c~h$^{-1}$. If real, this might indicate a steady change \nin physical conditions at the base of the jet, or perhaps the emergence \nof a new knot component moving outwards with a velocity similar to the \nreference component, but as yet unresolved by our 0.5 mas beam.\nIn this regard, it is interesting to note the slight extension of\nthe core of quasar B in PA 132\\degr given by the Gaussian model fit.\n\nThe low rms derived from fits to the expansion of the B reference component \nindicate that we have been overly conservative in our estimate of \n$18~\\mu$as for the error in reference point positions. Errors at least \n2 times smaller are implied, corresponding to a sixtieth of the beamwidth. \nIt is interesting to note that such small errors are also implied in the \nwork of Owsianik \\& Conway (\\cite{owsianik98}), where the low scatter in \nthe plot of expansion of the CSO source \\object{0710+439} allows an \nexpansion rate of $14.1~\\pm~1.6~\\mu$as~yr$^{-1}$ to be determined.\n\nThere are no obvious systematic motions within quasar A, but the ``noise'' \nin the estimates of position along its axis are much larger.\nThis noise, along with any associated underlying changes in source\nsubstructure, provides a fundamental limit to estimates of\nany systematic core motion in A. Improvements on the estimates of (or upper\nbounds to) the relative motion between the quasars, or of the\nindividual motion of the A core, will require a considerable\nincrease in the temporal baseline of VLBI monitoring.\n\n\\newpage\n\n\\appendix \n\n\\section {Hybrid Double Mappping (HDM)}\n\n\n{\\bf A.1 Principle of Hybrid Double Mapping} \\\\\n\n\\noindent\nThe visibility function, $V$, measured at time $t$, on a baseline between\nantennas $i$ and $j$, is represented by a complex function with amplitude $A$, \nphase $P$:\n\n\\[ V(i,j) = A * e^{i[\\phi]}(t) \\]\n\n\\noindent\nFor this analysis it is convenient to indentify 3 contributions to\nthe visibility phase:\n\n\\[ \\phi(i,j) = \\phi_{s}(u,v) + \\phi_{p}(u,v) + \\phi_{m}(t) \\]\n\n\\noindent\nwhere \n\n\\begin{description} \n\\item [$\\phi_s$] is due to source structure, evaluated w.r.t. a reference\nposition for the source. \\\\\n\n \\item [$\\phi_p$] is due to any offset of the \ntrue source position from the reference position. \\\\\n\nBoth $\\phi_s$ and \n$\\phi_p$ are functions of the resolution coordinates, $u$ and $v$, at time \n$t$. \\\\\n\n\\item [$\\phi_m$] is due to inaccuracies in the correlator model calculation of\n the interferometer geometry and the signal propagation delays\n in the ionosphere, troposphere and receiving system; it is an \n unknown function of time. \\\\\n This term can be represented by the difference of two\n ''antenna-based'' phases, $\\theta_i$ and $\\theta_j$, since it can \n be related to the \n difference in signal arrival times at the two sites.\n (This analysis is a simplification which ignores possible\n ''non-closing'' instrumental baseline phase terms arising from\n e.g. un-matched bandpasses and polarisation impurities.) \n\\end{description}\n\n\\[ \\phi(i,j) = \\phi_s(u,v) + \\phi_p(u,v) + \\theta_i(t) - \\theta_j(t) \\]\n\n\\noindent\nIn conventional hybrid mapping, an iterative procedure is used\nto separate out the antenna-based phase terms from the ''source'' terms;\nthe latter must produce a consistent and physically plausible source\nstructure after Fourier transformation of the corrected visibility:\n\n\\[ \\underbrace {A * e^{i[\\phi_s+\\phi_p]}(u,v)}_{corrected \\: visibility} = \nV(i,j) * \\underbrace {e^{-i[\\theta_i(t)-\\theta_j(t)]}}_{antenna \\: phase \\: terms} \\] \n\n\\noindent\nHowever, the position offset term, $\\phi_p$, can also be expressed as a difference \nin wavefront arrival times at the 2 antennas and so it is also\n''absorbed'' in antenna phase terms $\\theta_i'$, $\\theta_j'$; \nthe ''absolute'' position information is lost:\n\n\\[ \\underbrace {A * e^{i[\\phi_s]}(u,v)}_{corrected \\: visibility} = \nV(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\: phase\n\\: terms} \\]\n\n\\noindent\nIn Hybrid Double Mapping (HDM), the visibility functions of two \nsources observed simultaneously are added. For a close source pair, we \nmake the same assumption as for conventional phase-referencing - that the \nmodel error phase terms are essentially the same for both sources. We make \na further assumption that the $u,v$ coordinates are also essentially the same\nfor both sources, for each baseline and time. The visibility sum, $V^1 + V^2$,\ncan then be re-written: \\\\\n\n\n\\[ \\underbrace {(A^1 * e^{i[\\phi^1_{s}]} + A^2 * e^{i[\\phi^2_{s}+(\\phi^2_{p}\n-\\phi^1_{p})]})(u,v)}_{corrected \\: visibility \\: sum} = \\]\n\\[ \\;\\;\\; \\vspace*{2cm} = V^{sum}(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\:\n phase \\: terms} \\] \n\n\n%\\begin{eqnarray*}\n%\\lefteqn{ \\[ \\underbrace {(A_1e^{i[\\phi_{1s}]}+A_2e^{i[\\phi_{2s}+(\\phi_{2p}-\\phi_{1p})]})(u,v)}_{corrected \\: visibility \\: sum} = } \\\\\n%& & V^{sum}(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\:\n%phase \\: terms} \\] \n%\\end{eqnarray*}\n\n\\noindent\nThis may be recognised as the visibility function of a ''composite''\nsource consisting of the sum of the brightness distributions of sources\n1 and 2, with antenna-based phase error terms $\\theta_i'$, $\\theta_j'$, \nas before.\nThe HDM method consists of performing the normal hybrid mapping\nprocedure with the visibility sum, resulting in the separation of the\nantenna-based errors, and a physically plausible map of the sum of\nthe two source brightness distrubutions. An important point is that,\nwhereas the {\\it origin} of the map of the composite source is arbitrary (as\nit depends on the position of the starting model), the {\\it separation} of\nthe two source brightness distributions within the composite map\n(determined by $\\phi^2_{p}-\\phi^1_{p}$) is fixed during the phase \nseparation procedure,\nand is equal to the {\\it difference} of the errors in the two source\npositions used for correlation. We call this the ''residual separation''. \\\\\n\n\\noindent\n{\\bf A.2 Practical aspects} \\\\\n\n\\noindent\nThere are some practical aspects to be considered. If the source\ncoordinates used in the correlator model are very precise, then the\nresidual separation may be less than the interferometer beamwidth, and\nthe two source distributions will lie on top of each other. \nIn this case it is desireable to\nintroduce an artificial position offset into one of the\nsource visibility functions before forming the visibility sum, to\nensure that the two source reference features are well separated in the\nHDM map. One should also arrange that the peak of one source\ndoes not lie on the sidelobe response of the other in the \"dirty\" map,\nas this may degrade the CLEAN deconvolution process in the mapping step.\\\\\n\n\\noindent\n Another important consideration is that the time-averaged samples\nof the summed visibility function contain equal contributions from both\nsource visibility functions. When both sources are observed\nsimultaneously this will normally be the case, except when different\namounts of data are lost in the two separate correlator passes needed\nfor the two source positions. It is important to edit the data sets\ncarefully to fulfil this condition. \\\\\n\n\\noindent\n The range of validity of the assumption that the $(u,v)$\ncoordinates for the two sources are the same depends on the ''dilution\nfactor'', i.e. the reciprocal of the source separation, measured in\nradians. The $(u,v)$ value assigned to the summed visibility will be\nincorrect for either source by roughly 1 part in the dilution factor\n(roughly 1 in 6000 for 1038+528A,B). \nThis is equivalent to having source visibility phase errors of this\norder, and thus limits the size of an HDM map to be less than the\nbeamwidth times the dilution factor; the residual separation should be\nmuch smaller than this value.\\\\\n\n\\noindent\nIn the actual analysis used in this work, we first made a rough \ncorrection to the phase of the summed visibility of 1038+528 A + B, using\nthe antenna phase and phase derivative errors from fringe-fitting\n1038+528A using a point source model. However, there is no reason why\none should not fringe-fit the summed visibility function directly. \\\\\n\n\\noindent\n{\\bf A.3 Applications} \\\\\n\n\\noindent\nThe HDM method can in principle be applied\nwhenever two (or more !) radio sources are observed simultaneously,\nbut are correlated at separate field centres; however, \nthey must be close enough so that the conditions of same $(u,v)$\ncoverage and same correlator model errors apply.\nThe method uses the structures of BOTH sources simultaneously to\nseparate out the antenna phase errors, as opposed to a single source in \nsimple hybrid mapping.\nIf both sources are strong (as with 1038+528 A and B),\nconstraining the (single) antenna phase solutions with two structures\nshould lead to a more rigorous and robust separation between the\nsource and antenna phase terms.\nOne field of application is in high resolution VLBI imaging of\ngravitational lens systems with wide image separations (e.g. \nimages A and B of QSO 0957+561 with 6.1 arcsec separation)\nwhere preserving the necessary wide field-of-view from a single \ncorrelation may result in inconveniently large data sets.\nWhen one source is very weak, however,\nthere is probably little to be gained over normal hybrid mapping. \\\\\n\n\\noindent\nFor relative astrometry studies (as described in this paper),\nthe HDM method has some advantages over conventional phase-reference \nmapping and explicit phase-differencing methods.\nIn phase-differencing astrometry, separate hybrid maps must be made of\nboth sources to correct for source structural phase terms and \nthe antenna phase errors are NOT constrained to be the same. Imperfect \nseparation between source and antenna phase terms can increase the noise \non the differenced phase, as well as lead to possible systematic errors.\nIn phase-reference astrometry, only one of the sources is used to solve\nfor the antenna phase terms; imperfect separation can lead to extra\nphase noise in the phase-referenced visibility of the ''target'' source.\nIn HDM we use both source\nstructures simultaneously to separate the (common) antenna error\nphases from that of a single \"structure\" in which the \nreference points of the two sources are spaced by the residual separation.\\\\\n\n\\noindent\nWhen the separation between the two sources of a pair exceeds\nthe telescope primary beamwidths, astrometric and phase-reference \nobservations \nmust involve switching between the sources, and the visibility phase of at \nleast one of the sources must normally be interpolated in the observing gap. \nThe condition that must be fulfilled for HDM to work in\nthis case is that an equal number of observations of both sources must\nbe added to form an average visibility function for the length of the\n''solution interval'' in the phase self-calibration step of HDM.\nThis length is generally limited by the coherence time of the\natmosphere, and would imply a very fast switching cycle in most cases.\nAnother application for HDM could be in the the analysis of\n''cluster-cluster'' VLBI (see e.g. Rioja et al. \\cite{rioja97b}), \nin which two or more sources are observed simultaneously on VLBI baselines \nby using more than one telescope at each site.\n\n\n\\begin{acknowledgements}\n\nWe thank Dave Graham for help with the observations in Effelsberg,\nTony Beasley for asistance at the VLBA, and Mark Reid for useful comments\non the text. M.J.R. wishes to acknowledge support for this research by the\nEuropean Union under contract CHGECT920011.\nThe National Radio Astronomy Observatory is a facility\nof the National Science Foundation operated under cooperative\nagreement by Associated Universities, Inc.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \ned. Reid M., Moran J., Kluwer, p. \\ 523 \n\n\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \nVery Long Baseline Interferometry and the VLBA, eds. Zensus J.A., \nDiamond P.J., Napier P.J., ASP Conference Series, Vol. 82, p. \\ 327.\n\n\\bibitem[1986]{blandford86} Blandford R.D., K\\\"onigl A., 1986, \nApJ 308, 83\n\n\\bibitem[1983]{marca83} Marcaide J.M., Shapiro I.I., 1983, AJ 88, 1133 \n\\bibitem[1984]{marca84} Marcaide J.M., Shapiro I.I., 1984, ApJ 276, 56\n\\bibitem[1994]{marca94} Marcaide J.M., El\\'{o}segui P., Shapiro I.I., 1994, \n AJ 108, 368 \n\\bibitem[1983]{narlikar83} Narlikar J.V., Subramanian K., 1983, \nApJ 273, 44\n\\bibitem[1978]{owen78} Owen F.N., Porcas R.W., Neff S.G., 1978, \nAJ 83, 1009\n\\bibitem[1980]{owen80} Owen F.N., Wills B.J., Wills D., 1980, ApJ 235, L57\n\\bibitem[1998]{owsianik98} Owsianik I., Conway J.E., 1998, A\\&A 337, 69\n\\bibitem[1986]{porcas87} Porcas R.W., 1987, Superluminal Radio Sources, ed.\n Zensus A., Pearson A., Cambridge University Press, p. \\ 12\n\\bibitem[1996]{porcas96} Porcas R.W., Rioja M.J., 1996, Proc. of the 11th \nWorking Meeting on European VLBI for Geodesy and Astrometry, Ed. Elgered\nG., p. \\ 209\n\\bibitem[1993]{rioja93} Rioja M.J., 1993, PhD. Thesis, Universidad de Granada\n\\bibitem[1997]{rioja97} Rioja M.J., Marcaide J.M., El\\'osegui P., \nShapiro I.I., 1997, A\\&A 325, 383 \n\\bibitem[1997]{rioja97b} Rioja M.J., Stevens E.,\nGurvits L., et al., 1997, {\\it Vistas in Astronomy} 41 (2), 213 \n%\\bibitem[2000]{rioja00} Rioja, M.J., Porcas, R.W., 2000, {\\it in preparation}\n\\bibitem[1975]{robertson75} Robertson D.S., 1975, PhD Thesis, MIT\n%\\bibitem[1996]{romney96} Romney, J.D., 1996, (VLBA email memorandum \n%of 14 March) \n\\bibitem[1986]{thompson86} Thompson A.R., Moran J.M., Swenson G.W., 1986, \nInterferometry and Synthesis in Radio Astronomy. Wiley-Interscience, \nNew York, p. 400\n\n\\end{thebibliography}{}\n\n\n\n\n\\end{document}\n\n"}],"string":"[\n {\n \"name\": \"rioja_17jan2000.tex\",\n \"string\": \"% aa.dem\\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\\n% demonstration file\\n% (c) Springer-Verlag HD\\n%-----------------------------------------------------------------------\\n%\\n%\\\\documentclass[referee]{aa} % for a referee version\\n%\\n\\\\documentclass{aa}\\n%\\n\\\\usepackage{psfig}\\n\\n\\\\begin{document}\\n\\n \\\\thesaurus{03 % A&A Section 3: Extragalactic astronomy\\n (03.09.2; % Instrumentation: interferometers,\\n 03.20.2; % Techniques: interferometric, \\n 05.01.1; % Astrometry,\\n 13.18.2)} % Radio continuum: general.\\n%\\n \\\\title{A phase-reference study of the quasar pair 1038+528A,B }\\n% \\\\title{A phase-reference study of the}\\n% \\\\subtitle{quasar pair 1038+528A,B }\\n\\n% \\\\subtitle{I. Overviewing the $\\\\kappa$-mechanism}\\n\\n \\\\author{Mar\\\\'{\\\\i}a J. Rioja \\n \\\\inst{1}\\n \\\\inst{2}\\n \\\\and\\n Richard W. Porcas\\\\inst{3}\\n% \\\\fnmsep\\\\thanks{Just to show the usage\\n% of the elements in the author field}\\n }\\n\\n \\\\offprints{Mar\\\\'{\\\\i}a J. Rioja}\\n\\n \\\\institute{Observatorio Astron\\\\'omico Nacional (OAN), Apdo. 1143, \\n E-28800 Alcal\\\\'a de Henares, Spain \\\\\\\\\\n email: rioja@oan.es\\n \\\\and\\n Joint Institute for VLBI in Europe (JIVE), \\n NL-7990 AA Dwingeloo, The Netherlands \\\\\\\\\\n \\\\and\\n Max-Planck Institut f\\\\\\\"ur Radioastronomie, Auf dem H\\\\\\\"ugel 69,\\n D-53121 Bonn, Germany \\\\\\\\\\n email: porcas@mpifr-bonn.mpg.de \\n% \\\\thanks{The university of heaven temporarily does not\\n% accept e-mails}\\n }\\n\\n \\\\date{Received 5 October, 1999; accepted XX }\\n\\n \\\\titlerunning{Relative Astrometry of 1038+528AB}\\n \\\\authorrunning{Rioja \\\\& Porcas}\\n\\n \\\\maketitle\\n \\n \\\\begin{abstract}\\n\\nWe present results from $\\\\lambda$ 3.6~cm observations of the quasar pair \\n\\\\object{1038+528} A and B, made in 1995 using the VLBA together with the \\nEffelsberg 100m telescope. We describe the use of a phase-referencing \\ntechnique to measure the astrometric separation between the quasars.\\nWe also introduce a new data analysis method - \\\"hybrid double mapping\\\" - \\nwhich preserves the relative astrometric information in a single VLBI \\nhybrid map for close source pairs. We combine our measurements with those \\nfrom three previous epochs, the earliest in 1981. \\nOur new observations confirm the evolution within the structure of quasar B, \\npreviously proposed to explain the measured change in the relative separation \\nof the pair. Our upper bound for any systematic proper motion between the \\nmass centres of quasars A and B is 10~$\\\\mu$as~yr$^{-1}$. This is set by the \\nlimited precision in defining the reference points in the quasars at \\ndifferent epochs and by possible instabilities of the source \\\"core\\\" locations.\\nA separate analysis enables us to put more stringent upper limits to any \\ncore motions along the two source axes.\\n\\n \\\\keywords{Instrumentation: interferometers --\\n Techniques: interferometric --\\n Astrometry --\\n Radio continuum: general\\n }\\n \\\\end{abstract}\\n\\n%\\n%________________________________________________________________\\n\\n\\\\section{Introduction}\\n\\nThe quasar pair 1038+528~A,B (Owen et al. \\\\cite{owen78}) \\nconsists of two\\nflat-spectrum radio sources, with redshifts 0.678 and 2.296 (Owen et\\nal. \\\\cite{owen80}), separated on the sky by only 33\\\\arcsec. \\nThis system provides a unique opportunity to carry out high precision, relative\\nastrometric studies using the full\\nprecision of VLBI relative phase measurements, \\nsince most sources of phase errors are common for the 2 sources\\n(Marcaide \\\\& Shapiro \\\\cite{marca83}).\\n\\n VLBI studies of the mas-scale structure of flat-spectrum quasars\\nshow that they typically have ``core-jet'' morphologies, consisting of a highly\\ncompact feature (the ``core'') located at the base of an extended linear feature \\nor line of lower brightness components (the ``jet'').\\nBoth 1038+528 A and B exhibit such structures.\\nIn standard models of extragalactic radio sources, these radio-emitting \\nfeatures\\narise from a collimated beam of plasma which is ejected with a highly \\nrelativistic bulk velocity from a region close to a central massive object \\nsuch as a black hole (see eg. Blandford \\\\& K\\\\\\\"onigl \\\\cite{blandford86}).\\nWhilst jet features may correspond to shocks in the moving plasma, and \\ncan give rise to the observed ``superluminal'' component motions in some \\nsources (Porcas \\\\cite{porcas87}),\\nthe ``core'' emission is thought to arise from a more-or-less permanent location close to\\nthe origin of the beam, where the ambient conditions correspond to a transition\\nfrom optically thick to optically thin emission at the observed frequency.\\nAlthough the ``core'' position may thus be frequency-dependent, for a fixed\\nobserving frequency\\nthe core should provide a stable marker, anchored to the central mass of\\nthe quasar, whose location can be used to define a precise position for\\nthe object as a whole.\\nAlthough short time-scale variations in physical conditions may cause\\nsmall changes in the ``core'' location, over long time-scales it may be\\nused to track any systematic proper motion of the quasar.\\n\\nThe results from a near decade-long VLBI monitoring program on 1038+52A,B at\\n$\\\\lambda$ 3.6 and 13~cm (from 1981.2 to 1990.5) \\nare reported by Rioja et al. (\\\\cite{rioja97}), whose main conclusions \\ncan be summarized as follows:\\n\\n\\\\begin{enumerate}\\n\\n\\\\item There is no evidence of any relative proper motion between the \\n quasars A and B. The uncertainties in the astrometric parameters \\n result in an upper bound to any systematic relative \\n motion between the cores of 10~$\\\\mu$as~yr$^{-1}$, consistent\\n with zero.\\n\\n\\\\item A compact feature within the jet of quasar B, chosen as the \\n reference point for the structure, expands away from the core at \\n a steady, slow rate of $\\\\sim~18~\\\\pm~5~\\\\mu$as~yr$^{-1}$, corresponding \\n to v=$(0.8~\\\\pm~0.2)~h^{-1}$~c for a Hubble constant,\\n H$_0$ = 100~h~km~s$^{-1}$~Mpc$^{-1}$; q$_0=0.5$. These values are used \\n here throughout.\\n\\n\\\\item The accuracy of the relative separation measurement is limited by \\n noise and source structure, with estimated precisions of about \\n $50~\\\\mu$as at $\\\\lambda$ 3.6~cm at any epoch.\\n\\n\\\\item Confirmation of the consistently large offset (about 0.7 mas) between\\n the positions of the peak of brightness (``core'') at $\\\\lambda$ 3.6 \\n and 13~cm in quasar A.\\n\\n\\\\end{enumerate}\\n\\nNew VLBI observations of this pair were made in November 1995 (1995.9) \\nat $\\\\lambda$ 2, 3.6 and 13~cm. In this paper we report on results from \\nour analysis of the 3.6~cm observations and investigate the temporal \\nevolution of the source structures and relative separation from all \\nfour epochs spanning $\\\\sim 15$ years. \\nInvestigations of frequency-dependent source structure have also been made \\nfrom a comparison of the astrometric measurements\\nof the separations between A and B at all 3 wavelengths observed in 1995;\\nthese will be presented elsewhere (Rioja \\\\& Porcas in preparation).\\n\\nOur new observations are described in Sect. 2. In Sect. 3 we describe\\nthe data reduction and mapping techniques used, and in Sect. 4 an analysis\\nof the measurements in the maps.\\nIn Sect. 5 we compare the astrometric results from these observations\\nwith those from previous epochs and analyse the changes in \\nseparation. Conclusions are presented in Sect. 6.\\n\\n%__________________________________________________________________\\n\\n\\\\section{Observations}\\n\\nThe pair of radio sources 1038+528 A and B was observed with the\\nNRAO Very Long Baseline Array (VLBA) on November 10, 1995,\\nfor a total of 13 hours, alternating every 13 minutes between\\nobservations in dual 3.6/13~cm mode and observations at 2~cm. The\\n100m telescope at Effelsberg was also included in the array for the\\n3.6/13~cm scans. The primary beamwidths of all the antennas were\\nsufficiently large that both sources could be observed simultaneously\\nat all wavelengths. Each 10 minute observation of 1038+52A,B was\\npreceded by a 3 minute observation of the compact calibration source\\n\\\\object{0917+624}, to monitor the behaviour of the array.\\n\\nAll stations used VLBA terminals to record an aggregate \\nof 64 MHz bandwidth for each scan, using 1-bit sampling, subdivided into\\n8 channels (mode 128-8-1). For the dual 3.6/13~cm scans, four 8-MHz channels\\nwere recorded for each band (2254.5--2286.5 MHz; 8404.5--8436.5 MHz), \\nusing \\nRHC polarisation. At 2~cm, eight 8-MHz channels (15\\\\,331.5--15\\\\,395.5 MHz)\\nwere recorded in LHC polarisation.\\n\\nThe correlation was made at the VLBA correlator in Socorro (New Mexico).\\nAs for previous epochs, two separate ``passes'' were needed, using different \\nfield centres for the two sources, to recover data\\nfor both the A and B quasars from the single observation. \\nOutput data sets were generated for the two sources, consisting of the\\nvisibility functions averaged to 2 s, with samples every 1 MHz in frequency\\nacross the bands. \\n\\n\\\\section{Data reduction} \\n\\nWe used the NRAO AIPS package for the data reduction. \\nWe applied standard fringe-fitting, amplitude and phase (self-) calibration \\ntechniques and produced hybrid maps of each quasar. \\nThe astrometric analysis was done using two different mapping methods: \\na ``standard'' phase-referencing approach, transferring phase solutions\\nfrom one quasar to the other\\n(see e.g. Alef \\\\cite{alef88}; Beasley \\\\& Conway \\\\cite{beasley95}) and a \\nnovel mapping method for astrometry of close pairs\\nof sources, hybrid double mapping (HDM) (Porcas \\\\& Rioja \\\\cite{porcas96}). \\nBoth routes preserve the signature of the relative separation of the source \\npair present in the calibrated phases. These analysis paths are described \\nin Sects. 3.1 to 3.3 below. \\n\\n\\\\subsection{Hybrid mapping in AIPS} \\n\\nWe applied standard VLBI hybrid mapping\\ntechniques in AIPS for the analysis of the observations of both\\nquasars A and B. We used the\\ninformation on system temperature, gain curves and telescope gains measured at\\nthe individual array elements, to calibrate the raw correlation\\ncoefficients. \\nWe used the AIPS task FRING to estimate residual antenna-based phases\\nand phase derivatives (delay and rate) at intervals of a few minutes.\\nIt is important to realise that FRING is a global self-calibration\\nalgorithm, and performs an initial phase self-calibration also. We ran\\nFRING on the A quasar data set, with a point-source input model.\\n\\nAnticipating our phase-referencing scheme (Sect. 3.2) we applied the antenna\\nphase, delay and rate solutions from A to both the A and B data sets, and\\naveraged them in time to 60 s, and over the total observed bandwidth of 32 MHz.\\nAfter suitable editing of the data, we made hybrid maps of both quasars,\\nusing a number of iterations of a cycle including the mapping task MX and\\nfurther phase self-calibration with CALIB.\\n\\nFig.~\\\\ref{fig1}a and b show the hybrid maps for both sources at 3.6~cm \\nin 1995.9. \\nThe maps are made using uniform weighting of the visibilities, a map\\ncell size of 0.15 mas and a circular CLEAN restoring beam of 0.5 mas\\n(these same mapping parameters are used throughout this work).\\nThe ``dirty'' beam has a central peak of 0.57 x 0.47 mas in PA -29\\\\degr\\n(PA = position angle, defined starting at North, increasing through East).\\nThe root-mean-square (rms) levels in the A and B maps, in regions away \\nfrom the source structures (estimated using AIPS task IMSTAT) are 1.0 and \\n0.12 mJy/beam respectively, an indication that dynamic range considerations \\ndominate over thermal noise in determining the map noise levels. \\n\\n%%% FIGURE 1\\n\\n\\\\begin{figure*}\\n\\\\centerline{\\n{\\\\psfig{figure=fig1a.ps,width=6.cm}}\\n\\\\put (-150,150) {\\\\bf {a)}}\\n{\\\\psfig{figure=fig1b.ps,width=6.cm}}\\n\\\\put (-150,150) {\\\\bf {b)}}\\n}\\n\\\\caption{VLBI hybrid maps of 1038+528 at 3.6~cm. Uniform weighting, \\nCLEAN beam 0.5 x 0.5 mas, pixel size 0.15 mas, tick interval 1 mas.\\n{\\\\bf a} Quasar A. Contours at 3,6,12,24... mJy/beam.\\n{\\\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy/beam.\\n\\\\label{fig1}} \\n\\\\end{figure*}\\n\\n\\\\subsection{Phase referencing in AIPS}\\n\\nIn order to make an astrometric estimate of the separation between\\nquasars A and B at this 4th epoch, we first used a \\\"conventional\\\" \\nphase-reference\\ntechnique to make maps of the quasars which preserve the relative phase\\ninformation.\\nIn practice this consists of using the antenna-based residual terms \\nderived from the analysis of the data of one ``reference'' source (A), \\nto calibrate the data from simultaneous observations of the other \\\"target\\\" \\nsource (B).\\nThe reference quasar source structure must first \\nbe estimated from a hybrid map, and then fed back into\\nthe phase self-calibration process to produce estimates of the antenna-based \\nresiduals, free from contamination by source structure. \\n\\nPhase referencing techniques work under the assumption that the\\nangular separation between the reference and target sources is smaller\\nthan the isoplanatic patch size (i.e. the effects of unmodelled perturbations,\\nintroduced by the propagation medium,\\non the observed phases of both sources are not very different) and that \\nany instrumental terms are common. Geometric errors in the correlator model\\nmust also be negligible.\\n\\nAssuming that the antenna residuals have been ``cleanly'' estimated using the\\nreference source data, the calibrated phases of the target \\nsource should be free from the errors mentioned above, but still retain the\\ndesired signature of the source structure and relative position\\ncontributions. The Fourier Transformation of the calibrated visibility\\nfunction of the target source produces a ``phase referenced'' map. The\\noffset of the brightness distribution from the centre of this map reflects\\nany error in the assumed relative separation in the correlator model.\\nIf the reference source has a true ``point'' structure and is at the\\ncentre of its hybrid map, this offset will be equal to the error;\\nmore generally, one should also measure the offset of a\\nreference point in the reference source map, and estimate the\\nerror in the source separation used in the correlator model from the difference\\nbetween the target and reference source offsets.\\n\\nIn general, the success of the phase-referencing technique is critically\\ndependent on the angular separation of the target and reference sources.\\nSimultaneous observation of the sources, as was possible here, significantly \\nsimplifies the procedure, eliminates the need for temporal interpolation,\\nand reduces the propagation of errors introduced in the\\nanalysis. While random errors increase the noise level in the phase\\nreferenced map, systematic errors may bias the estimated angular\\nseparation.\\n\\nFor our implementation of phase-referencing using AIPS, we chose\\nto re-FRING the (calibrated) A data set, using our hybrid map of quasar \\nA as an input model, and applied the adjustments to the antenna phase, \\ndelay and rate solutions to both the A and B data sets before re-averaging. \\nWe then made maps of both A and B using MX, performing no further phase \\nself-calibration. These are our ``phase-reference astrometry'' (PRA) \\nmaps (shown in Fig.~\\\\ref{fig2}a and b) on which we performed\\nastrometric measurements (see Sect. 4.2). Although the rms noise levels \\nin the PRA maps are slightly higher than in the corresponding hybrid maps \\n(2.0~mJy~beam$^{-1}$ for A and 0.24~mJy~beam$^{-1}$ for B),\\nour procedure ensures that the A and B\\nvisibility functions from which they are derived have been calibrated \\nidentically. \\n\\n%%% FIGURE 2\\n\\n\\\\begin{figure*}\\n\\\\centerline{\\n{\\\\psfig{figure=fig2a.ps,width=6.cm}}\\n\\\\put (-150,150) {\\\\bf {a)}}\\n\\\\put (-84.5,88.5) {\\\\bf {+}}\\n{\\\\psfig{figure=fig2b.ps,width=6.cm}}\\n\\\\put (-150,150) {\\\\bf {b)}}\\n\\\\put (-85,88) {\\\\bf {+}}\\n}\\n\\\\caption{VLBI phase-reference astrometry maps. Map parameters as in Fig. 1.\\nAstrometry reference points are indicated with a cross.\\n{\\\\bf a} Quasar A. Contours at 3.5,7,14,28... mJy~beam$^{-1}$.\\n{\\\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy~beam$^{-1}$.\\n\\\\label{fig2}} \\n\\\\end{figure*}\\n\\n\\n\\\\subsection{New mapping method for astrometry of close source pairs} \\n\\nWhile the conventional phase-referencing approach worked well for our\\nNovember 1995 observations of 1038+52A and B, the method relies on\\nmaking a good estimate of the antenna residuals from just one of the \\nsources - the reference. We have devised an alternative method which\\nextends the standard VLBI self-calibration procedure to work on both\\nsources together, for cases where they have been observed simultaneously,\\nand when either could be used as the reference (see Appendix A).\\n\\nThe basis of the new method is to recognise that, since the visibility \\nfunctions for both sources are corrupted by the same (antenna-based) \\nphase and phase derivative errors, the sum of the two visibilities also \\nsuffers the same errors. We form the point-by-point sum of the two data \\nsets, creating a new one which represents the visibility function of a \\n``compound source'' consisting of a superposition of the two structures, \\ncorrupted by the common antenna phase errors.\\nIf the source separation is close enough, the (summed) data as\\na function of the (averaged) uv-coordinates can be\\nFourier Transformed to form a map of the\\ncompound source structure, and (iterative) self-calibration in FRING or CALIB\\nyields the antenna-based residuals. The advantage of this approach is that\\nthe antenna-based residuals are determined using both source structures\\nsimultaneously, and may thus reduce the chance that reference source structural\\nphase terms contaminate the residuals. We term this process ``Hybrid Double\\nMapping'' (HDM); a detailed description is given in Porcas \\\\& Rioja \\n(\\\\cite{porcas96}).\\n\\nIt is convenient to shift the source position in one of the data\\nsets (by introducing artificial phase corrections)\\nprior to the combination into a compound-source data set, to avoid \\nsuperposition of the images in the map. The phase self-calibration \\nsteps which are then applied to the combined data set are \\nidentical to the case of a single source. In HDM the information\\non the angular separation between the sources is preserved in the \\nprocess of self-calibration of the combined visibilities, and can be measured\\ndirectly from the compound-image map;\\nthe relative positions between the individual source images in the \\ncompound map, taken together with any artificial position shift introduced,\\ngive the error in the assumed angular separation in the correlator model. \\nIn this approach one must be careful to use the same number of visibility\\nmeasurements in each time interval from the two data sets, in order to avoid\\nthe predominance of data from a particular source. \\n\\nFig.~\\\\ref{fig3} shows the HDM map of quasars A and B in 1995.9 at \\n$\\\\lambda$ 3.6~cm; \\nthe B source is artificially offset by -4 mas in declination.\\nThe rms noise in the map is 0.82~mJy~beam$^{-1}$ - higher than that in \\nthe hybrid map of B but lower than in that of A.\\n\\n\\n%%%FIGURE 3\\n\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n{\\\\psfig{figure=fig3.ps,width=6.cm}}\\n}\\n\\\\caption{HDM map of 1038+52 (A+B). Map parameters as in Fig. 1. \\nQuasar B has been offset by -4.0 mas in\\ndeclination. Contours at 3,6,12,24... mJy~beam$^{-1}$. \\n\\\\label{fig3}} \\n\\\\end{figure}\\n\\n\\n\\n\\\\section{Analysis of the maps} \\n\\n\\\\subsection{Source structures} \\n\\nThe 1995.9 hybrid maps of quasars A and B at $\\\\lambda$ 3.6~cm \\n(Fig.~\\\\ref{fig1}) show the core-jet structures typical of quasars at \\nmas scales. They may be compared with maps from previous epochs given \\nin Rioja et al. (\\\\cite{rioja97}). \\nThe structure of A in the new map shows no major changes with respect \\nto previous epochs. There is a prominent peak at the SW end of the\\nstructure (the ``core'') and a jet extending in PA 15--25\\\\degr\\n~containing at least two ``knot'' components (k1 and k2).\\n\\nThe new map of B at 3.6~cm is qualitatively similar to\\nthose from previous epochs. It shows 2 point-like components separated\\nby just under 2 mas in PA 127\\\\degr.\\nSpectral arguments support the identification of\\nthe NW component as a ``core'' (Marcaide \\\\& Shapiro \\\\cite{marca84}); \\nthe SE component, corresponding to a knot in the jet, has been used as \\na reference component in previous astrometric studies.\\nThe separation between these 2 components in 1995.9 has increased, \\ncontinuing the expansion along the axis of the source, as discovered \\nfrom previous epochs of observations at this wavelength (Rioja et al. \\n\\\\cite{rioja97}).\\nThere is no trace of the third, extreme SE component, seen in maps\\nof this source at 13~cm. This feature is evidently of lower surface\\nbrightness at 3.6~cm and is resolved out at the resolution of these \\nobservations.\\n\\nWe used AIPS task IMSTAT to estimate total flux densities for quasars A and\\nB (within windows surrounding the sources in the hybrid maps). The values \\nare given in Table~\\\\ref{tab1}.\\nTable~\\\\ref{tab1} also lists the fluxes and relative positions of the \\nmost prominent features in the maps of A and B, obtained using task JMFIT to\\nfind parameters of elliptical Gaussian functions which best\\nfit the various source sub-components. The formal errors from the fits,\\nhowever, do not give realisitic values for the parameter uncertainties.\\nThe distribution of flux between the core and k1 in quasar A, and their\\nrelative separation, are quite uncertain, for example. \\n\\n%%%TABLE 1\\n\\\\begin{table*}\\n\\\\caption {Parameters derived from the Hybrid Maps of 1038+528 A and B.} \\n\\n\\\\vspace*{0.25cm}\\n\\n\\\\begin{center}\\n\\\\begin{tabular} {|c|c|c|c|c|c|c|c|c|c|} \\\\hline\\n & S-tot & & S-pk & S-int & maj.& min. & PA & sep. & PA \\\\\\\\\\n & (mJy) & &(mJy/b) & (mJy) & (mas) & (mas) & (deg) & (mas) & (deg) \\\\\\\\\\n\\\\hline\\n1038+528 A & 603.0 & core & 301.6 & 355.3 & 0.28 & 0.12 & 3 & - & - \\\\\\\\\\n & & k1 & 171.8 & 235.5 & 0.42 & 0.16 & 13 & 0.639 & 15.1 \\\\\\\\\\n & & k2 & 9.3 & 14.0 & - & - & - & 1.796 & 24.8 \\\\\\\\\\n&&&&&&&&& \\\\\\\\\\n1038+528 B & 86.5 & core & 33.5 & 40.9 & 0.32 & 0.11 & 132 & - & - \\\\\\\\\\n & & ref & 24.6 & 34.4 & 0.39 & 0.24 & 123 & 1.869 & 127.1 \\\\\\\\ \\n\\\\hline \\\\hline\\n\\\\end{tabular}\\n\\\\end {center}\\n\\\\label{tab1}\\n\\\\end{table*}\\n\\n\\n\\\\subsection{Estimating positions of reference features} \\n\\nThe astrometric measurement of a separation between two non-point sources\\nmust always refer to the measured positions of reference points within \\nmaps (or other representations) of the source structures. \\nThe selection of suitable reference points is crucial in monitoring\\nprograms, where the results from the analysis of a multi-epoch \\nseries of observations are compared. \\nIdeally, a reference point should correspond to the peak of\\na strong, unresolved component, which is well separated from\\nother radio emission within the source structure.\\n\\nFor the 1995.9 epoch observations of 1038+528 A,B we selected the same \\nreference features as those used for the analyses of previous observing \\nepochs. These are the ''core'' component for quasar A, and the prominent \\nSE component for quasar B.\\nThese features are labelled with a cross in Fig.~\\\\ref{fig2}a and b.\\nThe core of A is indeed strong and compact, but has the disadvantage\\nthat it merges with knot k1.\\nAlthough the SE component of B is no longer the strongest feature at 3.6~cm,\\nit has always been strong at both 3.6 and 13~cm wavelengths,\\nis reasonably compact and is easily distinguishable\\nin maps made at longer wavelengths, thus facilitating spectral studies.\\nOur astrometric analysis refers to the measured positions of the peaks\\nof these components in A and B. We used the AIPS task MAXFIT to measure \\nthe position of these peaks in the PRA and HDM maps.\\nMAXFIT defines the location of a peak in a given map region by fitting \\na quadratic function to the peak pixel value and those of the adjacent pixels.\\nA comparison of this method of defining the peak position with that used\\nfor earlier epochs is described in the next section. \\n\\n\\\\subsection{Position error analysis} \\n\\nAn analysis of errors presented in Rioja et al. (\\\\cite{rioja97}) shows \\nthat the dominant uncertainty in the astrometric measurements of the \\nseparation between this close pair of quasars comes from the limited \\nreproducibility of the reference point positions in the VLBI maps, \\nfrom epoch to epoch. The magnitude of this effect\\nis hard to quantify, however, since it depends on the nature of the\\nsource brightness distribution surrounding the reference point, and\\nthe method used to define the position of the peak, in addition\\nto the resolution of the array and the signal-to-noise\\nratio of the peak in the map.\\n\\nA rough estimate of the error due solely to finite signal-to-noise in\\nthe maps is given by dividing the beam size by the ratio of the\\ncomponent peak to the rms noise level in the maps (see e.g. \\nThompson et al. \\\\cite{thompson86}). \\nThis yields values of 3.3, 3.5 and 1.4~$\\\\mu$as for the A and B PRA \\nmaps and the HDM map. These may be taken to represent lower limits to \\nthe reference point position errors; realistic errors will be larger,\\nand will depend on the nature of the reference features \\nand the manner in which the position is estimated.\\n\\nIt is important to choose a definition of the reference point position \\nsuch that it can be reproduced reliably from epoch to epoch, and is as \\nindependent as possible from the parameters used in making the map \\n(e.g. cell size and beam width).\\nThe AIPS task JMFIT can be used to fit an elliptical Gaussian to a component\\nin a CLEAN map, for example. However, the position of the peak of the \\nGaussian depends on how asymmetric the component brightness distribution \\nis, and the area of the map to which the fit is restricted. MAXFIT fits \\njust to the local maximum around the peak map value, and is thus less \\nsensitive to the rest of the distribution.\\n\\nWe have attempted to quantify some limits to reproducibility arising from \\nthe use of MAXFIT for defining the peak position in CLEAN maps.\\nWe investigated the effect of changing the true position of a point-like\\nsource with respect to the pixel sampling (here 3.3 pixels per beam) \\nby offsetting the source position in 10 increments of 1/10 of a pixel \\nin the visibility domain, mapping and CLEANing the new data sets, and \\nestimating the new positions in the CLEAN maps using MAXFIT. The\\nmaximum discrepancy found between the values of the artificial offset\\nand the shift derived by MAXFIT was 1/20 of a pixel.\\nThis corresponds to 8~$\\\\mu$as in our 3.6~cm maps.\\n\\nFor the analysis of previous observing epochs, the reference points\\nwere defined to be the centroid of the most prominent delta functions \\nfrom which the CLEAN source map was derived (Rioja et al. \\\\cite{rioja97}).\\nWe examined possible systematic differences resulting from these\\ndifferent definitions of reference points.\\nOne might expect the largest discrepancies to arise when the underlying\\nsource structure near the reference point is asymmetric, as in quasar A.\\nWe investigated such differences by determining ``centroid'' positions for\\nboth A and B reference components, using various criteria for excluding\\nclean components from the calculation; this included the ``25 percent\\nof the value at the peak'' threshold used for earlier epochs.\\nFor A the difference between this centroid position and the MAXFIT\\nvalue was 0.12 pixel (18~$\\\\mu$as). For B the difference was less\\nthan 0.1 pixel.\\nThese are probably the largest potential sources of error arising from using\\ndifferent methodologies at different epochs.\\n\\nOur use of two different mapping procedures - phase-reference mapping\\nand HDM - also gives some insight into the size of position errors resulting\\nfrom standard CLEAN + phase self-cal mapping algorithms.\\nThe differences between the separation estimates from the PRA maps and the\\nHDM map are 27 and 28~$\\\\mu$as in RA and Dec respectively.\\nThis would suggest that differences in the positions of peaks in \\nmaps reconstructed in different ways may vary at the 14~$\\\\mu$as level.\\n\\nAfter considering the various possible effects which can limit the\\naccuracy of postion estimates, we adopt a ``conservative'' value for \\nthe error in estimating the peak position in our $\\\\lambda$ 3.6~cm maps,\\nembracing all the effects detailed above, of $18~\\\\mu$as\\n(this corresponds to a thirtieth of the CLEAN beam).\\nThe associated estimated error for a separation measurement between\\nthe two sources is $25~\\\\mu$as.\\n\\n\\n\\\\subsection{Astrometry results} \\n\\nTable~\\\\ref{tab2} lists the results of our astrometric measurements of \\nreference point positions in the maps.\\nThey are presented as changes in measured separation between the \\nreference points in A and B in 1995.9, with respect to their separation \\nin 1981.3. \\nThe values given from the phase-reference technique correspond to the \\ndifference between the A and B reference feature position offsets in \\ntheir respective PRA map. The values derived from HDM have been corrected \\nfor the artificial offset introduced before adding the A and B source \\nvisibilities.\\n\\n%%%TABLE 2\\n\\n\\\\begin{table}\\n\\\\caption{Change in the separation between quasars A and B in 1995.9\\nwith respect to 1981.2, estimated using standard phase referencing \\n(PRA) and hybrid double mapping (HDM) techniques.}\\n\\\\begin{center}\\n\\n\\\\vspace*{0.25cm}\\n\\n\\\\begin{tabular} {|c| c| c|} \\\\hline \\n$\\\\Delta(\\\\Delta \\\\alpha)$ $\\\\cos \\\\delta_A$ & $\\\\Delta(\\\\Delta \\\\delta)$ & Method \\\\\\\\ \\n$[\\\\mu$as$]$ & $[\\\\mu$as$]$ & \\\\\\\\ \\\\hline \\\\hline\\n% (%) = Without Correlator position offset: RA -159muas; DEC 74 muas\\n% 11 & 175 & Phase Referencing \\\\\\\\\\n -148 & 249 & PRA \\\\\\\\\\n% -16 & 203 & HDM$^1$ \\\\\\\\\\n% -175 & 277 & HDM$^1$ \\\\\\\\ \\\\hline \\\\hline\\n -175 & 277 & HDM \\\\\\\\ \\\\hline \\\\hline\\n% -7.5 & 204 & HDM$^2$ \\\\\\\\\\n% -167 & 278 & HDM$^2$ \\\\\\\\\\n% -9 & 180 & HDM$^3$ \\\\\\\\ \\\\hline\\n% -168 & 254 & HDM$^3$ \\\\\\\\ \\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\label{tab2}\\n\\\\end{table}\\n\\n\\nAll these values have been corrected for a small error in the AIPS calculation\\nof the u,v coordinates in the frequency-averaged data set.\\n(Distances measured within the maps must be adjusted\\nby a small correction factor of\\n$1 - \\\\Delta \\\\nu \\\\ast (2~\\\\nu)^{-1} = 0.998$.) \\n \\\\\\\\\\n\\nTable~\\\\ref{tab3} lists the coordinates of the reference source (A) adopted in\\nthe analysis and the measured coordinate separation between quasars A\\nand B in 1995.9.\\n\\n%%%TABLE 3\\n\\n\\\\begin{table*}\\n\\\\caption{{\\\\it Fixed} source coordinates used for quasar A\\nin the astrometric analysis (these coordinates correspond to GSFC global\\nsolution GLB831 (Chopo Ma, priv. comm.)), and\\nseparation between quasars A and B measured in 1995.9.}\\n\\n\\\\begin{center}\\n\\n\\\\vspace*{0.25cm}\\n\\n\\\\begin{tabular} { |l| r| r|} \\\\hline\\n{\\\\bf Coordinates} & {\\\\bf RA} (J2000) \\\\hspace*{0.5cm} & {\\\\bf DEC} (J2000) \\\\hspace*{0.5cm}\\n \\\\\\\\ \\\\hline \\\\hline\\n{\\\\it Reference Source {\\\\bf (A)}} & 10$^h$ 41$^m$ 46\\\\fs781613 \\n\\\\hspace*{0.05cm} & 52$^0$ 33\\\\arcmin 28\\\\farcs23373 \\\\hspace*{0.05cm} \\\\\\\\ \\\\hline \\n{\\\\it Relative Sep. {\\\\bf (B-A)}} & $2\\\\fs1160588 $ \\n& $27\\\\farcs376325$ \\\\\\\\\\n{\\\\it Estimated error {\\\\bf (B-A)}} & $\\\\pm 0\\\\fs0000027$ & $ \\\\pm 0\\\\farcs000025$ \\\\\\\\ \\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\label{tab3}\\n\\\\end{table*}\\n\\n\\n\\\\section{Comparison of astrometry at all 4 epochs} \\n\\nIn this section we make a comparison of the astrometric\\nmeasurements from the series of 4 epochs of observations.\\nAny increase of the temporal baseline in the program of monitoring the \\nseparation between A and B should result in a more precise \\nidentification of any systematic trends,\\nwith an improved elimination of random contributions.\\nIn Sect. 5.1 we justify comparing\\nthe astrometric values measured at the various epochs, even\\nthough non-identical observing, post-processing and analysis\\nprocedures were involved.\\nIn Sect. 5.2 we present the astrometric results from the 4 epochs.\\nIn Sects. 5.3, 5.4, 5.5 and 5.6 we present various analyses of these\\nresults, and attempt to quantify, or put upper-limits to,\\nproper motions within and between the A and B quasars.\\n\\n\\n\\\\subsection{Comparison between the techniques used at different epochs}\\n\\nBefore attempting a comparison of the astrometric results from \\nthe 4 observing epochs, we need to\\nshow that any bias in the astrometric estimates introduced by the\\nuse of different procedures is small compared with other errors in\\nthe measurements for the individual epochs.\\nThe consistency between the results from previous epochs of observations \\nhas been exhaustively tested (Marcaide et al. \\\\cite{marca94}; \\nRioja et al. \\\\cite{rioja97}).\\nWe outline here the largest changes involved in the fourth epoch, 1995.9,\\nwith respect to previous ones:\\n\\n\\\\begin{enumerate}\\n\\n\\\\item The observing array and frequency set-up used in the fourth epoch\\nwas different from previous epochs of observations \\n(frequency range 8404.5 to 8436.5 MHz instead of 8402.99 to 8430.99 MHz\\nat first 3 epochs). This results in a different coverage of the {\\\\it UV} \\nplane, leading to changes in the reconstruction of the source images. \\nInvestigations of such effects by Marcaide et al. (\\\\cite{marca94}) show that\\nthe effect on the astrometric anaylsis is only a few $\\\\mu$as. \\nIt is important to note that the observations at all 4 epochs have\\ncomparable resolutions and sample the same range of structural scales\\nin the sources.\\n\\n\\\\item The processing of the fourth epoch was done using the VLBA correlator,\\nwhich uses a theoretical model derived from CALC 8.2; we used AIPS to\\nanalyse the data with visibility phases residual to that model.\\nFor previous epochs the correlation was done at the MPIfR (Bonn) MK3\\ncorrelator, and an analysis of the data using total phases was made\\nwith VLBI3 (Robertson \\\\cite{robertson75}).\\nThe differences between CALC 8.2 and the one implemented in VLBI3 \\npropagate into changes of only 1-2~$\\\\mu$as in the astrometric analysis\\nof the 1038+528 A-B separation (Rioja \\\\cite{rioja93}, Rioja et al. \\n\\\\cite{rioja97}). \\nThis is because any such differences are ``diluted'' by the source \\nseparation expressed in radians - \\n$10^{-4}$ in the case of this very close source pair.\\n\\n\\\\item The values used in the analysis of previous epochs for\\nEarth Orientation Parameters (EOP), stations and reference source coordinates\\nwere consistently derived from a single global solution provided by Goddard \\nSpace Flight Center (GSFC). \\nFor the correlation of the fourth epoch, the values used for \\nEOP were derived from IERS solutions, and the station coordinates from \\nUSNO catalogs.\\nWe have made a comparison of the values derived for all the parameters at\\nthe 4 epochs from a single global solution from IERS (namely IERS eopc04),\\nwith the actual values\\nused in the individual epoch analysis. The difference between the corresponding\\nEOP values is always less than 4 mas. Such discrepancies propagate into \\nerrors in the relative position estimates at each epoch of only a few \\n$\\\\mu$as.\\n\\n\\\\item Our astrometric analysis in AIPS using a phase-referencing approach and\\nHDM differs from the phase difference method used in VLBI3 analysis.\\nComparisons show that these procedures are equivalent \\n(Porcas \\\\& Rioja \\\\cite{porcas96}; Thompson et al. \\\\cite{thompson86}).\\nBoth involve the definition of reference points in source maps;\\nuncertainties in the reference point positions \\n(as described in Sect. 4.3) arise in the same way.\\n\\n\\\\item Finally, a minor VLBA correlator error (Romney priv. comm.) caused\\nincorrect time labels to be attached to the visibility records, resulting in\\nincorrect ({\\\\it u,v}) values. \\nThe effect on the relative visibility phases for our source pair is small\\n($\\\\sim 0.004$\\\\degr) and can be neglected.\\n\\n\\\\end{enumerate}\\n\\n The magnitudes of all of the effects reported in this section are\\nmuch smaller than our estimate in Sect. 4.3 of the uncertainity in reproducing\\nthe reference point in the source, from epoch to epoch, and we are thus\\njustified in comparing the astrometric results from all 4 epochs.\\n\\n\\n\\\\subsection{Astrometric separations at the 4 epochs} \\n\\nThe astrometric measurements of the separations between the reference \\npoints in A and B at $\\\\lambda$ 3.6~cm from 4 epochs are presented in \\nFig.~\\\\ref{fig4}.\\nIt includes our new 1995.9 measurement and those from three earlier epochs, \\nin 1981.3, 1983.4 and 1990.5, reported in Marcaide \\\\& Shapiro \\n(\\\\cite{marca84}), Marcaide et al. (1994) and Rioja et al. (\\\\cite{rioja97}), \\nrespectively. The origin of the plot represents the separation at epoch 1.\\n\\n%%% FIGURE 4\\n\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n{\\\\psfig{figure=fig4.ps,width=6.cm}}\\n}\\n\\\\caption{Measured separations between the A and B reference points at epochs\\n2 (1983.4), 3 (1990.5) and 4 (1995.9), with respect to epoch 1 (1981.2).\\nPlotted error bars correspond to $25~\\\\mu$as.\\n\\\\label{fig4}} \\n\\\\end{figure}\\n\\n\\nChanges with time in Fig.~\\\\ref{fig4} represent the vector difference between\\nany motions of the reference points in quasars A and B.\\nThe near-orthogonal nature of the source axes in 1038+52 A,B (along\\nwhich one might expect any motion to occur) simplifies the\\ninterpretation of any trends seen. The new 1995.9 value follows the\\nsame steady trend towards the NW shown by the three previous epochs.\\nRioja et al. (\\\\cite{rioja97}) interpreted this as an outward expansion of the\\nreference component in quasar B at a rate of $18~\\\\pm~5~\\\\mu$as~yr$^{-1}$, \\nand quoted an upper bound on any proper motion of quasar A of \\n$10~\\\\mu$as~yr$^{-1}$.\\n\\n\\\\subsection{Vector decomposition} \\n\\nIn this section we attempt to separate the individual contributions from \\nthe 2 quasars in the astrometric separation measurements presented in \\nFig.~\\\\ref{fig4}. We make no assumption about the stability of either \\ncomponent, but\\nassume that any displacements of the A or B reference points from their \\npositions at epoch 1 are along the corresponding source axis directions.\\nThis is a plausible assumption if the reference point coincides \\nwith a non-stationary component moving along a ballistic trajectory, \\nor with the location of the peak of brightness within an active core \\nor near the base of jet, where changes during episodes of activity are \\nlikely to occur along the jet direction.\\nThis approach is closely related to that used previously \\nby Rioja et al. (\\\\cite{rioja97}). For fixed assumed source axes for A and B,\\nit results in a unique decomposition of the changes in the A-B separation\\ninto separate A and B displacements, from 1981 to 1995.\\n\\nIt is clear that the dominant contribution to the separation changes\\nseen in Fig.~\\\\ref{fig4} comes from quasar B, \\nin which the source axis is well defined by the 127\\\\degr PA of\\nthe separation between core and reference components.\\nFor quasar A the source axis bends, from the inner ``core'' region \\n(PA = 15\\\\degr) to the outer jet components, and it is not so clear which \\ndirection should be chosen.\\n\\nIn our analysis we tried a range of values for fixing the A source axis \\n(0 to 45\\\\degr ~in steps of 5\\\\degr).\\nFor each, we calculated A and B reference-point displacements at epochs 2, \\n3 and 4 with respect to epoch 1.\\nThen we performed a least-squares fit to the B displacements with time to\\nestimate a linear expansion rate for the B reference feature along \\nPA 127\\\\degr. In Fig.~\\\\ref{fig5} we plot the deconvolved B reference point \\ndisplacements from the analysis with the A source axis fixed at \\nPA 25\\\\degr (the value adopted by Rioja et al. \\\\cite{rioja97}).\\nThe fitted expansion rate is $16.9~\\\\pm~0.6~\\\\mu$as~yr$^{-1}$;\\nthe error and associated rms values take account of the small number \\nof points and 2 degrees of freedom. This rate agrees well with the value\\nof $18~\\\\pm~5~\\\\mu$as~yr$^{-1}$ deduced by Rioja et al. (\\\\cite{rioja97}).\\nThe rms residual from the fit (7~$\\\\mu$as) is low, and vindicates\\nour use of measurements derived from differing techniques for\\ninvestigating the relative proper motion between A and B. \\n\\n%%% FIGURE 5\\n\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n{\\\\psfig{figure=fig5.ps,width=6.cm}}\\n}\\n\\\\caption{Changes in position of reference component in B along PA 127\\\\degr,\\ndeduced from deconvolution of the A-B separation measurements. Assumed source\\naxis for A is 25\\\\degr.\\nPlotted error bars correspond to $25~\\\\mu$as.\\n\\\\label{fig5}} \\n\\\\end{figure}\\n\\n\\n\\\\subsection{Structural evolution within 1038+528 B} \\n\\nOur deconvolution analysis of the changes in separation measured between \\nall 4 epochs supports the finding, previously proposed, that the B reference\\ncomponent moves along the source axis, away from the B core.\\nIn this section we make an independent determination of the separation \\nrate between the core and reference component in B from measurements \\nwithin the maps at the 4 epochs.\\n\\nFig.~\\\\ref{fig6} shows the separation between the core and reference \\ncomponent in B at the four epochs plotted against time. For epochs 1--3 \\nwe used the values given in Rioja et al. (\\\\cite{rioja97}). For 1995.9 we \\nused AIPS task UVFIT to estimate a separation from the B visibility data \\ndirectly, in order to follow the methodology used for the other epochs as \\nclosely as possible; the value obtained was 1.895 mas.\\nThe slope from a least-squares fit corresponds to an expansion rate \\nof $13.0~\\\\pm~0.7~\\\\mu$as~yr$^{-1}$.\\nIn the standard picture of extragalactic radio sources, the ``core'' is\\nstationary, so this corresponds to an outward expansion of the\\nreference component along PA 127\\\\degr.\\n\\n%%% FIGURE 6\\n\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n{\\\\psfig{figure=fig6.ps,width=6.cm}}\\n}\\n\\\\caption{Changes in the position of the reference component in B \\nalong PA 127\\\\degr, from measurements of its separation from the core\\nin hybrid maps of B.\\nPlotted error bars correspond to $25~\\\\mu$as.\\n\\\\label{fig6}} \\n\\\\end{figure}\\n\\n\\nThe rms of the fit (8~$\\\\mu$as) is again surprisingly low, implying\\ntypical errors in the separation measurements at each epoch \\n(both within the B structure and between the reference points)\\nof only about 10--12$~\\\\mu$as along the direction of the B source axis.\\nThis is considerably less than the estimate of position separation \\nerrors given in Sect. 4.3. \\n\\n\\\\subsection{Relative proper motion }\\n\\nThe analysis presented in the previous sections demonstrate\\nclearly that the chosen reference component within quasar B is\\nunsuitable for use as a marker for tracing any relative proper motion\\nbetween quasars A and B. The value of its expansion velocity derived \\nin Sect. 5.4 appears to differ significantly from that deduced by \\nvector-decomposition in Sect. 5.3. Although the difference between \\nthese estimates, if real, could be interpreted as motion of the core of B \\nat a rate of $\\\\sim 4~\\\\mu$as~yr$^{-1}$, this is not a conclusive result\\nsince differences of this order arise from choosing different values of \\nPA for the motion in A in the vector decomposition method.\\n\\nA more suitable tracer of relative proper motion between the quasars is \\nthe variation of the separation between the cores of A and B.\\nWe have used the separations between the core and reference component\\nmeasured in the B map at each epoch, and the astrometric\\nseparations between A and B, to calculate the separations between the\\nA and B cores at each epoch; these are plotted in Fig.~\\\\ref{fig7}.\\nThe area occupied by the points defines an upper limit of \\n$\\\\sim 10~\\\\mu$as~yr$^{-1}$ for any relative proper motion between \\nthe A and B cores, and hence between the quasars themselves, during\\nthe period of nearly 15 years for which the separation has been\\nmonitored with VLBI.\\nThe limit seems to be set by the relatively large deviation of the\\n1995.9 epoch point in the direction of the A source axis, presumably\\narising from the difficulty in defining the reference point at the\\nA ``core'' from epoch to epoch. \\n\\n%%% FIGURE 7\\n\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n{\\\\psfig{figure=fig7.ps,width=6.cm}}\\n}\\n\\\\caption{Separation between the cores of A and B (with respect to epoch 1),\\nderived by correcting the A-B reference point separation measurements with the\\ncore-reference separations measured in the B hybrid maps.\\nPlotted error bars correspond to $25~\\\\mu$as.\\n\\\\label{fig7}} \\n\\\\end{figure}\\n\\n\\n\\\\subsection{Possible ``core'' motions ? } \\n\\nFinally, we investigate any possible residual motions of the ``cores'' \\nin A and B. The most likely causes of any such apparent motions are \\nchanges in the relative brightness or positions of features in the \\nsource structures at a resolution below that of the maps.\\nOne might expect that these, too, would produce effects predominantly\\nalong the source axis directions.\\nWe therefore used the vector deconvolution method on the plot of\\ncore-core separation with time to study displacements of the cores\\nalong their source axis directions.\\nFig.~\\\\ref{fig8}a and b show plots of the separated contributions from \\nB and A, for an assumed A source axis PA 25\\\\degr.\\nThe displacements for the B core seem to increase systematically.\\nThe fitted rate is $3.8~\\\\pm~0.3~\\\\mu$as~yr$^{-1}$, indicating a possible \\nslow outward motion. The displacements for the A core do not seem to \\nvary systematically - the fitted slope is $5.5~\\\\pm~3.6~\\\\mu$as~yr$^{-1}$.\\nHere the scatter is considerably larger, reflecting both the difficulties of\\ndefining the reference point along the A core-jet axis, and\\nalso, perhaps, real ``jitter'' of the position of the peak due to variations \\nin the ``core'' substructure. These plots indicate the level of stability \\nof the individual core positions; the fits represent realistic upper limits \\nto any possible systematic core motion in the A and B quasars along their \\nsource axis directions.\\n\\n%%% FIGURE 8\\n\\n\\\\begin{figure*}\\n\\\\centerline{\\n{\\\\psfig{figure=fig8a.ps,width=6.cm}}\\n\\\\put (-140,140) {\\\\bf {a)}}\\n{\\\\psfig{figure=fig8b.ps,width=6.cm}}\\n\\\\put (-130,140) {\\\\bf {b)}}\\n}\\n\\\\caption{Residual motions of the cores using the deconvolution approach.\\n {\\\\bf a} Displacements of B core along PA 127\\\\degr; \\n{\\\\bf b} Displacements of A core along PA 25\\\\degr. \\nPlotted error bars correspond to $25~\\\\mu$as.\\n\\\\label{fig8}} \\n\\\\end{figure*}\\n\\n\\n\\\\section{Conclusions} \\n\\nThe series of astrometric VLBI measurements of the separation between \\nthe quasar pair 1038+528 A and B, spanning\\nnearly 15 years, provides excellent material for investigating \\nthe relative proper motion of two extragalactic radio sources and\\nthe positional stability of their cores.\\nThe changes measured in the separations between quasars A and B \\nat 3.6~cm are dominated by the motion of the reference feature in quasar B. \\nThese astrometric results, and measurements in the hybrid maps of B are\\ncompatible with an expansion rate for the B reference component of \\n13--17$~\\\\mu$as~yr$^{-1}$.\\nAt a redshift of 2.296 this translates to an apparent\\ntransverse velocity of 0.55--0.70~c~h$^{-1}$.\\nWe note that this is an order of magnitude smaller than the more\\ntypical superluminal velocities seen in many quasars; it is a \\nrare example of a subluminal velocity measured for a knot in a quasar jet.\\n\\nAfter correcting for the motion of the reference component in B,\\nwe can put a conservative upper bound to any relative proper\\nmotion between the quasars of $10~\\\\mu$as~yr$^{-1}$.\\nDespite the increase in temporal baseline, this upper bound is no\\nbetter than that given by Rioja et al. (\\\\cite{rioja97}).\\nIts value is related to the difficulty in reproducing a stable reference\\nposition along the A source axis near its ``core''.\\n\\nTheories in which the redshifts of quasars do not indicate cosmological\\ndistances, and in which quasars are ``local'' and have high Doppler\\nredshifts (e.g. Narlikar \\\\& Subramanian \\\\cite{narlikar83}) are incompatible \\nwith our measured upper-limit to relative proper motion. Quasars at \\n100 Mpc distance moving at relativistic speeds would have proper motions \\nof the order of $600~\\\\mu$as~yr$^{-1}$, nearly 2 orders of magnitude \\ngreater than our limit. Assuming cosmological distances,\\nour limit corresponds to apparent transverse velocities of \\n0.43~c~h$^{-1}$ and 0.22~c~h$^{-1}$ at the redshifts of the B and A\\nquasars, respectively.\\n\\nWe have investigated the way in which the definition of \\nreference points in a map may be only loosely ``fixed'' to the radio\\nsource structure, especially when the latter is strongly asymmetric.\\nWe have also developed an alternative analysis route - Hybrid Double\\nMapping - for imaging both sources of a close pair simultaneously, and\\nat the same time preserving their relative astrometric information\\nin a single map.\\n\\nThe surprisingly low rms from the fits of linear expansion in quasar B,\\nand the discrepancy between the two estimates \\n($16.9~\\\\pm~0.6~\\\\mu$as~yr$^{-1}$ from the astrometric measurements and\\n $ 13.0~\\\\pm~0.7~\\\\mu$as~yr$^{-1}$ from the hybrid maps)\\nare suggestive of (but do not prove) a residual motion of the core \\nin quasar B; our decomposition along the source axis direction gives a fit\\nof $3.8~\\\\pm~0.3~\\\\mu$as~yr$^{-1}$, corresponding to an apparent transverse \\nvelocity of 0.17~c~h$^{-1}$. If real, this might indicate a steady change \\nin physical conditions at the base of the jet, or perhaps the emergence \\nof a new knot component moving outwards with a velocity similar to the \\nreference component, but as yet unresolved by our 0.5 mas beam.\\nIn this regard, it is interesting to note the slight extension of\\nthe core of quasar B in PA 132\\\\degr given by the Gaussian model fit.\\n\\nThe low rms derived from fits to the expansion of the B reference component \\nindicate that we have been overly conservative in our estimate of \\n$18~\\\\mu$as for the error in reference point positions. Errors at least \\n2 times smaller are implied, corresponding to a sixtieth of the beamwidth. \\nIt is interesting to note that such small errors are also implied in the \\nwork of Owsianik \\\\& Conway (\\\\cite{owsianik98}), where the low scatter in \\nthe plot of expansion of the CSO source \\\\object{0710+439} allows an \\nexpansion rate of $14.1~\\\\pm~1.6~\\\\mu$as~yr$^{-1}$ to be determined.\\n\\nThere are no obvious systematic motions within quasar A, but the ``noise'' \\nin the estimates of position along its axis are much larger.\\nThis noise, along with any associated underlying changes in source\\nsubstructure, provides a fundamental limit to estimates of\\nany systematic core motion in A. Improvements on the estimates of (or upper\\nbounds to) the relative motion between the quasars, or of the\\nindividual motion of the A core, will require a considerable\\nincrease in the temporal baseline of VLBI monitoring.\\n\\n\\\\newpage\\n\\n\\\\appendix \\n\\n\\\\section {Hybrid Double Mappping (HDM)}\\n\\n\\n{\\\\bf A.1 Principle of Hybrid Double Mapping} \\\\\\\\\\n\\n\\\\noindent\\nThe visibility function, $V$, measured at time $t$, on a baseline between\\nantennas $i$ and $j$, is represented by a complex function with amplitude $A$, \\nphase $P$:\\n\\n\\\\[ V(i,j) = A * e^{i[\\\\phi]}(t) \\\\]\\n\\n\\\\noindent\\nFor this analysis it is convenient to indentify 3 contributions to\\nthe visibility phase:\\n\\n\\\\[ \\\\phi(i,j) = \\\\phi_{s}(u,v) + \\\\phi_{p}(u,v) + \\\\phi_{m}(t) \\\\]\\n\\n\\\\noindent\\nwhere \\n\\n\\\\begin{description} \\n\\\\item [$\\\\phi_s$] is due to source structure, evaluated w.r.t. a reference\\nposition for the source. \\\\\\\\\\n\\n \\\\item [$\\\\phi_p$] is due to any offset of the \\ntrue source position from the reference position. \\\\\\\\\\n\\nBoth $\\\\phi_s$ and \\n$\\\\phi_p$ are functions of the resolution coordinates, $u$ and $v$, at time \\n$t$. \\\\\\\\\\n\\n\\\\item [$\\\\phi_m$] is due to inaccuracies in the correlator model calculation of\\n the interferometer geometry and the signal propagation delays\\n in the ionosphere, troposphere and receiving system; it is an \\n unknown function of time. \\\\\\\\\\n This term can be represented by the difference of two\\n ''antenna-based'' phases, $\\\\theta_i$ and $\\\\theta_j$, since it can \\n be related to the \\n difference in signal arrival times at the two sites.\\n (This analysis is a simplification which ignores possible\\n ''non-closing'' instrumental baseline phase terms arising from\\n e.g. un-matched bandpasses and polarisation impurities.) \\n\\\\end{description}\\n\\n\\\\[ \\\\phi(i,j) = \\\\phi_s(u,v) + \\\\phi_p(u,v) + \\\\theta_i(t) - \\\\theta_j(t) \\\\]\\n\\n\\\\noindent\\nIn conventional hybrid mapping, an iterative procedure is used\\nto separate out the antenna-based phase terms from the ''source'' terms;\\nthe latter must produce a consistent and physically plausible source\\nstructure after Fourier transformation of the corrected visibility:\\n\\n\\\\[ \\\\underbrace {A * e^{i[\\\\phi_s+\\\\phi_p]}(u,v)}_{corrected \\\\: visibility} = \\nV(i,j) * \\\\underbrace {e^{-i[\\\\theta_i(t)-\\\\theta_j(t)]}}_{antenna \\\\: phase \\\\: terms} \\\\] \\n\\n\\\\noindent\\nHowever, the position offset term, $\\\\phi_p$, can also be expressed as a difference \\nin wavefront arrival times at the 2 antennas and so it is also\\n''absorbed'' in antenna phase terms $\\\\theta_i'$, $\\\\theta_j'$; \\nthe ''absolute'' position information is lost:\\n\\n\\\\[ \\\\underbrace {A * e^{i[\\\\phi_s]}(u,v)}_{corrected \\\\: visibility} = \\nV(i,j) * \\\\underbrace {e^{-i[\\\\theta_i'(t)-\\\\theta_j'(t)]}}_{antenna \\\\: phase\\n\\\\: terms} \\\\]\\n\\n\\\\noindent\\nIn Hybrid Double Mapping (HDM), the visibility functions of two \\nsources observed simultaneously are added. For a close source pair, we \\nmake the same assumption as for conventional phase-referencing - that the \\nmodel error phase terms are essentially the same for both sources. We make \\na further assumption that the $u,v$ coordinates are also essentially the same\\nfor both sources, for each baseline and time. The visibility sum, $V^1 + V^2$,\\ncan then be re-written: \\\\\\\\\\n\\n\\n\\\\[ \\\\underbrace {(A^1 * e^{i[\\\\phi^1_{s}]} + A^2 * e^{i[\\\\phi^2_{s}+(\\\\phi^2_{p}\\n-\\\\phi^1_{p})]})(u,v)}_{corrected \\\\: visibility \\\\: sum} = \\\\]\\n\\\\[ \\\\;\\\\;\\\\; \\\\vspace*{2cm} = V^{sum}(i,j) * \\\\underbrace {e^{-i[\\\\theta_i'(t)-\\\\theta_j'(t)]}}_{antenna \\\\:\\n phase \\\\: terms} \\\\] \\n\\n\\n%\\\\begin{eqnarray*}\\n%\\\\lefteqn{ \\\\[ \\\\underbrace {(A_1e^{i[\\\\phi_{1s}]}+A_2e^{i[\\\\phi_{2s}+(\\\\phi_{2p}-\\\\phi_{1p})]})(u,v)}_{corrected \\\\: visibility \\\\: sum} = } \\\\\\\\\\n%& & V^{sum}(i,j) * \\\\underbrace {e^{-i[\\\\theta_i'(t)-\\\\theta_j'(t)]}}_{antenna \\\\:\\n%phase \\\\: terms} \\\\] \\n%\\\\end{eqnarray*}\\n\\n\\\\noindent\\nThis may be recognised as the visibility function of a ''composite''\\nsource consisting of the sum of the brightness distributions of sources\\n1 and 2, with antenna-based phase error terms $\\\\theta_i'$, $\\\\theta_j'$, \\nas before.\\nThe HDM method consists of performing the normal hybrid mapping\\nprocedure with the visibility sum, resulting in the separation of the\\nantenna-based errors, and a physically plausible map of the sum of\\nthe two source brightness distrubutions. An important point is that,\\nwhereas the {\\\\it origin} of the map of the composite source is arbitrary (as\\nit depends on the position of the starting model), the {\\\\it separation} of\\nthe two source brightness distributions within the composite map\\n(determined by $\\\\phi^2_{p}-\\\\phi^1_{p}$) is fixed during the phase \\nseparation procedure,\\nand is equal to the {\\\\it difference} of the errors in the two source\\npositions used for correlation. We call this the ''residual separation''. \\\\\\\\\\n\\n\\\\noindent\\n{\\\\bf A.2 Practical aspects} \\\\\\\\\\n\\n\\\\noindent\\nThere are some practical aspects to be considered. If the source\\ncoordinates used in the correlator model are very precise, then the\\nresidual separation may be less than the interferometer beamwidth, and\\nthe two source distributions will lie on top of each other. \\nIn this case it is desireable to\\nintroduce an artificial position offset into one of the\\nsource visibility functions before forming the visibility sum, to\\nensure that the two source reference features are well separated in the\\nHDM map. One should also arrange that the peak of one source\\ndoes not lie on the sidelobe response of the other in the \\\"dirty\\\" map,\\nas this may degrade the CLEAN deconvolution process in the mapping step.\\\\\\\\\\n\\n\\\\noindent\\n Another important consideration is that the time-averaged samples\\nof the summed visibility function contain equal contributions from both\\nsource visibility functions. When both sources are observed\\nsimultaneously this will normally be the case, except when different\\namounts of data are lost in the two separate correlator passes needed\\nfor the two source positions. It is important to edit the data sets\\ncarefully to fulfil this condition. \\\\\\\\\\n\\n\\\\noindent\\n The range of validity of the assumption that the $(u,v)$\\ncoordinates for the two sources are the same depends on the ''dilution\\nfactor'', i.e. the reciprocal of the source separation, measured in\\nradians. The $(u,v)$ value assigned to the summed visibility will be\\nincorrect for either source by roughly 1 part in the dilution factor\\n(roughly 1 in 6000 for 1038+528A,B). \\nThis is equivalent to having source visibility phase errors of this\\norder, and thus limits the size of an HDM map to be less than the\\nbeamwidth times the dilution factor; the residual separation should be\\nmuch smaller than this value.\\\\\\\\\\n\\n\\\\noindent\\nIn the actual analysis used in this work, we first made a rough \\ncorrection to the phase of the summed visibility of 1038+528 A + B, using\\nthe antenna phase and phase derivative errors from fringe-fitting\\n1038+528A using a point source model. However, there is no reason why\\none should not fringe-fit the summed visibility function directly. \\\\\\\\\\n\\n\\\\noindent\\n{\\\\bf A.3 Applications} \\\\\\\\\\n\\n\\\\noindent\\nThe HDM method can in principle be applied\\nwhenever two (or more !) radio sources are observed simultaneously,\\nbut are correlated at separate field centres; however, \\nthey must be close enough so that the conditions of same $(u,v)$\\ncoverage and same correlator model errors apply.\\nThe method uses the structures of BOTH sources simultaneously to\\nseparate out the antenna phase errors, as opposed to a single source in \\nsimple hybrid mapping.\\nIf both sources are strong (as with 1038+528 A and B),\\nconstraining the (single) antenna phase solutions with two structures\\nshould lead to a more rigorous and robust separation between the\\nsource and antenna phase terms.\\nOne field of application is in high resolution VLBI imaging of\\ngravitational lens systems with wide image separations (e.g. \\nimages A and B of QSO 0957+561 with 6.1 arcsec separation)\\nwhere preserving the necessary wide field-of-view from a single \\ncorrelation may result in inconveniently large data sets.\\nWhen one source is very weak, however,\\nthere is probably little to be gained over normal hybrid mapping. \\\\\\\\\\n\\n\\\\noindent\\nFor relative astrometry studies (as described in this paper),\\nthe HDM method has some advantages over conventional phase-reference \\nmapping and explicit phase-differencing methods.\\nIn phase-differencing astrometry, separate hybrid maps must be made of\\nboth sources to correct for source structural phase terms and \\nthe antenna phase errors are NOT constrained to be the same. Imperfect \\nseparation between source and antenna phase terms can increase the noise \\non the differenced phase, as well as lead to possible systematic errors.\\nIn phase-reference astrometry, only one of the sources is used to solve\\nfor the antenna phase terms; imperfect separation can lead to extra\\nphase noise in the phase-referenced visibility of the ''target'' source.\\nIn HDM we use both source\\nstructures simultaneously to separate the (common) antenna error\\nphases from that of a single \\\"structure\\\" in which the \\nreference points of the two sources are spaced by the residual separation.\\\\\\\\\\n\\n\\\\noindent\\nWhen the separation between the two sources of a pair exceeds\\nthe telescope primary beamwidths, astrometric and phase-reference \\nobservations \\nmust involve switching between the sources, and the visibility phase of at \\nleast one of the sources must normally be interpolated in the observing gap. \\nThe condition that must be fulfilled for HDM to work in\\nthis case is that an equal number of observations of both sources must\\nbe added to form an average visibility function for the length of the\\n''solution interval'' in the phase self-calibration step of HDM.\\nThis length is generally limited by the coherence time of the\\natmosphere, and would imply a very fast switching cycle in most cases.\\nAnother application for HDM could be in the the analysis of\\n''cluster-cluster'' VLBI (see e.g. Rioja et al. \\\\cite{rioja97b}), \\nin which two or more sources are observed simultaneously on VLBI baselines \\nby using more than one telescope at each site.\\n\\n\\n\\\\begin{acknowledgements}\\n\\nWe thank Dave Graham for help with the observations in Effelsberg,\\nTony Beasley for asistance at the VLBA, and Mark Reid for useful comments\\non the text. M.J.R. wishes to acknowledge support for this research by the\\nEuropean Union under contract CHGECT920011.\\nThe National Radio Astronomy Observatory is a facility\\nof the National Science Foundation operated under cooperative\\nagreement by Associated Universities, Inc.\\n\\n\\\\end{acknowledgements}\\n\\n\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \\ned. Reid M., Moran J., Kluwer, p. \\\\ 523 \\n\\n\\\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \\nVery Long Baseline Interferometry and the VLBA, eds. 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Wiley-Interscience, \\nNew York, p. 400\\n\\n\\\\end{thebibliography}{}\\n\\n\\n\\n\\n\\\\end{document}\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002097.extracted_bib","string":"\\begin{thebibliography}{}\n\n\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \ned. Reid M., Moran J., Kluwer, p. \\ 523 \n\n\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \nVery Long Baseline Interferometry and the VLBA, eds. Zensus J.A., \nDiamond P.J., Napier P.J., ASP Conference Series, Vol. 82, p. \\ 327.\n\n\\bibitem[1986]{blandford86} Blandford R.D., K\\\"onigl A., 1986, \nApJ 308, 83\n\n\\bibitem[1983]{marca83} Marcaide J.M., Shapiro I.I., 1983, AJ 88, 1133 \n\\bibitem[1984]{marca84} Marcaide J.M., Shapiro I.I., 1984, ApJ 276, 56\n\\bibitem[1994]{marca94} Marcaide J.M., El\\'{o}segui P., Shapiro I.I., 1994, \n AJ 108, 368 \n\\bibitem[1983]{narlikar83} Narlikar J.V., Subramanian K., 1983, \nApJ 273, 44\n\\bibitem[1978]{owen78} Owen F.N., Porcas R.W., Neff S.G., 1978, \nAJ 83, 1009\n\\bibitem[1980]{owen80} Owen F.N., Wills B.J., Wills D., 1980, ApJ 235, L57\n\\bibitem[1998]{owsianik98} Owsianik I., Conway J.E., 1998, A\\&A 337, 69\n\\bibitem[1986]{porcas87} Porcas R.W., 1987, Superluminal Radio Sources, ed.\n Zensus A., Pearson A., Cambridge University Press, p. \\ 12\n\\bibitem[1996]{porcas96} Porcas R.W., Rioja M.J., 1996, Proc. of the 11th \nWorking Meeting on European VLBI for Geodesy and Astrometry, Ed. Elgered\nG., p. \\ 209\n\\bibitem[1993]{rioja93} Rioja M.J., 1993, PhD. Thesis, Universidad de Granada\n\\bibitem[1997]{rioja97} Rioja M.J., Marcaide J.M., El\\'osegui P., \nShapiro I.I., 1997, A\\&A 325, 383 \n\\bibitem[1997]{rioja97b} Rioja M.J., Stevens E.,\nGurvits L., et al., 1997, {\\it Vistas in Astronomy} 41 (2), 213 \n%\\bibitem[2000]{rioja00} Rioja, M.J., Porcas, R.W., 2000, {\\it in preparation}\n\\bibitem[1975]{robertson75} Robertson D.S., 1975, PhD Thesis, MIT\n%\\bibitem[1996]{romney96} Romney, J.D., 1996, (VLBA email memorandum \n%of 14 March) \n\\bibitem[1986]{thompson86} Thompson A.R., Moran J.M., Swenson G.W., 1986, \nInterferometry and Synthesis in Radio Astronomy. Wiley-Interscience, \nNew York, p. 400\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002097.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \\ned. Reid M., Moran J., Kluwer, p. \\\\ 523 \\n\\n\\\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \\nVery Long Baseline Interferometry and the VLBA, eds. Zensus J.A., \\nDiamond P.J., Napier P.J., ASP Conference Series, Vol. 82, p. \\\\ 327.\\n\\n\\\\bibitem[1986]{blandford86} Blandford R.D., K\\\\\\\"onigl A., 1986, \\nApJ 308, 83\\n\\n\\\\bibitem[1983]{marca83} Marcaide J.M., Shapiro I.I., 1983, AJ 88, 1133 \\n\\\\bibitem[1984]{marca84} Marcaide J.M., Shapiro I.I., 1984, ApJ 276, 56\\n\\\\bibitem[1994]{marca94} Marcaide J.M., El\\\\'{o}segui P., Shapiro I.I., 1994, \\n AJ 108, 368 \\n\\\\bibitem[1983]{narlikar83} Narlikar J.V., Subramanian K., 1983, \\nApJ 273, 44\\n\\\\bibitem[1978]{owen78} Owen F.N., Porcas R.W., Neff S.G., 1978, \\nAJ 83, 1009\\n\\\\bibitem[1980]{owen80} Owen F.N., Wills B.J., Wills D., 1980, ApJ 235, L57\\n\\\\bibitem[1998]{owsianik98} Owsianik I., Conway J.E., 1998, A\\\\&A 337, 69\\n\\\\bibitem[1986]{porcas87} Porcas R.W., 1987, Superluminal Radio Sources, ed.\\n Zensus A., Pearson A., Cambridge University Press, p. \\\\ 12\\n\\\\bibitem[1996]{porcas96} Porcas R.W., Rioja M.J., 1996, Proc. of the 11th \\nWorking Meeting on European VLBI for Geodesy and Astrometry, Ed. Elgered\\nG., p. \\\\ 209\\n\\\\bibitem[1993]{rioja93} Rioja M.J., 1993, PhD. Thesis, Universidad de Granada\\n\\\\bibitem[1997]{rioja97} Rioja M.J., Marcaide J.M., El\\\\'osegui P., \\nShapiro I.I., 1997, A\\\\&A 325, 383 \\n\\\\bibitem[1997]{rioja97b} Rioja M.J., Stevens E.,\\nGurvits L., et al., 1997, {\\\\it Vistas in Astronomy} 41 (2), 213 \\n%\\\\bibitem[2000]{rioja00} Rioja, M.J., Porcas, R.W., 2000, {\\\\it in preparation}\\n\\\\bibitem[1975]{robertson75} Robertson D.S., 1975, PhD Thesis, MIT\\n%\\\\bibitem[1996]{romney96} Romney, J.D., 1996, (VLBA email memorandum \\n%of 14 March) \\n\\\\bibitem[1986]{thompson86} Thompson A.R., Moran J.M., Swenson G.W., 1986, \\nInterferometry and Synthesis in Radio Astronomy. Wiley-Interscience, \\nNew York, p. 400\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":97,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002098"},"title":{"kind":"string","value":"Chemistry in the Envelopes around Massive Young Stars"},"authors":{"kind":"list like","value":[{"author":"Ewine F.\\ van Dishoeck and Floris F.S.\\ van der Tak"}],"string":"[\n {\n \"author\": \"Ewine F.\\\\ van Dishoeck and Floris F.S.\\\\ van der Tak\"\n }\n]"},"abstract":{"kind":"string","value":"Recent observational studies of intermediate- and high-mass star-forming regions at submillimeter and infrared wavelengths are reviewed, and chemical diagnostics of the different physical components associated with young stellar objects are summarized. Procedures for determining the temperature, density and abundance profiles in the envelopes are outlined. A detailed study of a set of infrared-bright massive young stars reveals systematic increases in the gas/solid ratios, the abundances of evaporated molecules, and the fraction of heated ices with increasing temperature. Since these diverse phenomena involve a range of temperatures from $<100\\,$K to 1000~K, the enhanced temperatures must be communicated to both the inner and outer parts of the envelopes. This `global heating' plausibly results from the gradual dispersion of the envelopes with time. Similarities and differences with low-mass YSOs are discussed. The availability of accurate physical models will allow chemical models of ice evaporation followed by `hot core' chemistry to be tested in detail."},"latex":{"kind":"list like","value":[{"name":"dishoeck.tex","string":"% SAMPLE1.TEX -- WGAS sample paper with minimal markup.\n\n% Lines starting with \"%\" are comments; they will be ignored by LaTeX.\n\n\\documentstyle[11pt,newpasp,psfig,epsf,twoside]{article}\n\\def\\gtsim{{_>\\atop{^\\sim}}}\n\\def\\ltsim{{_<\\atop{^\\sim}}}\n\n\\begin{document}\n\n\\title{Chemistry in the Envelopes around Massive Young Stars}\n\\author{Ewine F.\\ van Dishoeck and Floris F.S.\\ van der Tak}\n\\affil{Leiden Observatory, P.O.\\ Box 9513, 2300 RA Leiden,\nThe Netherlands}\n\n\\begin{abstract}\nRecent observational studies of intermediate- and high-mass\n star-forming regions at submillimeter and infrared wavelengths are\n reviewed, and chemical diagnostics of the different physical\n components associated with young stellar objects are summarized.\n Procedures for determining the temperature, density and abundance\n profiles in the envelopes are outlined. A detailed study of a set of\n infrared-bright massive young stars reveals systematic increases in\n the gas/solid ratios, the abundances of evaporated molecules, and the\n fraction of heated ices with increasing temperature. Since these\n diverse phenomena involve a range of temperatures from $<100\\,$K to\n 1000~K, the enhanced temperatures must be communicated to both the\n inner and outer parts of the envelopes. This `global heating'\n plausibly results from the gradual dispersion of the envelopes with\n time. Similarities and differences with low-mass YSOs are discussed.\n The availability of accurate physical models will allow chemical\n models of ice evaporation followed by `hot core' chemistry to be\n tested in detail.\n\n\n\\end{abstract}\n\n\n%% Keywords: High-mass star formation, ices, hot cores, envelopes\n%% \n%% Objects: Orion-KL, Orion-IRc2, SGrB2, W~3 IRS5, W~3(H$_2$O), AFGL 2591,\n%% AFGL 2136, NGC 7538 IRS9, W~33A, G34.3, S 140, W~3 IRS4\n%% Molecules: CO, C$^{17}$O, CS, H$_2$CO, HC$_5$N, H$_2$O, CO$_2$,\n%% CH$_3$OH, CH$_3$OCH$_3$, CH$_3$CN, C$_2$H$_2$, S~I, PAHs\n%% OH, SiO, SO$_2$, CN, HCN, C~II, CO$^+$\n\n\\section{Introduction}\n\nMassive star-forming regions have traditionally been prime targets for\nastrochemistry owing to their bright molecular lines (e.g., Johansson\net al.\\ 1984, Cummins et al.\\ 1986, Irvine et al.\\ 1987, Ohishi 1997).\nMassive young stellar objects (YSOs) have luminosities of $\\sim 10^4 -\n10^6$ L$_\\odot$ and involve young O- and B-type stars. Because their\nformation proceeds more rapidly than that of low-mass stars and\ninvolves ionizing radiation, substantial chemical differences may be\nexpected. The formation of high mass stars is much less well\nunderstood than that of low-mass stars. For\nexample, observational phenomena such as ultracompact H II regions,\nhot cores, masers and outflows have not yet been linked into a single\nevolutionary picture. Chemistry may well be an important diagnostic\ntool in establishing such a sequence.\n \nMost of the early work on massive star-forming regions has centered on\ntwo sources, Orion--KL and SgrB2. Numerous line surveys at millimeter\n(e.g., Blake et al.\\ 1987, Turner 1991) and submillimeter (Jewell et\nal.\\ 1989, Sutton et al.\\ 1991, 1995, Schilke et al.\\ 1997)\nwavelengths have led to an extensive inventory of molecules through\nidentification of thousands of lines. In addition, the surveys have\nshown strong chemical variations between different sources.\n\nIn recent years, new observational tools have allowed a more detailed and\nsystematic study of the envelopes of massive YSOs. Submillimeter observations\nroutinely sample smaller beams (typically 15$''$ vs.\\ 30$''$--1$'$ ) and\nhigher critical densities ($\\geq 10^6$ vs.\\ $10^4$ cm$^{-3}$) than the earlier\nwork. Moreover, interferometers at 3 and 1 millimeter provide maps with\nresolutions of $0.5''$--5$''$. Finally, ground- and space-based infrared\nobservations allow both the gas and the ices to be sampled (e.g., Evans et\nal.\\ 1991, van Dishoeck et al.\\ 1999). These observational developments have\nled to a revival of the study of massive star formation within the last few\nyears. Recent overviews of the physical aspects of high-mass star formation\nare found in Churchwell (1999) and Garay \\& Lizano (1999).\n\n\nIn this brief review, we will first summarize available observational\ndiagnostics to study the different phases and physical components\nassociated with massive star formation. Subsequently, an overview of\nrecent results on intermediate mass YSOs is given, which are often\nbetter characterized than their high-mass counterparts because of\ntheir closer distance. Subsequently, we will discuss a specific sample\nof embedded massive YSOs which have been studied through a combination\nof infrared and submillimeter data. After illustrating\nthe modeling techniques, we address the question how the\nobserved chemical variations are related to evolutionary effects,\ndifferent conditions in the envelope (e.g., $T$, mass) or different\nluminosities of the YSOs. More extensive overviews of the chemical\nevolution of star-forming regions are given by van Dishoeck \\& Blake\n(1998), Hartquist et al.\\ (1998), van Dishoeck \\& Hogerheijde (1999)\nand Langer et al.\\ (2000). Schilke et al.\\ (this volume) present high\nspatial resolution interferometer studies, whereas Macdonald \\&\nThompson (this volume) focus on submillimeter data of hot\ncore/ultracompact H~II regions. Ices are discussed by Ehrenfreund \\&\nSchutte (this volume).\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig1.ps}{11.0cm}{0}{50}{50}{-150}{-30}\n\\caption{Overview of the SEST 230 GHz line survey of SgrB2 at the N, M and\nNW positions, illustrating the chemical differentiation in high-mass\nstar-forming regions (from:\nNummelin et al.\\ 1998).}\n\\label{fig-1}\n\\vspace{-0.3cm}\n\\end{figure}\n\n\n\\section{Submillimeter and Infrared Diagnostics}\n\nThe majority of molecules are detected at (sub-)millimeter\nwavelengths, and line surveys highlight the large variations in\nchemical composition between different YSOs, both within the same\nparent molecular cloud and between different clouds. The recent 1--3\nmm surveys of Sgr~B2 (Nummelin et al.\\ 1998, Ohishi \\& Kaifu 1999)\ndramatically illustrate the strong variations between various\npositions (see Figure~1). The North position is typical of\n`hot core'-type spectra, which are rich in lines of saturated\norganic molecules. This position has also been named \nthe `large molecule heimat'\n(e.g., Kuan \\& Snyder 1994, Liu \\& Snyder 1999). The Middle position\nhas strong SO and SO$_2$ lines, whereas the Northwest position has a\nless-crowded spectrum with lines of ions and long carbon chains. A\nsimilar differentiation has been observed for three positions in the\nW~3 giant molecular cloud by Helmich \\& van Dishoeck (1997), who\nsuggested an evolutionary sequence based on the chemistry.\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig2.ps}{10cm}{0}{55}{55}{-150}{-115}\n\\caption{ISO-SWS spectra of two massive YSOs at different evolutionary stages.\nCep A ($L \\approx 2.4\\times 10^4$ L$_{\\odot}$) is in the embedded\nstage, whereas S~106 ($L \\approx 4.2\\times 10^4$ L$_{\\odot}$) is\nin a more evolved stage (from:\nvan den Ancker et al.\\ 2000a).}\n\\label{fig-2}\n\\end{figure}\n\n\nThe availability of complete infrared spectra from 2.4--200 $\\mu$m\nwith the {\\it Infrared Space Observatory }(ISO) allows complementary\nvariations in infrared features to be studied. Figure~2 shows an\nexample of ISO--SWS and LWS spectra of two objects: Cep A ($L \\approx\n2.4\\times 10^4$ L$_{\\odot}$) and S~106 ($L \\approx 4.2\\times 10^4$\nL$_{\\odot}$). The Cep A spectrum is characteristic of the deeply\nembedded phase, in which the silicates and ices in the cold envelope\nare seen in absorption. The S~106 spectrum is typical of a more\nevolved massive YSO, with strong atomic and ionic lines in emission\nand prominent PAH features. A similar sequence has been shown by\nEhrenfreund et al.\\ (1998) for a set of southern massive young stars\nwith luminosities up to $4\\times 10^5$ L$_{\\odot}$.\n\nThe most successful models for explaining these different chemical\ncharacteristics involve accretion of species in an icy mantle during the\n(pre-)collapse phase, followed by grain-surface chemistry and evaporation of\nices once the YSO has started to heat its surroundings (e.g., Millar 1997). \nThe evaporated molecules subsequently drive a rapid high-temperature gas-phase\nchemistry for a period of $\\sim 10^4 - 10^5$ yr, resulting in complex,\nsaturated organic molecules (e.g., Charnley et al.\\ 1992, 1995; Charnley 1997;\nCaselli et al.\\ 1993, Viti \\& Williams 1999). The abundance ratios of species\nsuch as CH$_3$OCH$_3$/CH$_3$OH and SO$_2$/H$_2$S show strong variations with\ntime, and may be used as `chemical clocks' for a period of 5000--30,000 yr\nsince evaporation. Once most of the envelope has cleared, the ultraviolet\nradiation can escape and forms a photon-dominated region (PDR) at the\nsurrounding cloud material, in which molecules are dissociated into radicals\n(e.g., HCN $\\to$ CN) and PAH molecules excited to produce infrared emission.\nThe (ultra-)compact H~II region gives rise to strong ionic lines due to\nphotoionization.\n\n\\begin{table}[t]\n\\caption{Chemical characteristics of massive star-forming regions}\n\\begin{center}\\scriptsize\n\\begin{tabular}{lllll}\n\\hline\n\\noalign{\\smallskip}\nComponent & Chemical & Submillimeter & Infrared & Examples \\\\\n & characteristics & diagnostics & diagnostics \\\\\n\\tableline\n\\noalign{\\smallskip}\nDense cloud & Low-T chemistry &Ions, long-chains &Simple ices & SgrB2 (NW) \\\\\n & & (HC$_5$N, ...) & (H$_2$O, CO$_2$) \\\\\n\\noalign{\\smallskip}\nCold envelope & Low-T chemistry, & Simple species & Ices & N7538 IRS9, \\\\\n & Heavy depletions & (CS, H$_2$CO) & (H$_2$O, CO$_2$, CH$_3$OH)\n & W~33A \\\\\n\\noalign{\\smallskip}\nInner warm & Evaporation & High T$_{\\rm ex}$ & High gas/solid, High\n & GL 2591, \\\\\nenvelope & & (CH$_3$OH) & T$_{\\rm ex}$, Heated ices \n & GL 2136 \\\\\n & & & (C$_2$H$_2$, H$_2$O, CO$_2$) \\\\\n\\noalign{\\smallskip}\nHot core & High-T chemistry & Complex organics & Hydrides & Orion hot core, \\\\\n & & (CH$_3$OCH$_3$, CH$_3$CN, & (OH, H$_2$O) \n& SgrB2(N),G34.3 \\\\\n&&vib.\\ excited mol.) && W~3(H$_2$O) \\\\\n\\noalign{\\smallskip}\nOutflow: & Shock chemistry, & Si- and S-species & \n Atomic lines, Hydrides & W~3 IRS5, \\\\\nDirect impact &Sputtering & (SiO, SO$_2$) &([S I], H$_2$O) & SgrB2(M) \\\\\n\\noalign{\\smallskip}\nPDR, Compact & Photodissociation,& Ions, radicals & Ionic lines, PAHs\n& S~140, \\\\\nH~II regions & Photoionization & (CN/HCN, CO$^+$) &([NeII], [CII])\n& W~3 IRS4 \\\\\n \n%\\noalign{\\vspace{-0.8cm}}\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nTable~1 summarizes the chemical characteristics of the\nvarious physical components, together with the observational\ndiagnostics at submillimeter and infrared wavelengths. \nWithin the single-dish submillimeter and ISO beams,\nmany of these components are blended together and interferometer\nobservations will be essential to disentangle them. Nevertheless, the\nsingle-dish data are useful because they encompass the entire envelope\nand highlight the dominant component in the beam. Combined\nwith the above chemical scenario, one may then attempt to establish an\nevolutionary sequence of the sources.\n\nThe physical distinction between the `hot core' and the warm\ninner envelope listed in Table~1 is currently not clear: does the `hot\ncore' represent a separate physical component or is it simply the\ninner warm envelope at a different stage of chemical evolution? Even\nfrom an observational point of view, there appear to be different\ntypes of `hot cores': some of them are internally heated by the young\nstar (e.g., W~3(H$_2$O)), whereas others may just be dense clumps of\ngas heated externally (e.g., the Orion compact ridge). This point\nwill be further discussed in \\S\\S 4 and 5. Disks are not included in\nTable~1, because little is known about their chemical characteristics,\nor even their existence, around high-mass YSOs (see Norris, this\nvolume).\n\n\n\\section{Intermediate-Mass YSOs}\n\nIntermediate-mass pre-main sequence stars, in particular the so-called\nHerbig Ae/Be stars, have received increased observational attention in\nrecent years (see Waters \\& Waelkens 1998 for a review). These stars\nhave spectral type A or B and show infrared excesses due to \ncircumstellar dust. Typical luminosities are in the range $10^2 -\n10^4$ L$_{\\odot}$, and several objects have been located within 1 kpc\ndistance. Systematic mapping of CO and the submillimeter continuum of\na sample of objects has been performed by Fuente et al.\\ (1998) and\nHenning et al.\\ (1998). The data show the dispersion of the envelope\nwith time starting from the deeply embedded phase (e.g.,\nLkH$\\alpha$234) to the intermediate stage of a PDR (e.g., HD 200775\nilluminating the reflection nebula NGC 7023) to the more evolved stage\nwhere the molecular gas has disappeared completely (e.g., HD 52721).\nThe increasing importance of photodissociation in the chemistry is\nprobed by the increase in the CN/HCN abundance ratio. This ratio has\nbeen shown in other high-mass sources to be an excellent tracer of\nPDRs (e.g., Simon et al. 1997, Jansen et al.\\ 1995). Line surveys of\nthese objects in selected frequency ranges would be useful to\ninvestigate their chemical complexity, especially in the embedded\nphase.\n\nISO-SWS observations of a large sample of Herbig Ae/Be stars have been\nperformed by van den Ancker et al.\\ (2000b,c). In the embedded phase,\nshock indicators such as [S I] 25.2 $\\mu$m are strong, whereas in the\nlater phases PDR indicators such as PAHs are prominent. An excellent\nexample of this evolutionary sequence is provided by three Herbig Ae\nstars in the BD+40$^o$4124 region ($d\\approx 1$ kpc). The data\nsuggest that in the early phases, the heating of the envelope is\ndominated by shocks, whereas in later phases it is controlled by\nultraviolet photons.\n\n\n\\begin{figure}[t]\n\\vspace{-3.8cm}\n\\plottwo{dishoeck_fig3a.ps}{dishoeck_fig3b.ps}\n\\vspace{-0.3cm}\n\\caption{Left: ISO-LWS spectra of the intermediate mass YSO \nLkH$\\alpha$234, showing strong atomic fine-structure lines of\n[C II] 158 $\\mu$m and [O~I] 63 $\\mu$m, but weak molecular CO and\nOH lines. Right: CO excitation diagram, indicating the presence\nof a warm ($T\\approx 200-900$~K), dense ($n>10^5$ cm$^{-3}$) \nregion (from:\nGiannini et al.\\ 2000).}\n\\label{fig-3}\n\\vspace{-0.5cm}\n\\end{figure}\n\n\nISO-LWS data have been obtained for a similar sample of Herbig Ae/Be\nstars by Lorenzetti et al.\\ (1999) and Giannini et al.\\ (2000), and\nare summarized by Saraceno et al.\\ (1999). The [C II] 158 $\\mu$m and\n[O I] 63 and 145 $\\mu$m lines are prominent in many objects and are\ndue primarily to the PDR component in the large LWS beam ($\\sim\n80''$). High-$J$ CO and OH far-infrared lines have been detected in\nsome objects and indicate the presence of a compact, high temperature\nand density region of $\\sim$1000 AU in size, presumably tracing the\ninner warm envelope (see Figure~3).\nFar-infrared lines of H$_2$O are seen in low-mass YSO spectra, but are\nweak or absent in those of intermediate- and high-mass YSOs, with the\nexception of Orion-KL and SgrB2 (e.g., Harwit et al.\\ 1998, Cernicharo\net al.\\ 1997, Wright et al.\\ 2000). The absence of H$_2$O lines in\nhigher-mass objects may be partly due to the larger distance of these\nobjects, resulting in substantial dilution in the LWS beam. However,\nphotodissociation of H$_2$O to OH and O by the enhanced ultraviolet radiation\nmay also play a role.\n\nIn summary, both the submillimeter and infrared diagnostics reveal an\nevolutionary sequence from the youngest `Group I' objects to `Group\nIII' objects (cf.\\ classification by Fuente et al.\\ 1998), in which\nthe envelope is gradually dispersed. Such a sequence is analogous to\nthe transition from embedded Class 0/I objects to more evolved Class\nII/III objects in the case of low-mass stars (Adams et al.\\ 1987). The\nISO data provide insight into the relative importance of the heating\nand removal mechanisms of the envelope. At the early stages of\nintermediate-mass star formation, shocks due to outflows appear to\ndominate whereas at later stages radiation is more important.\n\n\\section{Embedded, Infrared-Bright Massive YSOs}\n\n\\subsection{Sample}\n\nThe availability of complete, high quality ISO spectra for a\nsignificant sample of massive young stars provides a unique\nopportunity to study these sources through a combination of infrared\nand submillimeter spectroscopy, and further develop these diagnostics.\nVan der Tak et al.\\ (2000a) have selected a set of $\\sim$10 deeply\nembedded massive YSOs which are bright at mid-infrared wavelengths (12\n$\\mu$m flux $>$ 100 Jy), have luminosities of $10^3 - 2\\times 10^5$\nL$_{\\odot}$ and distances $d\\leq$4 kpc. The sources are all in an\nearly evolutionary state (comparable to the `Class 0/I' or `Group I'\nstages of low- and intermediate-mass stars), as indicated by their\nweak radio continuum emission and absence of ionic lines and PAH\nfeatures. In addition to ISO spectra, JCMT submillimeter data and\nOVRO interferometer observations have been obtained. For most of the\nobjects high spectral resolution ground-based infrared data of CO,\n$^{13}$CO and H$_3^+$ are available (Mitchell et al.\\ 1990, Geballe \\&\nOka 1996, McCall et al.\\ 1999), and occasionally H$_2$ (Lacy et\nal.\\ 1994, Kulesa et al.\\ 1999). For comparison, 5 infrared-weak\nsources with similar luminosities are studied at submillimeter\nwavelengths only. This latter set includes hot cores and ultracompact\nH~II regions such as W~3(H$_2$O), IRAS 20126+4104 (Cesaroni et al.\\ \n1997, 1999), and NGC~6334 IRS1.\n\n\\subsection{Physical structure of the envelope}\n\nIn order to derive molecular abundances from the observations, a good\nphysical model of the envelope is a prerequisite. Van der Tak et al.\\ \n(1999, 2000a) outline the techniques used to constrain the temperature\nand density structure (Figure~4). The total mass within the\nbeam is derived from submillimeter photometry, whereas the size scale\nof the envelope is constrained from line and continuum maps. The dust\nopacity has been taken from Ossenkopf \\& Henning (1994) and yields\nvalues for the mass which are consistent with those derived from\nC$^{17}$O for warm sources where CO is not depleted\nonto grains.\n\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig4.ps}{7.7cm}{0}{45}{45}{-120}{-60}\n\\caption{Overview of method used for constraining the temperature and density\nstructure of envelopes. A power-law density structure with trial values\nfor the exponent\n$\\alpha_i$ and molecular abundances $X_j$ is adopted\n(based on: van der Tak et al.~2000a).}\n\\label{fig-4}\n\\end{figure}\n\n\nThe temperature structure of the dust is calculated taking the\nobserved luminosity of the source, given a power-law density structure\n(see below). At large distances from the star, the temperature follows\nthe optically thin relation $\\propto r^{-0.4}$, whereas at smaller\ndistances the dust becomes optically thick at infrared wavelengths and\nthe temperature increases more steeply (see Figure~5). It is assumed\nthat $T_{\\rm gas}=T_{\\rm dust}$, consistent with explicit calculations\nof the gas and dust temperatures by, e.g., Doty \\& Neufeld (1997)\nfor these high densities.\n\nThe continuum data are sensitive to temperature and column density,\nbut not to density. Observations of a molecule with a large dipole\nmoment are needed to subsequently constrain the density structure. One\nof the best choices is CS and its isotope C$^{34}$S, for which lines\nranging from $J$=2--1 to 10--9 have been observed. Assuming a\npower-law density profile $n(r)= n_o (r/r_o)^{-\\alpha}$, values of\n$\\alpha$ can be determined from minimizing $\\chi^2$ between the CS\nline data and excitation models. The radiative transfer in the lines\nis treated through a Monte-Carlo method. The best fit to the data on\nthe infrared-bright sources is obtained for $\\alpha = 1.0 - 1.5$,\nwhereas the hot core/compact H~II region sample requires higher\nvalues, $\\alpha \\approx 2$. This derivation assumes that the CS\nabundance is constant through the envelope; if it increases with\nhigher temperatures, such as may be the case for hot cores, the values\nof $\\alpha$ are lowered. Note that the derived values of\n$\\alpha=1.0-1.5$ are lower than those found for deeply embedded\nlow-mass objects, where $\\alpha\\approx 2$ (e.g., Motte et al.\\ 1998,\nHogerheijde et al.\\ 1999).\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig5.ps}{7.0cm}{-90}{45}{45}{-170}{260}\n\\vspace{-0.3cm}\n\\caption{Derived temperature and density structure for the envelope\naround the massive YSO\nGL 2591 (L=$2\\times 10^4$ L$_{\\odot}$, $d$=1 kpc). \nThe critical densities of the CS 2--1 and 10--9 lines are\nindicated, as are the typical beam sizes of the JCMT \nat 345 GHz and OVRO at 100 GHz (based on: van der Tak et \nal.\\ 1999).}\n\\label{fig-5}\n\\vspace{-0.5cm}\n\\end{figure}\n\n\nFigure 5 displays the derived temperature and density structure\nfor the source GL 2591, together with the sizes of the JCMT and\nOVRO beams. While the submillimeter data are weighted toward the\ncolder, outer envelope, the infrared absorption line observations sample\na pencil-beam line of sight toward the YSO and are more sensitive to\nthe inner warm ($\\sim 1000$~K) region. On these small scales, the\nenvelope structure deviates from a radial power law, which decreases\nthe optical depth at near-infrared wavelengths by a factor of \n$\\sim 3$ (van der Tak et al.\\\n1999).\n\n\nFor sources for which interferometer data are available, unresolved\ncompact continuum emission is detected on scales of a few thousand AU\nor less. This emission is clearly enhanced compared with that\nexpected from the inner ``tip'' of the power-law envelope, and its\nspectral index indicates optically thick warm dust, most likely in a\ndense circumstellar shell or disk. The presence of this shell or disk\nis also indicated by the prevalence of blue-shifted outflowing dense\ngas without a red-shifted counterpart on $< 10''$ scales.\n\n\n\\subsection{Chemical structure: infrared absorption lines}\n\nThe ISO-SWS spectra of the infrared-bright sources show absorption by\nvarious gas-phase molecules, in addition to strong features by ices.\nMolecules such as CO$_2$ (van Dishoeck et al.\\ 1996,\nBoonman et al.\\ 1999, 2000a), H$_2$O (van Dishoeck \\& Helmich 1996, Boonman\net al.\\ 2000b), CH$_4$ (Boogert et al.\\ 1998), HCN and C$_2$H$_2$\n(Lahuis \\& van Dishoeck 2000) have been detected (see also van\nDishoeck 1998, Dartois et al.\\ 1998).\n\nIn the infrared, absorption out of all $J$-levels is observed in a\nsingle spectrum. The excitation temperatures $T_{\\rm ex}$ of the\nvarious molecules, calculated assuming LTE, range from $\\ltsim 100$ to\n$\\sim 1000$~K between sources, giving direct information on \nthe physical component in which the molecules reside. While CO \nis well-mixed throughout the envelopes, H$_2$O, HCN and C$_2$H$_2$ are\nenhanced at high temperatures. In contrast, CO$_2$ seems to avoid the\nhottest gas. High spectral resolution ground-based data of HCN and\nC$_2$H$_2$ by Carr et al.\\ (1995) and Lacy et al.\\ (1989) for a few\nobjects suggest line widths of at most a few km s$^{-1}$, excluding an\norigin in outflowing gas.\n\nThe abundances of H$_2$O, HCN and C$_2$H$_2$ increase by factors of\n$\\gtsim 10$ with increasing $T_{\\rm ex}$ (see Figure~7). The warm\nH$_2$O must be limited to a $\\ltsim 1000$~AU region, since the pure\nrotational lines are generally not detected in the $80''$ ISO-LWS beam\n(Wright et al.\\ 1997). For CO$_2$, the abundance variation between\nsources is less than a factor of 10, and no clear trend with $T_{\\rm\n ex}$ is found. For the same sources, the H$_2$O and CO$_2$ ice\nabundances show a decrease by an order of magnitude, consistent with\nevaporation of the ices. However, the gas-phase H$_2$O and CO$_2$\nabundances are factors of $\\sim 10$ lower than expected if all\nevaporated molecules stayed in the gas phase, indicating that\nsignificant chemical processing occurs after evaporation. More\ndetailed modeling using the source structures derived from\nsubmillimeter data is in progress.\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig6.ps}{6.8cm}{-90}{50}{50}{-210}{260}\n\\caption{{\\it Left:}~Abundance of HCN,\n$N$(HCN)/$N_{\\rm tot}$(H$_2$), as a function of the\n$^{13}$CO excitation temperature measured by\nMitchell et al.\\ (1990). {\\it Middle:} Abundance of H$_2$O in the warm gas\n$N$(H$_2$O)/$N_{\\rm warm}$(H$_2$) as a function of $^{13}$CO excitation\ntemperature;\n{\\it Right:}~Abundance of H$_2$O ice as a function of\n$^{13}$CO excitation temperature. The same trend\nis found if the dust temperature, as derived from the 45/100 $\\mu$m\nflux, is used (based on: Lahuis \\& van Dishoeck 2000; van Dishoeck 1998).}\n\\label{fig-6}\n\\end{figure}\n\n\n\\subsection{Chemical structure: submillimeter emission}\n\nThe JCMT data of the infrared-bright objects show strong lines, but\nlack the typical crowded `hot core' spectra observed for objects such\nas W~3(H$_2$O) and NGC 6334 IRS1. Complex organics such as\nCH$_3$OCH$_3$ and CH$_3$OCHO are detected in some sources (e.g., GL\n2591, NGC 7538 IRS1), but are not as prominent as in the comparison\nsources. Yet warm gas is clearly present in these objects.\nIs the `hot core' still too small to be picked up by the\nsingle dish beams, or are the abundances of these molecules not (yet)\nenhanced?\n\nTo investigate this question, \nvan der Tak et al.\\ (2000b) consider the analysis of\ntwo species, H$_2$CO and CH$_3$OH. Both\nspecies have many lines throughout the submillimeter originating from\nlow- and high-lying energy levels. Given the physical structure\ndetermined in \\S 4.2, abundance {\\it profiles} can be constrained. Two\nextreme, but chemically plausible models are considered: (i) a model\nwith a constant abundance throughout the envelope. This model is\nmotivated by the fact that pure gas-phase reaction schemes do not show\nlarge variations in calculated abundances between 20 and 100~K; (ii) a\nmodel in which the abundance `jumps' to a higher value at the ice\nevaporation temperature, $T_d\\approx 90$~K. In this model, the\nabundances in the outer envelope are set at those observed in cold\nclouds, so that the only free parameter is the amount of abundance\nincrease.\n\nIt is found that the H$_2$CO data can be well fit with a constant\nabundance of a few $\\times 10^{-9}$ throughout the envelope. However,\nthe high $J,K$ data for CH$_3$OH require a jump in its abundance from\n$\\sim 10^{-9}$ to $\\sim 10^{-7}$ for the warmer sources. This is\nconsistent with the derived excitation temperatures: H$_2$CO has a\nrather narrow range of $T_{\\rm ex}$=50--90~K, whereas CH$_3$OH shows\n$T_{\\rm ex}$=30--200~K. Moreover, the interferometer maps of CH$_3$OH\nrule out constant abundance models. The jump observed for CH$_3$OH is\nchemically plausible since this molecule is known to be present in icy\ngrain mantles with abundances of 5--40\\% with respect to H$_2$O ice,\ni.e., $\\sim 10^{-7}-10^{-6}$ w.r.t.\\ H$_2$. Similar increases in the\nabundances of organic molecules (e.g., CH$_3$OH, C$_2$H$_3$CN, ....)\nare found with increasing $T_{\\rm dust}$ for a set of `hot--core'\nobjects by Ikeda \\& Ohishi (1999).\n\n\n\\subsection{Comparison with chemical models}\n\nBoth the infrared and submillimeter data show increases in the\nabundances of various molecules with increasing temperature. Four\ntypes of species can be distinguished: (i) `passive' molecules which\nare formed in the gas phase, freeze out onto grains during the cold\n(pre-)collapse phase and are released during warm-up without chemical\nmodification (e.g., CO, C$_2$H$_2$); (ii) molecules which are formed\non the grains during the cold phase by surface reactions and are\nsubsequently released into the warm gas (e.g., CH$_3$OH); (iii)\nmolecules which are formed in the warm gas by gas-phase reactions with\nevaporated molecules (e.g., CH$_3$OCH$_3$); (iv) molecules which are\nformed in the hot gas by high temperature reactions (e.g., HCN). These\ntypes of molecules\nare associated with characteristic temperatures of (a) $T_{\\rm\n dust}<20$~K, where CO is frozen out; the presence of CO ice is\nthought to be essential for the formation of CH$_3$OH; (b) $T_{\\rm\n dust} \\approx 90$~K, where all ices evaporate on a time scale of\n$<10^5$ yr; and (c) $T_{\\rm gas}>230$~K, where gas-phase reactions\ndrive the available atomic oxygen into water through the reactions O +\nH$_2$ $\\to$ OH $\\to$ H$_2$O (Ceccarelli et al.\\ 1996, Charnley 1997).\nAtomic oxygen is one of the main destroyers of radicals and carbon\nchains, so that its absence leads to enhanced abundances of species\nlike HCN and HC$_3$N in hot gas.\n\nWater is abundantly formed on the grains, but the fact that the\nH$_2$O abundance in the hot gas is not as large as that of the ices\nsuggests that H$_2$O is broken down to O and OH after evaporation by\nreactions with H$_3^+$. H$_2$O can subsequently be reformed in warm\ngas at temperatures above $\\sim$230~K, but Figure~7 indicates that not\nall available gas-phase oxygen is driven into H$_2$O, as the models\nsuggest. The low abundance of CO$_2$ in the warm gas is still a\npuzzle, since evaporation of abundant CO$_2$ ice is observed. The\nmolecule must be broken down rapidly in the warm gas, with no\nreformation through the CO + OH $\\to$ CO$_2$ reaction (see question by\nMinh).\n\n\\subsection{Evolution?}\n\nThe objects studied by van der Tak et al.\\ (2000a) are all in an early\nstage of evolution, when the young stars are still deeply embedded in\ntheir collapsing envelope. Nevertheless, even within this narrow\nevolutionary range, there is ample evidence for physical and chemical\ndifferentiation of the sources. This is clearly traced by the\nincrease in the gas/solid ratios, the increase in abundances of several\nmolecules, the decrease in the ice abundances, and the increase\nof the amount of crystalline ice with increasing temperature\n(Boogert et al.\\ 2000a).\n\nThe fact that the various indicators involve different\ncharacteristic temperatures ranging from $<$50 K (evaporation of\napolar ices) to 1000 K ($T_{\\rm ex}$ of gas-phase molecules)\nindicates that the heating is not a local effect, but that `global\nwarming' occurs throughout the envelope. Moreover, it cannot be a\ngeometrical line-of-sight effect in the mid-infrared data, since the\nfar--infrared continuum (45/100 $\\mu$m) and submillimeter line data\n(CH$_3$OH) show the same trend. Shocks with different filling factors\nare excluded for the same reason.\n\nCan we relate this `global warming' of the envelope to an evolutionary\neffect, or is it determined by other factors? The absence of a\ncorrelation of the above indicators with luminosity or mass of the\nsource argues against them being the sole controlling factor. The\nonly significant trend is found with the ratio of envelope mass over\nstellar mass. The physical interpretation of such a relation would be\nthat with time, the envelope is dispersed by the star, resulting in a\nhigher temperature throughout the envelope.\n\n\\section{Outstanding questions and future directions}\n\nThe results discussed here suggest that the observed chemical abundance and\ntemperature variations can indeed be used to trace the evolution of\nthe sources, and that, as in the case of low- and intermediate-mass\nstars, the dispersion of the envelope plays a crucial role. \nThe combination of infrared and submillimeter diagnostics\nis very important in the analysis. An\nimportant next step would be to use these diagnostics to probe a much\nwider range of evolutionary stages for high-mass stars, especially in\nthe hot core and (ultra-)compact H II region stages, to develop a more\ncomplete scenario of high-mass star formation. The relation between\nthe inner warm envelope and the `hot core' is still uncertain: several\nobjects have been observed which clearly have hot gas and evaporated\nices (including CH$_3$OH) in their inner regions, but which do not\nshow the typical crowded `hot core' submillimeter spectra. Are these\nobjects just on their way to the `hot core' chemical phase? Or is the\n`hot core' a separate physical component, e.g., a dense shell at the\nedge of the expanding hyper-compact H~II region due to the pressure\nfrom the ionized gas, which is still too small to be\npicked up by the single-dish beams? In either case, time or evolution\nplays a role and would constrain the ages of the infrared-bright\nsources to less than a few $\\times 10^4$ yr since evaporation.\nInterferometer data provide evidence for the presence of a separate\nphysical component in the inner 1000 AU, but lack the spatial\nresolution to distinguish a shell from any remnant disk, for example\non kinematic grounds. \n\nAn important difference between high- and low-mass objects may be the\nmechanism for the heating and dispersion of their envelopes. For\nlow-mass YSOs, entrainment of material in outflows is the\ndominant process (Lada 1999). For intermediate-mass stars, outflows\nare important in the early phase, but ultraviolet radiation\nbecomes dominant in the later stages (see \\S~3). The situation for\nhigh-mass stars is still unclear. The systematic increase in\ngas/solid ratios and gas-phase abundances point to global heating of\nthe gas and dust, consistent with a radiative mechanism. However, a\nclear chemical signature of ultraviolet radiation on gas-phase species\nand ices in the embedded phase has not yet been identified, making it\ndifficult to calibrate its effect. On the other hand, high-mass stars\nare known to have powerful outflows and winds, but a quantitative\ncomparison between their effectiveness in heating an extended part\nof the envelope and removing material is still\nlacking. Geometrical effects are more important in less embedded\nsystems, as is the case for low-mass stars, where the circumstellar\ndisk may shield part of the envelope from heating (Boogert et al.\\ \n2000b).\n\n\nTo what extent does the chemical evolution picture also apply to\nlow-mass stars? Many of the chemical processes and characteristics\nlisted in Table~1 are also known to occur for low-mass YSOs, but\nseveral important diagnostic tools are still lacking. In particular,\nsensitive mid-infrared spectroscopy is urgently needed to trace the evolution\nof the ices for low-mass YSOs and determine gas/solid ratios. Also,\nmolecules as complex as CH$_3$OCH$_3$ and C$_2$H$_5$CN have not yet\nbeen detected toward low-mass YSOs, although the limits are not very\nstringent (e.g., van Dishoeck et al.\\ 1995). Evaporation of ices\nclearly occurs in low-mass environments as evidenced by enhanced\nabundances of grain-surface molecules in shocks (e.g., Bachiller \\&\nP\\'erez-Guti\\'errez 1997), but whether a similar `hot core' chemistry\nensues is not yet known. Differences in the \nH/H$_2$ ratio and temperature structure in the (pre-)collapse\nphase may affect the\ngrain-surface chemistry and the ice composition,\nleading to different abundances of solid CH$_3$OH, which \nis an essential ingredient\nfor building complex molecules.\n\nFuture instrumentation with high spatial resolution ($< 1''$) and\nhigh sensitivity will be essential to make progress in our\nunderstanding of the earliest phase of massive star formation, in\nparticular the SMA and ALMA at submillimeter wavelengths, and SIRTF,\nSOFIA, FIRST and ultimately NGST at mid- and far-infrared wavelengths.\n\n\n\n\\acknowledgments\n\nThe authors are grateful to G.A. Blake, A.C.A.\\ Boogert, A.M.S.\\ Boonman, P.\\ \nEhrenfreund, N.J.\\ Evans, T.\\ Giannini, F.\\ Lahuis, L.G.\\ Mundy, A.\\ \nNummelin, W.A.\\ Schutte, A.G.G.M.\\ Tielens, and M.E.\\ van den Ancker\nfor discussions, collaborations and figures. 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D. 1995, \n\\apj, 447, 760 \n\n\\reference\nvan Dishoeck, E.F. \\& Helmich, F.P. 1996, A\\&A, 315, L177\n\n\\reference\nvan Dishoeck, E.F., Helmich, F.P., de Graauw, Th. et al. 1996,\nA\\&A, 315, L349\n\n\\reference\nvan Dishoeck, E.F. \\& Hogerheijde, M.R. 1999, in Origin of Stars and Planetary\nSystems,\neds.\\ C.J.\\ Lada and N.\\ Kylafis (Dordrecht:\nKluwer), p.\\ 97\n\n\\reference\nvan Dishoeck, E.F. et al.\\ 1999, in The Universe as seen by ISO,\neds.\\ P.\\ Cox and M.F.\\ Kessler (Noordwijk: ESTEC), ESA SP-427, p.\\ 437\n\n\n\\reference\nWaters, L.B.F.M.\\ \\& Waelkens, C.\\ 1998, ARAA, 36, 233\n\n\n\\reference\nWright, C.M., van Dishoeck, E.F., Helmich, F.P., Lahuis, F., Boogert, A.C.A.,\n\\& de Graauw, Th. 1997, \nin First ISO Workshop on Analytical Spectroscopy,\nESA SP-419, p. 37\n\n\\reference\nWright, C.M., van Dishoeck, E.F., Black, J.H., Feuchtgruber, H.,\nCernicharo, J., Gonz\\'alez-Alfonso, E., \\& de Graauw,\nTh.\\ 2000, A\\&A, in press \n\n\\end{references}\n\n\n\\begin{question}{M.\\ Ohishi}\nI agree with the point you mentioned, that the chemical differences among\nhot cores is due to a difference of evolutionary stage. Now we have\nseveral well-known hot cores such as Orion KL/S, W~3 IRS5/H$_2$O/IRS4,\nSgrB2 N/M/NW etc. Can you give us your personal view on the evolutionary\ndifferences of these sources?\n\\end{question} \n\n\\begin{answer}{E.F.\\ van Dishoeck}\nVan der Tak et al.\\ (2000a) argue that the infrared-bright objects such as W~3\nIRS5 represent an earlier evolutionary phase than the hot cores, on the basis\nof an anti-correlation with the radio continuum. The physical picture is that\nthe ionizing UV radiation and stellar winds push the hottest dust in the inner\nregions further out, decreasing the temperature of the dust and thus the\nnear-infrared continuum. At the same time, the size of the region which can be\nionized is increased. The `erosion' of the envelopes thus occurs from the\ninside out. For other sources, infrared diagnostics are lacking, so that the\nsituation is less clear. It would be great if chemistry could help to tie down\nthe time scales of the various phases.\n\\end{answer}\n\n\\begin{question}{W.\\ Irvine}\nHow do you interpret the behavior of the PAH features as a function of\nevolutionary stage in the sources that you discussed?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nThe absence of PAH features in the early embedded stage can be due either\nto a lack of ultraviolet radiation to excite the features or to an absence\nof the carriers. Manske \\& Henning (1999, A\\&A 349, 907) have argued \nfor the case of Herbig Ae/Be stars that\nthere should be sufficient radiation to excite PAHs in the envelope/disk\nsystem,\nso that the lack is likely due to the absence of the PAHs\nthemselves. Perhaps the PAHs have accreted into the icy mantles at the\nhigh densities in the inner envelope and do not evaporate\nand/or are chemically transformed into\nother more refractory species on grains. Alternatively, the region producing\nultraviolet radiation (H~II region) may be very small \nin these massive objects, and the photons may not reach the PAH-rich\nmaterial or have a very small beam filling factor.\nOnce the envelope breaks up and\nultraviolet radiation can escape to the less dense\nouter envelope, the PAH features from those\nregions will appear in spectra taken with large beams.\n\\end{answer}\n\n\\begin{question}{T.\\ Geballe}\nYou said that there is little evidence of the effect of ultraviolet radiation\non solid-state chemistry. Isn't the 4.6 $\\mu$m XCN feature a good example\nof that influence?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nThe `XCN' feature is indeed the best candidate for tracing the \nultraviolet processing\nof ices. If ascribed to OCN$^-$, it likely involves HNCO as\na precursor. In the laboratory, HNCO is produced by photochemical\nreactions of CO and NH$_3$, but in the interstellar medium grain surface\nchemistry is an alternative possibility which does not necessarily\ninvolve ultraviolet radiation (see Ehrenfreund \\& Schutte,\nthis volume). \n\\end{answer}\n\n\\begin{question}{Y.C.\\ Minh}\nDo you have an explanation of the low and constant abundances of CO$_2$\nin the gas phase?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nCharnley \\& Kaufman (2000, ApJ, 529, L111) argue that the evaporated CO$_2$ is\ndestroyed by reactions with atomic hydrogen at high temperatures in shocks.\nThis is an interesting suggestion, but needs to be tested against other\nspecies such as H$_2$O and H$_2$S which can be destroyed by\nreactions with atomic hydrogen as well. Also, the amount of material \nin the envelope that can be affected by shocks is not clear.\n\\end{answer}\n\n\\end{document}\n\n\n\n"}],"string":"[\n {\n \"name\": \"dishoeck.tex\",\n \"string\": \"% SAMPLE1.TEX -- WGAS sample paper with minimal markup.\\n\\n% Lines starting with \\\"%\\\" are comments; they will be ignored by LaTeX.\\n\\n\\\\documentstyle[11pt,newpasp,psfig,epsf,twoside]{article}\\n\\\\def\\\\gtsim{{_>\\\\atop{^\\\\sim}}}\\n\\\\def\\\\ltsim{{_<\\\\atop{^\\\\sim}}}\\n\\n\\\\begin{document}\\n\\n\\\\title{Chemistry in the Envelopes around Massive Young Stars}\\n\\\\author{Ewine F.\\\\ van Dishoeck and Floris F.S.\\\\ van der Tak}\\n\\\\affil{Leiden Observatory, P.O.\\\\ Box 9513, 2300 RA Leiden,\\nThe Netherlands}\\n\\n\\\\begin{abstract}\\nRecent observational studies of intermediate- and high-mass\\n star-forming regions at submillimeter and infrared wavelengths are\\n reviewed, and chemical diagnostics of the different physical\\n components associated with young stellar objects are summarized.\\n Procedures for determining the temperature, density and abundance\\n profiles in the envelopes are outlined. A detailed study of a set of\\n infrared-bright massive young stars reveals systematic increases in\\n the gas/solid ratios, the abundances of evaporated molecules, and the\\n fraction of heated ices with increasing temperature. Since these\\n diverse phenomena involve a range of temperatures from $<100\\\\,$K to\\n 1000~K, the enhanced temperatures must be communicated to both the\\n inner and outer parts of the envelopes. This `global heating'\\n plausibly results from the gradual dispersion of the envelopes with\\n time. Similarities and differences with low-mass YSOs are discussed.\\n The availability of accurate physical models will allow chemical\\n models of ice evaporation followed by `hot core' chemistry to be\\n tested in detail.\\n\\n\\n\\\\end{abstract}\\n\\n\\n%% Keywords: High-mass star formation, ices, hot cores, envelopes\\n%% \\n%% Objects: Orion-KL, Orion-IRc2, SGrB2, W~3 IRS5, W~3(H$_2$O), AFGL 2591,\\n%% AFGL 2136, NGC 7538 IRS9, W~33A, G34.3, S 140, W~3 IRS4\\n%% Molecules: CO, C$^{17}$O, CS, H$_2$CO, HC$_5$N, H$_2$O, CO$_2$,\\n%% CH$_3$OH, CH$_3$OCH$_3$, CH$_3$CN, C$_2$H$_2$, S~I, PAHs\\n%% OH, SiO, SO$_2$, CN, HCN, C~II, CO$^+$\\n\\n\\\\section{Introduction}\\n\\nMassive star-forming regions have traditionally been prime targets for\\nastrochemistry owing to their bright molecular lines (e.g., Johansson\\net al.\\\\ 1984, Cummins et al.\\\\ 1986, Irvine et al.\\\\ 1987, Ohishi 1997).\\nMassive young stellar objects (YSOs) have luminosities of $\\\\sim 10^4 -\\n10^6$ L$_\\\\odot$ and involve young O- and B-type stars. Because their\\nformation proceeds more rapidly than that of low-mass stars and\\ninvolves ionizing radiation, substantial chemical differences may be\\nexpected. The formation of high mass stars is much less well\\nunderstood than that of low-mass stars. For\\nexample, observational phenomena such as ultracompact H II regions,\\nhot cores, masers and outflows have not yet been linked into a single\\nevolutionary picture. Chemistry may well be an important diagnostic\\ntool in establishing such a sequence.\\n \\nMost of the early work on massive star-forming regions has centered on\\ntwo sources, Orion--KL and SgrB2. Numerous line surveys at millimeter\\n(e.g., Blake et al.\\\\ 1987, Turner 1991) and submillimeter (Jewell et\\nal.\\\\ 1989, Sutton et al.\\\\ 1991, 1995, Schilke et al.\\\\ 1997)\\nwavelengths have led to an extensive inventory of molecules through\\nidentification of thousands of lines. In addition, the surveys have\\nshown strong chemical variations between different sources.\\n\\nIn recent years, new observational tools have allowed a more detailed and\\nsystematic study of the envelopes of massive YSOs. Submillimeter observations\\nroutinely sample smaller beams (typically 15$''$ vs.\\\\ 30$''$--1$'$ ) and\\nhigher critical densities ($\\\\geq 10^6$ vs.\\\\ $10^4$ cm$^{-3}$) than the earlier\\nwork. Moreover, interferometers at 3 and 1 millimeter provide maps with\\nresolutions of $0.5''$--5$''$. Finally, ground- and space-based infrared\\nobservations allow both the gas and the ices to be sampled (e.g., Evans et\\nal.\\\\ 1991, van Dishoeck et al.\\\\ 1999). These observational developments have\\nled to a revival of the study of massive star formation within the last few\\nyears. Recent overviews of the physical aspects of high-mass star formation\\nare found in Churchwell (1999) and Garay \\\\& Lizano (1999).\\n\\n\\nIn this brief review, we will first summarize available observational\\ndiagnostics to study the different phases and physical components\\nassociated with massive star formation. Subsequently, an overview of\\nrecent results on intermediate mass YSOs is given, which are often\\nbetter characterized than their high-mass counterparts because of\\ntheir closer distance. Subsequently, we will discuss a specific sample\\nof embedded massive YSOs which have been studied through a combination\\nof infrared and submillimeter data. After illustrating\\nthe modeling techniques, we address the question how the\\nobserved chemical variations are related to evolutionary effects,\\ndifferent conditions in the envelope (e.g., $T$, mass) or different\\nluminosities of the YSOs. More extensive overviews of the chemical\\nevolution of star-forming regions are given by van Dishoeck \\\\& Blake\\n(1998), Hartquist et al.\\\\ (1998), van Dishoeck \\\\& Hogerheijde (1999)\\nand Langer et al.\\\\ (2000). Schilke et al.\\\\ (this volume) present high\\nspatial resolution interferometer studies, whereas Macdonald \\\\&\\nThompson (this volume) focus on submillimeter data of hot\\ncore/ultracompact H~II regions. Ices are discussed by Ehrenfreund \\\\&\\nSchutte (this volume).\\n\\n\\\\begin{figure}[t]\\n\\\\plotfiddle{dishoeck_fig1.ps}{11.0cm}{0}{50}{50}{-150}{-30}\\n\\\\caption{Overview of the SEST 230 GHz line survey of SgrB2 at the N, M and\\nNW positions, illustrating the chemical differentiation in high-mass\\nstar-forming regions (from:\\nNummelin et al.\\\\ 1998).}\\n\\\\label{fig-1}\\n\\\\vspace{-0.3cm}\\n\\\\end{figure}\\n\\n\\n\\\\section{Submillimeter and Infrared Diagnostics}\\n\\nThe majority of molecules are detected at (sub-)millimeter\\nwavelengths, and line surveys highlight the large variations in\\nchemical composition between different YSOs, both within the same\\nparent molecular cloud and between different clouds. The recent 1--3\\nmm surveys of Sgr~B2 (Nummelin et al.\\\\ 1998, Ohishi \\\\& Kaifu 1999)\\ndramatically illustrate the strong variations between various\\npositions (see Figure~1). The North position is typical of\\n`hot core'-type spectra, which are rich in lines of saturated\\norganic molecules. This position has also been named \\nthe `large molecule heimat'\\n(e.g., Kuan \\\\& Snyder 1994, Liu \\\\& Snyder 1999). The Middle position\\nhas strong SO and SO$_2$ lines, whereas the Northwest position has a\\nless-crowded spectrum with lines of ions and long carbon chains. A\\nsimilar differentiation has been observed for three positions in the\\nW~3 giant molecular cloud by Helmich \\\\& van Dishoeck (1997), who\\nsuggested an evolutionary sequence based on the chemistry.\\n\\n\\\\begin{figure}[t]\\n\\\\plotfiddle{dishoeck_fig2.ps}{10cm}{0}{55}{55}{-150}{-115}\\n\\\\caption{ISO-SWS spectra of two massive YSOs at different evolutionary stages.\\nCep A ($L \\\\approx 2.4\\\\times 10^4$ L$_{\\\\odot}$) is in the embedded\\nstage, whereas S~106 ($L \\\\approx 4.2\\\\times 10^4$ L$_{\\\\odot}$) is\\nin a more evolved stage (from:\\nvan den Ancker et al.\\\\ 2000a).}\\n\\\\label{fig-2}\\n\\\\end{figure}\\n\\n\\nThe availability of complete infrared spectra from 2.4--200 $\\\\mu$m\\nwith the {\\\\it Infrared Space Observatory }(ISO) allows complementary\\nvariations in infrared features to be studied. Figure~2 shows an\\nexample of ISO--SWS and LWS spectra of two objects: Cep A ($L \\\\approx\\n2.4\\\\times 10^4$ L$_{\\\\odot}$) and S~106 ($L \\\\approx 4.2\\\\times 10^4$\\nL$_{\\\\odot}$). The Cep A spectrum is characteristic of the deeply\\nembedded phase, in which the silicates and ices in the cold envelope\\nare seen in absorption. The S~106 spectrum is typical of a more\\nevolved massive YSO, with strong atomic and ionic lines in emission\\nand prominent PAH features. A similar sequence has been shown by\\nEhrenfreund et al.\\\\ (1998) for a set of southern massive young stars\\nwith luminosities up to $4\\\\times 10^5$ L$_{\\\\odot}$.\\n\\nThe most successful models for explaining these different chemical\\ncharacteristics involve accretion of species in an icy mantle during the\\n(pre-)collapse phase, followed by grain-surface chemistry and evaporation of\\nices once the YSO has started to heat its surroundings (e.g., Millar 1997). \\nThe evaporated molecules subsequently drive a rapid high-temperature gas-phase\\nchemistry for a period of $\\\\sim 10^4 - 10^5$ yr, resulting in complex,\\nsaturated organic molecules (e.g., Charnley et al.\\\\ 1992, 1995; Charnley 1997;\\nCaselli et al.\\\\ 1993, Viti \\\\& Williams 1999). The abundance ratios of species\\nsuch as CH$_3$OCH$_3$/CH$_3$OH and SO$_2$/H$_2$S show strong variations with\\ntime, and may be used as `chemical clocks' for a period of 5000--30,000 yr\\nsince evaporation. Once most of the envelope has cleared, the ultraviolet\\nradiation can escape and forms a photon-dominated region (PDR) at the\\nsurrounding cloud material, in which molecules are dissociated into radicals\\n(e.g., HCN $\\\\to$ CN) and PAH molecules excited to produce infrared emission.\\nThe (ultra-)compact H~II region gives rise to strong ionic lines due to\\nphotoionization.\\n\\n\\\\begin{table}[t]\\n\\\\caption{Chemical characteristics of massive star-forming regions}\\n\\\\begin{center}\\\\scriptsize\\n\\\\begin{tabular}{lllll}\\n\\\\hline\\n\\\\noalign{\\\\smallskip}\\nComponent & Chemical & Submillimeter & Infrared & Examples \\\\\\\\\\n & characteristics & diagnostics & diagnostics \\\\\\\\\\n\\\\tableline\\n\\\\noalign{\\\\smallskip}\\nDense cloud & Low-T chemistry &Ions, long-chains &Simple ices & SgrB2 (NW) \\\\\\\\\\n & & (HC$_5$N, ...) & (H$_2$O, CO$_2$) \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\nCold envelope & Low-T chemistry, & Simple species & Ices & N7538 IRS9, \\\\\\\\\\n & Heavy depletions & (CS, H$_2$CO) & (H$_2$O, CO$_2$, CH$_3$OH)\\n & W~33A \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\nInner warm & Evaporation & High T$_{\\\\rm ex}$ & High gas/solid, High\\n & GL 2591, \\\\\\\\\\nenvelope & & (CH$_3$OH) & T$_{\\\\rm ex}$, Heated ices \\n & GL 2136 \\\\\\\\\\n & & & (C$_2$H$_2$, H$_2$O, CO$_2$) \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\nHot core & High-T chemistry & Complex organics & Hydrides & Orion hot core, \\\\\\\\\\n & & (CH$_3$OCH$_3$, CH$_3$CN, & (OH, H$_2$O) \\n& SgrB2(N),G34.3 \\\\\\\\\\n&&vib.\\\\ excited mol.) && W~3(H$_2$O) \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\nOutflow: & Shock chemistry, & Si- and S-species & \\n Atomic lines, Hydrides & W~3 IRS5, \\\\\\\\\\nDirect impact &Sputtering & (SiO, SO$_2$) &([S I], H$_2$O) & SgrB2(M) \\\\\\\\\\n\\\\noalign{\\\\smallskip}\\nPDR, Compact & Photodissociation,& Ions, radicals & Ionic lines, PAHs\\n& S~140, \\\\\\\\\\nH~II regions & Photoionization & (CN/HCN, CO$^+$) &([NeII], [CII])\\n& W~3 IRS4 \\\\\\\\\\n \\n%\\\\noalign{\\\\vspace{-0.8cm}}\\n\\\\tableline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\end{table}\\n\\n\\nTable~1 summarizes the chemical characteristics of the\\nvarious physical components, together with the observational\\ndiagnostics at submillimeter and infrared wavelengths. \\nWithin the single-dish submillimeter and ISO beams,\\nmany of these components are blended together and interferometer\\nobservations will be essential to disentangle them. Nevertheless, the\\nsingle-dish data are useful because they encompass the entire envelope\\nand highlight the dominant component in the beam. Combined\\nwith the above chemical scenario, one may then attempt to establish an\\nevolutionary sequence of the sources.\\n\\nThe physical distinction between the `hot core' and the warm\\ninner envelope listed in Table~1 is currently not clear: does the `hot\\ncore' represent a separate physical component or is it simply the\\ninner warm envelope at a different stage of chemical evolution? Even\\nfrom an observational point of view, there appear to be different\\ntypes of `hot cores': some of them are internally heated by the young\\nstar (e.g., W~3(H$_2$O)), whereas others may just be dense clumps of\\ngas heated externally (e.g., the Orion compact ridge). This point\\nwill be further discussed in \\\\S\\\\S 4 and 5. Disks are not included in\\nTable~1, because little is known about their chemical characteristics,\\nor even their existence, around high-mass YSOs (see Norris, this\\nvolume).\\n\\n\\n\\\\section{Intermediate-Mass YSOs}\\n\\nIntermediate-mass pre-main sequence stars, in particular the so-called\\nHerbig Ae/Be stars, have received increased observational attention in\\nrecent years (see Waters \\\\& Waelkens 1998 for a review). These stars\\nhave spectral type A or B and show infrared excesses due to \\ncircumstellar dust. Typical luminosities are in the range $10^2 -\\n10^4$ L$_{\\\\odot}$, and several objects have been located within 1 kpc\\ndistance. Systematic mapping of CO and the submillimeter continuum of\\na sample of objects has been performed by Fuente et al.\\\\ (1998) and\\nHenning et al.\\\\ (1998). The data show the dispersion of the envelope\\nwith time starting from the deeply embedded phase (e.g.,\\nLkH$\\\\alpha$234) to the intermediate stage of a PDR (e.g., HD 200775\\nilluminating the reflection nebula NGC 7023) to the more evolved stage\\nwhere the molecular gas has disappeared completely (e.g., HD 52721).\\nThe increasing importance of photodissociation in the chemistry is\\nprobed by the increase in the CN/HCN abundance ratio. This ratio has\\nbeen shown in other high-mass sources to be an excellent tracer of\\nPDRs (e.g., Simon et al. 1997, Jansen et al.\\\\ 1995). Line surveys of\\nthese objects in selected frequency ranges would be useful to\\ninvestigate their chemical complexity, especially in the embedded\\nphase.\\n\\nISO-SWS observations of a large sample of Herbig Ae/Be stars have been\\nperformed by van den Ancker et al.\\\\ (2000b,c). In the embedded phase,\\nshock indicators such as [S I] 25.2 $\\\\mu$m are strong, whereas in the\\nlater phases PDR indicators such as PAHs are prominent. An excellent\\nexample of this evolutionary sequence is provided by three Herbig Ae\\nstars in the BD+40$^o$4124 region ($d\\\\approx 1$ kpc). The data\\nsuggest that in the early phases, the heating of the envelope is\\ndominated by shocks, whereas in later phases it is controlled by\\nultraviolet photons.\\n\\n\\n\\\\begin{figure}[t]\\n\\\\vspace{-3.8cm}\\n\\\\plottwo{dishoeck_fig3a.ps}{dishoeck_fig3b.ps}\\n\\\\vspace{-0.3cm}\\n\\\\caption{Left: ISO-LWS spectra of the intermediate mass YSO \\nLkH$\\\\alpha$234, showing strong atomic fine-structure lines of\\n[C II] 158 $\\\\mu$m and [O~I] 63 $\\\\mu$m, but weak molecular CO and\\nOH lines. Right: CO excitation diagram, indicating the presence\\nof a warm ($T\\\\approx 200-900$~K), dense ($n>10^5$ cm$^{-3}$) \\nregion (from:\\nGiannini et al.\\\\ 2000).}\\n\\\\label{fig-3}\\n\\\\vspace{-0.5cm}\\n\\\\end{figure}\\n\\n\\nISO-LWS data have been obtained for a similar sample of Herbig Ae/Be\\nstars by Lorenzetti et al.\\\\ (1999) and Giannini et al.\\\\ (2000), and\\nare summarized by Saraceno et al.\\\\ (1999). The [C II] 158 $\\\\mu$m and\\n[O I] 63 and 145 $\\\\mu$m lines are prominent in many objects and are\\ndue primarily to the PDR component in the large LWS beam ($\\\\sim\\n80''$). High-$J$ CO and OH far-infrared lines have been detected in\\nsome objects and indicate the presence of a compact, high temperature\\nand density region of $\\\\sim$1000 AU in size, presumably tracing the\\ninner warm envelope (see Figure~3).\\nFar-infrared lines of H$_2$O are seen in low-mass YSO spectra, but are\\nweak or absent in those of intermediate- and high-mass YSOs, with the\\nexception of Orion-KL and SgrB2 (e.g., Harwit et al.\\\\ 1998, Cernicharo\\net al.\\\\ 1997, Wright et al.\\\\ 2000). The absence of H$_2$O lines in\\nhigher-mass objects may be partly due to the larger distance of these\\nobjects, resulting in substantial dilution in the LWS beam. However,\\nphotodissociation of H$_2$O to OH and O by the enhanced ultraviolet radiation\\nmay also play a role.\\n\\nIn summary, both the submillimeter and infrared diagnostics reveal an\\nevolutionary sequence from the youngest `Group I' objects to `Group\\nIII' objects (cf.\\\\ classification by Fuente et al.\\\\ 1998), in which\\nthe envelope is gradually dispersed. Such a sequence is analogous to\\nthe transition from embedded Class 0/I objects to more evolved Class\\nII/III objects in the case of low-mass stars (Adams et al.\\\\ 1987). The\\nISO data provide insight into the relative importance of the heating\\nand removal mechanisms of the envelope. At the early stages of\\nintermediate-mass star formation, shocks due to outflows appear to\\ndominate whereas at later stages radiation is more important.\\n\\n\\\\section{Embedded, Infrared-Bright Massive YSOs}\\n\\n\\\\subsection{Sample}\\n\\nThe availability of complete, high quality ISO spectra for a\\nsignificant sample of massive young stars provides a unique\\nopportunity to study these sources through a combination of infrared\\nand submillimeter spectroscopy, and further develop these diagnostics.\\nVan der Tak et al.\\\\ (2000a) have selected a set of $\\\\sim$10 deeply\\nembedded massive YSOs which are bright at mid-infrared wavelengths (12\\n$\\\\mu$m flux $>$ 100 Jy), have luminosities of $10^3 - 2\\\\times 10^5$\\nL$_{\\\\odot}$ and distances $d\\\\leq$4 kpc. The sources are all in an\\nearly evolutionary state (comparable to the `Class 0/I' or `Group I'\\nstages of low- and intermediate-mass stars), as indicated by their\\nweak radio continuum emission and absence of ionic lines and PAH\\nfeatures. In addition to ISO spectra, JCMT submillimeter data and\\nOVRO interferometer observations have been obtained. For most of the\\nobjects high spectral resolution ground-based infrared data of CO,\\n$^{13}$CO and H$_3^+$ are available (Mitchell et al.\\\\ 1990, Geballe \\\\&\\nOka 1996, McCall et al.\\\\ 1999), and occasionally H$_2$ (Lacy et\\nal.\\\\ 1994, Kulesa et al.\\\\ 1999). For comparison, 5 infrared-weak\\nsources with similar luminosities are studied at submillimeter\\nwavelengths only. This latter set includes hot cores and ultracompact\\nH~II regions such as W~3(H$_2$O), IRAS 20126+4104 (Cesaroni et al.\\\\ \\n1997, 1999), and NGC~6334 IRS1.\\n\\n\\\\subsection{Physical structure of the envelope}\\n\\nIn order to derive molecular abundances from the observations, a good\\nphysical model of the envelope is a prerequisite. Van der Tak et al.\\\\ \\n(1999, 2000a) outline the techniques used to constrain the temperature\\nand density structure (Figure~4). The total mass within the\\nbeam is derived from submillimeter photometry, whereas the size scale\\nof the envelope is constrained from line and continuum maps. The dust\\nopacity has been taken from Ossenkopf \\\\& Henning (1994) and yields\\nvalues for the mass which are consistent with those derived from\\nC$^{17}$O for warm sources where CO is not depleted\\nonto grains.\\n\\n\\n\\\\begin{figure}[t]\\n\\\\plotfiddle{dishoeck_fig4.ps}{7.7cm}{0}{45}{45}{-120}{-60}\\n\\\\caption{Overview of method used for constraining the temperature and density\\nstructure of envelopes. A power-law density structure with trial values\\nfor the exponent\\n$\\\\alpha_i$ and molecular abundances $X_j$ is adopted\\n(based on: van der Tak et al.~2000a).}\\n\\\\label{fig-4}\\n\\\\end{figure}\\n\\n\\nThe temperature structure of the dust is calculated taking the\\nobserved luminosity of the source, given a power-law density structure\\n(see below). At large distances from the star, the temperature follows\\nthe optically thin relation $\\\\propto r^{-0.4}$, whereas at smaller\\ndistances the dust becomes optically thick at infrared wavelengths and\\nthe temperature increases more steeply (see Figure~5). It is assumed\\nthat $T_{\\\\rm gas}=T_{\\\\rm dust}$, consistent with explicit calculations\\nof the gas and dust temperatures by, e.g., Doty \\\\& Neufeld (1997)\\nfor these high densities.\\n\\nThe continuum data are sensitive to temperature and column density,\\nbut not to density. Observations of a molecule with a large dipole\\nmoment are needed to subsequently constrain the density structure. One\\nof the best choices is CS and its isotope C$^{34}$S, for which lines\\nranging from $J$=2--1 to 10--9 have been observed. Assuming a\\npower-law density profile $n(r)= n_o (r/r_o)^{-\\\\alpha}$, values of\\n$\\\\alpha$ can be determined from minimizing $\\\\chi^2$ between the CS\\nline data and excitation models. The radiative transfer in the lines\\nis treated through a Monte-Carlo method. The best fit to the data on\\nthe infrared-bright sources is obtained for $\\\\alpha = 1.0 - 1.5$,\\nwhereas the hot core/compact H~II region sample requires higher\\nvalues, $\\\\alpha \\\\approx 2$. This derivation assumes that the CS\\nabundance is constant through the envelope; if it increases with\\nhigher temperatures, such as may be the case for hot cores, the values\\nof $\\\\alpha$ are lowered. Note that the derived values of\\n$\\\\alpha=1.0-1.5$ are lower than those found for deeply embedded\\nlow-mass objects, where $\\\\alpha\\\\approx 2$ (e.g., Motte et al.\\\\ 1998,\\nHogerheijde et al.\\\\ 1999).\\n\\n\\\\begin{figure}[t]\\n\\\\plotfiddle{dishoeck_fig5.ps}{7.0cm}{-90}{45}{45}{-170}{260}\\n\\\\vspace{-0.3cm}\\n\\\\caption{Derived temperature and density structure for the envelope\\naround the massive YSO\\nGL 2591 (L=$2\\\\times 10^4$ L$_{\\\\odot}$, $d$=1 kpc). \\nThe critical densities of the CS 2--1 and 10--9 lines are\\nindicated, as are the typical beam sizes of the JCMT \\nat 345 GHz and OVRO at 100 GHz (based on: van der Tak et \\nal.\\\\ 1999).}\\n\\\\label{fig-5}\\n\\\\vspace{-0.5cm}\\n\\\\end{figure}\\n\\n\\nFigure 5 displays the derived temperature and density structure\\nfor the source GL 2591, together with the sizes of the JCMT and\\nOVRO beams. While the submillimeter data are weighted toward the\\ncolder, outer envelope, the infrared absorption line observations sample\\na pencil-beam line of sight toward the YSO and are more sensitive to\\nthe inner warm ($\\\\sim 1000$~K) region. On these small scales, the\\nenvelope structure deviates from a radial power law, which decreases\\nthe optical depth at near-infrared wavelengths by a factor of \\n$\\\\sim 3$ (van der Tak et al.\\\\\\n1999).\\n\\n\\nFor sources for which interferometer data are available, unresolved\\ncompact continuum emission is detected on scales of a few thousand AU\\nor less. This emission is clearly enhanced compared with that\\nexpected from the inner ``tip'' of the power-law envelope, and its\\nspectral index indicates optically thick warm dust, most likely in a\\ndense circumstellar shell or disk. The presence of this shell or disk\\nis also indicated by the prevalence of blue-shifted outflowing dense\\ngas without a red-shifted counterpart on $< 10''$ scales.\\n\\n\\n\\\\subsection{Chemical structure: infrared absorption lines}\\n\\nThe ISO-SWS spectra of the infrared-bright sources show absorption by\\nvarious gas-phase molecules, in addition to strong features by ices.\\nMolecules such as CO$_2$ (van Dishoeck et al.\\\\ 1996,\\nBoonman et al.\\\\ 1999, 2000a), H$_2$O (van Dishoeck \\\\& Helmich 1996, Boonman\\net al.\\\\ 2000b), CH$_4$ (Boogert et al.\\\\ 1998), HCN and C$_2$H$_2$\\n(Lahuis \\\\& van Dishoeck 2000) have been detected (see also van\\nDishoeck 1998, Dartois et al.\\\\ 1998).\\n\\nIn the infrared, absorption out of all $J$-levels is observed in a\\nsingle spectrum. The excitation temperatures $T_{\\\\rm ex}$ of the\\nvarious molecules, calculated assuming LTE, range from $\\\\ltsim 100$ to\\n$\\\\sim 1000$~K between sources, giving direct information on \\nthe physical component in which the molecules reside. While CO \\nis well-mixed throughout the envelopes, H$_2$O, HCN and C$_2$H$_2$ are\\nenhanced at high temperatures. In contrast, CO$_2$ seems to avoid the\\nhottest gas. High spectral resolution ground-based data of HCN and\\nC$_2$H$_2$ by Carr et al.\\\\ (1995) and Lacy et al.\\\\ (1989) for a few\\nobjects suggest line widths of at most a few km s$^{-1}$, excluding an\\norigin in outflowing gas.\\n\\nThe abundances of H$_2$O, HCN and C$_2$H$_2$ increase by factors of\\n$\\\\gtsim 10$ with increasing $T_{\\\\rm ex}$ (see Figure~7). The warm\\nH$_2$O must be limited to a $\\\\ltsim 1000$~AU region, since the pure\\nrotational lines are generally not detected in the $80''$ ISO-LWS beam\\n(Wright et al.\\\\ 1997). For CO$_2$, the abundance variation between\\nsources is less than a factor of 10, and no clear trend with $T_{\\\\rm\\n ex}$ is found. For the same sources, the H$_2$O and CO$_2$ ice\\nabundances show a decrease by an order of magnitude, consistent with\\nevaporation of the ices. However, the gas-phase H$_2$O and CO$_2$\\nabundances are factors of $\\\\sim 10$ lower than expected if all\\nevaporated molecules stayed in the gas phase, indicating that\\nsignificant chemical processing occurs after evaporation. More\\ndetailed modeling using the source structures derived from\\nsubmillimeter data is in progress.\\n\\n\\\\begin{figure}[t]\\n\\\\plotfiddle{dishoeck_fig6.ps}{6.8cm}{-90}{50}{50}{-210}{260}\\n\\\\caption{{\\\\it Left:}~Abundance of HCN,\\n$N$(HCN)/$N_{\\\\rm tot}$(H$_2$), as a function of the\\n$^{13}$CO excitation temperature measured by\\nMitchell et al.\\\\ (1990). {\\\\it Middle:} Abundance of H$_2$O in the warm gas\\n$N$(H$_2$O)/$N_{\\\\rm warm}$(H$_2$) as a function of $^{13}$CO excitation\\ntemperature;\\n{\\\\it Right:}~Abundance of H$_2$O ice as a function of\\n$^{13}$CO excitation temperature. The same trend\\nis found if the dust temperature, as derived from the 45/100 $\\\\mu$m\\nflux, is used (based on: Lahuis \\\\& van Dishoeck 2000; van Dishoeck 1998).}\\n\\\\label{fig-6}\\n\\\\end{figure}\\n\\n\\n\\\\subsection{Chemical structure: submillimeter emission}\\n\\nThe JCMT data of the infrared-bright objects show strong lines, but\\nlack the typical crowded `hot core' spectra observed for objects such\\nas W~3(H$_2$O) and NGC 6334 IRS1. Complex organics such as\\nCH$_3$OCH$_3$ and CH$_3$OCHO are detected in some sources (e.g., GL\\n2591, NGC 7538 IRS1), but are not as prominent as in the comparison\\nsources. Yet warm gas is clearly present in these objects.\\nIs the `hot core' still too small to be picked up by the\\nsingle dish beams, or are the abundances of these molecules not (yet)\\nenhanced?\\n\\nTo investigate this question, \\nvan der Tak et al.\\\\ (2000b) consider the analysis of\\ntwo species, H$_2$CO and CH$_3$OH. Both\\nspecies have many lines throughout the submillimeter originating from\\nlow- and high-lying energy levels. Given the physical structure\\ndetermined in \\\\S 4.2, abundance {\\\\it profiles} can be constrained. Two\\nextreme, but chemically plausible models are considered: (i) a model\\nwith a constant abundance throughout the envelope. This model is\\nmotivated by the fact that pure gas-phase reaction schemes do not show\\nlarge variations in calculated abundances between 20 and 100~K; (ii) a\\nmodel in which the abundance `jumps' to a higher value at the ice\\nevaporation temperature, $T_d\\\\approx 90$~K. In this model, the\\nabundances in the outer envelope are set at those observed in cold\\nclouds, so that the only free parameter is the amount of abundance\\nincrease.\\n\\nIt is found that the H$_2$CO data can be well fit with a constant\\nabundance of a few $\\\\times 10^{-9}$ throughout the envelope. However,\\nthe high $J,K$ data for CH$_3$OH require a jump in its abundance from\\n$\\\\sim 10^{-9}$ to $\\\\sim 10^{-7}$ for the warmer sources. This is\\nconsistent with the derived excitation temperatures: H$_2$CO has a\\nrather narrow range of $T_{\\\\rm ex}$=50--90~K, whereas CH$_3$OH shows\\n$T_{\\\\rm ex}$=30--200~K. Moreover, the interferometer maps of CH$_3$OH\\nrule out constant abundance models. The jump observed for CH$_3$OH is\\nchemically plausible since this molecule is known to be present in icy\\ngrain mantles with abundances of 5--40\\\\% with respect to H$_2$O ice,\\ni.e., $\\\\sim 10^{-7}-10^{-6}$ w.r.t.\\\\ H$_2$. Similar increases in the\\nabundances of organic molecules (e.g., CH$_3$OH, C$_2$H$_3$CN, ....)\\nare found with increasing $T_{\\\\rm dust}$ for a set of `hot--core'\\nobjects by Ikeda \\\\& Ohishi (1999).\\n\\n\\n\\\\subsection{Comparison with chemical models}\\n\\nBoth the infrared and submillimeter data show increases in the\\nabundances of various molecules with increasing temperature. Four\\ntypes of species can be distinguished: (i) `passive' molecules which\\nare formed in the gas phase, freeze out onto grains during the cold\\n(pre-)collapse phase and are released during warm-up without chemical\\nmodification (e.g., CO, C$_2$H$_2$); (ii) molecules which are formed\\non the grains during the cold phase by surface reactions and are\\nsubsequently released into the warm gas (e.g., CH$_3$OH); (iii)\\nmolecules which are formed in the warm gas by gas-phase reactions with\\nevaporated molecules (e.g., CH$_3$OCH$_3$); (iv) molecules which are\\nformed in the hot gas by high temperature reactions (e.g., HCN). These\\ntypes of molecules\\nare associated with characteristic temperatures of (a) $T_{\\\\rm\\n dust}<20$~K, where CO is frozen out; the presence of CO ice is\\nthought to be essential for the formation of CH$_3$OH; (b) $T_{\\\\rm\\n dust} \\\\approx 90$~K, where all ices evaporate on a time scale of\\n$<10^5$ yr; and (c) $T_{\\\\rm gas}>230$~K, where gas-phase reactions\\ndrive the available atomic oxygen into water through the reactions O +\\nH$_2$ $\\\\to$ OH $\\\\to$ H$_2$O (Ceccarelli et al.\\\\ 1996, Charnley 1997).\\nAtomic oxygen is one of the main destroyers of radicals and carbon\\nchains, so that its absence leads to enhanced abundances of species\\nlike HCN and HC$_3$N in hot gas.\\n\\nWater is abundantly formed on the grains, but the fact that the\\nH$_2$O abundance in the hot gas is not as large as that of the ices\\nsuggests that H$_2$O is broken down to O and OH after evaporation by\\nreactions with H$_3^+$. H$_2$O can subsequently be reformed in warm\\ngas at temperatures above $\\\\sim$230~K, but Figure~7 indicates that not\\nall available gas-phase oxygen is driven into H$_2$O, as the models\\nsuggest. The low abundance of CO$_2$ in the warm gas is still a\\npuzzle, since evaporation of abundant CO$_2$ ice is observed. The\\nmolecule must be broken down rapidly in the warm gas, with no\\nreformation through the CO + OH $\\\\to$ CO$_2$ reaction (see question by\\nMinh).\\n\\n\\\\subsection{Evolution?}\\n\\nThe objects studied by van der Tak et al.\\\\ (2000a) are all in an early\\nstage of evolution, when the young stars are still deeply embedded in\\ntheir collapsing envelope. Nevertheless, even within this narrow\\nevolutionary range, there is ample evidence for physical and chemical\\ndifferentiation of the sources. This is clearly traced by the\\nincrease in the gas/solid ratios, the increase in abundances of several\\nmolecules, the decrease in the ice abundances, and the increase\\nof the amount of crystalline ice with increasing temperature\\n(Boogert et al.\\\\ 2000a).\\n\\nThe fact that the various indicators involve different\\ncharacteristic temperatures ranging from $<$50 K (evaporation of\\napolar ices) to 1000 K ($T_{\\\\rm ex}$ of gas-phase molecules)\\nindicates that the heating is not a local effect, but that `global\\nwarming' occurs throughout the envelope. Moreover, it cannot be a\\ngeometrical line-of-sight effect in the mid-infrared data, since the\\nfar--infrared continuum (45/100 $\\\\mu$m) and submillimeter line data\\n(CH$_3$OH) show the same trend. Shocks with different filling factors\\nare excluded for the same reason.\\n\\nCan we relate this `global warming' of the envelope to an evolutionary\\neffect, or is it determined by other factors? The absence of a\\ncorrelation of the above indicators with luminosity or mass of the\\nsource argues against them being the sole controlling factor. The\\nonly significant trend is found with the ratio of envelope mass over\\nstellar mass. The physical interpretation of such a relation would be\\nthat with time, the envelope is dispersed by the star, resulting in a\\nhigher temperature throughout the envelope.\\n\\n\\\\section{Outstanding questions and future directions}\\n\\nThe results discussed here suggest that the observed chemical abundance and\\ntemperature variations can indeed be used to trace the evolution of\\nthe sources, and that, as in the case of low- and intermediate-mass\\nstars, the dispersion of the envelope plays a crucial role. \\nThe combination of infrared and submillimeter diagnostics\\nis very important in the analysis. An\\nimportant next step would be to use these diagnostics to probe a much\\nwider range of evolutionary stages for high-mass stars, especially in\\nthe hot core and (ultra-)compact H II region stages, to develop a more\\ncomplete scenario of high-mass star formation. The relation between\\nthe inner warm envelope and the `hot core' is still uncertain: several\\nobjects have been observed which clearly have hot gas and evaporated\\nices (including CH$_3$OH) in their inner regions, but which do not\\nshow the typical crowded `hot core' submillimeter spectra. Are these\\nobjects just on their way to the `hot core' chemical phase? Or is the\\n`hot core' a separate physical component, e.g., a dense shell at the\\nedge of the expanding hyper-compact H~II region due to the pressure\\nfrom the ionized gas, which is still too small to be\\npicked up by the single-dish beams? In either case, time or evolution\\nplays a role and would constrain the ages of the infrared-bright\\nsources to less than a few $\\\\times 10^4$ yr since evaporation.\\nInterferometer data provide evidence for the presence of a separate\\nphysical component in the inner 1000 AU, but lack the spatial\\nresolution to distinguish a shell from any remnant disk, for example\\non kinematic grounds. \\n\\nAn important difference between high- and low-mass objects may be the\\nmechanism for the heating and dispersion of their envelopes. For\\nlow-mass YSOs, entrainment of material in outflows is the\\ndominant process (Lada 1999). For intermediate-mass stars, outflows\\nare important in the early phase, but ultraviolet radiation\\nbecomes dominant in the later stages (see \\\\S~3). The situation for\\nhigh-mass stars is still unclear. The systematic increase in\\ngas/solid ratios and gas-phase abundances point to global heating of\\nthe gas and dust, consistent with a radiative mechanism. However, a\\nclear chemical signature of ultraviolet radiation on gas-phase species\\nand ices in the embedded phase has not yet been identified, making it\\ndifficult to calibrate its effect. On the other hand, high-mass stars\\nare known to have powerful outflows and winds, but a quantitative\\ncomparison between their effectiveness in heating an extended part\\nof the envelope and removing material is still\\nlacking. Geometrical effects are more important in less embedded\\nsystems, as is the case for low-mass stars, where the circumstellar\\ndisk may shield part of the envelope from heating (Boogert et al.\\\\ \\n2000b).\\n\\n\\nTo what extent does the chemical evolution picture also apply to\\nlow-mass stars? Many of the chemical processes and characteristics\\nlisted in Table~1 are also known to occur for low-mass YSOs, but\\nseveral important diagnostic tools are still lacking. In particular,\\nsensitive mid-infrared spectroscopy is urgently needed to trace the evolution\\nof the ices for low-mass YSOs and determine gas/solid ratios. Also,\\nmolecules as complex as CH$_3$OCH$_3$ and C$_2$H$_5$CN have not yet\\nbeen detected toward low-mass YSOs, although the limits are not very\\nstringent (e.g., van Dishoeck et al.\\\\ 1995). Evaporation of ices\\nclearly occurs in low-mass environments as evidenced by enhanced\\nabundances of grain-surface molecules in shocks (e.g., Bachiller \\\\&\\nP\\\\'erez-Guti\\\\'errez 1997), but whether a similar `hot core' chemistry\\nensues is not yet known. Differences in the \\nH/H$_2$ ratio and temperature structure in the (pre-)collapse\\nphase may affect the\\ngrain-surface chemistry and the ice composition,\\nleading to different abundances of solid CH$_3$OH, which \\nis an essential ingredient\\nfor building complex molecules.\\n\\nFuture instrumentation with high spatial resolution ($< 1''$) and\\nhigh sensitivity will be essential to make progress in our\\nunderstanding of the earliest phase of massive star formation, in\\nparticular the SMA and ALMA at submillimeter wavelengths, and SIRTF,\\nSOFIA, FIRST and ultimately NGST at mid- and far-infrared wavelengths.\\n\\n\\n\\n\\\\acknowledgments\\n\\nThe authors are grateful to G.A. Blake, A.C.A.\\\\ Boogert, A.M.S.\\\\ Boonman, P.\\\\ \\nEhrenfreund, N.J.\\\\ Evans, T.\\\\ Giannini, F.\\\\ Lahuis, L.G.\\\\ Mundy, A.\\\\ \\nNummelin, W.A.\\\\ Schutte, A.G.G.M.\\\\ Tielens, and M.E.\\\\ van den Ancker\\nfor discussions, collaborations and figures. 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(Berlin: Springer), p.\\\\ 279\\n\\n\\\\reference\\nSchilke, P., Groesbeck, T.D., Blake, G.A., \\\\& Phillips, T.G.\\\\ 1997,\\nApJS, 108, 301\\n\\n\\n\\\\reference\\nSimon, R., Stutzki, J., Sternberg, A., \\\\& Winnewisser, G.\\\\ 1997,\\nA\\\\&A, 327, L9\\n\\n\\\\reference\\nSutton, E.C., Jaminet, P.A., Danchi, W.C., \\\\& Blake, G.A.\\\\ 1991,\\nApJS, 77, 255\\n\\n\\\\reference\\nSutton, E.C., Peng, R., Danchi, W.C., et al.\\\\ 1995, ApJS, 97, 455\\n\\n\\\\reference\\nTurner, B.E.\\\\ 1991, ApJS, 76, 617\\n\\n\\\\reference\\nvan den Ancker, M. et al.\\\\ 2000a, A\\\\&A, submitted\\n\\n\\\\reference\\nvan den Ancker, M. et al.\\\\ 2000b, A\\\\&A, in press\\n\\n\\\\reference\\nvan den Ancker, M. et al.\\\\ 2000c, A\\\\&A, submitted\\n\\n\\\\reference\\nvan der Tak, F.F.S., van Dishoeck, E.F., Evans, N.J., Bakker, E.J., \\\\&\\nBlake, G.A.\\\\ 1999, ApJ, 522, 991\\n\\n\\\\reference\\nvan der Tak, F.F.S., van Dishoeck, E.F., Evans, N.J., \\\\& Blake, G.A.\\\\ 2000a,\\nApJ, in press\\n\\n\\\\reference\\nvan der Tak, F.F.S.\\\\ \\\\& van Dishoeck, E.F.\\\\ 2000b,\\nA\\\\&A, to be submitted\\n\\n\\\\reference\\nvan Dishoeck, E.F.\\\\ 1998, Far.\\\\ Disc., 109, 31\\n\\n\\\\reference\\nvan Dishoeck, E.F. \\\\& Blake, G.A.\\\\ 1998, ARAA, 36, 317\\n\\n\\n\\\\reference\\nvan Dishoeck, E. F., Blake, G. A., Jansen, D. J. \\\\& Groesbeck, T. D. 1995, \\n\\\\apj, 447, 760 \\n\\n\\\\reference\\nvan Dishoeck, E.F. \\\\& Helmich, F.P. 1996, A\\\\&A, 315, L177\\n\\n\\\\reference\\nvan Dishoeck, E.F., Helmich, F.P., de Graauw, Th. et al. 1996,\\nA\\\\&A, 315, L349\\n\\n\\\\reference\\nvan Dishoeck, E.F. \\\\& Hogerheijde, M.R. 1999, in Origin of Stars and Planetary\\nSystems,\\neds.\\\\ C.J.\\\\ Lada and N.\\\\ Kylafis (Dordrecht:\\nKluwer), p.\\\\ 97\\n\\n\\\\reference\\nvan Dishoeck, E.F. et al.\\\\ 1999, in The Universe as seen by ISO,\\neds.\\\\ P.\\\\ Cox and M.F.\\\\ Kessler (Noordwijk: ESTEC), ESA SP-427, p.\\\\ 437\\n\\n\\n\\\\reference\\nWaters, L.B.F.M.\\\\ \\\\& Waelkens, C.\\\\ 1998, ARAA, 36, 233\\n\\n\\n\\\\reference\\nWright, C.M., van Dishoeck, E.F., Helmich, F.P., Lahuis, F., Boogert, A.C.A.,\\n\\\\& de Graauw, Th. 1997, \\nin First ISO Workshop on Analytical Spectroscopy,\\nESA SP-419, p. 37\\n\\n\\\\reference\\nWright, C.M., van Dishoeck, E.F., Black, J.H., Feuchtgruber, H.,\\nCernicharo, J., Gonz\\\\'alez-Alfonso, E., \\\\& de Graauw,\\nTh.\\\\ 2000, A\\\\&A, in press \\n\\n\\\\end{references}\\n\\n\\n\\\\begin{question}{M.\\\\ Ohishi}\\nI agree with the point you mentioned, that the chemical differences among\\nhot cores is due to a difference of evolutionary stage. Now we have\\nseveral well-known hot cores such as Orion KL/S, W~3 IRS5/H$_2$O/IRS4,\\nSgrB2 N/M/NW etc. Can you give us your personal view on the evolutionary\\ndifferences of these sources?\\n\\\\end{question} \\n\\n\\\\begin{answer}{E.F.\\\\ van Dishoeck}\\nVan der Tak et al.\\\\ (2000a) argue that the infrared-bright objects such as W~3\\nIRS5 represent an earlier evolutionary phase than the hot cores, on the basis\\nof an anti-correlation with the radio continuum. The physical picture is that\\nthe ionizing UV radiation and stellar winds push the hottest dust in the inner\\nregions further out, decreasing the temperature of the dust and thus the\\nnear-infrared continuum. At the same time, the size of the region which can be\\nionized is increased. The `erosion' of the envelopes thus occurs from the\\ninside out. For other sources, infrared diagnostics are lacking, so that the\\nsituation is less clear. It would be great if chemistry could help to tie down\\nthe time scales of the various phases.\\n\\\\end{answer}\\n\\n\\\\begin{question}{W.\\\\ Irvine}\\nHow do you interpret the behavior of the PAH features as a function of\\nevolutionary stage in the sources that you discussed?\\n\\\\end{question}\\n\\n\\\\begin{answer}{E.F.\\\\ van Dishoeck}\\nThe absence of PAH features in the early embedded stage can be due either\\nto a lack of ultraviolet radiation to excite the features or to an absence\\nof the carriers. Manske \\\\& Henning (1999, A\\\\&A 349, 907) have argued \\nfor the case of Herbig Ae/Be stars that\\nthere should be sufficient radiation to excite PAHs in the envelope/disk\\nsystem,\\nso that the lack is likely due to the absence of the PAHs\\nthemselves. Perhaps the PAHs have accreted into the icy mantles at the\\nhigh densities in the inner envelope and do not evaporate\\nand/or are chemically transformed into\\nother more refractory species on grains. Alternatively, the region producing\\nultraviolet radiation (H~II region) may be very small \\nin these massive objects, and the photons may not reach the PAH-rich\\nmaterial or have a very small beam filling factor.\\nOnce the envelope breaks up and\\nultraviolet radiation can escape to the less dense\\nouter envelope, the PAH features from those\\nregions will appear in spectra taken with large beams.\\n\\\\end{answer}\\n\\n\\\\begin{question}{T.\\\\ Geballe}\\nYou said that there is little evidence of the effect of ultraviolet radiation\\non solid-state chemistry. Isn't the 4.6 $\\\\mu$m XCN feature a good example\\nof that influence?\\n\\\\end{question}\\n\\n\\\\begin{answer}{E.F.\\\\ van Dishoeck}\\nThe `XCN' feature is indeed the best candidate for tracing the \\nultraviolet processing\\nof ices. If ascribed to OCN$^-$, it likely involves HNCO as\\na precursor. In the laboratory, HNCO is produced by photochemical\\nreactions of CO and NH$_3$, but in the interstellar medium grain surface\\nchemistry is an alternative possibility which does not necessarily\\ninvolve ultraviolet radiation (see Ehrenfreund \\\\& Schutte,\\nthis volume). \\n\\\\end{answer}\\n\\n\\\\begin{question}{Y.C.\\\\ Minh}\\nDo you have an explanation of the low and constant abundances of CO$_2$\\nin the gas phase?\\n\\\\end{question}\\n\\n\\\\begin{answer}{E.F.\\\\ van Dishoeck}\\nCharnley \\\\& Kaufman (2000, ApJ, 529, L111) argue that the evaporated CO$_2$ is\\ndestroyed by reactions with atomic hydrogen at high temperatures in shocks.\\nThis is an interesting suggestion, but needs to be tested against other\\nspecies such as H$_2$O and H$_2$S which can be destroyed by\\nreactions with atomic hydrogen as well. Also, the amount of material \\nin the envelope that can be affected by shocks is not clear.\\n\\\\end{answer}\\n\\n\\\\end{document}\\n\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":98,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002099"},"title":{"kind":"string","value":"Geodetic Precession and the Binary Pulsar B1913+16"},"authors":{"kind":"list like","value":[{"author":"A. Karastergiou"},{"author":"M. Kramer"},{"author":"N. Wex"},{"author":"A. von Hoensbroech"}],"string":"[\n {\n \"author\": \"A. Karastergiou\"\n },\n {\n \"author\": \"M. Kramer\"\n },\n {\n \"author\": \"N. Wex\"\n },\n {\n \"author\": \"A. von Hoensbroech\"\n }\n]"},"abstract":{"kind":"string","value":"A change of the component separation in the profiles of the binary pulsar PSR B1913+16 has been observed for the first time (Kramer 1998) as expected by geodetic precession. In this work we extend the previous work by accounting for recent data from the Effelsberg 100-m telescope and Arecibo Observatory and testing model predictions. We demonstrate how the new information will provide additional information on the solutions of the system geometry."},"latex":{"kind":"list like","value":[{"name":"contrib1.tex","string":"\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Karastergiou, Kramer, Wex \\& von Hoensbroech}\n{Geodetic Precession and the Binary Pulsar B1913+16}\n\\pagestyle{myheadings}\n\\nofiles\n\n\\begin{document}\n\\title{Geodetic Precession and the Binary Pulsar B1913+16}\n\\author{A. Karastergiou, M. Kramer, N. Wex, A. von Hoensbroech}\n\\affil{\nMax Planck Institut f\\\"ur Radioastronomie, Auf dem H\\\"ugel 69, 53121 Bonn, Germany\n}\n\\begin{abstract}\nA change of the component separation in the profiles of the binary pulsar PSR B1913+16\nhas been observed for the first time (Kramer 1998) as\nexpected by geodetic precession.\nIn this work we extend the previous work by accounting\nfor recent data from the Effelsberg 100-m telescope and Arecibo Observatory\nand testing model predictions. We demonstrate how the new information will provide additional\ninformation on the solutions of the system geometry.\n\\end{abstract}\n\n\\vspace{-3ex}\n\n\\section{Introduction}\n\nThe binary pulsar PSR B1913+16 exhibits\na measurable amount of geodetic precession due to a misalignment of its\nspin axis and orbital angular momentum (relativistic spin orbit coupling) by an angle $\\delta$\n(see also Stairs et al., for geodetic precession in PSR B1534+12).\nThe angle between the line of sight and the spin axis, $\\zeta$, changes according to:\n\\begin{displaymath}\n\\cos\\zeta(t) = -\\cos\\delta\\cos i\n +\\sin\\delta\\sin i \\cos \\Omega_{{\\rm prec}} (t-T_0) \\;,\n\\end{displaymath}\nwhere $i$ is the orbital inclination of the binary system.\nGeneral Relativity (GR) predicts a rate of precession $\\Omega_{{\\rm prec}}=1.21$ deg yr$^{-1}$,\nleading to a change in the pulse profile and polarization characteristics with time.\n\\\\\nPrevious observations by Weisberg, Romani and Taylor (1989) detected\na change in the relative amplitude of the trailing and leading component, but no\nchange in the component separation. Also, there were no\nchanges in the position angle swing of the linear polarization noted (Cordes, Wasserman \\&\nBlaskiewicz 1990).\n\n\\section{Recent Observations Cast Some Light}\n\nThe evolution of the observed radio pulse profile of PSR B1913+16 would be\ndetermined when the four parameters\n$\\alpha, \\delta, \\rho, T_{0}$ were specified for a given $i$, where\n%\\begin{description}\n$\\alpha$ is the angle between the magnetic pole and the spin axis,\n$\\delta$ is as mentioned above,\n$\\rho$ is the angular radius of the emission cone and\n$T_{0}$ the epoch of precession.\n%\\end{description}\n\\nopagebreak\nBased on recent data from the Effelsberg 100-m telescope, Kramer (1998) first noticed a\nchange in the component separation $W$. This allows a solution region in parametric space\nthat respects GR and the\n{\\bf{\\underline{hollow cone model} (HCM)}}.\n\\begin{displaymath}\n W(t) = 2\\arccos\\left[\\frac{\\cos\\rho - \\cos\\alpha \\cos\\zeta(t)}\n {\\sin\\alpha \\sin\\zeta(t)}\\right] \n\\end{displaymath}\nEffelsberg polarization data has been used\nin respect with the \\underline{\\bf rotating vector} \\\\ \\underline{\\bf model} {\\bf(RVM)},\nto further narrow down the solution region.\n\\begin{displaymath}\n \\psi(t) = \\arctan\\left[\\frac{\\sin\\alpha\\sin(\\phi-\\phi_0)}\n {\\cos\\alpha \\sin\\zeta(t) - \\sin\\alpha\\cos\\zeta(t)}\\right] \\quad + const. \n\\end{displaymath}\n\nThe inclination of the binary orbit with respect to the line-of-sight, $i$,\nis known from timing observations modulo the ambiguity\n$i\\longrightarrow 180^\\circ - i$. The possibilities are:\nCase A: $i= 47.2^\\circ$, Case B: $i= 132.8^\\circ$ \n\n\\vspace{-2ex}\n\n\\section{The Solution Today}\n\n%\\parbox[t]{6cm}{\n\\begin{figure}[h]\n\\centerline{\n%\\hspace*{-1cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsffile{fig.eps}\n%\\caption{The solutions for $\\alpha$ and $\\delta$ are found in the unshaded regions\n%within the areas confined by the black curves and the bounding box}\n\\hspace{0.25cm}\n\\parbox[b]{6cm}{\\sloppy\nFigure 1. {\\small The pulse component separation data (Effelsberg + Arecibo) in conjunction with the HCM\nwas used to produce a $\\chi^{2}$ area plot indicating the $3\\sigma$ confidence level\nsolutions for $\\alpha$ and $\\delta$, areas inside the surfaces traced by the black lines.\nAll possible solutions were then fed into the RVM to produce\nposition angle curves, which were compared to Effelsberg polarization data,\nonly allowing for solutions in the unshaded areas. So, the solution must be located on\na black surface\ninside an unshaded region (for detailed explanation of this figure check out \n{\\it http://www.mpifr-bonn.mpg.de/staff/akara/psr1913})\n}}}\n\\end{figure}\n\nThe set of plausible solutions has been well limited, as shown in Fig 1.\nThe inclination of the binary orbit is most likely to be Case B rather than Case A (Wex, Kalogera, Kramer\n2000). More precise use of the polarization data plus a molding of the\ntwo models (HCM \\& RVM) to specifically suit PSR B1913+16\n(see also Weisberg \\& Taylor in these proceedings)\ncould further limit the solutions and\nenable a prediction on the future of this system.\n\n\\vspace{-2ex}\n\n\\begin{references}\n\\vspace{-2ex}\n\\reference\nCordes,~J.M., Wasserman,~I., \\& Blaskiewicz,~M. 1990, \\apj, 349, 546\n\n\\reference\nDamour,~T., \\& Ruffini,~R. 1974, Acad. Sci. Paris, 279, s\\'erie A, 971\n\n\\reference\nDamour,~T., \\& Taylor,~J.H. 1992, Phys. Rev. D, 45, 1840\n\n\\reference\nHulse,~R.A., \\& Taylor,~J.H. 1975, \\apj, 195, L51\n\n\\reference\nKramer,~M. 1998, \\apj, 509, 856\n\n\\reference\nTaylor,~J.H. 1999, Proceedings of the XXXIV'th Rencontres de Moriond, to be published\n\n\\reference\nWeisberg,~J.M., Romani,~R., \\& Taylor,~J.H. 1989, \\apj, 347, 1029\n\n\\reference\nWex,~N., Kalogera,~V., Kramer,~M. 2000, \\apj, 528, 401\n\n\\end{references}\n\n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"contrib1.tex\",\n \"string\": \"\\\\documentstyle[11pt,newpasp,twoside,epsf]{article}\\n\\\\markboth{Karastergiou, Kramer, Wex \\\\& von Hoensbroech}\\n{Geodetic Precession and the Binary Pulsar B1913+16}\\n\\\\pagestyle{myheadings}\\n\\\\nofiles\\n\\n\\\\begin{document}\\n\\\\title{Geodetic Precession and the Binary Pulsar B1913+16}\\n\\\\author{A. Karastergiou, M. Kramer, N. Wex, A. von Hoensbroech}\\n\\\\affil{\\nMax Planck Institut f\\\\\\\"ur Radioastronomie, Auf dem H\\\\\\\"ugel 69, 53121 Bonn, Germany\\n}\\n\\\\begin{abstract}\\nA change of the component separation in the profiles of the binary pulsar PSR B1913+16\\nhas been observed for the first time (Kramer 1998) as\\nexpected by geodetic precession.\\nIn this work we extend the previous work by accounting\\nfor recent data from the Effelsberg 100-m telescope and Arecibo Observatory\\nand testing model predictions. We demonstrate how the new information will provide additional\\ninformation on the solutions of the system geometry.\\n\\\\end{abstract}\\n\\n\\\\vspace{-3ex}\\n\\n\\\\section{Introduction}\\n\\nThe binary pulsar PSR B1913+16 exhibits\\na measurable amount of geodetic precession due to a misalignment of its\\nspin axis and orbital angular momentum (relativistic spin orbit coupling) by an angle $\\\\delta$\\n(see also Stairs et al., for geodetic precession in PSR B1534+12).\\nThe angle between the line of sight and the spin axis, $\\\\zeta$, changes according to:\\n\\\\begin{displaymath}\\n\\\\cos\\\\zeta(t) = -\\\\cos\\\\delta\\\\cos i\\n +\\\\sin\\\\delta\\\\sin i \\\\cos \\\\Omega_{{\\\\rm prec}} (t-T_0) \\\\;,\\n\\\\end{displaymath}\\nwhere $i$ is the orbital inclination of the binary system.\\nGeneral Relativity (GR) predicts a rate of precession $\\\\Omega_{{\\\\rm prec}}=1.21$ deg yr$^{-1}$,\\nleading to a change in the pulse profile and polarization characteristics with time.\\n\\\\\\\\\\nPrevious observations by Weisberg, Romani and Taylor (1989) detected\\na change in the relative amplitude of the trailing and leading component, but no\\nchange in the component separation. Also, there were no\\nchanges in the position angle swing of the linear polarization noted (Cordes, Wasserman \\\\&\\nBlaskiewicz 1990).\\n\\n\\\\section{Recent Observations Cast Some Light}\\n\\nThe evolution of the observed radio pulse profile of PSR B1913+16 would be\\ndetermined when the four parameters\\n$\\\\alpha, \\\\delta, \\\\rho, T_{0}$ were specified for a given $i$, where\\n%\\\\begin{description}\\n$\\\\alpha$ is the angle between the magnetic pole and the spin axis,\\n$\\\\delta$ is as mentioned above,\\n$\\\\rho$ is the angular radius of the emission cone and\\n$T_{0}$ the epoch of precession.\\n%\\\\end{description}\\n\\\\nopagebreak\\nBased on recent data from the Effelsberg 100-m telescope, Kramer (1998) first noticed a\\nchange in the component separation $W$. This allows a solution region in parametric space\\nthat respects GR and the\\n{\\\\bf{\\\\underline{hollow cone model} (HCM)}}.\\n\\\\begin{displaymath}\\n W(t) = 2\\\\arccos\\\\left[\\\\frac{\\\\cos\\\\rho - \\\\cos\\\\alpha \\\\cos\\\\zeta(t)}\\n {\\\\sin\\\\alpha \\\\sin\\\\zeta(t)}\\\\right] \\n\\\\end{displaymath}\\nEffelsberg polarization data has been used\\nin respect with the \\\\underline{\\\\bf rotating vector} \\\\\\\\ \\\\underline{\\\\bf model} {\\\\bf(RVM)},\\nto further narrow down the solution region.\\n\\\\begin{displaymath}\\n \\\\psi(t) = \\\\arctan\\\\left[\\\\frac{\\\\sin\\\\alpha\\\\sin(\\\\phi-\\\\phi_0)}\\n {\\\\cos\\\\alpha \\\\sin\\\\zeta(t) - \\\\sin\\\\alpha\\\\cos\\\\zeta(t)}\\\\right] \\\\quad + const. \\n\\\\end{displaymath}\\n\\nThe inclination of the binary orbit with respect to the line-of-sight, $i$,\\nis known from timing observations modulo the ambiguity\\n$i\\\\longrightarrow 180^\\\\circ - i$. The possibilities are:\\nCase A: $i= 47.2^\\\\circ$, Case B: $i= 132.8^\\\\circ$ \\n\\n\\\\vspace{-2ex}\\n\\n\\\\section{The Solution Today}\\n\\n%\\\\parbox[t]{6cm}{\\n\\\\begin{figure}[h]\\n\\\\centerline{\\n%\\\\hspace*{-1cm}\\n\\\\epsfxsize=7cm\\n\\\\epsfysize=7cm\\n\\\\epsffile{fig.eps}\\n%\\\\caption{The solutions for $\\\\alpha$ and $\\\\delta$ are found in the unshaded regions\\n%within the areas confined by the black curves and the bounding box}\\n\\\\hspace{0.25cm}\\n\\\\parbox[b]{6cm}{\\\\sloppy\\nFigure 1. {\\\\small The pulse component separation data (Effelsberg + Arecibo) in conjunction with the HCM\\nwas used to produce a $\\\\chi^{2}$ area plot indicating the $3\\\\sigma$ confidence level\\nsolutions for $\\\\alpha$ and $\\\\delta$, areas inside the surfaces traced by the black lines.\\nAll possible solutions were then fed into the RVM to produce\\nposition angle curves, which were compared to Effelsberg polarization data,\\nonly allowing for solutions in the unshaded areas. So, the solution must be located on\\na black surface\\ninside an unshaded region (for detailed explanation of this figure check out \\n{\\\\it http://www.mpifr-bonn.mpg.de/staff/akara/psr1913})\\n}}}\\n\\\\end{figure}\\n\\nThe set of plausible solutions has been well limited, as shown in Fig 1.\\nThe inclination of the binary orbit is most likely to be Case B rather than Case A (Wex, Kalogera, Kramer\\n2000). More precise use of the polarization data plus a molding of the\\ntwo models (HCM \\\\& RVM) to specifically suit PSR B1913+16\\n(see also Weisberg \\\\& Taylor in these proceedings)\\ncould further limit the solutions and\\nenable a prediction on the future of this system.\\n\\n\\\\vspace{-2ex}\\n\\n\\\\begin{references}\\n\\\\vspace{-2ex}\\n\\\\reference\\nCordes,~J.M., Wasserman,~I., \\\\& Blaskiewicz,~M. 1990, \\\\apj, 349, 546\\n\\n\\\\reference\\nDamour,~T., \\\\& Ruffini,~R. 1974, Acad. Sci. Paris, 279, s\\\\'erie A, 971\\n\\n\\\\reference\\nDamour,~T., \\\\& Taylor,~J.H. 1992, Phys. Rev. D, 45, 1840\\n\\n\\\\reference\\nHulse,~R.A., \\\\& Taylor,~J.H. 1975, \\\\apj, 195, L51\\n\\n\\\\reference\\nKramer,~M. 1998, \\\\apj, 509, 856\\n\\n\\\\reference\\nTaylor,~J.H. 1999, Proceedings of the XXXIV'th Rencontres de Moriond, to be published\\n\\n\\\\reference\\nWeisberg,~J.M., Romani,~R., \\\\& Taylor,~J.H. 1989, \\\\apj, 347, 1029\\n\\n\\\\reference\\nWex,~N., Kalogera,~V., Kramer,~M. 2000, \\\\apj, 528, 401\\n\\n\\\\end{references}\\n\\n\\\\end{document}\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":99,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002100"},"title":{"kind":"string","value":"Reionization of the Universe and the Photoevaporation of Cosmological Minihalos"},"authors":{"kind":"list like","value":[{"author":"Alejandro C. Raga \\affil{Instituto de Astronom\\'{\\i}a, Universidad Nacional Aut\\'onoma de M\\'exico}"}],"string":"[\n {\n \"author\": \"Alejandro C. Raga \\\\affil{Instituto de Astronom\\\\'{\\\\i}a, Universidad Nacional Aut\\\\'onoma de M\\\\'exico}\"\n }\n]"},"abstract":{"kind":"string","value":"The first sources of ionizing radiation to condense out of the dark and neutral IGM sent ionization fronts sweeping outward through their surroundings, overtaking other condensed objects and photoevaporating them. This feedback effect of universal reionization on cosmic structure formation is demonstrated here for the case of a cosmological minihalo of dark matter and baryons exposed to an external source of ionizing radiation with a quasar-like spectrum, just after the passage of the global ionization front created by the source. We model the pre-ionization minihalo as a truncated, nonsingular isothermal sphere in hydrostatic equilibrium following its collapse out of the expanding background universe and virialization. Results are presented of the first gas dynamical simulations of this process, including radiative transfer. A sample of observational diagnostics is also presented, including the spatially-varying ionization levels of C, N, and O in the flow if a trace of heavy elements is present and the integrated column densities of H~I, He~I and II, and C~IV thru the photoevaporating gas at different velocities which would be measured in absorption against a background source like that responsible for the ionization."},"latex":{"kind":"list like","value":[{"name":"shapiro.tex","string":"\\documentclass[proceedings]{rmaa}\n%%\n%% The file `rmaa.cls' should be somewhere in your TeX search path\n%% (e.g, in the current directory, or in a personal or system-wide\n%% directory of LaTeX packages. \n%%\n%% This will not work with old versions of LaTeX: any version\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\n%% complains that it doesn't recognise the command `\\documentclass'\n%% then your LaTeX installation needs updating!\n\n%% The following package allows one to do the citations\n%% semi-automatically. It defines the commands \\cite{KEY},\n%% \\scite{KEY}, and \\pcite{KEY} which respectively produce citations\n%% in the following styles: \n%% (AUTHOR YEAR)\n%% AUTHOR (YEAR)\n%% AUTHOR YEAR\n%% For this to work, you need to pay attention to the formatting of\n%% the `\\bibitem's in your `thebibliography ' environment, qv.\n\\usepackage{rmaacite}\n%% If you would rather do your citations by hand, then comment out the \n%% above line\n\n%% Here, you can put the definitions of your own personal macros.\n%% All the special commands defined in AASTEX 4.0 (e.g. \\ion{}{},\n%% \\gtrsim, \\arcsec, \\apj, etc) are already defined. I haven't checked \n%% if there are any new ones in AASTEX 5.0 yet. \n\\newcommand{\\thOr}{$\\theta^1\\,$C~Ori}\n\\newcommand{\\zero}{_0}\n\\newcommand{\\kms}{\\,\\mbox{km s$^{-1}$}}\n\\newcommand{\\Othree}{[\\ion{O}{3}]~5007\\AA}\n\\renewcommand{\\P}[1]{%\n\\ifnum#1=1\\hbox{OW~168--326E}\\fi\n\\ifnum#1=2\\hbox{OW~167--317}\\fi\n\\ifnum#1=3\\hbox{OW~163--317}\\fi\n\\ifnum#1=5\\hbox{OW~158--323}\\fi\n\\ifnum#1=0\\hbox{OW~171--334}\\fi}\n\n%%\n%% The following commands specify the title, authors etc\n%%\n\\title{Reionization of the Universe and the Photoevaporation of Cosmological\nMinihalos}\n\\author{Paul R. Shapiro \\affil{Department of Astronomy, The University of Texas at Austin, USA} \\and Alejandro C. Raga \\affil{Instituto de Astronom\\'{\\i}a, Universidad Nacional Aut\\'onoma de M\\'exico}}\n%\\author{Paul R. Shapiro \\altaffilmark{1} and Alejandro C. Raga \\altaffilmark{2}}\n%% \\affil{Instituto de Astronom\\'{\\i}a, UNAM, Morelia} }\n%\\altaffiltext{1}{Department of Astronomy, The University of Texas at Austin,\n%Austin, TX 78712 USA}\n%\\altaffiltext{2}{Instituto de Astronom\\'{\\i}a, UNAM, Mexico D.F., Mexico}\n%% Note that the \\affil{} command is inside the argument of the\n%% \\author{} command and that a short version of the address should go \n%% here. More complicated author/address examples are discussed in the \n%% Author Guide (`rmuser.tex') and illustrated in the example document\n%% `rmtest.tex' \n\n%% The full postal addresses are specified here - they will be typeset \n%% at the end of the article. Here is also the place to put email\n%% addresses. \n\\fulladdresses{\n\\item P. R. Shapiro: Department of Astronomy, University of Texas, Austin,\nTX 78712, USA (shapiro@astro.as.utexas.edu)\n\\item A. C. Raga: Instituto de Astronom\\'\\i a,\n UNAM, Apartado Postal 70-264, 04510 M\\'exico D. F.,\nM\\'exico (raga@astroscu.unam.mx)\n}\n%% Note that the `\\fulladdresses' command defines a list-like\n%% environment, so each separate address must be preceded by the\n%% `\\item' command (here there is only one, since the authors share the \n%% same address). \n\n%% Title/author for running headers\n\\shortauthor{Shapiro \\& Raga}\n\\shorttitle{Reionization and photoevaporation}\n%% These will automatically be converted to upper case in the current\n%% style. \n\n%% No more than 5 keywords, chosen from the standard list\n\\keywords{cosmology: theory --- galaxies: formation --- hydrodynamics ---\nintergalactic medium}\n\n%% The abstract:\n\n\\resumen{Las primeras fuentes de radiaci\\'on ionizante que se\n condensaron del IGM generaron frentes de ionizaci\\'on en sus\n alrededores, que iluminaron a otros objetos condensados y los\n fotoevaporaron. Mostramos la retroalimentaci\\'on causada por la\n reionizaci\\'on del Universo en la formaci\\'on de estructuras\n c\\'osmicas para el caso de un mini halo de materia oscura y bariones,\n ionizado por una fuente externa con un espectro similar al de los\n cu\\'asares, justo despu\\'es del paso del frente de ionizaci\\'on\n generado por la fuente. El mini halo es modelado, siguiendo su\n condensaci\\'on del gas en expansi\\'on as\\'{\\i} como su\n virializaci\\'on, como una esfera isot\\'ermica en equilibrio\n hidrost\\'atico. Se presentan los resultados de la primera simulaci\\'on\n hidrodin\\'amica del proceso incluyendo transferencia radiativa.\n Tambi\\'en se dan ejemplos de diagn\\'osticos observacionales,\n incluyendo la distribuci\\'on espacial del grado de ionizaci\\'on en\n el flujo de C, N y O si existen trazas de estos elementos en la\n densidad columnar integrada de H~I, He~I y II, as\\'{\\i} como el C~IV\n a diferentes velocidades en el gas fotoevaporado, que podr\\'{\\i}a\n ser observado en absorci\\'on en contra de la fuente de\n ionizaci\\'on.}\n\n\\abstract{ \nThe first sources of ionizing radiation to condense out of the dark and\nneutral IGM sent ionization fronts sweeping outward through their\nsurroundings, overtaking other condensed objects and photoevaporating them.\nThis feedback effect of universal reionization on cosmic structure \nformation is demonstrated here for the case of a cosmological minihalo of\ndark matter and baryons exposed to an external source of ionizing radiation\nwith a quasar-like spectrum, just after the passage of the global \nionization front created by the source. We model the pre-ionization\nminihalo as a truncated, nonsingular isothermal sphere in hydrostatic\nequilibrium following its collapse out of the expanding background universe\nand virialization. Results are presented of the first gas dynamical\nsimulations of this process,\nincluding radiative transfer. A sample of observational diagnostics is\nalso presented, including the spatially-varying ionization levels\nof C, N, and O in the flow if a trace of heavy elements is present and the \nintegrated column densities of H~I, He~I and II, and C~IV thru the \nphotoevaporating gas at different velocities which would be measured in\nabsorption against a background source like that responsible for the\nionization. }\n%% If your spanish is up to it, you may want to supply the resumen by\n%% uncommenting the following line:\n%\\resumen{Versi\\'on espa\\~nol del ``abstract''}\n%% Alternatively, you can leave the translation to the editors. \n\n\n%% This command is so LaTeX won't stop on errors. I've put it in so\n%% you will still be able to compile the file even if you have lost\n%% the associated PS files of the figures. \n\\nonstopmode\n\n%% The following command is necessary before beginning the text of\n%% your article. There should be a matching \\end{document} at the end\n%% of the file. \n\\begin{document}\n\n%% This command is necessary to typeset the title, abstract, etc. \n\\maketitle\n\n%%\n%% And here starts the text....\n%%\n\\section{Introduction}\n\\label{sec:intro}\nObservations of quasar absorption spectra indicate that the universe\nwas reionized prior to redshift $z=5$. Recent detections of H Lyman alpha\nemission lines from sources at even higher redshift ($z\\leq5.6$) strengthen\nthis conclusion \\cite{Hu98,Wey98}. As new discoveries push the observable\n horizon back in time ever-closer to the epoch of reionization at redshift \n$z>5$, increased awareness of its importance as a missing link in the \ntheory of galaxy formation has caused a great renewal of interest in\nuniversal reionization. If reionization took place early enough, then\nThompson scattering of cosmic microwave background (CMB) photons by free\nelectrons in an ionized intergalactic medium (IGM) would \nalso have left a detectable imprint on\nthe CMB observed today. Recent data on the first Doppler peak in\nthe angular spectrum of CMB anisotropy set limits which imply a \nreionization redshift $z\\lesssim40$ (model-dependent) \\cite{Gri98}.\n(For a review and references on reionization work prior to 1996,\nthe reader is referred to Shapiro 1995, while more recent developments are\nsummarized in Haiman \\& Knox 1999.)\n\nA review of the theory of reionization is outside the scope of this\nbrief report. In keeping with the focus of this meeting, I will\nconfine myself to a description of some recent progress on the\ncalculational side of the problem. To solve the full reionization\nproblem we must also solve the problem of how density fluctuations\nled to galaxy formation and this, in turn, led to secondary energy\nrelease in the form of ionizing and dissociating radiation by the\nstars and quasars formed inside early galaxies, as well as other forms of \nenergy release like supernova explosions, jets and winds, which in turn \ninfluenced the future course of galaxy formation. The modern context for\nthis description is the Cold Dark Matter (CDM) model, in which\na cold, pressure-free,\ncollisionless gas of dark matter dominates the\nmatter density and structure arises from the gravitational amplification of\na scale-free power-spectrum of\ninitially small-amplitude, Gaussian-random-noise primordial density\nfluctuations, in a hierarchical fashion, with small mass objects collapsing\nout first and merging together to form larger-mass objects which\nform later. The calculation of these effects poses an enormous multi-scale \ncomputational challenge, involving numerical gas dynamics coupled to \ngravitational N-body dynamics, which raises the bar of cosmological \nsimulation considerably by adding the requirement that radiative transfer\neffects be included, as well. To simplify matters,\nI will henceforth focus on just one of the central challenges of\nreionization theory, the effect of cosmological ionization fronts.\n\n\\section{Ionization Fronts in the IGM} \n\\label{sec:constraints}\n\nThe neutral, opaque IGM\nout of which the first bound objects condensed was dramatically reheated\nand reionized at some time between a redshift $z\\approx50$ and $z\\approx5$\nby the radiation released by some of these objects.\nAn early analysis of the inhomogeneous nature of reionization for the case\nof short-lived quasars occurring at random positions in a uniform\nIGM was described by Arons \\& Wingert (1972). In that treatment it was\nassumed that each quasar was instantaneously surrounded by an isolated \nH~II region, a ``relict H~II region'' undergoing recombination only, each\nsuch region filling\na volume containing just as many initially neutral H atoms as there were\nionizing photons emitted by the QSO during its lifetime. The effect\nof successive generations of QSO's was accounted for on a \nstatistically-averaged basis by allowing new generations of QSO's to turn \non at random positions, including those inside pre-existing relict H~II\nregions before their H atoms had fully recombined, leading eventually to \nthe complete overlap of these discrete ionized zones.\n\nWhen the first sources\nturned on, they actually\nionized their surroundings, not instantaneously, but\nrather by propagating weak, R-type\nionization fronts which moved outward supersonically with respect to both\nthe neutral gas ahead of and the ionized gas behind the front, racing ahead\nof the hydrodynamical response of the IGM, as first described by \nShapiro (1986) and Shapiro \\& Giroux (1987). These authors solved the\nproblem of the time-varying radius of a spherical I-front which surrounds \nisolated sources in a cosmologically-expanding IGM analytically, taking\nproper account of the I-front jump condition generalized to cosmological\nconditions. They applied these solutions to determine when the I-fronts\nsurrounding isolated sources would grow to overlap and, thereby,\ncomplete the reionization of the universe\n(Donahue \\& Shull 1987 and Meiksen \\& Madau 1993\nsubsequently adopted a similar approach to answer that question).\nThe effect of density inhomogeneity on the rate of I-front propagation\nwas described by a mean ``clumping factor'' $c_l>1$, which\nslowed the I-fronts by increasing the average recombination rate per H atom\ninside clumps. This suffices to describe the rate of I-front propagation\nas long as the\nclumps are either not self-shielding or, if so, only\nabsorb a fraction of the ionizing photons emitted by the central source. \nNumerical radiative transfer methods are currently under\ndevelopment to solve this problem in 3D for the inhomogeneous density \ndistribution which arises as cosmic structure forms, so far limited to a \nfixed density field without gas dynamics (e.g.\\ Abel, Norman, \\& Madau 1999;\nRazoumov \\& Scott 1999). The question of what\ndynamical effect the I-front had on the density inhomogeneity it\nencountered, however, requires further analysis. \n\n\nThe answer depends on the size and density of the clumps overtaken by\nthe I-front. The fate of linear density fluctuations depends upon\ntheir Jeans number, $L_J\\equiv\\lambda/\\lambda_J$, the wavelength in\nunits of the baryon Jeans length in the IGM at temperatures of order\n$10^4\\rm K$. Fluctuations with $L_J<1$ find their growth halted and\nreversed (cf.\\ Shapiro, Giroux, \\& Babul 1994). For nonlinear density\nfluctuations, however, the answer is more complicated, depending upon\nat least three dimensionless parameters, their internal Jeans number,\n$L_J\\equiv R_c/\\lambda_J$, the ratio of the cloud radius $R_c$ to the\nJeans length $\\lambda_J$ inside the cloud at about $10^4{\\rm K}$,\ntheir ``Str\\\"omgren number'' $L_s\\equiv 2 R_c/\\ell_s$, the ratio of\nthe cloud diameter $2R_c$ to the Str\\\"omgren length $\\ell_s$ inside\nthe cloud (the length of a column of gas within which the unshielded\narrival rate of ionizing photons just balances the total recombination\nrate), and their optical depth to H ionizing photons at 13.6 eV,\n$\\tau_{\\rm H}$, before ionization. If $\\tau_{\\rm H}<1$, the I-front\nsweeps across the cloud, leaving an ionized gas at higher pressure\nthan its surroundings, and exits before any mass motion occurs in\nresponse, causing the cloud to blow apart. If $\\tau_{\\rm H}>1$ and\n$L_s>1$, however, the cloud shields itself against ionizing photons,\ntrapping the I-front which enters the cloud, causing it to decelerate\ninside the cloud to the sound speed of the ionized gas before it can\nexit the other side, thereby transforming itself into a weak, D-type\nfront preceded by a shock. Typically, the side facing the source\nexpels a supersonic wind backwards towards the source, which shocks\nthe IGM outside the cloud, while the remaining neutral cloud material\nis accelerated away from the source by the so-called ``rocket effect''\nas the cloud photoevaporates (cf.\\ Spitzer 1978). As long as $L_J<1$\n(the case for gas bound to dark halos with virial velocity less than\n$\\rm 10\\,km\\,s^{-1}$), this photoevaporation proceeds unimpeded by\ngravity. For halos with higher virial velocity, however, $L_J>1$, and\ngravity competes with pressure forces. For a uniform gas of H density\n$n_{\\rm H,c}$, located a distance $r_{\\rm Mpc}$ (in Mpc) from a UV\nsource emitting $N_{\\rm ph,56}$ ionizing photons (in units of\n$\\rm10^{56}s^{-1}$), the Str\\\"omgren length is only\n$\\ell_s\\cong(100\\,{\\rm pc}) (N_{\\rm ph,56}/r_{\\rm Mpc}^2)(n_{\\rm\n H,c}/0.1\\,\\rm cm^{-3})^{-2}$. We focus in what follows on the\nself-shielded case which traps the I-front.\n \n\\section{The Photoevaporation of Dwarf Galaxy Minihalos\nOvertaken by a Cosmological Ionization Front}\n\\label{sec:anal}\n\n\n\n\n\nThe importance of this photoevaporation process has long been\nrecognized in the study of interstellar clouds exposed to ionizing\nstarlight (e.g. Oort \\& Spitzer 1955;\nSpitzer 1978; Bertoldi 1989; Bertoldi \\& McKee 1990;\nLefloch \\& Lazareff 1994; Lizano et al.\\ 1996). Radiation-hydrodynamical \nsimulations were performed in 2D in the early 1980's of\na stellar I-front overtaking a clump inside a molecular\ncloud (Sandford, Whitaker, \\& Klein 1982; Klein, Sandford, \\& Whitaker 1983).\nMore recently, 2D simulations for the case of circumstellar clouds\nionized by a single nearby star have also been performed\n(Mellema et al.\\ 1998). In the cosmological context, however,\nthe importance of this process has only recently been fully appreciated. \nIn proposing the expanding minihalo model to explain Lyman alpha\nforest (``LF'') quasar absorption lines, Bond, Szalay, \\& Silk (1988)\ndiscussed how gas originally confined by the gravity of dark\nminihalos in the CDM model would be expelled by pressure forces\nif photoionization by ionizing background radiation suddently\nheated all the gas to an isothermal condition at $T\\approx10^4\\rm K$.\nThe first radiation-hydrodynamical \nsimulations of the photoevaporation of a primordial density\ninhomogeneity overtaken by a cosmological I-front, however,\nwere described in Shapiro, Raga, \\& Mellema (1997, 1998).\nBarkana \\& Loeb (1999) subsequently considered the relative\nimportance of this process for dwarf galaxy minihalos of different masses\nin the CDM model, using static models of uniformly-illuminated spherical\nclouds in thermal and ionization equilibrium, taking H atom self-shielding\ninto account, and assuming that gas which is heated above the minihalo\nvirial temperature must be evaporated. They concluded that 50\\%--90\\% of \nthe gas in gravitationally bound objects when reionization\noccurred should have been evaporated.\n\\begin{figure}[h]\n\\parbox{0.5\\textwidth}{\n \\includegraphics[height=6.8cm]{shapiro_fig1.ps}}\n \\label{fig1}\n\\begin{minipage}{0.45\\textwidth}\n \\caption{MINIHALO INITIAL CONDITIONS BEFORE REIONIZATION:\nTruncated, nonsingular isothermal sphere (TIS) of gas and dark matter in\nhydrostatic equilibrium (Shapiro, Iliev, \\& Raga 1999) surrounded by the\ncorresponding self-similar spherical infall for an Einstein-de Sitter\nbackground universe (cf.\\ Bertschinger 1985). (a) (Top) gas density and (b)\n(Bottom) gas velocity versus distance from minihalo center.}\n\\end{minipage}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\parbox{0.5\\textwidth}{%\n \\includegraphics[height=7cm]{shapiro_fig2.ps}}\n \\label{fig2}\n\\begin{minipage}{0.45\\textwidth}\n \\caption{IONIZATION FRONT PHOTOEVAPORATES MINIHALO:\n(a) (Top) I-front position along $x$-axis versus time; (b) (Bottom) Mass\nfraction of the initial mass $M_{\\rm I}$ of minihalo hydrostatic \n core which remains neutral (H~I) versus time. }\n\\end{minipage}\n\\end{figure}\n\n\\begin{figure}[h]\n \\begin{center}\n \\leavevmode\n \\includegraphics[width=\\textwidth]{shapiro_fig3.ps}\n \\caption{PHOTOEVAPORATING MINIHALO.\n50 Myr after turn-on of quasar 1 Mpc to the left of computational box along\nthe $x$-axis. \n(a) (Upper Panel) isocontours of atomic density, logarithmically spaced, \nin $(r,x)-$plane of cylindrical coordinates; (b) (Lower Panel)\nvelocity arrows are plotted with length proportional to gas velocity.\nAn arrow of length equal to the spacing between arrows has velocity\n$30 \\kms$. Solid line shows current extent of gas originally in\nhydrostatic core. Dashed line is I-front (50\\% H-ionization contour).}\n \\label{fig3}\n \\end{center}\n\\end{figure}\n\n\\begin{figure}[p]\n \\begin{center}\n \\leavevmode\n \\includegraphics[height=0.7\\textheight]{shapiro_fig4.ps}\n \\caption{\n PHOTOEVAPORATING MINIHALO. One time-slice 50 Myr after turn-on\n of quasar located 1 Mpc away from cloud to the left of\n computational box along the $x$-axis. From top to bottom: (a)\n isocontours of pressure, logarithmically spaced, in\n $(r,x)-$plane of cylindrical coordinates; (b) pressure along the\n $r=0$ symmetry axis; (c) temperature; (d) H~I fraction; (e) He~I\n (solid) and He~II (dashed) fractions; (f) bound-free optical\n depth along $r=0$ axis at the threshold ionization energies for\n H~I (solid), He~I (dashed), He~II (dotted). Key features of the\n flow are indicated by the numbers which label them on the\n temperature plot: 1 = IGM shock; 2 = contact discontinuity\n between shocked cloud wind and swept up IGM; 3 = wind shock;\n between 3 and 4 = supersonic wind; 4 = I-front; 5 = boundary of\n gas originally in hydrostatic core; 6 = shock in shadow region\n caused by compression of shadow gas by shock-heated gas outside\n shadow.}\n \\label{fig4}\n \\end{center}\n\\end{figure}\n\n\\begin{figure}\n%\\parbox{0.55\\textwidth}\n\\begin{center}\n\\leavevmode\n{\\includegraphics[height=9.0cm]{shapiro_fig5.ps}}%\n%\\begin{minipage}{0.45\\textwidth}\n \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n MINIHALO I: IONIZATION STRUCTURE OF METALS.\n Carbon, nitrogen, and oxygen ionic fractions along symmetry\n axis at $t = 50\\rm\\,Myr$.}\n \\label{fig5}\n\\end{center}\n%\\end{minipage}\n% \\begin{center}\n% \\leavevmode\n% \\includegraphics[totalheight=4in]{shapiro_fig5.ps}\n% \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n% MINIHALO I: IONIZATION STRUCTURE OF METALS.\n% Carbon, nitrogen, and oxygen ionic fractions along symmetry\n% axis at $t = 50\\rm\\,Myr$.}\n% \\label{fig5}\n% \\end{center}\n\\end{figure}\n\nAs a first study of these important effects, \nShapiro, Raga, \\& Mellema (1997, 1998) simulated the\nphotoevaporation of a uniform, spherical, neutral, intergalactic cloud of \ngas mass $1.5\\times10^6M_\\odot$, radius $R_c=0.5\\,\\rm kpc$, \ndensity $n_{\\rm H,c}=0.1\\,{\\rm cm^{-3}}$ and $T=100\\,\\rm K$, located \n$1\\,\\rm Mpc$ from a quasar with emission spectrum $F_\\nu\\propto\\nu^{-1.8}$\n($\\nu>\\nu_{\\rm H}$) and $N_{\\rm ph}=10^{56}{\\rm s}^{-1}$, initially\nin pressure balance with\nan ambient IGM of density $0.001\\,\\rm cm^{-3}$ which\nat time $t=0$ had\njust been photoionized by the passage of\nthe intergalactic R-type I-front generated when the quasar turned on\n[i.e. $(L_J,L_s,\\tau_H)\\approx (0.1,10,10^3)$].\n [A standard top-hat \nperturbation which collapses and virializes at $z_{\\rm coll}=9$,\nfor example, with total mass $\\cong10^7M_\\odot$, has circular velocity\n$v_c\\cong7\\,\\rm km\\,s^{-1}$, $R_c\\cong560\\rm\\,pc$, and\n$n_{\\rm H,c}=0.1\\,\\rm cm^{-3}$, if $\\Omega_{\\rm bary}h^2=0.03$ and $h=0.5$.]\nThe cloud contained H, He, and heavy elements at $10^{-3}$\ntimes the solar abundance. Our simulations in 2D, axisymmetry used an\nEulerian hydro code with Adaptive Mesh Refinement and\nthe Van~Leer flux-splitting algorithm, which\nsolved nonequilibrium ionization rate equations (for H, He, C, N, O, Ne,\nand S) and included an explicit treatment of radiative transfer\nby taking into account the bound-free opacity of H and He \n(Raga et al.\\ 1995; Mellema et al.\\ 1997; Raga, Mellema, \\& Lundquist 1997).\nThe reader is referred to Shapiro et al.\\ (1997, 1998) for further details.\n\\begin{figure}\n%\\parbox{0.6\\textwidth}\n\\begin{center}\n\\leavevmode\n{\\includegraphics[height=8cm]{shapiro_fig6.ps}}%\n%\\begin{minipage}{0.4\\textwidth}\n \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n MINIHALO II. ABSORPTION LINES: \n Cloud column densities ($\\rm cm^{-2}$) along symmetry axis at\n different velocities. (Top) H~I; (Middle) He~I (solid) and\n He~II (dotted); (Bottom) C~IV. Each box labelled with time \n (in Myrs) since QSO turn-on.}\n \\label{fig6}\n%\\end{minipage}\n\\end{center}\n\\end{figure}\n\nHere we shall present for the first time the results of simulations\nof a more realistic, cosmological minihalo, in which the uniform cloud \ndescribed above is replaced by a self-gravitating,\ncentrally condensed object.\nOur initial condition before ionization, shown in Figure 1, is\nthat of a $10^7M_\\odot$ minihalo in an Einstein-de~Sitter\nuniverse ($\\Omega_{\\rm CDM}=1-\\Omega_{\\rm bary}$; $\\Omega_{\\rm\nbary}h^2=0.02$;\n$h=0.7$) which collapses out and virializes at $z_{\\rm coll}=9$,\nyielding a truncated, nonsingular isothermal sphere of radius \n$R_c=0.5\\,\\rm kpc$ in hydrostatic equilibrium\nwith virial temperature $T_{\\rm vir}=5900\\,\\rm K$\nand dark matter velocity dispersion $\\sigma=6.3\\,\\rm km\\,s^{-1}$,\naccording to the solution of Shapiro, Iliev, \\& Raga (1999),\nfor which the finite central density inside a radius about 1/30 of the\ntotal size of the sphere \nis 514 times the surface density. This\nhydrostatic core of radius $R_c$ is embedded in a self-similar,\nspherical, cosmological infall according to Bertschinger (1985).\nThe results of our simulation on an $(r,x)$-grid with $256\\times512$ cells\n(fully refined)\nare summarized in Figures~2--6.\nThe background IGM and infalling gas outside the minihalo are quickly\nionized, and the resulting pressure gradient in the infall region\nconverts the infall into an outflow.\nThe I-front is trapped, however, inside the hydrostatic core\nof the minihalo. Figure~2(a) shows the position of the I-front inside\nthe minihalo as it slows from weak, R-type to weak D-type as it advances\nacross the original hydrostatic core. Figure~2(b) shows the mass of the\nneutral zone within the original hydrostatic core shrinking as\nthe minihalo photoevaporates within about 70~Myrs. \nThis photoevaporation time is significantly less than that found previously for a similar-mass object with\nthe same external source in the uniform cloud case.\nFigures~3 and 4\nshow the structure of the photoevaporative flow 50~Myrs after the\nglobal I-front first overtakes the minihalo, with key features of\nthe flow indicated by the labels on the temperature plot in Figure~4.\nFigure~5 shows the spatial variation of the relative ionic abundances of\nC, N, O ions along the symmetry axis after 50~Myrs.\nAs in the case of the uniform cloud,\nFigure~5 shows the presence at 50~Myrs\nof low as well as high\nionization stages of the metals.\nCompared to the uniform cloud case at the same time-slice, however,\nFigure~5 shows a somewhat higher degree of ionization on the\nside facing the source than in those previous results.\nThe column densities of H~I, He~I and II, and C~IV for minihalo gas of\ndifferent velocities as seen along the symmetry axis at different times\nare shown in Figure~6. \nAt early times, the cloud gas resembles a weak\nDamped Lyman Alpha (``DLA'') absorber with small velocity width \n($\\sim10\\rm\\,km\\,s^{-1}$) and $N_{\\rm H\\,I}\\sim10^{20}\\rm cm^{-2}$,\nwith a \nLF-like red wing ($\\hbox{velocity width}\\,\\sim10\\,\\rm km\\,s^{-1}$)\nwith $N_{\\rm H\\,I}\\sim10^{16}\\rm cm^{-2}$ on the side moving toward\nthe quasar, with a C~IV feature with\n$N_{\\rm C\\,IV}\\sim10^{12}\\rm cm^{-2}$ displaced in\nthis same asymmetric way from the velocity of peak H~I column\ndensity. After 160~Myr,\nhowever, only a narrow H~I feature with LF-like column density\n$N_{\\rm H\\,I}\\sim10^{14}\\rm cm^{-2}$ remains, with \n$N_{\\rm He\\,II}/N_{\\rm H\\,I}\\sim10^2$ and\n$N_{\\rm C\\,IV}/N_{\\rm H\\,I}\\sim\\rm[C]/[C]_\\odot$. \nA comparison with the\nresults of the uniform cloud case in Shapiro et al.\\ (1997, 1998)\nshows that, despite their differences,\nthere is a surprising degree of similarity between the qualitative \nfeatures presented there and those found here for a highly \ncentrally-concentrated minihalo. Future work will extend this study to \nminihalos\nof higher virial temperatures, for which gravity competes more effectively\nwith photoevaporation.\n\n\n\\acknowledgements \nThis work was supported by NASA Grants NAG5-2785, NAG5-7363, and\nNAG5-7821, and NSF Grant ASC-9504046,\nand was made possible by a UT Dean's Fellowship and a National\nChair of Excellence, UNAM, M\\'exico awarded by CONACyT in 1997 to Shapiro.\nThis material is based in part upon work supported by the\nTexas Advanced Research Program under Grant No. 3658-0624-1999.\n\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format: \n%%\n%% \\bibitem[AUTHOR]{KEY} \n%%\n%% so that the \\cite{KEY}, etc. commands will work properly. \n%% \n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%% \n\\enlargethispage{4ex}\n\\begin{thebibliography}\n\n%\\bibitem[Bally et al.{}<1995>]{p:Bal95} \n% Bally, J., Devine, D. \\& Sutherland, R. 1995, In: S. Lizano \\&\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\n\n\\bibitem[{}<>]{}\nAbel, T., Norman, M. L., \\& Madau, P. 1999, ApJ, {523}, 66\n\n\\bibitem[{Arons} \\& {Wingert}<1972>]{Aro72}\n{Arons}, J., \\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\n\n\\bibitem[{}<>]{} Barkana, R., \\& Loeb, A. 1999, ApJ, {523}, 54\n\n\\bibitem[{}<>]{} \nBertoldi, F. 1989, ApJ, {346}, 735\n\n\\bibitem[{}<>]{} \nBertoldi, F., \\& McKee, C. 1990, ApJ, {354}, 529\n\n\\bibitem[{}<>]{}\nBertschinger, E. 1985, ApJS, {58}, 39\n\n\\bibitem[{}<>]{} \nBond, J. R., Szalay, A. S., \\& Silk, J. 1988, \nApJ, 324, 627\n\n\\bibitem[{}<>]{}\nDonahue, M., \\& Shull, J. M. 1987, ApJ, {323}, L13\n\n\\bibitem[{Griffiths}, {Barbosa}, \\& {Liddle}<1998>]{Gri98}\n{Griffiths}, L.~M., {Barbosa}, D., \\& {Liddle}, A.~R. 1998,\nMNRAS, {308}, 854\n\n\\bibitem[{Haiman} \\& {Knox}<1999>]{Hai99}\n{Haiman}, Z., \\& {Knox}, L. 1999, in ASP Conf.\\ Ser.\\ Vol.\\ 181, Sloan Summit on Microwave Foreground, ed.\\ A.~de~Oliveira \\& M. Tegmark (San Francisco: Astronomical Society of the Pacific), 227 (astro-ph/9902311)\n\n\\bibitem[{Hu}, {Cowie}, \\& {McMahon}<1998>]{Hu98}\n {Hu}, E.~M., {Cowie}, L.~L., \\& {McMahon}, R.~G. 1998, ApJ, {502}, 99\n\n\\bibitem[{}<>]{} \nKlein, R. I., Sandford, M. T., \\& Whitaker, R. W. 1983, \nApJ, {271}, L69\n\n\\bibitem[{}<>]{}\nLefloch, B., \\& Lazareff, B. 1994, \nA\\&A, {289}, 559\n\n\\bibitem[{}<>]{} \nLizano, S., Cant\\'o, J., Garay, G., \\& Hollenbach, D. 1996, \nApJ, {468}, 739\n\n\\bibitem[{}<>]{}\nMeiksen, A., \\& Madau, P. 1993,\nApJ, {412}, 34\n\n\\bibitem[{}<>]{} \nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\n Steffen, W., \\& Noriega-Crespo, A. 1998, \nA\\&A, {331}, 335\n\n\\bibitem[{}<>]{}\n Oort, J. H., \\& Spitzer, L. 1955, ApJ, {121}, 6\n\n\\bibitem[{}<>]{} \nRaga, A. C., Taylor, S. D., Cabrit, S., \\& Biro, S. 1995, \n A.Ap., {296}, 833\n\n\\bibitem[{}<>]{} \nRaga, A. C., Mellema, G., \\& Lundquist, P. 1997, ApJS, {109}, 517\n\n\\bibitem[{}<>]{}\nRazoumov, A., \\& Scott, D. 1999, MNRAS, {309}, 287 \n\n\\bibitem[{}<>]{}\nSandford, M. T., Whitaker, R. W., \\& Klein, R. I. 1982, ApJ, {260}, 183\n\n\\bibitem[{Shapiro}<1995>]{Sha95}\n{Shapiro}, P.~R. 1995, in ASP Conf.\\ Ser.\\ Vol.\\ 80, The Physics of the Interstellar Medium and\nThe Intergalactic Medium, ed. A.~Ferrara, C.~F.~McKee,\nC.~Heiles, \\& P.~R.~Shapiro (San Francisco: Astronomical Society of the Pacific), 55\n \n\\bibitem[{}<>]{} \nShapiro, P. R. 1986, PASP, {98}, 1014\n\n\\bibitem[{}<>]{} \nShapiro, P. R., \\& Giroux, M. L. 1987, ApJ, {321}, L107\n\n\\bibitem[{}<>]{}\n Shapiro, P. R., Giroux, M. L., \\& Babul, A. 1994, ApJ, {427}, 25\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Iliev, I. T., \\& Raga, A. C. 1999, MNRAS, {307}, 203\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1997, in {Structure and Evolution of the Intergalactic Medium From QSO \n Absorption Line Systems}, ed. P.~Petitjean \\& S.~Charlot (Gif-sur-Yvette: Editions Fronti\\'eres), 41\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1998, \nin Mem.\\ Soc.\\ Astron.\\ Italiana\\ Vol.\\ 69, {H$_2$ in the Early Universe}, ed. E.~Corbelli, D.~Galli, \\& F.~Palla, 463 (astro-ph/9804117)\n\n\\bibitem[{}<>]{} \nSpitzer, L. 1978, {Physical Processes in the Interstellar Medium} (New York: Wiley Interscience)\n\n\\bibitem[{Weymann} et al.{}<1998>]{Wey98}\n {Weymann}, R.~J., {Stern}, D., {Bunker}, A., {Spinrad}, H.,\n{Chaffee}, F.~H., {Thompson}, R.~I., \\& {Storrie-Lombardi}, L.~J. 1998\n ApJ, {505}, L95\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"shapiro.tex\",\n \"string\": \"\\\\documentclass[proceedings]{rmaa}\\n%%\\n%% The file `rmaa.cls' should be somewhere in your TeX search path\\n%% (e.g, in the current directory, or in a personal or system-wide\\n%% directory of LaTeX packages. \\n%%\\n%% This will not work with old versions of LaTeX: any version\\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\\n%% complains that it doesn't recognise the command `\\\\documentclass'\\n%% then your LaTeX installation needs updating!\\n\\n%% The following package allows one to do the citations\\n%% semi-automatically. It defines the commands \\\\cite{KEY},\\n%% \\\\scite{KEY}, and \\\\pcite{KEY} which respectively produce citations\\n%% in the following styles: \\n%% (AUTHOR YEAR)\\n%% AUTHOR (YEAR)\\n%% AUTHOR YEAR\\n%% For this to work, you need to pay attention to the formatting of\\n%% the `\\\\bibitem's in your `thebibliography ' environment, qv.\\n\\\\usepackage{rmaacite}\\n%% If you would rather do your citations by hand, then comment out the \\n%% above line\\n\\n%% Here, you can put the definitions of your own personal macros.\\n%% All the special commands defined in AASTEX 4.0 (e.g. \\\\ion{}{},\\n%% \\\\gtrsim, \\\\arcsec, \\\\apj, etc) are already defined. I haven't checked \\n%% if there are any new ones in AASTEX 5.0 yet. \\n\\\\newcommand{\\\\thOr}{$\\\\theta^1\\\\,$C~Ori}\\n\\\\newcommand{\\\\zero}{_0}\\n\\\\newcommand{\\\\kms}{\\\\,\\\\mbox{km s$^{-1}$}}\\n\\\\newcommand{\\\\Othree}{[\\\\ion{O}{3}]~5007\\\\AA}\\n\\\\renewcommand{\\\\P}[1]{%\\n\\\\ifnum#1=1\\\\hbox{OW~168--326E}\\\\fi\\n\\\\ifnum#1=2\\\\hbox{OW~167--317}\\\\fi\\n\\\\ifnum#1=3\\\\hbox{OW~163--317}\\\\fi\\n\\\\ifnum#1=5\\\\hbox{OW~158--323}\\\\fi\\n\\\\ifnum#1=0\\\\hbox{OW~171--334}\\\\fi}\\n\\n%%\\n%% The following commands specify the title, authors etc\\n%%\\n\\\\title{Reionization of the Universe and the Photoevaporation of Cosmological\\nMinihalos}\\n\\\\author{Paul R. Shapiro \\\\affil{Department of Astronomy, The University of Texas at Austin, USA} \\\\and Alejandro C. Raga \\\\affil{Instituto de Astronom\\\\'{\\\\i}a, Universidad Nacional Aut\\\\'onoma de M\\\\'exico}}\\n%\\\\author{Paul R. Shapiro \\\\altaffilmark{1} and Alejandro C. Raga \\\\altaffilmark{2}}\\n%% \\\\affil{Instituto de Astronom\\\\'{\\\\i}a, UNAM, Morelia} }\\n%\\\\altaffiltext{1}{Department of Astronomy, The University of Texas at Austin,\\n%Austin, TX 78712 USA}\\n%\\\\altaffiltext{2}{Instituto de Astronom\\\\'{\\\\i}a, UNAM, Mexico D.F., Mexico}\\n%% Note that the \\\\affil{} command is inside the argument of the\\n%% \\\\author{} command and that a short version of the address should go \\n%% here. More complicated author/address examples are discussed in the \\n%% Author Guide (`rmuser.tex') and illustrated in the example document\\n%% `rmtest.tex' \\n\\n%% The full postal addresses are specified here - they will be typeset \\n%% at the end of the article. Here is also the place to put email\\n%% addresses. \\n\\\\fulladdresses{\\n\\\\item P. R. Shapiro: Department of Astronomy, University of Texas, Austin,\\nTX 78712, USA (shapiro@astro.as.utexas.edu)\\n\\\\item A. C. Raga: Instituto de Astronom\\\\'\\\\i a,\\n UNAM, Apartado Postal 70-264, 04510 M\\\\'exico D. F.,\\nM\\\\'exico (raga@astroscu.unam.mx)\\n}\\n%% Note that the `\\\\fulladdresses' command defines a list-like\\n%% environment, so each separate address must be preceded by the\\n%% `\\\\item' command (here there is only one, since the authors share the \\n%% same address). \\n\\n%% Title/author for running headers\\n\\\\shortauthor{Shapiro \\\\& Raga}\\n\\\\shorttitle{Reionization and photoevaporation}\\n%% These will automatically be converted to upper case in the current\\n%% style. \\n\\n%% No more than 5 keywords, chosen from the standard list\\n\\\\keywords{cosmology: theory --- galaxies: formation --- hydrodynamics ---\\nintergalactic medium}\\n\\n%% The abstract:\\n\\n\\\\resumen{Las primeras fuentes de radiaci\\\\'on ionizante que se\\n condensaron del IGM generaron frentes de ionizaci\\\\'on en sus\\n alrededores, que iluminaron a otros objetos condensados y los\\n fotoevaporaron. Mostramos la retroalimentaci\\\\'on causada por la\\n reionizaci\\\\'on del Universo en la formaci\\\\'on de estructuras\\n c\\\\'osmicas para el caso de un mini halo de materia oscura y bariones,\\n ionizado por una fuente externa con un espectro similar al de los\\n cu\\\\'asares, justo despu\\\\'es del paso del frente de ionizaci\\\\'on\\n generado por la fuente. El mini halo es modelado, siguiendo su\\n condensaci\\\\'on del gas en expansi\\\\'on as\\\\'{\\\\i} como su\\n virializaci\\\\'on, como una esfera isot\\\\'ermica en equilibrio\\n hidrost\\\\'atico. Se presentan los resultados de la primera simulaci\\\\'on\\n hidrodin\\\\'amica del proceso incluyendo transferencia radiativa.\\n Tambi\\\\'en se dan ejemplos de diagn\\\\'osticos observacionales,\\n incluyendo la distribuci\\\\'on espacial del grado de ionizaci\\\\'on en\\n el flujo de C, N y O si existen trazas de estos elementos en la\\n densidad columnar integrada de H~I, He~I y II, as\\\\'{\\\\i} como el C~IV\\n a diferentes velocidades en el gas fotoevaporado, que podr\\\\'{\\\\i}a\\n ser observado en absorci\\\\'on en contra de la fuente de\\n ionizaci\\\\'on.}\\n\\n\\\\abstract{ \\nThe first sources of ionizing radiation to condense out of the dark and\\nneutral IGM sent ionization fronts sweeping outward through their\\nsurroundings, overtaking other condensed objects and photoevaporating them.\\nThis feedback effect of universal reionization on cosmic structure \\nformation is demonstrated here for the case of a cosmological minihalo of\\ndark matter and baryons exposed to an external source of ionizing radiation\\nwith a quasar-like spectrum, just after the passage of the global \\nionization front created by the source. We model the pre-ionization\\nminihalo as a truncated, nonsingular isothermal sphere in hydrostatic\\nequilibrium following its collapse out of the expanding background universe\\nand virialization. Results are presented of the first gas dynamical\\nsimulations of this process,\\nincluding radiative transfer. A sample of observational diagnostics is\\nalso presented, including the spatially-varying ionization levels\\nof C, N, and O in the flow if a trace of heavy elements is present and the \\nintegrated column densities of H~I, He~I and II, and C~IV thru the \\nphotoevaporating gas at different velocities which would be measured in\\nabsorption against a background source like that responsible for the\\nionization. }\\n%% If your spanish is up to it, you may want to supply the resumen by\\n%% uncommenting the following line:\\n%\\\\resumen{Versi\\\\'on espa\\\\~nol del ``abstract''}\\n%% Alternatively, you can leave the translation to the editors. \\n\\n\\n%% This command is so LaTeX won't stop on errors. I've put it in so\\n%% you will still be able to compile the file even if you have lost\\n%% the associated PS files of the figures. \\n\\\\nonstopmode\\n\\n%% The following command is necessary before beginning the text of\\n%% your article. There should be a matching \\\\end{document} at the end\\n%% of the file. \\n\\\\begin{document}\\n\\n%% This command is necessary to typeset the title, abstract, etc. \\n\\\\maketitle\\n\\n%%\\n%% And here starts the text....\\n%%\\n\\\\section{Introduction}\\n\\\\label{sec:intro}\\nObservations of quasar absorption spectra indicate that the universe\\nwas reionized prior to redshift $z=5$. Recent detections of H Lyman alpha\\nemission lines from sources at even higher redshift ($z\\\\leq5.6$) strengthen\\nthis conclusion \\\\cite{Hu98,Wey98}. As new discoveries push the observable\\n horizon back in time ever-closer to the epoch of reionization at redshift \\n$z>5$, increased awareness of its importance as a missing link in the \\ntheory of galaxy formation has caused a great renewal of interest in\\nuniversal reionization. If reionization took place early enough, then\\nThompson scattering of cosmic microwave background (CMB) photons by free\\nelectrons in an ionized intergalactic medium (IGM) would \\nalso have left a detectable imprint on\\nthe CMB observed today. Recent data on the first Doppler peak in\\nthe angular spectrum of CMB anisotropy set limits which imply a \\nreionization redshift $z\\\\lesssim40$ (model-dependent) \\\\cite{Gri98}.\\n(For a review and references on reionization work prior to 1996,\\nthe reader is referred to Shapiro 1995, while more recent developments are\\nsummarized in Haiman \\\\& Knox 1999.)\\n\\nA review of the theory of reionization is outside the scope of this\\nbrief report. In keeping with the focus of this meeting, I will\\nconfine myself to a description of some recent progress on the\\ncalculational side of the problem. To solve the full reionization\\nproblem we must also solve the problem of how density fluctuations\\nled to galaxy formation and this, in turn, led to secondary energy\\nrelease in the form of ionizing and dissociating radiation by the\\nstars and quasars formed inside early galaxies, as well as other forms of \\nenergy release like supernova explosions, jets and winds, which in turn \\ninfluenced the future course of galaxy formation. The modern context for\\nthis description is the Cold Dark Matter (CDM) model, in which\\na cold, pressure-free,\\ncollisionless gas of dark matter dominates the\\nmatter density and structure arises from the gravitational amplification of\\na scale-free power-spectrum of\\ninitially small-amplitude, Gaussian-random-noise primordial density\\nfluctuations, in a hierarchical fashion, with small mass objects collapsing\\nout first and merging together to form larger-mass objects which\\nform later. The calculation of these effects poses an enormous multi-scale \\ncomputational challenge, involving numerical gas dynamics coupled to \\ngravitational N-body dynamics, which raises the bar of cosmological \\nsimulation considerably by adding the requirement that radiative transfer\\neffects be included, as well. To simplify matters,\\nI will henceforth focus on just one of the central challenges of\\nreionization theory, the effect of cosmological ionization fronts.\\n\\n\\\\section{Ionization Fronts in the IGM} \\n\\\\label{sec:constraints}\\n\\nThe neutral, opaque IGM\\nout of which the first bound objects condensed was dramatically reheated\\nand reionized at some time between a redshift $z\\\\approx50$ and $z\\\\approx5$\\nby the radiation released by some of these objects.\\nAn early analysis of the inhomogeneous nature of reionization for the case\\nof short-lived quasars occurring at random positions in a uniform\\nIGM was described by Arons \\\\& Wingert (1972). In that treatment it was\\nassumed that each quasar was instantaneously surrounded by an isolated \\nH~II region, a ``relict H~II region'' undergoing recombination only, each\\nsuch region filling\\na volume containing just as many initially neutral H atoms as there were\\nionizing photons emitted by the QSO during its lifetime. The effect\\nof successive generations of QSO's was accounted for on a \\nstatistically-averaged basis by allowing new generations of QSO's to turn \\non at random positions, including those inside pre-existing relict H~II\\nregions before their H atoms had fully recombined, leading eventually to \\nthe complete overlap of these discrete ionized zones.\\n\\nWhen the first sources\\nturned on, they actually\\nionized their surroundings, not instantaneously, but\\nrather by propagating weak, R-type\\nionization fronts which moved outward supersonically with respect to both\\nthe neutral gas ahead of and the ionized gas behind the front, racing ahead\\nof the hydrodynamical response of the IGM, as first described by \\nShapiro (1986) and Shapiro \\\\& Giroux (1987). These authors solved the\\nproblem of the time-varying radius of a spherical I-front which surrounds \\nisolated sources in a cosmologically-expanding IGM analytically, taking\\nproper account of the I-front jump condition generalized to cosmological\\nconditions. They applied these solutions to determine when the I-fronts\\nsurrounding isolated sources would grow to overlap and, thereby,\\ncomplete the reionization of the universe\\n(Donahue \\\\& Shull 1987 and Meiksen \\\\& Madau 1993\\nsubsequently adopted a similar approach to answer that question).\\nThe effect of density inhomogeneity on the rate of I-front propagation\\nwas described by a mean ``clumping factor'' $c_l>1$, which\\nslowed the I-fronts by increasing the average recombination rate per H atom\\ninside clumps. This suffices to describe the rate of I-front propagation\\nas long as the\\nclumps are either not self-shielding or, if so, only\\nabsorb a fraction of the ionizing photons emitted by the central source. \\nNumerical radiative transfer methods are currently under\\ndevelopment to solve this problem in 3D for the inhomogeneous density \\ndistribution which arises as cosmic structure forms, so far limited to a \\nfixed density field without gas dynamics (e.g.\\\\ Abel, Norman, \\\\& Madau 1999;\\nRazoumov \\\\& Scott 1999). The question of what\\ndynamical effect the I-front had on the density inhomogeneity it\\nencountered, however, requires further analysis. \\n\\n\\nThe answer depends on the size and density of the clumps overtaken by\\nthe I-front. The fate of linear density fluctuations depends upon\\ntheir Jeans number, $L_J\\\\equiv\\\\lambda/\\\\lambda_J$, the wavelength in\\nunits of the baryon Jeans length in the IGM at temperatures of order\\n$10^4\\\\rm K$. Fluctuations with $L_J<1$ find their growth halted and\\nreversed (cf.\\\\ Shapiro, Giroux, \\\\& Babul 1994). For nonlinear density\\nfluctuations, however, the answer is more complicated, depending upon\\nat least three dimensionless parameters, their internal Jeans number,\\n$L_J\\\\equiv R_c/\\\\lambda_J$, the ratio of the cloud radius $R_c$ to the\\nJeans length $\\\\lambda_J$ inside the cloud at about $10^4{\\\\rm K}$,\\ntheir ``Str\\\\\\\"omgren number'' $L_s\\\\equiv 2 R_c/\\\\ell_s$, the ratio of\\nthe cloud diameter $2R_c$ to the Str\\\\\\\"omgren length $\\\\ell_s$ inside\\nthe cloud (the length of a column of gas within which the unshielded\\narrival rate of ionizing photons just balances the total recombination\\nrate), and their optical depth to H ionizing photons at 13.6 eV,\\n$\\\\tau_{\\\\rm H}$, before ionization. If $\\\\tau_{\\\\rm H}<1$, the I-front\\nsweeps across the cloud, leaving an ionized gas at higher pressure\\nthan its surroundings, and exits before any mass motion occurs in\\nresponse, causing the cloud to blow apart. If $\\\\tau_{\\\\rm H}>1$ and\\n$L_s>1$, however, the cloud shields itself against ionizing photons,\\ntrapping the I-front which enters the cloud, causing it to decelerate\\ninside the cloud to the sound speed of the ionized gas before it can\\nexit the other side, thereby transforming itself into a weak, D-type\\nfront preceded by a shock. Typically, the side facing the source\\nexpels a supersonic wind backwards towards the source, which shocks\\nthe IGM outside the cloud, while the remaining neutral cloud material\\nis accelerated away from the source by the so-called ``rocket effect''\\nas the cloud photoevaporates (cf.\\\\ Spitzer 1978). As long as $L_J<1$\\n(the case for gas bound to dark halos with virial velocity less than\\n$\\\\rm 10\\\\,km\\\\,s^{-1}$), this photoevaporation proceeds unimpeded by\\ngravity. For halos with higher virial velocity, however, $L_J>1$, and\\ngravity competes with pressure forces. For a uniform gas of H density\\n$n_{\\\\rm H,c}$, located a distance $r_{\\\\rm Mpc}$ (in Mpc) from a UV\\nsource emitting $N_{\\\\rm ph,56}$ ionizing photons (in units of\\n$\\\\rm10^{56}s^{-1}$), the Str\\\\\\\"omgren length is only\\n$\\\\ell_s\\\\cong(100\\\\,{\\\\rm pc}) (N_{\\\\rm ph,56}/r_{\\\\rm Mpc}^2)(n_{\\\\rm\\n H,c}/0.1\\\\,\\\\rm cm^{-3})^{-2}$. We focus in what follows on the\\nself-shielded case which traps the I-front.\\n \\n\\\\section{The Photoevaporation of Dwarf Galaxy Minihalos\\nOvertaken by a Cosmological Ionization Front}\\n\\\\label{sec:anal}\\n\\n\\n\\n\\n\\nThe importance of this photoevaporation process has long been\\nrecognized in the study of interstellar clouds exposed to ionizing\\nstarlight (e.g. Oort \\\\& Spitzer 1955;\\nSpitzer 1978; Bertoldi 1989; Bertoldi \\\\& McKee 1990;\\nLefloch \\\\& Lazareff 1994; Lizano et al.\\\\ 1996). Radiation-hydrodynamical \\nsimulations were performed in 2D in the early 1980's of\\na stellar I-front overtaking a clump inside a molecular\\ncloud (Sandford, Whitaker, \\\\& Klein 1982; Klein, Sandford, \\\\& Whitaker 1983).\\nMore recently, 2D simulations for the case of circumstellar clouds\\nionized by a single nearby star have also been performed\\n(Mellema et al.\\\\ 1998). In the cosmological context, however,\\nthe importance of this process has only recently been fully appreciated. \\nIn proposing the expanding minihalo model to explain Lyman alpha\\nforest (``LF'') quasar absorption lines, Bond, Szalay, \\\\& Silk (1988)\\ndiscussed how gas originally confined by the gravity of dark\\nminihalos in the CDM model would be expelled by pressure forces\\nif photoionization by ionizing background radiation suddently\\nheated all the gas to an isothermal condition at $T\\\\approx10^4\\\\rm K$.\\nThe first radiation-hydrodynamical \\nsimulations of the photoevaporation of a primordial density\\ninhomogeneity overtaken by a cosmological I-front, however,\\nwere described in Shapiro, Raga, \\\\& Mellema (1997, 1998).\\nBarkana \\\\& Loeb (1999) subsequently considered the relative\\nimportance of this process for dwarf galaxy minihalos of different masses\\nin the CDM model, using static models of uniformly-illuminated spherical\\nclouds in thermal and ionization equilibrium, taking H atom self-shielding\\ninto account, and assuming that gas which is heated above the minihalo\\nvirial temperature must be evaporated. They concluded that 50\\\\%--90\\\\% of \\nthe gas in gravitationally bound objects when reionization\\noccurred should have been evaporated.\\n\\\\begin{figure}[h]\\n\\\\parbox{0.5\\\\textwidth}{\\n \\\\includegraphics[height=6.8cm]{shapiro_fig1.ps}}\\n \\\\label{fig1}\\n\\\\begin{minipage}{0.45\\\\textwidth}\\n \\\\caption{MINIHALO INITIAL CONDITIONS BEFORE REIONIZATION:\\nTruncated, nonsingular isothermal sphere (TIS) of gas and dark matter in\\nhydrostatic equilibrium (Shapiro, Iliev, \\\\& Raga 1999) surrounded by the\\ncorresponding self-similar spherical infall for an Einstein-de Sitter\\nbackground universe (cf.\\\\ Bertschinger 1985). (a) (Top) gas density and (b)\\n(Bottom) gas velocity versus distance from minihalo center.}\\n\\\\end{minipage}\\n\\\\end{figure}\\n\\n\\n\\\\begin{figure}[t]\\n \\\\parbox{0.5\\\\textwidth}{%\\n \\\\includegraphics[height=7cm]{shapiro_fig2.ps}}\\n \\\\label{fig2}\\n\\\\begin{minipage}{0.45\\\\textwidth}\\n \\\\caption{IONIZATION FRONT PHOTOEVAPORATES MINIHALO:\\n(a) (Top) I-front position along $x$-axis versus time; (b) (Bottom) Mass\\nfraction of the initial mass $M_{\\\\rm I}$ of minihalo hydrostatic \\n core which remains neutral (H~I) versus time. }\\n\\\\end{minipage}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[h]\\n \\\\begin{center}\\n \\\\leavevmode\\n \\\\includegraphics[width=\\\\textwidth]{shapiro_fig3.ps}\\n \\\\caption{PHOTOEVAPORATING MINIHALO.\\n50 Myr after turn-on of quasar 1 Mpc to the left of computational box along\\nthe $x$-axis. \\n(a) (Upper Panel) isocontours of atomic density, logarithmically spaced, \\nin $(r,x)-$plane of cylindrical coordinates; (b) (Lower Panel)\\nvelocity arrows are plotted with length proportional to gas velocity.\\nAn arrow of length equal to the spacing between arrows has velocity\\n$30 \\\\kms$. Solid line shows current extent of gas originally in\\nhydrostatic core. Dashed line is I-front (50\\\\% H-ionization contour).}\\n \\\\label{fig3}\\n \\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}[p]\\n \\\\begin{center}\\n \\\\leavevmode\\n \\\\includegraphics[height=0.7\\\\textheight]{shapiro_fig4.ps}\\n \\\\caption{\\n PHOTOEVAPORATING MINIHALO. One time-slice 50 Myr after turn-on\\n of quasar located 1 Mpc away from cloud to the left of\\n computational box along the $x$-axis. From top to bottom: (a)\\n isocontours of pressure, logarithmically spaced, in\\n $(r,x)-$plane of cylindrical coordinates; (b) pressure along the\\n $r=0$ symmetry axis; (c) temperature; (d) H~I fraction; (e) He~I\\n (solid) and He~II (dashed) fractions; (f) bound-free optical\\n depth along $r=0$ axis at the threshold ionization energies for\\n H~I (solid), He~I (dashed), He~II (dotted). Key features of the\\n flow are indicated by the numbers which label them on the\\n temperature plot: 1 = IGM shock; 2 = contact discontinuity\\n between shocked cloud wind and swept up IGM; 3 = wind shock;\\n between 3 and 4 = supersonic wind; 4 = I-front; 5 = boundary of\\n gas originally in hydrostatic core; 6 = shock in shadow region\\n caused by compression of shadow gas by shock-heated gas outside\\n shadow.}\\n \\\\label{fig4}\\n \\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n%\\\\parbox{0.55\\\\textwidth}\\n\\\\begin{center}\\n\\\\leavevmode\\n{\\\\includegraphics[height=9.0cm]{shapiro_fig5.ps}}%\\n%\\\\begin{minipage}{0.45\\\\textwidth}\\n \\\\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\\n MINIHALO I: IONIZATION STRUCTURE OF METALS.\\n Carbon, nitrogen, and oxygen ionic fractions along symmetry\\n axis at $t = 50\\\\rm\\\\,Myr$.}\\n \\\\label{fig5}\\n\\\\end{center}\\n%\\\\end{minipage}\\n% \\\\begin{center}\\n% \\\\leavevmode\\n% \\\\includegraphics[totalheight=4in]{shapiro_fig5.ps}\\n% \\\\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\\n% MINIHALO I: IONIZATION STRUCTURE OF METALS.\\n% Carbon, nitrogen, and oxygen ionic fractions along symmetry\\n% axis at $t = 50\\\\rm\\\\,Myr$.}\\n% \\\\label{fig5}\\n% \\\\end{center}\\n\\\\end{figure}\\n\\nAs a first study of these important effects, \\nShapiro, Raga, \\\\& Mellema (1997, 1998) simulated the\\nphotoevaporation of a uniform, spherical, neutral, intergalactic cloud of \\ngas mass $1.5\\\\times10^6M_\\\\odot$, radius $R_c=0.5\\\\,\\\\rm kpc$, \\ndensity $n_{\\\\rm H,c}=0.1\\\\,{\\\\rm cm^{-3}}$ and $T=100\\\\,\\\\rm K$, located \\n$1\\\\,\\\\rm Mpc$ from a quasar with emission spectrum $F_\\\\nu\\\\propto\\\\nu^{-1.8}$\\n($\\\\nu>\\\\nu_{\\\\rm H}$) and $N_{\\\\rm ph}=10^{56}{\\\\rm s}^{-1}$, initially\\nin pressure balance with\\nan ambient IGM of density $0.001\\\\,\\\\rm cm^{-3}$ which\\nat time $t=0$ had\\njust been photoionized by the passage of\\nthe intergalactic R-type I-front generated when the quasar turned on\\n[i.e. $(L_J,L_s,\\\\tau_H)\\\\approx (0.1,10,10^3)$].\\n [A standard top-hat \\nperturbation which collapses and virializes at $z_{\\\\rm coll}=9$,\\nfor example, with total mass $\\\\cong10^7M_\\\\odot$, has circular velocity\\n$v_c\\\\cong7\\\\,\\\\rm km\\\\,s^{-1}$, $R_c\\\\cong560\\\\rm\\\\,pc$, and\\n$n_{\\\\rm H,c}=0.1\\\\,\\\\rm cm^{-3}$, if $\\\\Omega_{\\\\rm bary}h^2=0.03$ and $h=0.5$.]\\nThe cloud contained H, He, and heavy elements at $10^{-3}$\\ntimes the solar abundance. Our simulations in 2D, axisymmetry used an\\nEulerian hydro code with Adaptive Mesh Refinement and\\nthe Van~Leer flux-splitting algorithm, which\\nsolved nonequilibrium ionization rate equations (for H, He, C, N, O, Ne,\\nand S) and included an explicit treatment of radiative transfer\\nby taking into account the bound-free opacity of H and He \\n(Raga et al.\\\\ 1995; Mellema et al.\\\\ 1997; Raga, Mellema, \\\\& Lundquist 1997).\\nThe reader is referred to Shapiro et al.\\\\ (1997, 1998) for further details.\\n\\\\begin{figure}\\n%\\\\parbox{0.6\\\\textwidth}\\n\\\\begin{center}\\n\\\\leavevmode\\n{\\\\includegraphics[height=8cm]{shapiro_fig6.ps}}%\\n%\\\\begin{minipage}{0.4\\\\textwidth}\\n \\\\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\\n MINIHALO II. ABSORPTION LINES: \\n Cloud column densities ($\\\\rm cm^{-2}$) along symmetry axis at\\n different velocities. (Top) H~I; (Middle) He~I (solid) and\\n He~II (dotted); (Bottom) C~IV. Each box labelled with time \\n (in Myrs) since QSO turn-on.}\\n \\\\label{fig6}\\n%\\\\end{minipage}\\n\\\\end{center}\\n\\\\end{figure}\\n\\nHere we shall present for the first time the results of simulations\\nof a more realistic, cosmological minihalo, in which the uniform cloud \\ndescribed above is replaced by a self-gravitating,\\ncentrally condensed object.\\nOur initial condition before ionization, shown in Figure 1, is\\nthat of a $10^7M_\\\\odot$ minihalo in an Einstein-de~Sitter\\nuniverse ($\\\\Omega_{\\\\rm CDM}=1-\\\\Omega_{\\\\rm bary}$; $\\\\Omega_{\\\\rm\\nbary}h^2=0.02$;\\n$h=0.7$) which collapses out and virializes at $z_{\\\\rm coll}=9$,\\nyielding a truncated, nonsingular isothermal sphere of radius \\n$R_c=0.5\\\\,\\\\rm kpc$ in hydrostatic equilibrium\\nwith virial temperature $T_{\\\\rm vir}=5900\\\\,\\\\rm K$\\nand dark matter velocity dispersion $\\\\sigma=6.3\\\\,\\\\rm km\\\\,s^{-1}$,\\naccording to the solution of Shapiro, Iliev, \\\\& Raga (1999),\\nfor which the finite central density inside a radius about 1/30 of the\\ntotal size of the sphere \\nis 514 times the surface density. This\\nhydrostatic core of radius $R_c$ is embedded in a self-similar,\\nspherical, cosmological infall according to Bertschinger (1985).\\nThe results of our simulation on an $(r,x)$-grid with $256\\\\times512$ cells\\n(fully refined)\\nare summarized in Figures~2--6.\\nThe background IGM and infalling gas outside the minihalo are quickly\\nionized, and the resulting pressure gradient in the infall region\\nconverts the infall into an outflow.\\nThe I-front is trapped, however, inside the hydrostatic core\\nof the minihalo. Figure~2(a) shows the position of the I-front inside\\nthe minihalo as it slows from weak, R-type to weak D-type as it advances\\nacross the original hydrostatic core. Figure~2(b) shows the mass of the\\nneutral zone within the original hydrostatic core shrinking as\\nthe minihalo photoevaporates within about 70~Myrs. \\nThis photoevaporation time is significantly less than that found previously for a similar-mass object with\\nthe same external source in the uniform cloud case.\\nFigures~3 and 4\\nshow the structure of the photoevaporative flow 50~Myrs after the\\nglobal I-front first overtakes the minihalo, with key features of\\nthe flow indicated by the labels on the temperature plot in Figure~4.\\nFigure~5 shows the spatial variation of the relative ionic abundances of\\nC, N, O ions along the symmetry axis after 50~Myrs.\\nAs in the case of the uniform cloud,\\nFigure~5 shows the presence at 50~Myrs\\nof low as well as high\\nionization stages of the metals.\\nCompared to the uniform cloud case at the same time-slice, however,\\nFigure~5 shows a somewhat higher degree of ionization on the\\nside facing the source than in those previous results.\\nThe column densities of H~I, He~I and II, and C~IV for minihalo gas of\\ndifferent velocities as seen along the symmetry axis at different times\\nare shown in Figure~6. \\nAt early times, the cloud gas resembles a weak\\nDamped Lyman Alpha (``DLA'') absorber with small velocity width \\n($\\\\sim10\\\\rm\\\\,km\\\\,s^{-1}$) and $N_{\\\\rm H\\\\,I}\\\\sim10^{20}\\\\rm cm^{-2}$,\\nwith a \\nLF-like red wing ($\\\\hbox{velocity width}\\\\,\\\\sim10\\\\,\\\\rm km\\\\,s^{-1}$)\\nwith $N_{\\\\rm H\\\\,I}\\\\sim10^{16}\\\\rm cm^{-2}$ on the side moving toward\\nthe quasar, with a C~IV feature with\\n$N_{\\\\rm C\\\\,IV}\\\\sim10^{12}\\\\rm cm^{-2}$ displaced in\\nthis same asymmetric way from the velocity of peak H~I column\\ndensity. After 160~Myr,\\nhowever, only a narrow H~I feature with LF-like column density\\n$N_{\\\\rm H\\\\,I}\\\\sim10^{14}\\\\rm cm^{-2}$ remains, with \\n$N_{\\\\rm He\\\\,II}/N_{\\\\rm H\\\\,I}\\\\sim10^2$ and\\n$N_{\\\\rm C\\\\,IV}/N_{\\\\rm H\\\\,I}\\\\sim\\\\rm[C]/[C]_\\\\odot$. \\nA comparison with the\\nresults of the uniform cloud case in Shapiro et al.\\\\ (1997, 1998)\\nshows that, despite their differences,\\nthere is a surprising degree of similarity between the qualitative \\nfeatures presented there and those found here for a highly \\ncentrally-concentrated minihalo. Future work will extend this study to \\nminihalos\\nof higher virial temperatures, for which gravity competes more effectively\\nwith photoevaporation.\\n\\n\\n\\\\acknowledgements \\nThis work was supported by NASA Grants NAG5-2785, NAG5-7363, and\\nNAG5-7821, and NSF Grant ASC-9504046,\\nand was made possible by a UT Dean's Fellowship and a National\\nChair of Excellence, UNAM, M\\\\'exico awarded by CONACyT in 1997 to Shapiro.\\nThis material is based in part upon work supported by the\\nTexas Advanced Research Program under Grant No. 3658-0624-1999.\\n\\n%% When using the rmaacite package, the \\\\bibitem command should be of\\n%% the format: \\n%%\\n%% \\\\bibitem[AUTHOR]{KEY} \\n%%\\n%% so that the \\\\cite{KEY}, etc. commands will work properly. \\n%% \\n%% If you are doing the citations manually, then you can just use\\n%% `\\\\bibitem{}' instead. This will give you a warning about\\n%% `multiply-defined labels' which you can safely ignore.\\n%% \\n\\\\enlargethispage{4ex}\\n\\\\begin{thebibliography}\\n\\n%\\\\bibitem[Bally et al.{}<1995>]{p:Bal95} \\n% Bally, J., Devine, D. \\\\& Sutherland, R. 1995, In: S. Lizano \\\\&\\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\\n\\n\\\\bibitem[{}<>]{}\\nAbel, T., Norman, M. L., \\\\& Madau, P. 1999, ApJ, {523}, 66\\n\\n\\\\bibitem[{Arons} \\\\& {Wingert}<1972>]{Aro72}\\n{Arons}, J., \\\\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\\n\\n\\\\bibitem[{}<>]{} Barkana, R., \\\\& Loeb, A. 1999, ApJ, {523}, 54\\n\\n\\\\bibitem[{}<>]{} \\nBertoldi, F. 1989, ApJ, {346}, 735\\n\\n\\\\bibitem[{}<>]{} \\nBertoldi, F., \\\\& McKee, C. 1990, ApJ, {354}, 529\\n\\n\\\\bibitem[{}<>]{}\\nBertschinger, E. 1985, ApJS, {58}, 39\\n\\n\\\\bibitem[{}<>]{} \\nBond, J. R., Szalay, A. 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W. 1983, \\nApJ, {271}, L69\\n\\n\\\\bibitem[{}<>]{}\\nLefloch, B., \\\\& Lazareff, B. 1994, \\nA\\\\&A, {289}, 559\\n\\n\\\\bibitem[{}<>]{} \\nLizano, S., Cant\\\\'o, J., Garay, G., \\\\& Hollenbach, D. 1996, \\nApJ, {468}, 739\\n\\n\\\\bibitem[{}<>]{}\\nMeiksen, A., \\\\& Madau, P. 1993,\\nApJ, {412}, 34\\n\\n\\\\bibitem[{}<>]{} \\nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\\n Steffen, W., \\\\& Noriega-Crespo, A. 1998, \\nA\\\\&A, {331}, 335\\n\\n\\\\bibitem[{}<>]{}\\n Oort, J. H., \\\\& Spitzer, L. 1955, ApJ, {121}, 6\\n\\n\\\\bibitem[{}<>]{} \\nRaga, A. C., Taylor, S. D., Cabrit, S., \\\\& Biro, S. 1995, \\n A.Ap., {296}, 833\\n\\n\\\\bibitem[{}<>]{} \\nRaga, A. C., Mellema, G., \\\\& Lundquist, P. 1997, ApJS, {109}, 517\\n\\n\\\\bibitem[{}<>]{}\\nRazoumov, A., \\\\& Scott, D. 1999, MNRAS, {309}, 287 \\n\\n\\\\bibitem[{}<>]{}\\nSandford, M. T., Whitaker, R. W., \\\\& Klein, R. I. 1982, ApJ, {260}, 183\\n\\n\\\\bibitem[{Shapiro}<1995>]{Sha95}\\n{Shapiro}, P.~R. 1995, in ASP Conf.\\\\ Ser.\\\\ Vol.\\\\ 80, The Physics of the Interstellar Medium and\\nThe Intergalactic Medium, ed. A.~Ferrara, C.~F.~McKee,\\nC.~Heiles, \\\\& P.~R.~Shapiro (San Francisco: Astronomical Society of the Pacific), 55\\n \\n\\\\bibitem[{}<>]{} \\nShapiro, P. R. 1986, PASP, {98}, 1014\\n\\n\\\\bibitem[{}<>]{} \\nShapiro, P. R., \\\\& Giroux, M. L. 1987, ApJ, {321}, L107\\n\\n\\\\bibitem[{}<>]{}\\n Shapiro, P. R., Giroux, M. L., \\\\& Babul, A. 1994, ApJ, {427}, 25\\n\\n\\\\bibitem[{}<>]{}\\nShapiro, P. R., Iliev, I. T., \\\\& Raga, A. C. 1999, MNRAS, {307}, 203\\n\\n\\\\bibitem[{}<>]{}\\nShapiro, P. R., Raga, A. C., \\\\& Mellema, G. 1997, in {Structure and Evolution of the Intergalactic Medium From QSO \\n Absorption Line Systems}, ed. P.~Petitjean \\\\& S.~Charlot (Gif-sur-Yvette: Editions Fronti\\\\'eres), 41\\n\\n\\\\bibitem[{}<>]{}\\nShapiro, P. R., Raga, A. C., \\\\& Mellema, G. 1998, \\nin Mem.\\\\ Soc.\\\\ Astron.\\\\ Italiana\\\\ Vol.\\\\ 69, {H$_2$ in the Early Universe}, ed. E.~Corbelli, D.~Galli, \\\\& F.~Palla, 463 (astro-ph/9804117)\\n\\n\\\\bibitem[{}<>]{} \\nSpitzer, L. 1978, {Physical Processes in the Interstellar Medium} (New York: Wiley Interscience)\\n\\n\\\\bibitem[{Weymann} et al.{}<1998>]{Wey98}\\n {Weymann}, R.~J., {Stern}, D., {Bunker}, A., {Spinrad}, H.,\\n{Chaffee}, F.~H., {Thompson}, R.~I., \\\\& {Storrie-Lombardi}, L.~J. 1998\\n ApJ, {505}, L95\\n\\n\\\\end{thebibliography}\\n\\n\\\\end{document}\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002100.extracted_bib","string":"\\begin{thebibliography}\n\n%\\bibitem[Bally et al.{}<1995>]{p:Bal95} \n% Bally, J., Devine, D. \\& Sutherland, R. 1995, In: S. Lizano \\&\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\n\n\\bibitem[{}<>]{}\nAbel, T., Norman, M. L., \\& Madau, P. 1999, ApJ, {523}, 66\n\n\\bibitem[{Arons} \\& {Wingert}<1972>]{Aro72}\n{Arons}, J., \\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\n\n\\bibitem[{}<>]{} Barkana, R., \\& Loeb, A. 1999, ApJ, {523}, 54\n\n\\bibitem[{}<>]{} \nBertoldi, F. 1989, ApJ, {346}, 735\n\n\\bibitem[{}<>]{} \nBertoldi, F., \\& McKee, C. 1990, ApJ, {354}, 529\n\n\\bibitem[{}<>]{}\nBertschinger, E. 1985, ApJS, {58}, 39\n\n\\bibitem[{}<>]{} \nBond, J. R., Szalay, A. S., \\& Silk, J. 1988, \nApJ, 324, 627\n\n\\bibitem[{}<>]{}\nDonahue, M., \\& Shull, J. M. 1987, ApJ, {323}, L13\n\n\\bibitem[{Griffiths}, {Barbosa}, \\& {Liddle}<1998>]{Gri98}\n{Griffiths}, L.~M., {Barbosa}, D., \\& {Liddle}, A.~R. 1998,\nMNRAS, {308}, 854\n\n\\bibitem[{Haiman} \\& {Knox}<1999>]{Hai99}\n{Haiman}, Z., \\& {Knox}, L. 1999, in ASP Conf.\\ Ser.\\ Vol.\\ 181, Sloan Summit on Microwave Foreground, ed.\\ A.~de~Oliveira \\& M. Tegmark (San Francisco: Astronomical Society of the Pacific), 227 (astro-ph/9902311)\n\n\\bibitem[{Hu}, {Cowie}, \\& {McMahon}<1998>]{Hu98}\n {Hu}, E.~M., {Cowie}, L.~L., \\& {McMahon}, R.~G. 1998, ApJ, {502}, 99\n\n\\bibitem[{}<>]{} \nKlein, R. I., Sandford, M. T., \\& Whitaker, R. W. 1983, \nApJ, {271}, L69\n\n\\bibitem[{}<>]{}\nLefloch, B., \\& Lazareff, B. 1994, \nA\\&A, {289}, 559\n\n\\bibitem[{}<>]{} \nLizano, S., Cant\\'o, J., Garay, G., \\& Hollenbach, D. 1996, \nApJ, {468}, 739\n\n\\bibitem[{}<>]{}\nMeiksen, A., \\& Madau, P. 1993,\nApJ, {412}, 34\n\n\\bibitem[{}<>]{} \nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\n Steffen, W., \\& Noriega-Crespo, A. 1998, \nA\\&A, {331}, 335\n\n\\bibitem[{}<>]{}\n Oort, J. H., \\& Spitzer, L. 1955, ApJ, {121}, 6\n\n\\bibitem[{}<>]{} \nRaga, A. C., Taylor, S. D., Cabrit, S., \\& Biro, S. 1995, \n A.Ap., {296}, 833\n\n\\bibitem[{}<>]{} \nRaga, A. C., Mellema, G., \\& Lundquist, P. 1997, ApJS, {109}, 517\n\n\\bibitem[{}<>]{}\nRazoumov, A., \\& Scott, D. 1999, MNRAS, {309}, 287 \n\n\\bibitem[{}<>]{}\nSandford, M. T., Whitaker, R. W., \\& Klein, R. I. 1982, ApJ, {260}, 183\n\n\\bibitem[{Shapiro}<1995>]{Sha95}\n{Shapiro}, P.~R. 1995, in ASP Conf.\\ Ser.\\ Vol.\\ 80, The Physics of the Interstellar Medium and\nThe Intergalactic Medium, ed. A.~Ferrara, C.~F.~McKee,\nC.~Heiles, \\& P.~R.~Shapiro (San Francisco: Astronomical Society of the Pacific), 55\n \n\\bibitem[{}<>]{} \nShapiro, P. R. 1986, PASP, {98}, 1014\n\n\\bibitem[{}<>]{} \nShapiro, P. R., \\& Giroux, M. L. 1987, ApJ, {321}, L107\n\n\\bibitem[{}<>]{}\n Shapiro, P. R., Giroux, M. L., \\& Babul, A. 1994, ApJ, {427}, 25\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Iliev, I. T., \\& Raga, A. C. 1999, MNRAS, {307}, 203\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1997, in {Structure and Evolution of the Intergalactic Medium From QSO \n Absorption Line Systems}, ed. P.~Petitjean \\& S.~Charlot (Gif-sur-Yvette: Editions Fronti\\'eres), 41\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1998, \nin Mem.\\ Soc.\\ Astron.\\ Italiana\\ Vol.\\ 69, {H$_2$ in the Early Universe}, ed. E.~Corbelli, D.~Galli, \\& F.~Palla, 463 (astro-ph/9804117)\n\n\\bibitem[{}<>]{} \nSpitzer, L. 1978, {Physical Processes in the Interstellar Medium} (New York: Wiley Interscience)\n\n\\bibitem[{Weymann} et al.{}<1998>]{Wey98}\n {Weymann}, R.~J., {Stern}, D., {Bunker}, A., {Spinrad}, H.,\n{Chaffee}, F.~H., {Thompson}, R.~I., \\& {Storrie-Lombardi}, L.~J. 1998\n ApJ, {505}, L95\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002100.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}\\n\\n%\\\\bibitem[Bally et al.{}<1995>]{p:Bal95} \\n% Bally, J., Devine, D. \\\\& Sutherland, R. 1995, In: S. Lizano \\\\&\\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\\n\\n\\\\bibitem[{}<>]{}\\nAbel, T., Norman, M. L., \\\\& Madau, P. 1999, ApJ, {523}, 66\\n\\n\\\\bibitem[{Arons} \\\\& {Wingert}<1972>]{Aro72}\\n{Arons}, J., \\\\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\\n\\n\\\\bibitem[{}<>]{} Barkana, R., \\\\& Loeb, A. 1999, ApJ, {523}, 54\\n\\n\\\\bibitem[{}<>]{} \\nBertoldi, F. 1989, ApJ, {346}, 735\\n\\n\\\\bibitem[{}<>]{} \\nBertoldi, F., \\\\& McKee, C. 1990, ApJ, {354}, 529\\n\\n\\\\bibitem[{}<>]{}\\nBertschinger, E. 1985, ApJS, {58}, 39\\n\\n\\\\bibitem[{}<>]{} \\nBond, J. R., Szalay, A. S., \\\\& Silk, J. 1988, \\nApJ, 324, 627\\n\\n\\\\bibitem[{}<>]{}\\nDonahue, M., \\\\& Shull, J. M. 1987, ApJ, {323}, L13\\n\\n\\\\bibitem[{Griffiths}, {Barbosa}, \\\\& {Liddle}<1998>]{Gri98}\\n{Griffiths}, L.~M., {Barbosa}, D., \\\\& {Liddle}, A.~R. 1998,\\nMNRAS, {308}, 854\\n\\n\\\\bibitem[{Haiman} \\\\& {Knox}<1999>]{Hai99}\\n{Haiman}, Z., \\\\& {Knox}, L. 1999, in ASP Conf.\\\\ Ser.\\\\ Vol.\\\\ 181, Sloan Summit on Microwave Foreground, ed.\\\\ A.~de~Oliveira \\\\& M. Tegmark (San Francisco: Astronomical Society of the Pacific), 227 (astro-ph/9902311)\\n\\n\\\\bibitem[{Hu}, {Cowie}, \\\\& {McMahon}<1998>]{Hu98}\\n {Hu}, E.~M., {Cowie}, L.~L., \\\\& {McMahon}, R.~G. 1998, ApJ, {502}, 99\\n\\n\\\\bibitem[{}<>]{} \\nKlein, R. I., Sandford, M. T., \\\\& Whitaker, R. W. 1983, \\nApJ, {271}, L69\\n\\n\\\\bibitem[{}<>]{}\\nLefloch, B., \\\\& Lazareff, B. 1994, \\nA\\\\&A, {289}, 559\\n\\n\\\\bibitem[{}<>]{} \\nLizano, S., Cant\\\\'o, J., Garay, G., \\\\& Hollenbach, D. 1996, \\nApJ, {468}, 739\\n\\n\\\\bibitem[{}<>]{}\\nMeiksen, A., \\\\& Madau, P. 1993,\\nApJ, {412}, 34\\n\\n\\\\bibitem[{}<>]{} \\nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\\n Steffen, W., \\\\& Noriega-Crespo, A. 1998, \\nA\\\\&A, {331}, 335\\n\\n\\\\bibitem[{}<>]{}\\n Oort, J. H., \\\\& Spitzer, L. 1955, ApJ, {121}, 6\\n\\n\\\\bibitem[{}<>]{} \\nRaga, A. C., Taylor, S. D., Cabrit, S., \\\\& Biro, S. 1995, \\n A.Ap., {296}, 833\\n\\n\\\\bibitem[{}<>]{} \\nRaga, A. C., Mellema, G., \\\\& Lundquist, P. 1997, ApJS, {109}, 517\\n\\n\\\\bibitem[{}<>]{}\\nRazoumov, A., \\\\& Scott, D. 1999, MNRAS, {309}, 287 \\n\\n\\\\bibitem[{}<>]{}\\nSandford, M. T., Whitaker, R. W., \\\\& Klein, R. 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astro-ph0002001
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QSO Absorption Line Constraints on Intragroup High--Velocity Clouds
|
[
{
"author": "Jane~C.~Charlton\\altaffilmark{1}"
},
{
"author": "Christopher~W.~Churchill"
},
{
"author": "and Jane~R.~Rigby"
}
] |
We show that the number statistics of moderate redshift {\MgII} and Lyman limit absorbers may rule out the hypothesis that high velocity clouds are infalling intragroup material.
|
[
{
"name": "astro-ph0002001.tex",
"string": "\\documentstyle[emulateapj,rotate,times]{article}\n%\\documentstyle[11pt,rotate,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article}\n \n% this is the modification \n \n%-----------------------------------------------------------------------------\n%\n% personal LaTex mark--ups\n%\n%\n% **** DO NOT MODIFY BELOW **** **** DO NOT MODIFY BELOW **** \n%\n\\newcommand{\\etal}{et~al.\\ }\n\\newcommand{\\PVdblt}{{\\rm P}\\kern 0.1em{\\sc v}~$\\lambda\\lambda 1117, 1128$}\n\\newcommand{\\CaIIdblt}{{\\rm Ca}\\kern 0.1em{\\sc ii}~$\\lambda\\lambda 3934, 3969$}\n\\newcommand{\\AlIIIdblt}{{\\rm Al}\\kern 0.1em{\\sc iii}~$\\lambda\\lambda 1854, 1862$}\n\\newcommand{\\CIVdblt}{{\\rm C}\\kern 0.1em{\\sc iv}~$\\lambda\\lambda 1548, 1550$}\n\\newcommand{\\MgIIdblt}{{\\rm Mg}\\kern 0.1em{\\sc ii}~$\\lambda\\lambda 2796, 2803$}\n\\newcommand{\\NVdblt}{{\\rm N}\\kern 0.1em{\\sc v}~$\\lambda\\lambda 1238, 1242$} \n\\newcommand{\\SVIdblt}{{\\rm S}\\kern 0.1em{\\sc vi}~$\\lambda\\lambda 933, 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Fe}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\FeIII}{\\hbox{{\\rm Fe}\\kern 0.1em{\\sc iii}}}\n\\newcommand{\\MnII}{\\hbox{{\\rm Mn}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\MgI}{\\hbox{{\\rm Mg}\\kern 0.1em{\\sc i}}}\n\\newcommand{\\MgII}{\\hbox{{\\rm Mg}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\MgIII}{\\hbox{{\\rm Mg}\\kern 0.1em{\\sc iii}}}\n\\newcommand{\\NI}{\\hbox{{\\rm N}\\kern 0.1em{\\sc i}}}\n\\newcommand{\\NII}{\\hbox{{\\rm N}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\NIII}{\\hbox{{\\rm N}\\kern 0.1em{\\sc iii}}}\n\\newcommand{\\NV}{\\hbox{{\\rm N}\\kern 0.1em{\\sc v}}}\n\\newcommand{\\OVI}{\\hbox{{\\rm O}\\kern 0.1em{\\sc vi}}}\n\\newcommand{\\OI}{\\hbox{{\\rm O}\\kern 0.1em{\\sc i}}}\n\\newcommand{\\OII}{\\hbox{[{\\rm O}\\kern 0.1em{\\sc ii}]}}\n\\newcommand{\\OIV}{\\hbox{{\\rm O}\\kern 0.1em{\\sc iv}]}}\n\\newcommand{\\SI}{{\\rm S}\\kern 0.1em{\\sc i}}\n\\newcommand{\\SIV}{{\\rm S}\\kern 0.1em{\\sc iv}}\n\\newcommand{\\SVI}{{\\rm S}\\kern 0.1em{\\sc vi}}\n\\newcommand{\\SiI}{\\hbox{{\\rm Si}\\kern 0.1em{\\sc i}}}\n\\newcommand{\\SiII}{\\hbox{{\\rm Si}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\SiIII}{\\hbox{{\\rm Si}\\kern 0.1em{\\sc iii}}}\n\\newcommand{\\SiIV}{\\hbox{{\\rm Si}\\kern 0.1em{\\sc iv}}}\n\\newcommand{\\SII}{\\hbox{{\\rm S}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\SIII}{\\hbox{{\\rm S}\\kern 0.1em{\\sc iii}}}\n\\newcommand{\\NaI}{\\hbox{{\\rm Na}\\kern 0.1em{\\sc i}}}\n\\newcommand{\\TiII}{\\hbox{{\\rm Ti}\\kern 0.1em{\\sc ii}}}\n\\newcommand{\\kms}{\\hbox{km~s$^{-1}$}}\n\\newcommand{\\cmsq}{\\hbox{cm$^{-2}$}}\n\\newcommand{\\cc}{\\hbox{cm$^{-3}$}}\n \n%\n% **** DO NOT MODIFY ABOVE **** **** DO NOT MODIFY ABOVE **** \n%\n%-----------------------------------------------------------------------------\n%\\clubpenalty=450\n%\\widowpenalty=1000000\n\\tighten\n\\begin{document}\n \n%\\received{date month year}\n%\\accepted{date month year}\n%\\journalid{number}{date month year}\n%\\articleid{number}{number}\n%\\slugcomment{submitted to: {\\it The Astrophysical Journal Letters}}\n \n\\lefthead{CHARLTON ET~AL.}\n\\righthead{CONSTRAINTS ON INTRAGROUP HVCs}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\title{QSO Absorption Line Constraints on Intragroup High--Velocity\nClouds}\n\n\\author{Jane~C.~Charlton\\altaffilmark{1}, Christopher~W.~Churchill,\nand Jane~R.~Rigby}\n\\affil{The Pennsylvania State University, University Park, PA 16802 \\\\\ncharlton, cwc, [email protected]}\n\n\\altaffiltext{1}{Center for Gravitational Physics and Geometry}\n\n\\begin{abstract}\nWe show that the number statistics of moderate redshift {\\MgII} and\nLyman limit absorbers may rule out the hypothesis that high velocity\nclouds are infalling intragroup material.\n\\end{abstract}\n\n\\keywords{quasars: absorption lines --- intergalactic\nmedium --- Local Group}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Introduction}\n\nThe origin(s) of high--velocity clouds (HVCs), gaseous material that\ndeparts from the Galactic rotation law by more than 100~{\\kms}, is a\ntopic under debate.\nUndoubtedly, some HVCs arise from tidal streams (e.g.\\ the Magellanic\nStream), and from fountain processes local to the Galaxy\n(\\cite{wakker97}). \nRecently, however, the hypothesis that {\\it most\\/} HVCs are\ndistributed ubiquitously throughout the Local Group and are relics of\ngroup formation has returned to favor (\\cite{blitz};\n\\cite{braun-burton}).\n\nIn the intragroup HVC hypothesis\n(1) the cloud kinematics follow the Local Group standard of\nrest (LGSR), not the Galactic standard of rest (GSR), with\nthe exception of some HVCs related to tidal stripping or\nGalactic fountains (\\cite{blitz}; \\cite{braun-burton}); \n(2) the cloud Galactocentric distances are typically 1~Mpc; \n(3) the extended HVC cloud complexes are presently\naccreting onto the Milky Way;\n(4) the clouds are local analogs of the Lyman limit absorbers observed in\nquasar spectra; \n(5) the clouds have masses of $10^{7}$~M$_{\\odot}$ and greater; and \n(6) the metallicities are lower than expected if the material\noriginated from blowout or fountains from the Milky Way\n(\\cite{wakker99}; \\cite{bowen93}).\n\nBlitz \\etal (1999\\nocite{blitz}; hereafter BSTHB) suggest that there\nare $\\sim 300$ clouds above the $21$--cm $N({\\HI})$ detection threshold of \n$\\simeq 2 \\times 10^{18}$~{\\cmsq}. These clouds have radii $\\sim 15$~kpc \nand are ubiquitous throughout the group. \n\nBraun and Burton (1999\\nocite{braun-burton}, hereafter BB) \ncataloged $65$ Local Group CHVCs, which represent a \nhomogeneous subset of the HVC population discussed by BSTHB.\nHigh resolution $21$--cm observations (\\cite{bb-hires})\nshow that the CHVCs, have compact, $N({\\HI})>10^{19}$~{\\cmsq},\ncold cores with few {\\kms} FWHM surrounded by extended \n``halos'' with FWHM $\\sim 25$~{\\kms}.\nThe typical radius is $\\sim5$--$8$~kpc at the estimated distance\nof $\\sim700$~kpc. The BB sample is homogeneous but is not\ncomplete; they estimate that there could be as many as\n$200$ Local Group CHVCs.\n\nRecently, Zwaan and Briggs (2000\\nocite{zwaan}) reported\nevidence in contradiction of the intragroup hypothesis.\nIn a blind {\\HI} $21$--cm survey of extragalactic groups, sensitive to\n$N({\\HI}) \\sim 10^{18}$~{\\cmsq} (capable of detecting $\\simeq\n10^{7}$~M$_{\\odot}$ {\\HI} clouds), they failed to locate any\nextragalactic counterparts of the Local Group HVCs.\nThis is in remarkable contrast to the numbers predicted.\nIf intragroup HVCs exist around all galaxies or galaxy groups, and\nthe {\\HI} mass function is the same in extragalactic groups as measured\nlocally, then Zwaan \\& Briggs should have detected $\\sim70$ in groups\nand $\\sim 250$ around galaxies ($\\sim 10$ and $\\sim 40$ for the CHVCs,\nrespectively).\n\nThus, the Zwaan and Briggs\\nocite{zwaan} result is in conflict with\nthe intragroup HVC hypothesis.\nSince the hypothesized intragroup clouds are remnants of galaxy\nformation and are shown to be stable against destruction mechanisms\n(BSTHB\\nocite{blitz}), they are predicted to form at very high redshifts \nand to be ubiquitous in galaxy groups to the present epoch.\nIn this {\\it Letter}, we argue that the version of the intragroup HVC \nhypothesis presented by BSTHB is also in conflict with the observed\nredshift number density of moderate redshift $(z \\simeq 0.5)$ {\\MgII} \nand Lyman limit (LLS) quasar absorption line systems.\nWe also find that the properties of the extragalactic analogs\nof the BB CHVCs are severely constrained.\n\nIn general, the redshift number density of a non--evolving population\nof objects, to be interpreted as the number per unit redshift, is written\n\\begin{equation}\n\\frac{dN}{dz} = C_{f}\\frac{n\\sigma c}{H_0} \n\\left( 1 + z \\right) \\left( 1 + 2q_{0}z \\right) ^{-1/2} , \n\\label{eq:dndz}\n\\end{equation}\nwhere $C_{f}$ is the covering factor, $n$ is the number density of\nabsorbing structures, and $\\sigma$ and $C_{f}$ are the surface area\npresented by each structure and its covering factor for detectable\nabsorption. Throughout, we use $H_{0} = 100$~{\\kms}~Mpc$^{-1}$ and $q_0\n= 0.5$, which gives $dN/dz \\propto (1+z)^{1/2}$.\n\n\\section{M\\lowercase{g} II Systems}\n\\label{sec:mgii}\n\nThe statistics of {\\MgII} absorbers are well--established at $0.3 \\leq\nz \\leq 2.2$. \nFor rest--frame equivalent widths of $W({\\MgII}) > 0.3$~{\\AA}\n(``strong'' {\\MgII} absorption)\nSteidel \\& Sargent (1992\\nocite{ss92}) found $dN/dz = 0.8\\pm 0.2$ for\n$z\\simeq 0.5$ with a redshift dependence consistent with no evolution\nexpectations.\nNormal, bright ($L \\geq 0.1~L^{\\ast}$) galaxies are almost\nalways found within $40$~kpc of strong {\\MgII} absorbers\n(\\cite{bb91}; \\cite{bergeron92}; \\cite{lebrun93}; \\cite{sdp94};\n\\cite{s95}; \\cite{3c336}).\nFrom the Steidel, Dickinson, and Persson survey, all but $3$ of $58$ strong {MgII} absorbers, \ndetected toward $51$ quasars, have identified galaxies with a coincident\nredshift within that impact parameter (sky projected separation\nfrom the quasar line of sight) (see \\cite{cc96}).\nAlso, it is rare to observe a galaxy with an impact parameter less than \n$\\sim 40 h^{-1}$~kpc that does {\\it not\\/} give rise to {\\MgII} \nabsorption with $W({\\MgII}) > 0.3$~{\\AA} (\\cite{s95}). \nIn $25$ ``control fields'' of quasars, without observed strong {\\MgII} \nabsorption in their spectra, only two galaxies had impact parameters\nless than $40 h^{-1}$~kpc (see also \\cite{cc96}).\nAs such, the regions within $\\sim 40 h^{-1}$~kpc of typical galaxies\naccount for the vast majority of {\\MgII} absorbers above this\nequivalent width threshold; there is nearly a ``one--to--one''\ncorrespondence.\nIf we accept these results, it would imply that there is little\nroom for a contribution to $dN/dz$ from a population of intragroup\nclouds {\\it which have impact parameters much greater than $\\sim40 h^{-1}$~kpc}.\n\nHowever, the predicted cross section for {\\MgII} absorption from \nthe extragalactic intragroup clouds analogous to HVCs would be substantial.\nWe quantify the overprediction of the redshift path density by\ncomputing the ratio of $dN/dz$ of the intragroup clouds to that of\n{\\MgII} absorbing galaxies,\n\\begin{equation}\n\\frac{(dN/dz)_{cl}}{(dN/dz)_{gal}} = F \n \\left( \\frac{f_{cl}}{f_{gal}} \\right)\n \\left( \\frac{N_{cl}}{N_{gal}} \\right) \n \\left( \\frac{R_{cl}}{R_{gal}} \\right) ^{2} ,\n\\label{eq:ratio}\n\\end{equation}\nwhere $F$ is the fraction of {\\MgII} absorbing galaxies that reside in\ngroups having intragroup HVC--like clouds, $f_{cl}$ is the fraction\nof the area of the clouds and $f_{gal}$ is the fraction of the area\nof the galaxies that would produce $W({\\MgII}) > 0.3$~{\\AA} along the \nline of sight, and $N_{cl}$ and $N_{gal}$ are the number of clouds \nand galaxies per group, respectively.\nThe cross section of the group times the intragroup cloud covering\nfactor, $C_{f}\\cdot \\pi R^{2}_{gr}$, is equal to $N_{cl} \\cdot \\pi R^{2}_{cl}$.\nThe total predicted $dN/dz$ for {\\MgII} absorbers with $W({\\MgII}) >\n0.3$~{\\AA} is then,\n\\begin{equation}\n\\left( \\frac{dN}{dz} \\right) _{tot} =\n\\left( \\frac{dN}{dz} \\right) _{gal}\n\\left[ 1 + \\frac{(dN/dz)_{cl}}{(dN/dz)_{gal}} \\right] .\n\\label{eq:totaldndz}\n\\end{equation}\nIf virtually all {\\MgII} absorbers are accounted for by galaxies,\nit is required that $(dN/dz)_{tot} \\simeq (dN/dz)_{gal}$; the left\nhand side of Equation~\\ref{eq:ratio} must be very close to zero.\n\nIn the BSTHB version of the intragroup HVC model, the ``best''\nexpected values are $N_{cl}=300$ and $R_{cl} = 15$~kpc\n(BSTHB; \\cite{blitz-privcomm}); \nif we take $R_{gal} = 40$~kpc and $f_{gal} = 1$ (\\cite{s95}),\nand assuming $N_{gal} = 4$, we find that the covering factor for\n{\\MgII} absorption from extragalactic analogs to the Local Group HVCs\nwould exceed that from galaxies by a factor of $\\sim 10$ for $F=1$ and\n$f_{cl}=1$, giving $(dN/dz)_{tot} \\simeq 9$.\nMore recently, Blitz and Robinshaw (2000\\nocite{blitzdsph}) have\nsuggested that sizes may be smaller ($R_{cl} = 8$~kpc) when \nbeam--smearing is considered.\nConsidering this as an indication of uncertainties in the\nBSTHB parameters, and considering $2 < N_{gal} < 6$ for the\ntypical number of group galaxies, we find, for $F=1$ and\n$f_{cl}=1$, a range $2 < (dN/dz)_{cl}/(dN/dz)_{gal} < 21$.\nThis corresponds to $2.6 < (dN/dz)_{tot} < 17.6$.\nIt is unlikely that $F$ is significantly less than unity;\nthe majority of galaxies reside in groups like the Local Group\nthat would have HVC analogs.\nIn order that $(dN/dz)_{tot} \\sim (dN/dz)_{gal}$,\n$f_{cl} \\ll 0.2$ is required.\n\nIt is not clear what fraction $f_{cl}$ of\nHVCs with $N({\\HI})$ above the $10^{18}$~{\\cmsq} detection \nthreshold will give rise to $W({\\MgII}) \\geq 0.3$~{\\AA}\nbecause the equivalent width is sensitive\nto the metallicity and internal velocity dispersion of the clouds.\nBased upon Cloudy (\\cite{ferland}) photoionization equilibrium models, \na cloud with $N({\\HI}) \\simeq 10^{18}$~{\\cmsq}, subject to\nthe ionizing metagalactic background (\\cite{haardt-madau}), would give\nrise to {\\MgII} absorption with $N({\\MgII}) \\simeq\n10^{14}N_{18}(Z/Z_{\\odot})$~{\\cmsq}, where $N_{18}$ is the {\\HI}\ncolumn density in units of $10^{18}$~{\\cmsq} and $Z/Z_{\\odot}$ is the\nmetallicity in solar units.\nFor optically thick clouds, those with $N({\\HI}) \\geq\n10^{17.5}$~{\\cmsq}, this result is insensitive to the assumed\nionization parameter\\footnote{The ionization parameter is the ratio of\nthe number density of hydrogen ionizing photons to the number density\nof electrons, $n_{\\gamma}/n_{e}$.} over the range $10^{-4.5}$ to\n$10^{-1.5}$.\n\nBSTHB expect HVCs to have $Z/Z_{\\odot} \\sim 0.1$.\nFor $N_{18} = 2$ and $Z/Z_{\\odot} = 0.1$, clouds with internal\nvelocity dispersions of $\\sigma _{cl} \\geq 20$~{\\kms} (Doppler\n$b \\geq 28$~{\\kms}) give rise to $W({\\MgII}) \\geq 0.5$~{\\AA}.\nFor $\\sigma_{cl} = 10$~{\\kms} ($b = 14$~{\\kms}), $W({\\MgII}) = 0.3$~{\\AA}.\nThe CHVC ``halos'' typically have FWHM of $29$--$34$~{\\kms}, which\ncorresponds to $\\sigma _{cl} \\sim 12$--$14$~{\\kms} \n(\\cite{braun-burton}). \nThus it appears that most lines of sight through the BSTHB\nextragalactic analogs will produce strong {\\MgII} absorption.\nCertainly $f_{cl} > 0.2$, so there is a serious\ndiscrepancy between the predicted $(dN/dz)_{tot}$ and the\nobserved value.\n\nHowever, if the intragroup clouds have lower metallicities, this would\nresult in smaller $W({\\MgII})$. Unfortunately, there has only been\none metallicity estimate published for an HVC, which may or may not be\nrelated to the Galaxy. Braun and Burton (2000\\nocite{bb-hires}) estimate that\nCHVC 125+41-207, with $W({\\MgII}) = 0.15$~{\\AA}, has a metallicity of $0.04\n< Z/Z_{\\odot} < 0.07$, however this is quite uncertain because of the \neffects of beam smearing on measuring the $N({\\HI})$ value.\nBecause of the uncertainties, we simply state that a population of low\nmetallicity clouds could reduce the discrepancy\nbetween the predicted redshift density for intragroup clouds,\n$(dN/dz)_{cl}$, and the observed value of $(dN/dz)_{tot}$. However,\nthen the expected number of smaller $W({\\MgII})$ systems to arise from\nintragroup clouds would be increased.\n\nThe observed {\\MgII} equivalent width distribution rises rapidly below\n$0.3$~{\\AA} (``weak'' {\\MgII} absorbers), such that $dN/dz =\n2.2\\pm0.3$ for $W({\\MgII}) > 0.02$~{\\AA} at $z=0.5$ (\\cite{weak1}).\nTo this equivalent width limit, {\\MgII} absorption could be observed\nfrom intragroup HVCs with $N_{18}=2$ and metallicities as low as\n$Z/Z_{\\odot} = 0.0025$ [for $N({\\MgII}) = 10^{11.7}$~{\\cmsq},\n$W({\\MgII})$ is independent of $\\sigma _{cl}$]. However, almost all\n($9$ out of a sample of $10$) {\\MgII} absorbers with $W({\\MgII}) <\n0.3$~{\\AA} do {\\it not\\/} have associated Lyman limit breaks\n(\\cite{paper1}); that is, their $N({\\HI})$ is more than a decade below\nthe sensitivity of $21$--cm surveys. Thus, based upon available data,\nroughly $90$\\% of the ``weak'' {\\MgII} absorbers do not have the\nproperties of HVCs, and therefore are {\\it not\\/} analogous to the\nclouds invoked for the intragroup HVC scenario. If $10$\\% of the weak\n{\\MgII} absorbers are analogs to the intragroup HVCs, they would\ncontribute an additional $0.20$ to $(dN/dz)_{cl}$.\n\nSince the BB CHVC extragalactic analogs have smaller cross sections,\nwe should separately consider whether they would produce a discrepancy\nwith the observed {\\MgII} absorption statistics. BB observed\n$N_{cl}=65$ and inferred a typical $R_{cl} = 5$--$8$~kpc for the\nCHVCs, however a complete sample might have $N_{cl}=200$. Assuming\n$N_{gal}=2$--$6$, $R_{gal} = 40$~kpc, $f_{gal} = 1$, and $F=1$, for\nthe BB subsample of the HVC population, we obtain \n$0.17 f_{cl} < (dN/dz)_{cl}/(dN/dz)_{gal} < 4.0 f_{cl}$.\n\nThe cores of the CHVCs have $N({\\HI}) > 10^{19}$~{\\cmsq} and they\noccupy only about $15$\\% of the detected extent. \nFor $Z/Z_{\\odot} > 0.01$ and $\\sigma_{cl} = 10$~{\\kms}, these cores can produce\n$W({\\MgII}) \\ge 0.3$~{\\AA} over their full area. It follows that\n$f_{cl} = 0.15$, which yields $0.025 < (dN/dz)_{cl}/(dN/dz)_{gal} <\n0.6$. Depending on the specific parameters, there may or may not be a\nconflict with the observed $(dN/dz)_{tot}$ for strong {\\MgII}\nabsorption.\n\nThe ``halos'' of the CHVCs have $N({\\HI}) > 10^{18}$~{\\cmsq} and, as\ndiscussed above, would produce weak {\\MgII} absorption for\n$Z/Z_{\\odot} > 0.005$ over most of the cloud area. This implies\ncontribution to $(dN/dz)$ from BB CHVC analogs that is in the range\n$0.14 < (dN/dz)_{cl} < 3.2$. If the number were at the high end of\nthis range, the cross section would be comparable to the observed\n$(dN/dz)$ for weak {\\MgII} absorbers at $z=0.5$. However, as noted\nabove when considering the BSTHB scenario, there is a serious\ndiscrepancy. Only $\\sim 10$\\% of the weak {\\MgII} absorbers show a\nLyman limit break, so extragalactic analogs of the BB CHVCs can only\nbe a fraction of the weak {\\MgII} population. Regions of CHVCs at larger\nradii, with $N({\\HI})$ below the threshold of present $21$--cm\nobservations, are constrained to have $Z/Z_{\\odot} \\ll 0.01$ in order\nthat they do not produce a much larger population of weak {\\MgII}\nabsorbers with Lyman limit break than is observed.\n\n\\section{Lyman Limit Systems}\n\\label{sec:lls}\n\nThe redshift number density of LLS also places strong constraints on\nintragroup environments that give rise to Lyman breaks in quasar\nspectra. This argument is not sensitive to the assumed\ncloud velocity dispersion and/or metallicity.\n\nStatistically, $dN/dz$ for {\\MgII} systems is consistent\n(1~$\\sigma$) with $dN/dz$ for LLS.\nAt $z \\simeq 0.5$, LLS have $dN/dz = 0.5 \\pm 0.3$ (\\cite{kplls}) and\n{\\MgII} systems have $dN/dz = 0.8 \\pm 0.2$ (\\cite{ss92}).\nChurchill \\etal (2000a\\nocite{paper1}) found a Lyman limit break\n[i.e.\\ $N({\\HI}) \\geq 10^{16.8}$~{\\cmsq}] for each system in a sample\nof ten having $W({\\MgII}) > 0.3$~{\\AA}.\nLLS and {\\MgII} absorbers have roughly the same redshift number\ndensity and therefore {\\MgII}--LLS absorption must almost always arise \nwithin $\\sim 40$~kpc of galaxies (\\cite{s93}).\nAs such, there is little latitude for a substantial contribution\nto $dN/dz$ from intragroup Lyman limit clouds.\n\nUsing Equation~\\ref{eq:dndz}, we could estimate this contribution by\nconsidering the volume density of galaxy groups and the cross section\nfor HVC Lyman limit absorption in each.\nHowever, the volume density of groups is not well measured,\nparticularly out to $z=0.5$.\n\nInstead, we make a restrictive argument based upon a comparison\nbetween the cross sections for Lyman limit absorption of $L^{\\ast}$ \ngalaxies and for HVCs in a typical group (similar to the discussion of\n{\\MgII} absorbers in \\S~\\ref{sec:mgii}).\nAgain, we simply compare the values of $C_f$ for the different\npopulations of objects in a typical group.\nThe covering factor for HVCs within the group is\n\\begin{equation}\nC_f = N_{cl}\n\\frac{\\left(R_{cl}\\right)^2}{\\left(R_{gr}\\right)^2} .\n\\end{equation}\nThe best estimate for the BSTHB version of the intragroup HVC model,\nwith $N_{cl} = 300$, $R_{cl} = 15$~kpc, and a group radius \n$R_{gr} = 1.5$~Mpc, gives $C_{f} = 0.03$ for $N({\\HI}) \\simeq 2 \\times\n10^{18}$~{\\cmsq}. \nIf instead we use the BB number of observed CHVCs, $N_{cl} = 65$,\nand $R_{cl} = 5$--$8$~kpc, we obtain a much smaller number, \n$0.0007 < C_{f} < 0.0018$.\nHowever, if the BB sample is corrected for incompleteness such that\n$N_{cl} = 200$, these numbers increase so that\n$0.002 < C_{f} < 0.006$.\n\nIn comparison, a typical group with $\\sim4$ $L^{\\ast}$ galaxies, each with a\nLyman limit absorption cross section of $R_{cl} \\sim 40$~kpc, would\nhave $C_f = 0.002$. \nIf they existed with the properties discussed,\nthe extragalactic analogs to the BSTHB HVCs would dominate the\ncontribution of $L^{\\ast}$ galaxies to the $dN/dz$ of LLS by at least\na factor of $\\sim 15$, and this is only considering HVC regions with\n$N({\\HI}) > 2 \\times 10^{18}$~{\\cmsq} that are detected in the $21$--cm\nsurveys. \nAny extensions in area below this threshold value [down to\n$N({\\HI}) \\sim 5 \\times 10^{16}$~{\\cmsq}] would worsen the discrepancy.\nAs such, the BSTHB hypothesis is definitively ruled out.\n\nFor regions of BB CHVCs with $N({\\HI}) > 2 \\times 10^{18}$~{\\cmsq}, the\ncovering factor ranges from $C_f =0.0007$ to $C_f=0.006$ depending\non assumed sizes and corrections for incompleteness. This ranges\nfrom $35$--$300$\\% of the cross section for the $L^{\\ast}$ galaxies.\nThe {\\it total} observed $dN/dz$ for Lyman limit absorption \n(down to $\\log N({\\HI}) = 17$~{\\cmsq}) is only $\\sim 0.5$, even a $35$\\% \ncontribution to the Lyman limit cross section from HVCs \nthat are separate from galaxies creates a discrepancy.\nThis would imply that the result that most lines of sight within \n$40$~kpc of a typical $L^{\\ast}$ galaxy produce Lyman limit\nabsorption is incorrect.\nThis would further imply that there is a substantial population of\nstrong {\\MgII} absorbers without Lyman limit breaks\n(to account for $dN/dz = 0.8$ for strong {\\MgII}\nabsorption) or of strong {\\MgII} absorbers not associated\nwith galaxies. \nBoth types of objects are rarely observed\n(\\cite{paper1}; \\cite{bb91}; \\cite{bergeron92}; \\cite{lebrun93};\n\\cite{sdp94}; \\cite{s95}; \\cite{3c336}).\nFurthermore, $C_f=0.002$ for BB CHVCs only takes into account the\nfraction of the BB CHVC areas with $N({\\HI}) > 2 \\times 10^{18}$~{\\cmsq}.\nTherefore, the extended ``halos'' around the CHVCs are also\nconstrained not to contribute substantial cross section for Lyman\nlimit absorption along extragalactic lines of sight.\n\n\\section{Summary}\n\\label{sec:summary}\n\nWe have made straight--forward estimates of the\npredicted redshift number density at $z \\simeq 0.5$ of\n{\\MgII} and LLS absorption from hypothetical extragalactic\nanalogs to intragroup HVCs as expected by extrapolating from the BSTHB\nand BB Local Group samples. We find that it is difficult to reconcile\nthe intragroup hypothesis for HVCs with the observed $dN/dz$ of\n{\\MgII} and LLS systems.\n\nThe discrepancy between the $dN/dz$ of {\\MgII}--LLS absorbers and the\nobserved covering factor of ``intragroup'' HVCs could be reduced if\nthe HVCs have a clumpy structure. Such structure would result in\n{\\MgII}--LLS absorption observable only in some fraction, $f_{los}$,\nof the lines of sight through the cloud. Effectively, this reduces\nthe covering factor for Lyman limit absorption, or the value of\n$f_{cl}$ in equation (2) for {\\MgII} absorbers. Considering beam smearing\nin $21$--cm surveys, substructures would be detected above a\n$N({\\HI}) > 2 \\times 10^{18}$~{\\cmsq} $21$--cm detection threshold\nif their column densities were\n$N({\\HI})_{sub} > 2 \\times 10^{18}/f_{los}$~{\\cmsq}. The predicted\n$dN/dz$ for HVC--like clouds could be reduced by a factor of ten if\n$f_{los} \\leq 0.1$, giving $N({\\HI})_{sub} > 2 \\times\n10^{19}$~{\\cmsq}. All the gas outside these higher {\\HI} column\ndensity substructures would need to be below the Lyman limit or the\narguments in \\S~\\ref{sec:lls} would hold. It is difficult to\nreconcile such a density distribution with the high resolution\nobservations of BB CHVCs which show diffuse halos around the\ncore concentrations (\\cite{bb-hires}), but these ideas merit\nfurther consideration.\n\n\\subsection{The BSTHB Scenario}\n\nWe conclude that the predicted $dN/dz$ from the hypothetical\npopulation of intragroup HVCs along extragalactic sight lines to\nquasars from the BSTHB scenario would exceed: \n\n1) the $dN/dz$ of {\\MgII} absorbers with $W({\\MgII}) \\geq 0.3$~{\\AA}.\nThis class of absorber is already known to arise within $\\sim 40 h^{-1}$~kpc\nof normal, bright galaxies (\\cite{bb91}; \\cite{bergeron92};\n\\cite{lebrun93}; \\cite{sdp94}; \\cite{s95}; \\cite{3c336}).\n\n2) the $dN/dz$ of ``weak'' {\\MgII} absorbers with $0.02 < W({\\MgII}) <\n0.3$~{\\AA} absorption. \nIn principle, weak {\\MgII} absorption could\narise from low metallicity, $0.005 \\leq Z/Z_{\\odot} < 0.1$, intragroup\nHVCs. However, the majority of observed weak systems are already\nknown to be higher metallicity, $Z/Z_{\\odot} \\simeq 0.1$, sub--Lyman\nlimit systems (\\cite{weak1}; \\cite{rigby}).\n\n3) the $dN/dz$ of Lyman limit systems.\nThese would be produced by all extragalactic BSTHB HVC analogs\nregardless of metallicity.\nHowever, {\\it most\\/} Lyman limit systems are seen to arise within \n$\\simeq 40 h^{-1}$~kpc of luminous galaxies (\\cite{s93}; \\cite{paper2}).\n\nThese points do not preclude a population of infalling intragroup\nclouds which do not present a significant cross section for\n$21$--cm absorption, as predicted by CDM models\n(\\cite{iforget}; \\cite{moore}).\nIn fact, such intragroup objects could be related to sub--Lyman limit\nweak {\\MgII} absorbers (\\cite{rigby}).\n\n\\subsection{The BB Scenario}\n\nThe properties of the BB CHVC population are also significantly\nconstrained by {\\MgII} and Lyman limit absorber statistics:\n\n1) They {\\it could\\/} produce $W({\\MgII}) \\geq 0.3$~{\\AA} in excess of\nwhat is observed if a large incompleteness correction is applied\n(i.e. so that $N_{cl} = 200$), or if relatively large sizes ($R_{cl}\n\\sim 8$~kpc) are assumed.\n\n2) They would be expected to contribute to the $dN/dz$ of\nweak [$W({\\MgII}) > 0.02$~{\\AA}] {\\MgII} absorption.\nHowever, based upon observations (\\cite{paper1}), only $\\sim 10$\\% \nof the population of weak {\\MgII} absorbers have Lyman--limit breaks.\nTherefore, only a small fraction of weak {\\MgII} absorption could \narise in extragalactic BB CHVC analogs.\n\n3) The $dN/dz$ for Lyman limit absorption from the hypothesized BB\nCHVC population could be a significant\nfraction, or comparable to that expected from the local environments of\n$L^{\\ast}$ galaxies (within $40$~kpc); the observed value is already\nconsistent with that produced by the galaxies.\n\n4) The CHVCs are observed to have a cool core with $N({\\HI}) >\n10^{19}$~{\\cmsq}, surrounded by a halo which typically extends to\n$R_{cl} \\sim 5$~kpc. It is natural to expect that the {\\HI} extends\nout to larger radii at smaller $N({\\HI})$ and should produce a Lyman\nlimit break out to the radius at which $N({\\HI}) < 10^{16.8}$~{\\cmsq}.\nAlthough there is expected to be a sharp edge to the {\\HI} disk at\n$N({\\HI}) \\sim 10^{17.5}$ or $10^{18}$~{\\cmsq} (\\cite{maloney};\n\\cite{corbelli}; \\cite{dove}), physically we would expect that this\nedge would level off at $\\sim 10^{17.5}$~{\\cmsq}, such that a\nsignificant cross section would be presented at $10^{16.8} < N({\\HI})\n< 10^{17.5}$~{\\cmsq}. Another possibility is that there is a sharp\ncutoff of the structure at $N({\\HI}) \\sim 2 \\times 10^{18}$~{\\cmsq},\nbut this is contrived.\n\n\\section{Conclusion}\n\nWe are forced to the conclusion that there can only be a limited\nnumber of extragalactic infalling group HVC analogs at $z \\sim 0.5$.\nFuture data could force a reevaluation of the relationships between\ngalaxies, Lyman limit systems, and {\\MgII} absorbers, but it seems\nunlikely that the more serious inconsistencies we have identified\ncould be reconciled in this way. A clumpy distribution of {\\HI}\ncould be constructed that would reduce the discrepancy, but would\nrequire very diffuse material (below the Lyman limit) around dense \ncores. Evolution in the population of HVCs\nis another possibility. If the extragalactic background radiation\ndeclined from $z=0.5$ to the present, the clouds would have been more\nionized in the past, and therefore would have had smaller cross\nsections at a given $N({\\HI})$. However, this does not explain why\nZwaan and Briggs (2000\\nocite{zwaan}) do not see the $z=0$\nextragalactic analogs to the HVCS or CHVCs. Our results are entirely\nconsistent with theirs, and the implications are the same: the\ndiscrepancies between the Local Group HVC population and the\nstatistics of {\\MgII} and Lyman limit absorbers can only be reconciled\nif most of the extragalactic HVC analogs are within $100$--$200$~kpc\nof galaxies, and not at large throughout the groups.\n\n\\acknowledgements\nWe thank L. Blitz, J. Bregman, J. Mulchaey, B. Savage, K. Sembach,\nT. Tripp, and especially B. Wakker and Buell Jannuzi, and our\nreferees for stimulating discussions and comments.\nSupport for this work was provided by NSF grant AST--9617185\n(J. R. 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{
"name": "astro-ph0002001.extracted_bib",
"string": "\\begin{thebibliography}{XXX}\n\n\\bibitem[Bergeron \\& Boiss\\'e 1991]{bb91}\nBergeron, J., \\& Boiss\\'e, P. 1991, A\\&A, 243, 344\n\n\\bibitem[Bergeron \\etal 1992]{bergeron92}\nBergeron, J., Cristiani, S., \\& Shaver, P. A. 1992, A\\&A, 257, 417\n\n\\bibitem[Blitz \\etal 1999]{blitz}\nBlitz, L., Spergel, D. N., Teuben, P. J., Hartmann, D., \\& Burton, W. B. 1999,\nApJ, 514, 818\n\n\\bibitem[Blitz 2000, private communication]{blitz-privcomm}\nBlitz, L. 2000, private communication\n\n\\bibitem[Blitz \\& Robinshaw 2000]{blitzdsph}\nBlitz, L., \\& Robinshaw, T. 2000, ApJ, submitted\n\n\\bibitem[Bowen \\& Blades 1993]{bowen93}\nBowen, D. V., \\& Blades, J. C. 1993, ApJ, 403, L55\n\n\\bibitem[Braun \\& Burton 2000]{bb-hires}\nBraun, R., \\& Burton, W. B. 2000, A\\&A, in press\n\n\\bibitem[Braun \\& Burton 1999]{braun-burton}\nBraun, R., \\& Burton, W. B. 1999, A\\&A, 341, 437\n\n\\bibitem[Charlton \\& Churchill 1998]{mgii-profiles}\nCharlton, J. C., \\& Churchill, C. W. 1998, ApJ, 499, 181\n\n\\bibitem[Charlton \\& Churchill 1996]{cc96}\nCharlton, J. C., \\& Churchill, C. W. 1996, ApJ, 465, 631\n\n\\bibitem[Churchill \\etal 2000a]{paper1}\nChurchill, C. W., Mellon, R. R., Charlton, J. C., Jannuzi, B. T.,\nKirhakos, S., Steidel, C. C., \\& Schneider, D. P. 2000a, ApJ,\nin press\n\n\\bibitem[Churchill \\etal 2000b]{paper2}\nChurchill, C. W., Mellon, R. R., Charlton, J. C., Jannuzi, B. T.,\nKirhakos, S., Steidel, C. C., \\& Schneider, D. P. 2000b, ApJ,\nsubmitted\n\n\\bibitem[Churchill \\etal 1999]{weak1}\nChurchill, C. W., Rigby, J. R., Charlton, J. C., \\& Vogt, S. S. 1999,\nApJS, 120, 51\n\n\\bibitem[Corbelli \\& Salpeter 1994]{corbelli}\nCorbelli, E. and Salpeter, E. E. 1994, \\apj, 419, 104\n\n\\bibitem[Dove \\& Shull 1994]{dove}\nDove, J. B., and Shull, J. M. 1994, \\apj, 423, 196\n\n\\bibitem[Ferland 1996]{ferland}\nFerland, G. J. 1996, Hazy, University of Kentucky Internal Report\n\n\\bibitem[Haardt \\& Madau 1996]{haardt-madau}\nHaardt, F., \\& Madau, P. 1996, ApJ, 461, 20\n\n\\bibitem[Klypin \\etal 1999]{iforget}\nKlypin, A. A., Kravtsov, A. V., Valenzuela, O., \\& Prada, F. 1999,\nApJ, submitted\n\n\\bibitem[Le~Brun \\etal 1993]{lebrun93}\nLe~Brun, V., Bergeron, J., Boiss\\'e, P., \\& Christian, C. 1993,\nA\\&A, 279, 33\n\n\\bibitem[Maloney 1993]{maloney}\nMaloney, P. 1993, \\apj, 414, 57\n\n\\bibitem[Moore \\etal 1999]{moore}\nMoore, B., Ghigna, S., Governato, F., Lake, G., Quinn, T.,\nStadel, J., \\& Tozzi, P. 1999,\nApJ, 524, L19\n\n\\bibitem[Rigby \\etal 2000]{rigby}\nRigby, J. R., Charlton, J. C., Churchill, C. W. 2000, ApJ, in preparation\n\n\\bibitem[Steidel 1993]{s93}\nSteidel, C. C. 1993, in The Environment and Evolution of Galaxy, eds.\\\nJ. M. Shull \\& H. A. Thronson, Jr., (Dordrecht: Kluwer Academic), 263\n\n\\bibitem[Steidel 1995]{s95}\nSteidel, C. C. 1995, in QSO Absorption Lines, ed. G. Meylan (Garching:\nSpringer--Verlag), 139\n\n\\bibitem[Steidel, Dickinson, \\& Persson 1994]{sdp94}\nSteidel, C. C., Dickinson, M. \\& Persson, E. 1994, ApJ, 437, L75 \n\n\\bibitem[Steidel \\etal 1997]{3c336}\nSteidel. C. C., Dickinson, M., Meyer, D. M., Adelberger, K. L., \\&\nSembach, K. R. 1997, ApJ, 480, 568\n\n\n\\bibitem[Steidel \\& Sargent 1992]{ss92}\nSteidel, C. C., \\& Sargent, W. L. W. 1992, ApJS, 80, 1\n\n\\bibitem[Stengler--Larrea \\etal 1995]{kplls}\nStengler--Larrea, E. A. \\etal 1995, ApJ, 444, 64\n\n\\bibitem[Wakker \\etal 1999]{wakker99}\nWakker, B. P., Howk, J. C., Savage, B. D., Tufte, S. L., Renolds,\nR. J., van Woerden, H., Schwarz, U. J., Peletier, R. F., \\& Kalberla,\nP. M. W. 1999, Nature, 400, 388\n\n\\bibitem[Wakker \\& van Woerden 1997]{wakker97}\nWakker, B. P., and van Woerden, H. 1997, ARA\\&A, 35, 509\n\n\\bibitem[Zwaan \\& Briggs 2000]{zwaan}\nZwaan, M. A., \\& Briggs, F. H. 2000, ApJL, in press\n\n\\end{thebibliography}"
}
] |
astro-ph0002002
|
Point source models for the gravitational lens B1608+656: Indeterminacy in the prediction of the Hubble constant
|
[
{
"author": "Gabriela Surpi and Roger Blandford"
}
] |
We apply elliptical isothermal mass models to reproduce the point source properties, i.e. image positions, flux density ratios and time delay ratios, of the quadruple lens B1608+656. A wide set of suitable solutions is found, showing that models that only fit the properties of point sources are under-constrained and can lead to a large uncertainty in the prediction of H$_\circ$. We present two examples of models predicting H$_\circ\!=\!100{km\,s^{\!-\!1}Mpc^{\!-\!1}}$ ($\chi^2\!=\!4$) and H$_\circ\!=\!69{km\,s^{\!-\!1}Mpc^{\!-\!1}}$ ($\chi^2\!=\!24$).
|
[
{
"name": "gsurpi.tex",
"string": "\\documentstyle[11pt,paspconf,epsf]{article}\n\n\\begin{document}\n\\title{Point source models for the gravitational lens B1608+656:\nIndeterminacy in the prediction of the Hubble constant}\n\n\\author{Gabriela Surpi and Roger Blandford}\n\\affil{California Institute of Technology 130-33, Pasadena CA 91125, USA}\n\n\\begin{abstract}\nWe apply elliptical isothermal mass\nmodels to reproduce the point source properties, i.e.\nimage positions, flux density ratios and\ntime delay ratios,\nof the quadruple lens B1608+656.\nA wide set of suitable solutions is found, showing that\nmodels that only fit the properties of point sources\nare under-constrained and can lead to a large\nuncertainty in the prediction of H$_\\circ$. We present\ntwo examples of models predicting H$_\\circ\\!=\\!100{\\rm\nkm\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}}$ ($\\chi^2\\!=\\!4$)\nand H$_\\circ\\!=\\!69{\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}}$ ($\\chi^2\\!=\\!24$). \n\\end{abstract}\n\n\\keywords{gravitational lensing, models}\n\n\\vspace*{-0.4cm}\n\\section{Introduction}\n\nRelative positions, flux ratios and time delays of the 4\nimages in B1608+656 have been presented here by \nFassnacht (1999) and references therein ({\\it cf} Table~\\ref{obs}).\nKoopmans \\& Fassnacht (1999)\nhave concluded H$_\\circ\\!=\\!59^{+7}_{-6}{\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}}$\nwithin the context of a family of parametrized, isothermal models. Here, we\ninvestigate whether a larger set of models allows a wider\nrange of Hubble constants.\n%\\vspace*{-0.1cm}\n\\section{Elliptical isothermal models}\n\nFollowing Blandford \\& Kundi\\'c (1997),\nwe adopt a scaled lensing potential $\\psi$ composed of two elliptical\ncontributions to describe the lensing galaxies G1 and G2 plus \nexternal shear $\\gamma$:\n\\vspace*{-0.2cm}\n\\begin{equation}\n\\psi_= \\sum_{i=1}^2 \\,\\, b_i\\, \\{s_i^2+r_i^2\\, [1-e_i\\, \\cos (2(\\varphi_i-\\phi_i))]\\}^{1\\over 2}+\nr_1^2\\, \\gamma\\, \\cos (2(\\varphi_1-\\varphi_\\gamma))\n\\end{equation}\n\\vspace*{-0.2cm}\n\\normalsize\n\nHere $(r_i,\\varphi_i )$ are polar coordinates with origin at the\ncenter of each galaxy.\n$s$ measures the core radius, $e$ and $\\phi$\nthe ellipticity and position angle of the major axis.\nAt large radius the mass distribution is isothermal, \ngoing as $\\Sigma \\propto r^{-1}$. \nThe lenses will be fixed at $\\vec{x}_{G1}\\!=\\!(0.446,-1.063)''$ and\n$\\vec{x}_{G2}\\!=\\!(-0.276,-0.937)''$, the centroids in H band, which\nare less affected by reddening (Blandford, Surpi \\& Kundi\\'c 1999).\n\nWe minimize a $\\chi^2$ function.\nThe best fit achieved, hereafter Model A, has $\\chi^2\\!=\\!4.0$ and yields \n$H_{\\circ}\\!=\\!100{\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}}$.\nModels with lower values of $H_\\circ$ can also be\nbuilt fixing $H_\\circ$ and fitting the 3 time delays instead of the\ntime delay ratios. As an example we present the results of Model B\nhaving $H_\\circ\\!=\\!69{\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}}$\nand $\\chi^2\\!=\\!24.7$.\nThe parameters and predictions of Model A and B\nare displayed in Tables~\\ref{par} and~\\ref{obs} respectively.\nThey represent reasonable mass distributions given, especially,\nour ignorance of the dark matter distribution (Figure 1).\n\n\\section{Discussion}\n\nA variety of parametrized models \ncan reproduce the point source properties \nof B1608+656. This precludes an accurate determination of H$_\\circ$.\nTo break the degeneracy, extra constraints, associated with\nthe extended emission of the source, have to be incorporated.\nIt is also helpful to specify the distribution of dark matter\non larger scale than the image distribution. A similar conclusion\nhas been drawn by Williams \\& Saha (1999) using pixellated models.\n\\begin{figure}\n\\vspace*{-0.5cm}\n\\begin{center}\n\\leavevmode\n\\epsfysize=1.55in\n\\epsfbox{gsurpi1.eps}\n\\vspace*{-0.2cm}\n\\caption{Surface mass density in Models A and B}\n\\vspace*{-0.5cm}\n\\end{center}\n\\end{figure}\n\n\\begin{table}\n\\caption{Model parameters.} \\label{par}\n\\vspace*{-0.3cm}\n\\begin{center}\n\\footnotesize\n\\begin{tabular}{c|cc|cc}\n\\tableline\n&\\multicolumn{2}{c|}{Model~A~(H$_\\circ\\!=\\!100 \\scriptstyle\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}$)}\n&\\multicolumn{2}{c}{Model~B~(H$_\\circ\\!=\\!69 \\scriptstyle\\rm km\\,s^{\\!-\\!1}Mpc^{\\!-\\!1}$)}\\\\\n%\n\\cline{2-5}\n%\nParameters& G1 & G2 & G1 & G2 \\\\\n%\n\\tableline\n%\ns('') & 0.10 & 0.10 & 0.00 & 0.05 \\\\\nb & 0.9072 & 0.2453 & 0.7797 & 0.3429 \\\\\ne & 0.3269 & 0.6405 & 0.1570 & 0.3149 \\\\\n$\\phi(^\\circ)$ & 163.45 & 154.93 & 172.62 & 160.86 \\\\\n\\tableline\n$\\gamma,\\varphi_{\\gamma}(^\\circ)$ & 0.0876 & -10.92& 0.0473 & 12.47 \\\\\n%\n\\tableline\n%\n\\end{tabular}\n\\end{center}\n\\vspace*{-0.4cm}\n\\caption{Comparison between observations and model predictions.} \\label{obs}\n\\vspace*{-0.3cm}\n\\begin{center}\n\\footnotesize\n\\begin{tabular}{cccc}\n\\tableline\n%\nProperties & \\multicolumn{1}{c}{Observation}\n& \\multicolumn{1}{c}{Model A}\n& \\multicolumn{1}{c}{Model B} \\\\\n%\n\\tableline\n%\n$\\vec x_A('')$ & (~0.0000,~0.0000) $\\pm$ (0.0023,0.0023) & (~0.0000,~0.0000) & (~0.0000,~0.0000)\\\\\n$\\vec x_B('')$ & (-0.7380,-1.9612) $\\pm$ (0.0043,0.0046) & (-0.7382,-1.9613) & (-0.7365,-1.9518)\\\\\n$\\vec x_C('')$ & (-0.7446,-0.4537) $\\pm$ (0.0045,0.0049) & (-0.7443,-0.4544) & (-0.7422,-0.4575)\\\\\n$\\vec x_D('')$ & (~1.1284,-1.2565) $\\pm$ (0.0107,0.0124) & (~1.1271,-1.2582) & (~1.1269,-1.2207)\\\\\n%\n\\tableline\n%\n$F_A / F_B$ & 2.042 $\\pm$ 0.124 & 1.917 & 1.901 \\\\\n$F_C / F_B$ & 1.037 $\\pm$ 0.083 & 1.092 & 1.131 \\\\\n$F_D / F_B$ & 0.350 $\\pm$ 0.055 & 0.428 & 0.504 \\\\\n%\n\\tableline\n%\n%$T_{AB}/T_{CB}$ & 0.79 $\\pm$ 5.0 & 28.4 & 26.4 \\\\ \n%$T_{AB}/T_{DB}$ & 33.0 $\\pm$ 5.0 & 32.0 & 30.8 \\\\\n$T_{AB} (d)$ & 26.0 $\\pm$ 5.0 & 28.4 & 27.6 \\\\ \n$T_{CB} (d)$ & 33.0 $\\pm$ 5.0 & 32.0 & 31.7 \\\\\n$T_{DB} (d)$ & 73.0 $\\pm$ 5.0 & 68.4 & 71.3 \\\\\n%\n\\tableline\n%\n$\\chi^2$ & 0.0 & 4.0 & 24.7 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\vspace*{-1.0cm}\n\\begin{references}\n\\vspace*{-0.2cm}\n\\small\n\\reference Blandford, R., \\& Kundic, T. 1996 {\\it The Extragalactic\nDistance Scale}, p60\n\\reference Blandford, R., Surpi, G. \\& Kundi\\'c, T. 1999 these proceedings\n\\reference Fassnacht, C. 1999 these proceedings\n\\reference Koopmans, L.V., \\& Fassnacht, C.D. 1999\nastro-ph/9907258, to appear in \\apj\n\\reference Williams, L. L. R. \\& Saha, P. 1999 these proceedings\n\\end{references}\n\\end{document}\n\n\n\n"
}
] |
[] |
astro-ph0002003
|
Compact Stellar Systems in the Fornax Cluster: Super-massive Star Clusters or Extremely Compact Dwarf Galaxies?
|
[
{
"author": "M. J. Drinkwater$^{1}$"
},
{
"author": "J. B. Jones$^{2}$"
},
{
"author": "M. D. Gregg$^{3}$"
},
{
"author": "S. Phillipps$^{4}$"
}
] |
and %
|
[
{
"name": "fss4.tex",
"string": "%\n% LaTeX template file for\n% Publications of the Astronomical Society of Australia.\n% Version 2.4 - 28 April 1997\n%\n%\\documentstyle[12pt,psfig]{article}\n\\documentstyle[11pt,psfig]{article}\n%\n% Baselineskip may be altered if desired.\n%\n\\baselineskip=2em\n%\n% A few definitions. Do not change the reference command.\n%\n\\def\\reference{\\parskip 0pt\\par\\noindent\\hangindent 0.5 truecm}\n\\def\\s{{\\rm\\thinspace s}}\n\\def\\km{{\\rm\\thinspace km}}\n\n\\def\\kms{\\hbox{$\\km\\s^{-1}\\,$}}\n\\def\\bj{\\hbox{$b_j$}} \n\\def\\Bj{\\hbox{$b_j$}} \n\\def\\mo{\\hbox{M$_\\odot$}}\n\\def\\pc{{\\rm\\thinspace pc}}\n\n%\n% Text locations - these may be altered slightly if desired.\n%\n\\textwidth=17.5cm\n\\textheight=24.6 cm\n\\topmargin=-2.5cm\n\\oddsidemargin=-1.0cm\n\\evensidemargin=-1.0cm\n%\n% Start of document\n%\n\\begin{document}\n%\n% Title\n% Capitalise the title normally - do not use ALL CAPS.\n%\n\\title{Compact Stellar Systems in the Fornax Cluster:\nSuper-massive Star Clusters or Extremely Compact Dwarf Galaxies?\n}\n%\n\n% Authors\n% Here comes the author(s) of the paper. Please add the appropriate author\n% names for your paper and indicate within the $^...$ the number(s)\n% which corresponds to the institute(s) of each author. In this example\n% the second author has two institutional affiliations.\n% Add or remove authors as required, maintaining the \\and syntax between\n% each author, but no \\and after the last author.\n% **** IMPORTANT: Leave the closing curly bracket line as is. ******\n\n\\author{M. J. Drinkwater$^{1}$ \\and\n J. B. Jones$^{2}$ \\and\n M. D. Gregg$^{3}$ \\and\n S. Phillipps$^{4}$\n} % IMPORTANT: leave this curly bracket as the first character of this line.\n\n% Date - leave this blank.\n%\\date{resubmitted to PASA, 2000 January 24}\n\\date{to appear in {\\em Publications of the Astronomical Society of Australia}}\n\\maketitle\n\n% Institutions\n% Here fill in your institute name(s) and address(es)\n% The number in $^...$ indicates the author number. For example\n{\\center\n$^1$ School of Physics, University of Melbourne, Victoria 3010,\nAustralia\\\\[email protected]\\\\[3mm]\n$^2$ Department of Physics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, England, U.K.\\\\[email protected]\\\\[3mm]\n$^3$ University of California, Davis, \n and Institute for Geophysics and Planetary Physics, \n Lawrence Livermore National Laboratory,\n L-413, Livermore, CA 94550, USA\\\\[email protected]\\\\[3mm]\n$^4$ Department of Physics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, England, U.K.\\\\[email protected]\\\\[3mm]\n}\n\n% Abstract\n% Simply place your abstract between the \\begin{abstract} and\n% \\end{abstract} commands.\n%\n\\begin{abstract}\n% Place the abstract here.\n\nWe describe a population of compact objects in the centre of the\nFornax Cluster which were discovered as part of our 2dF Fornax\nSpectroscopic Survey. These objects have spectra typical of old\nstellar systems, but are unresolved on photographic sky survey plates.\nThey have absolute magnitudes $-13<M_B<-11$, so they are 10 times more\nluminous than any Galactic globular clusters, but fainter than any\nknown compact dwarf galaxies. These objects are all within 30\narcminutes of the central galaxy of the cluster, NGC 1399, but are\ndistributed over larger radii than the globular cluster system of that\ngalaxy. \n\nWe suggest that these objects are either super-massive star clusters\n(intra-cluster globular clusters or tidally stripped nuclei of dwarf\ngalaxies) or a new type of low-luminosity compact elliptical dwarf\n(``M32-type'') galaxy. The best way to test these hypotheses will be\nto obtain high resolution imaging and high-dispersion spectroscopy to\ndetermine their structures and mass-to-light ratios. This will allow\nus to compare them to known compact objects and establish if they\nrepresent a new class of hitherto unknown stellar system.\n\\end{abstract}\n\n{\\bf Keywords:}\ngalaxies: star clusters --- galaxies: dwarf --- galaxies: formation\n\n\\bigskip\n\n%\\twocolumn\n\n\\section{Introduction}\n\nIn cold dark matter (CDM) galaxy formation, small dense halos of\ndark matter collapse at high redshift and eventually merge to form the\nlarge virialised galaxy clusters seen today. The CDM model is very\ngood at reproducing large-scale structure, but only very recently have\nthe best numerical simulations (Moore et al.\\ 1998) had the resolution\nto trace the formation of small halos within galaxy clusters, with\nmasses $\\approx 10^9$M$_\\odot$. We do not yet know what the lower mass\nlimit is for the formation of halos in the cluster environment:\ndetermining the lower limit of galaxy mass in clusters will provide an\nimportant constraint on these models. Most of the smallest cluster\ngalaxies are low surface brightness dwarfs for which mass estimates\nare very difficult, though comparison with field low surface\nbrightness dwarfs would suggest that they may be dark matter dominated\n(e.g.\\ Carignan \\& Freeman 1988).\n\nIn this paper we describe a population of small objects we have found\nin the Fornax Cluster (see also Minniti et al.\\ 1998 and Hilker et\nal.\\ 1999) which have high surface brightness. The origin and nature\nof these objects is not yet clear, but if they are a product of the\ngalaxy formation process in clusters, their high surface brightness\nwill make it possible to probe the low-mass limit discussed\nabove. They may represent extreme examples of compact low luminosity\n(``M32-type'') dwarf ellipticals. Alternatively, these objects may be\nsuper-massive star clusters---there is a very large\npopulation of globular clusters associated with the central galaxy of\nthe Fornax Cluster, NGC 1399 (Grillmair et al.\\ 1994). These objects\nare generally similar to Galactic globular clusters with similar\ncolours and luminosities (Forbes et al.\\ 1998). There is evidence that\nthey are not all bound to the NGC 1399 system. Kissler-Patig et al.\\\n(1999) show that the kinematics of 74 of the globular clusters\nindicate that they are associated with the cluster gravitational\npotential rather than that of NGC 1399. They infer that the most\nlikely origin of these globular clusters is that they have been\ntidally stripped from neighbouring galaxies. This has also been\nsuggested by West et al.\\ (1995), although the effect would be diluted\nby the large number of halo stars that would presumably be stripped at\nthe same time.\n\nBassino, Muzzio \\& Rabolli (1994) suggest that the NGC 1399 globular\nclusters are remnants of the nuclei of dwarf nucleated galaxies that\nhave survived the disrupture of being captured by the central cluster\ngalaxy. A related suggestion is a second model proposed by West et\nal.\\ (1995) that intra-cluster globular clusters could have formed in\nsitu in the cluster environment. Bassino et al.\\ (1994) conclude\ntheir discussion by noting that remnant nuclei an order of magnitude\nlarger (and more luminous) than standard globular clusters would also\nbe formed in significant numbers, but that existing globular cluster\nsearches would not have included them. In Section~\\ref{sec-obs} of\nthis paper we describe how the observations of our {\\em Fornax\nSpectroscopic Survey} have sampled this part of the cluster population\nby measuring optical spectra of all objects brighter than $B_J=19.7$\nin the centre of the Fornax Cluster. In Section~\\ref{sec-prop} we\ndescribe the properties of a new population of compact objects found\nin the cluster that appear to be intermediate in size between globular\nclusters and the smallest compact dwarf galaxies. We discuss the\nnature of these objects in Section~\\ref{sec-discuss} and show that\nhigher resolution observations will enable us to determine if they are\nmore like globular clusters or dwarf galaxies.\n\n\\section{Discovery Observations: The Fornax Spectroscopic Survey}\n\\label{sec-obs}\n\nOur {\\em Fornax Spectroscopic Survey}, carried out with the 2dF\nmulti-object spectrograph on the Anglo-Australian Telescope (see\nDrinkwater et al.\\ 2000), is now 87\\% complete in its first field to\na limit of $B_J=19.7$. The 2dF field is a circle of diameter 2 degrees\n(i.e.\\ $\\pi$ square degrees of sky). We have measured optical spectra\nof some 4000 objects (some going fainter than our nominal limit) in a\n2dF field centred on the central galaxy of the Fornax Cluster (NGC\n1399). This survey is unique in that the targets (selected from\ndigitised UK Schmidt Telescope photographic sky survey plates) include\n{\\em all} objects, both unresolved (``stars'') and resolved\n(``galaxies'') in this large area of sky. The resolved objects\nmeasured are mostly background galaxies as expected with a minor\ncontribution from Fornax Cluster members. The unresolved objects are\nmostly Galactic stars and distant AGN, also as expected, but some are\ncompact starburst (and post-starburst) galaxies beyond the Fornax\nCluster (Drinkwater et al 1999a).\n\nFinally, in addition to the dwarf galaxies already listed in the\nFornax Cluster Catalog (FCC: Ferguson 1989) which we have confirmed as\ncluster members, we have found a sample of five very compact objects\nat the cluster redshift which are unresolved on photographic sky\nsurvey plates and not included in the FCC. These new members of the\nFornax Cluster are listed in Table~\\ref{tab-list} along with their\nphotometry measured from the UKST plates.\n\n\n\\begin{table*}\n\\caption{The new compact objects\n\\label{tab-list}}\n\\center\n\\begin{tabular}{lllll}\n\\hline\nName & RA (J2000) Dec & $B_J$& $M_B$ & cz \\\\\n & & (mag)& (mag) & (\\kms) \\\\\n\\hline\nThales 1 & 03 37 3.30 -35 38 4.6 &19.85 & $-11.1$ & 1507 \\\\\nThales 2 & 03 38 6.33 -35 28 58.8 &18.85 & $-12.1$ & 1328 \\\\\nThales 3$^1$ & 03 38 54.10 -35 33 33.6 &17.68 & $-13.2$ & 1595 \\\\\nThales 4$^2$ & 03 39 35.95 -35 28 24.5 &18.82 & $-12.1$ & 1936 \\\\\nThales 5 & 03 39 52.58 -35 04 24.1 &19.66 & $-11.2$ & 1337 \\\\\n\\hline\n\\end{tabular}\n\nNotes: (1) CGF 1-4 (2) CGF 5-4, both in Hilker et al.\\ (1999) \n\n\\end{table*}\n\n\nOur 2dF measurements of unresolved objects are 80\\% complete in the\nmagnitude range of these objects ($17.5<\\bj<20.0$). There is therefore\nabout one more similar compact object still to be found in in our\ncentral 2dF field. The number density of these objects is\ntherefore $6\\pm3$ per 2dF field ($\\pi$ square degrees). Two of\nthe objects (the two brightest) were also identified as cluster\nmembers by Hilker et al.\\ (1999). Hilker et al.\\ measured spectra of\nabout 50 galaxies brighter than $V=20$ in a square region of width\n0.25 degrees at the centre of the Fornax Cluster. In the ``galaxies''\nthey include objects which were very compact, but still resolved. By\ncontrast our own survey covers a much larger area and also includes all\nunresolved objects.\n\n\\section{Properties of the compact objects}\n\\label{sec-prop}\n\n\\subsection{Sizes}\n\nThese object images are unresolved and classified ``stellar'' in our\nUKST plate data, although imaging with the CTIO Curtis Schmidt shows\nthat the brightest two objects have marginal signs of extended\nstructure. In Fig.~\\ref{fig-image} we present R-band (Tech Pan\nemulsion + OG 590 filter) photographic images of these compact objects\nfrom the UKST. These were taken in seeing of about 2.2 arcseconds FWHM\nand the third object (Thales\\footnote{Thales of Miletus was the first\nknown Greek philosopher and scientist and possibly the earliest\nastronomer.} 3) is resolved with a 3.2 arcsecond FWHM. Applying a\nvery simple deconvolution of the seeing this corresponds to a scale\nsize (HWHM) of about 80 pc. This is much larger than any known\nglobular cluster, so this object, at least, is not a globular cluster.\nThe other objects are all unresolved, so must have scale sizes smaller\nthan this.\n\n\\begin{figure*}\n\\hfil \\psfig{file=fig_im.eps,angle=0,width=18cm}\n\\caption{R-band photographic images of the new compact objects. The\nimages are all from a single UKST exposure on Tech-Pan emulsion,\ndigitised by SuperCOSMOS (Miller et al.\\ 1992). Each image is 2.5\narcminutes across with North at the top and East to the left.\n\\label{fig-image}}\n\\end{figure*}\n\n\\subsection{Luminosity and Colours}\n\nThese new objects have absolute magnitudes $-13<M_B<-11$, based on a\ndistance modulus of 30.9 mag to the Fornax Cluster (Bureau et al.\\\n1996). These values are at the lower limit of dwarf galaxy\nluminosities (Mateo 1998), but are much more luminous than any known\nGalactic globular clusters (Harris, 1996) and the most luminous of the\nNGC1399 globulars (Forbes et al.\\ 1998) which have $M_B\\approx-10$.\nThe luminosities of the compact objects are compared to several other\npopulations of dwarf galaxy and star cluster in Fig.~\\ref{fig-lf}. We\nnote that the magnitude limit of the 2dF data corresponds to an\nabsolute magnitude of $M_B\\approx-11$ here. In order of decreasing\nluminosity the first comparison is with the dwarf ellipticals listed\nin the FCC as members of the Fornax Cluster. The possible M32-type\ngalaxies in the FCC are not included as none of them have yet been\nshown to be cluster members (Drinkwater, Gregg \\& Holman 1997). The\nFigure shows that the Fornax dEs have considerable overlap in\nluminosity with the compact objects, but morphologically they are very\ndifferent, being fully resolved low surface brightness\ngalaxies. Recently, several new compact dwarf galaxies have been\ndiscovered in the Fornax Cluster (Drinkwater \\& Gregg 1998) but these\nare all brighter than $M_B=-14$ and do not match any of the objects we\ndiscuss here. Binggeli \\& Cameron (1991) measured the luminosity\nfunction of the nuclei of nucleated dwarf elliptical galaxies in the\nVirgo Cluster. The Figure shows that this also overlaps the\ndistribution of the new compact objects. In this case the morphology\nis the same, so the compact objects could originate from the dwarf\nnuclei. The Figure also shows the luminosity functions of both the NGC\n1399 globular clusters (Bridges, Hanes \\& Harris, 1991) and Galactic\nglobular clusters (Harris 1996). These are quite similar and have no\noverlap with the compact objects.\n\nFor completeness we note that the luminosities of the compact objects\nhave considerable overlap with the luminosities of dwarf galaxies in\nthe Local Group (Mateo 1998), but even the most compact of the Local\nGroup dwarfs, Leo I ($M_B=-11.1$) would be resolved ($r_e\\approx 3''$)\nin our images at the distance of Fornax. The only population they\nmatch in both luminosity and morphology is the bright end of the\nnuclei of nucleated dwarf ellipticals.\n\n\\begin{figure}\n\\hfil \\psfig{file=fig_lf.eps,angle=0,width=9cm}\n\\caption{Distribution of absolute magnitude of the compact objects\n(filled histogram) compared to dEs in the Fornax Cluster (Ferguson\n1989; solid histogram), the nuclei of dE,Ns in the Virgo Cluster\n(Binggeli \\& Cameron 1991; short dashes), a model fit to the globular\nclusters around NGC 1399 (Bridges, Hanes \\& Harris, 1991; long dashes)\nand Galactic globular clusters (Harris 1996; dotted). Note: the\nmagnitude limit of our survey that found the compact objects\ncorresponds to $M_B=-11$.\n\\label{fig-lf}}\n\\end{figure}\n\n\n\\subsection{Spectral Properties}\n\nThe 2dF discovery spectra of these compact objects are shown in\nFigure~\\ref{fig-spec}. They have spectra similar to those of early\ntype dwarf galaxies in the sample (two are shown for comparison in the\nFigure) with no detectable emission lines. As part of the spectral\nidentification process in the {\\em Fornax Spectroscopic Survey}, we\ncross-correlate all spectra with a sample of stellar templates from\nthe Jacoby et al.\\ (1984) library. The spectra of the new compact\nobjects were best fit by K-type stellar templates, consistent with an\nold (metal-rich) stellar population. The dE galaxies observed with the\nsame system by contrast are best fit by younger F and early G-type\ntemplates. This gives some indication in favour of the compact objects\nbeing related to globular clusters, although we note that two of them\nwere analysed by Hilker et al.\\ (1999) in more detail without any\nconclusive results. We do not have the spectrum of a dE nucleus\navailable for direct comparison, but since our 2dF spectra are taken\nthrough a 2 arcsec diameter fibre aperture, the spectrum of FCC 211, a\nnucleated dE, is dominated by the nucleus. This spectrum was fitted by\na younger F-type stellar template, again suggestive of a younger\npopulation than the compact objects. We cannot draw any strong\nconclusions from these low-resolution, low signal-to-noise spectra.\n\n\\begin{figure}\n%\\hfil \\psfig{file=plot_spec.eps,angle=0,width=11.2cm}\n\\hfil \\psfig{file=plot_spec.eps,angle=0,width=9cm}\n\\caption{2dF discovery spectra of the five compact objects as well as\ntwo cluster dwarf galaxies for comparison. Note: the large scale\nripple in the spectrum of Thales~5 is an instrumental effect caused by\ndeterioration in the optical fibre used.\n\\label{fig-spec}}\n\\end{figure}\n\n\\subsection{Radial Distribution}\n\nThe main advantage of our survey over the previous studies of the NGC\n1399 globular cluster system (e.g.\\ Grillmair et al.\\ 1994, Hilker et\nal.\\ 1999) is that we have complete spectroscopic data over a much\nlarger field, extending to a radius of 1 degree (projected distance of\n270 kpc) from the cluster centre. This means that we can determine the\nspatial distribution of the new compact objects. In\nFigure~\\ref{fig-radial} we plot the normalised, cumulative radial\ndistribution of the new compact objects compared to that of foreground\nstars and cluster galaxies. This plot is the one used to calculate\nKolmogorov-Smirnov statistics and allows us to compare the\ndistributions of objects independent of their mean surface\ndensities. It is clear from the Figure that the new compact objects\nare very concentrated towards the centre of the cluster, at radii\nbetween 5 and 30 arcminutes (20--130 kpc). Their distribution is more\ncentrally concentrated than the King profile fitted to cluster members\nby Ferguson (1989) with a core radius of 0.7 degrees (190 kpc). The\nKolmogorov-Smirnov (KS) test gives a probability of 0.01 that the\ncompact objects have the same distributions as the FCC galaxies: they\nare clearly not formed (or acreted) the same way as average cluster\ngalaxies. To test the hypothesis that the compact objects are formed\nfrom nucleated dwarfs, we also plot the distribution of all the FCC\nnucleated dwarfs, as these are more clustered than other dwarfs\n(Ferguson \\& Binggeli 1994). However in the central region of interest\nhere the nucleated dwarf profile lies very close to the King profile\nof all the FCC galaxies, so this does not provide any evidence for a\ndirect link with the new compact objects.\n\nWest et al.\\ (1995) suggest that a smaller core radius should be used\nfor intra-cluster globular clusters (GCs). This profile, also shown in\nthe Figure, is more consistent with the distribution of the new\nobjects: the KS probability of the compact objects being drawn from\nthis distribution is 0.39.\n\n% calculate the KS statistics:\n% West: 0.8993707895 0.3936000764\n% FCC: 1.594319463 0.01239375863\n\n\n\\begin{figure}\n\\hfil \\psfig{file=fig_radial.eps,angle=0,width=9cm}\n\\caption{Cumulative radial distribution of the new compact objects\ncompared to the predicted distribution for intra-cluster globular\nclusters (West et al 1995) and the profile fit to the distribution of all\nFCC. Also shown is the distribution of all nucleated dwarfs in the FCC\nand all the unresolved objects (stars) observed in our 2dF survey.\n\\label{fig-radial}}\n\\end{figure}\n\nWe also note that the radial distribution of the compact objects is\nmuch more extended than the NGC 1399 globular cluster system as\ndiscussed by Grillmair et al.\\ and extends to three times the\nprojected radius of that sample. It unlikely that all the compact\nobjects are associated with NGC 1399. This is emphasised by a finding\nchart for the central 55 arcminutes of the cluster in\nFig.~\\ref{fig-apm} which indicates the location of the compact\nobjects. They are widely distributed over this field and Thales~3 in\nparticular is much closer to NGC 1404, although we note that its\nvelocity is not close to that of NGC 1404 (see below).\n\n\\begin{figure*}\n\\hfil \\psfig{file=figure5_10n.eps,width=15cm}\n\\caption{The central region of the Fornax Cluster with the positions\nof the new compact objects indicated by squares. This R-band\nphotographic image is from a single UKST exposure on Tech-Pan\nemulsion, digitised by SuperCOSMOS (Miller et al.\\ 1992).\n\\label{fig-apm}}\n\\end{figure*}\n\n\\subsection{Velocity Distribution}\n\nWe have some limited information from the radial velocities of the\ncompact objects. The mean velocity of all 5 ($1530\\pm110 \\kms$) is\nconsistent with that of the whole cluster ($1540\\pm50 \\kms$) (Jones \\&\nJones (1980). However, given the small sample, it is also consistent\nwith the velocity of NGC 1399 ($1425\\pm 4 \\kms$) as might be expected\nfor a system of globular clusters. Interestingly, the analysis of the\ndynamics of 74 globular clusters associated with NGC 1399 by\nKissler-Patig et al.\\ (1999) notes that their radial velocity\ndistribution has two peaks, at about 1300 and 1800\\kms.\nOur sample is far too small to make any conclusions about the dynamics\nof these objects at present.\n\n\\section{Discussion}\n\\label{sec-discuss}\n\nWe cannot say much more about the nature of these objects on the basis\nof our existing data. In ground-based imaging, they are intermediate\nbetween large GCs and small compact dwarf galaxies, so it becomes\nalmost a matter of semantics to describe them as one or the other. The\nmost promising way to distinguish between these possibilities is to\nmeasure their mass-to-light (M/L) ratios. If they are large, but\notherwise normal, GCs, they will be composed entirely of stars giving\nvery low M/L. If they are the stripped nuclei of dwarf galaxies we\nmight expect them to be associated with some kind of dark halo, but we\nwould not detect the dark halos at the small radii of these nuclei, so\nwe would also measure small M/L values. Alternatively, these objects\nmay represent a new, extreme class of compact dwarf elliptical\n(``M32-type'') galaxy. These would presumably have formed by\ngravitational collapse within dark-matter halos, so would have high\nmass-to-light-ratios, like dwarf galaxies in the Local Group (Mateo\n1998). One argument against this interpretation is the apparent lack\nof M32-like galaxies at brighter luminosities (Drinkwater \\& Gregg\n1998). If the compact objects are dwarf galaxies, they will represent\nthe faintest M32-like galaxies ever found. They may also fill in the\ngap between globular clusters and the fainter compact galaxies in the\nsurface brightness vs.\\ magnitude distribution given by Ferguson \\&\nBinggeli (1994).\n\nA further possibility is that these are small scale length ($\\sim\n100$~pc) dwarf spheroidal galaxies of only moderately low surface\nbrightness. While Local Group dSphs of equivalent luminosities\ngenerally have substantially larger scale sizes (and consequently\nlower surface brightnesses) (Mateo, 1998), Leo I for example has $M_B\n= -11.0$, and a scale length of only 110~pc (Caldwell et al., 1992),\nbut as we discuss above this would be resolved in our existing\nimaging.\n\nOur existing data will only allow us to estimate a conservative upper\nlimit to the mass of these objects. If we say that the core radii of\nthe objects are less than 75\\pc\\ and the velocity dispersions are less\nthan 400\\kms\\ (the resolution of our 2dF spectra) we find that the\nvirial mass must be less than $10^{10}\\mo$. For a typical luminosity\nof $M_B=-12$ this implies that $M/L < 2\\times 10^{3}$. This is not a\nvery interesting limit, so we plan to reobserve these objects at\nhigher spectral resolution from the ground and higher spatial\nresolution with the {\\em Hubble Space Telescope} (HST) in order to be\nsensitive to $M/L\\approx 100$. This will allow us to distinguish\nglobular clusters from dwarf galaxies.\n\nIn order to demonstrate what we could measure with high-resolution\nimages, we present two extreme possibilities in\nFigure~\\ref{fig-profile}: a very compact Galactic globular cluster and\na dwarf galaxy with an $r^{1/4}$ profile ($r_e=0.2$ arcsec), both\nnormalised to magnitudes of $B=19$ ($V=18.4$) and the Fornax cluster\ndistance. We also plot the PSF of the {\\em Space Telescope Imaging\nSpectrograph} (STIS) in the Figure for reference. The globular cluster\nprofile is that of NGC 2808 (Illingworth \\& Illingworth 1976) with the\nradius scaled to the distance of the Fornax Cluster and the surface\nbrightness then scaled to give the desired apparent magnitude. The\nglobular cluster profile is very compact and will only just be\nresolved with HST, but it will clearly be differentiated from the\ndwarf galaxy profile.\n\n\\begin{figure}\n\\hfil \\psfig{file=hst_glob_f2.eps,angle=0,width=9cm}\n\\caption{Predicted radial surface brightness profiles of the compact\nobjects in two extreme cases: (A) a Galactic globular cluster\n(Illingworth \\& Illingworth 1976) scaled 3 mag brighter in surface\nbrightness, and (B) a compact dwarf galaxy with an $r^{1/4}$\nprofile. Both are scaled to have total magnitudes of B=19 mag; they\nare not corrected for instrumental PSF which is also shown\n(C). \\label{fig-profile}}\n\\end{figure}\n\nIn addition to measuring the size of these objects for the mass\nmeasurement, the radial surface brightness profiles may also give\ndirect evidence for their origin and relationship to other kinds of\nstellar systems. For example, if they are the stripped nuclei of\ngalaxies, the remnants of the outer envelope might show up in the HST\nimages as an inflection in the surface brightness profile at large\nradius.\n\n\\section{Summary}\n\nWe have reviewed the observed properties of these new compact objects\ndiscovered in the Fornax Cluster. Their luminosities are intermediate\nbetween those of known globular clusters and compact dwarf galaxies,\nbut they are consistent with the bright end of the luminosity function\nof the the nuclei of nucleated dwarf ellipticals. The 2dF spectra are\nsuggestive of old (metal-rich) stellar populations, more like globular\nclusters than dwarf galaxies. Finally the radial distribution of the\ncompact objects is more centrally concentrated than cluster galaxies\nin general, but extends further than the known globular cluster system\nof NGC 1399.\n\nThese objects are most likely either massive star clusters (extreme\nglobular clusters or tidally-stripped dwarf galaxy nuclei) or very\ncompact, low-luminosity dwarf galaxies. In the latter case these new\ncompact objects would be very low-luminosity counterparts to the\npeculiar compact galaxy M32. This would be particularly interesting\ngiven the lack of M32-like galaxies at brighter luminosities\n(Drinkwater \\& Gregg 1998). With higher resolution images and spectra\nwe will be able to measure the mass-to-light ratios of these objects\nand determine which of these alternatives is correct.\n\n\n\n\\section*{Acknowledgements}\n\nWe thank the referee for helpful suggestions which have improved the\npresentation of this work. We wish to thank Dr.\\ Harry Ferguson for\nhelpful discussions and for providing the STIS profile. We also\nthank Dr.\\ Trevor Hales for assistance in the naming of the\nobjects. MJD acknowledges support from an Australian Research Council\nLarge Grant.\n\n\\section*{References}\n\n\\reference Caldwell, N., Armandroff, T.E., Seitzer, P., Da Costa,\nG.S., 1992, AJ, 103, 840\n\\reference Bassino, L.P., Muzzio, J.C., Rabolli, M. 1994, ApJ, 431, 634\n\\reference Binggeli, B., Cameron, L.M., 1991, A\\&A, 252, 27\n\\reference Bridges, T.J., Hanes, D.A., Harris, W.E., 1991, AJ, 101, 469\n\\reference Bureau, M., Mould, J.R., Staveley-Smith, L., 1996, ApJ,\n463, 60\n\\reference Carignan, C., Freeman, K.C. 1988, ApJ, 332, L33\n\\reference Drinkwater, M.J., Gregg, M.D., 1998, MNRAS, 296, L15\n\\reference Drinkwater, M.J., Gregg, M.D., Holman, B.A., 1997 in\nArnaboldi M., Da Costa G.S., Saha P., eds, ASP Conf. Ser. Vol. 116,\nThe Second Stromlo Symposium: The Nature of Elliptical Galaxies.\nAstron. Soc. Pac., San Francisco, p. 287\n\\reference Drinkwater, M.J., Phillipps, S., Gregg, M.D., Parker, Q.A.,\nSmith, R.M., Davies, J.I., Jones, J.B., Sadler, E.M., 1999a, ApJ, 511, L97\n\\reference Drinkwater, M.J., Phillipps, S., Jones, J.B., Gregg, M.D.,\nDeady, J.H., Davies, J.I., Parker, Q.A., Sadler, E.M., \nSmith, R.M. 2000, A\\&A, submitted\n\\reference Ferguson H.C., 1989, AJ, 98, 367\n\\reference Ferguson H.C., Binggeli, B., 1994, A\\&ARv, 6, 67\n\\reference Forbes, D.A., Grillmair, C.J., Williger, G.M., Elson,\nR.A.W., Brodie, J.P. 1998, MNRAS, 293, 325\n\\reference Grillmair, C.J., Freeman, K.C., Bicknell, G.V., Carter, D.,\nCouch, W.J., Sommer-Larsen, J., Taylor, K. 1994, ApJ, 422, L9\n\\reference Harris, W.E., 1996, AJ, 112, 1487\n\\reference Hilker, M., Infante, L., Vieira, G., Kissler-Patig, M.,\nRichtler, T., 1999, A\\&AS, 134, 75\n\\reference Illingworth, G., Illingworth, W. 1976, ApJSup, 30, 227\n\\reference Jacoby, G.H., Hunter, D.A., Christian, C.A., 1984, ApJSup,\n56, 257\n\\reference Jones, J.E., Jones, B.J.T. 1980, MNRAS, 191, 685\n\\reference Kissler-Patig, M., Grillmair, C.J., Meylan, G., Brodie,\nJ.P., Minniti, D., Goudfrooij, P., 1999, AJ, 117, 1206\n\\reference Mateo, M., 1998, Ann. Rev. Astron. Astrophys., 36, 435\n\\reference Minniti, D., Kissler-Patig, M., Goudfrooij, P., Meylan, G., 1998, AJ, 115, 121\n\\reference Miller, L. A., Cormack, W., Paterson, M., Beard, S., Lawrence, L., \n1992, in `Digitised Optical Sky Surveys', eds. H.T. MacGillivray, \nE.B Thomson, Kluwer Academic Publishers, p. 133\n\\reference Moore, B., Governato, F., Quinn, T., Stadel, J., Lake, G. 1998, ApJ, 499, L5\n\\reference West, M.J., Cote, P., Jones, C., Forman, W., Marzke, R.O. 1995 ApJ 453 L77\n\n\\end{document}\n\n"
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astro-ph0002004
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Extracting Energy from a Black Hole through Its Disk
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[
{
"author": "Li-Xin Li"
}
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When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, $ca/GM_H>0.36$ for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk ($M_H$ is the mass and $a M_H$ is the angular momentum of the black hole). This way the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from $ca/GM_H = 0.998$ to $ca/GM_H = 0.36$ by a thin Keplerian disk is $\approx 0.15 M_Hc^2$. This is larger than $\approx 0.09 M_Hc^2$ which can be extracted by the Blandford-Znajek mechanism.
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"name": "bh_disk.tex",
"string": "% bh_disk.tex for ApJ Letters\n\n\\documentstyle[12pt,aaspp4]{article}\n\\begin{document}\n\n\\title{Extracting Energy from a Black Hole through Its Disk}\n\n\\author{Li-Xin Li}\n\\affil{Princeton University Observatory, Princeton, NJ 08544--1001, USA}\n\\affil{E-mail: [email protected]}\n%\\affil{(November 5, 1999; Revised January 14, 2000)}\n\n\\begin{abstract}\nWhen some magnetic field lines connect a Kerr black hole with a disk \nrotating around it, energy and angular momentum are transferred between them. \nIf the black hole rotates faster than the disk, $ca/GM_H>0.36$ for a thin \nKeplerian disk, then energy and angular momentum are extracted from the black \nhole and transferred to the disk ($M_H$ is the mass and $a M_H$ is the \nangular momentum of the black hole). This way the energy originating\nin the black hole may be radiated away by the disk.\n\nThe total amount of energy that can be extracted from the black hole\nspun down from $ca/GM_H = 0.998$ to $ca/GM_H = 0.36$ by a thin Keplerian\ndisk is $\\approx 0.15 M_Hc^2$. This is larger than $\\approx 0.09 M_Hc^2$ \nwhich can be extracted by the Blandford-Znajek mechanism.\n\\end{abstract}\n\n\\keywords{black hole physics --- accretion disks --- magnetic fields}\n\n%\\section 1\n\\section{Introduction}\nExtraction of energy from a black hole or an accretion disk through\nmagnetic braking has been investigated by many people. As a rotating black hole\nis threaded by magnetic field lines which connect with remote astrophysical loads, \nenergy and angular momentum\nare extracted from the black hole and transported to the remote loads via Poynting\nflux (Blandford \\& Znajek 1977; Macdonald \\& Thorne 1982; Phinney 1983). This is\nusually called the Blandford-Znajek mechanism and has been suggested to be\na plausible process for powering jets in active galactic nuclei (Rees, Begelman,\nBlandford, \\& Phinney 1982; Begelman, Blandford, \\& Rees 1984) and gamma ray\nbursts (Paczy\\'nski 1993; Lee, Wijers, \\& Brown 1999). Similar\nprocess can happen to an accretion disk when some of magnetic field\nlines threading the disk are open and connect with remote astrophysical loads\n(Blandford 1976; Blandford \\& Znajek 1977; Macdonald \\& Thorne 1982; Livio,\nOgilvie, \\& Pringle 1999; Li 1999).\n\nIn this paper we investigate the effects of magnetic field lines connecting a\nKerr black hole with a disk surrounding it. This kind of\nmagnetic field lines are expected to exist and have important effects (Macdonald\n\\& Thorne 1982; Blandford 1999, 2000; Gruzinov 1999). We find that, with the\nexistence of such magnetic coupling between the black hole and the disk, energy\nand angular momentum are transfered between them. If the black hole rotates faster \nthan the disk, energy and angular momentum are extracted from the black hole and \ntransferred to the disk via Poynting flux. This is the case when\n$a/M_H>0.36$ for a thin Keplerian disk, where $M_H$ is the mass of the \nblack hole and $aM_H$ is the angular momentum of the black hole. \nThroughout the paper we use the geometric units with $G = c = 1$. The energy \ndeposited into the disk by the black hole is eventually radiated to infinity\nby the disk. This provides a way for extracting energy from a black hole through its\ndisk. If the disk has no accretion (or the accretion rate is very low), \nthe power of the disk \nessentially comes from the rotational energy of the black hole. We will show\nthat the magnetic coupling between the black hole and the disk has a higher\nefficiency in extracting energy from a Kerr black hole than the Blandford-Znajek\nmechanism.\n\n\n%\\section 2\n\\section{Transfer of Energy and Angular Momentum between a Black Hole and Its\nDisk by Magnetic Coupling}\nSuppose a bunch of magnetic field lines connect a rotating black\nhole with a disk surrounding it. Due to the rotation of the black hole\nand the disk, electromotive forces are induced on both the black hole's horizon \nand the disk (Macdonald \\& Thorne 1982; Li 1999)\n\\begin{eqnarray}\n {\\cal E}_H = {1\\over 2\\pi}\\Omega_H \\Delta\\Psi\\,, \\hspace{1cm}\n {\\cal E}_D = -{1\\over 2\\pi}\\Omega_D \\Delta\\Psi\\,,\n \\label{emf}\n\\end{eqnarray}\nwhere $\\Omega_H$ is the angular velocity of the black hole, $\\Omega_D$ is the\nangular velocity of the disk, $\\Delta\\Psi$ is the magnetic flux connecting\nthe black hole with the disk. The black hole and the disk form a closed\nelectric circuit, the electric current flows through the magnetic field lines \nconnecting them. Suppose the disk and the black hole rotates in the same direction, \nthen ${\\cal E}_H$ and ${\\cal E}_D$ have opposite signs. This means that energy\nand angular momentum are transferred\neither from the black hole to the disk or from the disk to the black hole, the\ndirection of transfer is determined by the sign of ${\\cal E}_H + {\\cal E}_D$. By the\nOhm's law, the current is $I = ({\\cal E}_H+{\\cal E}_D)/Z_H =\n\\Delta\\Psi(\\Omega_H-\\Omega_D)/(2\\pi Z_H)$, where $Z_H$ is the resistance of the \nblack hole which is of several hundred Ohms (the disk is perfectly conducting so\nits resistance is zero). The power deposited into the disk by the black hole is\n\\begin{eqnarray}\n P_{HD} = - I {\\cal E}_D\n = \\left({\\Delta\\Psi\\over 2\\pi}\\right)^2 \\,{\\Omega_D\n \\left(\\Omega_H - \\Omega_D\\right)\n \\over Z_H}\\,.\n \\label{pow3}\n\\end{eqnarray}\nThe torque on the disk produced by the black hole is\n\\begin{eqnarray}\n T_{HD} = {I\\over 2\\pi}\\Delta\\Psi =\n \\left({\\Delta\\Psi\\over 2\\pi}\\right)^2 \\,{\\left(\\Omega_H -\n\t \\Omega_D\\right)\n \\over Z_H}\\,.\n \\label{toq}\n\\end{eqnarray}\nAs expected, we have $P_{BH} = T_{BH}\\Omega_D$.\n\nThe signs of $P_{HD}$ and $T_{HD}$ are determined by the sign of \n$\\Omega_H-\\Omega_D$. When $\\Omega_H > \\Omega_D$, we have $P_{HD}>0$ \nand $T_{HD}>0$, energy and angular\nmomentum are transferred from the black hole to the disk.\nWhen $\\Omega_H < \\Omega_D$, we have $P_{HD} < 0$ and $T_{HD}<0$, energy \nand angular momentum are transferred from the disk to the black hole so the\nblack hole is spun up. For a disk with non-rigid rotation, $\\Omega_D$\nvaries with radius. For fixed values of $\\Delta\\Psi$,\n$\\Omega_H$, and $Z_H$, $P_{HD}$ peaks at $\\Omega_D = \\Omega_H/2$.\nHowever for realistic cases which is most important is when the\nmagnetic field lines touch the disk close to the inner boundary,\nso $\\Omega_D$ in Eq.~(\\ref{pow3}) and Eq.~(\\ref{toq}) can be taken \nto be the value\nat the inner boundary of the disk. According to Gruzinov (1999) the\nmagnetic fields will be more unstable against screw instability if the \nfoot-points \nof the field lines on the disk are far from the inner boundary of the disk.\n\nFor a thin Keplerian disk around a Kerr black hole in the equatorial plane, the\nangular velocity of the disk is (Novikov \\& Thorne 1973)\n\\begin{eqnarray}\n \\Omega_D(r)=\\left({M_H\\over r^3}\\right)^{1/2}{1\\over 1+a\\left(M_H/r^3\n \\right)^{1/2}}\\,,\n \\label{wd}\n\\end{eqnarray}\nwhere $r$ is the Boyer-Lindquist radius in Kerr spacetime. $\\Omega_D(r)$\ndecreases with increasing $r$. The angular velocity of a Kerr black hole is\n\\begin{eqnarray}\n \\Omega_H = {a\\over 2M_H r_H}\\,,\n \\label{wh}\n\\end{eqnarray}\nwhere $r_H = M_H + \\sqrt{M_H^2-a^2}$ is the radius of the event horizon.\n$\\Omega_H$ is constant on the horizon. The inner boundary of a Keplerian disk\nis usually assumed to be at the marginally stable orbit with radius\n(Novikov \\& Thorne 1973)\n\\begin{eqnarray}\n r_{ms}=M_H\\left\\{3+z_2-\\left[(3-z_1)(3+z_1+2z_2)\\right]^{1/2}\\right\\}\\,,\n \\label{rms}\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\n z_1=1+\\left(1-a^2/M_H^2\\right)^{1/3}\\left[\\left(1+a/M_H\\right)^{1/3}+\n \\left(1-a/M_H\\right)^{1/3}\\right]\\,,\n \\label{rms2}\n\\end{eqnarray}\nand\n\\begin{eqnarray}\n z_2=\\left(3a^2/M_H^2+z_1^2\\right)^{1/2}\\,.\n \\label{rms3}\n\\end{eqnarray}\nInserting Eq.~(\\ref{rms}) into\nEq.~(\\ref{wd}), we obtain the angular velocity of the disk at its inner \nboundary:\n$\\Omega_{ms} = \\Omega_D(r_{ms})$. For the Schwarzschild case (i.e $a = 0$) we \nhave $r_{ms} = 6 M_H$ and $\\Omega_{ms} = 6^{-3/2}M_H^{-1}\\equiv\\Omega_0$.\n\nAssuming the magnetic field lines touch the disk close to the inner boundary, \nwe have $P_{HD} \\approx P_0 f$\nwhere\n\\begin{eqnarray}\n P_0 = \\left({\\Delta\\Psi\\over 2\\pi}\\right)^2 {\\Omega_0^2\\over Z_H}\n \\label{psch}\n\\end{eqnarray}\nis the value of $-P_{HD}$ for the Schwarzschild case, and\n\\begin{eqnarray}\n f = {\\Omega_{ms}\\left(\\Omega_H -\\Omega_{ms}\\right)\\over \\Omega_0^2}\n \\label{ratio}\n\\end{eqnarray}\nis a function of $a/M_H$ only. The variation of $P_{HD}$ with $a/M_H$\nis shown in Fig.~\\ref{figure1}. We see that $P_{HD}>0$ when $0.36 < a/M_H <1$,\n$P_{HD}<0$ when $0\\le a/M_H<0.36$. $P_{HD}=0$ at $a/M_H \\approx 0.36$ and\n$a/M_H=1$ since $P_{HD}\\propto \\Omega_H-\\Omega_{ms}$ and $\\Omega_H = \\Omega_{ms}$ \nwhen $a/M_H\\approx 0.36$ and $a/M_H =1$.\nFor fixed $\\Delta\\Psi$, $M_H$, and $Z_H$, $P_{HD}$ peaks\nat $a/M_H\\approx 0.981$. $T_{HD}$ always has the same sign as $P_{HD}$ since\n$P_{HD} = T_{HD}\\Omega_D$ for a perfectly conducting disk.\n\n\n%\\section 3\n\\section{Extracting Energy from a Black Hole through Its Disk}\nWhen $a/M_H>0.36$, energy and angular momentum are extracted from the black hole\nand transferred to the disk. So a fast rotating black hole can pump its rotational\nenergy into a disk surrounding it through magnetic coupling between them.\nOnce the energy gets into the disk, it can be radiated to infinity either\nin the form of Poynting flux associated with jets or winds, or in the form\nof thermal radiation associated with dissipative processes in the disk.\nIf the disk is not accreting or its accretion rate is very low,\nthen the disk's power \ncomes from the rotational energy of the black hole.\nThis provides a way for {\\em indirectly} extracting energy from a rotating \nblack hole. Note, that the Blandford-Znajek mechanism is a way for \n{\\em directly} extracting energy from a rotating black hole\nto the remote load.\n\nIt is possible that the Blandford-Znajek mechanism provides a very ``clean''\nenergy beam, while energy extracted from the disk is ``dirty'', contaminated\nby matter from the disk corona (R. D. Blandford 1999a, private communication).\nHowever, we must keep in mind that there exists no quantitative model \ndemonstrating how to generate clean energy with the Blandford-Znajek process.\n\nLet us consider again our case, in which\nKerr black hole loses its energy and angular momentum through the \nmagnetic interaction with a thin Keplerian disk, with the magnetic field lines \ntouching the disk close to the marginally stable orbit. \nThe evolution of the mass \nand angular momentum of the black hole are given by\n\\begin{eqnarray}\n {d M_H\\over dt} = -2 P_{HD}\\,,\n \\hspace{1cm} {d J_H\\over dt} = -2 T_{HD}\\,,\n \\label{evol}\n\\end{eqnarray}\nwhere $P_{HD}$ and $T_{HD}$ are given by Eq.~(\\ref{pow3}) and Eq.~(\\ref{toq})\nrespectively, the factors $2$ come from the fact that a disk has\ntwo faces. From Eq.~(\\ref{evol}) we obtain ${dJ_H/ dM_H} = {1/\\Omega_{ms}}$,\nwhere we have used $P_{HD} \\approx T_{HD}\\Omega_{ms}$. Define the spin of a Kerr\nblack hole by $s \\equiv a/M_H = J_H/M_H^2$, then we have\n\\begin{eqnarray}\n {ds\\over d\\ln M_H} = {1\\over \\omega} - 2 s\\,,\n \\label{dsm}\n\\end{eqnarray}\nwhere $\\omega \\equiv M_H\\Omega_{ms}$ is a function of $s$ only. Eq.~(\\ref{dsm})\ncan be integrated\n\\begin{eqnarray}\n M_H(s) = M_{H,0} \\exp\\int_{s_0}^s{ds\\over\\omega^{-1}-2s}\\,,\n \\label{mh}\n\\end{eqnarray}\nwhere $M_{H,0} = M_H(s=s_0)$. Consider a Kerr black hole with initial mass $M_H$ \nand the initial spin $s = 0.998$, which is\nthe maximum value of $s$ that an astrophysical black hole can have (Thorne\n1974). As the black hole spins down to $s = 0.36$, the total amount of energy\nextracted from the black hole by the disk can be calculated with Eq.~(\\ref{mh}):\n$\\Delta E\\approx 0.15 M_H$.\nThis amount of energy will eventually be transported to infinity by the disk.\nIn a realistic case the magnetic field lines touch the disk not exactly at the \nmarginally stable orbit, the averaged angular velocity of the disk will be \nsomewhat smaller than $\\Omega_{ms}$, then the total amount of energy that \ncan be extracted\nfrom the black hole should be somewhat smaller than $0.15 M_H$.\n\nFor comparison let's calculate the amount of energy that can be extracted \nfrom a Kerr black hole by the Blandford-Znajek mechanism in the optimal case \ni.e. when the impedance matching condition is satisfied (cf. Macdonald \\&\nThorne 1982). To do so, we only need to replace $\\Omega_{ms}$ with\n$\\Omega_H/2$ in Eq.~(\\ref{mh}), since the power and torque of the black hole\nare related by $P_H = T_H\\Omega_F$ where $\\Omega_F$ is the angular velocity of \nmagnetic field lines, and in the optimal case $\\Omega_F = \\Omega_H/2$.\nThen we obtain that as the black hole spins down from $s = 0.998$ to $s = 0$ the\ntotal energy extracted from the black hole by the Blandford-Znajek mechanism\nis $\\approx 0.09 M_H$.\n\nWe find that the magnetic coupling between a black hole and a disk has a higher\nefficiency in extracting energy from the black hole than the Blandford-Znajek \nmechanism (see Fig.~\\ref{figure2}). This is because the energy extracted \nfrom the black hole by the magnetic coupling to the disk has a \nlarger ratio of energy to angular momentum than is the case for\nthe Blandford-Znajek mechanism.\n\n%\\section 4\n\\section{Conclusions}\nWhen a black hole rotates faster than the disk,\nwhich is the case if $a/M_H>0.36$ for a Kerr black hole with a \nthin Keplerian disk, then the black hole exerts a torque at the\ninner edge of the disk. The torque transfers energy\nand angular momentum from the black hole to the disk.\nThis is similar to the ``propeller'' mechanism in the case of a \nmagnetized neutron star with a disk (Illarionov \\& Sunyaev 1975). \nThe energy transfered to the disk \nis eventually radiated to infinity by the disk. This provides a mechanism for\nextracting energy from a black hole through its disk. \nFor a Kerr black hole with the initial mass $M_H$ and spin $a/M_H = 0.998$, \nthe total amount of energy that can be extracted by a thin Keplerian\ndisk is $\\approx 0.15 M_H$.\nTherefore, this is more efficient than the Blandford-Znajek mechanism\nwhich can extract only $\\approx 0.09 M_H$.\n\nWhen the black hole rotates slower than the disk, i.e. $0\\le a/M_H<0.36$,\nenergy and angular momentum are transferred from the disk to the black hole,\nand the disk accretes onto the black hole.\n\n\\acknowledgments{I am very grateful to Bohdan Paczy\\'nski for encouraging and \nstimulating discussions. This work was supported by the NASA grant NAG5-7016.}\n\n%REFERENCES\n\\begin{references}\n\n\\reference{} Begelman, M. C., Blandford, R. D., \\& Rees, M. Z. 1984, Rev.\n Mod. Phys., 56, 255\n\n\\reference{} Blandford, R. D. 1976, MNRAS, 176, 465\n\n\\reference{} Blandford, R. D. 1999, in Astrophysical Disks: An EC Summer\n School, Astronomical Society of the Pacific Conference Series,\n V. 160, ed. J. A. Sellwood \\& J. Goodman, 265\n\n\\reference{} Blandford, R. D. 2000, astro-ph/0001499\n\n\\reference{} Blandford, R. D., \\& Znajek, R. L. 1977, MNRAS, 179, 433\n\n\\reference{} Gruzinov, A. 1999, astro-ph/9908101\n\n\\reference{} Illarionov, A. F., \\& Sunyaev, R. A. 1975, A\\&A, 39, 185\n\n\\reference{} Lee, H. K., Wijers, R. A. M. J., \\& Brown, G. E. 1999, \n astro-ph/9906213\n\n\\reference{} Li, L. -X. 1999, astro-ph/9902352; to appear in\n Phys. Rev. D\n\n\\reference{} Livio, M., Ogilvie, G. I., \\& Pringle, J. E. 1999, ApJ, 512, 100\n\n\\reference{} Macdonald, D., \\& Thorne, K. S. 1982, MNRAS, 198, 345\n\n\\reference{} Novikov, I. D., \\& Thorne, K. S. 1973, in Black Holes, ed.\n C. DeWitt \\& B. S. DeWitt (NY: Gordon and Breach), 343\n\n\\reference{} Paczy\\'nski, B. 1993, in Relativistic Astrophysics and Particle\n Cosmology, ed. C. W. Akerlof \\& M. A. Srednicki, Ann. NY\n Acad. Sci., Vol. 688, 321\n\n\\reference{} Phinney, E. S. 1983, in Astrophysical Jets, ed.\n A. Ferrari \\& A. G. Pacholczyk (Dordrecht:\n\t D. Reidel Publishing Co.), 201\n\n\\reference{} Rees, M. J., Begelman, M. C., Blandford, R. D., \\& Phinney, E. S.\n 1982, Nature 295, 17\n\n\\reference{} Thorne, K. S. 1974, ApJ, 191, 507\n\n\\end{references}\n\n\\newpage\n%Figure Captions\n\\figcaption[fig1.ps]{Magnetic field lines connecting a black hole with an accretion\ndisk can transfer energy and angular momentum between them. In the figure is shown \nthe dependence of the power of the energy transfer on the spin of the black hole\nfor the model of a Kerr black hole with a thin Keplerian disk. The magnetic field lines\nare assumed to touch the disk close to the marginally stable orbit. The vertical \naxis shows the power $P_{HD}$ in unit of $P_0$, where $P_0$ is the value\nof $-P_{HD}$ for the Schwarzschild case. The horizontal axis shows $a/M_H$, where\n$M_H$ is the mass of the black hole, $a M_H$ is the angular momentum of the black\nhole. If $P_{HD}>0$, which is the case when $0.36<a/M_H <1$, energy and angular \nmomentum are transferred from the black hole to the disk; if $P_{HD}<0$, which \nis the case when $0\\le a/M_H <0.36$, energy and angular momentum are transferred from\nthe disk to the black hole. $P_{HD}$ peaks at $a/M_H\\approx 0.981$.\n\\label{figure1}}\n\n\\figcaption[fig2.ps]{The efficiency in extracting energy from a Kerr black hole\nas the black hole is spun down. The efficiency is defined by $\\eta = \\Delta E/M_H$,\nwhere $M_H$ is the mass of the black hole at its initial state with $a/M_H = 0.998$\n(the maximum value of $a/M_H$ that an astrophysical black hole can have). \n(So the left ends\nof the curves are at $a/M_H = 0.998$, not $a/M_H = 1$. Note that in the figure \n$a/M_H$ decreases from left to right.) The solid curve represents\nthe efficiency in extracting energy from a Kerr black hole through a thin Keplerian \ndisk, which ends at $a/M_H = 0.36$ since then the transfer of energy and angular \nmomentum from the black hole to the disk stops. With this mechanism, up to $\\approx \n15\\%$ of the initial mass of the black hole can be extracted. The dashed curve represents\nthe efficiency of the Blandford-Znajek mechanism, which ends at $a/M_H = 0$. With the\nBlandford-Znajek mechanism, up to $\\approx \n9\\%$ of the initial mass of the black hole can be extracted. \n\\label{figure2}}\n\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002005
|
A Comparison of Ultraviolet, Optical, and X-Ray Imagery of Selected Fields in the Cygnus Loop
|
[
{
"author": "\\sc Charles W.\\ Danforth\\altaffilmark{1}"
},
{
"author": "Robert H.\\ Cornett\\altaffilmark{2}"
},
{
"author": "N. A. Levenson\\altaffilmark{1}"
},
{
"author": "William P.\\ Blair\\altaffilmark{1}"
},
{
"author": "Theodore P.\\ Stecher\\altaffilmark{3}"
}
] |
During the Astro-1 and Astro-2 Space Shuttle missions in 1990 and 1995, far ultraviolet (FUV) images of five 40\arcmin\ diameter fields around the rim of the Cygnus Loop supernova remnant were observed with the Ultraviolet Imaging Telescope (UIT). These fields sampled a broad range of conditions including both radiative and nonradiative shocks in various geometries and physical scales. In these shocks, the UIT B5 band samples predominantly \ion{C}{4} $\lambda$1550 and the hydrogen two-photon recombination continuum. Smaller contributions are made by emission lines of \ion{He}{2} $\lambda$1640 and \ion{O}{3}] $\lambda$1665. We present these new FUV images and compare them with optical \Ha\ and [\ion{O}{3}], and ROSAT HRI X-ray images. Comparing the UIT images with those from the other bands provides new insights into the spatial variations and locations of these different types of emission. By comparing against shock model calculations and published FUV spectroscopy at select locations, we surmise that resonance scattering in the strong FUV permitted lines is widespread in the Cygnus Loop, especially in the bright optical filaments typically selected for observation in most previous studies.
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[
{
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\t\\@psdo\\@psfiga:=#1\\do\n\t\t {\\expandafter\\@setparms\\@psfiga,}}\n%\n% Compute bb height and width\n%\n\\newif\\ifno@bb\n\\newif\\ifnot@eof\n\\newread\\ps@stream\n\\def\\bb@missing{\n\t\\if@verbose{\n\t\t\\typeout{psfig: searching \\@p@sfile \\space for bounding box}\n\t}\\fi\n\t\\openin\\ps@stream=\\@p@sfile\n\t\\no@bbtrue\n\t\\not@eoftrue\n\t\\catcode`\\%=12\n\t\\loop\n\t\t\\read\\ps@stream to \\line@in\n\t\t\\global\\toks200=\\expandafter{\\line@in}\n\t\t\\ifeof\\ps@stream \\not@eoffalse \\fi\n\t\t%\\typeout{ looking at :: \\the\\toks200 }\n\t\t\\@bbtest{\\toks200}\n\t\t\\if@bbmatch\\not@eoffalse\\expandafter\\bb@cull\\the\\toks200\\fi\n\t\\ifnot@eof \\repeat\n\t\\catcode`\\%=14\n}\t\n\\catcode`\\%=12\n\\newif\\if@bbmatch\n\\def\\@bbtest#1{\\expandafter\\@a@\\the#1%%BoundingBox:\\@bbtest\\@a@}\n\\long\\def\\@a@#1%%BoundingBox:#2#3\\@a@{\\ifx\\@bbtest#2\\@bbmatchfalse\\else\\@bbmatchtrue\\fi}\n\\long\\def\\bb@cull#1 #2 #3 #4 #5 {\n\t\\dimen100=#2 bp\\edef\\@p@sbbllx{\\number\\dimen100}\n\t\\dimen100=#3 bp\\edef\\@p@sbblly{\\number\\dimen100}\n\t\\dimen100=#4 bp\\edef\\@p@sbburx{\\number\\dimen100}\n\t\\dimen100=#5 bp\\edef\\@p@sbbury{\\number\\dimen100}\n\t\\no@bbfalse\n}\n\\catcode`\\%=14\n%\n\\def\\compute@bb{\n\t\t\\no@bbfalse\n\t\t\\if@bbllx \\else \\no@bbtrue \\fi\n\t\t\\if@bblly \\else \\no@bbtrue \\fi\n\t\t\\if@bburx \\else \\no@bbtrue \\fi\n\t\t\\if@bbury \\else \\no@bbtrue \\fi\n\t\t\\ifno@bb \\bb@missing \\fi\n\t\t\\ifno@bb \\typeout{FATAL ERROR: no bb supplied or found}\n\t\t\t\\no-bb-error\n\t\t\\fi\n\t\t%\n\t\t\\count203=\\@p@sbburx\n\t\t\\count204=\\@p@sbbury\n\t\t\\advance\\count203 by -\\@p@sbbllx\n\t\t\\advance\\count204 by -\\@p@sbblly\n\t\t\\edef\\@bbw{\\number\\count203}\n\t\t\\edef\\@bbh{\\number\\count204}\n\t\t%\\typeout{ bbh = \\@bbh, bbw = \\@bbw }\n}\n%\n% \\in@hundreds performs #1 * (#2 / #3) correct to the hundreds,\n%\tthen leaves the result in @result\n%\n\\def\\in@hundreds#1#2#3{\\count240=#2 \\count241=#3\n\t\t \\count100=\\count240\t% 100 is first digit #2/#3\n\t\t \\divide\\count100 by \\count241\n\t\t \\count101=\\count100\n\t\t \\multiply\\count101 by \\count241\n\t\t \\advance\\count240 by -\\count101\n\t\t \\multiply\\count240 by 10\n\t\t \\count101=\\count240\t%101 is second digit of #2/#3\n\t\t \\divide\\count101 by \\count241\n\t\t \\count102=\\count101\n\t\t \\multiply\\count102 by \\count241\n\t\t \\advance\\count240 by -\\count102\n\t\t \\multiply\\count240 by 10\n\t\t \\count102=\\count240\t% 102 is the third digit\n\t\t \\divide\\count102 by \\count241\n\t\t \\count200=#1\\count205=0\n\t\t \\count201=\\count200\n\t\t\t\\multiply\\count201 by \\count100\n\t\t \t\\advance\\count205 by \\count201\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 10\n\t\t\t\\multiply\\count201 by \\count101\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 100\n\t\t\t\\multiply\\count201 by \\count102\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\edef\\@result{\\number\\count205}\n}\n\\def\\compute@wfromh{\n\t\t% computing : width = height * (bbw / bbh)\n\t\t\\in@hundreds{\\@p@sheight}{\\@bbw}{\\@bbh}\n\t\t%\\typeout{ \\@p@sheight * \\@bbw / \\@bbh, = \\@result }\n\t\t\\edef\\@p@swidth{\\@result}\n\t\t%\\typeout{w from h: width is \\@p@swidth}\n}\n\\def\\compute@hfromw{\n\t\t% computing : height = width * (bbh / bbw)\n\t\t\\in@hundreds{\\@p@swidth}{\\@bbh}{\\@bbw}\n\t\t%\\typeout{ \\@p@swidth * \\@bbh / \\@bbw = \\@result }\n\t\t\\edef\\@p@sheight{\\@result}\n\t\t%\\typeout{h from w : height is \\@p@sheight}\n}\n%% yves\n\\def\\compute@wfroms{\n\t\t%\\typeout{computewfroms: scale is \\@p@sscale}\t\n\t\t% computing : width = scale * (bbw / 100)\n\t\t\\in@hundreds{\\@p@sscale}{\\@bbw}{100}\n\t\t%\\typeout{ \\@p@sscale * \\@bbw / 100, = \\@result }\n\t\t\\edef\\@p@swidth{\\@result}\n\t\t%\\typeout{w from s: width is \\@p@swidth}\n}\n\\def\\compute@hfroms{\n\t\t%\\typeout{computehfroms: scale is \\@p@sscale}\t\n\t\t% computing : height = scale * (bbh / 100)\n\t\t\\in@hundreds{\\@p@sscale}{\\@bbh}{100}\n\t\t%\\typeout{ \\@p@sscale * \\@bbh / 100 = \\@result }\n\t\t\\edef\\@p@sheight{\\@result}\n\t\t%\\typeout{h from s : height is \\@p@sheight}\n}\n\\def\\compute@handw{\n\t\t\\if@scale\n%\t\t\t\\edef\\@p@sheight{\\@bbh}\n%\t\t\t\\edef\\@p@swidth{\\@bbw}\n\t\t\t\\compute@wfroms\n\t\t\t\\compute@hfroms\n\t\t\\else\n\t\t\t\\if@height \n\t\t\t\t\\if@width\n\t\t\t\t\\else\n\t\t\t\t\t\\compute@wfromh\n\t\t\t\t\\fi\t\n\t\t\t\\else \n\t\t\t\t\\if@width\n\t\t\t\t\t\\compute@hfromw\n\t\t\t\t\\else\n\t\t\t\t\t\\edef\\@p@sheight{\\@bbh}\n\t\t\t\t\t\\edef\\@p@swidth{\\@bbw}\n\t\t\t\t\\fi\n\t\t\t\\fi\n\t\t\\fi\n}\n%% finish\n\\def\\compute@resv{\n\t\t\\if@rheight \\else \\edef\\@p@srheight{\\@p@sheight} \\fi\n\t\t\\if@rwidth \\else \\edef\\@p@srwidth{\\@p@swidth} \\fi\n}\n%\t\t\n% Compute any missing values\n\\def\\compute@sizes{\n\t\\compute@bb\n\t\\compute@handw\n\t\\compute@resv\n}\n%\n% \\psfig\n% usage : \\psfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,\n%\t\t\trheight=, rwidth=, clip=}\n%\n% \"clip=\" is a switch and takes no value, but the `=' must be present.\n\\def\\psfig#1{\\vbox {\n\t% do a zero width hard space so that a single\n\t% \\psfig in a centering enviornment will behave nicely\n\t%{\\setbox0=\\hbox{\\ }\\ \\hskip-\\wd0}\n\t%\n\t\\ps@init@parms\n\t\\parse@ps@parms{#1}\n\t\\compute@sizes\n\t%\n\t\\ifnum\\@p@scost<\\@psdraft{\n\t\t\\if@verbose{\n\t\t\t\\typeout{psfig: including \\@p@sfile \\space }\n\t\t}\\fi\n\t\t%\n\t\t\\special{ps::[begin] \t\\@p@swidth \\space \\@p@sheight \\space\n\t\t\t\t\\@p@sbbllx \\space \\@p@sbblly \\space\n\t\t\t\t\\@p@sbburx \\space \\@p@sbbury \\space\n\t\t\t\tstartTexFig \\space }\n\t\t\\if@clip{\n\t\t\t\\if@verbose{\n\t\t\t\t\\typeout{(clip)}\n\t\t\t}\\fi\n\t\t\t\\special{ps:: doclip \\space }\n\t\t}\\fi\n\t\t\\if@prologfile\n\t\t \\special{ps: plotfile \\@prologfileval \\space } \\fi\n\t\t\\special{ps: plotfile \\@p@sfile \\space }\n\t\t\\if@postlogfile\n\t\t \\special{ps: plotfile \\@postlogfileval \\space } \\fi\n\t\t\\special{ps::[end] endTexFig \\space }\n\t\t% Create the vbox to reserve the space for the figure\n\t\t\\vbox to \\@p@srheight true sp{\n\t\t\t\\hbox to \\@p@srwidth true sp{\n\t\t\t\t\\hss\n\t\t\t}\n\t\t\\vss\n\t\t}\n\t}\\else{\n\t\t% draft figure, just reserve the space and print the\n\t\t% path name.\n\t\t\\vbox to \\@p@srheight true sp{\n\t\t\\vss\n\t\t\t\\hbox to \\@p@srwidth true sp{\n\t\t\t\t\\hss\n\t\t\t\t\\if@verbose{\n\t\t\t\t\t\\@p@sfile\n\t\t\t\t}\\fi\n\t\t\t\t\\hss\n\t\t\t}\n\t\t\\vss\n\t\t}\n\t}\\fi\n}}\n\\def\\psglobal{\\typeout{psfig: PSGLOBAL is OBSOLETE; use psprint -m instead}}\n\\catcode`\\@=12\\relax\n\n\n"
},
{
"name": "uit_pp.tex",
"string": "% Full graphical preprint version\n% latest text modification 1/21/00\n% latest format modification 1/28/00\n% chopped down size for Astro-ph archiving 1-31-00\n\n%%%*****************************************************************\n\\newcommand{\\Ha}{H$\\alpha$}\n\\newcommand{\\vel}{$\\rm km\\ s^{-1}$}\n\\newcommand{\\url}{http://www.pha.jhu.edu/$\\sim$danforth/uit/}\n\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\n%% EDITORIAL PERSONNEL WILL USE THE FIVE LINES BELOW.\n%% NO NEED FOR AUTHORS TO BOTHER WITH IT.\n\n%\\received{ }\n%\\accepted{ }\n%\\journalid{ }{ }\n%\\articleid{ }{ }\n%\\slugcomment{ }\n\n\\input{psfig}\n\\begin{document}\n\n\\title{A Comparison of Ultraviolet, Optical, and X-Ray Imagery of Selected\nFields in the Cygnus Loop}\n\n\\author{\\sc Charles W.\\ Danforth\\altaffilmark{1}, Robert H.\\\nCornett\\altaffilmark{2}, N. A. Levenson\\altaffilmark{1}, William P.\\\nBlair\\altaffilmark{1}, Theodore P.\\ Stecher\\altaffilmark{3}}\n\n\\altaffiltext{1}{Department of Physics and Astronomy, The Johns Hopkins\nUniversity, 3400 N. Charles Street, Baltimore, MD 21218; [email protected],\[email protected], [email protected]}\n\n\\altaffiltext{2}{Raytheon ITSS, 4400 Forbes Blvd., Lanham, MD 20706;\[email protected]}\n\n\\altaffiltext{3}{Laboratory for Astronomy and Solar Physics, NASA/GSFC, Code\n681, Greenbelt, MD 20771; [email protected]}\n\n\\begin{center}{Accepted for Publication January 27, 2000}\\end{center}\n\n\\begin{abstract}\nDuring the Astro-1 and Astro-2 Space Shuttle missions in 1990 and 1995, far\nultraviolet (FUV) images of five 40\\arcmin\\ diameter fields around the rim of\nthe Cygnus Loop supernova remnant were observed with the Ultraviolet Imaging\nTelescope (UIT). These fields sampled a broad range of conditions including\nboth radiative and nonradiative shocks in various geometries and physical\nscales. In these shocks, the UIT B5 band samples predominantly \\ion{C}{4}\n$\\lambda$1550 and the hydrogen two-photon recombination continuum. Smaller\ncontributions are made by emission lines of \\ion{He}{2} $\\lambda$1640 and\n\\ion{O}{3}] $\\lambda$1665. We present these new FUV images and compare them\nwith optical \\Ha\\ and [\\ion{O}{3}], and ROSAT HRI X-ray images. Comparing the\nUIT images with those from the other bands provides new insights into the\nspatial variations and locations of these different types of emission. By\ncomparing against shock model calculations and published FUV spectroscopy at\nselect locations, we surmise that resonance scattering in the strong FUV\npermitted lines is widespread in the Cygnus Loop, especially in the bright\noptical filaments typically selected for observation in most previous studies.\n\n\\end{abstract}\n\n\\keywords{ISM: nebulae --- ISM: supernova remnants --- ISM: shock waves ---\nultraviolet: imaging}\n\n\\section{Introduction}\nBecause of its large angular size and wide range of shock conditions, the\nCygnus Loop is one of the best laboratories for studying the environment and\nphysics of middle-aged supernova remnants (SNR). It covers a huge expanse in\nthe sky (2.8$\\times$3.5$\\rm ^o$) corresponding to 21.5$\\times$27 pc, at a newly\ndetermined distance of 440 pc (\\cite{Blair99}). The currently accepted view\nfor the Cygnus Loop is that it represents an explosion in a cavity produced by\na fairly massive precursor star (cf. \\cite{Levenson98}). The SN shock has\nbeen traveling relatively unimpeded for roughly ten parsecs and has only\nrecently begun reaching the denser cavity walls. The size of the cavity\nimplicates a precursor star of type early B. The interaction of the shock with\nthe complex edges of the cavity wall is responsible for the complicated mixture\nof optical and X-ray emission seen in superposition, and a dazzling variety of\noptical filament morphologies.\n\nPortions of the SN blast wave propagating through the fairly rarefied atomic\nshell ($<$1 cm$^{-3}$), show faint filaments with hydrogen\nBalmer-line-dominated optical spectra. These filaments represent the position\nof the primary blast wave and are often termed nonradiative shocks (because\nradiative losses are unimportant to the dynamics of the shock itself). Ambient\ngas is swept up and progressively ionized, emitting \\ion{He}{2}, \\ion{C}{4},\n\\ion{N}{5}, and \\ion{O}{6} lines in the FUV (Figure~1, bottom spectrum)\n(\\cite{Hester94}, \\cite{Raymond83}). Balmer-dominated emission arises from the\nfraction ($\\sim$0.3) of neutral hydrogen swept up by the shock that stands some\nchance of being excited and recombining before it is ionized in the post-shock\nflow (\\cite{Chevalier78}; \\cite{CKR80}).\n\nThe Balmer emission is accompanied by hydrogen two-photon events which produce\na broad continuum above 1216\\AA\\ peaking at $\\sim$1420\\AA\\\n(\\cite{Nussbaumer84}). For recombination and for high temperature shocks, the\nratio of two-photon emission to Balmer is nearly constant ($\\sim$8:1). In\nslow shocks ($\\sim$40\\vel) in neutral gas, the ratio can be enhanced\nconsiderably (\\cite{Dopita82}).\n\nBalmer-dominated filaments are very smooth and WFPC2 observations by Blair et\nal. (1999) show that they are exceedingly thin as well---less than one WFC\npixel across when seen edge-on, or $<6 \\times 10^{14}$ cm at our assumed\ndistance, in keeping with theoretical predictions (cf. \\cite{Raymond83}).\nPostshock temperatures reach millions of degrees and the hot material emits\ncopious soft X-rays. The density is low, however, and cooling is very\ninefficient. With time, as the shock continues to sweep up material, these\nfilaments will be able to start cooling more effectively and will evolve to\nbecome radiative filaments.\n\nThe bright optical filaments in the Cygnus Loop represent radiative shocks in\nmuch denser material, such as might be expected in the denser portions of the\ncavity wall. These shocks are said to be radiative (that is, energy losses\nfrom radiation are significant); they have more highly developed cooling and/or\nrecombination zones. The shocked material emits in the lines of a broad range\nof hot, intermediate, and low temperature ions, depending on the effective\n`age' of the shock at a given location and the local physical conditions. For\ninstance, a relatively recent encounter between the shock and a density\nenhancement (or similarly, a shock that has swept up a fairly low total column\nof material) may show very strong [O~III] $\\lambda 5007$ compared with \\Ha.\nThis would indicate that the coolest part of the flow, the recombination zone\nwhere the Balmer lines become strong, has not yet formed. Such shocks are said\nto be `incomplete' as the shocked material remains hot and does not yet emit in\nthe lower ionization lines.\n\nIn contrast, radiative filaments with the full range of ionization (including\nthe low ionization lines) are well approximated by full, steady-flow shock\nmodel calculations, such as those of \\cite{Raymond79}, \\cite{Dopita84}, and\nHartigan, Raymond, \\& Hartmann (1987; hereafter \\cite{HRH}). Morphologically,\nradiative complete filaments lack the smooth grace of nonradiative filaments\nor even radiative incomplete filaments in some cases (cf. \\cite{Fesen82}). The\nmore irregular appearance of these filaments is due partly to inhomogeneities\nin the shocked clouds themselves, partly to turbulence and/or thermal\ninstabilities that set in during cooling (cf. \\cite{Innes92} and references\ntherein), and partly to several clouds appearing along single lines of sight.\nOften the emission at a given filament position cannot be characterized by a\nsingle shock velocity.\n\nMuch of the above understanding of shock types and evolutionary stages has been\npredicated on UV/optical studies of the Cygnus Loop itself. The Cygnus Loop is\n a veritable laboratory for such studies because of its relative proximity,\nlarge angular extent and low foreground extinction (E[B $-$ V] = 0.08;\n\\cite{Fesen82}), and thus its accessibility across the electromagnetic\nspectrum. However, because of the range of shock interactions and shock types,\ncoupled with the significant complication of projection effects near the limb\nof the SNR, great care must be taken in order to obtain a full understanding of\nwhat is happening at any given position in the nebular structure.\n\nAlthough FUV spectra are available at a number of individual filament locations\nfrom years of observations with IUE and the shuttle-borne Hopkins Ultraviolet\nTelescope (HUT), the perspective obtainable from FUV imaging has been largely\nlacking. The Ultraviolet Imaging Telescope (UIT) was flown as part of the\nAstro-1 Space Shuttle mission in 1990 was used to observe a field in the Cygnus\nLoop through both mid-UV and far-UV (FUV) filters (\\cite{Cornett92}). In this\npaper, we report on additional FUV observations with UIT obtained during the\nAstro-2 shuttle mission in 1995. In addition to the field imaged during\nAstro-1, UIT observed four different regions around the periphery of the Cygnus\nLoop with a resolution comparable to existing optical and X-ray observations.\nThese fields sample the full range of physical and shock conditions and\nevolutionary stages in the SNR. We combine these data with existing\nground-based optical images and ROSAT HRI X-ray data to obtain new insights\ninto this prototypical SNR and its interaction with its surroundings.\n\nIn \\S2 we present the observations obtained with the UIT and review the\ncomparison data sets. In \\S3 we discuss the spectral content of the UIT filter\nused in the observations. In \\S4 we discuss examples of the various kinds of\nshocks as seen in the UIT fields, and summarize our conclusions in \\S5.\n\n\\section{UIT Observations and Comparison Data}\n\nUIT has flown twice on the Space Shuttle as part of the Astro-1 and Astro-2\nprograms (1990 December 2-10 and 1995 March 2-18). Together with the Hopkins\nUltraviolet Telescope (HUT) and the Wisconsin Ultraviolet Photo-Polarimeter\nExperiment, UIT explored selected UV targets. An f/9 Ritchey-Chretien\ntelescope with a 38 cm aperture and image intensifier systems produced images\nof circular 40\\arcmin\\ fields of view with $\\sim$3\\arcsec\\ resolution at field\ncenter (depending on pointing stability). Images were recorded on 70mm Eastman\nKodak IIa-O film which was developed and digitized at NASA/GSFC and processed\ninto uniform data products. Technical details on the hardware and data\nprocessing can be found in \\cite{Stecher92} and Stecher et al. (1997).\n\n%\\begin{table}\n\\noindent Table~1: UIT B5 Filter Observations in the Cygnus Loop\\\\\n\\begin{tabular}{lllll}\nPosition & RA(J2000)& Dec(J2000)& exposure (sec) & Figure\\\\\n\\hline\nW cloud & 20:45:38 & +31:06:33 & 1010 & 3\\\\\nNE nonrad & 20:54:39 & +32:17:29 & 2041 & 4\\\\\nNE cloud & 20:56:16 & +31:44:34 & 500 & 5\\\\\nXA region$\\rm^a$& 20:57:35 & +31:07:28 & 1280 & 6\\\\\nXA region & 20:57:04 & +31:07:45 & 1151 & 6\\\\\nXA region & 20:57:22 & +31:04:02 & 1516 & 6\\\\\nXA region & 20:57:24 & +31:03:51 & 1274 & 6\\\\\nSE cloud & 20:56:05 & +30:44:01 & 2180 & 7\\\\\n\\hline\n\\end{tabular}\\\\\n$\\rm^a$ Astro-1 image (cf. \\cite{Cornett92})\n\nAstro/UIT images are among the few examples of FUV images of SNRs, and UIT's B5\nbandpass ($\\sim1450$\\AA\\ to $\\sim1800$\\AA) encompasses severally generally\nhigh-excitation and heretofore unmapped lines that are often present in SNR\nshocks (Figure~1). UIT's two Astro flights have produced eight FUV images of\nfive different Cygnus Loop fields. Table~1 lists the observation parameters\nand field locations, which are indicated in Figure~2. We will refer to these\nfields by the names listed in Table~1. Since all four exposures of the XA\nregion (named by \\cite{HesterCox86}) are reasonably deep, we constructed a\nmosaic of the field using the IRAF\\footnotemark\\ IMCOMBINE task, resulting in\nsignificantly improved signal-to-noise in the overlapped region of the combined\nimage. In panel c of Figures 3 through 7, we show the five reduced UIT images\nas observed in the B5 filter bandpass. \\footnotetext{IRAF is distributed by\nthe National Optical Astronomy Observatories, which is operated by the\nAssociation of Universities for Research in Astronomy, Inc.\\ (AURA) under\ncooperative agreement with the National Science Foundation.}\n\nUIT images with long exposure times suffer from an instrumental malady dubbed\n``measles'' by the UIT team (\\cite{Stecher97}). Measles manifest themselves as\nfixed-pattern noise spikes in images with a large sunlight flux, such as long\ndaylight exposures or images of red, very bright sources (e.g. planets or the\nMoon). This effect is probably produced by visible light passing through\npinholes in either the output phosphor of the first stage or the bialkali\nphotocathode of the second stage of the UIT FUV image tube. The Cygnus Loop\nwas a daytime object for both the Astro-1 and Astro-2 flights, but the\nphenomenon is visible only in some of the longer exposures. Most dramatically,\nmeasles are seen in the northeast cloud nonradiative image (Figure~4) as a\ndarkening in the northwest corner; the individual ``measles'' are spread into a\nbackground by the binning used to produce these images. Various approaches to\nremoving the appearance of measles were attempted but none of them have yielded\nsatisfactory results. In practice, the measles, here arising from daylight sky\ncontamination, affect our analysis only by adding to the background level, so\nthe original images are presented here, ``measles'' and all.\n\nFor comparison with our FUV images, we show narrow-band optical images in\n[\\ion{O}{3}] $\\lambda$5007 and \\Ha+[\\ion{N}{2}] (which for simplicity we refer\nto as \\Ha) obtained with the Prime Focus Corrector on the 0.8 m telescope at\nMcDonald Observatory (cf. \\cite{Levenson98}). These images, shown in panels~a\nand b of Figures~3~--~7, are aligned and placed on a common scale of 5\\arcsec\\\nper pixel, which is similar to the FUV resolution of 3\\arcsec. The optical\nimages have each been processed with a 3-pixel median filter to remove faint\nstars and stellar residuals.\n\nIn addition, we show the soft X-ray (0.1--2.4 keV) emission for each field, as\nobserved with the {\\it ROSAT} High Resolution Imager (HRI) (from\n\\cite{Levenson97}). The resolution of the HRI imager is 6\\arcsec\\ on axis\ndegrading to 30\\arcsec\\ at the edge of each field. As with the optical data,\nthe X-ray images are aligned on a 5\\arcsec\\ per pixel scale. The HRI images\nhave additionally been smoothed with a 3-pixel FWHM gaussian and are shown in\npanel d of Figures~3~--~7. All images in Figures~3~--~7 are displayed on a\nlogarithmic scale.\n\nFigure~8 shows three-color composite images using \\Ha\\ as red, B5 as green, and\nthe {\\it ROSAT} HRI as blue. The color levels have been adjusted for visual\nappearance, to best show the relative spatial relationships of the different\nemissions. (The color composite for the Northeast nonradiative region is not\nshown, since little new information is gained above Figure~4 and because of the\nadverse effect of the measles.) This will be discussed in more detail below.\n\n\\section{Spectral Content of UIT Images}\n\nFigure~1 shows the UIT B5 filter profile superimposed on spectra of typical\nradiative and nonradiative filaments, as observed by HUT. Unlike typical SNR\nnarrow band images in the optical, the B5 filter is relatively broad and does\nnot isolate a single spectral line, but rather encompasses several strong,\nmoderately high ionization lines that are variable from filament to filament.\nCornett et al. (1992) point out that \\ion{C}{4} should dominate emission in\nthis bandpass since it is a strong line centered near the filter's peak\nthroughput, and since shock models predict this result for a range of important\nvelocities (cf. Figure~10 and accompanying discussion). Here we look at this\nmore closely over a larger range of shock velocities, and in particular also\ndiscuss the potential complicating effects of hydrogen two-photon recombination\ncontinuum emission, shock completeness, and resonance line scattering.\n\nEmpirical comparisons of IUE and HUT emission line observations can be used to\nquantify at what level the C~IV emission is expected to dominate the line\nemission detected through the B5 filter. For instance, in the highly radiative\nXA region (see Figure~7) we have compared a large number of FUV spectra both\non and adjacent to bright optical filaments against the throughput curve of B5\n(Danforth, Blair, \\& Raymond 2000; henceforth \\cite{DBR}). This comparison\nshows that on average the various lines contribute as follows:\n\\ion{C}{4} $\\lambda$1550, 42\\%;\n\\ion{O}{3}] $\\lambda$1665, 27\\%;\n\\ion{He}{2} $\\lambda$1640, 17\\%;\n\\ion{N}{4} $\\lambda$1486, 8\\%;\nand 6\\%\nfrom fainter emission lines. Using the HUT observation of \\cite{Long92}, we\nestimate for nonradiative shocks the B5 contributions are more like\n\\ion{C}{4} (60\\%),\n\\ion{He}{2} (28\\%),\nand all other species 12\\%.\nThese percentages are only approximate, of course, and will vary with shock\nvelocity, geometry and a host of other conditions, but they serve to highlight\nthe fact that, while \\ion{C}{4} is the strongest contributor to the line\nemission, it is not the only contributor.\n\nIn addition, while it is not obvious at the scale of Figure~1, a low level\ncontinuum is often seen in IUE and HUT spectra of Cygnus Loop filaments,\nespecially where optical \\Ha\\ emission is present and strong. This continuum\narises due to the hydrogen two-photon process (cf. \\cite{Osterbrock89}).\n\\cite{Benvenuti80} note that SNR shocks cause two-photon emission from hydrogen\nvia both collisional excitation and recombination into the 2$^2$S$_{1/2}$\nstate. The two-photon spectrum arises from a probability distribution of\nphotons that is symmetric about 1/2 the energy of Ly$\\alpha$ (corresponding to\n2431\\AA), resulting in a shallow spectral peak near 1420\\AA\\ and extending from\n1216\\AA\\ towards longer wavelengths, throughout the UV and optical region. The\nexpected (integrated) strength of this component is about 8 $\\times$ the \\Ha\\\nflux but is spread over thousands of Angstroms. However, the wide bandpass of\nthe B5 filter detects $\\sim$15\\%\nof the total two-photon flux available, enough to compete with line emission in\nthe bandpass. Further complicating the question, two-photon emission can also\nbe highly variable from filament to filament.\n\nBy using signatures from the images and spectra at other wavelengths, we can\ninterpret, at least qualitatively, what is being seen in the UIT images. For\ninstance, Figure~4 shows the NE rim of the SNR. The faint, smooth \\Ha\\\nfilament running along the edge of the X-ray emission is clearly a nonradiative\nfilament. The faint emission seen in the B5 image traces these faint Balmer\nfilaments well, and at this position, does not correlate particularly well with\nthe clumpy [\\ion{O}{3}] emission seen near the middle of the field. This\nimplies a relatively strong contribution from two-photon continuum, although as\nshown in the bottom spectrum of Figure~1, \\ion{C}{4} and \\ion{He}{2} are also\npresent in the filaments at some level.\n\nAs discussed earlier, in radiative filaments, higher ionization lines such as\n\\ion{O}{6} $\\lambda$1035, \\ion{N}{5} $\\lambda$1240, \\ion{C}{4} $\\lambda$1550,\nand [\\ion{O}{3}] $\\lambda$5007 become strong first, followed by lower\nionization lines like [\\ion{S}{2}] $\\lambda$6725, [\\ion{O}{1}] $\\lambda$6300,\nand the hydrogen Balmer lines. Hence, in filaments that show high optical\n[\\ion{O}{3}] to \\Ha\\ ratios, and are thus incomplete shocks, the B5 content\nprimarily arises from \\ion{C}{4} and other line emission. In older, more\ncomplete shocks where the optical [\\ion{O}{3}] to \\Ha\\ ratios are close to\nthose expected from steady flow shock models, two-photon emission again should\ncompete with the line emission and the B5 flux should arise from both sources.\nIt is difficult to assess these competing effects from Figures 3 -- 7 since the\nrelative intensities of the two optical images are not always obvious, but much\nof the variation in coloration in Figure~8 for bright radiative filaments is\ndue to the variation in relative amounts of line emission and two-photon\ncontinuum contributions to the B5 image.\n\nIn Figure~9, we show the XA field as seen with UIT (panel a) and ratio maps of\nthe UIT image against the aligned optical \\Ha\\ and [\\ion{O}{3}] images. Since\nthe ionization energies of \\ion{C}{4} (64.5 eV) and \\ion{O}{3} (54.9 eV) are\nsimilar (and to the extent that the B5 image contains a substantial component\nof \\ion{C}{4} emission), we would expect a ratio of B5 to \\Ha\\ to show evidence\nfor the transition from incomplete to complete shock filaments. Such a ratio\nmap is shown in panel b of Figure~9, and a systematic pattern is indeed seen.\nThe white filaments, indicative of a relatively low value of the ratio (and\nhence relatively strong \\Ha\\ filaments) tend to lie systematically to the\nright. These filaments tend to be closer to the center of the SNR, and hence\nshould have had more time (on average) to cool and recombine. Of course, there\nis significant evidence for projection effects in this complicated field as\nwell. Indeed, one interpretation of Figure~9b is that we are separating some\nof these projection effects, and are seeing two separate `systems' of filaments\nthat are at differing stages of completeness.\n\nAnother way of assessing the expected contributions of line emission and\ntwo-photon emission to the B5 flux is by comparing to shock model calculations.\nWe use the equilibrium preionization ``E'' series shock models of Hartigan,\nRaymond, \\& Hartmann (1987, \\cite{HRH}) to investigate variations in spectral\ncontributions to the UIT images as a function of shock velocity. Figure~10\nshows how various spectral components are predicted to change in relative\nintensity as shock velocity increases for this set of planar, complete, steady\nflow shock models. As expected, the key contributors to the B5 bandpass are\nindeed \\ion{C}{4} and two-photon continuum, although between $\\sim$100 --\n200~\\vel\\ these models indicate \\ion{C}{4} should dominate.\n\nThis is quite at odds with `ground truth', as supplied by careful comparisons\nat the specific locations of IUE and HUT spectra within the UIT fields of\nview. We note that the two-photon flux per \\AA\\ in HUT and IUE spectra is low\nand thus difficult to measure accurately since background levels are poorly\nknown. Even so, it is quite clear from comparisons such as those of\n\\cite{Benvenuti80} and Raymond et al. (1988) that nowhere do we see \\ion{C}{4}\ndominate at the level implied by Figure~10. (Indeed such studies indicate that\ntwo-photon should dominate! As will be discussed more thoroughly in \\S4,\n\\cite{Benvenuti80} and others give two-photon fluxes which overwhelm \\ion{C}{4}\nin the B5 band by a factor of 5-10. Interestingly, consideration of\nincompleteness effects only serves to exacerbate this discrepancy since the\nexpected two-photon emission should be weaker or absent. Something else is\ngoing on.\n\nThat `something else' is apparently resonance line scattering. It has long\nbeen suspected that the strong UV resonance lines, like \\ion{N}{5}\n$\\lambda$1240, \\ion{C}{2} $\\lambda$1335, and \\ion{C}{4} $\\lambda$1550, are\naffected by self-absorption along the line of sight, either by local gas within\nthe SNR itself or by the intervening interstellar medium. We can expect\nsignificant column depth from the cavity wall of the remnant itself. Since\nfilaments selected for optical/UV observation have tended to be bright, and\nsince many such filaments are edge-on sheets of gas with correspondingly high\nline of sight column densities (\\cite{Hester87}), the spectral observations are\nlikely affected in a systematic way.\n\nWhile this has been known for some years (\\cite{Raymond81}), the UIT data\npresented here indicate just how widespread resonance line scattering is in the\nCygnus Loop and how significantly the \\ion{C}{4} intensity may be reduced by\nthis effect. Figure~9c shows a ratio map of the B5 image to the [\\ion{O}{3}]\noptical image of the XA region (cf. \\cite{Cornett92}). Since [\\ion{O}{3}] is\na forbidden transition, its optically thin emission is not affected by\nresonance scattering. The ionization potentials for \\ion{C}{4} and\n[\\ion{O}{3}] are similar, so this ratio should provide some information about\nresonance scattering, if a significant fraction of the B5 image can be\nattributed to \\ion{C}{4}. Hence, this ratio image shows where resonance line\nscattering is most important, and provides information on the 3-dimensional\nstructure of regions within the SNR.\n\nThe B5 image gives the {\\em appearance} of smaller dynamic range and lower\nspatial resolution than [O~III] because we see optically thick radiation from\nonly a short distance into the filaments. The highest saturation (lowest\nratios, or light areas in Figure~9c) occurs in the cores of filaments and dense\nclouds, such as the three regions indicated in Figure~9a. The ``spur''\nfilament was studied in detail by \\cite{Raymond88} and is probably an edge-on\nsheet of gas. The region marked `B' is the turbulent, incomplete shocked cloud\nobserved with HUT during Astro-1 (\\cite{Blair91}). The XA region is also a\nshocked cloud or finger of dense gas that is likely elongated in our line of\nsight (cf. \\cite{HesterCox86}; \\cite{DBR}). What is surprising, however, is the\nextent to which the light regions in Figure~9c extend beyond the cloud cores\ninto regions of more diffuse emission. This indicates that significant\nresonance scattering is very widespread in the Cygnus Loop. The diminished\n\\ion{C}{4} flux also boosts the relative importance of two-photon emission in\nthe B5 bandpass and explains the discrepancy between numerous spectral\nobservations and the shock model predictions shown in Figure~10.\n\nUIT's B5 images are particularly useful in that they sample two important shock\nphysics regimes--the brightest radiative shocks arising in dense clouds and the\nprimary blast wave at the edge of the shell. However, it is evidently\ndifficult to predict the spectral content of B5 images alone without detailed\nknowledge of the physics of the emitting regions. Nonetheless, B5 images are\nuseful in combination with [\\ion{O}{3}]$\\lambda$5007 and \\Ha\\ images as\nempirical tools. The image combinations allow us to determine whether\n\\ion{C}{4} or two-photon dominates, in two clear-cut cases. 1) In regions\nwhere B5 images closely resemble [\\ion{O}{3}] images, the B5 filter is\ndetecting radiative shocks with velocities in the range 100-200 \\vel\\ and\ntherefore primarily \\ion{C}{4}. 2) In regions where B5 images closely resemble\n\\Ha, the B5 filter is detecting largely two-photon emission from recombination\nof hydrogen in radiative shocks or from collisional excitiation of hydrogen in\nnonradiative shocks.\n\n\\section{Discussion}\n\nEach of the fields in our study portrays a range of physical conditions and\ngeometries, and hence filament types, seen in projection in many cases. By\ncomparing the UV, X-ray and optical emissions, we can gain new insights into\nthese complexities. In this section, we discuss the spatial relationships\nbetween the hot, intermediate and cooler components seen in these images.\n\n\\subsection{The Western Cloud}\n\nIn the Western Cloud field (Figure~3) the B5 image of the bright north-south\nfilaments resembles the [\\ion{O}{3}]5007\\AA~ images very closely. The\nfilaments are clearly portions of a radiative shock viewed edge-on to our line\nof sight. The Western Cloud has been studied spectroscopically at optical\nwavelengths by \\cite{Miller74} and in the FUV by \\cite{Raymond80b}.\n\nThis region shows a case where a cloud is evidently being overrun by a shock,\nand the cloud is much larger than the scale of the shock. The cloud is\nelongated in the plane of the sky of dimensions perhaps 1$\\times$10 pc\n(\\cite{Levenson98}) and represents an interaction roughly 1000 years old\n(\\cite{Levenson96}). The main north-south radiative filament is bright in all\nwavelengths, with good detailed correlation between B5 and [\\ion{O}{3}]. \\Ha\\\nis seen to extend farther to the east, toward the center or 'behind' the shock,\nas is expected in a complete shock stratification.\n\nBright X-rays (Figure~3d) are seen to lag behind the radiative filaments by\n1-2\\arcmin\\ (0.15 to 0.3 pc). This is indicative of a reverse shock being\ndriven back into the interior material from the dense cloud. This\ndoubly-shocked material shows enhanced brightness of about a factor of 2. From\nthis, Levenson et al. (1996) derive a cloud/ambient density contrast of about\n10.\n\nAttempts to fit shock models to optical observations of the bright filament\nhave been frustrated by the large [\\ion{O}{3}]/H$\\beta$ ratio. A shock\nvelocity of 130 \\vel\\ was found by \\cite{Raymond80b} using IUE line strengths\nand assuming a slight departure from steady flow and depleted abundances in\nboth C and Si. \\cite{Raymond80b} also note that much of the hydrogen\nrecombination zone predicted by steady flow models is absent, implying that the\ninteraction is fairly young.\n\nAs seen in the \\Ha\\ image, a Balmer-dominated filament projects from the south\nof the bright radiative filament toward the northwest. \\cite{Raymond80a} find\nthat the optical spectrum of the filament contains nothing but hydrogen Balmer\nlines. High-resolution observations of the \\Ha\\ line (\\cite{Treffers81}) show\na broad component and a narrow component, corresponding to the pre- and\npost-shock conditions in the filament, with a resulting estimated shock\nvelocity of 130-170 \\vel. The filament may be a foreground or background piece\nof the blast wave not related to the radiative portion of the shock, or a\nrelated piece of blast wave that is travelling through the atomic (rather than\nmolecular) component. It is visible in both \\Ha\\ (Figure~3a) and B5\n(Figure~3c) though generally not in other bands; thus the B5 flux for this\nfilament arises primarily from the two-photon process. There is a small\nsegment of the filament visible in [\\ion{O}{3}] where the shock may be becoming\nradiative, visible in B5 as a brightening near the southern end of the\nfilament.\n\nThe X-ray luminosity behind this nonradiative filament is much fainter than\nthat observed to the east of the main radiative filament, since there is no\nreverse shock associated with the nonradiative filament to boost the brightness\n(\\cite{Hester94}). The absence of X-rays to the west of this filament confirms\nthat it represents the actual blast front. As expected, the peak X-ray flux\nlags behind the \\Ha\\ and B5 flux by roughly one arcminute (0.1 pc). This\nrepresenting the ``heating time'' of gas behind the shock.\n\nA CO cloud is seen just to the south of the Western Cloud field\n(\\cite{Scoville77}). The presence of CO clearly indicates material with\nmolecular hydrogen at densities of 300-1000 cm$^{-3}$. The nonradiative\nfilament runs closely along the T$_{antenna}$=5K contour of the CO cloud,\nindicating this shock is moving through the atomic component at this stage, but\nshowing no sign of interaction with the molecular cloud.\n\n\\subsection{Northeast Nonradiative Region}\n\nThe canonical example of nonradiative filaments in any context lies on the\nnorth and northeast rim of the Cygnus Loop. There, smooth Balmer filaments\nextend counterclockwise from the northern limb (Figure~4), and can be seen\nprominently in \\Ha\\ in Figure~5a. Small portions of this shock system have\nbeen extensively studied by Raymond et al. (1983), Blair et al. (1991),\n\\cite{Long92}, Hester, Raymond \\& Blair (1994), and most recently by Blair et\nal. (1999). The filaments are clearly visible in \\Ha\\ (Figure~4a) as well as\nB5 (Figure~4c), but invisible along most of their length in [\\ion{O}{3}]\n(Figure~4b) except for small segments. These segments represent portions of the\nshock front where a slightly higher density has allowed the shock to become\npartially radiative. The shocked, T$\\sim10^{6}$K gas emits in an\nedge-brightened band of X-rays (Figure~4d). The brightness variations in\nX-rays confirm that the nonradiative filaments are simply wrinkles in the blast\nwave presenting larger column densities to our line of sight.\n\nSpectroscopic observations of selected locations on the filaments indicate that\nthe B5 filter observes nonradiative filaments as a mixture of \\ion{C}{4} and\ntwo-photon emission. \\cite{Long92} find an intrinsic ratio of two-photon\nemission to \\ion{C}{4} of 4.3, which gives an observed ratio in B5 of 0.65.\nRaymond et al. (1983) find fluxes in the same filament which give an observed\nratio of 1.6; in a nearby filament, Hester, Raymond \\& Blair (1994) find a\nratio near 2.0. These filaments all have velocities of around 170 \\vel. It is\nlikely that much of the ISM carbon is locked up in grains in the preshock\nmedium, thus boosting the ratio.\n\nThe system of thin filaments in the NE nonradiative field extends to the south\nand is visible in \\Ha\\ ahead of the radiative Northeast Cloud (Figure~5)\ndiscussed below.\n\n\\subsection{The Northeast Cloud}\n\nThe Northeast Cloud (Figure~5) radiative filaments, south and east of the field\ndiscussed above, make up one of the brightest systems in the Cygnus Loop. The\ninteraction of the SN blast wave and the denser cavity wall is most evident at\nthis location. A complex of radiative filaments can be seen, apparently\njumbled together along our line of sight, displaying the signs of a complete\nshock undergoing radiative cooling. The X-ray edge marking the SN blast wave\nis well separated from the optical and UV filaments, implying a strongly\ndecelerated shock and cooling that has continued for some time. Stratification\nof different ionic species is evident, with [\\ion{O}{3}] in sharp filaments to\nthe east, and more diffuse \\Ha\\ behind (Figure~8b).\n\nThe Northeast Cloud extends into the southern portions of the NE nonradiative\nfield (Figure~4) as well. However, the exposure time for this FUV image is a\nfactor of four shorter than that in Figure~4c, so the nonradiative filaments\nare not detected above the background. There are a few UV-bright sections which\ncorrespond closely with bright [\\ion{O}{3}] knots. However, other equally\nbright [\\ion{O}{3}] knots in the region do not have corresponding FUV knots.\nThis may be evidence for a range of shock velocities, or it may be portions of\nthe shocks that are in transition from nonradiative to radiative conditions.\n\nUsing IUE spectra \\cite{Benvenuti80} measure the two-photon continuum for one\nof the brightest radiative positions within the NE cloud, with a resulting\nobserved two-photon/\\ion{C}{4} ratio of 5.0. Observations of other radiative\nregions both in the Cygnus Loop and in other SNRs similar in morphology and\nspectrum give ratios between 1.7 and 10 (\\cite{Raymond88}; various unpublished\ndata). Therefore, while conditions vary widely within these shocked regions,\nspectroscopy indicates that resonance scattering of \\ion{C}{4} causes us to see\n2-6 times more flux from two-photon emission than from other ions in the field.\n Yet the B5 morphology of most of the field resembles [\\ion{O}{3}] far more\nthan \\Ha, as we would expect if two-photon emission were dominant. The\napparent conflict is likely caused by the fact that most lines of sight through\nthis region undoubtedly encounter material with a broad range of physical\nconditions. Furthermore, the UIT NE cloud exposure is the shortest of our set.\n Only regions bright in both \\Ha\\ and [\\ion{O}{3}] show up in B5.\n\n\\subsection{The XA Field}\n\nThe XA field (Figure~6) is a complicated region of predominantly radiative\nfilaments, noteworthy because an extremely bright and sharp X-ray edge\ncorresponds closely to a bright knot of UV/visible emission\n(\\cite{HesterCox86}). Indeed, this region is seen to be bright in many\nwavelengths including radio (\\cite{Green90}; \\cite{Leahy97}) and infrared\n(\\cite{Arendt92}). Strong \\ion{O}{6} $\\lambda$1035 emission is seen\n(\\cite{Blair91}) as well as other high-ionization species; \\ion{N}{5},\n\\ion{C}{4}, \\ion{O}{3}] (\\cite{DBR}) and [\\ion{Ne}{5}] (\\cite{Szentgyorgyi99}).\nSee DBR for a more detailed analysis of this region.\n\nIn general, the B5 emission corresponds closely to optical [\\ion{O}{3}].\nHowever, while optical images show a high contrast between the brightest\n`cloud' regions and others in 'empty' space, B5 contrast is lower\n(\\cite{Cornett92}). This suggests contributions from a high column depth of\ndiffuse \\ion{C}{4} and/or two-photon emission. We are either looking at\ndiffuse material through the edge of a cavity wall or are seeing emission from\nface on sheets of gas. \\cite{DBR} show evidence that the bright 'cloud' in the\ncenter is not isolated and may be a density enhancement in the cavity wall or a\nfinger of denser material projecting in from the east. The entire blast wave\nin the region appears indented from the otherwise circular extent of the SNR\n(\\cite{Levenson97}) implying that the disturbance is produced by a cloud\nextended several parsecs in our line of sight. The visible structure is likely\nthe tip of a much larger cloud.\n\nLevenson et al. (1998) suggest a density enhancement in the cavity wall,\nresulting in rapid shock deceleration and accounting for the bright emission.\nIUE and HUT observations show evidence for a 150 \\vel\\ cloud shock in the dense\ncore of XA itself (the west-pointing V shape in the center of the field) and a\nfaster, incomplete shock in the more diffuse regions to the north and south\n(\\cite{DBR}). Two parallel, largely east-west filaments are seen flanking the\ncentral 'cloud'. The X-ray emission is seen to drop off dramatically south of\nthe two long radial filament systems.\n\nBlair et al. (1991) report HUT observations of a radiative but incomplete cloud\nshock directly to the north of XA marked `B' in Figure~9a. This region\nfeatures almost complete cooling with the exception of \\Ha\\ and cooler ions.\nRaymond et al. (1988) studied the Spur filament and found a completeness\ngradient along the length of it. This filament is well-defined in B5 as well\nas the optical bands.\n\nThe XA region is the one region in the Cygnus Loop where preionization is\nvisible ahead of the shock front (\\cite{Levenson98}). This preionization is\ncaused by X-ray flux from the hot, postshock gas ionizing neutral material\nacross the shock front. The emission measure is high enough in this\nphotoionized preshock gas that it is clearly visible as a diffuse patch of\nemission a few arc minutes to the east of the main XA knot in the center of the\nfield in both \\Ha\\ and B5. The B5 flux presumably arises almost entirely from\ntwo-photon emission in this case since no [\\ion{O}{3}] is seen (and hence no\nstrong UV line emission is expected).\n\nOne unique ability of the B5 filter becomes apparent in the XA region; that of\ndetecting nonradiative shocks in ionized gas. In the X-ray (Figure~6d) we see\na bulge of emission to the north and east of the brightest knot (Hester \\&\nCox's XA region proper). This bulge does not show up in either of the optical\nbands, but the perimeter is visible in the FUV at the edge of the X-ray\nemission in Figure~6c. This region has likely been ionized by X-ray flux from\nthe hot post-shock gas. A nonradiative shock is now propagating through it\nand, lacking a neutral fraction to radiate in \\Ha, is seen only in high ions\nsuch as \\ion{C}{4}. This filament is becoming more complete in its southern\nextremity (the `B' location in Figure~9a) and is emitting in [\\ion{O}{3}] as\nwell. This filament also appears to connect to the nonradiative filament seen\nin \\Ha\\ in the Northeast cloud (Figure~5a).\n\n\\subsection{The Southeast Cloud}\n\nThe Southeast Cloud (Figure~7) presents an interesting quandry. In the optical\nit appears as a small patch of radiative emission with a few associated\nnonradiative filaments. \\cite{Fesen92} hypothesize that it represents a small,\nisolated cloud at a late stage of shock interaction. Indeed, the resemblance\nto the late-stage numerical models of \\cite{Bedogni90} and \\cite{Stone92} is\nstriking.\n\nMore recent X-ray analysis (\\cite{Graham95}) suggests that the shocked portion\nof the southeast cloud is merely the tip of a much larger structure. Indeed,\nit is probably similar to the Western and Northeastern Clouds but at an even\nearlier point in its evolution. \\cite{Fesen92} note that the age of the\ninteraction is probably $4.1\\times 10^3$ years based on an assumed blast wave\nvelocity. Given the revised distance estimate of Blair et al. (1999), this age\nbecomes $2.3\\times 10^3$ years.\n\nIn \\Ha\\ (Figure~7a) we see a set of nonradiative filaments to the southeast of\nthe cloud. These filaments are visible very faintly in B5 (Figure~7c) as\nwell.Given the complete lack of X-ray emission (Figure~7d) to the east, these\nfilaments are the primary blast wave. The fact that these filaments are\nindented from the circular rim of the SNR implies the blast wave is diffracting\naround some object much larger than the visible emission and extended along our\nline of sight (\\cite{Graham95}).\n\nFesen et al. identify a filament segment seen to the west of the SE\ncloud--visible in both \\Ha\\ and our B5 image--as a reverse shock driven back\ninto the shocked medium. The X-ray emission, however, demonstrates that this\nis instead due the primary forward-moving blast wave. X-ray enhancement is\nseen to the west of the cloud, not the east as we would expect from a doubly\nshocked system. Furthermore, the optical filament is Balmer-dominated, which\nrequires a significant neutral fraction in the pre-shock gas, which would not\noccur at X-ray producing temperatures (\\cite{Graham95}). These points suggest\nthat the filament segment seen is a nonradiative piece of the main blast wave\nnot obviously related to the other emission in the area. The relative\nfaintness and lack of definition compared to other nonradiative filaments\nsuggests that it is not quite parallel to our line of sight.\n\nMeanwhile, the densest material in the shocked cloud tip has cooled enough to\nemit in ionic species like [\\ion{O}{3}] (Figure~7b) and \\ion{C}{4}. Gas\nstripping resulting from instabilities in the fluid flow along the edges of the\ncloud is seen as 'windblown streamers' on the north and south as well as\ndiffuse emission (because of a less favorable viewing angle) to the east. The\nB5 image shows great detail of the cloud shock and closely resemble the\n[\\ion{O}{3}] filaments, but with an added ``tail'' extending to the southeast.\nThe main body of the cloud shock as viewed in B5 is likely composed of\n\\ion{C}{4} and \\ion{O}{3}] emission while the ``tail'' may be an example of a\nslow shock in a neutral medium and have an enhanced two-photon flux\n(\\cite{Dopita82}). The shock velocity in the cloud is quoted by Fesen et al.\nas $<$60 \\vel\\ though this is based on the identification of the western\nsegment as a reverse shock. Given the bright [\\ion{O}{3}] and B5 emission in\nthe cloud shock, it seems more likely that the cloud shock is similar to other\nstructures to the north where shock velocities are thought to be more nearly\n140 \\vel.\n\nThere is a general increase in signal in the northern half of the SE FUV field\n(Figure~7c). It is unclear whether this is primarily due to the background\n``measles'' noted in \\S2 or if this represents diffuse, hot gas emitting\n\\ion{C}{4} as is seen in the halo around the central knot of XA. There is very\nfaint emission seen in both \\Ha\\ and [\\ion{O}{3}] in the area which could\nrepresent a region of more nearly face-on emitting gas.\n\n\\section{Concluding Remarks}\n\nThe UIT B5 band, although broader than ideal for SNR observations, provides a\nunique FUV spectral window. Under some conditions, the B5 bandpass provides\nimages of radiative filaments overrun by very high-speed shocks. Under other\nconditions, B5 observes nonradiative filaments at the extreme front edge of SNR\nblast waves. Combined with other image and spectral data, the B5 band can\nprovide unique insights into complex, difficult-to-model shock phenomena such\nas \\ion{C}{4} resonance scattering and shock completeness.\n\nIn nonradiative filaments, B5 flux comes from a mixture of \\ion{C}{4} as it\nionizes up and two-photon emission from preshock neutral hydrogen. In general,\nnonradiative filament morphology is very similar in B5 and \\Ha, implying that\ntwo-photon emission, originating in the same regions as \\Ha, is the primary\ncontributor to the B5 images. One unique capability of B5 imaging is its\nability to capture nonradiative shocks in ionized media. We see one example of\nsuch in Figure~6c where a nonradiative shock is faintly seen in \\ion{C}{4} and\n\\ion{He}{2}.\n\nRadiative filaments usually show good correlation between B5 and [\\ion{O}{3}]\nmorphology, suggesting that B5 flux arises in ions with similar excitation\nenergies such as \\ion{C}{4}. Existing models for simple, complete shocks\nindicate the same origin.\n\nHowever, existing FUV spectra complicate this picture, indicating that these\nregions should be dominated by two-photon flux which we would expect to follow\nmore closely the \\Ha\\ morphology. Observational selection restricts detailed\nspectral information to only the very brightest knots and filaments.\nPresumably, these bright regions also suffer the greatest resonance scattering\nin \\ion{C}{4}$\\lambda$1550, decreasing its observed flux; in fact, DBR found\nunexpectedly strong resonance scattering even away from the bright filaments\nand knots. Despite this, morphological similarities between B5 and\n[\\ion{O}{3}] in radiative filaments strongly suggest that, at least away from\nthe brightest filaments and cloud cores, B5 flux is dominated by \\ion{C}{4}.\n\n\\paragraph{Acknowledgements}\n\nThe authors wish to thank John Raymond for valuable discussions and the use of\nunpublished HUT data. We would also like to thank an anonymous referee for\nseveral valuable suggestions including using FUV images to trace nonradiative\nfilaments through ionized regions. Funding for the UIT project has been\nthrough the Spacelab Office at NASA headquarters under project number 440-551.\n\n\\begin{thebibliography}{Danforth00}\n\\bibitem[Arendt, Dwek, \\& Leisawitz 1992]{Arendt92}\nArendt, R.G., Dwek, E., \\& Leisawitz, D. 1992, \\apj, 400, 562\n\\bibitem[Bedogni \\& Woodward (1990)]{Bedogni90}\nBedogni, R. \\& Woodward, P. R. 1990, \\aap, 231, 481\n\\bibitem[Benvenuti, Dopita, \\& D'Odorico (1980)]{Benvenuti80}\nBenvenuti, P., Dopita, M., \\& D'Odorico, S. 1980, \\apj, 238, 601\n\\bibitem[Blair et al. 1991]{Blair91}\nBlair, W. P., et al. 1991, \\apjl, 379, L33\n\\bibitem[Blair et al. 1999]{Blair99}\nBlair, W. P., Sankrit, R., Raymond, J. C. \\& Long, K. S., 1999, AJ, 118, 942\n\\bibitem[Chevalier, Kirshner, \\& Raymond 1980]{CKR80}\nChevalier, R. A., Kirshner, R. P., \\& Raymond, J. C. 1980, \\apj, 235, 186\n\\bibitem[Chevalier \\& Raymond 1978]{Chevalier78}\nChevalier, R. A., \\& Raymond, J. C. 1978, \\apjl, 225, L27\n\\bibitem[Cornett et al. 1992]{Cornett92}\nCornett, R. H., et al. 1992, \\apj, 395, L9\n\\bibitem[DBR]{DBR}\nDanforth, C. W., Blair, W. P., \\& Raymond, J. C. 2000, in prep. (DBR)\n\\bibitem[Dopita, Binette, \\& Schwartz, 1982]{Dopita82}\nDopita, M. A., Binette, L., \\& Schwartz, R. D. 1982, \\apj, 261, 183\n\\bibitem[Dopita, Binette, \\& Tuohy (1984)]{Dopita84}\nDopita, M. A., Binette, L. \\& Tuohy, I. R., 1984, \\apj, 282, 142\n\\bibitem[Fesen, Blair, \\& Kirshner 1982]{Fesen82}\nFesen, R. A., Blair, W. P., \\& Kirshner, R. P. 1982, \\apj, 262, 171\n\\bibitem[Fesen, Kwitter, \\& Downes (1992)]{Fesen92}\nFesen, R. A., Kwitter, K. B. \\& Downes, R. A. 1992, \\aj, 104, 719\n\\bibitem[Graham et al. 1995]{Graham95}\nGraham, J. R., Levenson, N. A., Hester, J. J., Raymond, J. C., \\& Petre, R.\n1995, \\apj, 444, 787\n\\bibitem[Green 1990]{Green90}\nGreen, D. A. 1990, \\aj, 100, 1927\n\\bibitem[HRH]{HRH}\nHartigan, P., Raymond, J. C., \\& Hartmann, L., 1987, \\apj, 316, 323 (HRH)\n\\bibitem[Hester \\& Cox 1986]{HesterCox86}\nHester, J. J., \\& Cox, D. P., 1986, \\apj, 300, 675\n\\bibitem[Hester 1987]{Hester87}\nHester, J. J. 1987, \\apj, 314, 187\n\\bibitem[Hester, Raymond, \\& Danielson 1986]{Hester86}\nHester, J. J., Raymond, J. C., \\& Danielson, G. E. 1986, \\apj, 303, L17\n\\bibitem[Hester, Raymond, \\& Blair 1994]{Hester94}\nHester, J. J., Raymond, J. C., \\& Blair, W. P. 1994, \\apj, 420, 721\n\\bibitem[Innes (1992)]{Innes92}\nInnes, D. E. 1992, \\aap, 256, 660\n\\bibitem[Leahy et al. 1997]{Leahy97}\nLeahy, D. A., Roger, R. S., \\& Ballantyne, D. 1997, \\aj, 114, 2081\n\\bibitem[Levenson et al. 1996]{Levenson96}\nLevenson, N. A., Graham, J. R., Hester, J. J., \\& Petre, R. 1996, \\apj, 468,\n323\n\\bibitem[Levenson et al. 1997]{Levenson97}\nLevenson, N. A., et al. 1997, \\apj, 484, 304\n\\bibitem[Levenson et al. 1998]{Levenson98}\nLevenson, N. A., Graham, J. R., Keller, L. D., \\& Richter, M. J. 1998, \\apjs,\n118, 541\n\\bibitem[Long et al. (1992)]{Long92}\nLong, K. S., et al. 1992, \\apj, 400, 214\n\\bibitem[Miller (1974)]{Miller74}\nMiller, J. S. 1974, \\apj, 189, 239\n\\bibitem[Nussbaumer \\& Schmutz 1984]{Nussbaumer84}\nNussbaumer, H., \\& Schmutz, W. 1984, \\aap 138, 495\n\\bibitem[Osterbrock 1989]{Osterbrock89}\nOsterbrock, D. S., 1989, ``\\it{Astrophysics of Gaseous Nebulae and Active\nGalactic Nuclei}\\rm'', Mill Valley, CA, University Science Books\n\\bibitem[Raymond (1979)]{Raymond79}\nRaymond, J. C. 1979, \\apjs, 39, 1\n\\bibitem[Raymond et al. (1980a)]{Raymond80a}\nRaymond, J. C., Davis, M., Gull, T. R., \\& Parker, R. A. R. 1980a, \\apj, 238,\nL21\n\\bibitem[Raymond et al. (1980b)]{Raymond80b}\nRaymond, J. C., Black, J. H., Dupree, A. K., Hartmann, L., \\& Wolff, R. S.\n1980b, \\apj, 238, 881\n\\bibitem[Raymond et al. 1981]{Raymond81}\nRaymond, J. C., Black, J. H., Dupree, A. K., Hartmann, L., \\& Wolff, R. S.\n1981, \\apj, 246, 100\n\\bibitem[Raymond et al. 1983]{Raymond83}\nRaymond, J. C., Blair, W. P., Fesen, R. A. \\& Gull, T. R. 1983, \\apj, 324, 869\n\\bibitem[Raymond et al. 1988]{Raymond88}\nRaymond, J. C., et al. 1988, \\apj, 324, 869\n\\bibitem[Scoville et al. 1977]{Scoville77}\nScoville, N. Z., Irvine, W. M., Wannier, P. G., \\& Predmore, C. R. 1977, \\apj,\n216, 320\n\\bibitem[Smith et al. 1996]{Smith96}\nSmith, E. P., et al. 1996, \\apjs, 104, 287\n\\bibitem[Stecher et al. (1992)]{Stecher92}\nStecher, T. P., et al. 1992, \\apj, 395, L1\n\\bibitem[Stecher et al. 1997]{Stecher97}\nStecher, T. P., et al. 1997, \\pasp, 109, 584\n\\bibitem[Stone \\& Norman (1992)]{Stone92}\nStone, J. M., \\& Norman, M. L., 1992, \\apjl, 390, L17\n\\bibitem[Szentgyorgyi et al. 2000]{Szentgyorgyi99}\nSzentgyorgyi, A. H., Raymond, J. C., Hester, J. J., \\& Curiel, S. 2000, \\apj,\nin press\n\\bibitem[Treffers 1981]{Treffers81}\nTreffers, R. R. 1981, \\apj, 250, 213\n\\end{thebibliography}\n\n\\clearpage\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig1.ps,width=6in}}\n\\figcaption[]{\\protect\\small{Two typical UV spectra of SNR filaments. The top, a\nradiative filament (Blair et al. 1991), shows lines of many different ions.\nThe bottom, a nonradiative filament (Long et al. 1992), shows lines of only the\nhighest ionization species. The dashed curve superimposed on the two spectra\nrepresents the throughput of UIT's B5 filter as a function of wavelength.}}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig2.ps,width=5in}}\n\\figcaption[]{\\protect\\small{An \\Ha\\ mosaic of the entire Cygnus Loop (courtesy\nLevenson et al. 1998) with the 40\\arcmin\\ UIT fields superimposed and\nlabeled.}}\n\\end{figure}\n\n\\begin{figure}\n\\figcaption[]{\\protect\\small{The Western Cloud as viewed in a) \\Ha, b)\n[\\protect\\ion{O}{3}]$\\lambda$5007, c) B5, and d) the ROSAT High Resolution Imager\n(HRI). All bands show a bright north-south radiative complex similar to that\nseen in the Northeast Cloud (Figure~5) but with apparently simpler geometry.\nTwo bright, parallel filaments suggest two points of tangency to our line of\nsight. In \\Ha\\ (a) and B5 (c) we also see a nonradiative filament diverging to\nthe northwest of the bright radiative region. X-rays are seen behind this\nfilament in (d). A reverse shock generates higher temperatures and brighter\nX-ray emission at the radiative region. With the exception of the nonradiative\nfilament, the B5 and the [\\protect\\ion{O}{3}] (b) show a high degree of correlation,\nsuggesting origin of the B5 flux in high-excitation ionic species. Each field\nis 40\\arcmin\\ across. For Figures 3-7, both optical fields have been\nmedian-filtered with a 3-pixel (15 \\arcsec) box. The HRI field has been\nsmoothed with a 3-pixel gaussian. All fields are aligned and oriented with\nnorth at the top and east to the left. All image intensities are displayed\nlogarithmically. (Please see attached file uitfig3.jpg or \\url\\ for\nfull-resolution image.)}}\n\n\\figcaption[]{\\protect\\small{The Northeast Nonradiative Region, containing the classic\nnonradiative filaments, viewed as in Figure~3. The SN blast wave propagates\nthrough the atomic shell at v$\\sim$400 \\vel. Thin filamentary emission arises\nfrom the preshock neutral fraction as it heats up, and is seen in \\Ha\\ (a).\nLittle or no emission is seen from this filament in [\\protect\\ion{O}{3}] (b). The\nshock is visible in B5 (c) through both two-photon processes (closely linked to\n\\protect\\Ha\\ emission) and to a lesser extent through high-ionization species--in this\ncase \\protect\\ion{C}{4}. The ROSAT HRI image (d) shows the $\\sim10^{6}$K\nX-ray-emitting post-shock gas in a band behind the shock front. (Please see\nattached file uitfig4.jpg or \\url\\ for full-resolution image.)}}\n\n\\figcaption[]{\\protect\\small{The Northeast Cloud as viewed in Figure~3. \\protect\\Ha\\ (a) shows\nsmooth nonradiative filaments to the east of a more complex mass of radiative\nfilaments. [\\protect\\ion{O}{3}] (b) shows a radiative filament structure complicated by\nline-of-sight coincidence of several emitting regions. The short B5 exposure\n(c) shows radiative structures well but is not deep enough to show the\nnonradiative filaments. The ROSAT image (d) shows that flux from hot gas\nbehind the blast wave is considerably enhanced by the strongly decelerating\nshocks in the denser radiative region. (Please see attached file uitfig5.jpg\nor \\url\\ for full-resolution image.)}}\n\n\\figcaption[]{\\protect\\small{The XA region as viewed in Figure~3. This region displays\na complex region of cloud-shock interactions, including dense, bright filaments\nwhose \\protect\\ion{C}{4} emission is apparently strongly affected by resonance\nscattering and a range of shock completeness (see Figures 9c and 10). (Please\nsee attached file uitfig6.jpg or \\url\\ for full-resolution image.)}}\n\n\\figcaption[]{\\protect\\small{The South East Cloud viewed as in Figure~3. This small\npatch of emission is likely the tip of a much larger cloud early in the stages\nof shock interaction. B5 morphology (c) closely matches both \\protect\\Ha\\ (a) and\n[\\protect\\ion{O}{3}] (b). The primary differences are faint features common only to B5\nand \\Ha: the ``tail'' extending south of the cloud, and faint diffuse\nmaterial--nonradiative blast wave filaments--in the southern half of the field.\n X-rays (d) show a region of emission much larger than the optical/UV cloud\nwith a slight flux depression or ``hole'' in the center. (Please see attached\nfile uitfig7.jpg or \\url\\ for full-resolution image.)}}\n\n\\figcaption[]{\\protect\\small{Three-color images of the Western Cloud (a), the Northeast\nCloud (b), the XA Region (c) and the Southeast Cloud (d). \\protect\\Ha\\ is in red, B5\nemission in green and X-rays in blue. All intensities are displayed\nlogarithmically and colors have been adjusted to best show spatial\nrelationships. (Please see attached file uitfig8.jpg or \\url\\ for\nfull-resolution image.)}}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig9.ps,width=6.5in}}\n\\figcaption[]{\\protect\\small{The effects of completeness and resonance scattering. a)\nUIT B5 image of the XA region. b) A ``completeness map'' generated by taking\nthe ratio of B5 to \\protect\\Ha. Light areas represent more complete cooling while dark\nareas are less complete. Complete shocks emit predominantly two-photon\nemission in the B5 band while incomplete regions tend toward higher \\protect\\ion{C}{4}\ncontributions. c) ``Saturation map'' generated from B5 and [\\protect\\ion{O}{3}]. Dark\nregions show areas of higher resonance scattering of \\protect\\ion{C}{4}.}}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=fig10.eps,width=3.5in}}\n\\figcaption[]{\\protect\\small{B5 flux as a function of velocity for the shock models of\nHartigan, Raymond, \\& Hartmann (1987). The various dashed lines show the flux\nfrom selected ionic species multiplied by the B5 filter throughput, as a\nfunction of radiative shock velocity. The solid line is the total B5 flux\ncalculated as a sum of 0.80$\\times$\\protect\\ion{C}{4}$\\lambda$1550,\n0.55$\\times$\\protect\\ion{He}{2}$\\lambda$1640, 0.54$\\times$\\protect\\ion{O}{3}]$\\lambda$1665, and\n0.15$\\times$two-photon emission. These models hold only for complete,\nsingle-velocity shocks and do not take account of resonance scattering or other\ncomplications. In these models \\protect\\ion{C}{4} emission dominates the B5 bandpass\nat all but the lowest velocities.}}\\label{models}\n\\end{figure}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002005.extracted_bib",
"string": "\\begin{thebibliography}{Danforth00}\n\\bibitem[Arendt, Dwek, \\& Leisawitz 1992]{Arendt92}\nArendt, R.G., Dwek, E., \\& Leisawitz, D. 1992, \\apj, 400, 562\n\\bibitem[Bedogni \\& Woodward (1990)]{Bedogni90}\nBedogni, R. \\& Woodward, P. R. 1990, \\aap, 231, 481\n\\bibitem[Benvenuti, Dopita, \\& D'Odorico (1980)]{Benvenuti80}\nBenvenuti, P., Dopita, M., \\& D'Odorico, S. 1980, \\apj, 238, 601\n\\bibitem[Blair et al. 1991]{Blair91}\nBlair, W. P., et al. 1991, \\apjl, 379, L33\n\\bibitem[Blair et al. 1999]{Blair99}\nBlair, W. P., Sankrit, R., Raymond, J. C. \\& Long, K. S., 1999, AJ, 118, 942\n\\bibitem[Chevalier, Kirshner, \\& Raymond 1980]{CKR80}\nChevalier, R. A., Kirshner, R. P., \\& Raymond, J. C. 1980, \\apj, 235, 186\n\\bibitem[Chevalier \\& Raymond 1978]{Chevalier78}\nChevalier, R. A., \\& Raymond, J. C. 1978, \\apjl, 225, L27\n\\bibitem[Cornett et al. 1992]{Cornett92}\nCornett, R. H., et al. 1992, \\apj, 395, L9\n\\bibitem[DBR]{DBR}\nDanforth, C. W., Blair, W. P., \\& Raymond, J. C. 2000, in prep. (DBR)\n\\bibitem[Dopita, Binette, \\& Schwartz, 1982]{Dopita82}\nDopita, M. A., Binette, L., \\& Schwartz, R. D. 1982, \\apj, 261, 183\n\\bibitem[Dopita, Binette, \\& Tuohy (1984)]{Dopita84}\nDopita, M. A., Binette, L. \\& Tuohy, I. R., 1984, \\apj, 282, 142\n\\bibitem[Fesen, Blair, \\& Kirshner 1982]{Fesen82}\nFesen, R. A., Blair, W. P., \\& Kirshner, R. P. 1982, \\apj, 262, 171\n\\bibitem[Fesen, Kwitter, \\& Downes (1992)]{Fesen92}\nFesen, R. A., Kwitter, K. B. \\& Downes, R. A. 1992, \\aj, 104, 719\n\\bibitem[Graham et al. 1995]{Graham95}\nGraham, J. R., Levenson, N. A., Hester, J. J., Raymond, J. C., \\& Petre, R.\n1995, \\apj, 444, 787\n\\bibitem[Green 1990]{Green90}\nGreen, D. A. 1990, \\aj, 100, 1927\n\\bibitem[HRH]{HRH}\nHartigan, P., Raymond, J. C., \\& Hartmann, L., 1987, \\apj, 316, 323 (HRH)\n\\bibitem[Hester \\& Cox 1986]{HesterCox86}\nHester, J. J., \\& Cox, D. P., 1986, \\apj, 300, 675\n\\bibitem[Hester 1987]{Hester87}\nHester, J. J. 1987, \\apj, 314, 187\n\\bibitem[Hester, Raymond, \\& Danielson 1986]{Hester86}\nHester, J. J., Raymond, J. C., \\& Danielson, G. E. 1986, \\apj, 303, L17\n\\bibitem[Hester, Raymond, \\& Blair 1994]{Hester94}\nHester, J. J., Raymond, J. C., \\& Blair, W. P. 1994, \\apj, 420, 721\n\\bibitem[Innes (1992)]{Innes92}\nInnes, D. E. 1992, \\aap, 256, 660\n\\bibitem[Leahy et al. 1997]{Leahy97}\nLeahy, D. A., Roger, R. S., \\& Ballantyne, D. 1997, \\aj, 114, 2081\n\\bibitem[Levenson et al. 1996]{Levenson96}\nLevenson, N. A., Graham, J. R., Hester, J. J., \\& Petre, R. 1996, \\apj, 468,\n323\n\\bibitem[Levenson et al. 1997]{Levenson97}\nLevenson, N. A., et al. 1997, \\apj, 484, 304\n\\bibitem[Levenson et al. 1998]{Levenson98}\nLevenson, N. A., Graham, J. R., Keller, L. D., \\& Richter, M. J. 1998, \\apjs,\n118, 541\n\\bibitem[Long et al. (1992)]{Long92}\nLong, K. S., et al. 1992, \\apj, 400, 214\n\\bibitem[Miller (1974)]{Miller74}\nMiller, J. S. 1974, \\apj, 189, 239\n\\bibitem[Nussbaumer \\& Schmutz 1984]{Nussbaumer84}\nNussbaumer, H., \\& Schmutz, W. 1984, \\aap 138, 495\n\\bibitem[Osterbrock 1989]{Osterbrock89}\nOsterbrock, D. S., 1989, ``\\it{Astrophysics of Gaseous Nebulae and Active\nGalactic Nuclei}\\rm'', Mill Valley, CA, University Science Books\n\\bibitem[Raymond (1979)]{Raymond79}\nRaymond, J. C. 1979, \\apjs, 39, 1\n\\bibitem[Raymond et al. (1980a)]{Raymond80a}\nRaymond, J. C., Davis, M., Gull, T. R., \\& Parker, R. A. R. 1980a, \\apj, 238,\nL21\n\\bibitem[Raymond et al. (1980b)]{Raymond80b}\nRaymond, J. C., Black, J. H., Dupree, A. K., Hartmann, L., \\& Wolff, R. S.\n1980b, \\apj, 238, 881\n\\bibitem[Raymond et al. 1981]{Raymond81}\nRaymond, J. C., Black, J. H., Dupree, A. K., Hartmann, L., \\& Wolff, R. S.\n1981, \\apj, 246, 100\n\\bibitem[Raymond et al. 1983]{Raymond83}\nRaymond, J. C., Blair, W. P., Fesen, R. A. \\& Gull, T. R. 1983, \\apj, 324, 869\n\\bibitem[Raymond et al. 1988]{Raymond88}\nRaymond, J. C., et al. 1988, \\apj, 324, 869\n\\bibitem[Scoville et al. 1977]{Scoville77}\nScoville, N. Z., Irvine, W. M., Wannier, P. G., \\& Predmore, C. R. 1977, \\apj,\n216, 320\n\\bibitem[Smith et al. 1996]{Smith96}\nSmith, E. P., et al. 1996, \\apjs, 104, 287\n\\bibitem[Stecher et al. (1992)]{Stecher92}\nStecher, T. P., et al. 1992, \\apj, 395, L1\n\\bibitem[Stecher et al. 1997]{Stecher97}\nStecher, T. P., et al. 1997, \\pasp, 109, 584\n\\bibitem[Stone \\& Norman (1992)]{Stone92}\nStone, J. M., \\& Norman, M. L., 1992, \\apjl, 390, L17\n\\bibitem[Szentgyorgyi et al. 2000]{Szentgyorgyi99}\nSzentgyorgyi, A. H., Raymond, J. C., Hester, J. J., \\& Curiel, S. 2000, \\apj,\nin press\n\\bibitem[Treffers 1981]{Treffers81}\nTreffers, R. R. 1981, \\apj, 250, 213\n\\end{thebibliography}"
}
] |
astro-ph0002006
|
ULTRA HIGH ENERGY COSMIC RAYS: the theoretical challenge
|
[
{
"author": "A. V. Olinto\\thanksref{corr}"
}
] |
The origin of the highest-energy cosmic rays remains a mystery. The lack of a high energy cutoff in the cosmic ray spectrum together with an apparently isotropic distribution of arrival directions have strongly constrained most models proposed for the generation of these particles. An overview of the present state of theoretical proposals is presented. Astrophysical accelerators as well as top-down scenarios are reviewed along with their most general signatures. The origin and nature of these ultra-high energy particles will be tested by future observations and may indicate as well as constrain physics beyond the standard model of particle physics.
|
[
{
"name": "physrepf.tex",
"string": "\\def\\la{\\hbox{{\\lower -2.5pt\\hbox{$<$}}\\hskip -8pt\\raise\n-2.5pt\\hbox{$\\sim$}}}\n\\def\\ga{\\hbox{{\\lower -2.5pt\\hbox{$>$}}\\hskip -8pt\\raise\n-2.5pt\\hbox{$\\sim$}}}\n\n\\documentstyle{elsart}\n\n\\begin{document}\n\\begin{frontmatter}\n\\title{ULTRA HIGH ENERGY COSMIC RAYS: the theoretical challenge }\n\\author{A. V. Olinto\\thanksref{corr}}\n\\thanks[corr]{Corresponding author. E-mail: [email protected]}\n\\address{Department of Astronomy \\& Astrophysics, \\\\ \\& Enrico Fermi\nInstitute, \\\\\nThe University of Chicago, Chicago, IL 60637}\n \n\\begin{abstract}\nThe origin of the highest-energy cosmic rays remains a mystery. \nThe lack of a high energy cutoff in the cosmic ray spectrum \ntogether with an apparently isotropic distribution of arrival\ndirections have strongly constrained most models proposed for the\ngeneration of these particles. An overview of the present state of\ntheoretical proposals is presented.\nAstrophysical accelerators as well as top-down scenarios are reviewed\nalong with their most general signatures. The origin and nature of\nthese ultra-high energy particles will be tested by future\nobservations and may indicate as well as constrain physics beyond the\nstandard model of particle physics. \n\n\n\\end{abstract}\n\n\\begin{keyword}\ncosmic rays \\sep ultra-high energy \\sep origin \\sep acceleration\n\\sep \n\\end{keyword}\n\\end{frontmatter}\n\n\\section{Introduction}\n\nThe detection of cosmic rays with energies above $10^{20}$ eV has\ntriggered considerable interest on the origin and nature of these\nparticles. As reviewed by Watson \\cite{watson99} in this volume, many\nhundreds of events with energies above\n$10^{19}$ eV and about 20 events above $10^{20}$ eV have now been\nobserved by a number of experiments such as AGASA\n\\cite{takeda98,takeda99,Haya94}, Fly's Eye\n\\cite{bird}, Haverah Park \\cite{L91}, Yakutsk \\cite{Yak90}, and most\nrecently the High Resolution Fly's Eye \\cite{hires}. \n\nMost unexpected is the significant flux of\nevents observed above $\\sim 7 \\times 10^{19}$ eV \\cite{takeda98} with no\nsign of the Greisen-Zatsepin-Kuzmin (GZK) cutoff \\cite{GZK66}. \nA cutoff should be present if the ultra-high energy\nparticles are protons, nuclei, or photons from extragalactic sources. \nCosmic ray protons of energies above a few $10^{19}$ eV lose energy\nto photopion production off the cosmic microwave background (CMB) and\ncannot originate further than about $50\\,$Mpc away from Earth. Nuclei \nare photodisintegrated on shorter distances due to the infrared\nbackground \\cite{PSB76SS99} while the radio background\nconstrains photons to originate from even closer systems \n\\cite{bere70PB96}.\n\nIn addition to the presence of events past the GZK cutoff, there has\nbeen no clear counterparts identified in the arrival direction of the\nhighest energy events. If these events are protons, cosmic ray\nobservations should finally become astronomy! At these high energies\nthe Galactic and extragalactic magnetic fields do not affect their\norbits significantly so that they should point\nback to their sources within a few degrees. Protons at $10^{20}$\neV propagate mainly in straight lines as they traverse the Galaxy since\ntheir gyroradii are $\\sim $ 100 kpc in $ \\mu$G fields which is\ntypical in the Galactic disk. Extragalactic fields are expected to\nbe $\\ll \\mu$G \\cite{KronVallee,BBO99}, and induce at most \n$\\sim$ 1$^o$ deviation from the source. Even if\nthe Local Supercluster has relatively strong fields, the highest energy\nevents may deviate at most $\\sim$ 10$^o$ \n\\cite{RKB98,SLB99}. At present, no correlations between arrival directions\nand plausible optical counterparts such as sources in the Galactic\nplane, the Local Group, or the Local Supercluster have been clearly\nidentified. Ultra high energy cosmic ray (UHECR) data are consistent\nwith an isotropic distribution of sources in sharp contrast to the\nanisotropic distribution of light within 50 Mpc from Earth.\n\nThe absence of a GZK cutoff and the isotropy of arrival directions are\ntwo of the many challenges that models for the origin of UHECRs face.\nThis is an exciting open field, with many scenarios being proposed but \nno clear front runner. Not only the origin of these \nparticles may be due to physics beyond the standard model of particle\nphysics, but their existence can be used to constrain extensions of the\nstandard model such as violations of Lorentz invariance (see, e.g.,\n\\cite{ABGG00}). \n\nIn the next section, a brief summary of the\nchallenges faced by all theoretical models is given. \nIn \\S3, astrophysical accelerators or ``bottom-up'' scenarios are\nreviewed, hybrid models are discussed in \\S4, and\ntop-down scenarios in \\S5. To conclude,\nfuture observational tests of UHECR models and their implications are\ndiscussed in \\S6. For previous reviews of UHECR models, the reader\nis encouraged to consult\n\\cite{hillas84,BBDGP90,gaisser90,bland99,berez99,BS99}. \n\n\\section{The Challenge}\n\nIn attempting to explain the origin of UHECRs, models confront a number\nof challenges. The extreme energy is the greatest challenge that models\nof astrophysical acceleration face while for top-down models the\nobserved flux represents the highest hurdle. To complete the puzzle,\nmodels have to match the spectral shape, the primary composition, and\nthe arrival direction distribution of the observed events.\n\n \n{\\it 2.1 Energy}\n\nThe observed highest energy event at $3.2 \\times 10^{20}$ eV\n\\cite{bird} argues for the existence of Zevatrons in\nnature \\cite{bland99}, accelerators that reach as high as one ZeV \n(ZeV=10$^{21}$ eV) which is a billion times the energy limit of current\nterrestrial accelerators. The energetic requirements at the source may\nbe even more stringent if the distance traveled by the UHE\nprimaries from source to Earth is larger than typical interaction\nlengths. As can be seen from Figure 1 of\n\\cite{watson99} (from \\cite{cronin92}), if $3 \\times 10^{20}$ eV is\ntaken as a typical energy for protons travelling in straight lines,\naccelerators located further than 30 Mpc need to reach above 1 ZeV while\nthose located further than 60 Mpc require over 10 ZeV energies. \nDepending on the strength and structure of the magnetic field along\nthe primary's path, the distance traveled can be significantly larger\nthan the distance to the source. As magnetic fields above $\\sim\n10^{-8}$ G may thread extragalactic space \\cite{RKB98,BBO99,FP99}, protons\ntravel in curved paths and sources need to be either more energetic or\nlocated closer to Earth \\cite{WME96,BO99,SLB99}. \n\n \nThere are great difficulties with finding plausible accelerators for\nsuch extremely energetic particles \\cite{bland99}. As discussed in \\S3,\neven the most powerful astrophysical objects such as radio galaxies and\nactive galactic nuclei can barely accelerate charged particles to energies\nas high as $10^{20}$ eV. If the origin of these events date back to the\nearly universe, then the energy is not as challenging since typical\nsymmetry breaking scales that give rise to early universe relics can be\nwell above the ZeV scale (\\S5). \n\n\n{\\it 2.2 Flux} \n\n At 10$^{20}$ eV, the observed flux of UHECRs is about $\\sim$ 1\nevent/km$^2$/century which has strongly limited our ability to gather\nmore than 20 events after decades of observations\n\\cite{watson99}. Although challenging to observers, the flux is not \nparticularly constraining in terms of general requirements on\nastrophysical sources. In fact, this flux equals the flux of\ngamma-rays in {\\it one} gamma-ray burst that may have taken place in a\n50 Mpc radius volume around us \\cite{W95,V95}. In terms of an average\nenergy density, UHECRs correspond to $\\sim 10^{-21}$ erg/cm$^3$, about\n8 orders of magnitude less than the cosmic background radiation. \n\nAlthough less constraining to astrophysical accelerators, flux\nrequirements are very challenging for top-down scenarios. The dynamics\nof topological defect generation and evolution generally selects the\npresent horizon scale as the typical distance between defects which\nimplies a very low flux. Some scenarios such as monopolia, cosmic\nnecklaces, and vortons have\nadditional scales and may avoid this problem.\nThe possibility of a long lived relic particle that cluster as dark\nmatter can also more easily meet the flux requirements than general\ntop-down models (\\S5).\n\n \n{\\it 2.3 Spectrum} \n\nThe energy spectrum of cosmic rays below the expected GZK cutoff (i.e.,\nbetween $\\sim 10^8\\,$eV and $\\la 10^{19}\\,$eV) is well established to\nhave a steep energy dependence: $N(E) \\propto E^{-\\gamma}$, with\n$\\gamma\\approx 2.7$ up to the ``knee'' at $E\\simeq 10^{15}$ eV and\n$\\gamma\\approx 3.1$, for $10^{15}$ eV $\\la E \\la 10^{19}$ eV. Cosmic\nrays of energy below the knee are widely accepted to originate in shocks\nassociated with galactic supernova remnants (see, e.g., \\cite{A94}),\nbut this mechanism has difficulties producing particles of higher energies\n\\cite{NMA95}. Larger shocks, such as those associated with galactic\nwinds, could reach energies close to the knee \\cite{JM87} and\nsupernova explosions into stellar winds may explain cosmic rays beyond\nthe knee \\cite{SBG93}. Although the source of cosmic rays above the\nknee is not clear, the steepening of the spectrum argues for a similar\norigin with an increase in losses or decrease in confinement time\nabove the knee. However, the events with energy above\n$10^{19.5}\\,$eV show a much flatter spectrum with $1 \\la \\gamma\n\\la 2$. The drastic change in slope suggests the emergence of a {\\it\nnew component} of cosmic rays at ultra-high energies. This new\ncomponent is generally thought to be extragalactic \\cite{A94,bird},\nalthough, depending on its composition, it may also originate in the\nGalaxy \\cite{ZPPR98,OEB99}, in an extended halo\n\\cite{V95}, or in the dark matter halo \\cite{BKV97}. Galactic and halo\norigins for UHECRs ease the difficulties with the lack of a GZK cutoff but\nrepresent an even greater challenge to acceleration mechanisms. \n\n{\\it 2.4 Propagation - Losses and Magnetic Fields}\n\nIn order to contrast plausible candidates for UHECR sources with the\nobserved spectrum and arrival direction distribution, the propagation\nfrom source to Earth needs to be taken into account. Propagation\nstudies involve both the study of losses along the primaries' path as\nwell as the structure and magnitude of cosmic magnetic fields that\ndetermine the trajectories of charged primaries and influence the\ndevelopment of the electromagnetic cascade (see, e.g.,\n\\cite{LOS95PJ96}).\n\nFor primary protons the main loss processes are pair production \n\\cite{Blu70} and photopion production off the CMB that gives rise to\nthe GZK cutoff \\cite{GZK66}. For straight line propagation, loss\nprocesses limit sources of 10$^{20}$ eV to be within $\\sim$ 50\nMpc from us and a clear cutoff should be present at\n$\\sim 7 \\times 10^{19}$ eV. Even with the small number of accumulated\nevents at the highest energies, the AGASA spectrum seems incompatible \nwith a GZK cutoff for a homogeneous extragalactic source distribution\n\\cite{takeda98}. The shape of the cutoff can be modified if the\ndistribution of sources is not homogeneous \\cite{BG88,MT99a} and if \nthe particle trajectories are not rectilinear (e.g., the case of\nsizeable intergalactic magnetic fields) \n\\cite{WME96,S97,MT97,SLO97,BO99,SLB99}. In fact, if the observed\ndistribution of galaxies in the local universe is used to simulate the\nrange of possible cutoff shapes, the AGASA spectrum is still \nconsistent with sources distributed with the luminous matter given the\npoor statistics\n\\cite{MT99a}. The need for a new component should become apparent\nwith the increased statistics of future observatories \\cite{watson99}. \n\nCharged particles of energies up to $10^{20}\\,$eV can be deflected\nsignificantly in cosmic magnetic fields. In a constant magnetic field\nof strength $B= B_6 \\mu$G, particles of energy $E= E_{20}10^{20}{\\rm\neV}$ and charge $Ze$ have Larmor radii of\n$r_L \\simeq 110$ kpc $(E_{20}/B_6 Z)$. If the UHECR primaries are\nprotons, only large scale intergalactic magnetic fields affect their\npropagation significantly \n\\cite{WME96,S97,MT97,SLO97,BO99,SLB99} unless the Galactic halo has \nextended fields \\cite{S97}. For higher $Z$, the Galactic magnetic\nfield can strongly affect the trajectories of primaries\n\\cite{ZPPR98,HMR99}.\n\n Whereas Galactic magnetic fields are reasonably\nwell studied, extragalactic fields are still very\nill understood \\cite{KronVallee}. Faraday rotation measures indicate large\nmagnitude fields ($\\sim\n\\mu$G) in the central regions of clusters of\ngalaxies. In regions between clusters, the presence of\nmagnetic fields is evidenced by synchrotron emission but the strength\nand structure are yet to be determined. On the largest\nscales, limits can be imposed by the observed isotropy of the CMB\nand by a statistical interpretation of Faraday rotation measures of light\nfrom distant quasars. The isotropy of the CMB can \nconstrain the present horizon scale fields\n$B_{H_0^{-1}} \\la 3 \\times 10^{-9}$ G \\cite{BFS97}. Although the\ndistribution of Faraday rotation measures have large non-gaussian tails,\na reasonable limit can be derived using the median of the distribution\nin an inhomogeneous universe: for fields assumed to be constant on the\npresent horizon scale, $B_{H_0^{-1}} \\la 10^{-9}$ G; for fields with 50\nMpc coherence length, $B_{50 {\\rm Mpc}}\n\\la 6 \\times 10^{-9}$ G; while for 1 Mpc coherence length, $B_{Mpc}\n\\la 10^{-8}$ G \\cite{BBO99}. These limits apply to a $\\Omega_b h^2 =\n0.02$ universe and use quasars up to redshift $z=2.5$. Local\nstructures can have fields above these upper limits as long as they are\nnot common along random lines of site between\n$z$ = 0 and 2.5 \\cite{RKB98,BBO99,FP99}.\n\nOf particular interest is the field in the local 10 to 20 Mpc volume\naround us. If the Local Supercluster has fields of about\n$10^{-8}$ G or larger, the propagation of ultra high energy protons\nbecomes diffusive and the spectrum and angular distribution at the\nhighest energies are significantly modified\n\\cite{WW79GWW80BGD89,RKB98,BO99}. As shown in Figure 1 (from\n\\cite{BO99}), a source with spectral index \n$\\gamma\\ga 2$ that can reach $E_{max} \\ga 10^{20}$ eV is constrained by\nthe overproduction of lower energy events around 1 to 10 EeV (EeV $\\equiv\n10^{18}$ eV).\nFurthermore, the structure and magnitude of magnetic fields in the\nGalactic halo\n\\cite{S97,HMR99} or in a possible Galactic wind can also affect\nthe observed UHECRs. In particular, if\nour Galaxy has a strong magnetized wind, what appears to be an isotropic\ndistribution in arrival directions may have\noriginated on a small region of the sky such as the Virgo cluster\n\\cite{ABMS99}. In the future, as sources of\nUHECRs are identified, large scale magnetic fields will be\nbetter constrained \\cite{LSOS97}.\n\n\\begin{figure}\n\\vspace{80mm}\n\\caption{Flux vs. Energy with $E_{max} = 10^{21}$ eV at source. Choices\nof source distance r(Mpc), spectral index $\\gamma$, proton\nluminosity $L_p$(erg/s), and LSC field B($\\mu$G) are: solid line (13\nMpc, 2.1, $2.2 \\times 10^{43}$ erg/s, 0.05 $\\mu$G); dotted line (10\nMpc, 2.1, $10^{43}$ erg/s, 0.1 $\\mu$G); dashed line (10 Mpc, 2.4, 3.2\n$\\times 10^{43}$ erg/s, 0.1 $\\mu$G); and dashed-dotted line (17 Mpc, \n2.1, $3.3 \\times 10^{43}$ erg/s, 0.05 $\\mu$G). Data points from \n\\cite{Haya94,bird}.}\n\\end{figure}\n\nIf cosmic rays are heavier nuclei, the attenuation length is shorter \nthan that for protons due to photodisintegration on the infrared\nbackground \\cite{PSB76SS99}. However, UHE nuclei may be of Galactic\norigin. For large enough charge, the trajectories of UHE nuclei\nare significantly affected by the Galactic magnetic field\n\\cite{HMR99} such that a Galactic origin can appear isotropic\n\\cite{ZPPR98}. The magnetically induced distortion of the flux\nmap of UHE events can give rise to some higher flux regions where\ncaustics form and some much lower flux regions (blind spots) even for\nan originally isotropic distribution of sources\n\\cite{HMR99}. Such propagation effects are one of the reasons why\nfull-sky coverage is necessary for resolving the UHECR puzzle.\n\nThe trajectories of neutral primaries are not affected\nby magnetic fields. If associated\nwith luminous systems, sources of UHE neutral primaries should point back\nto their nearby sources. The lack of counterpart identifications suggests\nthat if the primaries are neutral, their origin involves physics beyond\nthe standard model (\\S4 \\& \\S5). \n\n\n{\\it 2.5 Cosmography} \n\nThe distribution of arrival directions of UHECRs can in principle hold\nthe key to solving the UHECR puzzle. Within a 50 Mpc radius volume\naround us, the most well-known luminous structures are the Galactic\nplane, the Local Group and the large-scale galaxy distribution with a\nrelative overdensity around the Local\nSupercluster. The Galactic halo is another noteworthy structure that\nis expected to be a spheroidal overdensity of dark matter centered at\nthe Galactic disk while the dark matter distribution on larger scales\ncorrelates with the luminous matter distribution. For\nthe few highest energy events, there is presently no strong evidence\nof correlations between the events' arrival direction and any of the \nknown nearby luminous structures: the distribution is consistent with\nisotropy\n\\cite{takeda99,SH99}. For slightly lower\nenergies, some correlations may have been detected. For events around\n40 EeV, a positive correlation with the Supergalactic plane is found but\nonly at the 1 $\\sigma$ level \\cite{Uchi99}. For even lower energies, a\nmore significant correlation was recently announced by AGASA: the arrival\ndirection distribution of\n EeV events shows a correlation with the Galactic\ncenter and the nearby Galactic spiral arms \\cite{Haya99}. If\nconfirmed, this correlation would be strong evidence for a Galactic\norigin of EeV cosmic rays.\n\n{\\it 2.6 Composition}\n\nAn excellent discriminator between proposed models is the composition\nof the primaries. In general, Galactic disk models have to invoke\nheavier nuclei such as iron to be consistent with the isotropic\ndistribution, while extragalactic\nastrophysical models tend to favor proton primaries. Photon primaries\nare more common among top-down scenarios although nucleons can reach\ncomparable fluxes for some models \\cite{BS99}. Experimentally, the \ncomposition can be determined by the muon content of the shower in \nground arrays and the depth of\nshower maximum in fluorescence detectors \\cite{watson99}. \nUnfortunately, the muon content analysis is not very effective\nat the highest energies. Data from the largest air shower array, AGASA,\ndisfavor photon primaries and indicate a fixed composition across the EeV\nto 100 EeV range but does not distinguish nuclei from proton primaries\n\\cite{Y99}. The shower development of the highest energy event ever\ndetected, the 320 EeV Fly's Eye event, is consistent with either proton\nor iron \\cite{bird} and also disfavors a photon primary\n\\cite{HVSV95}. This event constrains\nhypothetical hadronic primaries to have masses below\n$\\sim $ 50 GeV \\cite{AFK98}. Since fluctuations in shower\ndevelopment are usually large, strong composition constraints await\nlarger statistics of future experiments. \n \n{\\it 2.7 Clusters of Events}\n\nA final challenge for models of UHECRs is the possible small scale\nclustering of arrival directions\n\\cite{Haya96,takeda99,Uchi99}. AGASA reported that\n their 47 events above 40 EeV show three double coincidences\n(doublets) and one triple coincidence (triplet) in arrival\ndirections, a $\\la 1$\\% chance probability\n\\cite{takeda99}. Adding to the AGASA data that of Haverah Park,\nVolcano Ranch, and Yakutsk, the 51 events above 50 EeV show one\ndoublet and two triplets \\cite{Uchi99}. Although these could be due to\na statistical fluctuation since the chance probability for the\ncombined set is $\\sim 10 \\%$\n\\cite{Uchi99}, they may indicate the position of the sources. (When\nlimited to $\\pm 10^o$ around the Supergalactic plane the chance\nprobability decreases to $\\sim 1\\%$.) If these clusters\nindicate the position of sources, the arrival times and energies of\nsome of the events are inconsistent with a burst and require long lived\nsources. Furthermore, if the clustering is confirmed by larger data\nsets and their distribution correlates with some known matter\ndistributions in the nearby universe, the composition of the primaries\n\\cite{cronin96} as well as the magnitude of extragalactic magnetic\nfields would be strongly constrained \\cite{LSOS97,SLO97}. Alternative\nexplanations for the clustering involve either the effect of caustics\nin the propagation due to magnetic fields \\cite{HMR99} or the\nclustering of dark matter in the halo of the Galaxy. \n\n\n\\section{Facing the Challenge with Zevatrons}\n\nThe challenge put forth by these observations has generated two different\napproaches to reaching a solution: a `bottom-up' and a `top-down'. A\nbottom-up approach involves looking for {\\it Zevatrons}\n\\cite{bland99}, possible acceleration sites in known astrophysical\nobjects that can reach ZeV energies, while a top-down\napproach involves the decay of very high mass relics from the early\nuniverse and physics beyond the standard model of particle physics.\nBottom-up models are discussed first and top-down models in the next\nsection.\n\n\\begin{figure}\n\\vspace{80mm}\n\\caption{$B$ vs. $L$, for $E_{max} = 10^{20}$ eV, $Z=1$\n(dashed line) and $Z=26$ (solid line).}\n\\end{figure}\n\n\nAcceleration of UHECRs in astrophysical plasmas occurs when large-scale\nmacroscopic motion, such as shocks and turbulent flows, is transferred\nto individual particles. The maximum energy of accelerated particles,\n$E_{\\rm max}$, can be estimated by requiring that the gyroradius of the\nparticle be contained in the acceleration region. Therefore, for a\ngiven strength, $B$, and coherence\nlength, $L$, of the magnetic field embedded in an astrophysical plasma,\n$E_{\\rm max} = Ze \\, B \\, L$, where $Ze$ is the charge of the particle.\nThe ``Hillas plot'' \\cite{hillas84} in Figure 2 shows that, for\n$E_{max} \\ga 10^{20}$ eV and $Z \\sim 1$, the only known astrophysical\nsources with reasonable $B L $ products are neutron stars ($B\n\\sim 10^{13}$ G, $L \\sim 10$ km), active galactic nuclei (AGNs) ($B\n\\sim 10^{4}$ G, $L \\sim 10$ AU), radio lobes of AGNs ($B \\sim 0.1\\mu$G,\n$L \\sim 10$ kpc), and clusters of galaxies ($B \\sim \\mu$G, $L \\sim\n100$ kpc). \n\n\nIn general, when these sites are considered more carefully, one finds\ngreat difficulties due to either energy losses in the acceleration\nregion or the great distances of known sources from our\nGalaxy \\cite{SSB94}. In many of these objects shock acceleration is\ninvoked as the primary acceleration mechanism. Although effective in\nthe acceleration of lower energy cosmic rays, shock acceleration is\nunable to reach ZeV energies for most plausible acceleration sites\n\\cite{NMA95} with the possible exception of shocks in\nradio lobes. Unipolar inductors are often\ninvoked as plausible alternative to shocks \n\\cite{BBDGP90,bland99}.\n\n\n\n\\smallskip\n{\\it 3.1 Cluster Shocks}\n\nMoving from right to left on Figure 2, cluster shocks are reasonable\nsites to consider for UHECR acceleration, since $E_{max}$ particles\ncan be contained by cluster fields. However, the propagation of these\nhigh energy particles inside the cluster medium is such that they do\nnot escape without significant energy losses. In fact, efficient\nlosses occur on the scales of clusters of galaxies for the same reason\nthat a GZK cutoff is expected, namely, the photopion production off\nthe CMB. Losses limit UHECRs in cluster shocks to reach at most\n$\\sim$ 10 EeV \\cite{KRJ96KRB97}.\n\n\\smallskip\n{\\it 3.2 AGN - Jets and Radio Lobes}\n\nExtremely powerful radio galaxies are likely astrophysical\nUHECR accelerators \\cite{hillas84,BS87} (for a\nrecent review see \\cite{B97}). Jets from the central black-hole of\nthe active galaxy end at a termination shock where the interaction of\nthe jet with the intergalactic medium forms radio lobes and `hot\nspots'. Of special interest are the most powerful AGNs such as\nFanaroff-Riley class II objects \\cite{FR74}. Particles accelerated in\nhot spots of FR-II sources via first-order Fermi acceleration may reach\nenergies well above an EeV and may explain the spectrum up to the GZK\ncutoff \\cite{RB93}. A nearby specially powerful source\n may be able to reach energies past the\ncutoff \\cite{RB93}. Alternatively, the crossing of the\ntangential discontinuity between the relativistic jet and the\nsurrounding medium may also be able to make protons reach the necessary\nenergies \\cite{Ost99}. The spectrum of UHECR primaries formed by the\nlatter proposal is flatter than the Fermi acceleration at the hot spots\nscenario. Improved statistics of events past the GZK cutoff by future\nexperiments should better determine the spectral index, and therefore, \ndiscriminate between plausible sites for UHECR\nacceleration in radio sources. \n\nBoth hot spots and tangential jet\ndiscontinuity models avoid the efficient loss processes faced by\nacceleration models in AGN central regions (\\S 3.3).\nHowever, the location of possible sources is problematic\nfor both types of mechanisms. Extremely powerful AGNs\nwith radio lobes and hot spots are rare and far apart. The closest known\nobject is M87 in the Virgo cluster ($\\sim$ 18 Mpc away) and could be\na main source of UHECRs. Although a single nearby source may be able\nto fit the spectrum for a given strength and structure of the\nintergalactic magnetic field\n\\cite{BO99}, it is unlikely to match the observed arrival direction\ndistribution. After M87, the next known nearby source is NGC315 which\nis already too far at a distance of\n$\\sim $ 80 Mpc. \n\nA recent proposal gets around\nthis challenge by invoking a Galactic wind with a strongly magnetized\nazimuthal component \\cite{ABMS99}. Such a wind can significantly alter\nthe paths of UHECRs such that all the observed arrival directions of\nevents above 10$^{20}$ eV trace back to the Virgo cluster close to M87\n \\cite{ABMS99}. If our Galaxy has a wind with\nthe required characteristics to allow for this magnetic focusing is\nyet to be determined. Future observations of UHECRs from the Southern\nHemisphere (e.g., the Southern Auger Site\n\\cite{cronin92}) will provide data on\npreviously unobserved parts of the sky and help distinguish plausible\nproposals for the effect of local magnetic fields on arrival\ndirections. Once again full sky coverage is a key\ndiscriminator of such proposals. \n\n\n \\smallskip\n{\\it 3.3 AGN - Central Regions}\n\n\nThe powerful engines that give rise to the observed jets and radio\nlobes are located in the central regions of active galaxies and are\npowered by the accretion of matter onto supermassive black holes. It\nis reasonable to consider the central engines themselves as the likely\naccelerators\n\\cite{hillas84,T86,BBDGP90}. In principle, the nuclei of generic\nactive galaxies (not only the ones with hot spots) can accelerate\nparticles via a unipolar inductor \n\\cite{T86} not unlike the one operating in pulsars\n\\cite{GJ69}. In the case of AGNs, the magnetic field is provided by\nthe infalling matter and the spinning black hole horizon provides the\nimperfect conductor for the unipolar induction. Close to the horizon\nof a black hole ($R\\simeq GM/c^2$) with a mass M\n$= 10^{9} M_9 \\ {\\rm M}_{\\odot}$, the electromotive force is\n\\cite{BZ77,T86}:\n$emf \\propto cBR \\approx 4.4 \\times 10^{20} B_4 M_9 {\\rm Volts} $ \nfor a magnetic field $B=10^4 B_4$ G. It is reasonable to expect that\nsuch fields are reached in some nearby AGNs. \nIn addition, the arrival direction of events above $5 \\times 10^{19}$\neV correlate qualitatively well with active galaxies within 100 Mpc\n\\cite{Cro99}. Although it is not clear how statistically significant\nthe correlation is, the clustering of UHECR events in the same regions of\nthe sky where clusters of AGNs reside is certainly tantalizing.\n\nThe problem with AGNs as UHECR sources is two-fold: first, UHE particles\nface debilitating losses in the acceleration region due to the intense\nradiation field present in AGNs, and second, the\nspatial distribution of objects should give rise to a GZK cutoff of the\nobserved spectrum. In the central regions of AGNs, loss processes are\nexpected to downgrade particle energies well below the maximum\nachievable energy. This limitation has led to the proposal that quasar\nremnants, supermassive black holes in centers of inactive galaxies, are\nmore effective UHECR accelerators\n\\cite{BG99}. In this case, losses are not as significant. In addition,\nthe problem with the rarity of very luminous radio sources (\\S 3.2) is\nalso avoided since any galaxy with a supermassive quiescent black hole\ncould host a UHECR accelerator. \n\n \nQuasar remnants are manifestly underluminous such that\n losses in the acceleration region are kept at\na reasonably low level \\cite{BG99}. Although presently underluminous, \nthe underlying supermassime black holes are likely to be sufficiently \nspun-up for individual particles to be accelerated. \nAn incomplete sample of 32 massive dark objects\n(MDOs) in the nearby universe\n(of which 8 are within 50 Mpc) \\cite{Ma98} finds about 14 MDOs \nwhich could have fields strong enough for an $emf \\ga 10^{20}$\nVolts \\cite{BG99}. From the number density and accretion evolution of\nquasars, more than 40 quasar remnants are expected to have\n$\\ga 4 \\times 10^{8}$ M$_{\\odot}$ within a 50\nMpc volume while more than a dozen would have $\\ga 10^{9}$\nM$_{\\odot}$ \\cite{CT92}.\n\nThe second difficulty with AGNs mentioned above, namely the spatial\ndistribution and the GZK cutoff induced by the more distance galaxies, is\nnot avoided by the quasar remnants proposal unless the spectrum is\nfairly hard. However, it is still within the errors of the current\nUHECR spectrum the possibility that a GZK cutoff is presently hidden\ndue to the effect of the local clustering of galaxies\n\\cite{MT99a}. This ambiguity should be lifted and a GZK cutoff made\napparent by future experiments.\n\n\n \\smallskip\n{\\it 3.4 Neutron Stars}\n\nFrom Figure 2, the last astrophysical objects capable of accelerating\nUHECRs are neutron stars (see, e.g., \\cite{hillas84,BBDGP90}).\nWith the recent identification of ``magnetars'' \\cite{TD95} (neutron\nstars with fields of $\\ga 10^{14}$ G) as the sources of soft gamma\nray repeaters \\cite{Kou98}, neutron stars have strong enough fields\nto reach past the required $E_{max}$ as in Figure 2. Acceleration\nprocesses inside the neutron star light cylinder are bound to fail\nmuch like the AGN central region case: ambient magnetic and radiation\nfields induce significant losses \n\\cite{VMO97}. However, the plasma that expands beyond the light\ncylinder is freer from the main loss processes and may be accelerated\nto ultra high energies.\nOne possible solution to the UHECR puzzle is the proposal that\nthe early evolution of neutron stars may be responsible for the flux\nof cosmic rays beyond the GZK cutoff \n\\cite{Be92,OEB99,BEO99}. In this case, UHECRs originate mostly in the\nGalaxy and the arrival directions require that the primaries have large\n$Z$ (i.e., primaries are heavier nuclei).\n\n\nNewly formed, rapidly rotating neutron stars may accelerate iron\nnuclei to UHEs through relativistic MHD winds beyond \ntheir light cylinders \\cite{OEB99,BEO99}. The nature of the\nrelativistic wind is not yet clear, but observations of the Crab\nNebula indicate that most of the rotational energy emitted by the\npulsar is converted into the flow kinetic energy of the particles in\nthe wind (see, e.g., \\cite{BL98}). Recent observations of the Crab Nebula\nby the Chandra satellite indicate both a complex disk and jet structure\nthat is probably associated with the magnetic wind as well as the presence\nof iron in the expanding shell. Understanding the structure\nof observable pulsar winds such as the Crab nebula will help determine if\nduring their first years pulsars were efficient Zevatrons.\n\nIf most of the magnetic energy in\nthe wind zone is converted into particle kinetic energy and the rest\nmass density of the wind is not dominated by electron-positron pairs, \n particles in the wind can reach a maximum energy of\n$E_{max} \\simeq 8 \\times 10^{20} \\, Z_{26} B_{13} \\Omega_{3k}^2 \\,\n{\\rm eV}, $ for iron nuclei ($Z_{26} \\equiv Z/26 = 1)$, neutron star\nsurface fields $B = 10^{13} B_{13} $ G, and initial rotation frequency\n$\\Omega = 3000 \\Omega_{3k}$ s$^{-1}$. In the rest frame of the wind,\nthe plasma is relatively cold while in the star's rest frame the\nplasma moves with Lorentz factors $\\gamma \\sim 10^9 - 10^{10}$. \n \nIron nuclei can\nescape the remnant of the supernova without suffering significant\nspallation about a year after the explosion. As the\nejected envelope of the pre-supernova star expands, the young neutron\nstar spins down and $E_{max}$ decreases. Thus, a requirement for\nrelativistic winds to supply UHECRs is that the column density of\nthe envelope becomes transparent to UHECR iron before the spin rate\nof the neutron star decreases significantly. The allowed parameter\nspace for this model is shown in Figure 3. Magnetars with the\nlargest surface fields spin down too quickly for iron nuclei to escape\nunless the remnant is asymmetric with lower density ``holes.'' The\nspectrum of UHECRs accelerated by young neutron star winds is\ndetermined by the evolution of the rotational frequency which gives\n$\\gamma \\simeq 1$, at the hard end of the allowed $\\gamma$ range\n(\\S 2.3). \n\n\\begin{figure}\n\\vspace{80mm}\n\\caption{Allowed regions of $\\Omega$ vs. $B$ for $E_{cr}=10^{20}$ eV\n(solid line) and $ 3\\times 10^{20}$ eV (dashed lines) with envelope\nmasses $M_{env}=50 M_{\\odot}$ and $5 M_{\\odot}$. Horizontal line\nindicates the minimum period for neutron stars $\\sim 0.3$ ms.}\n\\end{figure}\n\nDepending on the structure of Galactic\nmagnetic fields, the trajectories of iron nuclei from Galactic\nneutron stars may be consistent with the observed arrival directions of\nthe highest energy events \\cite{ZPPR98}. Moreover, if cosmic rays \nof a few times $10^{18}$ eV are protons of Galactic origin, the\nisotropic distribution observed at these energies is indicative of the\ndiffusive effect of the Galactic magnetic fields on iron at\n$\\sim 10^{20}$ eV. \n\nAnother recent proposal involving neutron stars suggests that\nrelativistic winds formed around neutron star binaries may generate\nhigh energy cosmic rays in a single shot $\\Gamma^2$ acceleration \n\\cite{GA99}, where $\\Gamma$ is the bulk Lorentz factor. However, the\n$\\Gamma^2$ acceleration process is likely to be very inefficient \nwhich renders the proposal insufficient for explaining UHECRs\n\\cite{BeOs99}. \n \nIn general, there is an added bonus to considering the existence of\nZevatrons in Galactic systems: one may find Pevatrons or Evatrons\ninstead. These may explain the origin of cosmic rays from the\nknee at 10$^{15}$ eV up to the ``ankle'' at 10$^{18}$ eV that remain\nlargely unidentified. \n\n \\smallskip\n{\\it 3.5 Gamma-Ray Bursts}\n\nBefore moving on to more exotic explanations for the origin of UHECRs,\none should consider astrophysical phenomena that\nmay act as Zevatrons not included in Figure\n2. In effect, transient high energy phenomena such as gamma-ray\nbursts (bursts of $\\sim 0.1 - 1 $ MeV photons that last up to a few \nseconds) may accelerate protons to ultra-high energies \n\\cite{W95,V95}. The systems that generate gamma-ray\nbursts (GRBs) remain unknown\nbut evidence that GRBs are of cosmological origin and involve a\nrelativistic fireball has been mounting with the recent discovery of\nX-ray, optical, and radio afterglows \\cite{C97G97F97} and the\nsubsequent identification of host galaxies and their redshifts.\n\nAside from both having unknown origins, GRBs and UHECRs have some\nsimilarities that argue for a common origin. Like UHECRs, GRBs are\ndistributed isotropically in the sky \\cite{BATSE92}, and\nthe average rate of $\\gamma$-ray energy emitted by GRBs is comparable\nto the energy generation rate of UHECRs of energy $>10^{19}$ eV in a\nredshift independent cosmological distribution of sources\n\\cite{W95}, both have $ \n\\approx 10^{44}{\\rm erg\\ Mpc}^{-3}{\\rm yr}^{-1} .$ \n\nAlthough the systems that generate GRBs \nhave not been identified, they are likely to involve a\nrelativistic fireball (see, e.g., \\cite{fireballs}). Cosmological\nfireballs may generate UHECRs through Fermi acceleration\nby internal shocks\n\\cite{W95,V95}. In this model the\ngeneration spectrum is estimated to be \n$dN/dE\\propto E^{-2}$ which is consistent with observations\nprovided the efficiency with which the wind\nkinetic energy is converted to $\\gamma$-rays is similar to the\nefficiency with which it is converted to UHECRs \\cite{W95}. \n Acceleration to $>10^{20}$ eV is possible provided\nthat $\\Gamma$ of the fireball shocks are large enough\nand that the magnetic field is close to equipartition.\n\n\nThere are a few problems with the GRB--UHECR common origin\nproposal. First, events past the GZK cutoff require that only GRBs\nfrom $\\la 50$ Mpc contribute. However, only {\\it one} burst is\nexpected to have occurred within this region over a period of 100 yr. \nTherefore, a very large dispersion of $\\ga$ 100 yr in\nthe arrival time of protons produced in a single burst is a necessary\ncondition. The deflection by random\nmagnetic fields combined with the energy spread of the particles\nis usually invoked to reach the required dispersion\n\\cite{W95,WME96}. If the dispersion in time is achieved, the energy\nspectrum for the nearby source(s) is expected to be very narrowly \npeaked $\\Delta E/E\\sim1$ \\cite{W95,WME96,LSOS97}.\nSecond, the fireball shocks may not be able to reach the\nrequired $\\Gamma$ factors for UHECR shock acceleration \\cite{GA99}.\nThird, UHE protons are likely to loose most of their energy as they\nexpand adiabatically with the fireball \\cite{RM98}. However, \nif acceleration happens by internal shocks in regions where the\nexpansion becomes self-similar, protons may escape without significant\nlosses \\cite{W99}. Fourth, the observed arrival times of different\nenergy events in some of the UHE clusters\n argues for long lived sources not bursts (\\S 2.7). These clusters can\nstill be due to fluctuations but should become clear in future experiments\n\\cite{SLO97}. Finally, the present flux of UHE protons from GRBs is\nreduced to\n$\\la 10^{42}{\\rm erg\\ Mpc}^{-3}{\\rm yr}^{-1}$, if a redshift dependent\nsource distribution that fits the GRB data is\nconsidered \\cite{Ste99} (see also \\cite{FP99,D99}).\n \n\n\\section{Hybrid Models}\n\nThe UHECR puzzle has inspired proposals that use Zevatrons to\ngenerate UHE particles other than protons, nuclei, and photons.\nThese use physics beyond the standard model in a bottom-up approach,\nthus, named hybrid models.\n\nThe most economical among such proposals involves a familiar\nextension of the standard model, namely, neutrino masses. The most \ncommon solution to the atmospheric or the solar neutrino\nproblems entails neutrino oscillations, and hence, neutrino\nmasses (see, e.g., \\cite{B89}).\nRecently, the announcement by SuperKamiokande on atmospheric neutrinos \nhas strengthened the evidence for neutrino oscillations and the\npossibility that neutrinos have a small mass \\cite{SK99}. If\nsome flavor of neutrinos have masses $\\sim 1$ eV, the relic\nneutrino background will cluster in halos of galaxies and clusters of\ngalaxies. High energy neutrinos ($\\sim 10^{21}$ eV) accelerated in\n Zevatrons can annihilate on the neutrino background and\nform UHECRs through the hadronic Z-boson decay \\cite{We97FMS97}. \n\nThis proposal is\naimed at generating UHECRs nearby (in the Galactic halo and Local Group\nhalos) while using Zevatrons that can be much further than the GZK\nlimited volume, since neutrinos do not suffer the GZK losses. It is not\nclear if the goal is actually achieved since the production in the\nuniform non-clustered neutrino background may be comparable to \nthe local production depending on the neutrino masses\n\\cite{Wa99}. In addition, the Zevatron needed to accelerate protons above\nZeVs that can produce ZeV neutrinos as secondaries is quite spectacular and\npresently unknown, requiring an energy generation in excess of\n$\\sim 10^{48} {\\rm erg\\ Mpc}^{-3}{\\rm yr}^{-1}$ \\cite{Wa99}.\n\nAnother suggestion is that the UHECR primary is a new \nparticle. For instance, a stable or very long\nlived supersymmetric neutral hadron of a few GeV, named {\\it\nuhecron}, could explain the UHECR events and evade the present\nlaboratory bounds\n\\cite{Fa96CFK98}. (Note that the mass of a hypothetical hadronic\nUHECR primary can be limited by the shower development of the Fly's\nEye highest energy event to be\n below $\\la 50$ GeV \\cite{AFK98}.) Both the long lived new\nparticle and the neutrino Z-pole proposals involve neutral particles which\nare usually harder to accelerate (they are created as secondaries of even\nhigher energy charged primariess) but\ncan traverse large distances without being affected by the cosmic magnetic\nfields. Thus, a signature of such hybrid models for future experiments is\na clear correlation between the position of powerful Zevatrons in the sky\nsuch as distant compact radio quasars and the arrival direction of UHE\nevents\n\\cite{FB98}. \n\n\nTopological defects have also been suggested as possible UHE primaries\n\\cite{P60}. Monopoles of masses between $\\sim 10^{9} - 10^{10}$ GeV \nhave relic densities below the Parker limit and can be easily\naccelerated to ultra high energies by the Galactic magnetic field\n\\cite{KW96}. The main challenges to this proposal are the observed \nshower development for the Fly's Eye event that seems to be\ninconsistent with a monopole primary and the arrival directions not\nshowing a preference for the local Galactic magnetic field \\cite{MN98}.\n\nAnother exotic primary that can use a Zevatron to reach ultra high\nenergies is the vorton. Vortons are small loops of superconducting\ncosmic string stabilized by the angular momentum of charge carriers\n\\cite{DS89}. Vortons can be a component of the dark\nmatter in galactic halos and be accelerated in astrophysical\nZevatrons \\cite{BP97}. Although not yet clearly demonstrated, the\nshower development profile is also the likely liability of this model.\n\n\n\\section {Top-Down Models}\n\nIt is possible that none of the astrophysical scenarios are able to \nmeet the challenge posed by the UHECR data as more\nobservations are accumulated. In that case, the alternative\nis to consider top-down models. For example, if the primaries are\nnot iron, the distribution in the sky remains isotropic with better\nstatistics, and the spectrum does not show a GZK cutoff, UHECRs are\nlikely to be due to the decay of very massive relics from the early\nuniverse.\n\n This possibility was the most attractive to my dear\ncolleague and friend, David N. Schramm, to whom this volume is\ndedicated. After learning with the work of Hill \\cite{H83} that high\nenergy particles would be produced by the decay of supermassive Grand\nUnified Theory (GUT) scale particles (named X-particles)\nin monopole-antimonopole annihilation, Schramm joined Hill in proposing\nthat such processes would be observed as the highest energy cosmic\nrays \\cite{SH83HS83}. Schramm realized the\npotential for explaining UHECRs with physics at very high energies well\nbeyond those presently available at terrestrial accelerators. One\nwinter in Aspen, CO, he remarked pointing to the ski lift `why walk up\nif we can start at the top'. His\n enthusiasm for this problem only grew after his pioneering work\n\\cite{HS8597}. In the last\nconference he attended, an OWL workshop at the University of Maryland\n \\cite{Owl97}, he summarized the meeting by reminding us\nthat in this exciting field the most conventional proposal involves\nsupermassive black holes and that the best fit models involve physics\nat the GUT scale and beyond. In this field our imagination is the\nlimit (as well as the low number of observed events). \n\nThe lack of a clear astrophysical solution for\nthe UHECR puzzle has encouraged a number of interesting proposals based\non physics beyond the standard model such as monopolia annihilation,\nthe decay of ordinary and superconducting cosmic strings, cosmic\nnecklaces, vortons, and superheavy long-lived relic particles, to name\na few. Due to the lack of space and a number of recent thorough\nreviews, only a brief summary of the general features of\nthese proposals will be given here. The interested reader is encouraged\nto consult the following reviews by long-time collaborators of David\nSchramm \\cite{berez99,BS99} and references therein.\n\nThe idea behind top-down models is that relics of the very\nearly universe, topological defects (TDs) or superheavy relic (SHR)\nparticles, produced after or at the end of inflation, can\ndecay today and generate UHECRs. Defects, such as cosmic strings,\ndomain walls, and magnetic monopoles, can be generated through the\nKibble mechanism\n\\cite{Ki76} as symmetries are broken with the\nexpansion and cooling of the universe (see, e.g., \\cite{TDs}). \nTopologically stable defects can survive to the present and\ndecompose into their constituent fields as they collapse, \nannihilate, or reach critical current in the case of superconducting\ncosmic strings. The decay products, superheavy gauge and higgs bosons,\ndecay into jets of hadrons, mostly pions. Pions in the jets\nsubsequently decay into $\\gamma$-rays, electrons, and neutrinos. Only a\nfew percent of the hadrons are expected to be nucleons \\cite{H83}.\nTypical features of these scenarios are a predominant release of\n$\\gamma$-rays and neutrinos and a QCD\nfragmentation spectrum which is considerably harder than the case of\nshock acceleration. \n\n\nZeV energies are not a challenge for top-down models since symmetry\nbreaking scales at the end of inflation typically are $\\gg 10^{21}$\neV (typical X-particle masses vary between \n$\\sim 10^{22} - 10^{25}$ eV) . Fitting the observed flux\nof UHECRs is the real challenge since the typical distances between TDs\nis the Horizon scale,\n$H_0^{-1} \\simeq 3 h^{-1}$ Gpc. The low flux hurts proposals based on\nordinary and superconducting cosmic strings \n\\cite{berez99,BS99}. Monopoles usually suffer the opposite\nproblem, they would in general be too numerous. Inflation succeeds in\ndiluting the number density of monopoles \\cite{G81} \nusually making them too rare for UHECR production. To reach the\nobserved UHECR flux, monopole models usually involve some degree of\nfine tuning. If enough monopoles and antimonopoles survive from the\nearly universe, they can form a bound state, named monopolium, \nthat decay generating UHECRs through monopole-antimonopole\nannihilation \\cite{H83,BS95}. The lifetime of monopolia may be too short\nfor this csenario to succeed unless they are connected by\nstrings \\cite{PO99}.\n\nOnce two symmetry breaking scales are invoked, a combination of\nhorizon scales gives room to reasonable number densities. This can be\narranged for cosmic strings that end in monopoles making a monopole\nstring network or even more clearly for cosmic necklaces\n\\cite{BV97}. Cosmic necklaces are hybrid defects where each\nmonopole is connected to two strings resembling beads on a cosmic\nstring necklace. Necklace networks may evolve to configurations that\ncan fit the UHECR flux which is ultimately generated by the\nannihilation of monopoles with antimonopoles trapped in the string\n\\cite{BV97,BBV98}. \n\n\\begin{figure}\n\\vspace{80mm}\n\\caption{Proton and $\\gamma$-ray fluxes from necklaces for \n$m_X= 10^{14}$ GeV (dashed lines), $10^{15}$ GeV (dotted \nlines), and $10^{16}$ GeV (solid lines) normalized to\nthe observed data.\n$\\gamma$-high and $\\gamma$-low correspond to two extreme cases \nof $\\gamma$-ray absorption (see, \\cite{BBV98}).}\n\\end{figure}\n\nIn addition to fitting the UHECR flux, topological defect\nmodels are constrained by limits on the flux of high energy photons\nobserved by EGRET (10 MeV to 100 GeV). The energy density of lower\nenergy cascade photons generated by UHE photons and electrons off the\nCMB and radio background is limited to $\\la 10^{-6}$ eV/cm$^3$. \nFigure 4 shows the predicted flux for necklace\nmodels given different radio backgrounds and different masses for the\nX-particle (from \\cite{BBV98}). As can be seen from the Figure, protons\ndominate the flux at lower energies while photons tend to dominate at\nhigher energies depending on the radio background. If future data can\nsettle the composition of UHECRs from 0.01 to 1 ZeV, these models will\nbe well constrained.\n\n\n\nAnother interesting possibility is the recent proposal that UHECRs are\nproduced by the decay of unstable superheavy relics that live much\nlonger than the age of the universe \\cite{BKV97,KR97}. \nSHRs may be produced at the end of inflation by non-thermal effects\nsuch as a varying gravitational field, parametric resonances during\npreheating, instant preheating, or the decay of topological defects\n(see, e.g., \\cite{KT99}). \nSHRs have unusually long lifetimes insured by\ndiscrete gauge symmetries and a sufficiently\nsmall percentage decays today producing UHECRs \\cite{BKV97,CKR99KT99}.\nAs in the topological defects case, the decay of these relics also\ngenerate jets of hadrons. \nThese particles behave like cold\ndark matter and could constitute a fair fraction of the halo of our\nGalaxy. Therefore, their halo decay products would not be limited by\nthe GZK cutoff allowing for a large flux at UHEs.\n The flux of UHECRs predicted by SHRs clustered in our halo\nis plotted in Figure 5 (from \\cite{BBV98}). It is clear that the\nspectrum is not power law (unlike the case of shock acceleration) and\nthat photon fluxes dominate. \n\n\\begin{figure}\n\\vspace{80mm}\n\\caption{SHRs or monopolia decay fluxes\n(for $m_X= 10^{14} ~GeV$):\nnucleons from the halo ({\\it protons}), $\\gamma$-rays\nfrom the halo ({\\it gammas}) and extragalactic protons. Solid, dotted\nand dashed curves correspond to different model parameters\n(see \\cite{BBV98}).}\n\\end{figure}\n\n\nFrom Figures 4 and 5 it is clear that future experiments should be\nable to probe these hypotheses. For instance, in the case of SHR\nand monopolium decays, the arrival\ndirection distribution should be close to isotropic but show an\nasymmetry due to the position of the Earth in the Galactic Halo\n\\cite{BBV98,DT98BSW99BM99}. Studying plausible halo models and the\nexpected asymmetry will help constrain halo distributions especially\nwhen larger data sets are available from future experiments. High\nenergy gamma ray experiments such as GLAST will also help constrain\nthe SHR models due to the products of the electromagnetic cascade\n\\cite{B99}.\n\n\n\n\\section{Conclusion}\n\nNext generation experiments such as the High Resolution Fly's Eye\n\\cite{hires2} which recently started operating, the Pierre Auger\nProject \\cite{cronin92} which is now under construction, the\nproposed Telescope Array \\cite{Teshima92}, and\nthe OWL-Airwatch satellite \\cite{St97} will \nsignificantly improve the data at the extremely-high end of the cosmic\nray spectrum \\cite{watson99}. With these observatories a clear\ndetermination of the spectrum and spatial distribution of UHECR\nsources is within reach. \nThe lack of a GZK cutoff should become apparent with Auger\n\\cite{MT99a} and most extragalactic Zevatrons may be ruled out.\n The observed spectrum will distinguish Zevatrons from\ntop-down models by testing power laws versus QCD fragmentation fits. \nThe cosmography of sources should also become clear and able to\n discriminate between plausible populations for UHECR sources. \nThe correlation of arrival directions for events with\nenergies above\n$10^{20}$ eV with some known structure such as the Galaxy, the\nGalactic halo, the Local Group or the Local Supercluster would be key\nin differentiating between different models. For instance, a\ncorrelation with the Galactic center and disk should become apparent\nat extremely high energies for the case of young neutron star winds\n\\cite{SH99}, while a correlation with the large scale galaxy\ndistribution should become clear for the case of quasar remnants.\nIf SHRs or monopolia are responsible for UHECR production, the arrival\ndirections should correlate with the dark matter distribution and show\nthe halo asymmetry. For these signatures to be tested, full sky\ncoverage is essential. Finally, an excellent discriminator would be\nan unambiguous composition determination of the primaries. In\ngeneral, Galactic disk models invoke iron nuclei to be consistent\nwith the isotropic distribution, extragalactic Zevatrons\ntend to favor proton primaries, while photon primaries are more common\nfor early universe relics. The hybrid detector of the Auger Project\nshould help determine the composition by measuring simultaneously\nthe depth of shower maximum and the muon content of the same\nshower. \n\n\nIn addition to explaining the origin of UHECRs, GUT to Planck scale\nphysics can potentially be probed by the existence of UHECRs. For\ninstance, the breaking of Lorentz invariance can change the\nthreshold for photopion production significantly in such a way as to\nbe constrained by a clear observation of the GZK cutoff\n\\cite{ABGG00}. There are great gains to be made if the data at the\nhighest energies is improved by a few orders of magnitude. The\nprospect of testing extremely high energy physics as well as solving\nthe UHECR puzzle given all the presently proposed models sends a\nstrong message that the challenge is back in the observational arena.\nFortunately, observers have accepted the challenge and \nare building and planning experiments large\nenough to resolve these open questions\n\\cite{watson99}. \n\n\n\\section*{Acknowledgment}\n \nIt has been a great pleasure to have known David N. Schramm and to be\nable to contribute to this volume in his honor. Dave was a kind \nmentor and friend who is missed with {\\it saudades.} Many thanks to\nmy ``ultra-high energy'' collaborators, P. Blasi and R. Epstein,\nfor the careful reading of the manuscript, many ongoing discussions,\nand for providing most of the figures. I am also very grateful to I.\nAlbuquerque, V. Berezinsky, P. Biermann, J. Cronin, G. Farrar, T. Gaisser,\nM. Lemoine, G. Sigl, T. Stanev, A. Watson, and T. Weiler for their\ncomments on the manuscript. This work was supported by NSF through grant\nAST 94-20759 and DOE grant DE-FG0291 ER40606.\n\n\\begin{thebibliography}{9}\n\n\\bibitem{watson99} A. A. Watson, accompaning paper in this\nvolume (1999). \n\n\\bibitem{takeda98} M. Takeda et al., Phys. Rev. Lett.\n81 (1998) 1163. \n\n\\bibitem{takeda99} M. Takeda et al. preprint astro-ph/9902239\n(submitted to Astrophys. J.).\n\n\\bibitem{Haya94} N. Hayashida Phys. Rev. Lett. 73 (1994) 3491.\n\n\n\\bibitem{bird} D. J. Bird et al. Astrophys J. 441 (1995)\n144; Phys. Rev. Lett. 71 (1993) 3401; \nAstrophys. J. 424 (1994) 491.\n\n\\bibitem{L91} M. A. Lawrence, R. J. O. Reid \nand A. A. Watson, J. Phys. G. Nucl. Part. Phys. 17 (1991) 773.\n\n\\bibitem{Yak90} N. N. Efimov et al., Ref. Proc. International Symposium\non {\\it Astrophysical Aspects of the Most Energetic Cosmic Rays}, eds.\nM. Nagano and F. Takahara (World Scientific, Singapore, 1991), p. 20;\n\n\n\\bibitem{hires} D. 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"string": "\\begin{thebibliography}{9}\n\n\\bibitem{watson99} A. A. Watson, accompaning paper in this\nvolume (1999). \n\n\\bibitem{takeda98} M. Takeda et al., Phys. Rev. Lett.\n81 (1998) 1163. \n\n\\bibitem{takeda99} M. Takeda et al. preprint astro-ph/9902239\n(submitted to Astrophys. J.).\n\n\\bibitem{Haya94} N. Hayashida Phys. Rev. Lett. 73 (1994) 3491.\n\n\n\\bibitem{bird} D. J. Bird et al. Astrophys J. 441 (1995)\n144; Phys. Rev. Lett. 71 (1993) 3401; \nAstrophys. J. 424 (1994) 491.\n\n\\bibitem{L91} M. A. Lawrence, R. J. O. Reid \nand A. A. Watson, J. Phys. G. Nucl. Part. Phys. 17 (1991) 773.\n\n\\bibitem{Yak90} N. N. Efimov et al., Ref. Proc. International Symposium\non {\\it Astrophysical Aspects of the Most Energetic Cosmic Rays}, eds.\nM. Nagano and F. Takahara (World Scientific, Singapore, 1991), p. 20;\n\n\n\\bibitem{hires} D. Kieda et al., HiRes Collaboration, Proceeds. 26th\nICRC Salt Lake (1999).\n\n\\bibitem{GZK66} K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G. T. \nZatsepin and V. A. Kuzmin, Sov. Phys. JETP Lett. 4 (1966) 78.\n\n\\bibitem{PSB76SS99} J. L. Puget, F. W. Stecker, and J. H. Bredekamp,\n Astrophys. J. 205 (1976) 638; F. W. Stecker and M. H. Salamon,\nAstrophys. J. 512 (1999) 521.\n\n\\bibitem{bere70PB96} V. S.\nBerezinsky, Yad. Fiz. 11 (1970) 339;\n R. J. Protheroe and P. L. Biermann,\nAstropart. Phys. 6 (1996) 45; erratum ibid. 7 (1997) 181. \n\n\\bibitem{KronVallee} P. P. Kronberg, Rep. Prog. Phys., 57 (1994) 325;\nJ. P. Vall\\'{e}e, Fundamentals of Cosmic Physics, 19 (1997) 1.\n\n\\bibitem{BBO99} P. Blasi, S. Burles, and A. V. Olinto, Astrophys.\nJ. 512 (1999) L79.\n\n\\bibitem{RKB98} D. Ryu, H. Kang and P. L. Bierman, Astron.\nAstrophys. 335 (1998) 19.\n\n\\bibitem{SLB99} G. Sigl, M. Lemoine, and P. Biermann, \nAstropart. Phys. 10 (1999) 141.\n\n\\bibitem{ABGG00} L. Gonzalez-Mestres, Nucl. Phys. B\n(Proc. Suppl.) 48 (1996) 131; S. Coleman and S. L. Glashow,\n Phys. Rev. D 59 (1999) 116008;\n H. Sato and T. Tati, Prog. Theor. Phys. 47 (1972) 1788; \n D. A. Kirzhnits and V. A. Chechin, Sov. J. Nucl. Phys.\n15 (1972) 585; R. Aloisio, P. Blasi, P Ghia,\nand A. Grillo, preprint INFN/AE-99/24.\n\n\\bibitem{hillas84} A. M. Hillas, Ann. Rev. Astron.\nAstrophys. 22 (1984) 425.\n\n\\bibitem{BBDGP90} V. S. Berezinsky, S.V. Bulanov, V. A. Dogiel, \nV. L. Ginzburg, and V. S. Ptuskin, Astrophysics of Cosmic Rays,\n(Amsterdam: North Holland, 1990).\n\n\\bibitem{gaisser90} T. K. Gaisser, {\\it Cosmic Rays and Particle\nPhysics}, Cambridge University Press (Cambridge, England, 1990).\n\n\\bibitem{bland99} R. D. Blandford, e-print astro-ph/9906026,\n {\\it Particle Physics and the Universe}, eds. Bergstrom,\nCarlson and Fransson (Physica Scripta, World Scientific, 1999).\n\n\\bibitem{berez99} V. S. Berezinsky, Nucl.Phys. (Proc.Suppl.) 70 (1999)\n419. \n\n\\bibitem{BS99} P. Bhattacharjee and G. Sigl, preprint\nastro-ph/9811011, Phys. Reps. in press.\n\n\\bibitem{cronin92} J. W. Cronin, Nucl. Phys. B. (Proc. 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astro-ph0002007
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"string": "\\documentstyle[12pt]{article}\n\\textheight 9in\n\\textwidth 6.5in\n\\bibliography{unsrt}\n\\renewcommand{\\baselinestretch}{2}\n\\begin{document}\n\\begin{center}\n{\\bf {\\Large {The Cosmological Quark-Hadron Transition and \\\\\nMassive Compact Halo Objects}}}\\\\\n\\vskip 0.2in\nShibaji Banerjee$^a$, Abhijit Bhattacharyya$^b$, Sanjay K. Ghosh$^c$, Sibaji \nRaha$^{a,d}$ \\\\and \\\\ Bikash Sinha$^{b,e}$\\\\\n\\end{center}\n\\vskip 0.2in\n\\noindent\n$^a$ Physics Department, Bose Institute, 93/1, A.P.C. Road, Calcutta 700 009, \nINDIA\\\\\n$^b$ Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Calcutta 700 064, \nINDIA\\\\\n$^c$ Theory Group, TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. V6T 2A3, \nCANADA\\\\\n$^d$ Nuclear Theory Group, Brookhaven National Laboratory, Bldg. 510A, Upton, \nLong Island, New York 11973-5000, USA\\\\\n$^e$ Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Calcutta 700 064,\nINDIA \n\\vskip 0.2in\n\\noindent\n{\\bf {One of the abiding mysteries in the so-called standard cosmological \nmodel is the nature of the dark matter. It is universally accepted that \nthere is an abundance of matter in the universe which is non-luminous, due to \ntheir very weak interaction, if at all, with the other forms of matter, \nexcepting of course the gravitational attraction. Speculations as to the \nnature of dark matter are numerous, often bordering on exotics, and searches\nfor such exotic matter is a very active field of astroparticle physics at the\ndawn of the new century. Nevertheless, in recent years, there has been \nexperimental evidence \\cite{alcock,aubourg} for at least one form of dark \nmatter - the massive compact halo objects detected through gravitational \nmicrolensing effects proposed by Paczynski some years ago \\cite{pac}. To \ndate, no clear consensus as to what these objects, referred to in the \nliterature as well as in the following by the acronym MACHO, are made of; \nfor a brief discussion of some of the suggestions, see below. In this work, \nwe show that they find a natural explanation as leftover relics from the \n{\\it putative} first order cosmic quark - hadron phase transition that is \npredicted by the standard model of particle interactions to have occurred \nduring the microsecond epoch of the early universe.}} \n\\par\nSince the first discovery of MACHO only a few years ago, a lot of effort has \nbeen spent in studying them observationally, as well as theoretically. It is \nbeyond the scope of the present work to cite them adequately; see, for \nexample, Sutherland \\cite{sut}. Based on about 14 Milky way halo MACHOs \ndetected in the direction of the Large Magellanic Cloud (we are not addressing\nthe events found toward the galactic bulge), the most probable mass estimate \n\\cite{sut} for MACHOs is in the vicinity of 0.5$M_{\\odot}$, substantially \nhigher than the fusion threshold of 0.08$M_{\\odot}$. Assuming that MACHOs \nare subject to the limit on total baryon number imposed by the Big Bang \nNucleosyntheis (BBN), there have been suggestions that they could be white \ndwarfs \\cite{fields}. It is difficult to reconcile this with the absence of \nsufficient active progenitors of appropriate masses in the galactic halo. On \nthe other hand, there have been suggestions \\cite{schramm,jedamzik} that they\ncould be primordial black holes (PBHs) ($\\sim$ 1$M_{\\odot}$), arising from \nhorizon scale fluctuations triggered by pre-existing density fluctuations \nduring the cosmic quark - hadron phase transition. \nWhile this would not violate the BBN limits on baryon number, the Hawking \nradiation from such primordial black holes would interfere with the observed \n$\\gamma$ background, which is thought to be reasonably well understood. It is \nthus safe to conclude that the nature of MACHOs continues to be dark, in the \nsense of begging elucidation.\n\\par\nWe propose that the MACHOs are not subject to the BBN limit on baryon number,\ninsofar as they do not participate in the BBN process, just like the PBHs. On \nthe other hand, they do not radiate, via the Hawking process or otherwise,\nhaving evolved out of the quark nuggets which could have been formed in the\ncosmic quark - hadron phase transition, at a temperature of $\\sim$ 100 MeV\nduring the microsecond era in the history of the early universe. In a \nseminal work in 1984, Witten \\cite{wit} argued that strange quark matter\ncould be the {\\it true} ground state of {\\it Quantum Chromodynamics} (QCD),\nthe underlying field theory of strong interactions and that in a first \norder phase transition from quark - gluon matter to hadronic matter, a \nsubstantial amount of baryon number could be trapped in the quark phase \nwhich could evolve into strange quark nuggets (SQNs) through weak \ninteractions. QCD - motivated studies of baryon evaporation from SQN-s have \nestablished \\cite{pijush,sumiyoshi} that primordial SQN-s with baryon \nnumbers above $\\sim$ 10$^{40 - 42}$ would indeed be cosmologically stable. \nMore recently, some of the present authors have shown that without much \nfine tuning, these stable SQNs could provide the entire closure density \n($\\Omega \\sim$ 1) \\cite{apj} and in a subsequent work, some of us have \ncalculated the distribution of SQN-s produced in the (first order) cosmic \nQCD transition \\cite{abhijit1,abhijit2} for various nucleation models, with \nthe result that for a reasonable set of parameters, the distribution is \nrather sharply peaked at values of baryon number ($\\sim$ 10$^{42-44}$), \nevidently in the stable sector. It was also seen that there were almost no \nSQNs with baryon number exceeding 10$^{46-47}$, comfortably lower than the \nhorizon limit of 10$^{49}$ baryons at that time.\n\\par\nIt is therefore most relevant to investigate the fate of these SQNs and \ntheir implications on the later evolution of the universe. While they have\nenormous appetite for neutrons, becoming more and more strongly bound in the\nprocess, the total surface area of these large SQNs is not big enough \nto absorb so many neutrons as to interfere with BBN \\cite{madsen}. They\nremain in equilibrium upto the neutrino decoupling temperature $T_{\\nu} \\sim$ \n1 MeV beyond which they freeze out. From then on, they are subject only to \nthe gravitational interaction. Unlike the usual baryons which are bound by the \nphoton pressure till the recombination era, SQNs become free to collapse at\ntemperatures below $\\sim$ 1 MeV. Let us thus roughly estimate the number of \nSQNs contained within the Jeans length at a temperature of 1 MeV. For our\npresent purpose, we take the SQNs to have the same common mass of 10$^{44}$\nwith an abundance of 10$^7$ at T $\\sim$ 100 MeV \\cite{apj}. \n\\par\nA measure of the Jeans length for the present purpose may be obtained without \nhaving recourse to the usual hydrodynamic prescription, just by demanding \nthat the total gravitational energy in the Jeans volume should be greater \nthan or equal to the pressure energy :\n\\begin{equation}\nG(\\frac{4}{3} \\pi R_J^3 \\rho_r)^2/R_J = v_s^2 \\rho_r \\frac{4}{3} \\pi R_J^3\n\\end{equation}\nwhere the subscript $r$ to $\\rho$ indicates that the universe is still \nradiation dominated and $v_s$ stands for the velocity of sound (=$\\frac{1}{\n\\sqrt{3}}$). We then have : \n\\begin{equation}\nR_J = \\frac{m_{pl}}{\\sqrt{{4 \\pi \\rho_r}}} \\sim 1.633 t\n\\end{equation}\nwhich is just less than the distance to the horizon $d_H (\\sim 2t$ in the \nradiation era \\cite{kolb}). It thus seems that a general relativistic \ntreatment is not strictly required, as was to be somewhat expected at least \nfor the SQNs, given their enormous mass. \n\\par\nThe number of SQNs within the horizon as a function of temperature is given \nby $ N_N = 10^7 \\left( \\frac{100 MeV}{T}\\right )^3$ so that the density \nof SQNs is $n_N = N_N / V_H = N_N / \\left( \\frac{4}{3} \\pi (2t)^3 \\right)$. \nOne can readily see that the total number of SQNs in $R_J$ at $T$ = 1 MeV \nturns out to be $\\sim$ 0.58 X 10$^{12-13}$. If all these SQNs clump into one, \nit would then have a mass of $\\sim$ 0.5M$_{\\odot}$, making them ideal \nMACHO candidates. \n\\par\nIt is obvious that there can be no further clumping of these already clumped \nSQNs; at subsequent times, the density of such objects would be so low that \nit would be hard to find more than one or two of them within one Jeans radius.\nA very crude estimate of the collapse time of all the SQNs within $R_J$ can \nbe carried out to ascertain that indeed such a timescale is comparable to the\nlifetime of the universe at that temperature.\n\\par\nWe conclude that gravitational clumping of the primordial SQNs formed in a\nfirst order cosmic quark - hadron phase transition appears to be a plausible \nexplanation for the observed halo MACHOs. Needless to say, the estimates \npresented here should serve only as guidelines and a detailed simulation would\nof course be needed before any firm conclusions can be drawn. Whether the \nspatial as well as the size distributions of the SQNs can serve as the \nnecesary initial fluctuations need also to be carefully looked into. Such a\nstudy is on our present agenda and we hope to present the results in due \ncourse. \n\\par \nThe work of S.B. was supported in part by the Council of Scientific \\& \nIndustrial Research (CSIR), New Delhi. SR would like to thank the Nuclear \nTheory group at Brrokhaven National Laboratory for their warm hospitality \nwhere part of this work was carried out. \n \n\n\\begin{thebibliography}{99}\n\\bibitem{alcock} Alcock, C. {\\it et al.} (MACHO Collaboration) 1993, {\\it \nNature (London)} {\\bf {365}} 621\n\\bibitem{aubourg} Aubourg, E. {\\it et al.} (EROS Collaboration) 1993, {\\it\nNature (London)} {\\bf {365}} 623\n\\bibitem{pac} Paczynski, B., 1986 {\\it Astrophys. J.} {\\bf {304}} 1\n\\bibitem{sut} Sutherland, W., 1998 {\\it astro - ph} / 9811185\n\\bibitem{fields} Fields, B. D., Freese, K. and Graff, D. S., 1998 {\\it New\nAstron.} {\\bf 3} 347\n\\bibitem{schramm} Schramm, D. N., 1998 in : {\\it Physics and Astrophysics of \nQuark - Gluon Plasma (ICPA-QGP'97)} (Eds. Sinha, B., Viyogi, Y. P. and \nSrivastava, D. K.), 29, Narosa Publishing, New Delhi.\n\\bibitem{jedamzik} Jedamzik, K., 1998 {\\it Phys. Rep.} {\\bf {307}} 155\n\\bibitem{wit} Witten, E., 1984 {\\it Phys. Rev.} {\\bf {D30}} 272\n\\bibitem{pijush} Bhattacharjee, P., Alam, J., Sinha, B. and Raha, S., 1993 \n{\\it Phys. Rev.} {\\bf {D48}} 4630\n\\bibitem{sumiyoshi} Sumiyoshi, K. and Kajino, T, 1991 {\\it Nucl. Phys. (Proc. \nSuppl.)} {\\bf {24}} 80\n\\bibitem{apj} Alam, J., Raha, S. and Sinha, B., 1999 {\\it Astrophys. J.}\n{\\bf 513} 572\n\\bibitem{abhijit1} Bhattacharyya, A. {\\it et al.} 1999 {\\it Nucl. Phys.}\n{\\bf A661} 629c \n\\bibitem{abhijit2} Bhattacharyya, A. {\\it et al.} 2000 {\\it Phys. Rev. D} \n(in press)\n\\bibitem{madsen} Madsen, J. and Riisager, K., 1985 {\\it Phys. 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{
"name": "astro-ph0002007.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{alcock} Alcock, C. {\\it et al.} (MACHO Collaboration) 1993, {\\it \nNature (London)} {\\bf {365}} 621\n\\bibitem{aubourg} Aubourg, E. {\\it et al.} (EROS Collaboration) 1993, {\\it\nNature (London)} {\\bf {365}} 623\n\\bibitem{pac} Paczynski, B., 1986 {\\it Astrophys. J.} {\\bf {304}} 1\n\\bibitem{sut} Sutherland, W., 1998 {\\it astro - ph} / 9811185\n\\bibitem{fields} Fields, B. D., Freese, K. and Graff, D. S., 1998 {\\it New\nAstron.} {\\bf 3} 347\n\\bibitem{schramm} Schramm, D. N., 1998 in : {\\it Physics and Astrophysics of \nQuark - Gluon Plasma (ICPA-QGP'97)} (Eds. Sinha, B., Viyogi, Y. P. and \nSrivastava, D. K.), 29, Narosa Publishing, New Delhi.\n\\bibitem{jedamzik} Jedamzik, K., 1998 {\\it Phys. Rep.} {\\bf {307}} 155\n\\bibitem{wit} Witten, E., 1984 {\\it Phys. Rev.} {\\bf {D30}} 272\n\\bibitem{pijush} Bhattacharjee, P., Alam, J., Sinha, B. and Raha, S., 1993 \n{\\it Phys. Rev.} {\\bf {D48}} 4630\n\\bibitem{sumiyoshi} Sumiyoshi, K. and Kajino, T, 1991 {\\it Nucl. Phys. (Proc. \nSuppl.)} {\\bf {24}} 80\n\\bibitem{apj} Alam, J., Raha, S. and Sinha, B., 1999 {\\it Astrophys. J.}\n{\\bf 513} 572\n\\bibitem{abhijit1} Bhattacharyya, A. {\\it et al.} 1999 {\\it Nucl. Phys.}\n{\\bf A661} 629c \n\\bibitem{abhijit2} Bhattacharyya, A. {\\it et al.} 2000 {\\it Phys. Rev. D} \n(in press)\n\\bibitem{madsen} Madsen, J. and Riisager, K., 1985 {\\it Phys. Lett.}\n{\\bf {B158}} 208\n\\bibitem{kolb} Kolb, E. W. and Turner, M. S., 1990 {\\it The Early Universe},\nAddison-Wesley Publishing Co., Redwood City. \n \n\\end{thebibliography}"
}
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astro-ph0002008
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ISO-SWS spectroscopy of NGC 1068 \footnote{Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, the Netherlands and the United Kingdom) with the participation of ISAS and NASA.}
|
[
{
"author": "D.~Lutz\\footnote{Max-Planck-Institut f\\\"ur extraterrestrische Physik, Postfach 1603, 85740 Garching, Germany}"
},
{
"author": "E.~Sturm$^2$"
},
{
"author": "R.~Genzel$^2$"
},
{
"author": "A.F.M.~Moorwood\\footnote{European Southern Observatory, Karl-Schwarzschild-Stra\\ss\\/e 2, 85748 Garching, Germany}"
},
{
"author": "A.~Sternberg$^5$"
}
] |
We present ISO-SWS spectroscopy of NGC 1068 for the complete wavelength range 2.4 to 45$\mu$m at resolving power $\sim$1500. Selected subranges have been observed at higher sensitivity and full resolving power $\sim$2000. We detect a total of 36 emission lines and derive upper limits for 13 additional transitions. Most of the observed transitions are fine structure and recombination lines originating in the narrow line region (NLR) and the inner part of the extended emission line region. %An electron density of $n_e=2000$\,cm$^{-3}$ represents the average %conditions of that region. We compare the line profiles of optical lines and reddening-insensitive infrared lines to constrain the dynamical structure and extinction properties of the narrow line region. The most likely explanation of the considerable differences found is a combination of two effects. (1) The spatial structure of the NGC\,1068 narrow line region is a combination of a highly ionized outflow cone and lower excitation extended emission. (2) Parts of the narrow line region, mainly in the receding part at velocities above systemic, are subject to extinction that is significantly suppressing optical emission from these clouds. Line asymmetries and net blueshifts remain, however, even for infrared fine structure lines suffering very little obscuration. This may be either due to an intrinsic asymmetry of the NLR, as perhaps also suggested by the asymmetric radio continuum emission, or due to a very high column density obscuring component which is hiding part of the narrow line region even from infrared view. We present detections and limits for 11 rotational and ro-vibrational emission lines of molecular hydrogen (H$_2$). They arise in a dense molecular medium at temperatures of a few hundred Kelvin that is most likely closely related to the warm and dense components seen in the near-infrared H$_2$ rovibrational transitions, and in millimeter wave tracers (CO, HCN) of molecular gas. Any emission of the putative pc-scale molecular torus is likely overwhelmed by this larger scale emission. In companion papers we use the SWS data to derive the spectral energy distribution emitted by the active nucleus of NGC\,1068 (\cite{alexander00}), to put limits on infrared emission from the obscured broad line region (\cite{lutz00}), and discuss the continuum and its features in conjunction with SWS spectra of other galaxies (\cite{sturm00}).
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[
{
"name": "obspaper.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4]{article}\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\\slugcomment{Accepted for publication in the Astrophysical Journal}\n\n% Authors may supply running head information\n\n\\lefthead{}\n\\righthead{ISO-SWS spectroscopy of NGC 1068}\n\n\\begin{document}\n\n\\title{ISO-SWS spectroscopy of NGC 1068\n\\footnote{Based on observations with ISO, an\n ESA project with instruments funded by ESA Member States (especially the PI\n countries: France, Germany, the Netherlands and the United Kingdom) with the\n participation of ISAS and NASA.}\n }\n\n\\author{D.~Lutz\\footnote{Max-Planck-Institut f\\\"ur extraterrestrische Physik,\n Postfach 1603, 85740 Garching, Germany},\n E.~Sturm$^2$,\n R.~Genzel$^2$,\n A.F.M.~Moorwood\\footnote{European Southern Observatory,\n Karl-Schwarzschild-Stra\\ss\\/e 2, 85748 Garching, Germany},\n T.~Alexander\\footnote{Institute for Advanced Study, Olden Lane,\n Princeton, NJ 08540, USA},\n H.~Netzer\\footnote{School of Physics and Astronomy and Wise Observatory,\n Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv\n University, Ramat Aviv, Tel Aviv 69978, Israel},\n A.~Sternberg$^5$\n }\n\n\n\n\\begin{abstract}\nWe present ISO-SWS spectroscopy of NGC 1068 for the complete wavelength \nrange 2.4\nto 45$\\mu$m at resolving power $\\sim$1500. Selected subranges have been\nobserved at higher sensitivity and full resolving power $\\sim$2000. We \ndetect a total of 36 emission lines\nand derive upper limits for 13 additional transitions. Most of the observed \ntransitions are fine structure and recombination lines originating in the\nnarrow line region (NLR) and the inner part of the extended emission line region.\n%An electron density of $\\rm n_e=2000$\\,cm$^{-3}$ represents the average \n%conditions of that region.\n\nWe compare the line profiles of optical lines and reddening-insensitive \ninfrared lines to constrain the dynamical structure and extinction\nproperties of the narrow line region.\nThe most likely explanation of the considerable differences found is\na combination of two effects. (1) The spatial structure of the NGC\\,1068 \nnarrow line region is a combination of a highly ionized outflow \ncone and lower excitation extended emission. (2) Parts of the narrow line\nregion, mainly in the receding part at velocities above systemic, are subject \nto extinction that is significantly suppressing optical emission from\nthese clouds. Line asymmetries and net blueshifts remain, however, even for\ninfrared fine structure lines suffering very little obscuration. This may\nbe either due to an intrinsic asymmetry of the NLR, as perhaps also suggested \nby the asymmetric radio continuum emission, or due to a very high column \ndensity obscuring component which is hiding part of the narrow line region\neven from infrared view. \n\nWe present detections and limits for 11 rotational and ro-vibrational emission \nlines of molecular hydrogen (H$_2$). They arise in a dense molecular medium at \ntemperatures of a few hundred Kelvin that is most likely closely related to\nthe warm and dense components seen in the near-infrared H$_2$ rovibrational \ntransitions, and in millimeter wave tracers (CO, HCN) of molecular gas. Any \nemission of the putative\npc-scale molecular torus is likely overwhelmed by this larger scale\nemission.\n\nIn companion papers we use the SWS data to derive the spectral energy \ndistribution\nemitted by the active nucleus of NGC\\,1068 (\\cite{alexander00}), to put\nlimits on infrared emission from the obscured broad line region \n(\\cite{lutz00}), and discuss\nthe continuum and its features in conjunction with SWS spectra of other galaxies\n(\\cite{sturm00}).\n\\end{abstract}\n\n\\keywords{galaxies: individual (NGC 1068) --- galaxies: Seyfert--- \ninfrared: ISM: lines and bands}\n\n\\section{Introduction}\n\nNGC\\,1068 is one of the nearest and probably the\nmost intensely studied Seyfert 2 galaxy. Observations in all wavelength\nbands from radio to hard X-rays have formed a uniquely detailed picture\nof this object.\nNGC 1068 has played a key role in the development of unified scenarios\nfor Seyfert 1 and Seyfert 2 galaxies (\\cite{antonucci85}),\nin the study of molecular gas in the nuclear region of Seyferts\n(e.g. \\cite{myers87}; \\cite{tacconi94}),\nand in elucidating the importance of star formation activity coexistent\nwith the AGN, both on\nlarger (e.g. \\cite{telesco88}) and smaller (\\cite{macchetto94}; \\cite{thatte97})\nscales. NGC 1068 hosts a prominent Narrow Line Region (NLR) that is \napproximately cospatial with a linear radio source with two lobes\n(\\cite{wilson83}). The narrow emission line region has been extensively\ncharacterized from subarcsecond clouds probed by HST (\\cite{evans91};\n\\cite{macchetto94}), the \n$\\approx 5$ arcseconds of the NLR hosting most of the line flux\n(e.g. \\cite{walker68}; \\cite{shields75}; \\cite{cecil90}), and\nthe ionization cone and extended emission line region \n(\\cite{pogge88}; \\cite{unger92}) extending to radii of at least 30\\arcsec\\/ \n(1\\arcsec\\/ = 72 pc at the distance of 14.4 Mpc, \\cite{tully88}). \nThe velocity field is complex, with an ensemble of rapidly\nmoving clouds dominating the inner arcseconds and a more quiescent rotation\npattern prevailing at larger radii (e.g. \\cite{walker68}; \\cite{alloin83};\n\\cite{meaburn86}; \\cite{cecil90}). While most of the excitation of the narrow\nline region and the extended emission line region is likely through \nphotoionization\nby the central AGN (\\cite{marconi96}), high resolution observations suggest \nkinematic disturbance and possibly shock excitation of regions close to the \nradio outflow (e.g. \\cite{axon98}). \n\nWith ESA's {\\it Infrared Space Observatory} ISO, sensitive mid-infrared \nspectroscopy of AGNs became possible, with detections of a broad range \nof low- and high-excitation fine structure lines, recombination lines,\nand pure rotational lines from such sources\n(\\cite{moorwood96}; \\cite{sturm99}; \\cite{alexander99})).\nModel predictions of the mid-IR spectra of AGN had been obtained prior to \nISO (e.g. \\cite{spinoglio92}), but observations were restricted by limited\nsensitivity and focussed primarily on the continuum emission and broad\nfeatures rather than emission lines. \n\nIn this paper, we present the ISO-SWS\nspectra of NGC\\,1068 and draw conclusions on the structure of\nthe narrow line region that can be obtained mainly from the comparison\nof optical and reddening-insensitive infrared lines, and discuss the \nnature of the mid-infrared molecular hydrogen emission.\nThe ISO-SWS data of NGC\\,1068 are analysed further in several \ncompanion papers.\nAlexander et al. (2000) use photoionization modelling based on the ISO fine \nstructure line set and other NLR lines to model the shape of the AGN's spectral\nenergy distribution.\nLutz et al. (2000) analyze limits on emission from the obscured broad line \nregion.\nFinally, Sturm et al. (2000) discuss continuum energy distribution and \nfeatures of NGC\\,1068 in conjunction with ISO-SWS spectra of other galaxies.\n\nOur paper is organised as follows. In \\S 2 we discuss the ISO-SWS observations\nand data reduction. \\S 3 presents results and implications of the\ndensity of the narrow line region. \\S 4 uses infrared line profiles in \ncomparison to optical ones to constrain the structure of the narrow line region.\nWe discuss the mid-infrared molecular hydrogen emission in \\S 5 and summarize\nin \\S 6. \n\n%\n%\n\\section{Observations and data reduction}\n\\label{sect:obs}\n\nWe have \nused the Short Wavelength Spectrometer SWS (\\cite{degraauw96}) on board\nthe {\\it Infrared Space Observatory} ISO (\\cite{kessler96})\nto observe the nuclear region of NGC\\,1068. In \nTable~\\ref{tab:listobs} we present a log of our observations. We carried\nout observations in the\nSWS01 mode which provides a full 2.4 -- 45$\\mu$m scan at slightly reduced \nspectral resolving power, as well as\n observations in the SWS02 and SWS06 modes targeted at full resolution \nobservations of individual lines or short ranges.\nBecause of the large width of the emission lines in the NGC\\,1068 narrow line\nregion, we have mostly relied on the SWS06 mode which can be set up to \nprovide\nwider continuum baselines than standard SWS02 line scans. We supplement\nobservations from our ISO guaranteed and open time with serendipitous \ninformation on some fine structure lines obtained in another ISO project\n(PI G.~Stacey), the main results of which are to be presented elsewhere.\n\nTable~\\ref{tab:listobs} includes also the position angle of the long\naxis of the SWS apertures for the various observations. Our \npointing was always centered on the nucleus of NGC 1068, but the SWS apertures\nrange from 14\\arcsec$\\times$20\\arcsec\\ at short wavelengths to \n20\\arcsec$\\times$33\\arcsec\\ at the longest wavelengths (\\cite{degraauw96}).\nAt the long wavelengths, we partly include the $\\sim$15\\arcsec\\ \nradius ring of star forming regions encircling the nucleus of NGC 1068. \nThe apertures were always oriented in approximately north-south (or south-north)\ndirection, with position angles between -11\\arcdeg\\/ and -23\\arcdeg\\/.\n\nWe have analyzed the data using the SWS Interactive Analysis (IA) system\n(\\cite{lahuis98}; \\cite{wieprecht98})\nand calibration files of July 1998. A preliminary account of part of\nthe observations is given by Lutz et al. (1997). Since then, calibration\nfiles have been updated for wavelength calibration and in particular\nwith respect to the SWS relative spectral \nresponse function, leading to more reliable intercalibration\nbetween the `AOT bands' forming a full SWS spectrum. \nOur data reduction started in the standard way and \ncontinued with steps of (interactive) dark current \nsubtraction and matching up- and downscans. We eliminated data from\nthose detectors of band 3 that were most noisy during a particular revolution,\nand from interactively identified regions\nwith single detector signal jumps in bands 1 and 2, and simultaneous \n12-detector signal\njumps in band 3. After relative spectral response correction and flux \ncalibration, we `flatfielded' the 12 detectors of a band to a consistent level,\ncorrected for the ISO velocity, and extracted the AAR data product. Redundant \nscans\nof the same line were shifted to a consistent level. Single-valued spectra were\nproduced by kappa-sigma clipping the AAR dot cloud and rebinning it with a \nresolution of typically 3000 which does not lead to significant smearing for\nNGC\\,1068 linewidths. For those ranges affected by fringes, the single-valued \nspectra were defringed using the iterative sine fitting option of the aarfringe\nmodule within the SWS Interactive Analysis.\n\nThe large number of observations required special treatment of redundant data.\nIn addition, observations from revolution 285 where apparently affected by a\nslight ($\\approx\\/2-3\\arcsec$?) pointing problem, which occured\noccasionally in the earlier phase of \nthe ISO mission. Since SWS beam profiles in some AOT bands are peaked and \nslightly offset with respect to the nominal pointing (A. Salama, 1999, \npriv. comm.), modest pointing offsets can cause \nnoticeable flux losses in some AOT bands and resulting band mismatches. Such\nmismatches were evident in revolution 285 band 3 data. Since most of the \nNGC 1068 mid-infrared flux comes from a small region (\\cite{cameron93};\n\\cite{braatz93}; \\cite{bock98}),\nwe corrected for this problem and the small scatter between other observations\nby the following scaling procedure: For the SWS01 full spectrum obtained in\nrevolution 285, the individual AOT bands were scaled\nto obtain both good match at band limits, and good agreement with the\noverall flux level as estimated from our other SWS data and ground-based\nphotometry (\\cite{lebofsky78}; \\cite{rieke75}). At wavelengths below \n10$\\mu$m photometry from different epochs should be used with great caution \nbecause of the known\nvariability (\\cite{glass97}), our fluxes are however in good agreement with\nthe photometry of Glass for the ISO epoch. All other data were then scaled\nto this SWS01 spectrum by the ratio inferred from the continuum flux densities.\nWe believe the final flux scale to be accurate within the 20-30\\% typical for\nSWS data (\\cite{schaeidt96}).\n\nAccurate wavelength calibration of the SWS grating spectrometer is central\nfor part of our line profile analysis, since shifts between lines in \nNGC\\,1068 tend to be of the order 300\\,km/s or less (\\cite{marconi96}).\nValentijn et al. (1996) deduce an accuracy of $\\sim$30km/s from extensive \ncalibrations during the SWS performance verification phase. Since then, \na slow secular drift in SWS wavelength calibration has been calibrated to \nsimilar accuracy. We have tested the \nwavelength calibration of the NGC\\,1068 data, using identical calibration files\nto analyze spectra of the planetary nebulae NGC\\,7027 and NGC\\,6543 taken close\nto revolution 633 where some of the most important NGC\\,1068 lineprofiles were\ntaken. We confirm the excellent accuracy from these observations, the largest\nerror not exceeding the value given by Valentijn et al. (1996). This test and\nthe good internal consistency of velocities measured in NGC\\,1068 for \ndifferent lines \nfrom the same species spanning most of the SWS wavelength range \n(e.g. H$_2$, see Table~\\ref{tab:lineflux}) leads us to adopt an upper limit of \n50 km/s for any systematic errors in our wavelength scale, taking into\naccount a margin for mispointing. \n\nTwo emission features, which were\ntentatively detected in the preliminary analysis of Lutz et al. (1997)\ncould not be confirmed with the larger observational database and the\nimproved calibration. A broad\nemission feature near 19$\\mu$m, which might be interpreted as silicate\nemission, is not confirmed with the new spectral response calibration.\nAn emission line at 28$\\mu$m was identified as an unusually strong H$_2$ S(0) \nline. This identification \nwas later found suspect\nbecause of the line's larger width compared to the other H$_2$ lines\nobserved in NGC 1068. \nThe line was not confirmed in deeper follow up observations.\nDetailed inspection of the original data indeed\nshows that it is an artifact of a highly unlikely coincidence of detector \n`glitches' at the expected wavelength of the S(0) transition.\n \n%\n\\section{Results}\n\\label{sect:res}\n\nThe 2.4-45$\\mu$m full spectrum of NGC\\,1068 is displayed in \nFigure~\\ref{fig:fullspec}. Some solid state features \nare superposed on the strong AGN-heated mid-infrared continuum.\nThese include 3.4$\\mu$m C-H absorption, 9.6$\\mu$m silicate absorption, and \n7.7, 8.6, 11.3$\\mu$m `PAH' emission\n(see Sturm et al (2000) for a discussion in conjunction with other SWS\nspectra of galaxies).\nBright fine structure emission lines, mainly originating in the narrow\nline region, are already visible in the full spectrum.\nFigures~\\ref{fig:ionspec} and \\ref{fig:h2spec} show individual emission\nlines. The display range is chosen to be $\\pm$2500\\,km/s around systemic \nvelocity for recombination and\nfine structure lines, and $\\pm$1000\\,km/s for the much narrower molecular \nlines. Throughout this paper, we adopt a systemic velocity of 1148km/s\n(\\cite{brinks97}). Good rest wavelengths are available for the observed \ntransitions\nfrom the literature and from recent ISO determinations (\\cite{feuchtgruber97}).\nMany lines were observed repeatedly, Figures~\\ref{fig:ionspec} and \n\\ref{fig:h2spec}\nshow only the best quality data. Table~\\ref{tab:lineflux} lists the measured\nline fluxes and limits, presenting averages of independent measurements with\nhigher weight given to better data. Table~\\ref{tab:lineflux} includes \nalso upper limits for some transitions (not shown in \nFigure~\\ref{fig:ionspec}) that were observed with good enough signal-to-noise \nratio. We list such limits for \ntransitions from elements like Na or Ar where other ionization stages are\ndetected.\n\nFluxes of relatively narrow lines,\nfor example from H$_2$ and [\\ion{Si}{2}], were measured by direct integration\nof the continuum subtracted line profiles. The large linewidth makes this\nprocedure error prone for faint lines from the NLR, where continuum definition\nis the main source of measurement error. \nThe relative constancy of NLR line profiles\nover a wide range of lower ionization potentials (see below) lead us to adopt\na different procedure to measure fluxes for the NLR lines: We derived a simple\ntwo-gaussian template from the brightest NLR lines\n([\\ion{O}{4}] 25.89$\\mu$m (note nearby [\\ion{Fe}{2}]),\n[\\ion{Ne}{5}] 24.32$\\mu$m, [\\ion{Ne}{6}] 7.652$\\mu$m) and used fits of this \ntemplate (Figure~\\ref{fig:allprof}) plus\na linear continuum to measure the fluxes of fainter NLR lines. The two\ngaussian components have FWHM 333 and 1246\\,km/s, peak ratio narrow/wide \n1.34, and the wider component is blueshifted by 100km/s. In fitting, we varied\nonly continuum flux and slope, total line flux, and total velocity. \nThe fluxes measured this way\nagreed very well ($\\lesssim$10\\%) with those determined by direct integration \nnot only for the lines used to derive the template, but also for other bright\nNLR lines like [\\ion{Mg}{8}]\\,3.028$\\mu$m. The fit thus preserves the \nfluxes for bright lines and is preferable for faint lines\nwhere continuum subtraction is the dominant source of error. \n\nFor the blended lines of [\\ion{Mg}{7}] and H$_2$ (0-0) S(7) near 5.5$\\mu$m,\nwe list the fluxes resulting from a tentative gaussian fit using\ntwo components for [\\ion{Mg}{7}] and one component for H$_2$.\nThe uncertainty of the S(7) flux is particularly large,\nup to a factor 2. The H$_2$ excitation diagram\n(Figure~\\ref{fig:excit}) in fact suggests that it may be overestimated.\nSimilar caution has to be applied to\nthe tentative flux listed for the [\\ion{Fe}{2}] 25.99$\\mu$m line. A slight\nshoulder appears in the long wavelength wing of the [\\ion{O}{4}] \n25.89$\\mu$m transition, but its flux is very uncertain and may at best be good\nenough to serve for consistency checks with other [\\ion{Fe}{2}] lines. \nFeuchtgruber et al. (1997) discuss evidence that the lines of [\\ion{Ar}{3}]\nand [\\ion{Mg}{7}] at 9.0$\\mu$m are blended at the resolution of SWS.\nWe list only a total flux in Table~\\ref{tab:lineflux}.\n\nWe detect a weak unidentified feature at rest wavelength about 7.555$\\mu$m. \nIf real, its width would suggest a NLR origin.\nAn instrumental origin due to an imperfection of the relative spectral response\nfunction (RSRF) cannot be excluded but is unlikely since the RSRF shows\nvery little structure at that wavelength. Also, instrumental `ghosts' to \nstrong SWS \nlines are not known at such a level. \nA possible interpretation of this feature is that it is a blueshifted\n($\\sim$3800 km/s) component of the nearby strong [\\ion{Ne}{6}] line containing\n$\\sim$1.5\\% of the total line flux. Residual instrumental fringing prevents\nus from looking for analogous components near other strong lines such\nas [\\ion{Ne}{5}] or [\\ion{O}{4}].\nAt this point, the \nfeature must be considered as possibly real but without an obvious identification\nby a line that is potentially strong in AGN spectra. Also, no line is seen at\nthis wavelength in archival ISO spectra of the high excitation planetary nebula\nNGC\\,6302.\n\nWe postpone a detailed discussion of the line profiles to \nsection~\\ref{sect:prof}.\nFigures~\\ref{fig:ionspec} and \\ref{fig:h2spec} already suggest, however, \nthat we are dealing with \nthree distinct components: Fine structure transitions from species with\nlower ionization potential $\\gtrsim$ 40 eV (i.e. from [\\ion{Ne}{3}] upwards)\nhave similar wide profiles and apparently originate in the NLR. \nFine structure lines from lower ionization stages, in particular \n[\\ion{Ne}{2}] and [\\ion{S}{3}], are narrower and are most likely\ncontaminated by star formation within their beams. This limits their use\nin modelling of the AGN-excited NLR spectrum (\\cite{alexander00}) \nto upper limits rather than measurements. Inspection of\nFigure~\\ref{fig:ionspec} suggests that the starburst contribution \nstrongly dominates the low excitation lines like [\\ion{S}{3}] 33.48$\\mu$m \nand [\\ion{Si}{2}] 34.81$\\mu$m which\nare measured with the largest aperture. Lines measured with intermediate\napertures like [\\ion{Ne}{2}] 12.81$\\mu$m and in particular [\\ion{S}{3}] \n18.71$\\mu$m still show strong wings and will have a considerable NLR\ncontribution. The smallest line widths are measured\nfor transitions of molecular hydrogen.\n\n\\subsection{Density of the narrow line region}\n\\label{subsect:density}\n\nThe fine structure lines detected by SWS can be used to determine the density \nand, in conjunction with optical forbidden lines, the electron temperature\nof the line emitting gas in the narrow line and coronal line regions. \nDifferences in infrared\nand optical lineprofiles (\\S \\ref{sect:prof}) discourage a \ndetermination of\nelectron temperatures from the integrated fluxes, which would not account\nfor significant variations in extinction across the NLR. A reliable average \ndensity can be determined, however, from the mid-infrared lines alone which\nare insensitive to electron temperature and extinction variations. \nThe contribution of starburst excitation to the density-sensitive forbidden \nlines can be estimated using the large line\nwidth variation between the NLR and the circumnuclear ring of star formation\nregions.\n\nThe most suitable NLR density diagnostic is provided by the ratio of the \n[\\ion{Ne}{5}] transitions at 14.32 and 24.32$\\mu$m. These lines cannot be\ndiluted significantly by circumnuclear star formation since they are undetected\nin starburst galaxies (\\cite{genzel98}). They were\nobserved with the same SWS aperture size and with good signal-to-noise.\nAdopting the same atomic data as Alexander et al. (1999, see also their Figure\n3 for diagrams of several density sensitive ratios) and an electron\ntemperature of 10000\\,K, the observed [\\ion{Ne}{5}] ratio of 1.39 corresponds to\nan electron density $\\rm n_e\\sim 2000$\\,cm$^{-3}$ in the region of the NLR\nwhere species with lower ionization potential near 100eV prevail.\n\nA seemingly discrepant result is obtained from the [\\ion{S}{3}] transitions\nat 18.71 and 33.48$\\mu$m -- the observed ratio of 0.73 is consistent with\nthe low density limit and corresponds to $\\rm n_e\\lesssim 500$\\,cm$^{-3}$.\nBut, Figure~\\ref{fig:ionspec} shows the line profiles of the two transitions\nto be quite different: [\\ion{S}{3}] 18.71$\\mu$m shows strong wide wings\nand is apparently NLR-dominated with small starburst contamination. In \ncontrast, the larger aperture of [\\ion{S}{3}] 33.48$\\mu$m collects more\nemission from the starburst ring showing up as a strong narrow component\nof the profile. If {\\em all} 18.71$\\mu$m emission were from a NLR at \n2000\\,cm$^{-3}$, the NLR contribution to the 33.48$\\mu$m flux would be\nabout 1/3, consistent with the weaker wings of this line. \n\nA similar problem may affect, to a lesser degree, the density sensitive\nratio of the [\\ion{Ne}{3}] transitions at 15.55 and 36.01$\\mu$m.\nThe observed ratio of 8.9 is lower than but probably still consistent \nwith the low \ndensity limit ($\\sim$12) which applies up to the $\\rm n_e\\sim 2000$\\,cm$^{-3}$ derived\nfrom [\\ion{Ne}{5}]. The modest signal-to-noise ratio of the 36.01$\\mu$m line\nmakes it impossible to use the line profile to assess starburst contamination \nin the large aperture. A crude estimate can be obtained assuming that the ratio\nof {\\em starburst} [\\ion{Ne}{3}] 36.01$\\mu$m and [S\\,III] 33.48$\\mu$m seen\nadditionally in the large aperture is 0.03--0.04 \nas in the prototypical starburst M\\,82 (\\cite{foerster98}). Then, \n$\\gtrsim$10\\%\\ of the 36.01$\\mu$m line would be starburst contamination,\nbringing the ratio closer to its low density limit value.\nThe density in NLR regions dominated by lower excitation species like\n[\\ion{S}{3}] and [\\ion{Ne}{3}] hence appears consistent with that\nfor the higher excitation region containing [\\ion{Ne}{5}].\n\nWith respect to the coronal line region, the observed ratio 0.55 of the \n[\\ion{Si}{9}] lines at 2.584 and 3.936$\\mu$m is close to its low\ndensity limit which implies $\\rm n_e\\lesssim 10^6$\\,cm$^{-3}$. \nThe same limit is found for the Circinus galaxy (\\cite{moorwood96}) and\nNGC 4151 (\\cite{sturm99}). Such a density limit is consistent with all\npopular scenarios for coronal line formation in AGN except for origin in a \nvery dense transition region between NLR and BLR. \n%\n%\n\\section{Line profiles and the structure of the narrow line region}\n\\label{sect:prof}\n\nIntegrated emission lines profiles are an indirect tool to constrain the \ndynamical structure and extinction properties\nof the narrow line region. Different lines probe different parts\nof the NLR and the velocity field is generally far from uniform. \nWith the advent of linear optical detectors, considerable effort was devoted\nto studies of both forbidden and permitted optical line profiles in Seyfert \ngalaxies. \nAlthough there is still no full\nconsensus among different studies of the NLR forbidden lines, the\nemerging picture is as follows.\\\\\n(1) The forbidden lines in most cases\nshow blue asymmetries in the sense of a sharper falloff to the red than to the\nblue. Line centroids are blueshifted with respect to the systemic\nvelocity, whereas line peaks in high resolution spectra are close to systemic\nvelocity. \nThis has been most thoroughly studied in moderate excitation species\nincluding [\\ion{O}{3}] 5007\\AA\\/\n(e.g. \\cite{heckman81}; \\cite{vrtilek85}; \\cite{whittle85a}; \\cite{dahari88}) \nbut holds also for the higher excitation\ncoronal lines (\\cite{penston84}).\\\\\n(2) Line widths and blueshifts often vary between different species \nobserved in the same source. Line profiles appear\nto be correlated with the ionization potential and/or the critical\ndensity. There are indications, but no complete consensus, that the \ncorrelation with the critical density may be the fundamental one\n(e.g. \\cite{pelat81}; \\cite{penston84}; \\cite{whittle85b};\n\\cite{derobertis86}; \\cite{appenzeller88}).\n\nVarious scenarios have been put forward to explain these\ntrends. Most of them invoke extinction to explain blue\nasymmetries, and the most popular ones assume outflow in a dusty\nNLR, with higher excitation species probably originating closer\nto the central source in regions of higher velocity and obscuration.\nIt is obvious that observations of {\\em infrared} NLR emission are a\npowerful independent method to test such scenarios: near- and mid- infrared\nlines suffer more than an order of magnitude less extinction than in the \noptical. The combination of optical and infrared data should hence elucidate\nthe role of dust obscuration.\nComparison of recombination line profiles in the optical with infrared ones\nwould be advantageous because of the relative insensitivity of recombination\nline emissivities to local gas conditions. The line-to-continuum ratio of\nrecombination lines in the infrared is low, however, and better profiles\nare obtained for coronal and fine structure lines which additionally \ncover a wide range of excitations.\nSturm et al. (1999) have presented a first such analysis using ISO-SWS\nobservations of NGC\\,4151. On the basis of the similarity of optical and\ninfrared profiles, they ruled out the most simple scenario of an outflowing\nNLR with pervasive dust, and suggested either a geometrically thin but\noptically highly thick obscuring disk, or an intrinsic asymmetry of the NLR.\n\nBecause of the large flux and width of its `narrow' lines, NGC\\,1068\nis best suited for a line profile analysis at the modest resolving\npower ($\\sim$2000) of ISO-SWS. Optical line profiles have been observed at \nvery high\nresolving power by various groups (e.g. \\cite{pelat80}; \\cite{alloin83};\n\\cite{meaburn86}; \\cite{veilleux91}; \\cite{dietrich98})\nand show complex, multi-peaked structure related to individual cloud \ncomplexes within the narrow line region of NGC\\,1068. \nMarconi et al. (1996) have \nextended this work into the near infrared. At lower resolving power,\nthey do not discriminate the fine details of the best optical profiles\nbut derive the line centroids by Gaussian fits for a large set of near-infrared\nand optical lines. They find that all optical and near-infrared high excitation \nlines are significantly blueshifted with respect to systemic velocity\n($>$200km/s for lower ionization potential $\\gtrsim$ 20eV).\nThey interpret this significant trend as a consequence of non-isotropic flows\nor ionization patterns rather than selective extinction effects.\n\nWe extracted\nline profiles for five high signal-to-noise SWS lines by subtracting\na linear continuum fitted outside 2500km/s from the line center and normalizing\nto the peak of the line. These five lines originate in species spanning a wide \nrange of excitation potentials ranging from 55 to 303eV and are shown in\nFigure~\\ref{fig:allprof}. The remaining uncertainty of these profiles is\ndominated by noise for the high excitation lines of [\\ion{Mg}{8}] and\n[\\ion{Si}{9}] and by continuum uncertainties for the other lines.\nThese could be both due to weak underlying real continuum features\n(e.g. PAH near [\\ion{Ne}{6}]) and due to residual fringing ([\\ion{Ne}{5}]\nand [\\ion{O}{4}]). We do not show low excitation lines with significant \nstarburst contribution, and the [\\ion{Ne}{5}] 14.32$\\mu$m and \n[\\ion{Ne}{3}] 15.55$\\mu$m lines which are \nconsistent with those shown in Figure~\\ref{fig:allprof} but more uncertain\ndue to fringing. Brackett $\\alpha$ has a much lower line to continuum ratio but\nstill good signal-to-noise ratio, and a line profile similar to \nthe fine structure lines, as discussed by Lutz et al. (2000) in the context \nof putting limits on a broad line region contribution. \n\nFor lines too faint to derive a good line profile, we fitted a single\ngaussian plus linear continuum to derive at least a centroid velocity\n(Table~\\ref{tab:lineflux}). While\nsuch a gaussian is not a good approximation to the intrinsic NLR profile,\nwe adopted it for simplicity and for consistency with the \noptical/near-infrared data of Marconi et al. (1996). We also fitted\nthe two-component NLR profile of Figure~\\ref{fig:allprof} but do not list the\nderived velocities since they agree with the simple gaussian fit except for\nan offset that is constant within the uncertainties. From repeated observations\nfor some of these lines, we estimate an error of $\\lesssim$50km/s. \nFor lines with no velocity listed in \nTable~\\ref{tab:lineflux}, we estimate that the uncertainty of deriving \nthe centroid of a broad noisy line is too large to include it into an \nanalysis of NGC\\,1068. None of them, however, is discrepant by more than\n$\\approx$300km/s which would suggest misidentification. \n\nIn the following subsections, we will derive a large aperture optical NLR\nline profile for comparison with the ISO data, compare optical and infrared\nprofiles and centroid velocities, and interpret the differences found.\n\n\\subsection{A large aperture optical line profile}\n\\label{subsect:ksoprofile}\n\nMismatch between the typically\nsmall optical apertures and the large mid-IR ones is important\nwhen attempting to compare optical and mid-IR line profiles.\nDatacubes from imaging spectroscopy would be ideal to extract optical line \nprofiles matching the ISO apertures. At this point, however, published imaging\nspectroscopy of NGC\\,1068 is either limited in field size (\\cite{pecontal97})\nor lacks wavelength coverage: The datacube of Cecil et al. (1990) has\nbeen obtained with 2600km/s total coverage in the [\\ion{N}{2}] lines that are\nadditionally heavily blended with H$\\alpha$, making it difficult to determine\nthe extent to which broad components are missing in their total line profile\n(their Fig.~7).\n\nWe make use of two auxiliary large aperture optical spectra to address \nthe problem of aperture mismatch: A 4000 to 7800\\AA\\/ spectrum from\nWise Observatory (WO, S. Kaspi 1999, priv. communication), providing good \nfluxes of the brightest lines \nin a $10\\arcsec\\times\\/15\\arcsec$ aperture (position angle 0\\arcdeg), and a \nhigh spectral \nresolution Coud\\'e Echelle spectrum from Karl Schwarzschild Observatory \nTautenburg (KSO, E. Guenther 1999, priv. communication), providing a \ngood [\\ion{O}{3}] line profile (though not good fluxes) in a \n$6.8\\arcsec\\times\\/15\\arcsec$ aperture (mean position angle -28\\arcdeg\\/, \nvarying during integration). In addition, we estimated relative \nemission line fluxes in our apertures by integrating over the\ncorresponding regions of a narrow band [\\ion{O}{3}] map (R. Pogge, \nM.M. deRobertis, 1999, unpublished data).\nBoth the Wise spectrum and the [\\ion{O}{3}] map confirm that ISO line fluxes \nof the NGC\\,1068 NLR can be sensibly compared to smaller aperture \noptical data, since those already sample most of the flux in the narrow\nline region. For example, a 4\\arcsec\\/ diameter aperture will already get \n$\\approx$70\\% of the flux in the ISO aperture.\nThe fluxes measured in the large Wise aperture for the brightest optical lines\nagree within $\\sim$30\\% with published smaller aperture ones (e.g. \n\\cite{shields75}; \\cite{koski78}; \\cite{marconi96}). \n\nFigure~\\ref{fig:ksoveill} displays our KSO $6.8\\arcsec\\times\\/15\\arcsec$ \naperture [\\ion{O}{3}] 5007\\AA\\/ line profile in comparison to its \n$2.5\\arcsec\\times\\/2.5\\arcsec$ equivalent (\\cite{veilleux91}). The line profile\nchanges induced by this more than tenfold increase in aperture area are \nrelatively modest and fit expectations from high resolution longslit\nspectroscopy. While the major components of Veilleux' spectrum are\nwell reproduced in the KSO data, their ratios differ somewhat leading to an \noverall slightly wider profile. This is fully consistent with observations\nof relatively broad components over larger regions not sampled by Veilleux' \naperture\n(\\cite{pelat80}; \\cite{alloin83}; \\cite{meaburn86}). The only feature\nin the KSO profile not present in the Veilleux profile is an additional\nnarrow feature at or slightly redshifted from systemic velocity. This feature\nalmost certainly corresponds to the `velocity spike' in the NE region of the\nNLR detected by many authors but seen perhaps most clearly in the data of\nMeaburn \\& Pedlar (1986). This feature is missed by Veilleux' aperture but\npartly covered by the KSO data.\n\nThe KSO aperture is still about three times smaller in area than the SWS \napertures through which the best fine structure line profiles have been taken.\nThe drop in [\\ion{O}{3}] surface brightness with radius is so rapid\n(e.g. Fig. 1 of Meaburn \\& Pedlar 1986) that only modest differences \nin the total line profile are expected. An exception to this\nis the NE region of the NLR about 6\\arcsec\\/ from the nucleus\nwhich was incompletely covered. The KSO slit orientation cannot\nbe chosen freely and was approximately aligned with the ISO\napertures but not with the NLR (PA -28\\arcdeg\\/\ninstead of PA $\\approx$30\\arcdeg\\/), missing part of the NE end of the NLR. \nLong slit spectroscopy (e.g. \\cite{meaburn86}) \nshows this NE region to be dominated by the narrow `velocity spike' near\nsystemic velocity which is already seen in the comparison of KSO and\nVeilleux (1991) profiles. We hence expect this spike to be more\nprominent in an optical line profile fully equivalent to the ISO aperture.\nIntegrating the [\\ion{O}{3}] map over the ISO and KSO apertures we estimate \na need to add $\\sim$11\\% to the KSO flux to account for the NE region and \nother low surface brightness emission near systemic velocity. We have taken\nthis into account by adding such a narrow (FWHM 150km/s) component \nto the KSO profile, and will use this \nin the following as basis of our optical line profile \ncomparison (see also Figure~\\ref{fig:ksoveill}).\nUse of such a modified profile is supported by the spectrum of Pelat \\&\nAlloin (1980) which was obtained with a rotating longslit sweeping across the\nNE region of the NLR, and showing a similar narrow spike (their component 5).\n\n\\subsection{Line profile variations}\n\nThe optical and infrared line profiles in NGC\\,1068 differ strongly. This is most\nevident in Figure~\\ref{fig:opto4} which compares the profiles of \n[\\ion{O}{4}] 25.89$\\mu$m and [\\ion{O}{3}] 5007\\AA\\/. We chose [\\ion{O}{4}]\nas the representative infrared line since it was observed with very good S/N \nand is close to \n[\\ion{O}{3}] in lower ionization potential of the emitting species \n(55 vs. 35eV), ensuring origin in a similar region of the NLR. Critical \ndensities ($1.0\\times10^4$\\,cm$^{-3}$ vs. $7.0\\times10^5$\\,cm$^{-3}$) match\nless well than [\\ion{Ne}{5}] or [\\ion{Ne}{6}] would, but this is less relevant\ngiven the low NLR density we have inferred (see \\S \\ref{subsect:density}). \n\nThe optical [\\ion{O}{3}] line profile is both blueshifted and broader than \nthe infrared [\\ion{O}{4}] line profile. \nThere are however also significant similarities. Shoulders near\n-900\\,km/s and $\\sim$350\\,km/s are present in both profiles. \nAdopting different relative scalings (Figure~\\ref{fig:opto4}), the \nimpression arises that the two profiles in fact agree fairly well over\nparts of their extent if the scaling is set properly. The main \ndifference lies in {\\em different relative strengths of blue wing, center,\nand red wing}, the infrared profile having a stronger red wing and center.\n\nThe four highest quality infrared profiles are compared in \nFigure~\\ref{fig:procomp} using a spread velocity scale. The most obvious\nand significant variation is in [\\ion{Mg}{8}] which is both broader and\nmore blueshifted than the lower excitation lines. The same is observed for\nthe more noisy [\\ion{Si}{9}] line.\nAs already noted, the [\\ion{O}{4}],[\\ion{Ne}{5}], and [\\ion{Ne}{6}] profiles \nwith excitation energies ranging from 55 to 126eV are \nvery similar but the overplot shows some variation in detail.\nThere is a minor shift in the narrow core of the [\\ion{Ne}{6}] line which is,\nhowever, not significant compared to the quoted systematic \nuncertainty. Comparing [\\ion{Ne}{5}] to [\\ion{O}{4}] taken\n from the same observation there is even less shift. Concerning\nthe broader wings, there are significant differences in addition to\nthe possible presence of [\\ion{Fe}{2}] at $\\approx$1100km/s in the \n[\\ion{O}{4}] profile. There is a trend from [\\ion{O}{4}] to [\\ion{Ne}{6}] \nin the blue wing becoming stronger and the red wing fainter.\n\nSuch profile variations determine the line centroids derived from \ngaussian fits (Table~\\ref{tab:lineflux}) to which we add a centroid\nof 1015 km/s derived in the same way for our extrapolated large aperture \noptical [\\ion{O}{3}]\nprofile. Anticipating that the shifts may reflect several\npartially degenerate influences, we show in Figure~\\ref{fig:centroids}\ncentroid velocities as a function of lower ionization potential, critical \ndensity, and extinction for the particular line. The extinction values are\nrelative and based on a preliminary ISO-based extinction curve for the center\nof our Galaxy (\\cite{lutz97a}). \n\nThe trend observed in the ISO data for the velocity centroids as a function\nof ionization potential\n(Figure~\\ref{fig:centroids}) is markedly different from the equivalent\ndataset obtained in the optical and near-infrared (Figure~\\ref{fig:centroids},\ndata taken from Marconi et al. \n1996). In both data sets the velocity centroids of the lowest excitation \nnon-NLR lines\n(H$_2$, [\\ion{Fe}{2}]) are close to systemic. However, none of the ISO \nlines reach the large blueshifts observed consistently over a wide \nexcitation range in \nthe optical and near-infrared. \nThe data sets are least discrepant at the high excitation end.\nHere, [\\ion{Si}{9}] 3.936$\\mu$m is common to both sets and agrees\nwithin the errors, though being somewhat less blueshifted in the ISO data. \nThe discrepancy is largest at intermediate excitation\n(20-200eV) where the optical/NIR lines are all strongly blueshifted while\nthe ISO lines only slowly deviate from systemic velocity as excitation\nincreases.\n\n\\subsection{Interpretation of the profile differences}\n\nIn addition to the cloud distribution and kinematics, line profiles \nreflect the emissivities of fine structure or forbidden lines \nin the narrow line region clouds, which are affected by many\nparameters: ionization equilibrium, density, electron temperature, and \nextinction. \nIf any of these\nparameters vary among kinematically distinct structural components of the\nNLR, line profile variations will result that in turn can help elucidate\nthe NLR structure. \nAn important aspect is that some of these parameters\nare partially degenerate in infrared datasets: Shorter wavelength (2-5$\\mu$m)\nlines which suffer higher extinction are also typically high excitation coronal \nlines with high critical densities, whereas the longer wavelengths are \ndominated by ions of lower excitation with transitions\nwith lower critical densities.\n\nHere we have assumed that the observed lines are emitted locally, with no \ncontribution of scattered light. This is not strictly \ncorrect for part of the NGC 1068 narrow line region, in particular the NE\nregion (\\cite{capetti95}; \\cite{inglis95}). The impact \nof scattering on our analysis depends on the properties \nof the scatterer. If scattering is wavelength-independent, our profile\ncomparison is\nunaffected since scattering would effectively only redistribute\nthe line emission spatially within our large apertures. If (dust) scattering\ndecreases with wavelength, shorter wavelength line profiles would be modified \nmore strongly. We estimate the effect on the integrated line\nprofiles is not large, since the [\\ion{O}{3}] polarisations measured by\nInglis et al. (1995) reach at most a few percent in regions that are in addition\nminor contributors to the total flux, and since the considerable spatial \nvariation in line profiles is not suggestive of scattered radiation\noriginating in a central source. \n\n%Aperture differences can\n%significantly bias the comparison of optical and near-IR line\n%profiles, and it is essential to verify that this is not the case\n%here. The different apertures of the ISO lines pose no problem as they\n%are all large enough to include the entire NLR. On the other hand,\n%optical lines are often taken with much smaller apertures. \n%Our optical [\\ion{O}{3}] profile taken through a large aperture \n%\\S \\ref{subsect:ksoprofile} addresses\n%this problem, and confirms that there are\n%significant differences between the optical and mid-IR line profiles.\n%Although the optical aperture is still smaller than the ISO aperture\n%and requires some extrapolation by adding a model narrow component,\n%the uncertainty in the extrapolation cannot explain the profile\n%difference. First, the profiles differ not only in the strength of the\n%narrow component, but also in the relative strengths of the blue and\n%red wings. Second, an attempt to scale the optical profiles to the IR\n%ones by matching their broad components still fails to account for\n%about 1/3 of the IR flux in the large optical aperture (Fig.~\\ref{fig:opto4}). \n%This is well\n%beyond the uncertainties in the [OIII] map and is inconsistent with\n%the [OIII] flux measurement in the large aperture Wise spectrum. Thus,\n%we believe that the optical/IR profile differences are not an artefact\n%of aperture effects but rather reflect real differences.\n \nIt is unlikely that density\nvariations play a direct role in the profile variations.\nOur density estimate of $\\rm n_e\\sim2000 cm^{-3}$\nis too far below the relevant critical densities, making much higher\ndensities over a significant part of the NLR unlikely, which would be required \nto create the variations. Strictly speaking however, this estimate applies \nonly to the moderately excited (100eV) gas, and our upper limit for the \ncoronal region \ndensity is still consistent with densities higher than the critical densities \nof some lower excitation line. Strong collisional suppression of\npart of some low critical density fine structure line profiles is also unlikely\nfrom the similarity of their line centroids to that of the recombination line \nBrackett $\\alpha$. We hence believe that the clear correlation of centroid\nvelocities with fine structure line critical density \n(Figure~\\ref{fig:centroids}b) is mostly a secondary consequence of the \ncorrelation with ionization potential.\n\nVariations in electron temperature can also affect the line profiles.\nEmissivities of optical forbidden lines like [\\ion{O}{3}] 5007\\AA\\/ strongly vary with\nelectron temperature while the infrared fine structure lines originate close\nto the ground state and are much less sensitive to temperature. Hence, at least\nthose profile variations seen among the infrared lines (Figures\n\\ref{fig:procomp} and \\ref{fig:centroids}) must be unrelated to temperature\nfluctuations.\nFor the optical/IR profile variations there is a basic ambiguity\nof an optical component being faint due to low electron temperature or\ndue to high extinction. Optical electron temperature determinations e.g.\nfrom [\\ion{O}{3}] 4363\\AA\\//5007\\AA\\/ are not available for the\nvarious kinematic components of NGC\\,1068. \nThe line profiles of\nthe temperature insensitive recombination lines in the optical and IR\ndo not resemble each other, but rather follow the shapes of the forbidden \noptical and IR lines, respectively (\\cite{veilleux91}, Fig.~\\ref{fig:ionspec}). \nThis is inconsistent with temperature variations being the main origin\nof profile variations.\n\nThe exclusion of other factors suggests that ionization structure and\nextinction are the main source of the observed variation of optical/IR line \nprofiles. Previous studies of the spatial and \nkinematical structure of the NGC\\,1068 NLR (e.g. \\cite{cecil90}, \n\\cite{marconi96}) point to the existence of two spatial and\nkinematical components. The first is\na strong ionization cone with associated blueshifted outflow, \nwith the highest excitation species likely\nconcentrated towards the central and fastest part of this cone. The second\nis an extended system of photoionized clouds closer to \nsystemic velocity.\nThe correlation between the ISO centroid \nvelocities and the ionization potential (Figure~\\ref{fig:centroids}a)\nfits this picture well. If the\nrelative importance of the fast outflow gradually increases towards high\nexcitation lines, the gradual centroid shift is easily explained.\nHowever, the marked differences between optical [\\ion{O}{3}] and \ninfrared [\\ion{O}{4}] profile (Figure~\\ref{fig:opto4})\nand the different optical and infrared centroid velocities at\nsimilar ionization potential (Figure~\\ref{fig:centroids}a, including data from \nMarconi et al. 1996) show that this picture must be incomplete.\nWe suggest that these remaining differences are due to extinction\nvariations across the NLR, with a general trend of higher exctinction in the\nredshifted (SW) than in the blueshifted (NE) part. \nThe optical profile can be\nexplained by an intrinsic profile similar to that of the IR lines\nwhose line center and red wing are reddened by a few magnitudes,\nleading to the obscuration of about half of the total line flux.\nA similar extinction pattern is suggested by the increase of polarization \nfrom the blue to the red wing of the {\\em narrow} lines in the central\narcseconds (\\cite{antonucci85}; \\cite{bailey88}; \\cite{inglis95}), \nattributed to absorption by aligned grains.\n \nConsidering that the optical profiles are modified by extinction, it is \nimportant to recognize that the less obscured near- and mid-infrared lines\nremain blueshifted with respect to systemic velocity, high excitation ones\nmore strongly than lower excitation ones. Also, coronal line emission\nobserved in the little obscured near-infrared is still much stronger in \nthe northeast cone than in the\nsouthwest (\\cite{thompson99}). This might be due to heavy \nextinction of an intrinsically symmetric NLR, or due to a real asymmetry.\nNo distinction can be made from the present data.\nA trend with IR extinction is not clear in Figure~\\ref{fig:centroids}c and\nwould be difficult to separate from the trends with ionization potential and \ncritical density because of the mentioned degeneracy.\nAn intrinsically asymmetric NLR with outflow preferentially towards the \nobserver is fully consistent with the observations of NGC\\,1068. The difference\nin strength of the two radio lobes (\\cite{wilson83}) may be in support of\nsuch an asymmetric scenario, although the relation between radio lobe flux and\nNLR emission is certainly not simple.\nConsistency with an asymmetric NLR was also noted for the\nISO spectra of NGC\\,4151 (\\cite{sturm99}). However, large randomly oriented AGN \nsamples should not\nshow the preferential blueshift which is noted at least in optical \nsamples. An alternative scenario of a geometrically small but \noptically highly thick screen (disk or torus) obscuring part of the receding \nNLR region was proposed by Sturm et al. (1999) for NGC 4151. Such a scenario\ncan also fit the NGC\\,1068 data provided the screen obscures a \nrelatively larger fraction of the coronal line region than of the\nlarger NLR which is dominated by medium excitation species. \nThis is not implausible given the similar (arcsecond) spatial scale of\nthe central concentration of high column density molecular gas \n(e.g. \\cite{tacconi94}) and the\ncoronal line region as mapped in [\\ion{Si}{6}] (\\cite{thompson99}; \n\\cite{thatte00}). \nWhile studies of few individual sources will remain ambiguous, a search\nfor preferential shifts using high resolution near- or mid-infrared spectroscopy\nshould address this issue provided the sample of Seyferts is large enough and \nnot biased by orientation of a putative asymmetric outflow, as may be the case\nwhen identifying Seyferts in the optical.\n\nOverall, the structure of the NGC\\,1068 narrow line region seems to \ndetermine the optical/infrared line profiles via differences in weight of \noutflowing cone and extended components, and additional extinction \nvariations that are significant for the optical wavelength range. \nThe relative weight of the cone is larger for higher excitation species.\nA tantalizing ambiguity remains that cannot\nbe resolved from a single source study: Is the NLR intrinsically one-sided\nor is there a very high obscuration screen blocking also part of the IR\nemission from our view?\n%\n%\n\\section{Molecular hydrogen emission}\n\nNGC\\,1068 was the first galaxy detected in the rovibrational transitions\nof molecular hydrogen (\\cite{thompson78}) and has been studied since in \nconsiderable detail both in these lines tracing fairly excited molecular\nmaterial (e.g. \\cite{oliva90}; \\cite{blietz94}; \\cite{davies98}), and by \nmillimeter wave interferometry tracing\ncolder components (e.g. \\cite{tacconi94}; \\cite{sternberg94}; \n\\cite{helfer95}; \\cite{schinnerer99}). The system of dense, warm \ncloud cores in the central few arcseconds inferred from the millimeter\nstudies calls for observations in the pure rotational transitions of molecular \nhydrogen, which trace gas of typically a few 100K, intermediate between the \nnear-infrared and millimeter wave tracers.\n\nOur SWS observations of these lines (Figure~\\ref{fig:h2spec}, \nTable~\\ref{tab:lineflux}) are summarized in the H$_2$ excitation diagram of\nFigure~\\ref{fig:excit}. The diagram has a curved shape suggestive of a \nmixture of temperatures, as expected from other\ngalaxies observed with ISO in the rotational lines of molecular hydrogen\n(\\cite{rigopoulou96}; \\cite{sturm96}; \\cite{valentijn96a}; \\cite{kunze96};\n\\cite{spoon00}). \nThe location\nof the S(3) point slightly below the general trend suggests a moderate \nextinction towards this line whose wavelength is near the center of the silicate \nabsorption feature ($\\rm A_{9.6\\mu\\/m}\\lesssim 1$). As noted earlier, the flux for \nthe heavily blended S(7) line is very uncertain, so that the shorter wavelength\nrovibrational lines of similar excitation will probably be a more \ntrustworthy representation of the\nexcitation diagram at these upper level energies. \n\nWhile the higher rotational lines like S(5) and S(7) probe the same\nexcited but low mass component as the near-infrared rovibrational lines,\nthe bulk of the warm gas observed with ISO will reside in the component\ntraced by the S(1) line. In estimating its mass, we will assume a hydrogen\northo/para (O/P) ratio in equilibrium at the local temperature\n(\\cite{sternberg99}). Combining the S(1) flux with the S(0) limit on\none hand and the S(3) detection on the other, the temperature of the S(1) \nemitting gas is found to lie in the range 140K$\\le$T$\\lesssim$375K, \nassuming the extinction\ncorrection for S(3) is modest and aperture effects are minor. Because of the \nvery steep temperature sensitivity\nof the rotational line emissivities, the corresponding mass varies drastically,\nbetween about $\\rm 4\\times\\/10^6M_{\\sun}$ for the 375 K case and \n$\\rm 1.5\\times\\/10^8M_{\\sun}$ for the 140 K case. For comparison with\nother mass estimates, we will adopt $\\sim$200\\,K and\n$\\rm \\sim\\/2.5\\times\\/10^7M_{\\sun}$ as a possible approximation\nto the curvature of the excitation diagram. This mass would be of the\norder 5\\% of the total gas mass estimated from the \nCO interferometric map (\\cite{helfer95} and priv. comm.) within the \n17$\\mu$m ISO beam. Compared to a similar\nestimate for the starburst galaxy NGC\\,3256 (\\cite{rigopoulou96}, 3\\% for 150K\nwarm gas temperature), the fraction of warm gas and/or its temperature must\nbe higher, but not exceeding on average that inferred by Kunze et al. (1996) \nfor the highly active star forming region in the `overlap region' of the \nantenna galaxies (8\\% for 200K warm gas temperature). \n\nThe NGC\\,1068 molecular\nhydrogen emission sampled by SWS may represent a mixture of relatively cool \ngas from the 15\\arcsec\\/ radius molecular ring partly covered by the longer \nwavelength apertures, and a warmer component from the unusually dense\nand warm central few arcseconds (\\cite{tacconi94}; \\cite{blietz94}).\nKnowing from the S(3) measurement that the extinction to the H$_2$ emitting \nregion\ncannot be very large, we can compare our 1-0 Q(3) flux to 1-0 S(1) fluxes\nmeasured in smaller apertures (1.4 to 2.2$\\times10^{-20}$W\\,cm$^{-2}$;\n\\cite{blietz94}; \\cite{thompson78}). Our Q(3) line flux falls in the middle \nof that\nrange. Since the intrinsic Q(3)/S(1) flux ratio is 0.7, the implication\nis that the central few arcseconds dominate\nat least for the more highly excited hydrogen lines, though there may be \nsome extended contribution.\nSome of the molecular hydrogen emission in NGC\\,1068 may originate in\nX-ray irradiated gas. We include in Table~\\ref{tab:lineflux} upper limits\nfor two transitions of H$_3^+$ which have been proposed as a signature of\nX-ray heated molecular gas (\\cite{draine90}). We note, however, that these \nlimits are not at all stringent and are fully consistent with even the\n`high' end of H$_3^+$ flux expectations for X-ray illumination. Estimates are \nuncertain, see e.g. the much lower predictions of Maloney et al. (1996). \n \nThe question can be raised whether the NGC\\,1068 H$_2$ spectra in fact contain\na direct signature of a parsec-scale molecular torus. Krolik and Lepp (1989)\nhave modelled molecular line emission of such an X-ray illuminated torus,\npredicting emission in some molecular hydrogen lines like (0-0) S(5) that\nmay under favorable conditions be detectable at ISO-SWS sensitivities.\nFor NGC\\,1068 it is evident that larger scale emission may swamp any\npossible torus emission, as already cautioned by Krolik and Lepp (1989).\nThe ISO data smoothly complement the near-infrared emission originating\nin larger scale ($\\sim$100pc) clouds, following an excitation diagram\nplausibly ascribed to the same clouds. If any torus emission were present\nat lower level, it may be difficult to discriminate from the larger scale\nemission since, depending on\nblack hole mass and spatial scale, its velocity width could be very similar to\nthe larger scale emission. The widths of our H$_2$ rotational lines are \nconsistent with those for CO observed on 100pc and larger scales, with\nno evidence for other kinematic components. However, even if the rotational\nemission does not trace a compact torus, it may still be excited\nto a significant fraction by UV radiation, X-rays or shocks related to the AGN.\n\n\n\n\\section{Summary}\n\nISO-SWS spectroscopy provides the first detailed census of the mid-infrared\nspectrum of the prototypical Seyfert 2 galaxy NGC\\,1068. We\nhave detected 36 emission \nlines on top of the strong AGN-heated continuum. Most lines originate in the\nNLR characterized by a density of $\\sim$2000\\,cm$^{-3}$.\n\nWe have compared the mid-infrared ISO line profiles with optical emission line\nprofiles produced in the NLR.\nThe line profiles are consistent with a model where the NLR is a \ncombination of a highly ionized outflow and lower excitation extended emission,\nwith extinction significantly affecting the optical line profiles.\nRemaining blueshift and asymmetry of the least obscured lines may reflect \neither intrinsic asymmetry of the NLR or an additional very high column density\nobscuring component.\n\nWe detect strong emission from warm molecular hydrogen, which most likely \noriginates on the\n100pc to kpc scale, and which is also probed by emission in near-infrared and \nmillimeter wave tracers\nof molecular material. This emission masks any possible emission from a\nputative parsec-scale molecular torus.\n\nCompanion papers use the SWS data to model the spectral energy distribution of \nthe active nucleus, to put limits on emission from the obscured broad line \nregion, and discuss the continuum and its features. \n\n\\acknowledgments\nWe are grateful to Eike Guenther and Shai Kaspi for obtaining optical spectra\nthat were invaluable in the interpretation of the ISO spectra, and to \nRichard Pogge and M.M. de Robertis for providing us with an\nunpublished [\\ion{O}{3}] image of NGC\\,1068. \nSWS and the ISO Spectrometer\nData Center at MPE are supported by DLR (DARA) under grants 50 QI 8610 8 and\n50 QI 9402 3.\nWe acknowledge support by the German-Israeli Foundation (grant \nI-0551-186.07/97).\n\n\\clearpage\n\\begin{thebibliography}{}\n\\bibitem[Alexander et al. 1999]{alexander99} Alexander T., Sturm E., Lutz D., \n Sternberg A., Netzer H., Genzel R. 1999, \\apj, 512, 204\n\\bibitem[Alexander et al. 2000]{alexander00} Alexander T., et al., submitted to\n ApJ\n\\bibitem[Alloin et al. 1983]{alloin83} Alloin D., Pelat D., Boksenberg A., \n Sargent W.L.W. 1983, \\apj, 275, 493\n\\bibitem[Antonucci \\& Miller 1985]{antonucci85} Antonucci R.R.J., Miller J.S.\n 1985, \\apj, 297, 621\n\\bibitem[Appenzeller \\& \\\"Ostreicher 1988]{appenzeller88} Appenzeller I., \n \\\"Ostreicher R. 1988, \\aj, 95, 45\n\\bibitem[Axon et al. 1998]{axon98} Axon D.J., Marconi A., Capetti A., \n Macchetto F.D., Schreier E., Robinson A., 1998, \\apj, 496, L75\n\\bibitem[Bailey et al. 1988]{bailey88} Bailey J., Axon D.J., Hough J.H.,\n Ward M.J., McLean I., Heathcote S.R. 1988, \\mnras, 234, 899 \n\\bibitem[Blietz et al. 1994]{blietz94} Blietz M., Cameron M., Drapatz S.,\n Genzel R., Krabbe A., van der Werf P., Sternberg A., Ward M. 1994, \\apj,\n 421, 92\n\\bibitem[Bock et al. 1998]{bock98} Bock J.J., Marsh K.A., Ressler M.E., \n Werner M.W. 1998, \\apj, 504, L5\n\\bibitem[Braatz et al. 1993]{braatz93} Braatz J.A., Wilson A.S., Gezari D.Y.,\n Varosi F., Wilson A.S. 1993, \\apj, 409, L5\n\\bibitem[Brinks et al. 1997]{brinks97} Brinks E., Skillman E.D., Terlevich\n R.D., Terlevich E. 1997, \\apss, 248, 31\n\\bibitem[Cameron et al. 1993]{cameron93} Cameron M., Storey J.W.V., \n Rotaciuc V., Genzel R., Verstraete L., Drapatz S., Siebenmorgen R., Lee T.J.\n 1993, \\apj, 419, 136 \n\\bibitem[Capetti et al. 1995]{capetti95} Capetti A., Axon D.J., Macchetto F., \n Sparks W.B., Boksenberg A. 1995, \\apj, 446, 155\n\\bibitem[Cecil et al. 1990]{cecil90} Cecil G., Bland J., Tully R.B. 1990,\n \\apj, 355, 70\n\\bibitem[Dahari \\& De Robertis 1988]{dahari88} Dahari O., De Robertis M.M.\n 1988, \\apj, 331, 727\n\\bibitem[Davies et al. 1998]{davies98} Davies R., Sugai H., Ward M.J. 1998,\n \\mnras, 300, 388\n\\bibitem[De Robertis \\& Osterbrock 1986]{derobertis86} De Robertis M.M., \n Osterbrock D. 1986, \\apj, 301, 727\n\\bibitem[Dietrich \\& Wagner 1998]{dietrich98} Dietrich M., Wagner S.J. 1998,\n \\aap, 338, 405\n\\bibitem[Draine 1989]{draine89} Draine B.T. 1989, in: \"Proc. 22nd Eslab\n Symposium on Infrared Spectroscopy in Astronomy\", ESA SP-290,\n (Noordwijk: ESA), 93\n\\bibitem[Draine \\& Woods 1990]{draine90} Draine B.T., Woods D.T. 1990, \\apj, \n 363, 464\n\\bibitem[Evans et al. 1991]{evans91} Evans I.N., Ford H.C., Kinney A.L., \n Antonucci R.R.J., Armus L., Caganoff S., 1991, \\apj, 369, 27\n\\bibitem[Feuchtgruber et al. 1997]{feuchtgruber97} Feuchtgruber H., et al.\n 1997, \\apj, 487, 962\n\\bibitem[F\\\"orster-Schreiber 1998]{foerster98} F\\\"orster-Schreiber N. 1998,\n PhD Thesis, Ludwig-Maximilians-Universit\\\"at M\\\"unchen\n\\bibitem[Genzel et al. 1998]{genzel98} Genzel R., et al.\n 1998, \\apj, 498, 579\n\\bibitem[Glass 1997]{glass97} Glass I.S. 1997, \\apss, 248, 191\n\\bibitem[de Graauw et al. 1996]{degraauw96} de Graauw Th., et al. 1996,\n \\aap, 315, L49\n\\bibitem[Heckman et al. 1981]{heckman81} Heckman T.M., Miley G.K., \n van Breugel W.J.M., Butcher H.R. 1981, \\apj, 247, 403\n\\bibitem[Helfer \\& Blitz 1995]{helfer95} Helfer T.T., Blitz L. 1995, \\apj,\n 450,90\n\\bibitem[Hummer \\& Storey 1987]{hummer87} Hummer D.G., Storey P.J. 1987,\n \\mnras, 224, 801\n\\bibitem[Inglis et al. 1995]{inglis95} Inglis M.D., Young S., Hough J.H.,\n Gledhill T., Axon D.J., Bailey J.A., Ward M.J. 1995, \\mnras, 275, 398\n\\bibitem[Kessler et al. 1996]{kessler96} Kessler M.F., et al. 1996, \\aap, \n 315, L27\n\\bibitem[Koski 1978]{koski78} Koski A.T. 1978, \\apj, 223, 56\n\\bibitem[Krolik \\& Begelman 1988]{krolik88} Krolik J.H., Begelman M.C. 1988,\n \\apj, 329, 702\n\\bibitem[Krolik \\& Lepp 1989]{krolik89} Krolik J.H., Lepp S. 1989, \\apj,\n 347, 149\n\\bibitem[Kunze et al. 1996]{kunze96} Kunze D., et al. 1996, \\aap, 315, L101\n\\bibitem[Lahuis et al. 1998]{lahuis98} Lahuis F., et al. 1998, in\n Astronomical Data Analysis Software and Systems VII, A.S.P.\n Conference Series, Vol. 145, eds. 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R. Albrecht, R.N. Hook and H.A.\n Bushouse, p.279\n\\bibitem[Whittle 1985a]{whittle85a} Whittle M. 1985a, \\mnras, 213, 1\n\\bibitem[Whittle 1985b]{whittle85b} Whittle M. 1985b, \\mnras, 216, 817\n\\bibitem[Wilson \\& Ulvestad 1983]{wilson83} Wilson A.S., Ulvestad J.S. 1983,\n \\apj, 275, 8\n\\end{thebibliography}\n\n%\n% here come the tables\n%\n\n\\clearpage\n\\begin{table}\n\\caption{Journal of SWS observations of NGC\\,1068}\n\\begin{tabular}{cccrc}\n\\tableline\n\\tableline\nRevolution&Date &AOT &Duration&Slit Position angle\\\\\n &UT & &s &\\arcdeg\\\\\n\\tableline\n285 &28-Aug-1996&SWS01&6538 &-11\\\\\n285 &28-Aug-1996&SWS02&3212 &-11\\\\\n605 &13-Jul-1997&SWS06&4080 &-23\\\\\n633 &10-Aug-1997&SWS06&8410 &-16\\\\\n643 &20-Aug-1997&SWS06&5710 &-13\\\\\n788 &12-Jan-1998&SWS06&7766 &157\\\\\n788 &12-Jan-1998&SWS02&1990 &157\\\\\n792 &15-Jan-1998&SWS06&14642 &158\\\\\n806 &29-Jan-1998&SWS06&11810 &162\\\\\n818 &11-Feb-1998&SWS06&2134 &165\\\\\n\\tableline\n\\end{tabular}\n\\label{tab:listobs}\n\\end{table}\n\n\\clearpage\n\\renewcommand{\\baselinestretch}{1.0}\n\\begin{table}\n\\caption{NGC\\,1068 emission lines measured with ISO-SWS}\n\\scriptsize\n\\begin{tabular}{lrrrccr}\n\\tableline\n\\tableline\nLine &$\\lambda_{\\rm rest,vac}$&E$_{\\rm Ion}$\\tablenotemark{a}\n &Flux &Meth\\tablenotemark{b}\n &Aperture&Velocity\\tablenotemark{c}\\\\\n &$\\mu$m &eV &10$^{-20}$\\,W\\,cm$^{-2}$&\n &$\\arcsec\\times\\arcsec$&km/s\\\\\n\\tableline\nH$_2$ (1-0) Q(3)& 2.424 & 0.0& 1.7&i&14$\\times$20&1140\\\\\n{}[Si\\,IX] & 2.584 &303.2& 3.0&f&14$\\times$20& \\\\\nBr $\\beta$, H$_2$ (1-0) O(2)&2.626&13.6&4.1\\tablenotemark{d}&f&14$\\times$20&\\\\\n{}[Mg\\,VIII] & 3.028 &224.9& 11.0&f&14$\\times$20&1000\\\\\n{}[Ca\\,IV] & 3.207 & 50.9& 1.3&f&14$\\times$20& \\\\\nH$_2$ (1-0) O(5)& 3.235 & 0.0& 0.8&i&14$\\times$20&1120\\\\\nPf $\\gamma$ & 3.741 &13.6&$<$4.0&u&14$\\times$20& \\\\\n{}[Si\\,IX] & 3.936 &303.2& 5.4&f&14$\\times$20& 950\\\\\nBr $\\alpha$ & 4.052 & 13.6& 6.9&f&14$\\times$20&1110\\\\\nH$_3^+1,2,3_{+1}\\rightarrow3,3$&4.350&0.0&$<$3.0&u&14$\\times$20& \\\\\n{}[Mg\\,IV] & 4.487 & 80.1& 7.4&f&14$\\times$20& \\\\\n{}[Ar\\,VI] & 4.530 & 75.0& 15.0&f&14$\\times$20& \\\\\nPf $\\beta$ & 4.654 &13.6&$<$10.0&u&14$\\times$20& \\\\\n{}[Na\\,VII] & 4.685 &172.1&$<$11.0&u&14$\\times$20& \\\\\nH$_2$ (0-0) S(9)& 4.695 & 0.0&$<$3.5&u&14$\\times$20& \\\\\n{}[Fe\\,II] & 5.340 & 7.9& 5.0&i&14$\\times$20&1120\\\\\n{}[Mg\\,VII] & 5.503 &186.5& 13.0&s&14$\\times$20& \\\\\nH$_2$ (0-0) S(7)& 5.511 & 0.0&3.5::&s&14$\\times$20& \\\\\n{}[Mg\\,V] & 5.610 &109.2& 18.0&f&14$\\times$20& \\\\\nH$_2$ (0-0) S(5)& 6.910 & 0.0& 5.9&i&14$\\times$20&1180\\\\\n{}[Ar\\,II] & 6.985 & 15.8& 13.0&i&14$\\times$20& \\\\\n{}[Na\\,III] & 7.318 & 47.3& 5.8&f&14$\\times$20& \\\\\nPf $\\alpha$ & 7.460 &13.6&$<$3.0&u&14$\\times$20& \\\\\nUnidentified &$\\sim$7.555 & ---& 1.8&f&14$\\times$20& \\\\\n{}[Ne\\,VI] & 7.652 &126.2&110.0&f&14$\\times$20&1030\\\\\n{}[Fe\\,VII] & 7.815 & 99.1& 3.0&f&14$\\times$20& \\\\ \n{}[Ar\\,V] & 7.902 &59.8&$<$12.0&u&14$\\times$20& \\\\\nH$_2$ (0-0) S(4)& 8.025 & 0.0& 3.5&i&14$\\times$20&1130\\\\\n{}[Na\\,VI] & 8.611 &138.4&$<$16.0&u&14$\\times$20& \\\\\n{}[Ar\\,III]/[Mg\\,VII]&8.991&27.6/186.5&25.0&f&14$\\times$20& \\\\\n{}[Fe\\,VII] & 9.527 & 99.1& 4.0&f&14$\\times$20& \\\\\nH$_2$ (0-0) S(3)& 9.665 & 0.0& 6.0&i&14$\\times$20&1130\\\\\n{}[S\\,IV] &10.511 & 34.8& 58.0&f&14$\\times$20& \\\\\nH$_2$ (0-0) S(2)&12.279 & 0.0&$<$8.0&u&14$\\times$27& \\\\\n{}[Ne\\,II] &12.814 & 21.6& 70.0&i&14$\\times$27&1080\\\\\n{}[Ar\\,V] &13.102 &59.8&$<$16.0&u&14$\\times$27& \\\\\n{}[Ne\\,V] &14.322 & 97.1& 97.0&f&14$\\times$27&1020\\\\\n{}[Ne\\,III] &15.555 & 41.0&160.0&f&14$\\times$27&1090\\\\\nH$_3^+5,0\\rightarrow4,3$&16.331&0.0&$ <$6.0&u&14$\\times$27& \\\\\nH$_2$ (0-0) S(1)&17.035 & 0.0& 7.7&i&14$\\times$27&1120\\\\\n{}[Fe\\,II] &17.936 &7.9&$<$10.0&u&14$\\times$27& \\\\\n{}[S\\,III] &18.713 & 23.3& 40.0&i&14$\\times$27&1120\\\\\n{}[Ne\\,V] &24.318 & 97.1& 70.0&f&14$\\times$27&1060\\\\\n{}[O\\,IV] &25.890 & 54.9&190.0&f&14$\\times$27&1100\\\\\n{}[Fe\\,II] &25.988 & 7.9&8.0::&s&14$\\times$27& \\\\\nH$_2$ (0-0) S(0)&28.219 & 0.0&$<$2.5&u&20$\\times$27& \\\\\n{}[S\\,III] &33.418 & 23.3& 55.0&i&20$\\times$33&1110\\\\\n{}[Si\\,II] &34.815 & 8.2& 91.0&i&20$\\times$33&1110\\\\\n{}[Ne\\,III] &36.014 & 41.0& 18.0&f&20$\\times$33& \\\\\n\\tableline\n\\end{tabular}\n\\label{tab:lineflux}\n\\tablenotetext{a}{Lower ionization potential of the stage leading to the\ntransition}\n\\tablenotetext{b}{Method of flux measurement: f = fit of double-gaussian NLR \n profile, \n i = direct integration, u = 3$\\sigma$ upper limit assuming a line width of\n 1000km/s (ions) or 300km/s (molecules), s = special fit. See also text.}\n\\tablenotetext{c}{Heliocentric velocity determined from fitting a single \ngaussian plus continuum to the -- sometimes complex -- line profile.}\n\\tablenotetext{d}{Brackett $\\beta$ is blended with H$_2$ (1-0) O(2). From the\n(1-0) Q(3) and (1-0) O(5) fluxes, we estimate a (1-0) O(2) contribution of \n$\\sim0.4\\times\\/10^{-20}$\\,W\\,cm$^{-2}$ to the total flux}\n\\end{table}\n\n\\normalsize\n\\renewcommand{\\baselinestretch}{1.6}\n\n%\n% here come the figure captions\n%\n\n\\clearpage\n\n\\figcaption[fig_fullspec.eps]{Complete 2.4--45$\\mu$m ISO-SWS spectrum of \nNGC\\,1068. Some of the brightest emission lines are indicated.\n\\label{fig:fullspec}}\n\n\\figcaption[fig_ionspec.eps]{ISO-SWS spectra of lines emerging in the ionized\nmedium of NGC\\,1068. Flux densities in Jy are shown for a range of \n$\\pm$2500\\,km/s around systemic velocity. Most lines originate in the narrow \nline region but some low excitation \nlines have a significant starburst contribution. The two lines shown dashed\nwere observed in SWS01 mode, all others in full resolution SWS06 mode.\n\\label{fig:ionspec}}\n\n\\figcaption[fig_h2spec.eps]{ISO-SWS spectra of molecular transitions in \nNGC\\,1068. Flux densities in Jy are shown for a range of \n$\\pm$1000\\,km/s around systemic velocity. The line shown dashed\nwas observed in SWS01 mode, all others in full resolution SWS02 or SWS06 modes.\n\\label{fig:h2spec}}\n\n\\figcaption[fig_allprof.eps]{Normalized line profiles for five high signal\nto noise fine structure lines in NGC 1068, covering a range of lower \nionization potentials from 55 to 303eV. The velocity scale is with respect \nto the heliocentric systemic velocity of 1148\\,km/s. Short lines in the upper\nright part of the panels indicate the SWS resolution at that wavelength.\nIn the lower right panel, we show a combination of two gaussians which\nprovides a reasonable approximation to the mid-infrared NLR line profiles \nover this wide range of ionization potentials. We have used fits of such \na profile to measure {\\em fluxes} of fainter lines.\n\\label{fig:allprof}}\n\n\\figcaption[fig_ksoveill.eps]{Comparison of the large aperture [\\ion{O}{3}] \n5007\\AA\\/ profile obtained at Karl Schwarzschild Observatory with the smaller\naperture one of Veilleux (1991). The velocity scale is with respect to the \nheliocentric systemic velocity of 1148\\,km/s - note that this\ndiffers from the original figure of Veilleux (1991). The dashed line indicates\na suggested extrapolation of the KSO spectrum to the larger ISO aperture\nof 14\\arcsec$\\times$20\\arcsec, taking into account extended narrow \nemission near systemic velocity, mainly from the NE region of the NLR.\nSee text for details.\n\\label{fig:ksoveill}}\n\n\\figcaption[fig_opto4.eps]{Comparison of the infrared [O\\,IV] and\noptical [O\\,III] line profiles. The peak of the optical profile\nis normalized to 1, 0.8, 0.6, and 0.4 times the peak of the infrared\nprofile in the four panels.\nThe optical profile is the modified KSO profile of Figure 5\nsmoothed to the SWS resolution at the wavelength of [\\ion{O}{4}]. While many \nstructures are present in both optical and infrared profile, there \nare pronounced differences in the relative strengths of center and blue/red\nwings. \n\\label{fig:opto4}}\n\n\\figcaption[fig_procomp.eps]{Direct comparison of the four highest \nsignal-to-noise fine structure line profiles. The velocity scale is with \nrespect to the heliocentric systemic velocity of 1148\\,km/s.\n\\label{fig:procomp}}\n\n\\figcaption[fig_centroids.eps]{Centroid velocities for NGC\\,1068 emission \nlines, derived from fits of a single gaussian. Systemic velocity is indicated\nby the dashed line in the upper left panel. The correlation with ionization\npotential includes all ISO lines with a velocity listed in \nTable~\\ref{tab:lineflux} (crosses) with the addition of the optical [\\ion{O}{3}] line\n(shown as an asterisk in all graphs). For comparison with the ISO\nmid-infrared results, centroid velocities of optical/near-infrared\nlines as derived by Marconi et al. (1996) are shown as small diamonds in the\nupper left panel. The graphs showing velocity as a function\nof critical density and of extinction are restricted to lines dominated by the\nNLR according to the line profile. The velocities shown are accurate to\n$\\lesssim$50km/s. \n\\label{fig:centroids}}\n\n\\figcaption[fig_excit.eps]{\nExcitation diagram for the molecular hydrogen lines measured with SWS in \nNGC\\,1068.\n\\label{fig:excit}}\n\n%\n% here come the figures\n%\n\\clearpage\n\n\\plotone{fig_fullspec.eps}\n\n\\clearpage\n\n\\plotone{fig_ionspec.eps}\n\n\\clearpage\n\n\\plotone{fig_h2spec.eps}\n\n\\clearpage\n\n\\plotone{fig_allprof.eps}\n\n\\clearpage\n\n\\plotone{fig_ksoveill.eps}\n\n\\clearpage\n\n\\plotone{fig_opto4.eps}\n\n\\clearpage\n\n\\plotone{fig_procomp.eps}\n\n\\clearpage\n\n\\plotone{fig_centroids.eps}\n\n\\clearpage\n\n\\plotone{fig_excit.eps}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002008.extracted_bib",
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}
] |
astro-ph0002009
|
The giant radio galaxy 8C\,0821+695 and its environment
|
[
{
"author": "L. Lara\\inst{1}"
},
{
"author": "K.-H. Mack\\inst{2,3}"
},
{
"author": "M. Lacy\\inst{4}"
},
{
"author": "U. Klein\\inst{3}"
},
{
"author": "W.D. Cotton\\inst{5,6}"
},
{
"author": "L. Feretti\\inst{2}"
},
{
"author": "G. Giovannini\\inst{2,7}"
},
{
"author": "M. Murgia\\inst{2,8}"
}
] |
We present new VLA and Effelsberg observations of the radio galaxy 8C\,0821+695. We have obtained detailed images in total intensity and polarization of this 2 Mpc sized giant. The magnetic field has a configuration predominantly parallel to the source main axis. We observe Faraday rotation at low frequencies, most probably produced by an ionized medium external to the radio source. The spectral index distribution is that typical of FR II radio galaxies, with spectral indices gradually steepening from the source extremes towards the core. Modeling the spectrum in the lobes using standard synchrotron loss models yields the spectral age of the source and the mean velocity of the jet-head with respect to the lobe material. The existence of a possible backflow in the lobe is considered to relate spectral with dynamical determinations of the age and the velocity with respect to the external medium. Through a very simple model, we obtain a physical characterization of the jets and the external medium in which the radio galaxy expands. The results in 8C\,0821+695 are consistent with a relativistic jet nourishing the lobes which expand in a hot, low density halo. We infer a deceleration of the source expansion velocity which we explain through a progressive increase in the hot-spot size. \keywords{galaxies: individuals (8C\,0821+695) galaxies: active -- intergalactic medium -- radio continuum: galaxies }
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{
"name": "lara.tex",
"string": "%----------------------------------------------%\n% REFERENCES \n%----------------------------------------------%\n\\def\\aa{A\\&A} %Astronomy & Astrophysics%\n\\def\\aasup{A\\&AS} %A & A Supplements%\n\\def\\anj{AJ} %Astronomical Journal%\n\\def\\apj{ApJ} %Astrophysical Journal%\n\\def\\apjs{ApJS} %Astrophysical Journal Supplements\n\\def\\baas{BAAS} %Bulletin of the American A.S.%\n\\def\\mn{MNRAS} %Monthly Notices of the Royal...%\n\\def\\nat{Nature} %Nature%\n\\def\\pasp{PASP} %Publ. of the Astr. Soc. of the Pacific%\n\\def\\sci{Science} %Science%\n\\def\\rev{ARA\\&A} %Annual Review of Astronomy & Astrophysics%\n\\def\\nar{NewAR} %New Astronomy Reviews%\n%\n% Phantom character to adjust tables%\n%\n\\def\\phe{\\phantom{1}}\n\\def\\ph2{\\phantom{88}}\n\\def\\ph.8{\\phantom{.8}}%\n%----------------------------------------------------------\n%\n%\\documentclass[referee]{aa}\n\\documentclass{aa}\n%\\documentclass{/a/iaa16u/home/iaa16u2/lucas/papers/macros/aa/aa}\n%\n%\\addtolength{\\topmargin}{1 cm} \n\n\\begin{document}\n\n\\thesaurus{11.09.1 8C 0821+695; 11.01.2; 11.03.3; 13.18.1} \n\n\\title{The giant radio galaxy 8C\\,0821+695 and its environment}\n\n\n\\author{L. Lara\\inst{1} \\and \nK.-H. Mack\\inst{2,3} \\and M. Lacy\\inst{4} \\and U. Klein\\inst{3} \\and\nW.D. Cotton\\inst{5,6} \\and L. Feretti\\inst{2} \\and\nG. Giovannini\\inst{2,7} \\and M. Murgia\\inst{2,8}}\n\\offprints{L. Lara}\n\n\\institute{Instituto de Astrof\\'{\\i}sica de Andaluc\\'{\\i}a (CSIC),\nApdo. 3004, 18080 Granada, Spain\n\\and \nIstituto di Radioastronomia (CNR), Via P. Gobetti 101, I-40129\nBologna, Italy\n\\and\nRadioastronomisches Institut der Universit\\\"at Bonn, Auf dem H\\\"ugel\n71, D-53121 Bonn, Germany\n\\and\nIGPP, L-413, Lawrence Livermore National Laboratory, Livermore, CA\n94550, USA\n%Astrophysics, Department of Physics, Keble Road, Oxford OX1 3RH (England)\n\\and\nNational Radio Astronomy Observatory, 520 Edgemont Road,\nCharlottesville, VA 22903-2475, USA\n\\and \nSterrewacht Leiden, Niels Bohrweg 2, 2300-RA Leiden, The Netherlands\n\\and\nDipartimento di Fisica, Universit\\`a di Bologna, Via B. Pichat 6/2,\nI-40127 Bologna, Italy\n\\and\nDipartimento di Astronomia, Universit\\`a di Bologna, Via Ranzani 2,\nI-40127 Bologna, Italy }\n\n\\date{Received / Accepted}\n\n\\authorrunning{Lara et al.} \n\\titlerunning{GRG 8C\\,0821+695 and its environment}\n\n\n\\maketitle\n\n\\begin{abstract}\n\nWe present new VLA and Effelsberg observations of the radio galaxy\n8C\\,0821+695. We have obtained detailed images in total intensity and\npolarization of this 2 Mpc sized giant. The magnetic field has a\nconfiguration predominantly parallel to the source main axis. We\nobserve Faraday rotation at low frequencies, most probably produced by\nan ionized medium external to the radio source. The spectral index\ndistribution is that typical of FR II radio galaxies, with spectral\nindices gradually steepening from the source extremes towards the\ncore. Modeling the spectrum in the lobes using standard synchrotron\nloss models yields the spectral age of the source and the mean\nvelocity of the jet-head with respect to the lobe material. The\nexistence of a possible backflow in the lobe is considered to relate\nspectral with dynamical determinations of the age and the velocity\nwith respect to the external medium. Through a very simple model, we\nobtain a physical characterization of the jets and the external medium\nin which the radio galaxy expands. The results in 8C\\,0821+695 are\nconsistent with a relativistic jet nourishing the lobes which expand\nin a hot, low density halo. We infer a deceleration of the source\nexpansion velocity which we explain through a progressive increase in\nthe hot-spot size.\n\n\n\\keywords{galaxies: individuals (8C\\,0821+695)\n galaxies: active -- intergalactic medium -- radio continuum:\n galaxies }\n\\end{abstract}\n\n\n\n\\section{Introduction}\n\nGiant Radio Galaxies (GRGs) constitute an unusual class of radio\nsources with projected linear sizes larger than 1 Mpc\\footnote{We\nassume H$_{0}$=75 $ \\mathrm{km\\,s^{-1}\\,Mpc^{-1}}$ and q$_{0}=0.5$\nthroughout this paper.}. These objects, although giant in size, do not\nstand out in luminosity, most of them being of low surface-brightness\n(Subrahmanyan et al. \\cite{subra2}). Moreover, the enormous size of\nGRGs sometimes hampers the identification of emission from two distant\nlobes as part of an individual object (e.g. B2~1358+305; Parma et\nal. \\cite{parma}). Probably, these are the reasons why to date there\nare only about 50 known GRGs (Ishwara-Chandra \\& Saikia\n\\cite{ishwara}; Schoenmakers et al. \\cite{arno1}). Only recently, \nradio surveys like the Northern VLA Sky Survey (NVSS; Condon et al.\n\\cite{nvss}) or the Westerbork Northern Sky Survey (WENSS; Rengelink\net al. \\cite{wenss}) allow sensitive searches of GRGs with adequate\nangular resolution.\n\nTwo basic scenarios have been envisaged to explain the outstanding\nsizes of GRGs. First, their lobes could be fed by extremely powerful\ncentral engines which would endow the jets with the necessary thrust\nto bore their long way through the ambient medium. Second, GRGs could\nbe normal radio sources evolving in very low-density environments\noffering little resistance to the expansion of the jets. While the\nfirst possibility requires the existence of prominent cores and\nhot-spots, which are not always observed (Ishwara-Chandra \\& Saikia\n\\cite{ishwara}), the second possibility is supported by the high degree \nof polarization found in GRGs also at low frequencies (Willis \\& O'Dea\n\\cite{willis}) and seems to be the most plausible scenario in most\ncases (Mack et al. \\cite{mack97b}). It seems that the expansion of a\nradio galaxy in a low density environment during a time long enough to\nallow reaching Mpc sizes, rather than higher than usual radio powers\nor expansion velocities, are the two basic ingredients to build up the\nGRG population (Schoenmakers et al. \\cite{arno2}).\n\nGRGs are located in regions hardly accessible via direct observations:\nthey do not reside in rich galaxy clusters (Subrahmanyan et\nal. \\cite{subra2}) and the X-ray emission around their host galaxies\nis usually weak (Mack et al. \\cite{mack97a}). However, information\nabout the ambient medium at very large distances from the host\ngalaxies can still be gained through the study of their radio\nproperties. Most GRGs probe the intergalactic medium (IGM) providing\ninformation about the density of matter outside galactic halos, adding\nimportant observational constraints to current cosmological models\n(Begelman \\& Cioffi \\cite{begelman}; Nath \\cite{nath}).\n\nWe discuss in this paper new observations of the GRG 8C\\,0821+695, a\nFanaroff-Riley type II (Fanaroff \\& Riley \\cite{fanaroff}). It is\noptically identified with a faint $M_{R}\\sim 22.2$ galaxy at a\nredshift of 0.538 (Lacy et al. \\cite{lacy}). Its high redshift,\ncompared to other GRGs, renders 8C\\,0821+695 a very interesting object\nsince it provides information on the external environment at large\ncosmological distances. No X-ray source coincident with the radio\nsource is found in the Bright Point Source catalogue from the ROSAT\nAll Sky Survey. At the distance of 8C\\,0821+695, one arcsecond\ncorresponds to 4.9 kpc.\n\n\n\\section{Observations and data analysis}\n\nWe observed 8C\\,0821+695 with the VLA in the framework of a complete\nsample of large angular size radio sources selected from the NVSS (see\nLara et al. \\cite{lara} for a sample description), and with the 100-m\nEffelsberg telescope. We also incorporate for the discussion maps from\nthe NVSS and WENSS, and maps presented by Lacy et al.\n(\\cite{lacy}). The data have been calibrated according to the scale of\nBaars et al. (\\cite{baars}).\n\n\n\\subsection{WENSS and NVSS maps}\n\n8C\\,0821+695 appears as a straight $\\sim$7\\arcmin\\ long FR II radio\nsource in the NVSS and the WENSS maps, with its main axis at a\nposition angle (P.A.) of 11\\degr, measured north through east.\n\nThe WENSS map (Fig.~\\ref{lowres}a), at a frequency of 327 MHz and an\nangular resolution of 57\\farcs7$\\times$54\\farcs0, presents two\nprominent lobes (N and S) connected by a continuous bridge of\nemission, although the position of the core is not evident at all.\n\nThe NVSS map (Fig.~\\ref{lowres}b), made at a frequency of 1400 MHz and\nan angular resolution of 45\\arcsec, shows a prominent central core\nstraddling the two radio lobes. The N-lobe has higher surface\nbrightness than the S-lobe. The mean fractional polarization\n($p_{m}$) at 1400 MHz is $p_{m}$=23\\% in the N-lobe and $p_{m}$=26\\%\nin the S-lobe, while the core is unpolarized. The E-vectors have a\nsimilar and rather uniform orientation in the N- and S-lobes, oblique\nto the source main axis.\n\n\\begin{figure*}\n\\vspace{9cm}\n\\special{psfile=larafig1.ps hoffset=0 voffset=-230 \nhscale=85 vscale=85 angle=0}\n%\\rule{0.4pt}{4cm}% line thickness, height of picture\n\\caption{\nLow resolution maps of 8C\\,0821+695 from {\\bf a)} WENSS (327 MHz),\n{\\bf b)} NVSS (1400 MHz) and {\\bf c)} Effelsberg observations (10.6\nGHz). Contours are spaced by factors of $\\sqrt{2}$ in brightness, with\nthe lowest at 3 times the rms noise level. The superimposed vectors\nrepresent the polarization position angle (E-vector), with lengths\nproportional to the amount of polarization. From left to right, we\nlist below the rms noise level, the equivalence of $1\\arcsec$ length\nin polarized intensity and the Gaussian beam used in convolution: rms\n= 3.3, 0.45 and 0.5 mJy beam$^{-1}$; $1\\arcsec$ = 33 and 20 $\\mu$Jy\nbeam$^{-1}$; Beam = $57\\farcs7 \\times 54\\farcs0$ P.A. $0\\degr$,\n$45\\arcsec \\times 45\\arcsec$ and $69\\arcsec\\times69\\arcsec$. }\n\\label{lowres}\n\\end{figure*}\n\n\\subsection{Effelsberg observations}\n\nWe observed 8C\\,0821+695 with the 100-m Effelsberg telescope at 10.6\nGHz (Tab.~\\ref{obs}) in order to obtain information about the\nmorphology and polarization properties at high frequencies. The\nobservational and data reduction procedures were those detailed by\nGregorini et al. (\\cite{gregorini}). The maps were CLEANed as\ndescribed by Klein \\& Mack (\\cite{kleinmack}). We made 40 coverages\nresulting --after combining-- in a final noise level of 0.5 mJy/beam\nin total power and 0.1 mJy/beam in the polarized channels. The\npolarization maps were corrected for the non-Gaussian noise\ndistribution of the polarized intensity, as described by Wardle \\&\nKronberg (\\cite{wardle}). This is of particular importance in case of\npolarized low-brightness regions, e.g. in extended radio lobes.\n \nThe 10.6 GHz map (Fig.~\\ref{lowres}c), with an angular resolution of\n$69\\arcsec$, shows three components corresponding to the core and the\ntwo lobes. The superimposed vectors represent the electrical\nfields. Since at this high frequency Faraday effects are most probably\nnegligible, a rotation by 90\\degr~ immediately yields the direction of\nthe projected magnetic field. It is oriented predominantly parallel\nto the source main axis. The degree of polarization at this frequency\nis 26\\% in both lobes.\n\nWe also observed 8C\\,0821+695 with the 100-m telescope at 4850 MHz.\nAfter combination of 10 coverages we reached the confusion limit of\n0.6 mJy/beam in total intensity, while the noise level was 0.1\nmJy/beam in the polarization channels. Because of the large beam size\n(143\\arcsec), this map does not reveal any additional morphological\ndetails, so we do not need to display it here. The degree of\npolarization derived from the Effelsberg map at 4850 MHz is 19\\% in\nthe N- and S-lobes.\n\n\\begin{table}[b]\n\\caption[]{Observations of 8C\\,0821+695}\n\\label{obs}\n\\begin{tabular}{lrrcr}\n\\hline\nInstrument & $\\nu$ & $\\Delta\\nu$ & Duration & Date \\\\ & (MHz) & (MHz)\n & (min) & \\\\\n\\hline\nNVSS & 1400 & 100 & -- & 23 Nov 93 \\\\ WENSS & 327 & 5 & -- & -- \\\\\nVLA-C & 1425 & 50 & 10 & 19 Feb 96 \\\\ & 4860 & 100 & 10 & 19 Feb 96 \\\\\nVLA-B & 1425 & 50 & 10 & 19 Nov 95 \\\\ & 4860 & 100 & 10 & 25 May 97 \\\\\nEffelsberg & 10550 & 300 & -- & 28 Aug 94 \\\\ & 4850 & 500 & -- & 27\nFeb 98 \\\\\n\\hline \n\\end{tabular}\n\\end{table}\n\n\n\\subsection{VLA observations}\n\nWe made continuum observations of 8C\\,0821+695 with the VLA in the B-\nand C-configurations at 1425 and 4860 MHz in dual polarization (see Tab.~\\ref{obs}). The\ninterferometric phases were calibrated with the nearby source\nJ0903+679, except during 4860 MHz observations with the B-array, for\nwhich J0841+708 was used as phase calibrator. The radio sources 3C286\nand 3C48 served as primary flux density calibrators. Data from the B\nand C arrays were combined in order to take advantage of the higher\nB-array resolution and of the higher C-array sensitivity to extended\nemission. The calibration and mapping of the data were carried out\nwith the NRAO AIPS package. Maps at 4860 MHz had to be corrected from\nprimary beam attenuation. In addition, correction for the non-Gaussian\nnoise distribution in the polarized intensity map was applied.\n\nThe VLA map at 1425 MHz shows a well defined compact core, and two\nlobes of extended emission (Fig.~\\ref{vla}a). The N-lobe is dominated\nby a compact component, suggesting the existence of a faint hot-spot\nat the end of the jet, while a similar feature is not observed in the\nS-lobe. The polarized emission of 8C\\,0821+695 at 1425 MHz comes\npredominantly from this hot-spot in the N-lobe. At this position, the\ndegree of polarization is 30\\%. It is 20\\% in the rest of the N-lobe\nand 25\\% in the S-lobe. As in the NVSS map, the electric vectors are\ninclined with respect to the source main axis, probably due to Faraday\nrotation.\n\n\n\\begin{figure*}\n\\vspace{13cm}\n%\\rule{0.4pt}{4cm}% line thickness, height of picture\n\\special{psfile=larafig2.ps hoffset=25 voffset=-140 \nhscale=75 vscale=75 angle=0} \n\\caption{\n{\\bf a-b} VLA B+C-array maps of 8C\\,0821+695 at 1425 (left) and 4860\nMHz (right). Vectors represent the polarization position angle\n(E-vector), with length proportional to the amount of polarization\n(1\\arcsec~ corresponds to 35 $\\mu$Jy beam$^{-1}$ on the 1425 MHz map\nand to 12.5 $\\mu$Jy beam$^{-1}$ on the 4860 MHz map). Contours are\nspaced by factors of $\\sqrt{2}$ in brightness, with the lowest at 3\ntimes the rms level (rms = 0.13 and 0.1 mJy beam$^{-1}$,\nrespectively). The Gaussian beam size is 9\\arcsec$\\times$9\\arcsec~in\nboth maps.\n} \n\\label{vla}\n\\end{figure*}\n\nThe VLA map of 8C\\,0821+695 at 4860 MHz is displayed in\nFig.~\\ref{vla}b. At this frequency, the core is the most prominent\nfeature. The hot-spot in the N-lobe appears at the end of an\nelongated structure aligned with the radio axis. The N-lobe shows\nclear oscillations in its ridge line that are reminiscent of the\n``dentist drill'' model which assumes a jitter of the jet-head with\ntime (Scheuer \\cite{scheuer}). On the other hand, the S-lobe appears\nmuch more ``relaxed'' and without a strong hot-spot. We measure a\ntotal source length of 6\\farcm95 from Fig.~\\ref{vla}b, which\ncorresponds to a projected linear size of 2 Mpc. The north-to-south\narm ratio is 0.89.\n\nThe polarized emission of 8C\\,0821+695 at 4860 MHz is again dominated\nby the N-lobe hot-spot, where we measure a mean degree of polarization\nof 22\\%, reaching 26\\% in the brightest peak. E-vectors are\npredominantly oriented perpendicularly to the source main axis. We do\nnot detect significant polarization in the S lobe at this frequency\nand resolution.\n\nOur highest resolution observations (VLA B-array at 4860 GHz) provide\nthe following coordinates for the compact core of 8C\\,0821+695\n(J2000.0): RA = 08$^h$25$^m$ 59\\fs770, DEC = +69\\degr 20\\arcmin\n38\\farcs59, fully consistent with the position of the host galaxy.\n\n\n\\section{Results}\n\n\\subsection{Rotation Measure and depolarization}\n\nWe have estimated the Rotation Measure ($RM$) over the two radio lobes\nof 8C\\,0821+695. To do that, we convolved the NVSS 1400 MHz and the\nVLA 4860 MHz polarization maps to the beam of the Effelsberg 10.6 GHz\nmap (a circular Gaussian beam of $69\\arcsec$ FWHM), and applied the\nAIPS task RM. Although the convolution of the VLA map with such a\nlarge beam is in general not advisable, in this case the orientation\nof the polarization vectors was not seriously affected. We did not use\nthe Effelsberg 4850 MHz map because of its too low angular resolution,\nwhich would prevent us from finding any possible structure in the $RM$\ndistribution. Even so, we obtain a rather uniform $RM$ over the two\nlobes of 8C\\,0821+695, with an average value of $-20$ rad~m$^{-2}$.\n\nThe uniform and similar distributions of the electric field P.A. and of\nthe $RM$ over the two lobes suggest that the contribution of the radio\nsource to the observed $RM$ is negligible. Moreover, the mean\ngalactic $RM$ at the position of 8C\\,0821+695 (galactic coordinates $l=\n145\\fdg7$ and $b= 33\\fdg54$) lies between $-30$ rad~m$^{-2}$ and 0\nrad~m$^{-2}$ (Simard-Normandin \\& Kronberg \\cite{simard}), consistent\nwith our observed value. We thus conclude that the observed Faraday\nrotation is most plausibly of galactic origin, although a small local\nhalo contribution between $-20$ to 10 rad~m$^{-2}$ cannot be excluded.\n\nThe fractional polarizations derived at different frequencies are\nessentially consistent with the lack of depolarization at low\nfrequencies. This is clearly derived from the comparison of the low\nresolution data (10.6 and 5 GHz Effelsberg data and 1.4 GHz data from\nNVSS), taking into account that the 5 GHz data have a much larger beam\nand therefore are likely to suffer from beam depolarization. The higher\nresolution VLA data show that the two lobes are still highly polarized\nat 1.4 GHz, in agreement with the presence of a magnetic field ordered\non the restoring beam scale. We ascribe the lack of detected\npolarization in the S-lobe at 5 GHz, with 9\\arcsec~resolution, to the\nlower sensitivity of this image to extended structure.\n\n\n\\subsection{The broad-band radio-spectrum of 8C\\,0821+695}\n\nWe have compiled all available flux density measurements on\n8C\\,0821+695 and have plotted them as a function of frequency giving\nvalues, when possible, for the whole source, the two lobes and the\ncore separately (Tab.~\\ref{flux}; Fig.~\\ref{espectro}). We have\nobtained the spectral index $\\alpha$ (defined so that the flux\ndensity $S \\propto \\nu^{-\\alpha}$) of the different components from linear \nfits to the data: $\\alpha_N=1.15\\pm0.02$; $\\alpha_S=1.10\\pm0.04$. \nOn the other hand, the core shows a flat spectrum with\na mean $\\alpha = 0.30\\pm 0.07$.\n%below 4.9 GHz \n%and a steep one at higher frequencies.\n\n\n\\begin{figure}\n\\vspace{7cm}\n\\special{psfile=larafig3.ps hoffset=-100 voffset=-190\nhscale=70 vscale=70 angle=0} \n%\\rule{0.4pt}{4cm}\n\\caption{Radio spectrum of 8C\\,0821+695 and its\ncomponents. See\nTable~\\ref{flux} for numerical values and their references.} \n\\label{espectro}\n\\end{figure}\n\n\n\\begin{table}[b]\n\\caption[]{Flux density of 8C\\,0821+695}\n\\label{flux}\n\\begin{tabular}{rr@{$\\pm$}rrrcc}\n\\hline\n\\multicolumn{1}{c}{Freq.} & \\multicolumn{5}{c}{Integrated flux density of} & Ref. \\\\\n & \\multicolumn{2}{c}{Entire source} & N lobe & S lobe & Core & \\\\ \n\\multicolumn{1}{c}{(MHz)} & \\multicolumn{2}{c}{(mJy)} &\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}& \\multicolumn{1}{c}{(mJy)}& \\\\\n\\hline\n38 &6300\\ph.8 &600\\ph.8 &\\multicolumn{1}{c}{--}&\\multicolumn{1}{c}{--}& -- & (1) \\\\\n151 &1495\\ph.8 &170\\ph.8 &989\\ph.8 &470\\ph.8 & -- & (2) \\\\\n327 &750\\ph.8 &80\\ph.8 &\\multicolumn{1}{c}{--}&\\multicolumn{1}{c}{--}& -- & (3) \\\\\n327 &623\\ph.8 &31\\ph.8 &358\\ph.8 &252\\ph.8 & -- & (4) \\\\\n1400 &144\\ph.8 &7\\ph.8 &78\\ph.8 &55\\ph.8 & 9\\ph.8 & (5) \\\\\n1425 &130\\ph.8 &7\\ph.8 &69\\ph.8 &53\\ph.8 & 8\\ph.8 & (6) \\\\\n1465 &130\\ph.8 &3\\ph.8 &68\\ph.8 &52\\ph.8 & 8\\ph.8 & (2) \\\\\n4850 & 34.5 &4\\ph.8 &18\\ph.8 &10.5 & -- & (7) \\\\\n4860 & 34\\ph.8 &2\\ph.8 &15\\ph.8 &12\\ph.8 & 7\\ph.8 & (6) \\\\\n5000 & 28\\ph.8 &2\\ph.8 &\\multicolumn{1}{c}{--}&\\multicolumn{1}{c}{--}& 6\\ph.8 & (2) \\\\\n10550& 16.6 &0.8 &7.3 &5.2 & 4.1 & (7) \\\\\n\\hline \n\\end{tabular}\n\\begin{list}{}{}\n\\item[](1) Rees 1990; (2) Lacy et al. 1993; (3) Wieringa 1991; \n\\item[](4) WENSS; (5) NVSS; (6) This work, VLA; \n\\item[](7) This work, Effelsberg\n\\end{list}\n\\end{table}\n\n\n\nIn order to study the dependence of the spectral properties of\n8C\\,0821+695 with frequency and distance from the core, we have made\nthree low resolution spectral index maps using the 10.6 GHz\nEffelsberg, the 1400 MHz NVSS, the 327 MHz WENSS and the 151 MHz CLFST\nmap by Lacy et al.~(\\cite{lacy}). To construct the $\\alpha$-maps, all\ntotal intensity maps were convolved to a circular beam of $69\\arcsec$,\nand then were registered to the nominal position of the core.\nFigure~\\ref{index} displays spectral index profiles along the main\nradio axis for the three frequency intervals, with plotted 1-$\\sigma$\nerrors deduced taking into account the rms noise level of each image\nand the uncertainties in their flux density scales. The core shows up\nas a flattening of the spectrum at the center of the higher frequency\nprofiles. In both lobes we find an overall steepening of the spectrum\nfrom the extremes towards the compact core, a behaviour typical of FR\nII radio sources. In addition, the steepening of the spectrum with\nincreasing frequency is also evident from this plot. The spectrum\nat low frequencies is rather flat in the source extremes. This result\nis expected since these regions are dominated by the flat spectrum\nhot-spot like regions and is consistent with the injection spectral\nindex derived in Sect.~3.4.\n\n\n\n\n\\begin{figure}\n\\vspace{7cm}\n\\special{psfile=larafig4.ps hoffset=-100 voffset=-190 \nhscale=70 vscale=70 angle=0} \n%\\rule{0.4pt}{4cm}\n\\caption{Profiles of the spectral index of 8C\\,0821+695 along its main axis \nwith an angular resolution of 69\\arcsec. \n$- - -$: spectral index between 151 and 327 MHz; \n$-\\cdot-\\cdot-$: spectral index between 327 and 1400 MHz; \n\\line(1,0){25} : spectral index between 1400 and 10550 MHz.} \n\\label{index}\n\\end{figure}\n\nTo study in detail the spectral index distribution over 8C\\,0821+695 we\nhave made a high-resolution $\\alpha$-map registering our VLA maps at 1425\nand 4860 MHz to the position of the core and performing a \npixel-by-pixel evaluation of the spectral index between these two frequencies\n(Fig.~\\ref{alfamap}). We find the same general trends observed at\nlower resolutions, but convolved with a now evident structure in the\n$\\alpha$-distribution. The core shows a flat spectrum between these\ntwo frequencies. The lobes present similar spectral indices, although\nthe N-lobe hints at a slightly steeper spectrum which, if real, would\nindicate a more efficient energy dissipation in this region.\n\n\\begin{figure}\n\\vspace{12.5cm}\n\\special{psfile=larafig5.ps hoffset=-35 voffset=-30 \nhscale=50 vscale=50 angle=0}\n%\\rule{0.4pt}{4cm}\n\\caption{Spectral index, in grey-scale, of 8C\\,0821+695 between \n4860 and 1425 MHz, with an angular resolution of 9\\arcsec$\\times$9\\arcsec. \nThe contours\nrepresent total intensity at 5 GHz to facilitate the identification of\nemission regions in the radio source with spectral trends. Numerical values\nof the mean spectral index over selected regions are indicated for clarity.} \n\\label{alfamap}\n\\end{figure}\n\n\\subsection{Physical parameters of 8C\\,0821+695}\n\n\\begin{table*}[]\n\\caption[]{Physical parameters for the N- and S- lobes}\n\\label{param}\n\\begin{tabular}{cccccc}\n\\hline\nDistance & FWHM & Brightness & B$_{me}$ & u$_{me}$ & P$_{eq}$ \\\\\n (kpc) & (kpc) &(mJy/beam$^a$) &($\\eta^{-2/7}\\mu$G)& ($\\eta^{-4/7}$J m$^{-3}$) \n& ($\\eta^{-4/7}$N $m^{-2}$)\\\\ \n\\hline\n\\multicolumn{6}{c} {North lobe} \\\\\n\\hline\n {\\phe}340 & {\\phe}85 & {\\phe}2.5 &{\\phe}3.8 & 1.4$\\times 10^{-13}$ & 8.5$\\times 10^{-14}$ \\\\ \n \\phe 480 & \\phe 98 & \\phe 1.9 &\\phe 3.4 & 1.1$\\times 10^{-13}$ & 6.7$\\times 10^{-14}$ \\\\\n \\phe 630 & 109 & \\phe 4.6 &\\phe 4.3 & 1.7$\\times 10^{-13}$ & 1.0$\\times 10^{-13}$ \\\\\n \\phe 775 & 104 & \\phe 7.3 &\\phe 4.9 & 2.3$\\times 10^{-13}$ & 1.4$\\times 10^{-13}$ \\\\\n \\phe 923 & \\phe 27 & 42.6 &12.0 & 1.3$\\times 10^{-12}$ & 8.2$\\times 10^{-13}$ \\\\\n\\hline \n\\multicolumn{6}{c} {South lobe} \\\\\n\\hline\n \\phe 433 & \\phe 91 & {\\phe}0.8 & {\\phe}2.7 & 6.9$\\times 10^{-14}$ & 4.3$\\times 10^{-14}$ \\\\\n \\phe 579 & \\phe 85 & {\\phe}1.4 & {\\phe}3.3 & 9.9$\\times 10^{-14}$ & 6.1$\\times 10^{-14}$ \\\\\n \\phe 726 & \\phe 98 & {\\phe}3.1 & {\\phe}3.9 & 1.4$\\times 10^{-13}$ & 8.9$\\times 10^{-14}$ \\\\\n \\phe 872 & \\phe 79 & {\\phe}6.8 & {\\phe}5.2 & 2.5$\\times 10^{-13}$ & 1.6$\\times 10^{-13}$ \\\\\n 1019 & 104 & {\\phe}8.8 & {\\phe}5.2 & 2.5$\\times 10^{-13}$ & 1.6$\\times 10^{-13}$ \\\\\n\\hline \\\\\n\\end{tabular}\n\\begin{list}{}{}\n\\item[$^a$] The beam is a circular Gaussian of 15\\arcsec$\\times$15\\arcsec\n\\end{list}\n\\end{table*}\n\nWe have measured the FWHM and the surface brightness at several\npositions on the ridge line of 8C\\,0821+695 by fitting Gaussians to\nsurface brightness profiles taken perpendicular to the source main\naxis in the high-sensitivity 1400 MHz map by Lacy et al.\n(\\cite{lacy}). The deconvolution of the width and surface brightness\nwas done following Appendix A in Killeen et al. (\\cite{killeen}). We\nused the standard formulae of synchrotron radiation (e.g. Miley\n\\cite{miley}) to calculate the minimum energy density $u_{me}$ at\nthese positions and the corresponding magnetic field $B_{me}$, which\nis approximately the equipartition field. The total pressure is\nassumed to be that of equipartition between particles and magnetic\nfield, $P_{eq}=0.62~u_{me}$. Besides, the following assumptions were\nmade in the calculations: {\\em i)} the magnetic field is assumed to be\nrandom; {\\em ii)} the energy of particles is equally stored in the\nform of relativistic electrons and heavy particles; {\\em iii)} lower\nand upper frequency cutoffs were set to 10 MHz and 100 GHz,\nrespectively; {\\em iv)} the spectral index is 1.1; and {\\em v)} the\nline-of-sight depth is equal to the deconvolved FWHM. The results are\nlisted in Tab.~\\ref{param} as a function of the filling factor of the\nemitting regions $\\eta$.\n\n\n\\subsection{Spectral aging}\n\nBased on the maps at 151~MHz (Lacy et al.~\\cite{lacy}), 327~MHz\n(WENSS), 1.4~GHz (NVSS), 4.8~GHz (VLA) and 10.4~GHz (Effelsberg), we\nhave performed a spectral aging analysis of 8C\\,0821+695. We have\ndetermined the spectrum at different positions of the source averaging\nthe flux density over selected regions with a beam equivalent area\n($69\\arcsec$) in order to insure independent measurements. Three\nselected regions were centered on the N-lobe (at the position of the\nhot-spot and at 711 and 364 kpc from the core) and other three on the\nS-lobe (at the southern extreme and at 903 and 553 kpc from the core).\n\nWe show in Fig.~\\ref{spectra} the spectra of the different selected\nregions and the fits to the data after the application of synchrotron\nloss models. Left and right panels refer to the N- and S-lobe,\nrespectively. The spectra at the source extremes (top panels) are\nbest fitted by the continuous injection model (CI; Pacholczyk\n\\cite{pacholczyk}), giving an injection spectral index of $\\alpha_{inj}\n= 0.4$ for the northern hot-spot and $\\alpha_{inj} = 0.6 $ for the\nsouthern extreme of the source, in agreement with the low frequency\nspectral index in Fig.~\\ref{index}. The spectra in these regions show\na break at low frequencies ($\\sim 1$ GHz) with a moderate steepening\nafterwards. However, the flat spectrum of the hot-spots at low\nfrequencies might indicate that the source here is optically thick and\nany spectral fit in these regions must be taken with\ncaution. Moreover, Meisenheimer et al. (\\cite{meisenheimer}) find that\nlow frequency breaks at hot-spots are more likely related to the ratio\nbetween the outflow distance and the outflow velocity of the\npost-shocked material after the Mach disk rather than to synchrotron\naging. Thus, we will not use the information of the break frequency\nat the source extremes to derive synchrotron ages.\n\nMiddle panels in Fig.~\\ref{spectra} correspond to the spectra taken at\n711 kpc (N-Lobe) and 903 kpc (S-Lobe) from the core, respectively.\nOur data do not allow us to distinguish between the Jaffe-Perola (JP;\nJaffe \\& Perola \\cite{jaffe}) or the Kardashev-Pacholczyk (KP;\nKardashev \\cite{kardashev}, Pacholczyk \\cite{pacholczyk}) synchrotron\nloss models, both producing equivalent results. An injection spectral\nindex $\\alpha_{inj} = 0.7$ has been found and kept fixed in these\nfits. The discrepancy between the injection spectral index in the\nlobes and in the hot-spots is similar to that found in Cygnus~A\n(Carilli et al.~\\cite{carilli}), although a physical interpretation of\nthis fact remains unclear. The derived break frequencies are 15 GHz\nat 711 kpc in the N-lobe and 18 GHz at 903 kpc in the S-lobe.\n\nBottom panels in Fig.~\\ref{spectra} refer to the two regions nearest\nto the core, at 363 kpc (N-Lobe) and 553 kpc (S-Lobe). Again, fits\nusing KP and JP models are indistinguishable. The break frequency is\n1.6 GHz in the N-lobe and 2.2 GHz in the S-lobe. Due to the sharp\ncut-off, the flux densities at 4.8 and 10 GHz are below the noise\nlevel. In the fit we kept $\\alpha_{inj} = 0.7$ as a fixed parameter.\n\nSynchrotron ages were derived from the break frequencies in the lobes \nusing the equation (Carilli et al.~\\cite{carilli}):\n\\begin{equation}\nt_{syn}=1.61\\times 10^3 \\frac{\\sqrt{{\\rm B}_{\\rm eq}}}{{\\rm B}_{\\rm eq}^2 +\n{\\rm B}_{\\rm IC}^2} \\frac{1}{\\sqrt{\\nu_{\\rm B}(1+{\\rm z})}}.\n\\end{equation}\nThe synchrotron age $t_{syn}$ is given in Myr, the break frequency\n$\\nu_{\\rm B}$ in GHz and magnetic fields in $\\mu$G. For the strength of \nthe equipartition magnetic\nfield B$_{\\rm eq}$ we took the corresponding values from\nTab.~\\ref{param}, and a magnetic field equivalent to the Inverse\nCompton microwave background of ${\\rm B}_{\\rm IC} = 7.7\\mu$G (${\\rm\nB}_{\\rm IC} = 3.25 (1+{\\rm z})^2 $). \nThe spectral ages derived from the data are plotted in Fig.~\\ref{age}.\nThe errors in the spectral ages \ncan be derived from the uncertainties of ${\\rm B}_{\\rm eq}$ and \n$\\nu_{\\rm B}$; however, when \n${\\rm B}_{\\rm eq} \\sim \\frac{{\\rm B}_{\\rm IC}}{\\sqrt{3}}$ (as it is\napproximately given in our case), the total error is dominated by the\nuncertainties of the break frequencies.\nTherefore errors in Fig.~\\ref{age} depend directly on the errors in the break \nfrequencies which we have estimated considering the 1-$\\sigma$ region\nof allowance in the space of free-parameters in the fits. \nA weighted least-square fit yields a mean expansion velocity\nof 0.08 c for both lobes, which represents a measure of the rate of\nseparation of the jet-head from the lobe material. The source spectral\nage, obtained by extrapolation of the age profiles up to the core, is\n42 Myr. We note that the derived expansion velocity is consistent with that \nobtained assuming a zero age at the hot-spots, supporting the reliability of \nour spectral fit argument.\n\n\n\\begin{figure}\n\\vspace{10cm}\n\\special{psfile=larafig6.ps hoffset=-10 voffset=-75\nhscale=49 vscale=49 angle=0}\n%\\rule{0.4pt}{4cm}\n\n\\caption{Spectra at different regions of 8C\\,0821+695. Left and right panels \nrefer to the N- and S-lobe, respectively. Upper panels correspond to the \nspectra at the source extremes (hot-spots), fitted by CI model. Middle and\nbottom panels correspond to lobe regions at 711 and 364 kpc (N-lobe),\nand 903 and 553 kpc (S-lobe) from the core, respectively, where data have\nbeen fitted with a KP (continuous line) and JP (dashed line) models.\nUpper limits in the bottom panels are at the rms noise level of the \ncorresponding maps.}\n\n\\label{spectra}\n\\end{figure}\n\n\n\\begin{figure}\n\\vspace{7cm}\n\\special{psfile=larafig7.ps \nhoffset=20 voffset=-50\nhscale=35 vscale=35 angle=0}\n%\\rule{0.4pt}{4cm}\n\\caption{Spectral ages as a function of core distance in 8C\\,0821+695. \nFilled dots refer to the N-lobe; triangles to the S-lobe. A mean expansion\nvelocity of 0.08 c is derived from a linear fit to the data. A source\nspectral age of 42 Myrs is derived from the extrapolation at zero distance.} \n\\label{age}\n\\end{figure}\n\n\n\n\\section{Discussion}\n\n\\subsection{The ``conical'' lobe}\n\nIn this section we propose a simple scenario of a jet nourishing a radio \nlobe with the aim of \nconstraining the physical parameters of the\njet itself and of the ambient medium surrounding the radio emission. We\nconsider the geometry outlined in Fig.~\\ref{dibu} for the jet and the\nlobe of a radio galaxy, and assume that\nthe external medium is uniform and steady. Relativistic corrections\nare not taken into account here, since lobe propagation velocities are\nsmall compared with the speed of light (eg. Begelman et al. \\cite{begelman2}). \n\n\nIn general, the ratio of the advance speed of the\nemitting body (the jet-head velocity $v_{h}$) to the \nsound speed of the unperturbed external region ($v_{s}$), is \nrelated to the angle between the shock front and the velocity direction \n(the Mach angle $\\Phi$), through the equation:\n\\begin{eqnarray}\n\\sin\\Phi & = & \\frac{v_{s}}{v_{h}} \\nonumber \\\\ \n & = & \\frac{1}{v_{h}}\\sqrt{\\frac{\\gamma P_{a}}{\\rho_{a}}},\n\\label{1}\n\\end{eqnarray}\nwhere $\\gamma$, $P_{a}$ and $\\rho_{a}$ are the adiabatic index, the pressure \nand the mass density of the ambient medium, respectively.\nThe mass density may also be written $\\rho_{a}=\\sigma n_{a}$, \nwhere $\\sigma$ is\nthe mean atomic weight and $n_{a}$ is the number of particles \nper unit volume. Assuming an ideal gas, the pressure, density and temperature\nare related through the equation of state $P_a = n_a k T_a$, where $k$ is the \nBoltzmann's constant and $T_a$ is the temperature of the ambient medium. \nEquation~\\ref{1} provides a relationship between\n$v_h$, the lobe geometry and the properties of the external medium. \n\n\\begin{figure}\n\\vspace{9cm}\n\\special{psfile=larafig8.ps hoffset=-30 voffset=-80 \nhscale=50 vscale=50 angle=0}\n\\caption{Top: schematic representation of the jet and the lobe of a radio \ngalaxy expanding in an uniform and homogeneous environment. \nBottom: translation of this scheme to the northern lobe of 8C\\,0821+695. \n\\label{dibu}}\n\\end{figure}\n\n\n \nWe note that $v_h$ as given in Eq.~\\ref{1} corresponds to the advance\nvelocity of the jet-head with respect to the external medium at the\ntime of the observations since it depends only on local conditions\nmeasured close to the hot-spot. On the other hand, determinations\nbased on aging arguments (Sect.~3.4) correspond to the jet-head\nvelocity measured with respect to the lobe emitting material and\naveraged over the whole life of the radio source ($\\langle v'_{h}\n\\rangle$). Even if all our assumptions are correct, these two \nestimations of the advance velocity, $v_h$ and $\\langle\nv'_{h}\\rangle$, may be different {\\em i)} if the backflow $v_{bf}$ of\nthe lobe material is not negligible or {\\em ii)} if the jet-head is\naccelerated, so that comparing mean and instantaneous velocities is\nmeaningless. Besides, incorrect assumptions (e.g. deviations from\nminimum energy conditions, a break frequency distribution not related to\nthe separation velocity, wrong estimations of the external physical\nparameters, etc.) may lead to differing results (see Carilli et\nal. \\cite{carilli} for a detailed discussion). In the following we\nwill consider that all our assumptions are reasonably good\napproximations to the real physical situation.\n\nThe absence or presence of diffuse extended tails of emission\nperpendicular to the source axis provide information of how important\nthe backflow of lobe material is. In general, we will consider that the \nmean backflow\nvelocity is a factor $\\epsilon$ of the mean advance velocity of\nthe jet-head with respect to the external medium, i.e. $\\langle v_{bf} \\rangle\n= \\epsilon \\langle v_h \\rangle$, so that the velocity of the head with\nrespect to the lobe $\\langle v'_{h} \\rangle = (1+\\epsilon) \\langle v_h\n\\rangle$. Similarly, the spectral age is related to the dynamical age of\nthe source as $t=(1+\\epsilon) t_{syn}$. Moreover, we can assume a\nconstant jet-head deceleration and determine the initial head velocity\n$v_{hi}$ as\n\\begin{equation}\nv_{hi}=2(1+\\epsilon)^{-1} \\langle v'_{h} \\rangle - v_{h}. \n\\label{2}\n\\end{equation}\n\n\n\n\nOn the other hand, the \nbalance of the ram pressure of the ambient medium and the thrust of the jet, \nspread over the cross-sectional area $A_{h}$ of the bow\nshock at the end of the jet is (Begelman \\& Cioffi 1989):\n\\begin{equation}\nv_{h}\\sim\\sqrt{\\frac{L_{j}}{\\sigma~n_{a}v_{j}A_{h}}},\n\\label{3}\n\\end{equation}\nwhere $L_j$ is the total jet power and $v_j$ is the jet bulk\nvelocity. In an uniform medium and if these two jet parameters were\nconstant with time, a varying $v_h$ could be obtained through a\nvariation in the contact surface $A_h$. \nWe note that a constant $A_{h}$ and $n_{a}$ decreasing \nwith core distance would lead to $v_{h}$ increasing with time, \na situation highly unplausible (Loken et al. \\cite{loken}). Although a \ncombination of both\nsituations might occur leading to a given $v_{h}$ evolution,\nwe will neglect density variations for simplicity.\nTherefore, from \nEq.~\\ref{3}, we find a relation between $v_h$ and $A_h$ at present\nand initial conditions:\n\\begin{equation}\nA_h = A_{hi} \\left( \\frac{v_{hi}}{v_h} \\right )^2 .\n\\label{4}\n\\end{equation}\n\nThis relation translates to an opening angle ($\\theta$),\ndefined by the time evolution of the contact surface, given by\n\\begin{equation}\n\\tan \\theta = \\frac{\\sqrt{\\frac{A_h}{\\pi}} \n\\left(1- \\frac{v_{h}}{v_{hi}} \\right )}{l},\n\\label{5}\n\\end{equation}\nwhere $l$ is the total jet length.\n\n\\subsection{Application to 8C\\,0821+695}\n\nThe N-lobe of 8C\\,0821+695 clearly resembles the simple geometry\noutlined in Fig.~\\ref{dibu}, so it seems reasonable to apply the\nprevious analysis to this lobe. Even if we need to make several \nassumptions and the uncertainties of our results are high, we obtain at least \nan idea of the order of magnitude of the different parameters, which is the\naim of these calculations.\n\nFrom the VLA maps at 4860 and 1425 MHz (Fig.~\\ref{vla}), we measure\nan angle $\\Phi=12^{\\circ}$ at the N-lobe (see Fig.~\\ref{dibu}).\nHowever, we note that this value is a lower limit to the true Mach\nangle since we implicitly assume that the edge of the synchrotron\nemitting region defines the lobe contact discontinuity, and that this\ndiscontinuity is coincident with the\nbow shock produced by the jet-head advance in the external\nmedium. Such assumption underestimates the true Mach angle, since it\nimplies that the region of shocked external medium between the contact \ndiscontinuity and the bow shock is negligible. Moreover, we assume \n$\\sigma=1.4$~amu,\n$\\gamma=\\frac{5}{3}$ and an upper limit of $T_a=10^7$~K for the\nexternal medium temperature (Barcons et al. \\cite{barcons}).\n\nWe have accepted the minimum energy conditions and used the NVSS and WENSS \nmaps to derive the cocoon pressure at low brightness regions in the\nlobes of 8C\\,0821+695, far away from the hot-spot; we obtain $P_c\n\\sim 1.5\\times 10^{-14}$ Nm$^{-2}$. Strictly speaking, this value\nconstitutes an upper limit to the external pressure $P_a$ since the\nbridges in FR II radio sources are most probably overpressured with\nrespect to the surrounding medium (e.g. Subrahmanyan \\& Saripalli\n\\cite{subra1}; Nath \\cite{nath}). However, observations (Subrahmanyan\net al. \\cite{subra2}) and models (Kaiser \\& Alexander \\cite{kaiser})\nindicate that the lobes of FR II radio galaxies grow in a self-similar\nway, so that GRGs are expected to have the lowest pressures, being\ncloser to a situation of pressure equilibrium with the outer medium\nthan other FR II radio galaxies. Thus, we can reasonably assume for\nour calculations that the low-brightness regions in\nthe lobes of 8C\\,0821+695 provide a good approximation of the ambient\ngas pressure $P_{a}$ (see also Schoenmakers et al. \\cite{arno2}). In fact, \nthe pressure we obtain is as low as\nthat found at the very periphery of galaxy clusters, confirming that\nthe environment of this giant source is tenuous. \n\nConsidering the upper limit temperature of $10^7$~K for the ambient\ngas, the particle density resulting from the equation of state is\nabout $10^2$~m$^{-3}$. This density is consistent with the limit on\n$RM$ ($|RM| \\le 20$ rad m$^{-2}$) if the ambient uniform magnetic\nfield is about 0.5 $\\mu$G and the Faraday depth less than 1 Mpc, which\nare reasonable values since we do not expect a strong field to be\ndistributed over large regions.\n\n\nFrom Eq.~\\ref{1}, we obtain $v_h \\sim 5\\times 10^{-3}$~c which, \naccording to our assumptions is an\nupper limit to the true jet-head velocity. Besides,\nfrom spectral aging arguments (Sect.~3.4) we obtained a mean expansion\nvelocity of the head with respect to the lobe material $\\langle v'_{h}\n\\rangle = 0.08$~c. On the other hand, Lacy et al. (\\cite{lacy}) find \nevidence of a tail at the base of the N-lobe and suggest a backflow speed \nclose to the advance speed of the head. According to that, we will \nassume $\\epsilon \\simeq 1$, so\nthat $\\langle v_{h} \\rangle \\simeq \\langle v_{bf} \\rangle \\simeq\n0.04$~c. Using Eq.~\\ref{2}, we estimate an initial jet-head velocity\n$v_{hi} \\sim 0.075$~c.\n\n\nThe area of the head contact surface $A_{h}$ can be derived by fitting\nan elliptical Gaussian to the northern hot-spot at 5 GHz. We obtain a\ndeconvolved angular diameter of $\\sim 5\\arcsec$ ($\\sim 25$ kpc). \nWe can then\ncalculate the total power of the jet from Eq.~\\ref{3}, assuming a\njet bulk velocity $v_j \\sim$c (Fernini et al. \\cite{fernini}). \nWe obtain $L_j = 7.1\\times 10^{37}$\nW. Alternatively, we can estimate the total power from the average\nminimum energy density ($\\bar{u}_{me}=2.7\\times 10^{-13}$ J m$^{-3}$; \nTab.~\\ref{param}), the volume of the source\n(simplified to a cylinder of 2~Mpc$\\times$200~kpc) and its dynamical age \n$t=2 t_{syn} = 84$ Myr, giving\n$L = 9\\times 10^{37}$W, fully consistent with the previous result. \n\nFrom Eq.~\\ref{4}, the angular diameter of the jet contact surface at the\ninitial stages of the source is about 0\\farcs33. The\nincrease in the contact surface from this value to the measured one \n($5\\arcsec$) requires an opening angle $\\theta$, defined by the hot-spot \nsize evolution, of 0\\fdg7 (Eq.~\\ref{5}).\nThus, a small increase of the hot-spot size with time can naturally \nexplain the deceleration of the\njet-head and the difference in the velocity determinations from local\nand global conditions.\n\n\nFinally, the radio power of the northern lobe $L_{r}$ can be derived from the \nobserved flux density and spectral index:\n\\begin{equation}\nL_{r}=4\\pi D_{L}^{2}\\int_{\\nu_{1}}^{\\nu_{2}}S(\\nu)d\\nu ,\n\\end{equation}\nwhere $D_{L}$ is the luminosity distance, and $\\nu_{1}=10$ MHz and \n$\\nu_{2}=100$ GHz are\nthe assumed lower and upper frequency cutoffs. Since $S(\\nu)\\propto \n\\nu^{-\\alpha}$ and $\\alpha=1.1$, we obtain\n$ L_{r}=6.9\\times 10^{35}$ W. $L_{r}$ being about two orders of magnitude \nlower than $L_{j}$ would indicate that most of the jet power is devoted \nto the expansion of the lobe against the external medium. Results are \nsummarized in Table~\\ref{param2}.\n\n\n\n\\noindent\n\n\\begin{table}[h]\n\\caption[]{8C\\,0821+695 and its environment}\n\\label{param2}\n\\begin{tabular}{rrll} \n\\hline \nAmbient density & $n_{a} $ & $\\sim 100$ & m$^{-3}$ \\\\\nAmbient pressure & $P_{a} $ & $\\sim 1.5\\times 10^{-14}$ & N m$^{-2}$\\\\ \nPresent head velocity & $v_{h} $ & $\\sim 0.005$ & c \\\\\nMean head velocity &$\\langle v_h \\rangle$ & $\\sim 0.04$ & c \\\\ \nInitial head velocity & $v_{hi}$ & $\\sim 0.075$ & c \\\\\nSpectral Age & $t_{syn}$& $\\sim 4.2\\times 10^{7}$ & yr \\\\\nDynamical Age & $t $ & $\\sim 8.4\\times 10^{7}$ & yr \\\\ \nNorthern jet Power & $L_{j}$ & $\\sim 7\\times 10^{37}$ & W \\\\ \nN-lobe radio power & $L_{r}$ & $\\sim 7\\times 10^{35}$ & W \\\\ \nOpening angle & $\\theta$ & $\\sim 0\\fdg7$ & \\\\ \n\\hline \n\\end{tabular}\n\\end{table}\n\nThe S-lobe does not present such a suitable morphology for the\napplication of the previous simple model since the head of the lobe\ndoes not have a clear cone-like appearance (see Sect.~2.3). \nFrom the observed arm-ratio, we might deduce that the external medium here\ncould be more tenuous than in the northern lobe region.\n\n\n\\section{Conclusions}\n\nWe present new radio observations made with the VLA and the 100-m\nEffelsberg radio telescope, of the GRG 8C\\,0821+695 at different\nfrequencies and angular resolutions. Our data have been analyzed\ntogether with survey and literature data in order to study the details\nof a high-redshift GRG, and obtain information about the external\nmedium surrounding the radio source.\n\n8C\\,0821+695 is a straight 2 Mpc long FR II radio source, with a\nnorth-to-south arm-ratio of 0.89. The N-lobe contains a hot-spot,\nresponsible for most of the source polarized emission. The S-lobe\npresents a more relaxed structure, without a well defined hot-spot.\nAt high frequencies ($\\nu\\geq 1400$~MHz) 8C\\,0821+695 shows a\nprominent compact core. We have not found any trace of the jets\nnourishing the lobes.\n\nThe spectral index distribution over the lobes of 8C\\,0821+685 is\ntypical of FR II-type radio galaxies, showing a gradual steepening\nfrom the outer ends towards the core. The mean lobe spectral index is\n$\\alpha=1.1$. The core has a flat spectrum with $\\alpha= 0.3$. Using\nthe available data, we have made a spectral-aging analysis of the\nsource lobes, providing the dependence of the spectral break frequency\nand the synchrotron age with the distance from the core. We obtain a\nmean expansion velocity of the jet head with respect to the lobe\nmaterial of $0.08$~c, and a spectral age of 42 Myr. This age determination\nmight be affected by the possible existence of backflow of material\nin the lobe, being a lower limit to the true age. The age we derive for \n8C\\,0821+695 is of the order of ages estimated for other GRGs \n(Schoenmakers et al. \\cite{arno2}). \n\nWe have studied the $RM$ over the lobes of 8C\\,0821+695, obtaining a\nsmooth and uniform distribution, which we ascribe to Faraday rotation\nmostly produced by the Galactic medium. Equipartition conditions have\nbeen assumed in order to derive physical parameters of the lobes at\ndifferent positions, yielding magnetic fields, pressures and energy\ndensities that are consistent with estimated values in other GRGs.\n\nUnder very simple assumptions we have estimated physical parameters of\nthe jet and the external medium of 8C\\,0821+695. We find that the\npresent expansion velocity is significantly lower than the mean\nexpansion velocity even if backflow is allowed, implying the existence\nof deceleration. We explain this deceleration by an increase of the\ncross-sectional area of the bow shock at the end of the jet with\ntime. We note that external density estimates in the literature for\nother GRGs usually consider the contact surface measured at the time\nof the observations together with mean quantities (like the expansion\nvelocity derived from aging arguments), resulting in external\ndensities lower than the density we obtain. However, our results are\nstill consistent with GRGs evolving in poor density regions.\n\n\\begin{acknowledgements}\n\nWe thank the referee Dr. R. Perley for helpful and constructive\ncomments to the paper. The National Radio Astronomy Observatory is a\nfacility of the National Science Foundation operated under cooperative\nagreement by Associated Universities, Inc. This research has made use\nof the NASA/IPAC Extragalactic Database (NED) which is operated by the\nJet Propulsion Laboratory, California Institute of Technology, under\ncontract with the National Aeronautics and Space Administration. This\nresearch is supported in part by the Spanish DGICYT (PB97-1164). KHM\nwas supported by the European Commission, TMR Programme, Research\nNetwork Contract ERBFMRXCT96-0034 ``CERES''. LF, GG and MM acknowledge\na partial support by the Italian Ministry for University and Research\n(MURST) under grant Cofin98-02-32.\n\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[1977]{baars} Baars J.M.W., Genzel R., Pauliny-Toth I.I.K., Witzel A.,\n1977, \\aa, 61, 99\n\n\\bibitem[1991]{barcons} Barcons X., Fabian A.C. \\& Rees M.J., 1991, Nature, \n350, 685\n\n\\bibitem[1984]{begelman2} Begelman M.C., Blandford R.D., Rees M.J., 1984, Rev. Mod. Phys., 56, 255\n\n\\bibitem[1989]{begelman} Begelman M.C., Cioffi D.F., 1989, \\apj, 345, L21\n\n\\bibitem[1991]{carilli} Carilli C., Perley R.A., Dreher J.H., Leahy J.P., \n1991, \\apj, 383, 554\n\n\\bibitem[1998]{nvss} Condon J.J., Cotton W.D., Greisen E.W., Yin Q.F.,\nPerley R.A., Taylor G.B., Broderick J.J., 1998, \\anj, 115, 1693\n\n\\bibitem[1974]{fanaroff} Fanaroff B.L., Riley J.M., 1974, \\mn, 167, 31\n\n\\bibitem[1997]{fernini} Fernini I., Burns J.O., Perley R.A., 1997, \\anj, \n114, 2292 \n\n\\bibitem[1992]{gregorini} Gregorini L., Klein U., Parma P., Wielebinski R., \nSchlickeiser R., 1992, \\aasup, 94, 13 \n\n\\bibitem[1999]{ishwara} Ishwara-Chandra C.H., Saikia D.J., 1999, \\mn, 309, 100 \n\n\\bibitem[1973]{jaffe} Jaffe W.J., Perola G.C., 1973, \\aa, 26, 423\n\n\\bibitem[1997]{kaiser} Kaiser C.R., Alexander P., 1997, \\mn, 286, 215\n\n\\bibitem[1962]{kardashev} Kardashev, N.S., 1962, \\anj, 6, 317\n\n\\bibitem[1986]{killeen} Killeen N.E.B., Bicknell G.V., Ekers R.D., 1986,\n\\apj, 302, 306\n\n\\bibitem[1995]{kleinmack} Klein U., Mack K.-H., 1995, Proceedings Workshop\non ``Multi-Feed Systems for Radio Telescopes'', Tucson,\nEd. D.T. Emerson, ASP Conference Series \n\n\\bibitem[1993]{lacy} Lacy M., Rawlings S., Saunders R., Warner P.J., 1993, \n\\mn, 264, 721\n\n\\bibitem[1999]{lara} Lara L., M\\'arquez I., Cotton W.D., Feretti L., Giovannini G., Marcaide J.M., Venturi T., 1999, \\nar, 43, 643\n\n\\bibitem[1992]{loken} Loken C., Burns D.O., Clarke D.A., Norman M.L., 1992, \\apj, 392, 54\n\n\\bibitem[1997a]{mack97a} Mack K.-H., Kerp J., Klein U., 1997a, \\aa, 324, 870\n\n\\bibitem[1997b]{mack97b} Mack K.-H., Klein U., O'Dea C.P., Willis A.G., \n1997b, \\aa, 123, 423\n\n\\bibitem[1989]{meisenheimer} Meisenheimer K., R\\\"oser H.-J., Hiltner P.R., \nYates M.G., Longair M.S., Chini R., Perley R.A., 1989, \\aa, 219, 63 \n\n\\bibitem[1980]{miley} Miley G., 1980, \\rev, 18, 165\n\n\\bibitem[1995]{nath} Nath B.B., 1995, \\mn, 274, 208\n\n\\bibitem[1970]{pacholczyk} Pacholczyk, A.G., 1970, Radio Astrophysics (San Francisco: Freeman)\n\n\\bibitem[1996]{parma} Parma P., de Ruiter H.R., Mack K.-H., van Breugel W., \nDey A., Fanti R., Klein U., 1996, \\aa, 311, 49\n\n\\bibitem[1990]{rees} Rees N., 1990, \\mn, 244, 233\n\n\\bibitem[1980]{simard} Simard-Normandin M., Kronberg P.P., 1980, \\apj, 242, 74\n\n\\bibitem[1997]{wenss} Rengelink R., Tang Y., de Bruyn A.G., Miley G.K., \nBremer M.N., R\\\"ottgering H.J.A., Bremer M.A.R., 1997, \\aasup, 124, 259 \n\n\\bibitem[1982]{scheuer} Scheuer P.A.G., 1982, in Heeschen D.S., Wade C.M. eds,\nProc. IAU Symp. 97, ``Extragalactic Radio Sources''. Reidel,\nDordrecht, p.163 \n\n\\bibitem[2000a]{arno1} Schoenmakers A.P., de Bruyn A.G., R\\\"ottgering H.J.A.,\nvan der Laan H., 2000a, \\aa, in preparation\n\n\\bibitem[2000b]{arno2} Schoenmakers A.P., Mack K.-H., de Bruyn A.G.,\nR\\\"ottgering H.J.A., Klein U., van der Laan H., 2000b, \\aa, in press\n\n\\bibitem[1993]{subra1} Subrahmanyan R., Saripalli L., 1993, \\mn, 260, 908\n\n\\bibitem[1996]{subra2} Subrahmanyan R., Saripalli L., Hunstead R.W., 1996, \n\\mn, 279, 257\n\n\\bibitem[1974]{wardle} Wardle J.F.C., Kronberg P.P., 1974,\n\\apj, 194, 249\n\n\\bibitem[1991]{wieringa} Wieringa M., 1991, PhD. Thesis, Univ. Leiden\n\n\\bibitem[1990]{willis} Willis A.G., O'Dea C.P., 1990, in ``Galactic and \nIntergalactic Magnetic Fields'' IAU Symp. 140, Beck R., Kronberg P.P. \\& \nWielebinski R. (eds.), Reidel, Dordrecht, p.455\n\n\n\\end{thebibliography}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002009.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1977]{baars} Baars J.M.W., Genzel R., Pauliny-Toth I.I.K., Witzel A.,\n1977, \\aa, 61, 99\n\n\\bibitem[1991]{barcons} Barcons X., Fabian A.C. \\& Rees M.J., 1991, Nature, \n350, 685\n\n\\bibitem[1984]{begelman2} Begelman M.C., Blandford R.D., Rees M.J., 1984, Rev. Mod. Phys., 56, 255\n\n\\bibitem[1989]{begelman} Begelman M.C., Cioffi D.F., 1989, \\apj, 345, L21\n\n\\bibitem[1991]{carilli} Carilli C., Perley R.A., Dreher J.H., Leahy J.P., \n1991, \\apj, 383, 554\n\n\\bibitem[1998]{nvss} Condon J.J., Cotton W.D., Greisen E.W., Yin Q.F.,\nPerley R.A., Taylor G.B., Broderick J.J., 1998, \\anj, 115, 1693\n\n\\bibitem[1974]{fanaroff} Fanaroff B.L., Riley J.M., 1974, \\mn, 167, 31\n\n\\bibitem[1997]{fernini} Fernini I., Burns J.O., Perley R.A., 1997, \\anj, \n114, 2292 \n\n\\bibitem[1992]{gregorini} Gregorini L., Klein U., Parma P., Wielebinski R., \nSchlickeiser R., 1992, \\aasup, 94, 13 \n\n\\bibitem[1999]{ishwara} Ishwara-Chandra C.H., Saikia D.J., 1999, \\mn, 309, 100 \n\n\\bibitem[1973]{jaffe} Jaffe W.J., Perola G.C., 1973, \\aa, 26, 423\n\n\\bibitem[1997]{kaiser} Kaiser C.R., Alexander P., 1997, \\mn, 286, 215\n\n\\bibitem[1962]{kardashev} Kardashev, N.S., 1962, \\anj, 6, 317\n\n\\bibitem[1986]{killeen} Killeen N.E.B., Bicknell G.V., Ekers R.D., 1986,\n\\apj, 302, 306\n\n\\bibitem[1995]{kleinmack} Klein U., Mack K.-H., 1995, Proceedings Workshop\non ``Multi-Feed Systems for Radio Telescopes'', Tucson,\nEd. D.T. Emerson, ASP Conference Series \n\n\\bibitem[1993]{lacy} Lacy M., Rawlings S., Saunders R., Warner P.J., 1993, \n\\mn, 264, 721\n\n\\bibitem[1999]{lara} Lara L., M\\'arquez I., Cotton W.D., Feretti L., Giovannini G., Marcaide J.M., Venturi T., 1999, \\nar, 43, 643\n\n\\bibitem[1992]{loken} Loken C., Burns D.O., Clarke D.A., Norman M.L., 1992, \\apj, 392, 54\n\n\\bibitem[1997a]{mack97a} Mack K.-H., Kerp J., Klein U., 1997a, \\aa, 324, 870\n\n\\bibitem[1997b]{mack97b} Mack K.-H., Klein U., O'Dea C.P., Willis A.G., \n1997b, \\aa, 123, 423\n\n\\bibitem[1989]{meisenheimer} Meisenheimer K., R\\\"oser H.-J., Hiltner P.R., \nYates M.G., Longair M.S., Chini R., Perley R.A., 1989, \\aa, 219, 63 \n\n\\bibitem[1980]{miley} Miley G., 1980, \\rev, 18, 165\n\n\\bibitem[1995]{nath} Nath B.B., 1995, \\mn, 274, 208\n\n\\bibitem[1970]{pacholczyk} Pacholczyk, A.G., 1970, Radio Astrophysics (San Francisco: Freeman)\n\n\\bibitem[1996]{parma} Parma P., de Ruiter H.R., Mack K.-H., van Breugel W., \nDey A., Fanti R., Klein U., 1996, \\aa, 311, 49\n\n\\bibitem[1990]{rees} Rees N., 1990, \\mn, 244, 233\n\n\\bibitem[1980]{simard} Simard-Normandin M., Kronberg P.P., 1980, \\apj, 242, 74\n\n\\bibitem[1997]{wenss} Rengelink R., Tang Y., de Bruyn A.G., Miley G.K., \nBremer M.N., R\\\"ottgering H.J.A., Bremer M.A.R., 1997, \\aasup, 124, 259 \n\n\\bibitem[1982]{scheuer} Scheuer P.A.G., 1982, in Heeschen D.S., Wade C.M. eds,\nProc. IAU Symp. 97, ``Extragalactic Radio Sources''. Reidel,\nDordrecht, p.163 \n\n\\bibitem[2000a]{arno1} Schoenmakers A.P., de Bruyn A.G., R\\\"ottgering H.J.A.,\nvan der Laan H., 2000a, \\aa, in preparation\n\n\\bibitem[2000b]{arno2} Schoenmakers A.P., Mack K.-H., de Bruyn A.G.,\nR\\\"ottgering H.J.A., Klein U., van der Laan H., 2000b, \\aa, in press\n\n\\bibitem[1993]{subra1} Subrahmanyan R., Saripalli L., 1993, \\mn, 260, 908\n\n\\bibitem[1996]{subra2} Subrahmanyan R., Saripalli L., Hunstead R.W., 1996, \n\\mn, 279, 257\n\n\\bibitem[1974]{wardle} Wardle J.F.C., Kronberg P.P., 1974,\n\\apj, 194, 249\n\n\\bibitem[1991]{wieringa} Wieringa M., 1991, PhD. Thesis, Univ. Leiden\n\n\\bibitem[1990]{willis} Willis A.G., O'Dea C.P., 1990, in ``Galactic and \nIntergalactic Magnetic Fields'' IAU Symp. 140, Beck R., Kronberg P.P. \\& \nWielebinski R. (eds.), Reidel, Dordrecht, p.455\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002010
|
RADIATION SPECTRA FROM \\ADVECTION-DOMINATED ACCRETION FLOWS \\IN A GLOBAL MAGNETIC FIELD
|
[
{
"author": "MOTOKI KINO$^{1}$"
},
{
"author": "OSAMU KABURAKI and NAOHIRO YAMAZAKI"
}
] |
We calculate the radiation spectra from advection-dominated accretion flows (ADAFs), taking into account the effects of a global magnetic field. Calculation is based on the analytic model for magnetized ADAFs proposed by Kaburaki, where a large-scale magnetic field controls the accretion process. Adjusting a few parameters, we find that our model can well reproduce the observed spectrum of Sagittarius A$^{*}$. The result is discussed in comparison with those of well-known ADAF models, where the turbulent viscosity controls the accretion process.
|
[
{
"name": "ms.tex",
"string": " \n%-----------------------------------------------------------------------------\n\n% 2nd Revised Manuscript\n%\n% Author(s): KINO, Motoki, KABURAKI, Osamu and YAMAZAKI, Naohiro \n% Title: RADIATION SPECTRA FROM ADVECTION-DOMINATED ACCRETION FLOWS \n% IN A GLOBAL MAGNETIC FIELD \n% Submission: ApJ, Part 1\n%\n% CONTENTS:\n%\n% This file:\n% (1) Title Page\n% (2) Abstract & Subject Headings\n% (3) Text \n% (4) References\n% Figure(s):\n% (1) Fig. 1 (fig1.eps)\n% (2) Fig. 2 (best.eps)\n% (3) Fig. 3 (mass.eps)\n% (4) Fig. 4 (acc.eps)\n% (5) Fig. 5 (jiba.eps)\n% (6) Fig. 6 (delta.eps)\n% (7) Fig. 7 (mbest.eps)\n% (8) Fig. 8 (mmass.eps)\n% (9) Fig. 9 (macc.eps)\n% (10) Fig. 10 (mjiba.eps)\n% (11) Fig. 11 (mdelta.eps)\n% \n%\n%-------------------------------------------------------------------------------\n\n\\documentstyle[epsf,emulateapj]{article}\n\\begin{document}\n\n\\leftline{\\epsfbox{mark.eps}}\n\\vspace{-10.0mm}\n\\thispagestyle{empty}\n{\\baselineskip-4pt\n\\font\\yitp=cmmib10 scaled\\magstep2\n\\font\\elevenmib=cmmib10 scaled\\magstep1 \\skewchar\\elevenmib='177\n\\leftline{\\baselineskip20pt\n\\hspace{12mm} % for revtex\n\\vbox to0pt\n { {\\yitp\\hbox{Osaka \\hspace{1.5mm} University} }\n {\\large\\sl\\hbox{{Theoretical Astrophysics}} }\\vss}}\n\n%\n% Preprint numbers\n%\n{\\baselineskip0pt\n\\rightline{\\large\\baselineskip14pt\\rm\\vbox \n to20pt{\\hbox{OU-TAP-110}\n \\hbox{astro-ph/0002010} \n %\\hbox{\\today}\n\\vss}}\n}\n\\vskip15mm\n\n\\title {RADIATION SPECTRA FROM \\\\ADVECTION-DOMINATED \nACCRETION FLOWS \\\\IN A GLOBAL MAGNETIC FIELD}\n\\author { MOTOKI KINO$^{1}$, OSAMU KABURAKI and NAOHIRO YAMAZAKI}\n\\affil { Astronomical Institute, Graduate School of Science, \nTohoku University, \\\\Aoba-ku, Sendai 980-8578, Japan;\\\\\[email protected], [email protected], \[email protected]}\n%##############################\n\n\n\\begin{abstract}\nWe calculate the radiation spectra from advection-dominated \naccretion flows (ADAFs), taking into account the effects of \na global magnetic field.\nCalculation is based on the analytic model for magnetized \nADAFs proposed by Kaburaki, where a large-scale magnetic \nfield controls the accretion process.\nAdjusting a few parameters, we find that our model can well \nreproduce the observed spectrum of Sagittarius A$^{*}$. \nThe result is discussed in comparison with those of well-known \nADAF models, where the turbulent viscosity controls the accretion \nprocess. \n\\end{abstract}\n\n\\keywords{accretion, accretion disks---radiation\nmechanisms: non-thermal---Galaxy: center---magnetic fields} \n\n\n\\section{INTRODUCTION}\n\\footnotetext[1]{Present adress: Department of Earth and Space Science,\nGraduate School of Science, Osaka University, Toyonaka, Osaka\n560-0043, Japan\\\\\[email protected]}\nThe optically thin, advection-dominated accretion flows (ADAFs) have\nbeen studied by a number of authors during past several years\n(e.g. Narayan $\\&$ Yi 1994, 1995a, b; Abramowicz et al.\\ 1995;\nNakamura et al.\\ 1997, Manmoto, Mineshige \\& Kusunose 1997; Narayan et\nal.\\ 1998). \n These models are very successful in\ndescribing both spectra and dynamics of accreting black hole systems\nsuch as those in binaries and in low-luminosity active galactic nuclei\n(AGNs). The observed spectra can be explained as follows. The radio\nemission is due to the synchrotron emission in turbulent magnetic\nfields in the accretion flow. These synchrotron photons serve as seed\nphotons for the inverse Compton process by hot electrons.\nOnce-scattered Compton photons are mainly distributed in the optical\nband and twice-scattered Compton photons, in soft X-ray band.\nBremsstrahlung due to electron-electron and electron-proton collisions\ngives rise to the observed hard X-ray spectra.\n\nThus, these ADAF models provide a good framework for understanding \nthe observed spectra. \nIn these models, both angular momentum transfer and energy \ndissipation in the accretion flow is assumed to be undertaken by \nthe turbulent viscosity whose size is specified by so-called \n$\\alpha$ parameter. \nFor this reason, hereafter we call this type of models the \n``viscous'' ADAF model in this paper. \nThe magnetic fields are regarded as of turbulence origin and are \ndescribed by another parameter $\\beta$ which specifies the ratio \nof the magnetic pressure to the gas pressure.\n\nHowever there is no reason to believe that the turbulent viscosity\nis the only candidate that controls the accretion processes. \nRather, it is quite natural to think that some types of global \nmagnetic fields may play an essential role. \nIndeed, there are some evidences for the presence of such an \nordered magnetic field in the central region of our Galaxy \n(e.g., Yusef-Zadeh, Morris \\& Chance 1984). \nAs Kato, Fukue \\& Mineshige (1998) has pointed out the hydromagnetic \nturbulence in accretion disks may also generate global magnetic \nfields by dynamo processes due to the presence of helical motions.\nIn view of such circumstances, another type of ADAF model has been \nproposed by one of the present authors (Kaburaki 1999, 2000; hereafter \nreferred to as K99 and K00).\nIn order to distinguish it from the above viscous ADAF models, \nhereafter we call it the ``resistive'' ADAF models since energy \ndissipation in the accretion flow is due to the electric resistivity \nand angular momentum transfer is supported not by the viscosity \nbut by the magnetic stress of a large scale magnetic field.\n\nThe purpose of the present study is to calculate the expected \nradiation spectra from ADAFs in a global magnetic field \nbased on the resistive ADAF model, in order to compare its predictions \nwith those of the viscous ADAF models. \nAs a most suitable candidate for such a comparison, Sgr A$^*$ is taken \nup here because it has been observed in many wave lengths as \nthe nearest galactic nucleus and its spectrum has been reproduced \nmany times by the successively advancing viscous ADAF models. \n\nIn \\S \\ref{scaled}, we introduce the set of analytic solutions \nfor resistive ADAFs in a suitably scaled form and discuss their \nbasic characteristics.\nThe relevant radiation mechanisms and the methods of calculation \nof the fluxes are described in \\S \\ref{cal}. \nThese schemes are applied to Sgr A$^*$ in \\S \\ref{result} and the \nresults are discussed in comparison with those of the viscous ADAF \nmodels. \nFinally in \\S \\ref{sum}, we summerize the main results and discuss \nsome related issues. \n\n\n\\section{RESISTIVE ADAF SOLUTION}\\label{scaled}\n\nAs a basis of our calculation of spectra, we introduce here \nthe set of analytic solutions constructing the resistive \nADAF model. This set may be considered as a counterpart of \nthat found by Narayan $\\&$ Yi (1994, 1995a) in the viscous ADAF \nscheme, but it should be emphasized that the former is not a \nself-similar solution as the latter. \nIn the resistive ADAF model, there are three basic quantities \nand one parameter: mass of the central black hole $M$, mass accretion \nrate $\\dot{M}$, strength of the external magnetic field $\\vert B_0\\vert$ \nand half-opening angle of the flow $\\Delta$, respectively. \nWe introduce the following normalizations for these quantities and \nfor the radial distance $R$: \n\\begin{equation}\n m\\equiv \\frac{M}{10^{6}M_{\\odot}}, \\hspace{1em}\n \\dot m\\equiv \\frac{\\dot{M}}{\\dot{M}_{\\rm E}}, \\hspace{1em}\n b_{0}\\equiv \\frac{\\vert B_{0}\\vert}{1G}, \\hspace{1em}\n \\delta \\equiv \\frac{\\triangle}{0.1}, \\hspace{1em}\n\t r \\equiv \\frac{R}{R_{\\rm out}},\n\\end{equation}\nwhere $R_{\\rm out}$ denotes the radius of the disk's outer edge. \nThe Eddington accretion rate is defined by\n ${\\dot M}_{\\rm E} \\equiv L_{\\rm E}/( 0.1 c^{2})$, \nwhich includes the efficiency factor of $0.1$. \nNote that this definition of $\\dot{M}_{\\rm E}$ and the normalization \nfactor for black hole mass are different from those in K00.\nThe latter is chosen here as 10$^6$ $M_{\\odot}$ for the convenience \nof the discussion of Sgr A$^*$. \n\nIn spherical polar coordinates, the radius of outer edge and \nthe radial-part functions of relevant physical quantities (for \ntheir angular parts, see also K99, K00) are written as \n\\begin{equation}\n R_{\\rm out}=1.5 \\times 10^{16}\\ b_{0}^{-4/5}\\dot{m}^{2/5}m^{3/5}\n \\quad{\\rm cm},\n\\end{equation}\n\\begin{equation}\n \\vert b_{\\varphi}(r)\\vert=10\\ \\delta^{-1} b_{0} r^{-1} \\quad{\\rm G},\n \\label{eqn:B}\n\\end{equation}\n\\begin{equation}\n v_{\\rm K}(r)=0.9\\times 10^{8}\\ b_{0}^{2/5}\\dot{m}^{-1/5}m^{1/5}r^{-1/2}\n \\quad{\\rm cm}\\ {\\rm s}^{-1},\n\\end{equation}\n\\begin{equation}\n P(r)=4.0\\ \\delta^{-2}b_{0}^{2}r^{-2}\n \\quad{\\rm dyne\\ cm}^{-2},\n\\end{equation}\n\\begin{equation}\n T(r)=1.8\\times 10^{7}\\ b^{4/5}_{0}\\dot{m}^{-2/5}m^{2/5}r^{-1}\n \\quad{\\rm K},\n \\label{eqn:T}\n\\end{equation}\n\\begin{equation}\n \\rho (r)=1.3\\times 10^{-15}\\ \\delta^{-2}b_{0}^{6/5}\n \\dot{m}^{2/5}m^{-2/5}r^{-1} \\quad{\\rm g}\\ {\\rm cm^{-3}},\n\\end{equation}\nwhere $b_{\\varphi}$ is the toroidal magnetic field,\n$ v_{\\rm K}$ is the Kepler velocity,\n$P$ is the gas pressure, $T$ is the temperature (common to \nelectrons and ions) and $\\rho$ is the density. \nOwing to the non-negligible pressure term in the radial force \nbalance, the toroidal velocity in the disk is reduced by a factor \nof $1/\\sqrt{3}$ from the Kepler value. The surface density and \nthe optical depth are given, respectively, by \n\\begin{equation}\n \\Sigma(r)=\\Sigma = 4.1\\ \\delta^{-1}b^{2/5}_{0}\\dot{m}^{4/5}\n m^{1/5} \\quad{\\rm g}\\ {\\rm cm^{-2}},\n\\end{equation}\n\\begin{equation}\n\\tau_{\\rm es} (r) \\simeq \\frac{1}{2}\\kappa_{\\rm es}\\Sigma\t\n = 8.2\\times10^{-1}\\ \\delta^{-1} b_{0}^{2/5}\\dot{m}^{4/5}m^{1/5},\n\\end{equation}\nwhere $\\kappa_{\\rm es}$ is the opacity for electron scattering.\nNote that these are independent of $r$ in the present model. \n\nFig.\\ 1 shows a schematic picture of an accretion disk in a global\nmagnetic field, whose precise structure is described by the solution \ngiven above.\nOtherwise uniform external magnetic field is twisted by the rotational \nmotion of accreting plasma, and there develops a large toroidal \nmagnetic field in the middle latitude region. \nThe behavior of this component, especially within the geometrically \nthin accretion flow, is given as $-b_{\\varphi}\\tanh\\xi$ in the \nresistive ADAF solution, where $\\xi=(\\theta-\\pi/2)/\\Delta$ is the \nnormalized angular variable. \nOwing to the appearance of a global $b_{\\varphi}$, angular momentum of \nthe accreting plasma becomes able to be carried away by the magnetic \nstress to distant regions along the poloidal magnetic field. \nThe extraction of angular momentum guarantees the inward motion of \nthe plasma, which gradually becomes large until it reaches near \nthe rotational velocity at around the inner edge of the accretion disk. \nAlthough the magnetic lines of force are also bent inwardly toward \nthe center of gravitational attraction, it has been shown that the \ndominant component is the toroidal one. \nThis component also plays an essential role in the plasma confinement \ntoward the equatorial plane and keeps it geometrically thin through \nits magnetic pressure. \n\nBefore going into the detailed discussion of the radiative \nprocesses, we briefly mention some similarities and differences \nin the basic features of the viscous and resistive ADAF models.\nIt is worth noting that, in spite of the essential difference \nin the mechanisms of angular momentum transport and energy dissipation, \nthe predictions for quantities such as temperature, density and \noptical depth are quite similar in both models. \nThe temperatures in both models are as high as a fraction of the \nvirial temperature of ions. \nIndeed, this is the case in the viscous models, though the electron \ntemperature may deviates from it in the inner regions (e.g., \nNarayan \\& Yi 1995b), and so also in the resistive model as can be \nconfirmed from the analytic expression of $T$ (K99, K00). \nSuch a high temperature makes a sharp contrast with the case of \nstandard $\\alpha$-disks (e.g., Frank, King $\\&$ Raine 1992). \nFurther, for a sub-Eddington mass accretion rate, the optical depth is \ndominated by the electron scattering and is smaller than unity. \nThese are therefore common features of sub-Eddington ADAF models \nas expected. \n\nAs one of the main differences, it may be stressed that the magnetic \nfield in the resistive ADAF model is an ordered magnetic field and is \ndetermined self-consistently in the model from a boundary value. \nTherefore, the strength of the field is not a parameter as in the \nviscous ADAF models.\nThe ordered magnetic filed extract angular momentum from the \naccreting plasma and confines it in a disk structure \nagainst the gas pressure. \nGravitational energy is released in the disk as the Joule \nheating and also as compressional heating of the flow. \nIn the above analytic model of resistive ADAFs, these energies \nare fully advected down the stream. \nWe calculate the radiation from the disk as a small perturbation \nfrom this solution. \n\nAnother distinction may be in the energy partition between \nthe electron and ion components. \nThe viscous ADAF models assume that the viscous dissipation, \nwhich is large at large radii, heats mainly ions. Since the efficiency \nof radiation cooling is very small for ions compared with electrons \nand since energy transfer to the electron component is estimated to be \nnegligible (Manmoto et al. 1997) except in outer portions, the flow \nis fully advective in most portions. \nFor the electron component, on the other hand, the radiative \ncooling is balanced by the advective heating, near the inner edge. \nThe electron temperature, therefore, deviates downwards largely \nfrom the ion temperature thus realizing a two-temperature structure. \n\nIn contrast to the viscous heating, the resistive dissipation \nbecomes large at small radii and seems to preferentially heat \nthe electron component as suggested by Bisnovatyi-Kogan \\& Lovelace \n(1997). \nIn this case, the temperature difference is expected to remain \nrather small because the heating is effective for effective \nradiator. \nIn any case, the resistive ADAF model in its present version assume \na common temperature to both components, for simplicity. \nThe examination of its two-temperature version may belong to \na future work. \n\n\n\\section{CALCULATION OF SPECTRUM}\\label{cal}\n\nAs mentioned above, the radiation spectrum from a resistive ADAF \nis calculated based on the analytic solution introduced in the \nprevious section. \nBack reactions of the radiation cooling to this fully advective \nsolution are negligible as far as its fraction in the total cooling \nrate is small. \nThis has been roughly checked in a previous paper (K00). \nThe method of calculating radiation fluxes described in this \nsection will be applied to Sgr A$^*$ in the next section. \nThe observed spectrum of Sgr A$^*$ in the frequency range from \nradio up to X-ray range is successfully explained in the viscous \nADAF models by the three processes, i.e., synchrotron radiation, \nbremsstrahlung and inverse Compton scattering (Narayan, Yi \\& \nMahadevan 1995; Manmoto et al.\\ 1997; Narayan et al.\\ 1998). \nAlthough there may be some other components such as the \nradio-frequency excess over the Rayleigh-Jeans spectrum and \n$\\gamma$-ray peak both of which need separate explanations (see, e.g., \nMahadevan 1999 for the former, and Mahadevan, Narayan \\& Krolik 1997 \nfor the latter), we ignore these components here for simplicity. \n\nAmong the above three processes, the Compton scattering is treated \nseparately from the other processes of emission and absorption. \nTherefore, we divide the total flux into two parts: the flux \ndue to bremsstrahlung and synchrotron process $F_{\\nu}$ \nand that due to the inverse Compton process $F^{\\prime}_{\\nu}$. \nThe obtained fluxes are both integrated over the entire \nsurfaces (upper and lower ones) of a disk, and added up to obtain \nthe luminosity per unit frequency $L_{\\nu}$. \n\nTemperature in the flow is vertically isothermal in the present model. \nIn calculating the emission and absorption processes, \nthe flow is further assumed to be locally plane parallel. \nSolving the radiative diffusion equation at a given radius $R$, \nwe obtain the flux of the unscattered photons $F_{\\nu}$ \nemanating from one side of the disk (Rybicki \\& Lightman 1979) as \n\\begin{equation}\n F_{\\nu} =\\frac{2\\pi}{{\\sqrt 3}}B_{\\nu}\n \\left[1-\\exp(-2{\\sqrt 3}\\tau_{\\nu}^{*})\\right],\n \\label{eqn:Fnu}\n\\end{equation}\nwhere $B_{\\nu}$ is the Planck intensity and $\\tau_{\\nu}^{*}$ is \nthe vertical optical depth for absorption, \n\\begin{equation}\n \\tau_{\\nu}^{*}(R) \\simeq \\frac{{\\sqrt \\pi}}{2}\\kappa_{\\nu}R\\Delta.\n\\end{equation}\nAssuming the local thermodynamic equilibrium (LTE), we can express \nthe absorption coefficient $\\kappa_{\\nu}$ at the equatorial plane \nin terms of the volume emissivities $\\chi_{\\nu}$'s for bremsstrahlung \nand synchrotron processes: \n\\begin{equation}\n \\kappa_{\\nu}=\\frac{\\chi_{\\nu,\\rm br}+\\chi_{\\nu, \\rm sy}}\n {4\\pi B_{\\nu}}.\n\\end{equation}\nThus, equation (\\ref{eqn:Fnu}) includes not only the effect \nof free-free absorption but also of synchrotron \nself-absorption at low frequencies. \n\nAs the distribution function for thermal electrons, we assume \nthat of the relativistic Maxwellian (in its normalized form), \n\\begin{equation}\n N_{e}(\\gamma)d\\gamma=\\frac{\\gamma^{2}\\beta\n \\exp(-\\frac{\\gamma}{\\theta_{e}})}{\\theta_{e} K_{2}(\\frac{1}\n {\\theta_{e}})}d\\gamma,\n \\qquad \\theta_{e}=\\frac{k_{\\rm B} T_{e}}{m_{e}c^{2}},\n\\end{equation}\nbecause ADAFs tend to have so high temperatures that electron \nthermal energy can exceed its rest mass energy. \nHere, $\\gamma$ is the Lorentz factor, $k_{\\rm B}$ is the \nBoltzmann constant and $K_2$ is the 2nd modified Bessel function. \nActually, we use this formula only in the calculation of Comptonized \nphoton flux below, while in those of bremsstrahlung and \nsynchrotron processes we follow the works of Narayan \\& Yi (1995b), \nand Manmoto et al. (1997) where it is replaced by a numerical \nfitting function. \n\n\\subsection{Bremsstrahlung}\n\nAt relativistic temperatures, we must take into account not only \nelectron-proton but also electron-electron encounters. \nTherefore, the total bremsstrahlung cooling rate per unit volume \nis written as\n\\begin{equation}\n q^{-}_{{\\rm br}}=q^{-}_{ei}+q^{-}_{ee},\n\\end{equation}\nwhere the subscripts $ei$ and $ee$ denote the electron-ion and\nelectron-electron processes, respectively.\nThe explicit expressions of the cooling rates are as follows. \nFor the electron-proton process, \n\\begin{eqnarray}\n q^{-}_{ei}\n &=& 1.25\\ n_{e}^{2}\\sigma_{\\rm T}c\n \\alpha_{f}m_{e}c^{2}F_{ei}(\\theta_{e})\\nonumber \\\\\n &=& 1.48\\times 10^{-22}n_{e}^{2}F_{ei}(\\theta_{e})\n \\quad {\\rm ergs}\\ {\\rm cm}^{-3}\\ {\\rm s}^{-1},\n\\end{eqnarray}\nwhere $n_e$ is the electron number density, $\\alpha_{f}$ is the \nfine-structure constant and $\\sigma_{\\rm T}$ is the Thomson \ncross-section, and further \n\\begin{eqnarray}\n F_{ei}(\\theta_{e}) \n &=& 4\\left(\\frac{2\\theta_{e}}{\\pi^{3}}\\right)^{0.5}\n (1+1.781\\theta_{e}^{1.34}) \\qquad {\\rm for} \n \\quad \\theta_e <1, \\nonumber \\\\\n &=& \\frac{9\\theta_{e}}{2\\pi}\\ [\\ \\ln(1.123\\theta_{e}+0.48)+1.5] \\nonumber \\\\ \n && \\qquad {\\rm for} \\quad \\theta_e>1.\n\\label{eqn:Bei}\n\\end{eqnarray}\nFor the electron-electron process, \n\\begin{eqnarray}\n q^{-}_{ee}\n &=& n_{e}^{2}c r_{e}^{2}m_{e}c^{2}\\alpha_{f}\n \\ \\frac{20}{9\\pi^{0.5}}(44-3\\pi^{2})\\theta_{e}^{3/2}\\nonumber \\\\\n &&\\times (1+1.1\\theta_{e}+\\theta_{e}^{2}-1.25\\theta_{e}^{5/2})\n \\nonumber \\\\\n &=& 2.56 \\times 10^{-22} n_{e}^{2}\\theta_{e}^{3/2}\n (1+1.1\\theta_{e}+\\theta_{e}^{2}-1.25\\theta_{e}^{5/2}) \\nonumber \\\\\n && \\quad {\\rm ergs}\\ {\\rm cm}^{-3}\\ {\\rm s}^{-1} \n\\end{eqnarray}\nwhen $\\theta_e < 1$, and \n\\begin{eqnarray}\n q^{-}_{ee}\n &=& n_{e}^{2}c r_{e}^{2}m_{e}c^{2}\\alpha_{f}24\\theta_{e}(\\ln 2\n \\eta \\theta_{e}+1.28)\\nonumber \\\\\n &=& 3.40\\times 10^{-22}n_{e}^{2}\\theta_{e}(\\ln 1.123\n \\theta_{e}+1.28)\\nonumber \\\\\n && \\quad {\\rm ergs}\\ {\\rm cm}^{-3}\\ {\\rm s}^{-1}\n\\end{eqnarray}\nwhen $\\theta_e > 1$. \nHere, $r_{e}=e^{2}/m_{e}c^{2}$ is the classical electron radius\nand $\\eta=\\exp(-\\gamma_{E})=0.5616$.\n\nThe emissivity per frequency is given by \n\\begin{equation}\n \\chi_{\\nu,{\\rm br}} = q^{-}_{{\\rm br}}\\bar{G}\n \\ \\exp\\left(-\\frac{h\\nu}{k_{\\rm B} T_{e}}\\right)\n \\quad {\\rm ergs}\\ {\\rm cm}^{-3}\\ {\\rm s}^{-1}\\ {\\rm Hz}^{-1},\n\\label{eqn:Chi}\n\\end{equation}\nwhere $h$ is the Planck constant and $\\bar{G}$ is the Gaunt factor \nwhich is written (Rybicki $\\&$ Lightman 1979) as \n\\begin{eqnarray}\n \\bar{G} \n &=& \\frac{h}{k_{\\rm B}T_{e}}\\left(\\frac{3}{\\pi}\n \\frac{k_{\\rm B} T_e}{h\\nu} \\right)^{1/2} \n \\qquad {\\rm for} \\quad \\frac{h\\nu}{k_{\\rm B} T_e}>1, \\nonumber \\\\\n &=& \\frac{h}{k_{\\rm B}T_{e}}\\frac{\\sqrt{3}}{\\pi}\n \\ \\ln \\left(\\frac{4}{\\zeta}\\frac{k T_e}{h\\nu} \\right)\n \\quad {\\rm for}\\quad \\frac{h\\nu}{k_{\\rm B} T_e}<1.\n\\label{eqn:G}\n\\end{eqnarray}\n\nThe above cited formule contain a few minor defects. \nFor example, the non-relativistic limit calculated for electron-ion \nprocess from equations (\\ref{eqn:Bei}) and (\\ref{eqn:G}) differs by \nabout 35\\% from the standard formula (Rybicki \\& Lightman 1979). \nEquation (\\ref{eqn:G}) assumes the same values of the Gaunt factor \nfor both electron-electron and electron-ion processes. \nIn spite of these defects, we adopt the above formule according to \nNarayan \\& Yi (1995b) and Manmoto et al. (1997), considering that these \nare the best ones we can employ at present throughout the energy rage \nof our interest. \nThe adoption of the same formule as in the previous calculations is \nalso suitable for the purpose of comparison of the predictions of \ndifferent models, such as the viscous and resistive ones.\n\n\\subsection{Synchrotron Emission}\n\nSynchrotron emission is an essential process to produce \nthe radio wave-length part of the spectra from optically thin \nADAFs in AGNs. \nEspecially in the resistive ADAF model, some information about \nthe strength of the ambient magnetic field may be obtained \nfrom the process of spectral fitting. \n \nThe optically-thin synchrotron emissivity by relativistic Maxwellian \nelectrons is calculated from the formula (Narayan \\& Yi 1995b; \nMahadevan, Narayan \\& Yi 1996), \n\\begin{eqnarray}\n \\chi_{\\nu,{\\rm sy}}\n &=& 4.43\\times 10^{-30}\\ \\frac{4\\pi n_{e}\\nu}{K_{2}(1/\\theta_{e})} \n\\ I^{\\prime}\\left(\\frac{4\\pi m_{e} c \\nu}{3 e B\\theta_{e}^{2}}\\right)\\nonumber \\\\ \n& &\\qquad {\\rm ergs}\\ {\\rm cm}^{-3}\\ {\\rm s}^{-1}\\ {\\rm Hz}^{-1},\n \\label{eqn:synChi}\n\\end{eqnarray}\nwhere $e$ is the elementary charge and \n\\begin{eqnarray}\n I^{\\prime}(x)=\\frac{4.0505}{x^{1/6}}\n \\left( 1+\\frac{0.4}{x^{1/4}}+\\frac{0.5316}{x^{1/2}}\\right)\n \\exp(-1.8899x^{1/3}).\n\\end{eqnarray}\nIn equation(\\ref{eqn:synChi}), the argument of $I^{\\prime}$ is \nspecified as \n\\begin{eqnarray}\n x \\equiv \\frac{2\\nu}{3\\nu_{0}\\theta_{e}^{2}},\n \\quad \\nu_{0} \\equiv\\frac{e\\vert B\\vert}{2\\pi m_{e}c},\n\\end{eqnarray}\nwhere $B$ is the local value of magnetic field for which we substitute \n$b_{\\varphi}$. \n\n\\subsection{Inverse Compton Scattering}\n\nThe soft photons whose flux is given by equation (\\ref{eqn:Fnu}) \nare Compton scattered by the relativistic electrons in the flow. \nWe adopt the rate equation of Coppi \\& Blandford (1990) as the basis \nof our considerations. This equation applies to homogeneous, isotropic \ndistributions. \nThe first term on the right-hand side of their equation describes \nthe rate of decrease in the photon's number density with a given \nenergy owing to the scattering into other energies, while \nthe second term does the increase owing to the scattering into \nthis energy from other energies. \n\nIn the situations of our interest, we can neglect the first term \nbecause the number density of Comptonized photons are small compared with \nthat of the seed photons. \nInstead, we use the second term iteratively to calculate the effects \nof multiple scattering. \nThe scattering occurs on the average when the condition \n$c\\sigma_{\\rm T}n_edt=1$ is satisfied, where $t$ is time and $n_e$ \nis the number density of electrons. \nThe probability that such a condition is satisfied $j$-times \nbefore the photons come out of the surface may be given by \nthe Poisson formula, \n\\begin{eqnarray}\n p_j =\\frac{\\tau_{e}^j\\ {\\rm e}^{-\\tau_{e}}}{j!}.\n\\end{eqnarray}\nThen, the production rate for the photons with a normalized \nenergy $\\epsilon\\equiv h\\nu/m_e c^2$ is given by \n\\begin{eqnarray}\n \\lefteqn{ \\frac{d n(\\epsilon)}{c\\sigma_{\\rm T}n_e dt}\n = \\sum_{j=1}^{\\infty} p_j\\ \\int d\\gamma_j\\ldots d\\gamma_1 \n \\ N_e(\\gamma_j)\\ldots N_e(\\gamma_1) } \\nonumber \\\\\n & & \\times \\int d\\epsilon_j \\ldots d\\epsilon_1 \\nonumber \\\\ \n & & \\ \\Bigl[ P(\\epsilon;\\epsilon_j,\\gamma_j) \\ldots \n P(\\epsilon_2;\\epsilon_1,\\gamma_1) \n \\ R(\\epsilon_j,\\gamma_j) \\ldots \\nonumber \\\\\n & & R(\\epsilon_1,\\gamma_1) \n \\ n_{\\rm in}(\\epsilon_1) \\Bigl], \n \\label{eqn:Comp}\n\\end{eqnarray}\nwhere $m_e$ is the electron mass and $n_{\\rm in}$ is the number \ndensity of seed photons. \n\nThe non-dimensional scattering rate $R(\\epsilon,\\gamma)$ including \nKlein-Nishina cross section $\\sigma_{\\rm KN}$ is written explicitly \n(Coppi $\\&$ Blandford 1990) as \n\\begin{eqnarray}\n R(\\epsilon,\\gamma)\n &=& \\int_{-1}^1\\frac{d\\mu}{2}\\ (1-\\beta\\mu)\n \\ \\frac{\\sigma_{\\rm KN}(\\beta,\\ \\epsilon,\\ \\mu)}\n {\\sigma_{\\rm T}} \\nonumber\\\\\n &=&\\frac{3}{32 \\gamma^{2}\\beta \\epsilon^{2}}\n \\int^{2\\gamma (1+\\beta)\\epsilon}_{2\\gamma (1-\\beta)\\epsilon} dx\n\t\\left[\\left(1-\\frac{4}{x}-\\frac{8}{x^{2}}\\right)\n\t \\ln(1+x)\\right.\\nonumber \\\\\n &&\\left.+\\frac{1}{2}+\\frac{8}{x} -\\frac{1}{2(1+x)^{2}}\\right] \n \\qquad {\\rm cm}^{3}\\ {\\rm s}^{-1}.\n\\end{eqnarray}\nScattered-photon distribution is denoted by \n$P(\\epsilon;\\epsilon^{\\prime},\\gamma)$ and, in the present calculation, \napproximated by a $\\delta$-function (Lightman \\& Zdziarski 1987, \nFabian et al. 1986): \n\\begin{eqnarray}\n P(\\epsilon;\\epsilon^{\\prime},\\gamma)=\\delta\\left(\\epsilon\n -\\frac{4\\gamma^{2}}{3}\\epsilon^{\\prime}\\right).\n\\end{eqnarray}\nThis is merely for simplicity and a more exact expression has been \nderived by Jones (1968) and corrected afterwards by Coppi \\& \nBlandford (1990). \n\nAlthough the sum in equation (\\ref{eqn:Comp}) runs to infinity, \nit seems appropriate to assume that photons which are scattered more\nthan certain times become saturated and obey the Wien distribution\n$\\propto \\nu^3 \\exp(-h\\nu/kT_{e})$ (e.g., Manmoto et al. 1997). \nIn view of the smallness of the optical depth in most sub-Eddington \nADAFs ($ \\tau_{\\rm es} < 10^{-3}$, in the case of Sgr A$^*$), \nhowever, we truncate the power series in $\\tau_{\\rm es}$ at $j=2$ \nand ignore the saturation effect. \nAfter performing the integrations containing $\\delta$-functions \nand transforming the photon number densities into fluxes by \nmultiplying $ch\\epsilon/2$ on both sides of equation (\\ref{eqn:Comp}), \nwe obtain \n\\begin{equation}\n F_{\\nu}^{\\prime}(0) \n = {\\rm e}^{-\\tau_{\\rm es}}\\ \\left[\\tau_{\\rm es}F_{\\nu}^{(1)}\n + \\frac{\\tau_{\\rm es}^{\\ 2}}{2}F_{\\nu}^{(2)} \\right], \n\\end{equation} \nwhere once- and twice-scattered fluxes are given, respectively, by \n\\begin{equation}\n F_{\\nu}^{(1)} \\equiv \\int_1^{\\infty}d\\gamma_1\n% \\ \\frac{3N_e(\\gamma_1)}{4\\gamma_1^{\\ 2}}\n \\ N_e(\\gamma_1) %corrected\n \\ R\\left( \\frac{3\\epsilon}{4\\gamma_1^{\\ 2}}, \\ \\gamma_1 \\right)\n \\ F_{\\rm in} \\left( \\frac{3\\epsilon}{4\\gamma_1^{\\ 2}} \\right),\n\\end{equation}\n\\begin{eqnarray}\n F_{\\nu}^{(2)} \n &\\equiv& \\int_1^{\\infty}d\\gamma_2\\int_1^{\\infty}d\\gamma_1 \n% \\ \\frac{3N_e(\\gamma_2)}{4\\gamma_2^{\\ 2}}\n% \\ \\frac{3N_e(\\gamma_1)}{4\\gamma_1^{\\ 2}} \\nonumber\\\\\n \\ N_e(\\gamma_2)\\ N_e(\\gamma_1) \\nonumber\\\\ %corrected\n & &\\times\\ R\\left(\\frac{3\\epsilon}{4\\gamma_2^{\\ 2}},\\ \\gamma_2\\right)\n \\ R\\left(\\frac{3}{4\\gamma_2^{\\ 2}}\\frac{3\\epsilon}\n {4\\gamma_1^{\\ 2}},\\ \\gamma_1 \\right) \\nonumber \\\\ \n & &\\times\\ F_{\\rm in}\\left(\\frac{3}{4\\gamma_2^{\\ 2}}\n \\frac{3\\epsilon}{4\\gamma_1^{\\ 2}}\\right)\n\\end{eqnarray}\nwith the definition $F_{\\nu, {\\rm in}}=(ch\\epsilon/2)\nn_{\\rm in}(\\epsilon) \\equiv F_{\\rm in}(\\epsilon)$. \nAs the incident flux $F_{\\nu, {\\rm in}}$ in the above expressions, \nthe result from equation (\\ref{eqn:Fnu}) should be used. \nThe effects of low energy tail ($\\beta<1$) in the electron \ndistribution is neglected in performing the $\\gamma$-integrals. \n\n\\section{APPLICATION TO SAGITTARIUS A$^*$}\\label{result}\n\nIn order to compare the resistive ADAF model with the current \nmodels of viscous ADAFs in their predictions of spectra from \naccretion flows, we apply the former model to Sgr A$^*$. \nThe observed spectral data available so far have been compiled \nby Narayan et al. (1998). \nThey assume that the interstellar column density is $N_{\\rm H}=6 \n\\times 10^{22}\\ {\\rm cm}^{-2}$ and the distance to the Galactic \ncenter is $d=8.5\\ {\\rm kpc}$. \nIn judging the accuracy of fittings between the calculated and \nobserved spectra, a considerable weight has been put on the \nhigh resolution data points such as the VLBI radio (86 GHz) \ndata and the $ROSAT$ X-ray data. \nIt should be kept in mind, however, that the $ROSAT$ data may be \ninterpreted as an upper limit because its resolution (PSPC) \n$\\sim 20''$ is not considered as satisfactory and that other \nissues like the value of $N_{\\rm H}$ are still under discussion.\n\nWe discuss the two cases in the resistive model, which will be \ncalled the compact-disk and the extended-disk models, respectively. \nThese names come from the difference in extension of the disk \nwhich is represented by the radius ratio of the inner to the outer \nedges, $R_{\\rm in}/R_{\\rm out} = r_{\\rm in}$. \nAs confirmed below, this value is largely affected by the choice \nof position of the inner edge, $R_{\\rm in}$.\n\n\n \\subsection{Compact Disk Model}\n\nAccording to the spirit of original resistive ADAF model, the inner \nedge in this case is determined by the magnetic flux conservation \n(K00). This gives an expression \n\\begin{eqnarray}\nR_{\\rm in}=(1+\\Delta^{-1})^{-2}R_{\\rm out} \n \\simeq \\Delta^{2} R_{\\rm out},\n\\end{eqnarray}\nwhere the last expression is valid only for thin disks ($\\Delta \\ll 1$). \nNote that this procedure is independent of the notion of the marginally \nstable orbit around black holes. \nThe outer edge has been fixed, on the other hand, from the mass \nconservation as \n\\begin{eqnarray}\n R_{\\rm out}=\\left(\\frac{3GM{\\dot M^{2}}}{B_{0}^{4}}\\right)^{1/5}.\n\\end{eqnarray}\n\nFig.\\ 2 shows the best fit spectrum in this model and the set of best \nfit parameters is \n\\begin{eqnarray}\n & &M= 3.9 \\times10^{5}\\quad M_{\\odot}, \\nonumber \\\\ \n& & {\\dot M}=1.2\\times10^{-4} {\\dot M_{\\rm E}}\n = 1.0\\times10^{-6}M_{\\odot}\\ {\\rm yr}^{-1},\\qquad \\nonumber \\\\\n & &\\vert B_{0}\\vert = 0.7 \\quad {\\rm G}, \\qquad \n \\Delta= 0.14 \\quad {\\rm rad}. \n\\end{eqnarray}\nFrom these values, other quantities of our interest are fixed as follows: \n\\begin{eqnarray}\n & &R_{\\rm in} = 6.1 \\times 10^{12} \\quad {\\rm cm}, \\qquad \n R_{\\rm out} = 3.1 \\times 10^{14} \\quad {\\rm cm}, \\nonumber \\\\\n & &T=3.4 \\times 10^{8}\\ r^{-1} \\quad{\\rm K}, \\qquad \n \\vert b_{\\varphi}\\vert = 5.0\\ r^{-1} \\quad{\\rm G}, \\nonumber \\\\\n & &\\rho=1.8\\times10^{-17}\\ r^{-1} \\quad {\\rm g\\ cm}^{-3}, \\nonumber \\\\\n & & \\tau_{es}=3.1 \\times 10^{-4}.\n\\end{eqnarray}\nThus, it turns out that the inner edge of the present model is fairly \nlarge compared with the marginally stable orbit, $R_{\\rm ms}=3.5 \n\\times 10^{11}$ cm, for a Schwarzschild hole of the above mass. \n\nThe changes in the spectrum caused by varying central mass $M$, \naccretion rate $\\dot{M}$, external magnetic field $\\vert B_0\\vert$ \nand disk's half-opening angle $\\Delta$ are demonstrated in \nFigs. 3, 4, 5 and 6, respectively. \nThe spectral features are anyway quite analogous to those predicted \nby the viscous ADAF models. \nThe results of a detailed comparison between the resistive and viscous \nADAF models will be discussed in the final subsection, based on the \npredicted spectral features. \n\n\\subsection{Extended Disk Model}\n\nIn this model, the inner edge of the accretion disk is \nset at the radius of the marginally stable circular orbit \naround a Schwarzschild black hole, \n\\begin{eqnarray}\nR_{\\rm in}=R_{\\rm ms}=3R_{\\rm G}=\\frac{6GM}{c^{2}},\n\\end{eqnarray}\nwhere $R_{\\rm G}$ is the gravitational radius of the hole. \nThis choice is motivated by the expectation that at around \nthis radius the infall velocity inevitably becomes of \nthe order of the rotational velocity, (i.e., $\\Re\\sim 1$ where $\\Re$ \nis the magnetic Reynolds number, see K99, K00). \nThe definition of the outer edge is the same as in the compact disk \nmodel. \nNote that the above definition of the inner edge is adopted \nalso in the viscous ADAF models. \n\nThe best fit parameters in this model are \n\\begin{eqnarray}\n & &M= 1.0\\times10^{6} \\quad M_{\\odot}, \\nonumber \\\\ \n & & {\\dot M}=1.3\\times10^{-4} {\\dot M_{\\rm E}} \n = 2.9\\times10^{-6}\\quad M_{\\odot}\\ {\\rm yr}^{-1}, \\nonumber \\\\\n & &\\vert B_{0}\\vert = 1.0 \\times 10^{-6}\\quad {\\rm G}, \\qquad \n \\Delta= 0.20 \\quad {\\rm rad}.\n\\end{eqnarray}\nThese are used to fix the values of various scaled quantities: \n\\begin{eqnarray}\n & &R_{\\rm in} = 8.9\\times 10^{11} \\quad {\\rm cm}, \\qquad \n R_{\\rm out} = 2.7\\times 10^{19} \\quad {\\rm cm}, \\nonumber \\\\\n & &T = 1.0\\times 10^{4}\\ r^{-1} \\quad {\\rm K}, \\qquad \n \\vert b_{\\varphi}\\vert = 5.0\\times 10^{-6}\\ r^{-1} \n \\quad {\\rm G}, \\nonumber \\\\\n & &\\rho = 5.9\\times 10^{-25}\\ r^{-1}\n \\quad {\\rm g}\\ {\\rm cm}^{-3}, \\nonumber \\\\ \n & & \\tau_{es}= 1.3\\times 10^{-6}.\n\\end{eqnarray}\n\nThe best fit curve is shown in Fig. 7. \nThe changes in the spectrum caused by varying central mass $M$, \naccretion rate $\\dot{M}$, external magnetic field $\\vert B_0\\vert$ \nand disk's half-opening angle $\\Delta$ are demonstrated in \nFigs. 8, 9, 10 and 11, respectively. \nThe spectral shapes are very different from those of the \ncompact-disk case and of the viscous ADAF models. \nSynchrotron emission has a very wide peak and bremsstrahlung \nis negligibly small. \nThe former fact is due to a high temperature at the inner edge \n(see sub-subsection 4.3.2) and the latter, to lower densities \nin the disk. \nThe emission in the X-ray band is supported by the inverse Compton \nscattering from the radio band. \nThe temperature near the outer edge falls even to such a small \nvalue that the assumption of complete ionization becomes invalid. \nAlthough the position of outer edge may seem to be irrelevant \nfrom a viewpoint of spectrum, it is nevertheless important also in \nthis case as a fitting boundary of the inner magnetic field to the \nexternal one. \nThe fitting predicts that the boundary value is comparable to \nthe interstellar field (a few $\\mu$G). \n\nThe fitting both to 86 GHz and {\\it ROSAT} X-ray data points is \npossible also in this model. However, it is clear that the fitting \ncurve runs above the observed upper limits in the IR band. \nThe fitting in the frequency range from 100 to 1000 GHz also becomes \nconsiderably poor compared with the case of compact disk. \nFor these reasons, we judge that this model cannot reproduce \nthe observed broadband spectrum of Sgr A$^*$. \nThis fact suggests again that the inner edge of the accretion disk \ndoes not coincide with the marginally stable orbit. \nThe wide range of the disk's radii which is obtained from this \nfitting implies that $\\Re(R_{\\rm out}) \\sim 6\\times 10^3$. \nSince $\\Re(R)$ represents the ratio of toroidal to poloidal \nmagnetic fields, most parts of the disk are very likely to be \nunstable to global MHD instabilities of helical type. \nFor this reason too, we consider that the present case \n(i.e., $R_{\\rm in} = R_{\\rm ms}$) is quite unrealistic, at least, \nfor Sgr A$^*$. \n\n\\subsection{Viscous v.s. Resistive ADAFs}\n\n \\subsubsection{Dependence on Black Hole Mass} \n\nThe spectra calculated from ADAF models of both viscous and \nresistive types commonly have the saturated part at the lower \nends of the spectra due to the synchrotron self-absorption. \nIt is of great interest to see that the luminosity $\\nu L_{\\nu}$ \nof this part is essential to determine the mass of the central \nblack hole, in both types \nof models. \nEspecially, in the viscous model, the luminosity of this frequency \npart is determined almost only by the black hole mass. \nThe reason is as follows. \n\nThe temperature in ADAFs may be considered essentially as \nthe ion virial temperature and hence decreases as $\\sim R^{-1}$. \nApart from a numerical factor due to a reduced Keplerian rotation, \nthis is exactly true in the resistive model. \nThis is also true in the viscous models for the main part of \nan accretion flow except in the inner region where the electron \ntemperature deviates from the ion temperature and remains almost \nconstant (e.g., Narayan \\& Yi 1995b). \nTherefore, the contribution to the spectrum from each annulus of \nradius $R$ and width d$R$ is equal. \nIntegrating these contributions up to the outer edge, we obtain \n$L^{\\rm RJ}_{\\nu} \\propto T_{e}(R_{\\rm in})R_{\\rm in}R_{\\rm out} \n=T_e(R_{\\rm out})R_{\\rm out}^2$, where $R_{\\rm in}$ is \nthe radius of the disk's inner edge in the resistive model \nand of the outer edge of the two-temperature region in the \nviscous models. \n\nWe have $T_e R\\propto m$ commonly to both types of ADAF \nmodels. \nFurther, since radius scales as the gravitational radius \nin the case of viscous ADAFs, we obtain the mass dependence \n\\begin{equation}\n L^{\\rm RJ}_{\\nu} \\propto m^2 \\qquad \\mbox{(viscous ADAF)},\n\\end{equation} \nconfirming the above statement. \nOn the other hand, in the case of resistive ADAFs, we have \n\\begin{eqnarray} \n L^{\\rm RJ}_{\\nu} \\propto b_0^{-4/5}\\dot{m}^{2/5}m^{8/5} \n \\qquad \\mbox{(resistive ADAF)},\n\\end{eqnarray}\nwhere the dependences on the parameters other than $m$ have \ncome from the expression of $R_{\\rm out}$. \nIn spite of these dependences, the mass dependence is essential \nalso in this case. \nThis is because the dependence on $\\dot{m}$ is rather weak \nand the value of $b_0$ is strongly restricted from the position \nof the synchrotron peak (see the discussion below). \n\n \\subsubsection{Synchrotron Peak}\n\nWe estimate the synchrotron peak frequency following Mahadevan \n(1997), and examine its behavior in both viscous and resistive \nmodels.\nFor each annulus of radius $R$ and width d$R$, the synchrotron \nphotons in the radio range up to a critical frequency $\\nu_{\\rm c}$ \nare strongly self-absorbed and result in the Rayleigh-Jeans spectrum. \nTherefore, the critical frequency of the spectrum is determined \nby equating the contributions to $L_{\\nu}$ from optically thick \nand thin sides of the frequency: \n\\begin{eqnarray}\n & &2\\pi\\frac{\\nu_{\\rm c}^{2}}{c^{2}}k_{\\rm B}T_e(R) 2\\pi R\\ {\\rm d}R \\nonumber\\\\ \n & &= 4.43\\times 10^{-30}\\frac{4\\pi n_{e}\\nu_{\\rm c}}{K_{2}(1/\\theta_{e})}\n I^{\\prime}(x_{\\rm c})\\ 4\\pi\\Delta R^2\\ {\\rm d}R, \n\\end{eqnarray}\nwhere $x_{\\rm c}$ is defined as \n$x_{\\rm c}= 2\\nu_{\\rm c}/(3\\nu_0\\theta_e^2)$. \nSolving this equation, we can determine the value of $x_{\\rm c}$ \nnumerically (Appendix B of Mahadevan 1997). \nProvided that this value does not depend strongly on $R$, $\\Delta$ and \nother parameters, we obtain \n\\begin{eqnarray}\n \\nu_{\\rm c} = \\frac{3}{2}\\theta_{e}^{2}\\nu_{0}x_{\\rm c} \n \\propto T_e^{\\ 2}(r)B(r). \n\\end{eqnarray}\nIf the disk has uniform temperature and magnetic field, then \nthe synchrotron peak is rather sharp and has a well-defined peak \nfrequency at $\\nu_{\\rm c}$. \n\nWhen they vary with the radius $R$, however, substitution of \nthe $r$-dependences of $T_{\\rm e}$ and $B$ in both viscous and \nresistive ADAF models yield \n\\begin{eqnarray}\n \\nu_{\\rm c} \n &\\propto&\n \\alpha^{-1/2}(1-\\beta)^{1/2}\\dot{m}^{1/2}m^{-1/2}r^{-13/4} \\nonumber\\\\\n& & \\qquad \\mbox{(viscous ADAF)}, \\nonumber\\\\\n &\\propto& \\delta^{-1}b_0^{13/5}\\dot{m}^{-4/5}m^{4/5}r^{-3}\\nonumber\\\\\n & & \\qquad \\mbox{(resistive ADAF)}. \n\\label{eqn:nuc}\n\\end{eqnarray} \nThis means that $\\nu_{\\rm c}$ is larger for smaller radii and the \nhigher most cutoff is due to the inner edge. \nThe position of peak of the superposed emission is then given as \n$\\nu_{\\rm p}=\\nu_{\\rm c}(r_{\\rm p})$, where $r_{\\rm p}$ is the \nradius whose contribution to the synchrotron emission is most \ndominant. \nThe fairly narrow peak obtained in the compact-disk case indicates \nthat $r_{\\rm p}$ is located near the inner edge and the global peak \nshape is determined mainly by the inner most region of the disk. \n\nOn the contrary, the synchrotron peak becomes very broad and dull \nin the extended-disk case. \nWe have confirmed that the low-frequency side of the broad peak \nis due to a superposition of the contributions from annuli of \n$R_{\\rm ms} \\sim 10R_{\\rm ms}$. \nHowever, the dull shape on the high-frequency side of the peak may be \nmainly due to a resulting high temperature ($T\\sim 3\\times10^{10}$ K) \nat the smaller inner edge. \nActually, owing to this high temperature and low densities near the \ninner edge, the synchrotron self-absorption becomes less important \nin the high-frequency radio band and the intrinsic shape of the \nsynchrotron emission at the mildly relativistic temperature \n(Mahadevan et al. 1996) can appear on the high-frequency side. \n\nIn any case, since $r_{\\rm p}$ is a numerical factor, we can speak \nof the parameter dependences of the peak frequency $\\nu_{\\rm p}$ \nbased on equation (\\ref{eqn:nuc}). \nNote that the dependences on $m$ and $\\dot{m}$ have different \nsenses in the different ADAFs. \nThe most important difference between the two models is that \nthe dependence of $\\nu_{\\rm p}$ on the magnetic field is much more \nsensitive in the resistive model. \nTherefore, the field strength is determined more accurately there. \nAll the predicted dependences on $m$, $\\dot{m}$, $b_0$ and \n$\\delta$ are qualitatively confirmed in Figs. 2 through 5. \nFrom the above considerations on the synchrotron peak, we think that \nthe improvement of observational quality in submillimeter range is \nmost important for obtaining more exact values of the disk parameters. \n\n \\subsubsection{Bremsstrahlung}\n\nWe shall try here to grasp the qualitative behavior of the contribution \nfrom bremsstrahlung according to the usual non-relativistic scheme. \nThe contribution to a given frequency $\\nu$ from optically thin plasma \nin an annular volume of width d$R$ is proportional to $\\rho^2 T^{-1/2}\n\\exp[-h\\nu/k_{\\rm B}T]\\ R^2{\\rm d}R$. \nApart from the exponential factor, we have \n%\\begin{eqnarray}\n% \\rho^2 T^{-1/2} &\\propto& \\alpha^{-2}\\dot{m}^2 m^{-2}r^{-5/2}\n% \\qquad \\mbox{(viscous ADAF)}, \\nonumber \\\\\n% &\\propto& \\delta^{-4}b_0^2\\dot{m}m^{-1}r^{-3/2} \n% \\qquad \\mbox{(resistive ADAF)},\n%\\end{eqnarray}\n\\begin{eqnarray}\n \\rho^2 T^{-1/2}R^2{\\rm d}R \n &\\propto& \\alpha^{-2}\\dot{m}^2m r^{-1/2}{\\rm d}r\n \\qquad \\mbox{(viscous ADAF)}, \\nonumber \\\\\n &\\propto& \\delta^{-4}b_0^{-2/5}\\dot{m}^{11/5}m^{4/5} r^{1/2}{\\rm\n d}r \\nonumber\\\\\n & & \\qquad \\mbox{(resistive ADAF)}. \n\\end{eqnarray}\nTherefore, the relative importance of the inner and outer parts of \na disk can be seen from the ratio, \n\\begin{equation}\n f \\equiv \n \\frac{\\rho^2_{\\rm in}T^{-1/2}_{\\rm in}R^2_{\\rm in}\n \\exp[-h\\nu/k_{\\rm B}T_{\\rm in}]}\n {\\rho^2_{\\rm out}T^{-1/2}_{\\rm out}R^2_{\\rm out}\n \\exp[-h\\nu/k_{\\rm B}T_{\\rm out}]} \n \\simeq \\zeta^{\\pm 1/2}\\exp[h\\nu/k_{\\rm B}T_{\\rm out}],\n\\end{equation}\nwhere $\\zeta\\equiv R_{\\rm out}/R_{\\rm in} = r_{\\rm in}^{-1}$, and \nthe upper and lower signs in its exponent are for the viscous \nand resistive ADAFs, respectively. \n\nIt is evident from the above ratio that, in the viscous ADAF, the \ncontribution from the inner disk is always dominant (i.e., $f>1$) \nirrespective of the frequency $\\nu$. \nIn the resistive ADAF, however, it depends on the frequency, \nso that we introduce the critical frequency $\\nu_{\\rm c}^{\\prime}$ \nby the relation $f=1$. \nThis yields \n\\begin{equation}\n \\nu_{\\rm c}^{\\prime} = \\frac{\\ln\\zeta}{2}\n \\ \\frac{k_{\\rm B}T_{\\rm out}}{h}.\n\\end{equation}\nThen, the inner part contributes to the frequency range \n$\\nu > \\nu_{\\rm c}^{\\prime}$ and the outer part, \nto $\\nu < \\nu_{\\rm c}^{\\prime}$. \nIn fact, the critical frequency roughly coincides with the peak \nfrequency of the bremsstrahlung. \nThe luminosity above $\\nu_{\\rm c}^{\\prime}$ can be roughly estimated, \nby putting ${\\rm d}r\\sim r \\sim r_{\\rm in}$, as \n\\begin{eqnarray}\n L_{\\nu}^{\\rm br} \n &\\propto& \\alpha^{-2}\\dot{m}^2m \n \\qquad \\mbox{(viscous ADAF)}, \\nonumber \\\\\n &\\propto& \\delta^{-1}b_0^{-2/5}\\dot{m}^{11/5}m^{4/5} \n \\qquad \\mbox{(resistive ADAF)}, \n\\end{eqnarray}\nbecause $r_{\\rm in}$ is a numerical constant and, in particular, equal \nto $\\delta^2$ in the resistive ADAFs. \n\nIn the viscous ADAF models and in the compact-disk case of the \nresistive ADAF, the contributions from bremsstrahlung cause an X-ray \nbump in each predicted spectrum. \nThe dependences of this peak on the parameters $m$ and $\\dot{m}$ \nare qualitatively confirmed in Figs. 2 and 3, but those on $b_0$ \nand $\\delta$ are somewhat different from the above prediction, \nindicating a limitation of such a crude estimate as the above. \nThe critical frequencies calculated from the best fit values \nfor the compact and extended disks are $1.4\\times10^{19}$ Hz and \n$1.8\\times10^{15}$ Hz, respectively. \nThe former value is in good agreement with the peak of the reproduced \nspectrum. \nIn the extended-disk case, the contribution from the bremsstrahlung \nis negligibly small because the density throughout the disk becomes \ntoo small, and the X-ray range of the spectrum is explained by \nthe once-scattered Compton photons. \n\n\n\\section{Summary $\\&$ Discussion}\\label{sum}\n\nTo summarize the examinations in the previous section, \nboth viscous and resistive ADAF models can explain \nthe observed spectrum of Sgr A$^*$ equally well. \nIn spite of large differences in the basic mechanisms working \nin both models, the calculated spectra are quite similar, \nexcept for the extended-disk case in the resistive model. \nThis fact suggests that also the resistive ADAF model is \nquite powerful in explaining the behavior of other low luminosity \nAGNs (Narayan, Mahadevan \\& Quataert 1998).\nIn addition to these analogous aspects, the resistive model \nseems to have a possibility to explain such an essentially \ndifferent situation as appeared in the extended disk case. \nIn any case, when the presence of an ordered magnetic \nfield should be taken seriously in some AGNs or in some \nstellar-size black holes then the resistive ADAF model, \nwhose predictions on the radiation spectra are examined in \nthis paper, will serve the purpose. \n\nOne of the most remarkable features of the ADAF models \nis that the mass of the central black hole seems to be \ndetermined only from the fitting to the self-absorbed part \nof the observed spectrum. \nIn the case of Sgr A$^*$, the resistive ADAF model (hereafter \nrestricting to the case of compact disk) predicts the central \nmass of $3.9\\times 10^5\\ M_{\\odot}$ while the viscous \nmodels predict $1.0\\times10^6\\ M_{\\odot}$ (Manmoto et.al 1997) \nand $2.5\\times 10^6\\ M_{\\odot}$ (Narayan et al. 1998). \nThe accuracy of the fittings for other disk parameters \nthan the black hole mass will be greatly improved by the \nprecise determination of the position and height of the \nsynchrotron peak from observations. \n\nThe black hole mass predicted by the resistive ADAF model is \nevidently smaller compared with the predictions of the viscous \nADAF models. \nThe latter values are consistent with the dynamically reduced \nvalue of $2.5\\times10^6\\ M_{\\odot}$ (Haller et al.\\ 1996; \nEckart \\& Genzel 1997), which may be considered as an upper limit \nfor the black hole mass. \nIn the history of viscous ADAF models, the predicted black-hole \nmass was as small as $7\\times10^5\\ M_{\\odot}$ (Narayan et al.\\ \n1995). Afterwards, by the inclusion of compressive heating, \nit becomes consistent with the dynamical mass. \nSince this change is mainly due to the decrease in electron \ntemperature (Narayan et al.\\ 1998), the prediction of the resistive \nADAF model may also be increased if the development of its \ntwo-temperature versions results in a lower electron temperature. \nAs for the compressive heating, it is already included in the \nresistive model. \n\nIn spite of the resemblance in the predicted spectral shape, \nthere are of course many differences in the predictions of the \nviscous and resistive models. \nThe precise dependences on the relevant quantities of the \nluminosities of the self-absorbed part, the synchrotron peak and \nthe X-ray bump are different. \nEspecially, the dependence of the synchrotron peak-frequency \non the strength of magnetic field is much stronger for \nthe resistive model. \nThe essential difference in the geometry of an accretion flow may \nbe in the radius of the inner edge rather than in its vertical \nthickness. \nThe prediction of the resistive ADAF model for the inner-edge \nradius of the disk around Sgr A$^*$ is $\\sim 20R_{\\rm ms}$, \ninstead of the radius of marginally stable circular orbit \n$R_{\\rm ms}$. \nAlthough this result justifies the neglection of the general \nrelativistic effects in our treatment, various questions may \nbe raised about the behavior of infalling plasmas. \nAs for this point we only present an idea below from a \nviewpoint of global consistency, because its detailed analyses \nare beyond the scope of this paper. \n\nFig.\\ 1 shows an overview of the flow and magnetic field \nconfigurations (see K00, for more details). \nThe accretion flow would be decelerated near the inner edge \nby the presence of a strong poloidal magnetic field which is \nmaintained by the sweeping effect of the flow. \nAs a result, a certain fraction of the accreting plasma will \nbe turned its direction to go along the poloidal field lines, \nalthough the remaining fraction may fall into the central black \nhole. \nIf the poloidal current driven in the accretion disk can \nclose its circuit successfully around distant regions and along \nthe polar axis, a set of bipolar jets will be formed (Kaburaki \n$\\&$ Itoh 1987). \nEven if the mechanism for formation of jet does not work well, \nthe plasma within the inner edge is likely to extend to the polar \nregions. \n\nThe presence of the plasma within the inner edge of an accretion \ndisk and near the polar axis can be a possible source of the excess \nabove the self-absorbed slope in radio band of the observed spectrum. \nVery recent VLBI observations of Sgr A$^*$ (Krichbaum et al. 1998; \nLo et al. 1998) report that its intrinsic sizes in the east-west \ndirection at 215 GHz and 68GHz are about 20 $R_{\\rm G}$ (with \n$M=2.5\\times 10^6M_{\\odot}$). \nA half of this size (i.e., its radius) is just comparable to \nthe size of the inner edge $\\sim 60R_{\\rm G}$ of our model fitting \nwith $M=4\\times10^5M_{\\odot}$. \nHowever, the value of the black hole mass estimated from the spectral \nfitting may be increased if there is a possibility for Sgr A$^*$ \nto have a wind-type mass loss from the surfaces of its disk (such \npossibilities have been noted for various types of objects by, e.g., \nBlandford \\& Begelman 1999; Di Matteo et al. 1999; Quataert \\& \nNarayan 1999). \nIn such a case, the VLBI component becomes smaller than the size of \nthe inner edge.\n\nFrom the standpoint of the resistive ADAF, therefore, the above \nobservations should be interpreted as suggesting the presence of \na compact structure which is comparable to or smaller than the \ninner-edge radius of the accretion disk. \nIn view of the vertical elongation of this component reported by \nLo et al. (1998), this structure is very likely to be the root of \na jet as suggested by them. \nThis picture is very consistent with the view described above in \nrelation to Fig.\\ 1. \nIn this case, however, the location of the self-absorbed slope in \nthe $\\nu$-$\\nu L_{\\nu}$ diagram should be slightly shifted towards \nthe higher-frequency side so that the VLBI data points can be \nregarded as an excess from the disk's contribution. \n\\\\\n\nOne of the authors (M.\\ K.) would like to thank Tadahiro Manmoto \nfor many valuable comments on the viscous ADAF models. \nHe is also grateful to Umin Lee for his suggestions on some numerical \ntechnics. \n\n\\begin{references}\n\n \\reference{1}\n{Abramowicz, M.\\ A., Chen, X., Kato, S., Lasota, J.\\ -P., \n\\& Regev, O. 1995, \\apjl, 438, L37}\n \\reference{1}\n{Bisnovatyi-Kogan, G.\\ S., \\& Lovelace, R.\\ V.\\ E. 1997, \n\\apjl, 486, L43 }\n \\reference{1}\n{Blandford, R.\\ D., \\& Begelman, M.\\ C. 1999, \\mnras, 303, L1}\n \\reference{1}\n{Coppi, P.\\ S., \\& Blandford, R.\\ D. 1990, \\mnras, 245, 453}\n \\reference{1}\n{Di Matteo, T., Fabian, A.\\ C., Rees, M.\\ J., Carilli, C.\\ L., \n\\& Ivison, R.\\ J. 1999, \\mnras, 305, 492}\n \\reference{1}\n{Eckart, A., \\& Genzel, R. 1997, \\mnras, 284, 576}\n \\reference{1}\n{Fabian, A.\\ C., Blandford, R.\\ D., Guilbert, P.\\ W., \nPhinney, E.\\ S., \\& Cuellar, L. 1986, MNRAS, 221, 931}\n \\reference{1} \n{Frank, J., King, A., \\& Raine, D. 1992, Accretion Power \nin Astrophysics (Cambridge: Cambridge University Press)}\n \\reference{1}\n{Haller, J.\\ W., Rieke, M.\\ J., Rieke, G.\\ H., Tamblyn, P., \nClose, L., \\& Melia, F. 1996, \\apj, 456, 194}\n \\reference{1}\n{Jones, F.\\ C. 1968, Phys. Rev., 167, 1159}\n \\reference{1}\n{Kaburaki, O. 1999, in Disk Instabilities in Close Binary \nSystems, ed. S.\\ Mineshige et al. (Tokyo: Universal Academy \nPress), 325 (K99)}\n \\reference{1}\n{Kaburaki, O. 2000, \\apj, in press (astro-ph 9910252) (K00)}\n \\reference{1} \n{Kaburaki, O., \\& Itoh, M. 1987, A\\&A, 172, 191}\n \\reference{1}\n{Kato, S., Fukue, J., \\& Mineshige, S. 1998, Black-hole Accretion \nDisks (Kyoto: Kyoto University Press)}\n \\reference{1}\n{Krichbaum, T.\\ P., Graham, D.\\ A., Witzel, A., Greve, A., Wink, J.\\ E., \nGrewing, M., Colomer, F., de Vicente, P., G\\'{o}mez-Gonz\\'{a}lez, J., \nBaudry, A., \\& Zensus, J.\\ A. 1998, A\\&A, 335, L106}\n \\reference{1}\n{Lightman, A.\\ P., \\& Zdziarski, A.\\ A. 1987, \\apj, 319, 643}\n \\reference{1}\n{Lo, K.\\ Y., Shen, Z.-Q., Zhao, J.-H., \\& Ho, P.\\ T.\\ P. 1998, \n\\apj, 508, L61}\n \\reference{1}\n{Mahadevan, R. 1997, ApJ, 477, 585}\n \\reference{1}\n{Mahadevan, R. 1999, \\mnras, 304, 501 }\n \\reference{1}\n{Mahadevan, R., Narayan, R., \\& Krolik, J. 1997, \\apj, 486, 268}\n \\reference{1}\n{Mahadevan, R., Narayan, R., \\& Yi, I. 1996, ApJ, 465, 327}\n \\reference{1}\n{Manmoto, T., Mineshige, S., \\& Kusunose, M. 1997, ApJ, 489, 791}\n \\reference{1}\n{Nakamura, K.\\ E., Kusunose, M., Matsumoto, R., \\& Kato, S. 1997, \n\\pasj, 49, 503}\n \\reference{1}\n{Narayan, R., \\& Yi, I. 1994, ApJ, 428, L13}\n \\reference{1}\n{Narayan, R., \\& Yi, I. 1995a, ApJ, 444, 231}\n \\reference{1}\n{Narayan, R., \\& Yi, I. 1995b, ApJ, 452, 710}\n \\reference{1}\n{Narayan, R., Mahadevan, R., \\& Quataert, E. 1998, in Theory of \nBlack Hole Accretion Disks, ed. M.\\ A.\\ Abramowicz, G.\\ Bjornsson, \n\\& J.\\ E.\\ Pringle (Cambridge: Cambridge University Press), 148 \n(astro-ph 9803141)}\n \\reference{1}\n{Narayan, R., Yi, I., \\& Mahadevan, R. 1995, Nature, 374, 623}\n \\reference{1}\n{Narayan, R., Mahadevan, R., Grindlay, J.\\ E., Popham, \nP.\\ G.\\ \\& Gammie, C. 1998, \\apj, 492, 554}\n \\reference{1}\n{Quataert, E., \\& Narayan, R. 1999, \\apj, 520, 298}\n \\reference{1}\n{Rybicki, G.\\ B., \\& Lightman, A.\\ P. 1979, Radiative Processes \nin Astrophysics (New York: John Wiley \\& Sons)} \n \\reference{1}\n{Yusef-Zadeh, F., Morris, M., \\& Chance, D. 1984, \\nat, 310, 557}\n \n\\end{references}\n\n\\newpage %Delete this line when \\begin{figure} is used. \n\n\\begin{figure}\n \\plotone{fig1.eps}\n\\caption\n%\\figcaption %Delete this line when \\begin{figure} is used. \n{Schematic drawing of the global geometries of magnetic \nfield and plasma flow. \nA poloidally circulating current system (${\\bf j}_{\\rm p}$) driven \nby the rotational motion of accreting plasma generates a toroidal \nmagnetic field $b_{\\varphi}$ in addition to a nearly uniform \nexternal field. \nThe presence of this toroidal field outside the disk guarantees \nthe magnetic extraction of angular momentum from the disk. \nThis field also acts to confine the accreting flow toward the \nequatorial plane and has a tendency to collimate and accelerate \nthe plasma in the polar regions. \nIf the condition is favorable, the plasma in the polar regions \nmay form a set of bipolar jets. \nIn this paper, however, we focus our attention on the radiation \nspectrum from the accretion disk only. }\n\\end{figure}\n\n\\begin{figure}\n \\plotone{best.eps}\n%\\figcaption \n \\caption\n{The best fit spectrum of Sgr A$^{*}$ in the compact \ndisk model. \nThe resulting physical quantities are \n$M= 3.9\\times10^{5}\\ M_{\\odot}$,\n${\\dot M}=1.2\\times10^{-4}\\ \\dot{M}_{\\rm E},$\n$\\vert B_0\\vert = 0.7\\ {\\rm G}$ and $\\Delta= 0.14\\ {\\rm rad}$. \nThe four peaks indicated by S, C1, C2 and B denote \nthose due to synchrotron emission, once- and twice-scattered \n(although it is almost buried) Compton photons and bremsstrahlung, \nrespectively. \nThe data points are the same as those compiled by Narayan \net al. (1998).}\n\\end{figure}\n\n\\begin{figure}\n \\plotone{mass.eps}\n\\caption\n%\\figcaption \n {With increasing central mass, the luminosity $\\nu L_{\\nu}$ \nincreases globally, so that the self-absorbed part shifts upward \nand the synchrotron peak-frequency sifts to higher frequencies. \nThe direction of the shift of the synchrotron peak is different \nfrom the results of viscous ADAFs (Manmoto et al. 1997, \nNarayan et al. 1998). }\n \\end{figure}\n\n \\begin{figure}\n \\plotone{acc.eps}\n \\caption\n%\\figcaption \n{$\\dot{M}$-dependence of the spectrum. \nWith increasing mass accretion rate, the synchrotron peak \nshifts to lower frequencies while the self-absorbed luminosity \nis hardly affected. \nThe former behavior is opposite to that of viscous ADAFs. \nThe X-ray bump increases with $\\dot{M}$.}\n \\end{figure}\n\n \\begin{figure}\n \\plotone{jiba.eps}\n \\caption\n%\\figcaption \n{$\\vert B_0\\vert$-dependence of the spectrum. \nWith increasing magnetic field strength, the synchrotron peak shifts \nto higher frequencies while the self-absorbed luminosity is \nhardly affected. \nThe X-ray bump increases with increasing $\\vert B_0\\vert$, \nsuggesting a limitation of the crude estimate of $L_{\\nu}^{\\rm br}$ \ngiven in the text. }\n \\end{figure}\n\n\\begin{figure}\n \\plotone{delta.eps}\n \\caption\n%\\figcaption \n{$\\Delta$-dependence of the spectrum. \nWith increasing half-opening angle, the synchrotron peak \nshifts to lower frequencies while the self-absorbed luminosity \nis hardly affected. \nThe dependence of the X-ray bump on $\\Delta$ again suggests \na limitation of the crude estimate given in the text. }\n\\end{figure}\n\n\n\\begin{figure}\n \\plotone{mbest.eps}\n \\caption\n%\\figcaption \n{The best fit spectrum of Sgr A$^{*}$ in the \nextended disk model. \nThe resulting physical quantities are \n$M= 1.0\\times10^{6}\\ M_{\\odot}$, \n${\\dot M}=1.3\\times10^{-4}\\ {\\dot M_{\\rm E}}$, \n$\\vert B_{0}\\vert = 1.0 \\times 10^{-6}\\ {\\rm G}$,\n$\\Delta= 0.20\\ {\\rm rad}$. \nAmong the four peaks which are seen in the case of compact \ndisk, that of bremsstrahlung has disappeared owing to \nthe low densities in the extended disk, so that the X-ray bump \nis explained by once-scattered Compton photons. \nThe fitting both to 86 GHz and {\\it ROSAT} X-ray data points is \npossible also in this model. \nHowever, the fitting in the frequency range from 100 to 1000 GHz \nbecomes considerably poor compared with the case of compact disk, \nand it cannot be reconciled with the observed upper limits \nin the IR band. \nFor these reasons, we judge that this model cannot reproduce \nthe observed broadband spectrum of Sgr A$^*$. \n}\n\\end{figure}\n\n\\begin{figure}\n \\plotone{mmass.eps}\n\\caption\n%\\figcaption \n{$M$-dependence of the spectrum. \nThe tendency of the changes caused by varying $M$ is almost \nthe same as in the case of compact disk. }\n \\end{figure}\n\n \\begin{figure}\n \\plotone{macc.eps}\n \\caption\n%\\figcaption \n{$\\dot{M}$-dependence of the spectrum. \nWith increasing mass accretion rate, the synchrotron peak \nshifts to higher frequencies while the self-absorbed luminosity \nis hardly affected. \nThe former tendency is different from the case of compact disk.}\n \\end{figure}\n\n \\begin{figure}\n \\plotone{mjiba.eps}\n\\caption\n%\\figcaption \n{$\\vert B_0\\vert$-dependence of the spectrum. \nThe tendency is almost the same as in the case of compact disk.}\n \\end{figure}\n\n\\begin{figure}\n \\plotone{mdelta.eps}\n\\caption\n%\\figcaption \n{$\\Delta$-dependence of the spectrum. \nThe tendency is almost the same as in the case of compact disk.}\n \\end{figure}\n \n\n\n\n\\end{document}"
}
] |
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astro-ph0002011
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\vglue-3.0truecm \centerline{\japit For submission to Monthly Notices} %\centerline{\japit Accepted for publication in Monthly Notices} \vglue 2.5truecm % \noindent Gravitational lens magnification by Abell 1689: Distortion of the background galaxy luminosity function
|
[
{
"author": "S. Dye$^1$"
},
{
"author": "A.N. Taylor$^1$"
},
{
"author": "E.M. Thommes$^{1,2}$"
},
{
"author": "K. Meisenheimer$^2$"
},
{
"author": "C. Wolf$^{\\,\\,2}$"
},
{
"author": "J.A. Peacock$^1$"
},
{
"author": "Royal Observatory"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh EH9 3HJ"
},
{
"author": "U.K."
},
{
"author": "$^2$Max-Planck-Institut f\\\"{u}r Astronomie"
},
{
"author": "K\\\"{o}nigstuhl 17"
},
{
"author": "D-69117 Heidelberg"
},
{
"author": "Germany"
}
] |
Gravitational lensing magnifies the observed flux of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Under the assumption that these galaxies are a random sample of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use 9 filters observed over 12 hours with the Calar Alto 3.5m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 146 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to $0.25\mpcoh$ is $M_{2d}(<0.25\mpcoh)=(0.48\pm0.16)\times10^{15} \,h^{-1}{M}_{\odot}$, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the offset calibration and finite sampling. This result is in good agreement with that found by number count and shear--based methods and provides a new and independent method to determine cluster masses.
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[
{
"name": "lumfn.tex",
"string": "\\documentstyle[twocolumn,epsfig]{mn}\n%\\documentstyle[referee]{mn}\n\\voffset -0.7truecm\n\\def\\bigstrut{\\vrule width0pt height0.6truecm}\n\\font\\japit = cmti10 at 10truept\n%\\smallskip\\noindent\n\\include{epsf}\n\n\\title\n [Lens magnification by Abell 1689: Background galaxy\nluminosity function]\n{\\vglue-3.0truecm\n\\centerline{\\japit For submission to Monthly Notices}\n%\\centerline{\\japit Accepted for publication in Monthly Notices}\n\\vglue 2.5truecm\n%\n\\noindent\nGravitational lens magnification by Abell 1689:\nDistortion of the background galaxy luminosity function}\n\\author\n [Dye et al.]\n {S. Dye$^1$, A.N. Taylor$^1$, E.M. Thommes$^{1,2}$, K. Meisenheimer$^2$, \n\tC. Wolf$^{\\,\\,2}$, J.A. Peacock$^1$ \\\\\n $^1$Institute for Astronomy, University of Edinburgh,\n Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, U.K.\\\\\n $^2$Max-Planck-Institut f\\\"{u}r Astronomie, K\\\"{o}nigstuhl 17,\n D-69117 Heidelberg, Germany}\n\n\\def\\rmd{{\\rm d}}\n\\def\\mpcoh{\\,h^{-1}\\,{\\rm Mpc}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\ba}{\\begin{eqnarray}}\n\\newcommand{\\ea}{\\end{eqnarray}}\n\\newcommand{\\x}{\\mbox{\\boldmath $x$}}\n\\newcommand{\\qvec}{\\mbox{\\boldmath $q$}}\n\\newcommand{\\Qvec}{\\mbox{\\boldmath $Q$}}\n\\newcommand{\\k}{{\\boldmath k}}\n\\newcommand{\\I}{{\\boldmath I}}\n\\newcommand{\\tb}{\\mbox{\\boldmath $\\theta$}}\n\\newcommand{\\bb}{\\mbox{\\boldmath $\\beta$}}\n\\newcommand{\\kb}{\\mbox{\\boldmath $\\kappa$}}\n\\newcommand{\\bone}{\\mbox{\\boldmath $1$}}\n\\newcommand{\\bA}{\\mbox{\\boldmath $A$}}\n\\newcommand{\\bB}{\\mbox{\\boldmath $B$}}\n\\newcommand{\\bG}{\\mbox{\\boldmath $G$}}\n\\newcommand{\\Mpc}{{\\rm Mpc}}\n\\newcommand{\\lgl}{\\langle}\n\\newcommand{\\rgl}{\\rangle}\n\\newcommand{\\nn}{\\nonumber \\\\}\n\\def\\bib{\\parskip=0pt\\par\\noindent\\hangindent\\parindent\n \\parskip =2ex plus .5ex minus .1ex}\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nGravitational lensing magnifies the observed flux of galaxies behind\nthe lens. We use this effect to constrain the total mass in the\ncluster Abell 1689 by comparing the lensed luminosities of background\ngalaxies with the luminosity function of an undistorted field. Under\nthe assumption that these galaxies are a random sample of luminosity\nspace, this method is not limited by clustering noise. We use\nphotometric redshift information to estimate galaxy distance and\nintrinsic luminosity. Knowing the redshift distribution of the\nbackground population allows us to lift the mass/background degeneracy\ncommon to lensing analysis. In this paper we use 9 filters observed\nover 12 hours with the Calar Alto 3.5m telescope to determine the\nredshifts of 1000 galaxies in the field of Abell 1689. Using a\ncomplete sample of 146 background galaxies we measure the cluster mass\nprofile. We find that the total projected mass interior to $0.25\\mpcoh$\nis $M_{2d}(<0.25\\mpcoh)=(0.48\\pm0.16)\\times10^{15}\n\\,h^{-1}{\\rm M}_{\\odot}$, where our\nerror budget includes uncertainties from the photometric redshift\ndetermination, the uncertainty in the offset calibration and finite\nsampling. This result is in good agreement with that found by number\ncount and shear--based methods and provides a new and independent\nmethod to determine cluster masses.\n\n\\end{abstract}\n\n\n\\begin{keywords} \ngalaxies: clusters: general - cosmology: theory - gravitational lensing - \nlarge scale structure of Universe.\n\\end{keywords}\n\n\\section{Introduction}\n\nThe use of gravitational lensing as a means of cluster mass\nreconstruction provides a theoretically efficient approach without the\nequilibrium and symmetry assumptions which typically accompany virial\nand X-ray temperature methods. Mass determination through application\nof lens shear proves to give good resolution in mass maps although\nmeasurement of absolute quantities is not possible without external\ncalibration. This so called sheet-mass degeneracy (Falco, Gorenstein\n\\& Shapiro 1985) is broken however by methods which exploit the\nproperty of lens magnification.\n\nFirst recognised by Broadhurst, Taylor \\& Peacock (1995, BTP\nhereafter) as a viable tool for the reconstruction of cluster mass,\nlens magnification has the twofold effect of amplifying background\nsource galaxy fluxes as well as their geometrical size and\nseparation. This immediately permits two separate approaches for\nmeasuring lensing mass. The first involves selecting a sample of\nsources with a flat or near-flat number count slope. Magnification\nresults in a reduction of their local surface number density owing to\nthe dominance of their increased separation over the enhanced number\ndetectable due to flux amplification.\n\nAlthough contaminated by faint cluster members, Fort, Mellier \\&\nDantel-Fort (1997) first reported this dilution effect using B and I\nband observations of the cluster CL0024$+$1654. Later, Taylor et\nal. (1998, T98 hereafter) demonstrated how the dilution in surface\nnumber density of a colour-selected sample of red galaxies lying\nbehind the cluster Abell 1689 enables determination of its total mass\nprofile and 2d distribution. A projected mass interior to $0.24\\mpcoh$\nof $M_{2d}(<0.24\\mpcoh)=(0.50\\pm0.09)\n\\times10^{15}\\,h^{-1}{\\rm M}_{\\odot}$ was predicted, in good agreement\nwith the shear analysis of Tyson \\& Fischer (1995) who measured\n$M_{2d}(<0.24\\mpcoh)=(0.43\\pm0.02)\\times10^{15}\\,h^{-1} {\\rm\nM}_{\\odot}$ and Kaiser (1995) with a measurement of\n$M_{2d}(<0.24\\mpcoh)=(0.43\\pm0.04)\\times10^{15}\\,h^{-1} {\\rm\nM}_{\\odot}$. \n\nSince then, several authors have detected source number\ncount depletion due to cluster lensing. Athreya et al (1999) observe\nMS1008$-$1224 and use photometric redshifts to identify a background\npopulation of galaxies within which they measure depletion. Mayen \\&\nSoucail (2000) constrain the mass profile of MS1008$-$1224 by comparing\nto simulations of depletion curves. Gray et al (2000) measure\nthe first depletion in the near infra-red due to lensing by Abell\n2219. Finally and most recently, R\\\"{o}gnvaldsson et al. (2000)\nfind depletion in the source counts behind CL0024$+$1654 in the R band\nand for the first time, in the U band.\n\nThe second mass reconstruction approach permitted by magnification\nforms the primary focus of this paper. The amplification of flux by\nlens magnification introduces a measurable shift in the luminosity\nfunction of background source galaxies. With a sufficiently well\ndefined luminosity function derived from an unlensed offset field for\ncomparison, this shift can be measured to allow an estimate of the\nlens mass (BTP). This method relies upon a set of observed source\nmagnitudes which, if assumed to form an effective random sampling of\nluminosity space, is not limited by noise from background source\nclustering unlike the number count method (see Section \\ref{sec_morph}\nfor further discussion).\n\nThis paper presents the first application of mass reconstruction using\nlens flux magnification inferred from the luminosity function of\nbackground samples. Unlike the method of T98 who defined their\nbackground sample based on colour cuts, in this work photometric\nredshifts of all objects in the observed field have been\nestimated. This not only allows an unambiguous background source\nselection but alleviates the need to estimate source distances when\nscaling convergence to real lens mass.\n\nThe following section details the theory of mass reconstruction from\nlens magnification of background source magnitudes. Section\n\\ref{sec_photo_anal} describes the photometric analysis applied to\nobservations of A1689 with the redshifts which result. Observations of\nthe offset field which provide the absolute magnitude distribution\nrequired for comparison with the A1689 background source sample are\npresented in Section \\ref{sec_cadis_field}. From this, a\nparameterised luminosity function is calculated in Section\n\\ref{sec_cadis_schechter} necessary for application of the maximum\nlikelihood method. Following a discussion of sample incompleteness in\nSection \\ref{sec_completeness}, a mass measurement of A1689 is given\nin Section \\ref{sec_mass_determ} where the effects of sample\nincompleteness are quantified. Finally, a signal to noise study is\ncarried out in Section \\ref{sec_sn_calcs} to investigate the effects\nof shot noise, calibration uncertainty of the offset field and\nphotometric redshift error.\n\n\n\\section{Mass Reconstruction}\n\\label{sec_mass_recon}\n\nMeasurement of lens magnification of background source fluxes\nrequires a statistical approach in much the same way as do shear\nor number count depletion studies. The basis of this statistical\nmethod relies on the comparison of the distribution of lensed source\nluminosities with the luminosity function of an un-lensed offset\nfield. As Section \\ref{sec_morph} discusses further, for a fair\ncomparison, the population of sources detected behind the lens must be\nconsistent with the population of objects used to form this un-lensed\nreference luminosity function.\n\nThe effect of lens magnification by a factor $\\mu$ on a source is to\ntranslate its observed magnitude from $M$ to\n$M+2.5\\log_{10}\\mu$. In terms of the reference\nluminosity function, $\\phi(M,z)$, the probability of a background\ngalaxy with an absolute magnitude $M$ and redshift $z$ being magnified\nby a factor $\\mu$ is (BTP)\n\\be\n\\label{eq_lum_prob}\n{\\rm P}[M|\\mu,z]=\\frac{\\phi(M+2.5\\log_{10}\\mu(z),z)} {\\int\n\\phi(M+2.5\\log_{10}\\mu(z),z)\\rmd M}.\n\\ee \nMagnification depends on the geometry of the observer-lens-source\nsystem hence for a fixed lens and observer, $\\mu$ is a function of\nsource redshift. This redshift dependence comes from the familiar\ndimensionless lens surface mass density or\nconvergence, $\\kappa(z)$, and shear, $\\gamma(z)$, which are related to \n$\\mu(z)$ via,\n\\be\n\\label{eq_mag}\n\\mu(z)=\\left|[1-\\kappa(z)]^2 - \\gamma^2(z)\\right|^{-1}.\n\\ee\n\nWe wish to apply maximum likelihood theory using the probability in\nequation (\\ref{eq_lum_prob}) to determine lens magnification and hence\n$\\kappa$. A parametric luminosity function is therefore required and\nso we take $\\phi(M,z)$ to be a Schechter function (Schechter 1976),\n\\be\n\\label{eq_mag_schechter_function}\n\\phi(M,z)=\\phi^*(z)10^{0.4(M_*-M)(1+\\alpha)}\\exp\\left[-10^{0.4(M_*-M)}\\right].\n\\ee \nThe Schechter parameters $\\phi^*$, $M_*$ and $\\alpha$ are determined\nby fitting to the magnitude distribution of the offset field (see\nSection \\ref{sec_cadis_field}). T98 use $\\mu$ as a\nlikelihood parameter by adopting the simplification that all sources\nlie at the same redshift. However this is not possible when each source is\nattributed its own redshift. We must therefore express $\\mu$ in terms\nof a redshift depenent quantity and a source--independent likelihood\nparameter. \n\nThe most direct solution is to separate the convergence. Using the\nparameter $\\kappa_{\\infty}$ introduced by BTP as the convergence for\nsources at $z=\\infty$, we can write $\\kappa(z)$ as,\n\\ba\n\\label{eq_kappa_zs}\n\\kappa(z) &=& \\kappa_\\infty f(z), \\nn\nf(z) &=& \\frac{\\sqrt{1+z}-\\sqrt{1+z_{\\scriptscriptstyle L}}}{\\sqrt{1+z}-1}.\n\\ea\nWe therefore choose $\\kappa_\\infty$ as our likelihood parameter with\nall source redshift dependency being absorbed into the function $f$.\nThe lens surface mass density, $\\Sigma$, is then related to $\\kappa_\\infty$\nand the lens redshift, $z_{\\scriptscriptstyle L}$, by\n\\ba\n\\label{eq_kapinf_defn}\n\\Sigma(z_{\\scriptscriptstyle L}) &=& \\frac{cH_0}{8 \\pi G} \\kappa_\\infty \n\\left[\\frac{(1+z_{\\scriptscriptstyle L})^2}\n{\\sqrt{1+z_{\\scriptscriptstyle L}}-1}\\right] \\nn \n&=& 2.75 \\times 10^{14} \\kappa_\\infty\\left[\n\\frac{(1+z_{\\scriptscriptstyle L})^2}\n{\\sqrt{1+z_{\\scriptscriptstyle L}}-1}\\right] h M_\\odot \\Mpc^{-2}.\n\\ea\nHere, we assume an Einstein-de-Sitter universe for reasons of simplicity\nand because BTP show that this result depends only weakly on the\nchosen cosmological model.\n\nBefore choosing a likelihood function, consideration must be given\nto the shear term in equation (\\ref{eq_mag}). Since shear scales with\nsource redshift in the same way as the convergence, we use the\nso-called $\\kappa$ estimators discussed by T98 which relate $\\kappa$\nto $\\gamma$. At the extremes these are $\\gamma=\\kappa$ for the\nisothermal sphere or $\\gamma=0$ for the sheet-like mass. A third\nvariation, motivated by cluster simulations and the fact that it has\nan invertible $\\mu(\\kappa)$ relation, is $\\gamma\\propto\\kappa^{1/2}$\n(van Kampen 1998). This gives rise to the parabolic\nestimator which predicts values of $\\kappa$ between those\ngiven by the sheet and isothermal estimators. Using equation\n(\\ref{eq_mag}), the magnification for these three different cases\ntherefore relates to $\\kappa_{\\infty}$ via \n\\be\n\\label{eq_mu_redshift_depen}\n\\mu(z)=\\left\\{\\begin{array}{ll}\n\\left|1-2\\kappa_{\\infty}f(z)\\right|^{-1} & {\\rm iso.} \\\\\n\\left|\\left[\\kappa_{\\infty}f(z)-c\\right]\n\\left[\\kappa_{\\infty} f(z)-1/c\\right]\\right|^{-1} & {\\rm para.} \\\\\n\\left[1-\\kappa_{\\infty}f(z)\\right]^{-2} & {\\rm sheet}\n\\end{array}\\right. \n\\ee \nand hence three different estimations of $\\kappa_{\\infty}$ exist\nfor a given $\\mu$. The constant $c$ in the parabolic case is\nchosen to provide the best fit with the cluster simulations. As in\nT98, we take $c=0.7$ throughout this paper.\n\nThe likelihood function for $\\kappa_{\\infty}$ is then formed from\nequation (\\ref{eq_lum_prob}),\n\\be\n\\label{eq_magnitude_likelihood}\n{\\cal L}(\\kappa_{\\infty}) \\propto \\prod_{i} \n{\\rm P}[M_i|\\mu(\\kappa_{\\infty}),z_i]\n\\ee \nwhere $\\mu$ is one of the three forms in equation\n(\\ref{eq_mu_redshift_depen}) and the product applies to the\ngalaxies behind the cluster region under scrutiny.\nAbsolute surface mass densities are then calculated from $\\kappa_{\\infty}$\nusing equation (\\ref{eq_kapinf_defn}).\n\nThe probability distribution for $\\kappa_{\\infty}$ obtained from\nequation (\\ref{eq_lum_prob}) for a single galaxy is typically\ndouble-peaked as two solutions for $\\kappa_{\\infty}$\nexist for a given magnification. The choice of peak is determined by\nimage parity such that the peak at the higher value of\n$\\kappa_{\\infty}$ is chosen for a galaxy lying inside the critical\nline and vice versa. The chosen peak is then extrapolated to extend\nover the full $\\kappa_{\\infty}$ range before contributing\nto the likelihood distribution. In this way, a single-peaked likelihood\ndistribution is obtained.\n\nEvidently, calculation of lens surface mass density in this way\nrequires redshift and absolute magnitude data for background galaxies\ntogether with knowledge of the intrinsic distribution of magnitudes\nfrom an unlensed offset field. The next section details the\nphotometric analysis applied to our observations of Abell 1689 to\narrive at background object redshifts and absolute magnitudes.\n\n\\section{Photometric Analysis}\n\\label{sec_photo_anal}\n\n\\subsection{Data acquisition}\n\nObservations of Abell 1689 were performed with the Calar Alto 3.5m\ntelescope in Spain using 8 different filters, chosen for photometric\ndistinction between foreground, cluster and background objects. In\naddition, the I-band observations of T98 were included to bring the\ncombined exposure time to a total of exactly 12 hours worth of useable\ndata characterised by a seeing better than $2.1''$. Table\n\\ref{tab_a1689_filters} details the summed integration time for each\nfilter set together with the motivation for inclusion of the\nfilter. Note the narrow band filters 466/8, 480/10 and 774/13 which\nwere selected to pick out spectral features of objects lying at the\ncluster redshift of $z=0.185$ (Teague, Carter \\& Gray 1990).\n\n\\begin{table}\n\\vspace{4mm}\n\\centering\n\\begin{tabular}{|c|c|c|}\n\\hline\nFilter: $\\lambda_c/\\Delta\\lambda$ (nm) & t$_{\\rm int}$(s) & Use \\\\\n\\hline\n826/137 (I-band) & 6000 & Global SED\\\\\n774/13 & 6800 & H$_\\alpha$ at $z=0.185$\\\\\n703/34 & 4100 & Background $z$\\\\\n614/28 & 7700 & Background $z$\\\\\n572/21 & 6300 & Background $z$\\\\\n530/35 & 3300 & Background $z$\\\\\n480/10 & 4200 & 4000\\AA at $z=0.185$\\\\\n466/8 & 4800 & Ca H,K at $z=0.185$ \\\\\n457/96 (B-band) & 6000 & Global SED\\\\\n\\hline \n\\end{tabular}\n\\caption{The observations of Abell 1689 in all 9 filters (labelled as\n$\\lambda_c/\\Delta\\lambda\\equiv$ central wavelength/FWHM).\nt$_{int}$ gives the total integration time in each filter. The\nI-band data comes from T98.}\n\\label{tab_a1689_filters}\n\\end{table}\n\nImage reduction and photometry was performed using the MPIAPHOT\n(Meisenheimer \\& R\\\"{o}ser 1996) software written at the MPIA\nHeidelberg as an extension to the MIDAS reduction software package.\nImages were de-biased and flattened from typically four or five\nmedian filtered dusk sky flats observed each night for each filter\nset. Any large scale remnant flux gradients were subsequently removed\nby flattening with a second-order polynomial fitted to the image\nbackground. Cosmic ray removal was carried out using the pixel\nrejection algorithm incorporated in MPIAPHOT. All post-reduced images\nwere flattened to a $1\\sigma$ background flux variation of less than\n0.02 mag.\n\n\\subsection{Galaxy catalogue}\n\\label{sec_gal_cat}\n\nInstead of co-adding images in each filter set before object\ndetection, photometric evaluation was carried out on images\nindividually. In this way, an estimate of the uncertainty in the photon\ncount for each galaxy could be obtained.\nThe mean photon count $I^{(b,m)}$\nof a galaxy $m$ observed in a filter $b$ was calculated as the usual\nreciprocal-variance weighted sum, \n\\be\n\\label{eq_flux_weight}\nI^{(b,m)}=\n\\sum_i\\frac{I^{(b,m)}_i}{\\left(\\sigma_i^{(b,m)}\\right)^2}\n{\\Big /}\\left[\\sum_i\\left(\\sigma_i^{(b,m)}\\right)^{-2}\\right]\n\\ee\nwhere the summation acts over all images belonging to a particular\nfilter set and the error on $I^{(b,m)}$ is\n\\be\n\\label{eq_flux_weight_error}\n\\overline{\\sigma}^{(b,m)}=\\left[\\sum_i\\left(\n\\sigma_i^{(b,m)}\\right)^{-2}\\right]^{-1/2} .\n\\ee\nThe quantity $\\sigma_i^{(b,m)}$ is the standard deviation of\nbackground pixel values surrounding galaxy $m$ in image\n$i$. Background pixels were segregated by applying an appropriate cut\nto the histogram of counts in pixels within a box of size $13''\\times\n13''$ ($40\\times 40$ pixels) centred on the galaxy. This cut removed\nthe high count pixels belonging to the galaxy itself and any other\nneighbouring galaxies within the box.\n\nIntegrated galaxy photon counts were determined using MPIAPHOT which\nsums together counts in all pixels lying inside a fixed aperture of\nradius $6''$ centred on each galaxy. A `mark table' accompanying every\nimage in every filterset provided co-ordinates of galaxy centres.\nTables were fit within an accuracy of $<1''$ to individual images\nusing copies of a master table derived from the deepest co-added\nimage; that observed in the I-band. In this way consistent indexing\nof each galaxy was achieved throughout all catalogues. The master\ntable was generated using the object detection software `SExtractor'\n(Bertin \\& Arnouts 1996). Only galaxies were contained in the master\ntable, star-like objects being removed after identification by their\nhigh brightness and low FWHM. With a detection threshold of $3\\sigma$\nabove the average background flux, galaxies in the I-band image were\ncatalogued after coincidence matching with objects detected at the\n$3\\sigma$ level in the associated V-band data presented by\nT98. Despite cataloguing $\\sim 3000$ galaxies, the resulting number\nwas limited to a total of $\\sim 1000$ due to the relatively shallow\ndata observed with the 466/8 narrow-band filter.\n\n\\subsection{Photometry}\n\\label{sec_photom}\n\nThe integration of photon counts in an aperture of fixed size requires\nconstant seeing across all images to allow correct determination of\ncolours. To ensure constant seeing, all images were degraded by\nGaussian convolution to the worst seeing of $2.1''$ measured in the\n466/8 filter before galaxy counts were evaluated. The effects of\nchanging weather conditions were compensated for by normalising images\nwithin each filter set to an arbitrarily chosen image in that\nset. Normalisation was conducted by scaling the galaxy counts in each\nimage so that the average counts of the same stars in all images was\nequal. This ensured correct calculation of the weighted counts and the\nerror from equation (\\ref{eq_flux_weight}) and\n(\\ref{eq_flux_weight_error}). These quantities were later scaled to\ntheir calibrated photometric values.\n\nCalibration of the photometric fluxes from the weighted counts\nwas provided using the spectrum of the dominant elliptical galaxy in\nthe centre of A1689 taken from Pickles \\& van der Kruit\n(1991). Denoting this spectrum as the function $F_s(\\lambda)$, the\ncalibration scale factors $k_b$ for each filter $b$ were calculated\nusing\n\\be\n\\label{eq_standard_flux}\nI^{(b,s)}=k_b\\int \\rmd\\lambda\n\\frac{E(\\lambda)T_b(\\lambda)F_s(\\lambda)\\lambda}{hc}\n\\ee \nwhere the function $T_b(\\lambda)$ describes the filter transmission\nefficiency, $E(\\lambda)$ is the combined filter-independent efficiency\nof the detector and telescope optics and $I^{(b,s)}$ is the measured\nintegrated photon count rate of the central galaxy. The values of\n$k_b$ obtained in this way were only relatively correct owing to the\nlack of an absolute calibration of the published spectrum. Absolute\ncalibration scale factors were calculated from observations of the\nstandard star G60-54 (Oke 1990) in all filters in exactly the same\nmanner. Verification of this absolute calibration was provided by the\nconsistency of ratios of $k_b({\\rm absolute})/k_b({\\rm relative})$ to a\nzero point of $\\Delta m=2.11\\pm 0.01$ magnitudes averaged over all\nfilters.\n\nConsideration of equation (\\ref{eq_standard_flux}) shows that only the\nquantity \n\\be\n\\label{eq_photom_integral}\n\\int \\rmd\\lambda E(\\lambda)T_b(\\lambda)F_m(\\lambda)\\lambda = \n\\frac{hc \\, I^{(b,m)}}{k_b}\n\\ee\ncan be known for any galaxy $m$ with a calibrated photon count rate.\nThe required photometric flux \n\\be\n\\label{eq_filter_inten}\nF^{(b,m)}=\\int\\rmd\\lambda T_b(\\lambda)F_m(\\lambda)\n\\ee\ncan not therefore be directly determined\nwithout making an approximation such as the simplification of\nfilter transmission curves to top hat functions. Although this is\nacceptably accurate in narrow band filters, it is not\nfor broad band filters. \nThis problem was avoided by the more sophisticated technique of\nfitting model spectra to measured galaxy colours \nas the next section discusses.\n\n\\subsection{Photometric redshift evaluation}\n\nDirect calculation of photometric fluxes using equation\n(\\ref{eq_filter_inten}) was made possible by fitting model spectra to\nthe set of calibrated photon count rates measured for each galaxy\nacross all filters. Expressed more quantitatively, equation\n(\\ref{eq_photom_integral}) was applied for each filter to a library of\ntemplate spectra to arrive at a set of scaled filter counts for each\nspectrum. Galaxies were then allocated library spectra by finding the\nset of library colours which best fit the measured galaxy colours.\nNote that this differs from conventional template fitting where \nspectra are redshifted and scaled to fit observed colours in a much\nmore time costly manner.\n\nThe spectral library was formed from the template galaxy spectra of\nKinney et al. (1996). A regular grid of galaxy templates was\ngenerated, varying in redshift along one axis from $z=0$ to $z=1.6$ in\nsteps of $\\Delta z=0.002$ and ranging over 100 spectral types from\nellipticals, through spirals to starbursts along the other. \n\nThe set of photometric errors given by equation\n(\\ref{eq_flux_weight_error}) for an individual galaxy across all\nfilters gives rise to an error ellipsoid in colour space. Using the\nsize and location of these error ellipsoids, probabilities of each\nlibrary entry causing the observed sets of colours for each galaxy\nwere then calculated as \n\\be\n\\label{eq_prob_colour_fit}\np(\\qvec|z,s)=\\frac{1}{\\sqrt{(2\\pi)^n|V|}}\n\\exp\\left(-\\frac{1}{2}\\sum_{j=1}^n\\frac{[q_j-Q_j(z,s)]^2}{\\sigma_j^2}\\right)\n\\ee \nwhere $n$ is the number of colours, $\\sigma_j$ comes from propagation\nof the error given by equation (\\ref{eq_flux_weight_error}) and\n$V\\equiv{\\rm diag}(\\sigma_1^2,...,\\sigma_n^2)$. Each galaxy's position\nvector in colour space, $\\qvec\\equiv(q_1,...,q_n)$ is compared with\nthe colour vector $\\Qvec$ of the library spectrum with a given\nredshift $z$ and type $s$. Finding the maximum probability\ncorresponding to the closest set of matching colours therefore\nimmediately establishes redshift and galaxy type. An assessment of the\nuncertainty in this redshift is subsequently obtained directly from\nthe distribution of the probabilities associated with neighbouring\nlibrary spectra.\n \n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=82mm\n{\\hfill\n\\epsfbox{fig1.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small Redshift distribution of the 958 objects photometrically\nevaluated in the field of A1689. The grey histogram plots all 958\nredshifts whereas the black histogram plots only the 470 redshifts\nwith a $1\\sigma$ error in redshift of less than 0.05. The peak at\n$z\\simeq0.18$ is the contribution from the cluster galaxies.}\n\\label{a1689_z_dist}\n\\end{figure}\n\n\nFigure \\ref{a1689_z_dist} shows the distribution of the 958\nsuccessfully classified galaxy redshifts estimated from the full\nfilter set. We measure an average redshift error of \n$\\left<\\sigma_z\\right>=0.08$.\nThe maximum redshift limit of $z\\simeq 0.8$ comes from\nthe condition that the 4000\\AA\\ limit must lie in or blue-ward of the\nsecond reddest filter in the set. The peak at $z\\simeq 0.18$ in\nFigure \\ref{a1689_z_dist} is clearly the contribution from the cluster\ngalaxies. \n\nThe feature at $z\\simeq 0.4$ is most likely real and not an artifact\nof the photometric method. Such artifacts occur due to `redshift\nfocusing' when particular redshifts are measured more accurately than\nothers. Where the uncertainty is larger, galaxies can be randomly\nscattered out of redshift bins, producing under-densities and\ncorresponding over-densities where the redshift measurement is more\naccurate. This effect depends on the details of the filter set, being\nmore common when fewer filters are used, but can be modelled by Monte\nCarlo methods.\n\nThe top half of Figure \\ref{z_match} shows the results of one\nrealisation of such a Monte Carlo test for redshift focusing. The plot\nindicates how accurately the method reproduces redshifts of spectra\nscaled to ${\\rm I}=20$ with photometric noise levels\ntaken from the A1689 filter set. Each point represents a single\nlibrary spectrum. Reproduced spectral redshifts, $z_{\\rm phot}$, were\ndetermined by calculating colours through application of equation\n(\\ref{eq_filter_inten}) to the library spectra with redshifts $z_{\\rm\nlib}$. These colours were then randomly scattered by an amount\ndetermined from the filter-specific photometric error measured in the\nA1689 data before application of the redshift estimation method\noutlined above. The bottom half of Figure \\ref{z_match} shows the same\nplot generated using spectra scaled to ${\\rm I}=21$ with the same\nphotometric error taken from the A1689 data.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=70mm\n{\\hfill\n\\epsfbox{fig2.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small A single Monte Carlo realisation showing the accuracy\nof the photometric redshift evaluation method. Input library spectra\nwith redshifts $z_{\\rm lib}$ are scaled to ${\\rm I}=20$ (top) and\n${\\rm I}=21$ (bottom) and subsequently used to calculate sets of\ncolours using the A1689 filterset. These colours are randomly\nscattered by the filter-specific photometric errors measured in the\nA1689 data before calculating the reproduced redshifts $z_{\\rm phot}$.}\n\\label{z_match}\n\\end{figure}\n\nThe accuracy of reproduced redshifts at ${\\rm I}=20$ is clearly better\nthan those at ${\\rm I}=21$ where photometric noise is more\ndominant. The lack of any sign of redshift focusing in the vicinity of\n$z\\simeq 0.4$ leads us to conclude that the feature seen at this\nredshift in the A1689 data is probably real. The ${\\rm I}=21$ plot\nwhich corresponds approximately to our sample magnitude cut of ${\\rm\nB}=23.6$ (see Section \\ref{sec_completeness}) shows that galaxies at\nredshifs below $z=0.05$ have on average higher estimated redshifts.\nThis only marginally affects the overall redshift distribution and yet\npartly explains the lack of galaxies at $z<0.05$ in the A1689\nredshifts of Figure \\ref{a1689_z_dist}. It is worth emphasising here\nthat the significance of the peak at $z\\simeq0.18$ attributed to the\ncluster galaxies is far in excess of any effects of redshift focusing.\n\nFigure \\ref{photo_reliability} shows a comparison of the\nphotometrically determined redshifts $z_{\\rm phot}$ around the peak of\nthe redshift distribution of Abell 1689, with spectroscopically\ndetermined (Teague, Carter \\& Gray, 1990) redshifts $z_{\\rm spec}$. A\nvery slight bias between $z_{\\rm phot}$ and $z_{\\rm spec}$ can be\nseen. This bias is quantified by fitting the line $z_{\\rm phot}=z_{\\rm\nspec}+c$ by least-squares to the data points which gives\n$c=0.0036$. Referring to equation (\\ref{eq_error_fits}) shows that if\nthis small bias is applied to all redshifts in our sample, a\nnegligible difference of $\\Delta\\kappa_\\infty=0.001$ would result. Our\nfilter set was selected primarily to distinguish the cluster members,\nhence at higher redshift we must rely on our Monte Carlo estimates of\nthe redshift uncertainty (see Section \\ref{sec_source_uncert}).\n\nAbell 1689 lies in a region of sky where there is a very low level\nof galactic dust. Our redshifts are therefore not affected by this\nsource of contamination. However, dust in the cluster itself\nis another concern. We have modelled the effects of reddening by\ncluster dust and find that although magnitudes are slightly affected,\nthe redshifts remain the same.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=70mm\n{\\hfill\n\\epsfbox{fig3.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small Comparison of the photometric redshifts estimated in the \ncluster Abell 1689 with spectroscopically determined redshifts. The \ndistribution shows slight non-Gaussianity in the error distribution. The\nmean redshift of the cluster determined spectroscopically is $z=0.185$\n(Teague, Carter \\& Gray 1990), while the mean photometric redshift is $z=0.189\n\\pm 0.005$.}\n\\label{photo_reliability}\n\\end{figure}\n\n\\section{Offset field and lens calibration}\n\\label{sec_cadis_field}\n\nThe unlensed, intrinsic magnitude distribution required\nby the likelihood analysis was taken from an offset field observed as\npart of the Calar Alto Deep Imaging Survey (CADIS) conducted by the\nMax-Planck Institut f\\\"{u}r Astronomie, Heidelberg (Meisenheimer et\nal. 1998). Data for this survey were observed to a complete depth of\n${\\rm B}\\simeq24.5$ mag in 16 filters from the B-band to the K-band\nwith the 2.2m telescope at Calar Alto. We use the CADIS 16-hour field\nfor our mass calibration.\n\nUsing exactly the same methods outlined in the previous section for\nthe A1689 data, photometric redshifts and rest-frame absolute\nmagnitudes were determined for all objects in the field. In addition\nto galaxy templates in the spectral library however, \nquasar spectra from Francis et al. (1991) and stellar spectra from\nGunn \\& Stryker (1983) were also included, the primary motivation for\nthis difference being the CADIS quasar study. As a by-product, a more\nsophisticated object classification method was achieved by finding the\noverall object class yielding the highest significant probability\ngiven by equation (\\ref{eq_prob_colour_fit}). Details of this and the\nCADIS quasar study are given in Wolf et al. (1999). To ensure a fair\ncomparison between the offset field and the cluster field, the CADIS\nB-band ($\\lambda_c/\\Delta\\lambda=461/113$ nm) galaxy magnitudes were\nused with the A1689 B-band magnitudes in the likelihood analysis \ndiscussed in Section \\ref{sec_mass_recon}.\n\nInvestigation of evolution (see for example, Lilly et al. 1995, Ellis\net al. 1996) of the CADIS luminosity function is left for future\nwork. A preliminary study indicated no significant evolution which\nwould impact on the lens mass determination. We therefore applied the\nsame redshift selection as used for the Abell 1689 background sources,\nand assumed a no--evolution model.\n\nWe present two estimates of the calibration B-band luminosity function:\na nonparametric $1/V_{\\rm max}$ method (Section \\ref{sec_vmax}) and a \nmaximum likelihood parametric fit to a Schechter function \n(Section \\ref{sec_cadis_schechter}). The former method allows us to\nsee the distribution of luminosities without imposing a\npreconceived function, and gives a visual impression of the uncertainties\nin the parametric fit. In addition the $V_{\\rm max}$ approach allows \nus to make basic tests for sample completeness (we discuss this in \nSection \\ref{sec_completeness}). The latter maximum likelihood fit provides\na convenient function for performing the second likelihood analysis to\ndetermine lens magnification. We begin by describing the \nnonparametric method.\n\n\n\\subsection{The nonparametric CADIS B-band luminosity function}\n\\label{sec_vmax}\n\nAn estimate of the luminosity function of galaxies in the CADIS B band\nwas provided initially using the canonical $1/V_{\\rm max}$ method\nof Schmidt (1968). The\nquantity $V_{\\rm max}$ is computed for each galaxy as the comoving volume\nwithin which the galaxy could lie and still remain in the redshift and\nmagnitude limits of the survey. For an Einstein-de-Sitter universe,\nthis volume is,\n\\be\n\\label{eq_vmax}\nV_{\\rm max}=\\left(\\frac{c}{H_0}\\right)^3\\delta\\omega\n\\int^{{\\rm min}(z_u,z_{m_{\\rm max}})}_{{\\rm max}(z_l,\nz_{m_{\\rm min}})}\\rmd z \\frac{D^2(z)}{(1+z)^{3/2}} \\nn\n\\ee\nwhere $\\delta\\omega$ is the solid angle of the observed field of view\nand $D(z)$ is\n\\be\nD(z)=2(1-(1+z)^{-1/2}).\n\\ee\nThe upper limit of the integral in equation (\\ref{eq_vmax}) is set by\nthe minimum of the upper limit of the redshift interval chosen, $z_u$,\nand the redshift at which the galaxy would have to lie to have an\napparent magnitude of the faint limit of the survey,\n$z_{m_{\\rm max}}$. Similarly, the maximum of the lower limit of the chosen\nredshift interval, $z_l$, \nand the redshift at which the galaxy would\nhave to lie to have an apparent magnitude of the bright limit of the\nsurvey, $z_{m_{\\rm min}}$, forms the lower limit of the integral. This\nlower integral limit plays a non-crucial role when integrating over\nlarge volumes originating close to the observer where the volume\nelement makes only a relatively small contribution to $V_{\\rm max}$.\n\nThe redshifts $z_{m_{\\rm max}}$ and $z_{m_{\\rm min}}$ are calculated for each\nobject by finding the roots of\n\\be\n\\label{eq_app_abs_mag}\nM-m_{\\rm lim}+5\\log_{10}\\left[\\frac{(1+z)D(z)}{h_0}\\right] -K(z)=-42.39 \n\\ee \nwhere $M$ is the absolute magnitude of the object, $m_{\\rm lim}$ is the\nappropriate maximum or minimum survey limit and $K(z)$ is the\nK-correction. Although the K-correction for each object at its actual\nredshift was known from its apparent and absolute rest-frame\nmagnitude, the redshift dependence of this K-correction was not. In\nprinciple, this redshift dependence could have been calculated\ndirectly for each object using its best-fit spectrum returned from the\nphotometric analysis. However, the much simplified\napproach of approximating the K-correction as a linear function of\nredshift was employed. This was primarily motivated by its\nimproved efficiency and the relatively weak influence the K-correction\nwas found to have on the final luminosity function.\nLilly et al. (1995) find that the K-correction in their B-band for elliptical, \nspiral and irregular galaxies is proportional to redshift in the redshift \nrange $0\\leq z \\leq 0.8$. The following form for $K(z)$ \nwas thus adopted \n\\be\n\\label{eq_kcorr_approx}\nK(z)=\\frac{K(z_0)}{z_0}z\n\\ee\nwhere $K(z_0)$ is the K-correction of the object at its actual\nredshift $z_0$. \n\nOnce $V_{\\rm max}$ has been calculated for all objects, the \nmaximum likelihood estimated luminosity function\n$\\phi$ at the rest-frame absolute magnitude $M$ in bins of width\n$\\rmd M$ is then,\n\\be\n\\label{eq_vmax_lumfn}\n\\phi(M) \\rmd M = \\sum_i \\frac{1}{V_{{\\rm max},i}}\n\\ee\nwhere the sum acts over all objects with magnitudes between $M-\\rmd\nM/2$ and $M+\\rmd M/2$. \n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=83mm\n{\\hfill\n\\epsfbox{fig4.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small The CADIS B band object luminosity function calculated with\nthe $1/V_{\\rm max}$ formalism. Errors account only for errors in\nredshift. Points lie at bin centres, the widths of each chosen to hold\nthe same number of objects. There are 371 galaxies in total selected by\nthe redshift limits $0.3\\leq z \\leq 0.8$ and the apparent B magnitude\n$m_{\\rm B} \\leq 24.5$. The solid line is the Schechter function determined\nin Section \\ref{sec_cadis_schechter}.}\n\\label{cadis_lf_vmax}\n\\end{figure}\n\nFigure \\ref{cadis_lf_vmax} shows the luminosity function of B band\nmagnitudes from the CADIS offset field which has a solid viewing angle\nof $\\delta \\omega =100 \\,\\, \\rm{arcmin}^2$. To match the selection of\nobjects lying behind A1689, only objects within the redshift range\n$0.3\\leq z \\leq 0.8$ were chosen. A further restriction on the\napparent B magnitude of $m_{\\rm B} \\leq 24.5$ was applied for completeness\nof the sample (see Section \\ref{sec_completeness}), yielding a\ntotal of 371 galaxies. The data points in Figure \\ref{cadis_lf_vmax}\nare centred on bins chosen to maintain an equal number of objects in\neach. \n\nThe $1\\sigma$ errors shown here were calculated from\nMonte Carlo simulations. Object redshifts were randomly scattered\nin accordance with their associated errors provided in the\nCADIS dataset. For each realisation, the $V_{\\rm max}$ of each\nobject was re-calculated using the re-sampled redshift. The resulting\nstandard deviation of the distribution of values of $\\phi$ for each\nbin given by equation (\\ref{eq_vmax_lumfn}) was then taken as the\nerror. In this particular instance, no consideration was given to the\nmagnitude errors or the propagation of the redshift error into object\nmagnitudes. Section \\ref{sec_cadis_schechter} discusses this\nfurther. \n\n\\subsection{Parameterisation of the CADIS B-band luminosity function}\n\\label{sec_cadis_schechter}\n\nThe maximum likelihood method of Sandage, Tammann \\& Yahil (1979, STY\nhereafter) was employed to determine the Schechter function best\ndescribing the CADIS B-band magnitudes. This parameterisation is\nessential for the determination of lens mass using the likelihood\napproach.\n\nIn much the same way as the probability in equation\n(\\ref{eq_lum_prob}) was formed, the STY method forms the probability\n$p_i$ that a galaxy $i$ has an absolute magnitude $M_i$,\n\\be\n\\label{eq_schechter_p_i}\np_i\\equiv p(M_i|z_i)\\propto\\frac{\\phi(M_i)}\n{\\int^{{\\rm min}(M_{\\rm max}(z_i),M_2)}_{{\\rm max}\n(M_{\\rm min}(z_i),M_1)}\\phi(M)\\rmd M }\n\\ee\nwhere $M_{\\rm max}(z_i)$ and $M_{\\rm min}(z_i)$ are the absolute magnitude\nlimits corresponding to the apparent magnitude limits of the survey at\na redshift of $z_i$. Conversion of these apparent magnitude limits\nincludes the K-correction using equation (\\ref{eq_app_abs_mag})\nwith $z$ set to $z_i$. A further restriction is placed upon the\nintegration range by imposing another set of magnitude limits\n$M_1<M<M_2$ which for the CADIS data were set at the maximum and\nminimum absolute magnitudes found in the sample.\n\nThe likelihood distribution in this case is a two dimensional function\nof the Schechter parameters $M_*$ and $\\alpha$ formed from the product\nof all probabilities $p_i$. The best fit $M_*$ and $\\alpha$ are\ntherefore found by maximizing the likelihood function, \n\\be\n\\label{eq_schechter_likelihood}\n\\begin{array}{l} \n\\ln {\\cal L}(M_*,\\alpha)= \\\\\n\\sum_{i=1}^{N}\\left\\{\\ln\\phi(M_i)-\\ln\\int^{{\\rm min}(M_{\\rm max}\n(z_i),M_2)}_{{\\rm max}(M_{\\rm min}(z_i),M_1)}\\phi\\,\\rmd M \\right\\} + c_p\n\\end{array}\n\\ee\nwith the constant $c_p$ arising from the proportionality in equation\n(\\ref{eq_schechter_p_i}). An estimate of the errors on $M_*$ and\n$\\alpha$ are calculated by finding the contour in $\\alpha,M_*$ space\nwhich encompasses values of $\\alpha$ and $M_*$ lying within a\ndesired confidence level about the maximum likelihood\n${\\cal L}_{\\rm max}$. \n\nTo account for uncertainties in the Schechter parameters due to the\nredshift and magnitude errors derived by the photometric analysis,\nMonte Carlo simulations were once again performed. Redshifts and\nabsolute magnitudes of the entire sample were randomly scattered\nbefore re-application of the maximum likelihood process each time. The\nerror in absolute magnitude was calculated using simple error\npropagation through equation (\\ref{eq_app_abs_mag}) yielding,\n\\be\n\\label{eq_z_mag_error_prop}\n\\sigma^2_{M_i}=\\left(\\frac{K_i}{z_i}-\\frac{5}{\\ln 10}\\,\n\\frac{1-0.5(1+z_i)^{-1/2}}{1+z_i-(1+z_i)^{1/2}}\\right)^2\n\\sigma^2_{z_i}+\\sigma^2_{m_i}\n\\ee\nfor each object with redshift $z_i$ and apparent magnitude\n$m_i$. Here, the K-correction given by equation\n(\\ref{eq_kcorr_approx}) has been used such that the quantity $K_i\n\\equiv K(z_i)$ is calculated from equation (\\ref{eq_app_abs_mag})\nusing $m_i$, $M_i$ and $z_i$ as they appeared in the CADIS dataset.\nThe typical ratio of apparent magnitude to redshift error was found to\nbe $\\sigma_{m_i}/\\sigma_{z_i}\\sim 1\\%$ due to the relatively imprecise\nnature of photometric redshift determination.\n\nThe final errors on $M_*$ and $\\alpha$ were taken from an effectively\nconvolved likelihood distribution obtained by combining the scattered\ndistributions produced from the Monte Carlo simulations. Figure\n\\ref{cadis_likelihood} shows the final $1\\sigma$ and $2\\sigma$\nlikelihood contours calculated allowing for redshift and magnitude\nerrors. These predict the resulting parameters\n\\be\n\\label{params_ms_alpha_cadis}\nM_*=-19.43^{+0.47}_{-0.64} +5\\log_{10}h \n\\, , \\quad \\alpha=-1.45^{+0.25}_{-0.23}\n\\ee\nwhere projected $1\\sigma$ errors are quoted. For completeness, \nthe normalisation was also calculated to be\n\\be\n\\phi^*=0.0164\\,h^3 \\, {\\rm Mpc}^{-3},\n\\ee\nin this case where evolution of the luminosity function has been\nneglected.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=80mm\n{\\hfill\n\\epsfbox{fig5.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small Likelihood contours for the CADIS B-band Schechter\nparameters taking photometric redshift and magnitude error into\nconsideration. $1\\sigma$ and $2\\sigma$ confidence levels are plotted\ncorresponding to $\\Delta \\ln {\\cal L}=1.15$ and $3.09$ respectively.}\n\\label{cadis_likelihood}\n\\end{figure}\n\n\\section{Sample Consistency}\n\nEnsuring that the A1689 sample of sources is consistent with the CADIS\noffset field sample is necessary to prevent biases from entering our\nresults. The first level of compatibility we have already enforced by\napplying a redshift selection of $0.3\\leq z \\leq 0.8$ to both samples.\nThe second, discussed in Section \\ref{sec_completeness} below, is\nsample completeness. A slightly less obvious consideration must also\nbe given to galaxy morphological type as Section \\ref{sec_morph}\nexplains.\n\n\\subsection{Completeness}\n\\label{sec_completeness}\n\nDetermination of the faint magnitude limit beyond which both the A1689\nand CADIS data set become incomplete is important for the calculation\nof an accurate lens mass. Both samples must be complete for fair\ncomparison. Incorrect evaluation of the CADIS limiting magnitude\nresults in larger values of $V_{\\rm max}$ and hence a biased luminosity\nfunction not representative of the intrinsic A1689 distribution. Similarly, \ncompleteness of the A1689 sample also affects the lens mass\nin a manner quantified in Section \\ref{sec_incompleteness_effects}.\n\nEstimation of the completeness of both data sets was provided using\nthe $V/V_{\\rm max}$ statistic (Schmidt 1968). In this ratio, $V_{\\rm\nmax}$ is calculated using equation (\\ref{eq_vmax}) whereas $V$ is the\ncomoving volume described by the observer's field of view from the\nsame lower redshift limit in the integral of equation (\\ref{eq_vmax})\nto the redshift of the object. If a sample of objects is unclustered,\nexhibits no evolution and is complete, the position of each object in\nits associated volume $V_{\\rm max}$ will be completely random. In this\ncase, the distribution of the $V/V_{\\rm max}$ statistic over the range 0\nto 1 will be uniform with $\\langle V/V_{\\rm max}\\rangle=0.5$.\n\nIf the sample is affected by evolution such that more intrinsically\nbright objects lie at the outer edges of the $V_{\\rm max}$ volume,\nthen $V/V_{\\rm max}$ is biased towards values larger than 0.5. The\nreverse is true if a larger number of brighter objects lie nearby. If\nthe sample is incomplete at the limiting apparent magnitude chosen,\nestimations of $V_{\\rm max}$ will be on average too large and will\ncause $V/V_{\\rm max}$ to be biased towards values less than 0.5. The\nrequirement that $\\langle V/V_{\\rm max}\\rangle=0.5$ for completeness is also\nsubject to fluctuations due to finite numbers of objects. In the\nabsence of clustering, the uncertainty due to shot noise on\n$\\langle V/V_{\\rm max}\\rangle$ calculated from $N$ galaxies can \nbe simply shown to be\n\\be\n\\label{eq_sigma_v_vmax_av}\n\\sigma^2_{\\langle V/V_{\\rm max}\\rangle}=\\frac{1}{12N}.\n\\ee\n\nIn order to arrive at an apparent magnitude limit for the CADIS and\nA1689 fields, values of $\\langle V/V_{\\rm max}\\rangle$ were\ncalculated for different\napplied limiting magnitudes and plotted as shown in Figure\n\\ref{vmax_var}. The grey region in this plot corresponds to the\n$1\\sigma$ errors described by equation (\\ref{eq_sigma_v_vmax_av})\nwhich lessen at the fainter limiting magnitudes due to the inclusion\nof more objects. Clustering adds extra noise and so these errors are\nan underestimate of the true uncertainty (one can show that the\nuncertainty in $V/V_{\\rm max}$ increases by the square root of the average\nnumber of objects per cluster).\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=80mm\n{\\hfill\n\\epsfbox{fig6.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small Variation of $V/V_{\\rm max}$ with limiting apparent B\nmagnitude for the A1689 (top) and the CADIS (bottom) sample. The grey\nregion corresponds to the $1\\sigma$ errors described by equation\n(\\ref{eq_sigma_v_vmax_av}) which are an underestimate due to the\nunconsidered effects of galaxy clustering.}\n\\label{vmax_var}\n\\end{figure}\n\nWithout knowledge of the effects of clustering, Figure \\ref{vmax_var}\nshows that a limiting magnitude of $m_{\\rm B}\\leq 24.5$ for CADIS and\n$m_{\\rm B}\\leq 23.6$ for A1689 corresponds to a value of $\\langle\nV/V_{\\rm max}\\rangle \\simeq 0.5$ and thus completeness. These\nmagnitudes are in agreement with the apparent magnitude limits at\nwhich the number counts begin to fall beneath that measured by deeper\nsurveys (such as the B band observations of Lilly, Cowie \\& Gardner\n(1991) which extend to a depth of $m_{\\rm B}\\simeq 26$) and also\ncorrespond to a $10\\sigma$ object detection threshold deduced from the\nphotometry.\n\nFigure \\ref{m_z} shows the distribution of galaxies in the\nredshift--apparent magnitude plane in the Abell 1689 field. Abell 1689\nitself can clearly been seen at $z=0.18$. Superimposed is the region\nof parameter space we use for the mass determination with $0.3<z<0.8$\nand $18 \\leq m_{\\rm B} \\leq 23.6$ yielding 146 galaxies.\n\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=80mm\n{\\hfill\n\\epsfbox{fig7.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small The Abell 1689 (top) and CADIS $16^{\\rm h}$ (bottom) field\nredshift--apparent B magnitude parameter space. The dashed box\nhighlights the selection criteria for the 146 A1689 \nbackground galaxies.}\n\\label{m_z}\n\\end{figure}\n\n\\subsection{Morphological Type}\n\\label{sec_morph}\n\nPerhaps the most difficult inconsistency to quantify is that of\nvariation in galaxy morphological type between samples. It has been\nknown for some time that elliptical galaxies cluster more strongly\nthan spirals (Davis \\& Geller 1976) and that the elliptical fraction\nin clusters is an increasing function of local density (Dressler\n1980). One might therefore expect a sample of galaxies lying behind a\nlarge cluster such as A1689 to contain a higher proportion of\nellipticals than a sample of field galaxies away from a cluster\nenvironment. Since the luminosity function of E/S0 galaxies is thought\nto be different from that of spirals (see, for example, Chiba \\&\nYoshii 1999 and references therein), comparison of our A1689 sample\nwith the CADIS offset field sample may be expected to introduce a\nbias.\n\nA related issue stems from the fact that the determination of an\nobject's photometric redshift requires its detection in every filter\nbelonging to the filter set. Both the CADIS and A1689 filter sets\ncontain narrow band filters which cause the main restriction on which\nobjects enter into the photometric analysis. Our $V/V_{\\rm max}$ test\nin the B-band therefore does not give a true limiting B magnitude but\none which applies only to objects detectable across all filters. As\nlong as both samples under comparison are complete according to this\ntest, the sole consequence of this is that certain morphological types\nwill be under-represented. With the CADIS filter set of 16 filters\ndiffering from the 9 filters used for the observation of A1689, this\nagain might be expected to cause inconsistent galaxy types\nbetween fields, biasing results.\n\nFortunately, our photometric analysis yields morphological type in\naddition to redshift. We are therefore able to directly measure the\nfraction of galaxies of a given type in both samples and thus test for\nbiases. We find that in the CADIS sample, the ratio of E/S0:Spiral\ngalaxies is $12\\% \\pm 7\\%$ and for the A1689 sample, this is $25\\% \\pm\n13\\%$ with Poisson errors quoted. This is in reasonable agreement with\nthe canonical Postman and Geller (1984) E/S0:S fraction for field\ngalaxies of about 30\\%. Approximately $60\\%-70\\%$ of both samples are\nclassified as starburst galaxies. Given the uncertainty in these\nfractions, we would argue that as far as we can tell, they are\nconsistent with each other. Without a bigger sample of galaxies and\npossibly spectroscopically confirmed morphologies we are unable to do\nbetter although as the measurements stand, we would not expect any\nserious inconsistencies in morphology which would bias our results.\n\n\n\\section{Mass Determination}\n\\label{sec_mass_determ}\n\nTaking the CADIS luminosity function as a good estimate of the\nintrinsic distribution of A1689 source magnitudes in the range\n$0.3\\leq z \\leq 0.8$, we can calculate $\\kappa_\\infty$ and $\\Sigma$ assuming\na relation between $\\kappa$ and $\\gamma$. As noted in Section \n\\ref{sec_cadis_field}, in the absence of a detection of evolution\nof the luminosity function with redshift, we assume a no-evolution model\nfor the background sources in this field. In general, the occurrence\nof evolution is anticipated however we expect its inclusion in\nthe background model to have only a minor effect on the derived mass.\n\nFor the purpose of comparison with other studies we shall quote \nvalues of $\\kappa$ as well as $\\kappa_\\infty$ and $\\Sigma$. As \n$\\kappa$ is dependent on the source redshift, this is not a useful \nquantity to quote when the redshift distribution is known. The \nconvergence we quote is the redshift averaged quantity defined by\n\\be\n\\label{eq_kappa_scale}\n\\kappa=\\frac{\\kappa_{\\infty}}{N_b}\\sum_{i=1}^{N_b} f(z_i)=\n\\kappa_{\\infty} \\lgl f_b \\rgl\n\\ee\nwhere $N_b$ is the number of source galaxies. For the field of Abell 1689\nwe find that $\\langle f_b\\rangle =0.57$, giving an effective source \nredshift of $z_{\\rm eff}=0.45$.\n\n\\subsection{Sources of uncertainty}\n\\label{sec_source_uncert}\n\nThree sources of error on $\\kappa_{\\infty}$ were\ntaken into consideration:\n\\begin{itemize}\n\n\\item[1)] The maximum likelihood error obtained from the width of the\nlikelihood distribution at $\\ln {\\cal L}_{\\rm max}-0.5\\Delta \\chi^2$, with\n$\\Delta\\chi^2$ the desired confidence level. All object magnitudes and\nredshifts were taken as presented directly in the A1689 data while\nassuming the Schechter parameters from equation\n(\\ref{params_ms_alpha_cadis}). \n\n\\item[2)] The uncertainty of the Schechter parameters $M_*$ and $\\alpha$\nfrom the likelihood analysis of the CADIS offset field. \n\n\\item[3)] The redshift and magnitude uncertainties of individual objects\nin the A1689 data, derived from the photometric analysis. \n\n\\end{itemize}\nIn Section \\ref{sec_sn_calcs} we will show that the\ncontribution of each source of uncertainty to the overall error\ndepends on the number of galaxies included in the analysis. Taking all\n146 galaxies across the entire field of view, the errors from each\ncontributor listed above, expressed as a percentage of the total\nstandard deviation were found to be; 50\\% from the maximum likelihood\n(essentially the shot noise), 25\\% from the uncertainty in $M_*$ and\n$\\alpha$ and 25\\% from the redshift and magnitude error.\n\nThe latter two sources of error in the above list were simultaneously\nincluded using the Monte Carlo method. 1000 simulations were carried\nout, randomly drawing values of $M_*$ and $\\alpha$ from the convolved\nlikelihood distribution shown in Figure \\ref{cadis_likelihood}. For\neach realisation, redshifts and absolute magnitudes of objects in the\nA1689 field were scattered in exactly the same fashion as before with\nthe CADIS dataset using their associated photometric errors. The\nstandard deviation of the scattered values of $\\kappa_{\\infty}$\nproduced in this way was then added in quadrature to the uncertainty\nof the maximum likelihood error obtained from item one of the list\nabove to give the overall error.\n\nThe magnitude calibration error of $\\sigma_{\\Delta M}=0.01$ discussed in\nSection \\ref{sec_photom} was ignored. Inspection of the form of the\nSchechter function in equation (\\ref{eq_mag_schechter_function}) shows\nthat a systematic magnitude offset is exactly equivalent to an error\nin $M_*$. Clearly, the $1\\sigma$ error quoted for $M_*$ in equation \n(\\ref{params_ms_alpha_cadis}) completely overwhelms this magnitude \ncalibration uncertainty which was therefore deemed insignificant.\n\nFinally, the dependence of our measurement of $\\kappa_{\\infty}$\non the feature seen in the A1689 redshift distribution at $z\\simeq0.4$\nwas tested. We removed all galaxies\ncontributing to this peak and re-calculated the results of\nthe following two sections. Apart from a larger uncertainty due\nto the decreased number of objects, we found very little difference\nfrom the results obtained from the full dataset, indicating\nthat our measurement is not dominated by the concentration of\ngalaxies at $z\\simeq0.4$.\n\n\\subsection{The differential radial $\\kappa$ profile}\n\\label{sec_lum_radial_kappa_profile}\n\nBackground source objects from the A1689 data set were binned in\nconcentric annuli about the cluster centre for the calculation of a\nradial mass profile. The relatively small number of\nobjects contained in the sample however was unfortunately\ninsufficient to allow computation of a profile\nsimilar in resolution to that of T98.\n\nApart from the effects of shot noise, this limitation results from the\nsimple fact that bins which are too narrow do not typically contain a\nlarge enough number of intrinsically bright objects. This has the\neffect that the knee of the Schechter function assumed in the\nlikelihood analysis is poorly constrained. As equation\n(\\ref{eq_lum_prob}) shows, a large uncertainty in $M_*$ directly results\nin a large error on the magnification and hence on $\\kappa_{\\infty}$.\nExperimentation with a range of bin widths quickly showed that in\norder to achieve a tolerable precision for $\\kappa_{\\infty}$, bins had\nto be at least $\\sim 1.1$ arcmin in width. With the observed field of\nview, this gave a limiting number of three bins, illustrated spatially in\nthe lower half of Figure \\ref{lumfn_kap_profile}. In Section \\ref{aperture}\nwe find the average profile within an aperture, which provides a more\nrobust measurement of $\\kappa$.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=80mm\n{\\hfill\n\\epsfbox{fig8.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small {\\em Top} Comparison of radial $\\kappa$ profiles for A1689.\nData points show isothermal (lower) and sheet (upper) estimated\n$\\kappa$ obtained from this work. $1\\sigma$ error bars are\nplotted. The solid lines indicate the same isothermal/sheet\nestimator-bound profile\nobtained by T98 using integrated number counts with $1\\sigma$ errors\nshown by dashed lines. {\\em Bottom}: Spatial location of the annular\nbins on the A1689 field of view. Open dots are objects selected by\n$z>0.2$ and solid dots by $z\\leq 0.2$.}\n\\label{lumfn_kap_profile}\n\\end{figure}\n\nThe top half of Figure \\ref{lumfn_kap_profile} shows the \n$\\kappa$ data points. These were converted from the\nmaximum likelihood derived $\\kappa_{\\infty}$ for each bin using\nequation (\\ref{eq_kappa_scale}). The profile of T98 is shown\nsuperimposed for comparison. Upper points correspond to the sheet\nestimator while the lower points are due to the isothermal\nestimator. The $1\\sigma$ error bars plotted were calculated taking all\nthree contributions listed in Section \\ref{sec_source_uncert} into\naccount.\n\nDespite relatively large errors, the data points show an amplitude in\ngood agreement with the profile derived from the number count study of\nT98. These errors seem large in comparison to those of the number\ncount profile but the number count errors do not take the\nsystematic uncertainties in background count normalisation, number\ncount slope or background source redshift into consideration.\n\nIt is noticeable that the data points suggest a profile that is perhaps a\nlittle flatter than that derived by T98. It appears\nthat more mass is detected at larger radii although this is not\nparticularly significant.\n\n\\subsection{Aperture $\\kappa$ profile}\n\\label{aperture}\n\nIn addition to the radial profile, the variation of average surface\nmass density contained within a given radius can be calculated. By\napplying the likelihood analysis to the objects contained within an\naperture of varying size, a larger signal to noise can be attained at\nlarger radii where more objects are encompassed. With a small\naperture, the same low galaxy count problem is encountered as Figure\n\\ref{aperture_kappa} shows by the large uncertainty in this vicinity.\nIn this plot, the parabolic estimator of equation\n(\\ref{eq_mu_redshift_depen}) is used to obtain $\\kappa_{\\infty}$ since\nas T98 show, this is a good average of the isothermal and sheet\nestimators and agrees well their self-consistent axi-symmetric\nsolution. Application of the axi-symmetric solution is not viable in\nthis case since we are limited to only 3 bins.\n\nUsing equation (\\ref{eq_kappa_scale}), $\\kappa_\\infty$ is again scaled\nto $\\kappa$. The grey shaded region in Figure \\ref{aperture_kappa}\ndepicts the $1\\sigma$ errors, with the sources of uncertainty from\nSection \\ref{sec_source_uncert} taken into account. The thin solid\nand dashed black lines show the variation of aperture $\\kappa$ and its\nerror calculated by averaging the parabolic estimator profile\npresented in T98. The error does not account for uncertainties arising\nfrom background count normalisation, number count slope or background\nsource redshift. The results of T98 were shown to be in good\nagreement with the shear analysis of Kaiser (1996) and hence we find a\nconsistent picture of the mass amplitude and slope from all three\nindependent methods.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=83mm\n{\\hfill\n\\epsfbox{fig9.eps}\n\\hfill}\n\\epsfverbosetrue\n\\caption{\\small Variation of average surface mass density contained\nwithin a given radius R (thick dark line). $1\\sigma$ errors are shown\nby the grey shaded region. The thin black solid and dashed lines show\nthe average surface mass density and $1\\sigma$ errors (due to\nlikelihood analysis only) of the parabolic estimated profile of T98.}\n\\label{aperture_kappa}\n\\end{figure}\n\nAs expected from the results of Section \\ref{sec_lum_radial_kappa_profile},\ngenerally more mass than that predicted from the number counts is seen,\nespecially at large radii. The following section quantifies this\nfor a comparison with the projected mass result of T98.\n\n\\subsection{Projected mass}\n\nFrom the values of $\\kappa_{\\infty}$ used to generate the $\\kappa$\nprofile in Section \\ref{sec_lum_radial_kappa_profile} and the result\nof equation (\\ref{eq_kapinf_defn}), the cumulative projected masses in\nTable \\ref{tab_cum_masses} were calculated. Errors were derived from\npropagation of the errors on the binned values of $\\kappa_{\\infty}$.\n\n\\begin{table}\n\\centering\n\\begin{tabular}{|c|c|}\n\\hline\nRadius (arcsec) & $M_{2d}(<R)$ \\\\\n\\hline\n65 & $(0.16\\pm0.09)\\times 10^{15}h^{-1}{\\rm M}_{\\odot}$ \\\\\n130 & $(0.48\\pm0.16)\\times 10^{15}h^{-1}{\\rm M}_{\\odot}$ \\\\\n195 & $(1.03\\pm0.27)\\times 10^{15}h^{-1}{\\rm M}_{\\odot}$ \\\\\n\\hline\n\\end{tabular}\n\\caption{\\small Cumulative projected mass given\nby the profile of Section \\ref{sec_lum_radial_kappa_profile}.}\n\\label{tab_cum_masses}\n\\end{table}\n\nThese projected masses are in excellent agreement with those of\nT98. At the redshift of the cluster $1'=0.117\\mpcoh$ and hence the second\ncumulative mass listed in Table \\ref{tab_cum_masses} gives \\be\nM_{2d}(<0.25\\mpcoh)= (0.48\\pm0.16)\\times 10^{15}\\,h^{-1}{\\rm\nM}_{\\odot} \\ee which is perfectly consistent with the result from the\nnumber count study. The error here is comparable to the\n$30\\%$ error quoted for the result of T98 when allowing for all sources\nof uncertainty. The projected mass contained within 195 arcsec is a\nlittle higher than that predicted by T98 although remains arguably \nconsistent given the errors involved in each.\n\n\\subsection{Effects of sample incompleteness}\n\\label{sec_incompleteness_effects}\n\nOne final uncertainty not taken into consideration so far is that of\nsample incompleteness. Changing the limiting apparent B magnitude in\nthe determination of the CADIS luminosity function directly affects\nthe fitted values of $M_*$, $\\alpha$ and hence the maximum likelihood\n$\\kappa_{\\infty}$. Similarly, differing numbers of objects\nincluded in the A1689 sample from variations in its limiting magnitude\nalso has an influence on $\\kappa_{\\infty}$.\n\nTable \\ref{tab_cadis_kapi_var} quantifies this effect for the CADIS\nobjects. It can be seen that increasing the faint limit $m_{\\rm max}$\n(ie. including fainter objects) has little effect on $\\kappa_{\\infty}$\nuntil the limit $m_{\\rm max}\\simeq 24.5$ is reached. Beyond this limit,\n$\\kappa_{\\infty}$ starts to fall. Two inferences can therefore be\nmade. Firstly, this suggests that the magnitude limit in Section\n\\ref{sec_completeness} from the $V/V_{\\rm max}$ test, being\nconsistent with the limit here, was correctly chosen. Secondly,\n$\\kappa_{\\infty}$ is relatively insensitive to the choice of $m_{\\rm max}$\nif the sample is complete (and not smaller than the limit at which\nshot noise starts to take effect).\n\n\\begin{table}\n\\vspace{2mm}\n\\centering\n\\begin{tabular}{|c|cc|ccc|}\n\\hline\n$m_{\\rm max}$ & $M_*$ & $\\alpha$ & $\\kappa_{\\infty}({\\rm iso})$ &\n$\\kappa_{\\infty}({\\rm para})$ & $\\kappa_{\\infty}({\\rm sheet})$ \\\\\n\\hline\n25.5 & $-19.06$ & $-0.80$ & $0.61^{+0.03}_{-0.04}$ & $0.69^{+0.04}_{-0.06}$ &\n$0.76^{+0.07}_{-0.08}$ \\\\\n25.0 & $-19.25$ & $-1.10$ & $0.65^{+0.04}_{-0.04}$ & $0.77^{+0.06}_{-0.06}$ & \n$0.84^{+0.08}_{-0.09}$ \\\\\n24.5 & $-19.43$ & $-1.45$ & $0.70^{+0.06}_{-0.04}$ & $0.85^{+0.08}_{-0.08}$ &\n$0.96^{+0.10}_{-0.10}$ \\\\\n24.0 & $-19.98$ & $-1.87$ & $0.74^{+0.03}_{-0.04}$ & $0.91^{+0.13}_{-0.12}$ &\n$1.08^{+0.16}_{-0.17}$ \\\\\n23.5 & $-19.24$ & $-1.53$ & $0.75^{+0.04}_{-0.04}$ & $0.90^{+0.06}_{-0.07}$ &\n$1.10^{+0.10}_{-0.09}$ \\\\\n\\hline\n\\end{tabular}\n\\caption{Variation of limiting apparent B magnitude $m_{\\rm max}$ of the\nCADIS field and its effect on the Schechter parameters and the\nresulting value of $\\kappa_{\\infty}$. Values of $M_*$ assume\n$h=1$. The apparent magnitude limit of\n$b=23.6$ was assumed for the A1689 data in calculating the maximum\nlikelihood $\\kappa_{\\infty}$. Errors here are taken only from the\nwidth of the likelihood curves.}\n\\label{tab_cadis_kapi_var}\n\\end{table}\n\nThe effect of varying the magnitude limit of the A1689 sample is\nquantified in Table \\ref{tab_a1689_kapi_var}. A clear trend is also\nseen here; as its limiting faint magnitude $m_{\\rm max}$ is reduced,\n$\\kappa_{\\infty}$ falls. Assuming linearity, a rough estimate of the\nuncertainty of $\\kappa_{\\infty}$ given the uncertainty of the sample\nmagnitude limit is given by: \n\\be\n\\Delta\\kappa_{\\infty}=\\left\\{\\begin{array}{ll} \\sim 0.1\\Delta m_{\\rm max}\n& {\\rm isothermal} \\\\ \\sim 0.2\\Delta m_{\\rm max} & {\\rm parabolic} \\\\ \\sim\n0.4\\Delta m_{\\rm max} & {\\rm sheet} \\\\\n\\end{array}\\right.\n\\ee\n\n\\begin{table}\n\\centering\n\\begin{tabular}{|c|ccc|}\n\\hline\n$m_{\\rm max}$ & $\\kappa_{\\infty}({\\rm iso})$ & $\\kappa_{\\infty}({\\rm para})$ &\n$\\kappa_{\\infty}({\\rm sheet})$ \\\\\n\\hline\n24.5 & $0.77^{+0.03}_{-0.03}$ & $1.03^{+0.11}_{-0.11}$ &\n$1.30^{+0.15}_{-0.13}$ \\\\\n24.0 & $0.76^{+0.04}_{-0.04}$ & $0.94^{+0.10}_{-0.10}$ &\n$1.12^{+0.13}_{-0.12}$ \\\\\n23.5 & $0.69^{+0.06}_{-0.07}$ & $0.79^{+0.10}_{-0.11}$ &\n$0.92^{+0.13}_{-0.12}$ \\\\\n\\hline\n\\end{tabular}\n\\caption{Variation of the maximum likelihood determined $\\kappa_{\\infty}$\nwith limiting apparent B magnitude $m_{\\rm max}$ of the A1689 data. The\nSchechter parameters of Section \\ref{sec_cadis_schechter} were assumed\nin the likelihood analysis.}\n\\label{tab_a1689_kapi_var}\n\\end{table}\n\nReferring to Figure \\ref{vmax_var}, a suitable uncertainty in\n$m_{\\rm max}$ of the A1689 sample of say $\\pm0.2$ magnitudes might be\nargued. If this were the case, the projected masses of the previous\nsection calculated with the parabolic estimator would have a further\nerror of $\\sim 5\\%$ which is negligibly small.\n\n\\section{Signal-to-Noise Predictions}\n\\label{sec_sn_calcs}\n\nIncluding all possible contributions of uncertainty in the calculation\nof mass, the previous section showed that even with relatively few\ngalaxies, a significant cluster mass profile can be detected. One can\nmake predictions of the sensitivity of the method with differing input\nparameters potentially obtained by future measurements. This exercise\nalso serves as an optimisation study, enabling identification of\nquantities requiring more careful measurement and those which play an\ninsignificant part.\n\nThe most convenient means of carrying out this investigation is by\napplication of the reconstruction method to simulated galaxy\ncatalogues. Catalogues were therefore constructed by randomly sampling\nabsolute magnitudes from the Schechter function fitted to the CADIS\noffset field in Section \\ref{sec_cadis_schechter}. Redshifts were\nassigned to each magnitude by randomly sampling the distribution\nparameterised by T98 (their equation 22) from the Canada France\nRedshift Survey (Lilly et al. 1995). A range of catalogues were\nproduced, varying by the number of objects they contained and their\ndistribution of galaxy redshift errors modeled from the A1689 data.\n\n\\begin{figure}\n\\vspace{4mm}\n\\epsfxsize=80mm\n{\\hfill\n\\epsfbox{fig10.eps}\n\\hfill}\n\\epsfverbosetrue\n\\vspace{-5mm}\n\\caption{\\small Correlation of photometric redshift error with apparent\nB-band magnitude for the A1689 data. No significant\ncorrelation between $\\sigma_z$ and $z$ exists.}\n\\label{sz_vs_m}\n\\end{figure}\n\nFigure \\ref{sz_vs_m} shows how the distribution of photometric\nredshift error, $\\sigma_z$, correlates with the A1689 B-band apparent\nmagnitude. No significant correlation between $\\sigma_z$ and redshift\nwas found. Catalogue objects were thus randomly assigned redshift\nerrors in accordance with their apparent magnitude, given by the\ncorrelated distribution in Figure \\ref{sz_vs_m}. Different catalogues\nwere generated from different scalings of this distribution along the\n$\\sigma_z$ axis.\n\nEach catalogue was then lensed with a sheet mass characterised by\n$\\kappa_{\\infty}=1$ before applying the reconstruction. 1000 Monte Carlo\nrealisations were performed for each reconstruction, scattering object\nredshifts according to their assigned errors in the same manner as in\nthe reconstruction of A1689. Furthermore, to model the uncertainty\nassociated with the offset field, assumed values of the Schechter\nparameters $M_*$ and $\\alpha$ were once again subject to Monte Carlo\nrealisations. All catalogues were reconstructed assuming sets of\nSchechter parameters drawn from a range of scaled versions of the\ndistribution shown in Figure \\ref{cadis_likelihood}.\n\nThe resulting scatter measured in the reconstructed value of\n$\\kappa_{\\infty}$ for each catalogue and assumed $\\alpha$-$M_*$ scaling\nwas combined with the average maximum likelihood error across all\nrealisations of that catalogue to give an overall error. This total\nerror was found to be well described by,\n\\be\n\\label{eq_error_fits}\n\\sigma_{\\kappa_{\\infty}}^2 = \\frac{1+(2\\sigma_z)^2}{n} + \n(0.12\\sigma_{\\scriptscriptstyle M_*})^2 + (0.37\\sigma_{\\alpha})^2\n-0.18\\sigma_{\\alpha{\\scriptscriptstyle M_*}}\n\\ee\nwhere $n$ is the number of galaxies, $\\sigma_z$ is the sample average\nredshift error and $\\sigma_{\\scriptscriptstyle M_*}$ and\n$\\sigma_{\\alpha}$ are the projected errors on $M_*$ and $\\alpha$\nrespectively as quoted in equation (\\ref{params_ms_alpha_cadis}).\nThe quantity $\\sigma_{\\alpha{\\scriptscriptstyle M_*}}$ is the\ncovariance of $\\alpha$ and $M_*$ defined by\n\\be\n\\sigma_{\\alpha{\\scriptscriptstyle M_*}}=\n\\frac{\\int{\\cal L}(M_*,\\alpha)(M_*-\\langle M_*\\rangle)\n(\\alpha-\\langle\\alpha\\rangle)\\,\\,\\rmd M_* \\rmd \\alpha}\n{\\int{\\cal L}(M_*,\\alpha)\\,\\,\\rmd M_* \\rmd \\alpha}\n\\ee\nwhere the likelihood distribution ${\\cal L}$ is given by equation\n(\\ref{eq_schechter_likelihood}). We find that \n$\\sigma_{\\alpha{\\scriptscriptstyle M_*}}=0.039$ for the CADIS\noffset field. Equation (\\ref{eq_error_fits})\nis valid for $n\\geq20$ and $0.0 \\geq \\sigma_z \\geq 0.3$.\n\nEquation (\\ref{eq_error_fits}) shows that when the number of objects\nis low, shot noise dominates. With $n\\simeq200$ however, uncertainties\nfrom the calibration of the offset field start to become dominant.\nThe factor of 2 in the photometric redshift error term stems\nfrom the fact that redshift errors also\ntranslate directly into absolute magnitude errors through equation\n(\\ref{eq_z_mag_error_prop}). Another discrepancy arises when comparing\nthis redshift error with the redshift error contribution of 25\\%\nclaimed for the A1689 data in Section \\ref{sec_source_uncert}. This is\naccounted for by the fact that K-corrections were present in the A1689 \ndata whereas in the simulated catalogues there were not. \nEquation (\\ref{eq_z_mag_error_prop}) quantifies the increase in\nmagnitude error with the inclusion of K-corrections. This translates to\nan approximate increase of $20\\%$ in the overall error with\nan average K-correction of $-1.0$ for the A1689 data.\n\nEmphasis should be placed on the criteria for which equation\n(\\ref{eq_error_fits}) is valid. The predicted overall error rises\ndramatically when fewer than $\\simeq 20$ objects are included in the\nanalysis. Simulations with 15 objects resulted in maximum likelihood\nerrors rising to beyond twice that predicted by simple shot\nnoise. This stems mainly from the effect mentioned in Section\n\\ref{sec_lum_radial_kappa_profile}, namely\nthe failure of the likelihood method when the knee of the Schechter\nfunction is poorly constrained.\n\nThe most immediate improvement to a multi-colour study such as this\nwould therefore be to increase galaxy numbers. As previously noted,\nonly when bins contain $\\simeq 200$ objects do offset field\nuncertainties become important. Observing in broader filters is one\nway to combat the limit presented by galaxy numbers. Section\n\\ref{sec_gal_cat} noted how the 3000 galaxies detected in the I band\nimage were instantly reduced to 1000 by the shallow depth limit placed\nby the narrow 466/8 filter, even though both were observed to similar\nintegration times. Using broader filters will also inevitably give\nrise to less accurate photometric redshifts. However as the analysis\nof this section has shown, one can afford to sacrifice redshift\naccuracy quite considerably before its contribution becomes comparable\nto that of shot noise.\n\nDeeper observations provide another obvious means of increasing the\nnumber of galaxies. The error predictions above indicate that the\nexpected increase in galaxy numbers using an 8 metre class telescope\nwith the same exposure times as those in this work should reduce shot\nnoise by a factor of $\\sim 3$. Since deeper observations would also\nreduce redshift and offset field calibration uncertainties to\nnegligible levels, the only source of error would be shot noise. In\nthis case, the signal to noise for $\\kappa_{\\infty}$ from equation\n(\\ref{eq_error_fits}) becomes simply\n$\\kappa_{\\infty}\\sqrt{n}$ and hence our mass estimate for A1689 could\nbe quoted with a $9\\sigma$ certainty.\n\n\n\\section{Summary}\n\nPhotometric redshifts and magnitudes have been determined for objects\nin the field of Abell 1689 from multi-waveband observations. This has\nallowed calculation of the luminosity function of source galaxies\nlying behind the cluster. Comparison of this with the luminosity\nfunction obtained from a similar selection of objects in an\nunlensed offset field has resulted in the detection of a bias\nin the A1689 background object magnitudes attributed to lens\nmagnification by the cluster.\n\nTo ensure that systematic biases do not affect our results, we have\ngiven careful consideration to the consistency between both the A1689\ndataset and the CADIS offset field dataset. We find the distribution\nof galaxy types within the redshift range $0.3\\leq z \\leq 0.8$ applied\nto both samples to be very similar. This demonstrates that our lower\nredshift cutoff is sufficient to prevent objects in the A1689 dataset\nfrom being significantly influenced by the cluster environment.\n\nAfter allowing for sources of uncertainty due to redshift and\nmagnitude error, offset field calibration error and likelihood error\n(including shot noise), a significant radial mass profile for A1689\nhas been calculated.\nWe predict a projected mass interior to $0.25\\mpcoh$ of\n\\be\nM_{2d}(<0.25\\mpcoh)=(0.48\\pm0.16)\\times 10^{15}\\,\nh^{-1}{\\rm M}_{\\odot}\n\\ee\nin excellent agreement with the number count analysis of T98 \nand the shear results of Tyson \\& Fischer (1995) and Kaiser (1995).\n\nWe can compare the efficiency of the method presented\nin this paper in terms of telescope time and signal-to-noise with the\nnumber count method used by T98. The $5.5\\sigma$ result quoted by T98\ndoes not include uncertainty due to their background count\nnormalisation, number count slope or background source redshift\ndistribution. Adding these errors to their result gives an estimated\nsignal-to-noise of $3\\sigma$, the same as this work. Regarding\ntelescope time, we define a `total information content' for each study\nas the product of telescope collecting area and total integration\ntime. T98 observed 6000s in each of the V and I bands with the NTT\n3.6m. Comparing with the CA 3.5m telescope and 12 hours integration\ntime used in this study shows that we have amassed a total information \ncontent of approximately 3 times that required for the T98 result.\n\nDespite the extra time penalty induced by our method, we note that\ndeeper observations, especially in the narrow band filters used, would\nincrease the signal-to-noise of our result significantly since we are\ndominated by shot noise. Our signal-to-noise analyses in Section\n\\ref{sec_sn_calcs} showed that a $9\\sigma$\ndetection of mass would be possible using an 8 metre class telescope,\nequivalent to an increase in integration time by a factor of 5.\nThis is in contrast to T98 whose main source of\nuncertainty comes from the unknown source redshift distribution.\nShot-noise makes a negligible contribution to their error to the\nextent that increasing their total integration time by a factor of\nthree to match the total information content of this work would still\nresult in a signal-to-noise of $3\\sigma$ (Dye 1999).\n\nThis paper has been primarily devoted to establishing the viability of\nlens mass reconstruction using the luminosity function method. We have\nshown that the two main advantages over the number count method employed\nby T98 are that use of photometric redshifts have enabled breaking of\nthe mass/background degeneracy and that the technique is independent\nof their clustering if it is assumed that they form an effective random\nsampling of luminosity space.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\bigskip\n\\noindent{\\bf ACKNOWLEDGEMENTS} \\bib\\strut\n\n\\noindent\nSD thanks PPARC for a studentship and the IfA Edinburgh for funding,\nANT thanks PPARC for a research fellowship and \nEMT thanks the Deutsche Forschungsgemeinschaft for the research fellowship \nsupporting his stay in Edinburgh. We also thank\nTom Broadhurst for use of his I-band data and Narciso Benitez who\nperformed the original data reduction.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\bigskip\n\\noindent{\\bf REFERENCES}\n\\bib \\strut\n\n\\bib Athreya R., Mellier Y., van Waerbeke L., Fort B., Pell\\'{o} R.\n\t\\& Dantel-Fort M., 1999, submitted to A\\&A, astro-ph/9909518\n\n\\bib Bertin E. \\& Arnouts S., 1996, A\\&AS, 117, 393\n\n\\bib Broadhurst T.J., Taylor A.N. \\& Peacock J.A., 1995, ApJ, 438, 49\n\n\\bib Chiba M. \\& Yoshii Y., 1999, ApJ, 510, 42\n\n\\bib Davis M. \\& Geller M.J., 1976, ApJ, 208, 13\n\n\\bib Dressler A., 1980, ApJ, 236, 351\n\n\\bib Dye S., 1999, PhD Thesis, University of Edinburgh, UK\n\n\\bib Ellis R.S., Colless M., Broadhurst T., Heyl J., Glazebrook K., 1996,\n\tMNRAS, 280, 235\n\n\\bib Falco E.E., Gorenstein M.V. \\& Shapiro I.I., 1985, ApJ, 437, 56\n\n\\bib Fort B., Mellier Y. \\& Dantel-Fort M., 1997, A\\&A, 321, 353\n\n\\bib Francis P.J., Hewett P.C., Foltz C.B., Chaffee F.H., Weymann R.J.,\n\tMorris S.L., 1991, ApJ, 373, 465\n\n\\bib Gray M.E., Ellis R.E., Refregier A., B\\'{e}zecourt J., McMahon R.G.,\n\tBeckett M.G., Mackay C.D. \\& Hoenig M.D., 2000,\n\tsubmitted to MNRAS, astro-ph/0004161\n\n\\bib Gunn J.E. \\& Stryker L.L., 1983, ApJS, 52, 121\n\n\\bib Kaiser N., 1996, in O. Lahav, E. Terlevich, R.J. Terlevich, eds,\n\tProc. Herstmonceux Conf. 36, Gravitational Dynamics,\n\tCambridge University Press, p.181\n\n\\bib Kinney A.L., Calzetti D., Bohlin R.C., McQuade K., Storchi-Bergmann T.,\n\tSchmitt H.R., 1996, ApJ, 467, 38\n\n\\bib Lilly S.J., Cowie L.L. \\& Gardner J.P., 1991, ApJ, 369, 79\n\n\\bib Lilly S.J., Tresse L., Hammer F., Crampton D., Le F{\\'e}vre O., 1995\n\tApJ, 455, 108\n\n\\bib Mayen C. \\& Soucail G., 2000, submitted to A\\&A, astro-ph/0003332\n\n\\bib Meisenheimer K., R\\\"{o}ser H.J., 1996, MPIAPHOT User Manual, \n\tMPIA Heidelberg\n\n\\bib Meisenheimer K. et al., 1998, in S. D'Oderico, A.Fontana, E. Giallongo,\n\teds, ASP Conf. Ser. Vol. 146, The Young Universe: Galaxy Formation \n\tand Evolution at Intermediate and High Redshift, p.134\n\n\\bib Oke J.B., 1990, AJ, 99, 1621\n\n\\bib Parzen E., 1963, Proc. Symp. on Time Series Analysis, p.155,\n\ted. I.M. Rosenblatt\n\n\\bib Pickles A.J. \\& van der Kruit P.C., 1991, A\\&AS, 91, 1\n\n\\bib Postman M. \\& Geller M.J., 1984, ApJ, 281, 95\n\n\\bib R\\\"{o}gnvaldsson \\\"{O}.E., Greve T.R., Hjorth J., Gudmundsson E.H.,\n \tSigmundsson V.S., Jakobsson P., Jaunsen A.O., Christensen L.L.,\n\tvan Kampen E. \\& Taylor A.N., 2000, submitted to MNRAS,\n\tastro-ph/0009045\n\n\\bib Sandage A., Tammann G.A. \\& Yahil A., 1979, ApJ, 232, 352\n\n\\bib Schmidt M., 1968, ApJ, 151, 393\n\n\\bib Taylor A.N., Dye S., Broadhurst T.J., Benitez N., van Kampen E.,\n\t1998, ApJ, 501, 539\n\n\\bib Teague P.F., Carter D. \\& Gray P.M., 1990, ApJS, 72, 715\n\n\\bib Thommes E.M. et al., 1999, 'CADIS Revised Proposal', MPIA Publication\n\n\\bib Tyson J.A. \\& Fischer P., 1995, ApJ, 446, L55\n\n\\bib van Kampen E., 1998, MNRAS, 301, 389\n\n\\bib Wolf C., Meisenheimer K., R\\\"{o}ser H.J., Beckwith S., Fockenbrock H.,\n\tHippelein H., Phleps S., Thommes E., 1999, A\\&A, 343, 399\n\n\\end{document} \n\n"
}
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astro-ph0002012
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Integrable models of galactic discs with double nuclei
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[
{
"author": "P.O. Box 45195-159"
},
{
"author": "Gava Zang"
},
{
"author": "Zanjan"
},
{
"author": "IRAN"
}
] |
We introduce a new class of 2-D mass models, whose potentials are of St\"ackel form in elliptic coordinates. Our model galaxies have two separate strong cusps that form double nuclei. The potential and surface density distributions are locally axisymmetric near the nuclei and become {highly} non-axisymmetric outside the nucleus. The surface density diverges toward the cuspy nuclei with the law $\Sigma \propto r^{-2}$. Our model is sustained by four general types of regular orbits: {butterfly}, {nucleuphilic banana}, {horseshoe} and {aligned loop} orbits. Horseshoes and nucleuphilic bananas support the existence of cuspy regions. Butterflies and aligned loops control the non-axisymmetric shape of outer regions. Without any need for central black holes, our distributed mass models resemble the nuclei of M31 and NGC4486B. It is also shown that the self-gravity of the stellar disc can prevent the double nucleus to collapse.
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{
"name": "paperJR.tex",
"string": "\\documentstyle[epsf]{mn}\n%\\textwidth= 16 cm\n%\\textheight= 9 in\n\\topmargin= -2.0 cm\n%\\headheight=0.0 mm\n%\\oddsidemargin=0 cm\n%\\evensidemargin=0 cm\n%\\def\\thefootnote{}\n%\\renewcommand{\\baselinestretch}{2}\n\\newcommand{\\noi}{\\noindent}\n%\\newcommand{\\te}{\\text}\n%\\newcommand{\\Rg}{\\Rightarrow}\n%\\newcommand{\\bak}{\\backslash}\n%\\renewcommand{\\baselinestretch}{1}\n\n\\title[Integrable models of galactic discs]\n{Integrable models of galactic discs with double nuclei}\n\\author[M. A. Jalali and A. R. Rafiee]\n {M. A. Jalali \\thanks{E-mail: [email protected]} \n \\& A. R. Rafiee \\\\\n Institute for Advanced Studies in Basic Sciences, \n P.O. Box 45195-159, Gava Zang, Zanjan, IRAN}\n\n\\begin{document}\n\\label{firstpage}\n\\maketitle\n\n\\begin{abstract} \nWe introduce a new class of 2-D mass models, whose potentials\nare of St\\\"ackel form in elliptic coordinates. Our model \ngalaxies have two separate strong cusps that form double \nnuclei. The potential and surface density distributions \nare locally axisymmetric near the nuclei and become \n{\\it highly} non-axisymmetric outside the nucleus. The \nsurface density diverges toward the cuspy nuclei with the \nlaw $\\Sigma \\propto r^{-2}$. Our model is sustained by\nfour general types of regular orbits: {\\it butterfly},\n{\\it nucleuphilic banana}, {\\it horseshoe} and \n{\\it aligned loop} orbits. Horseshoes and nucleuphilic bananas \nsupport the existence of cuspy regions. Butterflies \nand aligned loops control the non-axisymmetric shape of outer \nregions. Without any need for central black holes, our \ndistributed mass models resemble the nuclei of M31 and \nNGC4486B. It is also shown that the self-gravity of the \nstellar disc can prevent the double nucleus to collapse.\n\\end{abstract}\n\n\\begin{keywords}\nstellar dynamics -- galaxies: kinematics and dynamics -- galaxies:\nnuclei -- galaxies: structure.\n\\end{keywords}\n\n\\section{INTRODUCTION}\n{\\it Hubble Space Telescope} (HST) data revealed that M31 and NGC4486B \nhave double nuclei (Lauer et al. 1996, hereafter L96; Tremaine 1995,\nhereafter T95). M31 has a bright nucleus (P1) displaced from the \ncentre of the isophotal lines of outer regions and a fainter nucleus \n(P2) just at the centre. NGC4486B exhibits a similar structure with\na minor difference: The centre of outer isophotes falls between\nP1 and P2. There are some explanations for the \nemergence of the double nuclei of these galaxies, among which the \neccentric disc model of T95 has been more impressive. In the \nmodel of T95, a central black hole (BH) enforces stars to move\non ``aligned\" Keplerian orbits, which may elongate in the same\ndirection as the long-axis of the model. Stars moving on\naligned Keplerian orbits linger near apoapsis and may result \nin P1. The mass of central ``supermassive\" BH should be much \ngreater than the mass of neighboring disc. Otherwise, the \nasymmetric growth of P1 won't allow the BH to remain\nin equilibrium. \n\nGoodman \\& Binney (1984) showed that central massive\nobjects enforce the orbital structure of stellar systems \nto evolve towards a steady symmetric state. This result \nwas then confirmed by the findings of Merritt \\& Quinlan \n(1998) and Jalali (1999, hereafter J99) in their study of \nelliptical galaxies with massive nuclear BHs. \nWithin the BH sphere of influence, highly non-axisymmetric \nstructure can only exist for a narrow range of BH mass \n(J99). The results of J99 show that {\\it long-axis tube} \norbits of non-axisymmetric discs with central massive BHs,\nelongate in the both $\\pm$ directions of long-axis. \nThus, the probabilities for the occurrence of two bright\nregions, in both sides of BH along the long-axis, are\nequal (these bright regions are supposed to be formed\nnear the apogee of long-axis tubes). By this hypothesis\none can interpret the double structure of NGC4486B by\nplacing a supermassive BH between P1 and P2. However,\nsome disadvantages arise in the case of M31. In \nthe nucleus of M31, the formation of P1 can still be \ndeduced from the behavior of long-axis tubes. But, \nthere is no mathematical proof for the ``coexistence\" of \nP1 and P2 when the centre of P2 coincides with BH's \nlocation.\n\nIn this paper we attempt to create a model based on the\nself-gravity of stellar discs to show that systems with \ndouble nuclei can exist even in the absence of central BHs. \nEspecial cases of our non-scale-free planar models are \neccentric discs, which display a collection of properties \nexpected in self-consistent cuspy systems.\nOur models are of St\\\"ackel form in elliptic coordinates\n(e.g., Binney \\& Tremaine 1987) for which the Hamilton-Jacobi \nequation separates and stellar orbits are regular. \n\nIn most galaxies, density diverges toward the centre in a \npower-law cusp. In the presence of a cusp, regular box orbits \nare destroyed and replaced by chaotic orbits (Gerhard \\& Binney 1985). \nThrough a fast mixing phenomenon, stochastic orbits cause the orbital \nstructure to become axisymmetric at least near the centre\n(Merritt \\& Valluri 1996). These results are confirmed by the findings\nof Zhao et al. (1999, hereafter Z99). Their study reveals that highly \nnon-axisymmetric, scale-free mass models can not be constructed \nself-consistently. Near the cuspy nuclei, the potential functions\nof our distributed mass models are proportional to $r^{-1}$ as\n$r \\rightarrow 0$. So, we attain an axisymmetric structure near\nthe nuclei which is consistent with the mentioned nature of\ndensity cusps. The slope of potential function changes sign as\nwe depart from the centre and our model galaxies considerably \nbecome non-axisymmetric. Non-axisymmetric structure is supported\nby {\\it butterfly} and {\\it aligned loop} orbits. Close to the \nlarger nucleus, loop orbits break down and give birth to a new \nfamily of orbits, {\\it horseshoe} orbits, which in turn generate \n{\\it nucleuphilic banana} orbits. Stars moving in horseshoe and \nbanana orbits lose their kinetic energy as they approach to the \nnuclei and contribute a large amount of mass to form cuspy \nregions. \n\n\\section{THE MODEL}\nLet us introduce the following family of planar potentials\nexpressed in the usual $(x,y)$ cartesian coordinates:\n\\begin{equation}\n\\Phi = K \\frac {(r_1+r_2)^{\\gamma}-\n\\beta(r_1-r_2)|r_1-r_2|^{\\gamma-1}}{2r_1r_2}, \\label{1}\n\\end{equation}\n\\begin{equation}\nr_1^2 = (x+a)^2+y^2,~~r_2^2 = (x-a)^2+y^2, \\label{2}\n\\end{equation}\n\\noi where $a$, $K>0$, $0 \\le \\beta \\le 1$ and $2 < \\gamma < 3$ \nare constant parameters. The points $(x=-a,y=0)$ and $(x=a,y=0)$\nare the nuclei of our 2-D model. We call them P1 and P2, \nrespectively. The distance between P1 and P2 is equal to $2a$.\nThe surface density distribution corresponding to $\\Phi$\nis determined by (Binney \\& Tremaine 1987)\n\\begin{equation}\n\\Sigma (x',y')=\\frac {1}{4 \\pi ^2 G}\n\\int \\int \\frac {(\\nabla ^2 \\Phi) {\\rm d}x{\\rm d}y}\n{\\sqrt {(x'-x)^2+(y'-y)^2}}. \\label{3}\n\\end{equation}\nIt is a difficult task to evaluate (\\ref{3}) analytically.\nSo, we have adopted a numerical technique to calculate\nthis double integral. The functions $\\Phi$ and $\\Sigma$ \nare cuspy at P1 and P2. To verify this, we investigate the \nbehavior of $\\Phi$ and $\\Sigma$ near the nuclei \n($r_1 \\rightarrow 0$ and $r_2 \\rightarrow 0$).\nSufficiently close to P1, we have $r_1 \\ll r_2$ that \nsimplifies (\\ref{1}) as follows\n\\begin{equation}\n\\Phi=\\frac {Kr_2^{\\gamma -1}}2 \n\\frac {(1+\\frac {r_1}{r_2})^{\\gamma}+\n\\beta (1-\\frac {r_1}{r_2})^{\\gamma}}{r_1}. \\label{4} \n\\end{equation}\n\\noi We expand $(1+\\frac {r_1}{r_2})^\\gamma$ \nand $(1-\\frac {r_1}{r_2})^\\gamma$ in terms of $r_1/r_2$ to \nobtain\n\\begin{equation}\n\\Phi=\\frac {Kr_2^{\\gamma -1}}{2r_1} \\sum_{n=0}^{\\infty} \n\\left [ \n\\frac {\\left ( 1 + (-1)^n \\beta \\right ) \\Gamma (\\gamma+1)}\n{n!\\Gamma (\\gamma -n+1)} \\left ( \\frac {r_1}{r_2} \\right )^n \n\\right ], \\label{5} \n\\end{equation}\n\\noi where $\\Gamma$ is the well known Gamma function. \nAs $r_1$ tends to zero, $r_2$ is approximated by $2a$ and\n$r_1/r_2 \\rightarrow 0$. Therefore, Equation (\\ref{5}) reads\n\\begin{equation}\n\\Phi \\approx \\frac {Q(1+\\beta)}{r_1},~~\nQ=\\frac 12 K(2a)^{\\gamma-1}, \\label{6}\n\\end{equation}\nfrom which one concludes\n\\begin{equation}\n\\Sigma \\propto Q(1+\\beta)r_1^{-2}. \\label{7}\n\\end{equation}\nSimilarly, it can readily be shown that the following \napproximations hold close to P2 ($r_2/r_1 \\rightarrow 0$),\n\\begin{eqnarray}\n\\Phi &\\approx& \\frac {Q(1-\\beta)}{r_2}, \\label{8} \\\\\n\\Sigma &\\propto& Q(1-\\beta)r_2^{-2}. \\label{9}\n\\end{eqnarray}\n\\noi In distant regions, when $r \\gg a$ (with $r^2=x^2+y^2$), \nthe potential function is approximated by\n\\begin{equation}\n\\Phi \\approx 2^{\\gamma-1}K r^{\\gamma-2}. \\label{10}\n\\end{equation}\n\\noi Correspondingly, \n\\begin{equation}\n\\Sigma \\propto r^{\\gamma-3}. \\label{11}\n\\end{equation}\n\\noi This shows that the surface density falls off outward if\n$\\gamma<3$. Besides, orbits will be bounded if the potential\n$\\Phi$ is concave in outer regions. This requirement\nimplies $\\gamma >2$. Thus, we are restricted to $2 < \\gamma < 3$. \nIn Fig.~1, we have plotted the isocontours of \n$\\Phi$ and $\\Sigma$ for $\\gamma=2.8$, $a=0.5$ and several\nchoices of $\\beta$. The 3-D views of $\\Phi$ and $\\Sigma$ have \nalso been demonstrated in Fig.~2. In \\S~5, the potential surface \nof Fig.~2a will be referred as {\\it potential hill}.\n\n\\begin{figure*}\n\\centerline{\\hbox{\\epsfxsize=2.0in\\epsfbox{fig1a.ps}\\hfill\n \\epsfxsize=2.0in\\epsfbox{fig1b.ps}\\hfill\n \\epsfxsize=2.0in\\epsfbox{fig1c.ps}}}\n\\centerline{\\hspace*{1.4in}$(a)$\\hfill$(b)$\\hfill$(c)$\\hspace{1.4in}}\n\\centerline{\\hbox{\\epsfxsize=2.0in\\epsfbox{fig1d.ps}\\hfill\n \\epsfxsize=2.0in\\epsfbox{fig1e.ps}\\hfill\n \\epsfxsize=2.0in\\epsfbox{fig1f.ps}}}\n\\centerline{\\hspace*{1.4in}$(d)$\\hfill$(e)$\\hfill$(f)$\\hspace{1.4in}}\n\\caption[Figure 1]{The potential ($\\Phi$) and surface density\n($\\Sigma$) isocontours for $\\gamma=2.8$, $a=0.5$ and $K=0.2$. \nFigures (a), (b) and (c) show the potential isocontours \nfor $\\beta=0$, $\\beta=0.75$ and $\\beta=1$, respectively.\nThe corresponding surface density isocontours are\nillustrated in Figures (d),(e) and (f).}\n\\end{figure*}\n\nFigs.~1 and 2 assure that the potential \nand surface density functions are cuspy at P1 and P2. \nRegardless of the values of constant parameters,\nthe potential $\\Phi$ has a local minimum at $(x=0,y=0)$. \nThis minimum point can easily be distinguished in Figs.~1a, 1b \nand 1c. As the surface density isocontours show, the cuspy \nzones are disjointed by two separatrices that transversally \nintersect each other at a saddle point located on the \n$x$-axis between P1 and P2. The $x$-coordinate of this \npoint can be determined through solving\n\\begin{equation}\n\\frac {\\partial \\Sigma (x,y)}{\\partial x}=0,~~y=0, \\label{12}\n\\end{equation}\n\\noi for $x$. \n\nThe parameter $\\beta$ controls the sizes of cuspy\nzones around P1 and P2. For $\\beta=0$, the sizes\nof two cuspy zones are equal and the model has\nreflection symmetries with respect to coordinate\naxes. For $0<\\beta <1$, the size of cuspy zone near\nP1 is larger than that of P2 and the model is only\nsymmetric with respect to the $x$-axis.\nThe cuspy region around P2 is shrunk to zero size\nwhen $\\beta=1$ and we attain an eccentric disc with\na single nuclear cusp. \nEquations (\\ref{6}) through (\\ref{9}) show that\nthe potential and surface density functions are approximately\naxisymmetric in the neighborhood of P1 and P2.\nAs we move outward, a ``highly\" non-axisymmetric structure occurs.\nFor the large values of $r$, the surface density monotonically\ndecreases outward and our model galaxies become rounder again. \nOur mass models are indeed hybrid ones, which reflect the \nproperties of density cusps and non-axisymmetric\nsystems, simultaneously. The centre of outer surface density \nisocontours falls at the middle of the centerline of P1 and P2. \nNevertheless, the effective cuspy zones around P1 and P2 have \ndifferent sizes.\n\n\\begin{figure*}\n\\centerline{\\epsfxsize=3.0in\\epsfbox{fig2a.ps}\\hfill\n \\epsfxsize=3.0in\\epsfbox{fig2b.ps}}\n\\centerline{\\hspace*{1.5in}$(a)$\\hfill$(b)$\\hspace*{1.4in}}\n\\caption[Figure 2]{The 3-D views of $\\Phi$ and $\\Sigma$\nfor $\\gamma=2.8$, $a=0.5$, $K=0.2$ and $\\beta=0.75$. \n(a) the potential function (b) the surface density\ndistribution.} \n\\end{figure*}\n\nIn what follows, we show that the potential $\\Phi$ \nis of St\\\"ackel form in elliptic coordinates. We then \nclassify possible orbit families, all of which are \nnon-chaotic.\n\n\\begin{figure*}\n\\centerline{\\epsfxsize=1.7in\\epsfbox{fig3a.ps}\n \\epsfxsize=1.7in\\epsfbox{fig3b.ps}\\hfill\n \\epsfxsize=1.7in\\epsfbox{fig3c.ps}\n \\epsfxsize=1.7in\\epsfbox{fig3d.ps}}\n\\centerline{\\hspace*{0.8in}$(a)$\\hspace*{1.5in}$(b)$\\hfill\n $(c)$\\hspace*{1.5in}$(d)$\\hspace*{0.8in}}\n\\centerline{\\epsfxsize=1.7in\\epsfbox{fig3e.ps}\n \\epsfxsize=1.7in\\epsfbox{fig3f.ps}\\hfill\n \\epsfxsize=1.7in\\epsfbox{fig3g.ps}\n \\epsfxsize=1.7in\\epsfbox{fig3h.ps}}\n\\centerline{\\hspace*{0.8in}$(e)$\\hspace*{1.5in}$(f)$\\hfill\n $(g)$\\hspace*{1.5in}$(h)$\\hspace*{0.8in}}\n\\caption[Figure 3]{The graphs of $f(u)$ and $g(v)$ for $\\beta=0.5$,\n$\\gamma=2.8$, $C=0.2$, $E=1.1$ and $a=0.5$. The horizontal\nlines indicate the levels of $I_2$ and $-I_2$ in the graphs\nof $f(u)$ and $g(v)$, respectively.\n(a) $I_2=0.3$ (b) $-I_2=-0.3$ (c) $I_2=0.15$\n(d) $-I_2=-0.15$ (e) $I_2=-0.04$ (f) $-I_2=0.04$ (g) $I_2=-0.2$ \n(h) $-I_2=0.2$.} \n\\end{figure*}\n\n\\section{ORBIT FAMILIES}\nWe carry out a transformation to elliptic coordinates\nas follows\n\\begin{equation}\nx=a \\cosh u \\cos v, \\label{13}\n\\end{equation}\n\\begin{equation}\ny=a \\sinh u \\sin v, \\label{14}\n\\end{equation}\n\\noi where $u \\geq 0$ and $0\\le v \\le 2 \\pi$.\nThe curves of constant $u$ and $v$ are confocal\nellipses and hyperbolas, respectively. P1 and P2\nare the foci of these curves. In the new coordinates, \nthe motion of a test star is determined by the Hamiltonian\n\\begin{equation}\n{\\cal H} = \\frac 1{2a^2(\\sinh ^2 u + \\sin ^2 v)} \n(p_u^2+p_v^2) + \\Phi (u,v), \\label{15}\n\\end{equation}\n\\noi where $p_u$ and $p_v$ denote the canonical momenta and \n\\begin{eqnarray}\n\\Phi &=& \\frac {F(u)+G(v)}{2a^2(\\sinh ^2 u + \\sin ^2 v)},\n\\label{16} \\\\\nF(u) &=& C (\\cosh u)^{\\gamma}, \\label{17} \\\\\nG(v) &=& -C \\beta \\cos v |\\cos v|^{\\gamma-1}, \\label{18} \\\\\nC &=& K (2a)^{\\gamma}. \\nonumber\n\\end{eqnarray}\n\\noi The transformed potential (\\ref{16})\nis of St\\\"ackel form for which the Hamilton-Jacobi\nequation separates and yields the second integral of\nmotion, $I_2$. We obtain\n\\begin{equation}\nI_2=p_u^2 - 2a^2 E \\sinh ^2 u + F(u), \\label{19}\n\\end{equation}\n\\noi or equivalently\n\\begin{equation}\n-I_2=p_v^2 - 2a^2 E \\sin ^2 v + G(v), \\label{20}\n\\end{equation}\n\\noi where $E$ is the total energy of the system,\n$E \\equiv {\\cal H}$. The potential function ($\\Phi$) \nis positive everywhere. Hence, we immediately \nconclude $E>0$. \n\nHaving the two isolating integrals $E$ and $I_2$, one can find\nthe possible regions of motion by employing the positiveness\nof $p_u^2$ and $p_v^2$ in (\\ref{19}) and (\\ref{20}).\nWe define the following functions:\n\\begin{eqnarray}\nf(u)&=& -2 a^2 E \\sinh ^2 u + F(u), \\label{21} \\\\\ng(v)&=& -2 a^2 E \\sin ^2 v + G(v). \\label{22}\n\\end{eqnarray}\n\\noi Since $p_u^2 \\geq 0$ and $p_v^2 \\geq 0$, one can write\n\\begin{eqnarray}\nI_2-f(u) &\\geq& 0, \\label{23} \\\\\n-I_2-g(v) &\\geq& 0. \\label{24}\n\\end{eqnarray}\n\n\\noi Orbits are classified based on the behaviour of \n$f(u)$ and $g(v)$. The most general form of $f(u)$ \nis attained for $\\gamma C<4a^2E$. In such a circumstance, \n$f(u)$ has a local maximum at $u=0$, $f_{\\rm M}=f(0)=C$, \nand a global minimum at $u=u_{\\rm m}$, $f_{\\rm m}=f(u_{\\rm m})$, \nwhere \n\\begin{equation}\n\\cosh u_{\\rm m}=\\left ( \\frac {4a^2E}{C\\gamma} \\right )^\n{\\frac {1}{\\gamma-2}}, \\label{25}\n\\end{equation}\n\\noi and\n\\begin{equation}\nf_{\\rm m}=-2a^2E \\sinh ^2 u_{\\rm m} + \nC (\\cosh u_{\\rm m})^{\\gamma}. \\label{26} \n\\end{equation}\n\\noi From (\\ref{23}) we obtain \n\\begin{equation}\nI_2 \\ge f_{\\rm m}. \\label{27}\n\\end{equation}\nOn the other hand, $g(v)$ has a global maximum at \n$v=\\pi$, $g_{\\rm M}=g(\\pi)=\\beta C$, and two global \nminima at $v=\\pi/2$ and $v=3\\pi/2$, \n$g_{\\rm m}$=$g(\\pi/2)$=$g(3\\pi/2)$=$-2a^2E$.\nTherefore, Inequality (\\ref{24}) implies\n\\begin{equation}\nI_2 \\le 2a^2E. \\label{28} \n\\end{equation}\nBy combining (\\ref{27}) and (\\ref{28}) one achieves\n\\begin{equation}\nf_{\\rm m} \\le I_2 \\le 2a^2E. \\label{29} \n\\end{equation}\n\\noi By taking $2< \\gamma < 3$ and $\\gamma C<4a^2E$ \ninto account, we arrive at $2a^2E>C$. Furthermore, \n$f_{\\rm m}$ and in consequence $I_2$, can take both \npositive and negative values. For a specified value \nof $E$, the following types of orbits occur as $I_2$ \nvaries.\n\n(i) {\\it Butterflies}. For $C \\le I_2 <2a^2E$, \nthe allowed values for $u$ and $v$ are\n\\begin{equation}\nu \\le u_0,~v_{b,1} \\le v \\le v_{b,2},\n~v_{b,3} \\le v \\le v_{b,4}, \\label{30}\n\\end{equation}\n\\noi where $u_0$ and $v_{b,i}$ ($i=1,2,3,4$) are the\nroots of $f(u)=I_2$ and $g(v)=-I_2$, respectively.\nAs Fig.~3a shows, the horizontal line that indicates\nthe level of $I_2$, intersects the graph of $f(u)$ at\none point, which specifies the value of $u_0$. The\nline corresponding to the level of $-I_2$ intersects\n$g(v)$ at four points that give the values of\n$v_{b,i}$s (Fig.~3b). In this case the motion\ntakes place in a region bounded by the coordinate\ncurves $u=u_0$ and $v=v_{b,i}$. The orbits fill\nthe shaded region of Fig.~4a. These are butterfly\norbits (de Zeeuw 1985) that appear around the\nlocal minimum of $\\Phi$ at ($x=0,y=0$).\n\n(ii) {\\it Nucleuphilic Bananas}. For $\\beta C \\le I_2 < C$\nthe equation $f(u)=I_2$ has two roots, $u_{n,1}$ and $u_{n,2}$, \nwhich can be identified by the intersections of $f(u)$ \nand the level line of $I_2$ (see Fig.~3c). In this case,\nthe equation $g(v)=-I_2$ has four real roots, \n$v=v_{n,i}$ ($i=1,2,3,4$), (Fig.~3d). \nThe allowed ranges of $u$ and $v$ will be\n\\begin{equation}\nu_{n,1} \\le u \\le u_{n,2},~\nv_{n,1} \\le v \\le v_{n,2},~\nv_{n,3} \\le v \\le v_{n,4}. \\label{31}\n\\end{equation}\n\\noi The orbits (Fig.~4b) are bound to the curves of \n$u=u_{n,1}$, $u=u_{n,2}$ and $v=v_{n,i}$. We call them \nnucleuphilic banana orbits, for they look like banana \nand bend toward the nuclei. \n\n\\begin{figure}\n\\centerline{\\hbox{\\epsfxsize=1.7in\\epsfbox{fig4a.ps}\n \\epsfxsize=1.7in\\epsfbox{fig4b.ps}}}\n\\centerline{\\hspace*{0.75in}$(a)$\\hfill$(b)$\\hspace{0.75in}}\n\\vspace{0.3cm}\n\\centerline{\\hbox{\\epsfxsize=1.7in\\epsfbox{fig4c.ps}\n \\epsfxsize=1.7in\\epsfbox{fig4d.ps}}}\n\\centerline{\\hspace*{0.75in}$(c)$\\hfill$(d)$\\hspace{0.75in}}\n\\vspace{0.3cm}\n\\centerline{\\hbox{\\epsfxsize=1.7in\\epsfbox{fig4e.ps}}}\n\\centerline{$(e)$}\n\\caption[Figure 4]{The possible families of orbits:\n(a) a butterfly orbit (b) nucleuphilic banana orbits\n(c) a horseshoe orbit (d) an aligned loop orbit (e)\na lens orbit associated with $\\beta=1$ and $I_2=C$.\nFor $\\beta \\not = 0$, the orbits are only symmetric \nwith respect to the $x$-axis. Loop orbits are exceptional;\nthey are always symmetric with respect to the coordinate axes.} \n\\end{figure}\n\n(iii) {\\it Horseshoes}. For $-\\beta C \\le I_2<\\beta C$, \nboth of the equations $f(u)=I_2$ and $g(v)=-I_2$ have \ntwo real roots. We denote these roots by $u=u_{h,i}$ \nand $v=v_{h,i}$ ($i=1,2$). \nIn other words, the level lines of $\\pm I_2$ \nintersect the graphs of $f(u)$ and $g(v)$ at two points \nas shown in Figs.~3e and 3f. The trajectories of \nstars fill the shaded region of Fig.~4c. \nWe call these horseshoe orbits.\n\n(iv) {\\it Aligned Loops}. For $f_m < I_2<-\\beta C$, \nthe equation $f(u)=I_2$ has two real roots, $u=u_{l,i}$ \n($i=1,2$) while the equation $g(v)=-I_2$ has\nno real roots and Inequality (\\ref{24}) is always \nsatisfied (Figs.~3g and 3h). The orbits fill a tubular \nregion as shown in Fig.~4d. We call these aligned loops \nbecause they are aligned with the surface density \nisocontours of outer regions. \n\n(v) {\\it Transitional cases}. For $I_2=2a^2E$, stars\nundergo a rectilinear motion on the $y$-axis with the\namplitude of $\\pm a \\sinh u_0$. For $I_2=f_{\\rm m}$,\nloop orbits are squeezed to an elliptical orbit defined\nby $u=u_{\\rm m}$. For $\\beta=0$, horseshoe orbits are\nabsent, leaving the other types of orbits symmetric\nwith respect to the coordinate axes. Banana orbits no\nlonger survive for $\\beta=1$ (eccentric disc model).\nIn this case, butterflies extend to a {\\it lens} orbit\nwhen $I_2=C$ (see Figure 4e).\nFor $\\gamma C > 4a^2E$, $f(u)$ is a monotonically\nincreasing function of $u$ and ``low-energy\"\nbutterflies are the only existing family of orbits. \nThese are small-amplitude liberations in the vicinity \nof the local minimum of $\\Phi$ at $(x=0,y=0)$.\n\n\\section{THE POSITIVENESS OF THE SURFACE DENSITY}\nThe sign of $\\Sigma$ is linked to that of $\\nabla ^2 \\Phi$ through\nEquation (\\ref{3}). To prove that $\\Sigma$ takes positive values for\nthe potentials of (\\ref{1}), it suffices to show that the Laplacian \nof $\\Phi$ is a positive function of $\\gamma$, $\\beta$, $u$ and $v$.\n\nConsider the Laplace equation in elliptic coordinates as\n\\begin{eqnarray}\n\\nabla ^2 \\Phi &=& \\frac {1}{a^2D}\n\\left ( \\Phi _{,uu} + \\Phi _{,vv} \\right ), \\label{laplace} \\\\\nD &=& \\sinh ^2u + \\sin ^2v, \\nonumber\n\\end{eqnarray}\nwhere $_{,s}$ denotes $\\frac {\\partial}{\\partial s}$.\nSubstituting from (\\ref{16}) into (\\ref{laplace}), leads to \n\\begin{equation}\n\\nabla ^2 \\Phi = \\frac {{\\cal F}(\\gamma,\\beta;u,v)} {2a^4D^4}, \\label{feq}\n\\end{equation}\nwith\n\\begin{eqnarray}\n{\\cal F} &=& D^2(F_{,uu}+G_{,vv})-D(F+G)(D_{,uu}+D_{,vv})\n\\nonumber \\\\\n&{}& -2D(F_{,u}D_{,u}+G_{,v}D_{,v})\\nonumber \\\\\n&{}& +2(F+G)(D_{,u}^2+D_{,v}^2). \\label{F_eq}\n\\end{eqnarray}\nFor the sake of simplicity, we assume $C=1$.\nWe show that the minimum of ${\\cal F}$ is always positive.\nWe prove our claim for \n$-\\frac {\\pi}{2}\\leq v \\leq \\frac {\\pi}{2}$, which implies \n$G(v)=-\\beta \\cos ^{\\gamma}v$ (a similar method can be repeated\nfor $\\frac {\\pi}{2}< v < \\frac {3\\pi}{2}$). In this case,\n${\\cal F}$ will be a linear, decreasing function of $\\beta$\n(because $\\Phi$ has such a property).\nTherefore, one concludes \n${\\cal F}(\\gamma,1;u,v) \\leq {\\cal F}(\\gamma,\\beta;u,v)$.\nFurthermore, ${\\cal F}$ directly depends on $\\cosh u$,\nwhich results in ${\\cal F}(\\gamma,1;0,v) \\leq {\\cal F}(\\gamma,1;u,v)$.\nHence, $\\nabla ^2 \\Phi$ is positive if \n${\\cal G}(\\gamma,v)\\equiv {\\cal F}(\\gamma,1;0,v) \\geq 0$.\nBy the evaluation of (\\ref{F_eq}) for $\\beta=1$ and $u=0$, \none finds out\n\\begin{eqnarray}\n{\\cal G}(\\gamma,v) &=& -\\gamma ^2 \\sin ^6 v \\cos ^{\\gamma -1}v +\n\\sin ^2 v (1-\\cos ^{\\gamma}v) \\nonumber \\\\ \n&{}& + \\gamma [\\sin ^4 v + \\cos ^{\\gamma-2}v(\\sin ^6 v \\nonumber \\\\\n&{}& - 3 \\cos ^2 v \\sin ^4 v)]. \\label{G_gam_v}\n\\end{eqnarray}\nWe have plotted ${\\cal G}(\\gamma,v)$ in Figure 5. On the evidence\nof this figure, ${\\cal G}$ is a positive function for\n$-\\frac {\\pi}{2}\\leq v \\leq \\frac{\\pi}{2}$ and $2<\\gamma <3$.\nThus, the surface density distribution takes positive values \nfor all of our model galaxies.\n\n\\begin{figure}\n\\centerline{\\hbox{\\epsfxsize=1.7in\\epsfbox{fig5.ps}}}\n\\caption[Figure 5]{The behaviour of ${\\cal G}(\\gamma,v)$ \nfor $-\\frac {\\pi}2 \\leq v \\leq \\frac {\\pi}2$ and $2<\\gamma <3$.} \n\\end{figure}\n\n\\section{DISCUSSION}\nIn his pioneering work, Euler showed \nthe separability of motion in the potential field of \ntwo {\\it fixed} Newtonian centres of attraction. This problem\nwas then completely solved by Jacobi (Pars 1965). It \nis physically impossible to keep apart these two ``point \nmasses\", for they will attract each other leading to\nan eventual collapse. However, the assumed masses \ncan be in equilibrium if they revolve around their\ncommon centre of mass (this is the classical \n3-body problem). Our planar model is indeed \nJacobi's problem in which we have replaced \ntwo fixed centres of gravitation with a continuous\ndistribution of matter, where mass concentration increases \ntowards two nuclei (P1 and P2) in power-law, strong cusps. \nThese nuclei are maintained by an interesting family of \norbits, nucleuphilic bananas. Below, we explain why the \nmentioned nuclei are generated and don't collapse. \n\nThe force exerted on a star is equal to $-\\nabla \\Phi$. \nThe motion under the influence of this force can be \ntracked on the {\\it potential hill} of Figure 2a. \nThis helps us to better imagine the motion trajectories.\n\n\\subsection{The behaviour of orbits}\nStars moving in nucleuphilic banana orbits undergo \nmotions {\\it near} the 1:2 resonance. They oscillate \ntwice in the $y$-direction for each $x$-axial \noscillation. The turning points of this group of \nstars lie on the curves $v=v_{n,i}$.\nThese hyperbolic curves can be chosen arbitrarily\nclose to P1 or P2. When stars approach P1 (or P2),\ntheir motion slows down (because they climb on the \ncuspy portion of the potential hill and considerably \nlose their kinetic energy while the potential\nenergy takes a maximum) and the orbital angular\nmomentum switches sign somewhere on $v=v_{n,i}$.\nThus, these stars spend much time in the vicinity\nof P1 (or P2) and deposit a large amount of mass.\nThis phenomenon is the main reason for the\ngeneration of cuspy zones around P1 and P2.\nStars moving in nucleuphilic bananas cross the \n$y$-axis quickly, and therefore, don't \ncontribute much mass to the region between the \nnuclei.\n\nHorseshoe orbits cause the sizes of cuspy zones \nto be different through the following mechanism.\nStars that start their motion sufficiently close\nto P1 (larger nucleus), are repelled from\nP1 because the force vector is not directed\ninward in this region. As they move outward,\ntheir orbits are bent and cross the $x$-axis\nwith non-zero angular momentum. These stars\nlinger only near P1, and in consequence, help\nthe cuspy zone around P1 grow more than that\nof P2. The asymmetry of nucleuphilic bananas,\nwith respect to the $y$-axis, is also an origin\nof the different sizes of cuspy zones. In fact,\nhorseshoe orbits are born once nucleuphilic\nbananas join together for $I_2=\\beta C$.\nHorseshoe and nucleuphilic banana orbits are\nthe especial classes of boxlets that appropriately\nbend toward the nuclei. The lack of such a property\nin centrophobic banana orbits causes the discs of\nSirdhar \\& Touma (1997) to be non-self-consistent.\n\nAligned loop orbits occur when the orbital angular\nmomentum is high enough to prevent the test particle\nto slip down on the potential hill. The boundaries\nof loop orbits are defined by the ellipses\n$u=u_{l,1}$ and $u=u_{l,2}$. The nuclear cusps are\nlocated at the foci of these ellipses.\nAligned loops have the same orientation as the\nsurface density isocontours (compare Figures 1 and\n4d). Thus, according to the results of Z99, it is \npossible to construct a self-consistent model using \naligned loop orbits.\n\nIt is worthy to note that butterfly orbits play a \nsignificant role in maintaining the non-axisymmetric\nstructure of the model at the moderate distances\nof ${\\cal O}(a)$.\n\n\\subsection{The nature of P1 and P2}\nThe points where the cusps have been located,\nare inherently unstable. With a small\ndisturbance, stars located at ($x=\\pm a,y=0$) are\nrepelled from these points because $-\\nabla \\Phi$\nis directed outward when $r_i \\rightarrow 0$\n($i=1,2$). But, the time that stars spend near the\nnuclei will be much longer than that of distant\nregions when they move in horseshoe and banana orbits.\nThe points P1 and P2 are unreachable, for they \ncorrespond to the energy level $E=+\\infty$. Based on \nthe results of this paper, we conjecture that there \nmay not be any mass concentration just at the centre of \ncuspy galaxies. However, a very dense region exists \n{\\it arbitrarily} close to the centre!\n\n\\subsection{The double nucleus can be in equilibrium}\nThe nuclei pull each other due to their mutual\ngravitational attraction and it seems that they must\ncollapse. However, we explain that in certain circumstances,\nthe double nucleus can be in {\\it static} equilibrium.\nAt first we estimate the mass inside the separatrices of\nthe surface density distribution (the mass of cuspy zones)\nand concentrate the matter at P1 and P2 (this\nis logical because the surface density distribution is\nalmost axisymmetric near the nuclei).\nIn this way, we obtain two point masses, $M_1$ and $M_2$.\nAccording to (\\ref{7}) and (\\ref{9}), the following relations\napproximately hold \n\\begin{eqnarray}\nM_i &=& \\int \\nolimits _{-\\pi}^{\\pi}\n \\int \\nolimits _{\\epsilon}^{r_{0i}}\n \\sigma _{i} r^{-1} {\\rm d}r {\\rm d}\\theta, \n~\\epsilon \\rightarrow 0, \\nonumber \\\\\n &=& 2 \\pi \\sigma _i \\log {\\frac {r_{0i}}{\\epsilon}},\n ~~i=1,2, \\label{32}\n\\end{eqnarray}\n\\noi where $r_{0i}$ are chosen as the radii of inner tangent\ncircles to the separatrices and the constant parameters \n$\\sigma _i$ are computed based on the surface density profile \nnear the nuclei. As $\\epsilon \\rightarrow 0$, $M_i$s diverge \nto infinity unless a negative mechanism prevents them to \ngrow. Consider the discs of radius $\\epsilon$ with the \ncentres located at $(\\pm a,0)$ and call them ${\\cal D}_1$ \nand ${\\cal D}_2$. Since P1 and P2 are ``locally\" unstable, \nwe rely on our previous argument that the matter is swept \nout from these points, allowing us to exclude ${\\cal D}_1$ \nand ${\\cal D}_2$ from our model for some $0< \\epsilon \\ll 1$. \nIn this way, $M_i$s take finite values. \n\n\\begin{figure}\n\\centerline{\\hbox{\\epsfxsize=1.7in\\epsfbox{fig6.ps}}}\n\\caption[Figure 5]{In this figure we have shown a circular\nring of matter of outer regions. The masses of cuspy zones\ncan approximately be computed and concentrated at the points\n($\\pm a,0$). The gravitational attraction of the ring upon\nthe point mass $M_1$ ($M_2$) is directed in the $x$-direction\ndue to the existing symmetry.} \n\\end{figure}\n\n$M_1$ and $M_2$ attract each other and start to move \nif they are not influenced by other gravitational sources.\nWe claim that the required extra force comes from the\ngravitational attraction of the matter of outer regions.\nConsider Figure 6 where $M_1$ and $M_2$ are shown along\nwith a ring of matter of outer regions. For brevity,\nwe assume $\\beta=0$, which yields $M_1=M_2=M$. Due to the \nexisting symmetry, the gravitational force exerted on \n$M_2$ by the assumed ring will have a resultant in the \n$x$-direction. When $r$ is sufficiently large, $r \\gg a$, \nthis force is calculated as follows\n\\begin{eqnarray}\nF_x(r) &=& GM \\sigma _{\\infty} \\int\\nolimits_{-\\pi}^{\\pi}\n\\frac {r^{\\gamma -2} \\cos \\phi {\\rm d} \\theta}\n{r^2+a^2-2ar\\cos \\theta}, \\label{33} \\\\\n\\cos \\phi &=& \\frac {r\\cos \\theta -a}\n{(r^2+a^2-2ar\\cos \\theta)^{1/2}}, \\label{34}\n\\end{eqnarray}\nwhere we have used \n$\\Sigma \\approx \\sigma _{\\infty} r^{\\gamma -3}$ with\n$\\sigma _{\\infty}$ being a positive constant (see Eq. (\\ref{11})).\nBy integrating $F_x(r)$ over $r$ from \nsome $r=R \\gg a$ to $r=\\infty$, the total force, due \nto the matter of outer regions, is found to be\n\\begin{equation}\nF_x = GM \\sigma _{\\infty} \\int\\nolimits_{R}^{\\infty} \n\\int\\nolimits_{-\\pi}^{\\pi}\n\\frac {r^{\\gamma -2} (r\\cos \\theta -a) {\\rm d} \\theta {\\rm d}r}\n{(r^2+a^2-2ar\\cos \\theta)^{3/2}}. \\label{35}\n\\end{equation}\nBy a change of independent variable as $\\xi =a/r$, the integrand\ncan be simplified in the form \n\\begin{eqnarray}\nF_x &=& b \\int\\nolimits_{0}^{\\xi _0} \\xi ^{2-\\gamma} {\\rm d}\\xi\n \\frac {{\\rm d}}{{\\rm d}\\xi} \\int\\nolimits_{0}^{\\pi}\n \\frac {{\\rm d}\\theta}{(1+\\xi ^2-2\\xi \\cos \\theta)^{1/2}},\n \\label{36} \\\\\nb &=& \\frac {2GM \\sigma _{\\infty}}{a^{3-\\gamma}}, \\label{37}\n\\end{eqnarray}\nwhere $\\xi_0=a/R$. Consequently,\n\\begin{equation}\nF_x = b \\int\\nolimits_{0}^{\\xi _0} \\xi ^{2-\\gamma} {\\rm d}\\xi\n \\frac {{\\rm d}}{{\\rm d}\\xi} \\sum _{n=0}^{\\infty} \\xi ^n\n \\int\\nolimits_{0}^{\\pi} P_n(\\cos \\theta) {\\rm d}\\theta,\n \\label{38} \n\\end{equation}\nwith $P_n$s being the well known Legendre functions.\nAccording to (Morse \\& Feshbach 1953)\n\\begin{eqnarray}\n\\int\\nolimits_{0}^{\\pi} P_{2k+1}(\\cos \\theta)\n{\\rm d} \\theta &=& 0, \\label{39} \\\\\n\\int\\nolimits_{0}^{\\pi} P_{2k}(\\cos \\theta)\n{\\rm d} \\theta &=& \\pi \\left [ \\frac {(2k)!}{(2^k k!)^2} \n\\right ] ^2 \\equiv c_{2k}, \\label{40}\n\\end{eqnarray}\none achieves\n\\begin{equation}\nF_x = b \\int\\nolimits_{0}^{\\xi _0} (\\xi ^{2-\\gamma} \n \\sum _{k=1}^{\\infty} 2k c_{2k} \\xi ^{2k-1})\n {\\rm d}\\xi. \\label{41} \n\\end{equation}\nIntegrating (\\ref{41}) over $\\xi$, yields\n\\begin{eqnarray}\nF_x &=& b Q(\\xi _0), \\label{42} \\\\\nQ(\\xi _0) &=& \\xi _0 ^{2-\\gamma}\n \\sum _{k=1}^{\\infty}\n \\frac {2k c_{2k}}{2k+2-\\gamma}\n \\xi _0 ^{2k}. \\label{43}\n\\end{eqnarray}\nIt is obvious that $Q$ is a positive function of $\\xi _0$.\nTherefore, from (\\ref{42}) one concludes $F_x>0$ indicating \nthat $M_2$ is pulled away from the centre. \n$M_2$ will be in static equilibrium if $F_x$ is\nbalanced with the gravitational force of $M_1$, i.e.,\n\\begin{equation}\nF_x=\\frac {GM_1M_2}{(2a)^2}=\\frac {GM^2}{(2a)^2}. \\label{44}\n\\end{equation}\nBy substituting from (\\ref{32}) and (\\ref{42}) into (\\ref{44}),\nwe obtain\n\\begin{equation}\n\\delta \\equiv \\frac {\\epsilon}{r_{01}} = e^{-s},~~s>0, \\label{45}\n\\end{equation}\nwhere $r_{01}=r_{02}$, $\\sigma _1=\\sigma _2$ \n(because we assumed $\\beta=0$) and\n\\begin{equation}\ns=\\frac {4 \\sigma _{\\infty} a^{\\gamma -1} Q(\\xi _0)}\n {\\pi \\sigma _1}. \\label{46}\n\\end{equation}\nOur numerical computations of $\\Sigma$ reveal that \n$\\sigma_{\\infty} \\gg \\sigma_i$, which guarantees \n$\\epsilon \\ll r_{01}$ as desired. Following a similar\nprocedure as above, one can show that the double \nnucleus remains in equilibrium for $\\beta >0$. \n\n\\subsection{The nuclei of M31 and NGC4486B}\nIn many respects, the surface density isocontours of\nour model galaxies are similar to the isophotal lines\nof the nuclei of M31 and NGC4486B. Our mass models\nare cuspy within two separatrices. Such curves can \nbe distinguished in the nuclei of M31 \nand NGC4486B (see L96 and T95).\nWe are not sure that the nuclei of M31 and NGC4486B are \nreally cuspy, because existing telescopes can not \nhighly resolve the regions around P1 and P2 (even HST \nimages contain ``few\" bright pixels at the locations of \nP1 and P2). Whatever the mass distribution inside these \nnuclei may be, our models reveal that double nuclei can \nexist even in the absence of supermassive BHs. \n\nThe nucleus of M31 can also be explained by the\neccentric disc corresponding to $\\beta=1$.\nIn such a circumstance, stars moving in butterfly orbits\nform a local group in the vicinity of ($x=0,y=0$).\nThe accumulation of stars around this local minimum\nof $\\Phi$ can create a faint nucleus like P2 (see T95).\nTherefore, P2 will approximately be located at the ``centre\"\nof loop orbits while the eccentric, brighter nucleus (P1)\nis at the location of the cusp. In other words, loop and\nhigh-energy butterfly orbits will control the overall shape\nof outer regions, horseshoe orbits will generate P1 and\nlow-energy butterflies will create P2.\n\n\\subsection{Challenging problems}\nIt is not known for us if there are rotationally\nsupported double structures or not. This idea comes\nfrom the fact that we can replace the point masses of\nthe restricted 3-body problem (the restricted 3-body \nproblem is usually expressed in a rotating frame) \nwith a continuous distribution of matter. Moreover, \nNGC4486B and the bulge of M31, are three dimensional \nobjects and the assumption of planar models seems\nto be a severe constraint.\n\nSo far we showed that the double nucleus can be in \nstatic equilibrium due to the existing gravitational \neffects of the model. The stability study of such\nstates, however, remains as a challenging problem.\n\nOur next goal is to apply the method of Schwarzschild\n(1979,1993) for the investigation of self-consistency.\n\n\\section{ACKNOWLEDGMENTS}\nThe authors wish to thank the anonymous referee for\nilluminating questions and valuable comments on the\npaper.\n\n\\begin{thebibliography}{}\n\\bibitem[R1]{BT87}Binney J., Tremaine S., 1987, Galactic Dynamics,\nPrinceton University Press, Princeton\n\\bibitem[R2]{dZ85}de Zeeuw P.T., 1985, MNRAS, 216, 273\n\\bibitem[R3]{GB85}Gerhard O.E., Binney J., 1985, MNRAS, 216, 467\n\\bibitem[R4]{GB84}Goodman~J., Binney~J., 1984, MNRAS, 207, 511\n\\bibitem[R5]{J99}Jalali M.A., 1999, MNRAS, 310, 97 (J99)\n\\bibitem[R7]{L96}Lauer T.R., et al., 1996, ApJ, 471, L79 (L96)\n\\bibitem[R8]{MQ98}Merritt D., Quinlan G.D., 1998, ApJ, 498, 625\n\\bibitem[R9]{MV96}Merritt D., Valluri M., 1996, ApJ, 471, 82\n\\bibitem[R11]{MF53}Morse, P.~M., Feshbach, H., 1953, Methods of \nTheoretical Physics, McGraw Hill, New York, Ch. 10\n\\bibitem[R12]{PARS}Pars L.A., 1965, A Treatise on Analytical Dynamics, \nJohn Wiley \\& Sons, Inc., New York\n\\bibitem[R13]{S79}Schwarzschild M., 1979, ApJ, 232, 236\n\\bibitem[R14]{S93}Schwarzschild M., 1993, ApJ, 409, 563\n\\bibitem[R15]{ST97}Sridhar S., Touma J., 1997, MNRAS, 287, L1-L4\n\\bibitem[R16]{T95}Tremaine S., 1995, AJ, 110, 628 (T95)\n\\bibitem[R17]{Z99}Zhao H.S., Carollo C.M. \\& de Zeeuw P.T., 1999, MNRAS, 304, \n457 (Z99)\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002012.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[R1]{BT87}Binney J., Tremaine S., 1987, Galactic Dynamics,\nPrinceton University Press, Princeton\n\\bibitem[R2]{dZ85}de Zeeuw P.T., 1985, MNRAS, 216, 273\n\\bibitem[R3]{GB85}Gerhard O.E., Binney J., 1985, MNRAS, 216, 467\n\\bibitem[R4]{GB84}Goodman~J., Binney~J., 1984, MNRAS, 207, 511\n\\bibitem[R5]{J99}Jalali M.A., 1999, MNRAS, 310, 97 (J99)\n\\bibitem[R7]{L96}Lauer T.R., et al., 1996, ApJ, 471, L79 (L96)\n\\bibitem[R8]{MQ98}Merritt D., Quinlan G.D., 1998, ApJ, 498, 625\n\\bibitem[R9]{MV96}Merritt D., Valluri M., 1996, ApJ, 471, 82\n\\bibitem[R11]{MF53}Morse, P.~M., Feshbach, H., 1953, Methods of \nTheoretical Physics, McGraw Hill, New York, Ch. 10\n\\bibitem[R12]{PARS}Pars L.A., 1965, A Treatise on Analytical Dynamics, \nJohn Wiley \\& Sons, Inc., New York\n\\bibitem[R13]{S79}Schwarzschild M., 1979, ApJ, 232, 236\n\\bibitem[R14]{S93}Schwarzschild M., 1993, ApJ, 409, 563\n\\bibitem[R15]{ST97}Sridhar S., Touma J., 1997, MNRAS, 287, L1-L4\n\\bibitem[R16]{T95}Tremaine S., 1995, AJ, 110, 628 (T95)\n\\bibitem[R17]{Z99}Zhao H.S., Carollo C.M. \\& de Zeeuw P.T., 1999, MNRAS, 304, \n457 (Z99)\n\\end{thebibliography}"
}
] |
astro-ph0002013
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CLUSTERING OF MASS AND GALAXIES
|
[
{
"author": "J.A. PEACOCK"
}
] |
These lectures cover various aspects of the statistical description of cosmological density fields. Observationally, this consists of the point process defined by galaxies, and the challenge is to relate this to the continuous density field generated by gravitational instability in dark matter. The main topics discussed are (1) nonlinear structure in CDM models; (2) statistical measures of clustering; (3) redshift-space distortions; (4) small-scale clustering and bias. The overall message is optimistic, in that simple assumptions for where galaxies should form in the mass density field allow one to understand the systematic differences between galaxy data and the predictions of CDM models.
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[
{
"name": "ini99.tex",
"string": "\\documentstyle[proceedings]{crckapb}\n\n%\n% JAP macros\n%\n\n\\let\\sec=\\section\n\\let\\ssec=\\subsection\n\\def\\half{{\\textstyle{\\scriptstyle 1\\over\\scriptstyle 2}}}\n\\def\\erf{{\\rm erf}}\n\\def\\japref{\\parskip=0pt\\par\\noindent\\hangindent\\parindent\n \\parskip =2ex plus .5ex minus .1ex}\n\\def\\eol{\\hfill\\break}\n\\def\\gs{\\mathrel{\\lower0.6ex\\hbox{$\\buildrel {\\textstyle >}\n \\over {\\scriptstyle \\sim}$}}}\n\\def\\ls{\\mathrel{\\lower0.6ex\\hbox{$\\buildrel {\\textstyle <}\n \\over {\\scriptstyle \\sim}$}}}\n\\newcount\\equationnum\n\\global\\equationnum=0\n\\def\\bookdisp#1$${\\leftline{\\hfill{$\\displaystyle#1$}\n \\global\\advance\\equationnum by 1\n \\hfill (\\the\\equationnum )}$$}\n\\everydisplay{\\bookdisp}\n\\def\\ss{\\rm\\scriptscriptstyle}\n\\def\\ssit{\\it\\scriptscriptstyle}\n\\def\\kms{{\\,\\rm km\\,s^{-1}}}\n\\def\\kmsmpc{{\\,\\rm km\\,s^{-1}Mpc^{-1}}}\n\\def\\hompc{{\\,h\\,\\rm Mpc^{-1}}}\n\\def\\mpcoh{{\\,h^{-1}\\,\\rm Mpc}}\n\\def\\japitem#1{\\medskip\\noindent\\rlap{#1}\\hglue 3em\\hangindent 3em}\n\n%\\def\\key#1{{\\bf #1}}\n\\def\\key#1{#1}\n\n%\\def\\vec#1{\\underline{#1}}\n\n\\def\\vec#1{\n\\setbox0=\\hbox{$#1$} \n \\dimen0=\\wd0 \n \\wd0=0.7\\wd0\n \\rlap{\\hbox to \\dimen0{\\hfil\\underline{\\phantom{\\box0}}\\hglue 1pt\\hfil}} \n#1\n}\n\n\n\\def\\year#1{ (#1)}\n\\def\\journ#1{{\\it #1},}\n\\def\\vol#1{{\\bf #1},}\n\\def\\page#1{#1}\n\\def\\book#1{{\\it #1}}\n\\def\\mnras{Mon. Not. R. Astr. Soc.}\n\\def\\mn{Mon. Not. R. Astr. Soc.}\n\\def\\qjras{Q. J. R. Astr. Soc.}\n\\def\\apj{Astrophys. J.}\n\\def\\apjs{Astrophys. J. Suppl.}\n\\def\\aj{Astr. J.}\n\\def\\pr{Phys. Rev.}\n\\def\\pl{Phys. Lett.}\n\\def\\pasp{Proc. Astr. Soc. Pacif.}\n\\def\\araa{Ann. Rev. Astr. Astrophys.}\n\\def\\nature{Nature}\n\\def\\aa{Astr. Astrophys.}\n\\def\\aas{Astr. Astrophys. Suppl.}\n\\def\\prl{Phys. Rev. Lett.}\n\\def\\prd{Phys. Rev. D}\n\\def\\rmp{Rev. Mod. Phys.}\n\\def\\science{Science}\n\n\\input epsf\n\n\\def\\japfig#1#2#3#4#5#6{\n\\begin{figure*}\n\\centering\\mbox{\\epsfxsize=0.9\\hsize\\epsfbox[#1 #2 #3 #4]{#5}}\n\\caption[]{#6}\n\\end{figure*}\n}\n\n\n%\n% Repair some of the vandalism inflicted on plain TeX\n% by that moron Lamport\n%\n\n\\def\\m@th{\\mathsurround=0pt }\n\\def\\eqalign#1{\\null\\,\\vcenter{\\openup1\\jot \\m@th\n \\ialign{\\strut\\hfil$\\displaystyle{##}$&$\\displaystyle{{}##}$\\hfil\n \\crcr#1\\crcr}}\\,}\n\n\\def\\topinsert{\\begin{figure}}\n\\def\\endinsert{\\end{figure}}\n\n\n\n\\begin{opening}\n\\title{CLUSTERING OF MASS AND GALAXIES}\n\\author{J.A. PEACOCK}\n\\institute{Institute for Astronomy,\nUniversity of Edinburgh\\\\\nRoyal Observatory, Edinburgh EH9 3HJ, UK}\n\\end{opening}\n\\begin{document}\n\n\\vglue -7.5truecm\n\\centerline{\nInvited lectures at the NATO ASI {\\it Structure Formation in the Universe\\/}}\n\\smallskip\n\\centerline{Cambridge, August 1999}\n\\vglue 6.5truecm\n\\noindent\n\n\n\\begin{abstract}\nThese lectures cover various aspects of the\nstatistical description of cosmological\ndensity fields. Observationally, this consists\nof the point process defined by galaxies, and the\nchallenge is to relate this to the continuous\ndensity field generated by gravitational instability\nin dark matter. The main topics discussed are\n(1) nonlinear structure in CDM models;\n(2) statistical measures of clustering;\n(3) redshift-space distortions;\n(4) small-scale clustering and bias.\nThe overall message is optimistic, in that\nsimple assumptions for where galaxies should\nform in the mass density field allow one\nto understand the systematic differences\nbetween galaxy data and the predictions of\nCDM models.\n\\end{abstract}\n\n\\sec{Preamble}\n\nThe subject of large-scale structure is in\na period of very rapid development.\nFor many years, this term would have meant only\none thing: the distribution of galaxies.\nHowever, we are increasingly able to probe the\nprimordial fluctuations through the CMB, so that\nthe problem of galaxy formation and clustering is\nnow only one aspect of the general picture of\nstructure formation.\nThe rationale for studying the large-scale\ndistribution of galaxies is therefore altering.\nTen years ago, we were happy to produce samples\nbased on a rather sparse random sampling of the\ngalaxy distribution, with the main aim of\ntying down statistics such as the large-scale\npower spectrum of number-density fluctuations.\nA major goal of the subject remains the measurement\nof the fluctuation spectrum for wavelengths\n$\\gs 100$~Mpc, and the demonstration that this\nagrees in shape with what can be inferred from the\nCMB. Nevertheless, we are now increasingly interested\nin studying the pattern of galaxies with the highest\npossible fidelity -- demanding deep, fully-sampled\nsurveys of the local universe. Such studies will\ntell us much about the processes by which galaxies formed\nand evolved within the distribution of dark\nmatter. The aim of these lectures is therefore to\nlook both backwards and forwards: reviewing the\nfoundations of the subject and looking forward to the\nfuture issues.\n\n\n\n\\sec{The CDM family album}\n\n\\ssec{The linear spectrum}\n\nThe basic picture of inflationary models (but also\nof cosmology before inflation) is of a\nprimordial power-law spectrum, written dimensionlessly\nas the logarithmic contribution to the fractional\ndensity variance, $\\sigma^2$:\n$$\n\\Delta^2(k)={d\\sigma^2\\over d\\ln k} \\propto k^{3+n},\n$$\nwhere $n$ stands for $n_{\\ss S}$ hereafter.\nThis undergoes linear growth\n$$\n\\delta_k(a) = \\delta_k(a_0)\\; \\left[{D(a)\\over D(a_0)}\\right] \\; T_k,\n$$\nwhere the linear growth law is\n$$\nD(a)=a\\, g[\\Omega(a)]\n$$\nin the matter era,\nand the growth suppression for low $\\Omega$ is\n$$\n\\eqalign{\ng(\\Omega) &\\simeq \\Omega^{0.65}\\ {\\rm (open)} \\cr\n&\\simeq \\Omega^{0.23}\\ {\\rm (flat)} \\cr\n}\n$$\nThe transfer function $T_k$ depends on the dark-matter\ncontent as shown in figure 1.\n\n\\japfig{31}{183}{499}{579}{japfig1.eps}\n{Transfer functions for various dark-matter models.\nThe scaling with $\\Omega h^2$ is exact only for the\nzero-baryon models; the baryon results are scaled from\nthe particular case $\\Omega_{\\ss B}=1$, $h=1/2$. \n}\n\n\nNote the baryonic oscillations in figure 1; these\ncan be significant even in CDM-dominated models\nwhen working with high-precision data.\nEisenstein \\& Hu (1998) are to be congratulated for\ntheir impressive persistence in finding an accurate\nfitting formula that describes these wiggles.\nThis is invaluable for carrying out a search of\na large parameter space.\n\n\n\\japfig{0}{0}{519}{582}{japfig2.eps}\n{This figure\nillustrates how the primordial power spectrum is\nmodified as a function of density in a CDM\nmodel. For a given tilt, it is always\npossible to choose a density that satisfies both the\nCOBE and cluster normalizations.}\n\n\\japfig{36}{192}{482}{578}{japfig3.eps}\n{For 10\\% baryons, the value of $n$ needed\nto reconcile COBE and the cluster normalization\nin CDM models.}\n\nThe state of the linear-theory spectrum after these\nmodifications is illustrated in figure 2.\nThe primordial power-law spectrum is reduced\nat large $k$, by an amount that depends on\nboth the quantity of dark matter and its\nnature. Generally the bend in the spectrum\noccurs near $1/k$ of order the horizon size\nat matter-radiation equality, $\\propto \n(\\Omega h^2)^{-1}$. For a pure CDM universe,\nwith scale-invariant initial fluctuations\n($n=1$), the observed spectrum depends only on two\nparameters. One is the shape $\\Gamma = \\Omega h$,\nand the other is a normalization. On the\nshape front, a government health warning is needed,\nas follows. It has been quite common to take\n$\\Gamma$-based fits to observations as indicating\na {\\it measurement\\/} of $\\Omega h$, but there are\nthree reasons why this may give incorrect answers:\n\n(1) The dark matter may not be CDM. An admixture of\nHDM will damp the spectrum more, mimicking a\nlower CDM density.\n\n(2) Even in a CDM-dominated universe, baryons can\nhave a significant effect, making $\\Gamma$ lower\nthan $\\Omega h$. An approximate formula for this\nis given in figure 2 (Peacock \\& Dodds 1994;\nSugiyama 1995).\n\n(3) The strongest (and most-ignored) effect is\ntilt: if $n\\ne 1$, then even in a pure CDM universe\na $\\Gamma$-model fit to the spectrum will give a\nbadly incorrect estimate of the density\n(the change in $\\Omega h$ is roughly $0.3(n-1)$;\nPeacock \\& Dodds 1994).\n\n\n\n\\ssec{Normalization}\n\nThe other parameter is the normalization.\nThis can be set at a number of points.\nThe COBE normalization comes from large angle\nCMB anisotropies, and is sensitive to the\npower spectrum at $k\\simeq 10^{-3}\\hompc$.\nThe alternative is to set the normalization\nnear the quasilinear scale, using the abundance of\nrich clusters. Many authors have tried this\ncalculation, and there is good agreement on the\nanswer:\n$$\n\\sigma_8 \\simeq (0.5 - 0.6) \\, \\Omega_m^{-0.6}.\n$$\n(White, Efstathiou \\& Frenk 1993; Eke et al. 1996; Viana \\& Liddle 1996).\nIn many ways, this is the most sensible normalization\nto use for LSS studies, since it does not rely\non an extrapolation from larger scales.\n\n\nWithin the CDM model, it is always possible to satisfy\nboth these normalization constraints, by appropriate\nchoice of $\\Gamma$ and $n$. This is illustrated in\nfigure 3. Note that vacuum energy affects the answer;\nfor reasonable values of $h$ and reasonable\nbaryon content, flat models require $\\Omega_m\\simeq 0.3$, whereas\nopen models require $\\Omega_m\\simeq 0.5$.\n\n\n\n\n\\ssec{The nonlinear spectrum}\n\nOn smaller scales ($k\\gs 0.1$), nonlinear effects become important.\nThese are relatively well understood so far as they affect the\npower spectrum of the mass (e.g. \nHamilton et al. 1991; Jain, Mo \\& White 1995;\nPeacock \\& Dodds 1996). \nBased on a fitting formula for the similarity solution\ngoverning the evolution of scale-free initial conditions,\nit is possible to predict the evolved spectrum in CDM\nuniverses to a few per cent precision (e.g. Jenkins et al. 1998).\n\nThese methods can cope with most smoothly-varying power\nspectra, but they break down for models with a large\nbaryon content. Figure 1 shows that rather large oscillatory\nfeatures would be expected if the universe was baryon\ndominated. The lack of observational evidence for \nsuch features is one reason\nfor believing that the universe might be dominated\nby collisionless nonbaryonic matter (consistent with\nprimordial nucleosynthesis if $\\Omega_m\\gs 0.1$).\n\n\\japfig{0}{25}{487}{544}{japfig4.eps}\n{Baryonic fluctuations in the spectrum can\nbecome significant for high-precision measurements.\nAlthough such features are much less important in the\ndensity spectrum than in the CMB (first panel), the\norder 10\\% modulation of the power is potentially\ndetectable. However, nonlinear evolution has the\neffect of damping all beyond the second\npeak. This second feature is relatively\nnarrow, and can serve as a clear proof of the past\nexistence of oscillations in the baryon-photon fluid\n(Meiksin, White \\& Peacock 1999).}\n\nNevertheless, \nbaryonic fluctuations in the spectrum can\nbecome significant for high-precision measurements.\nFigure 4 shows that order 10\\% modulation of the\npower may be expected in realistic baryonic\nmodels (Eisenstein \\& Hu 1998; Goldberg \\& Strauss 1998).\nMost of these features are however removed\nby nonlinear evolution.\nThe highest-$k$ feature to survive is usually\nthe second peak, which almost always lies\nnear $k=0.05\\,{\\rm Mpc}^{-1}$ (no $h$, for a change).\nThis feature is relatively\nnarrow, and can serve as a clear proof of the past\nexistence of baryonic oscillations in forming the \nmass distribution\n(Meiksin, White \\& Peacock 1999).\nHowever, figure 4 emphasizes that the easiest way\nof detecting the presence of baryons is likely to\nbe through the CMB spectrum. The oscillations\nhave a much larger `visibility' there, because\nthe small-scale CMB anisotropies come directly\nfrom the coupled radiation-baryon fluid, rather\nthan the small-scale dark matter perturbations.\n\n\n\\sec{Statistics}\n\nStatistical measures of the cosmological density field\nrelate to properties of\nthe dimensionless \\key{density perturbation field}\n$$\n\\delta ({\\bf x}) \\equiv {\\rho({\\bf x})-\\langle\\rho\\rangle \\over\n\\langle\\rho\\rangle},\n$$\nalthough $\\delta$ need not be assumed to be small. \n\n\\ssec{Correlation functions}\nThe simplest measure is the \\key{autocorrelation function}\nof the density perturbation\n$$\n\\xi_{\\ss A}({\\bf r}) \\equiv \\left\\langle \\delta({\\bf x})\\delta({\\bf x+ r})\\right\\rangle,\n$$\nThis is a straightforward statistical measure that can\nalso be computed for the dark-matter distribution in\n$N$-body simulations.\nFormally, the averaging operator here is an ensemble\naverage, but one generally appeals to the ergodic nature\nof the density field to replace this with a volume average.\n\nHowever, galaxies are a point process, so what astronomers can\nmeasure in practice is the\n\\key{two-point correlation function}, which gives the excess\nprobability for finding a neighbour a distance $r$\nfrom a given galaxy. By regarding this as the\nprobability of finding a pair with one object in each of the volume\nelements $dV_1$ and $dV_2$, \n$$\ndP=\\rho_0^2\\, [1+\\xi_2(r)]\\, dV_1\\, dV_2.\n$$\nIs it true that $\\xi_{\\ss A}(r)=\\xi_2(r)?$ Life would\ncertainly be simple if so, and much work on large-scale\nstructure has implicitly assumed the\n\\key{Poisson clustering hypothesis}, in which galaxies\nare assumed to be sampled at random from some continuous\nunderlying density field. Many of the puzzles in the field\ncan however be traced to the fact that this hypothesis\nis probably false, as discussed below.\n\nA related quantity is the \\key{cross-correlation function}.\nHere, one considers two different classes of\nobject (a and b, say), and the cross-correlation function\n$\\xi_{ab}$ is defined as the (symmetric) probability\nof finding a pair in which $dV_1$ is occupied by an object\nfrom the first catalogue and $dV_2$ by one from the second.\nBoth cross- and auto-correlation functions are readily extended\nto higher orders and considerations of $n$-tuples of points\nin a given geometry.\n\n\n\\ssec{Fourier space}\nFor the Fourier counterpart of this analysis, we assume\nthat the field is periodic within some box of side $L$,\nand expand as a Fourier series:\n$$\n\\delta({\\bf x}) = \\sum \\delta_{\\bf k} e^{-i{\\bf k\\cdot x}}.\n$$\nFor a real field, $\\delta_{\\bf k}(-{\\bf k})=\\delta^*_{\\bf k}({\\bf k})$.\nUsing this definition in the correlation function, most\ncross terms integrate to zero through the periodic boundary conditions, giving\n$$\n\\xi({\\bf r})=\n{V \\over (2\\pi)^3}\\int|\\delta_{\\bf k}|^2 e^{-i{\\bf k\\cdot r}} d^3 k.\n$$\nIn short, the correlation function is the Fourier transform of\nthe \\key{power spectrum}. \n\nWe shall usually express\nthe power spectrum in dimensionless form, as the variance per $\\ln k$\n($\\Delta^2(k) =d \\langle \\delta^2 \\rangle/d\\ln k \\propto k^3 P[k]$):\n$$\n\\Delta^2(k)\\equiv {V\\over (2\\pi)^3} \\, 4\\pi k^3\\, P(k)\n={2\\over \\pi}k^3\\int_0^\\infty\\xi(r)\\,\n{\\sin kr\\over kr}\\, r^2\\, dr.\n$$\nThis gives a more easily visualizable meaning to the power\nspectrum than does the quantity $V P(k)$, which has\ndimensions of volume: $\\Delta^2(k)=1$ means that there\nare order-unity density fluctuations from modes\nin the logarithmic bin around wavenumber $k$.\n$\\Delta^2(k)$ is therefore the natural choice for\na Fourier-space counterpart to the dimensionless quantity $\\xi(r)$.\n\nIn the days before inflation, the primordial power\nspectrum was chosen by hand, and the minimal\nassumption was a featureless power law:\n$$\n\\left\\langle|\\delta_k|^2\\right\\rangle \\equiv P(k) \\propto k^n\n$$\nThe index $n$ governs the balance between large-\nand small-scale power.\nSimilarly, a power-law spectrum implies a power-law\ncorrelation function.\nIf $\\xi(r)=(r/r_0)^{-\\gamma}$, with $\\gamma=n+3$,\nthe corresponding 3D power spectrum is\n$$\n\\Delta^2(k)={2\\over\\pi}\\,(kr_0)^{\\gamma}\\, \\Gamma(2-\\gamma) \\,\n \\sin {(2-\\gamma)\\pi\\over 2}\n\\equiv \\beta (kr_0)^\\gamma\n$$\n($=0.903 (kr_0)^{1.8}$ if $\\gamma=1.8$).\nThis expression is only valid for $n<0$ ($\\gamma<3$);\nfor larger values of $n$, $\\xi$ must become\nnegative at large $r$ (because $P(0)$ must vanish,\nimplying $\\int_0^\\infty \\xi(r)\\, r^2\\, dr=0$).\nA cutoff in the spectrum at large $k$ is needed\nto obtain physically sensible results.\n\nThe most interesting value of $n$ is the \\key{scale-invariant spectrum}, \n$n=1$, {\\it i.e.} $\\Delta^2\\propto k^4$. To see how the name arises,\nconsider a perturbation $\\delta\\Phi$ in the gravitational potential:\n$$\n\\nabla^2\\delta\\Phi= 4\\pi G\\rho_0\\delta\n\\quad\\Rightarrow\\quad \\delta\\Phi_k = -4\\pi G\\rho_0\\delta_k/k^2.\n$$\nThe two powers of $k$ pulled down by $\\nabla^2$ mean\nthat, if $\\Delta^2\\propto k^4$ for the power spectrum of \ndensity fluctuations, then $\\Delta^2_\\Phi$ is a constant.\nSince potential perturbations govern the flatness\nof spacetime, this says that the scale-invariant\nspectrum corresponds to a metric that is\na \\key{fractal}: spacetime has the same degree of\n`wrinkliness' on each resolution scale.\nThe total curvature fluctuations diverge, but only\nlogarithmically at either extreme of wavelength.\n\n\n\\ssec{Error estimates}\n\nA key question for these statistical measures is how accurate\nthey are -- i.e. how much does the result for a given\nfinite sample depart from the ideal statistic averaged over\nan infinite universe? Terminology here can be confusing,\nin that a distinction is sometimes made between\n\\key{sampling variance} and \\key{cosmic variance}.\nThe former is to be understood as arising from probing\na given volume only with a finite number of galaxies\n(e.g. just the bright ones), so that $\\sqrt{N}$\nstatistics limit our knowledge of the mass distribution\nwithin that region. The second term concerns whether\nwe have reached a fair sample of the universe, and \ndepends on whether there is significant power in\ndensity perturbation modes with wavelengths larger than\nthe sample depth. Clearly, these two aspects are \nclosely related.\n\nThe quantitative analysis of these errors is most simply\nperformed in Fourier space, and was given by \nFeldman, Kaiser \\& Peacock (1994). The results can be\nunderstood most simply by comparison with an idealized\ncomplete and uniform survey of a volume $L^3$, with\nperiodicity scale $L$. For an infinite survey, the arbitrariness of the spatial\norigin means that different modes are uncorrelated:\n$$\n\\langle \\delta_k({\\bf k}_{i})\\delta_k^*({\\bf k}_{j})\\rangle = P(k) \\delta_{ij}.\n$$\nEach mode has an exponential distribution in power (because the complex\ncoefficients $\\delta_k$ are 2D Gaussian-distributed variables on the\nArgand plane), for which the mean and rms are identical. The fractional\nuncertainty in the mean power measured over some $k$-space volume is\nthen just determined by the number of uncorrelated modes averaged over:\n$$\n{\\delta \\bar P \\over \\bar P} = {1\\over N_{\\rm modes}^{1/2}}; \\quad\\quad\nN_{\\rm modes} = \\left({L\\over 2\\pi}\\right)^3\\, \\int d^3 k.\n$$\nThe only subtlety is that, because the density field is real, modes\nat $k$ and $-k$ are perfectly correlated. Thus, if the $k$-space\nvolume is a shell, the effective number of uncorrelated modes is\nonly half the above expression.\n\nAnalogous results apply for an arbitrary survey selection function.\nIn the continuum limit, the Kroneker delta in the \nexpression for mode correlation would be\nreplaced a term proportional to a delta-function, $\\delta[{\\bf k}_{i}-{\\bf k}_{j}]$).\nNow, multiplying the infinite ideal survey by a survey window, $\\rho({\\bf r})$,\nis equivalent to convolution in\nthe Fourier domain, with the result that the power per mode is\ncorrelated over $k$-space separations of order $1/D$, where $D$ is the\nsurvey depth.\n\nGiven this expression for the fractional power, it is clear that the\nprecision of the estimate can be manipulated by appropriate\nweighting of the data: giving increased weight to the most distant\ngalaxies increases the effective survey volume, boosting the\nnumber of modes. This sounds too good to be true, and of course\nit is: the above expression for the fractional power error\napplies to the sum of true clustering power and shot noise. \nThe latter arises because we transform a point process. Given a set\nof $N$ galaxies, we would estimate Fourier coefficients via\n$\\delta_k=(1/N) \\sum_i \\exp(-i{\\bf k}\\cdot x_i)$. From this, the\nexpectation power is\n$$\n\\langle|\\delta_k|^2 \\rangle = P(k) + 1/N.\n$$\nThe existence of an additive discreteness correction is no problem,\nbut the {\\it fluctuations\\/} on the shot noise hide the \nsignal of interest. Introducing\nweights boosts the shot noise, so there is an optimum choice of weight that\nminimizes the uncertainty in the power after shot-noise subtraction.\nFeldman, Kaiser \\& Peacock (1994) showed that this weight is\n$$\nw = (1+\\bar n P)^{-1},\n$$\nwhere $\\bar n$ is the expected galaxy number density as a function of\nposition in the survey.\n\nSince the correlation of modes arises from the survey\nselection function, it is clear that weighting the data\nchanges the degree of correlation in $k$ space.\nIncreasing the weight in low-density\nregions increases the effective survey volume, and\nso shrinks the $k$-space coherence scale.\nHowever, the coherence scale continues to shrink as distant\nregions of the survey are given greater weight, whereas the noise\ngoes through a minimum. There is \nthus a trade-off between the competing desirable criteria of\nhigh $k$-space resolution and low noise.\nTegmark (1996) shows how weights may be chosen to\nimplement any given prejudice concerning the relative\nimportance of these two criteria.\nSee also Hamilton (1997b,c) for similar arguments.\n\n\n\\ssec{Karhunen-Lo\\`eve and all that}\n\nGiven these difficulties with correlated\nresults, it is attractive to seek a method\nwhere the data can be decomposed into a set\nof statistics that are completely uncorrelated with each other.\nSuch a method is provided by the\nKarhunen-Lo\\`eve formalism. Vogeley \\& Szalay (1996)\nargued as follows.\nDefine a column vector of data $\\vec{d}$;\nthis can be quite abstract in nature, and could\nbe e.g. the numbers of galaxies in a set of cells, or\na set of Fourier components of the transformed galaxy\nnumber counts. Similarly, for CMB studies, $\\vec{d}$ could\nbe $\\delta T/T$ in a set of pixels, or spherical-harmonic\ncoefficients $a_{\\ell m}$.\nWe assume that the mean can be identified and\nsubtracted off, so that $\\langle \\vec{d} \\rangle =0$ in\nensemble average. The statistical properties of the data are\nthen described by the covariance matrix\n$$\nC_{ij} \\equiv \\langle d_i d_j^* \\rangle\n$$\n(normally the data will be real, but it is\nconvenient to keep things general and include the complex\nconjugate). \n\nSuppose we seek to expand the datavector in\nterms of a set of new orthonormal vectors:\n$$\n{\\vec{d}} = \\sum_i a_i {\\vec{\\psi}}_i; \\quad\\quad\n{\\vec{\\psi}}^*_i \\cdot {\\vec{\\psi}}_j = \\delta_{ij}.\n$$\nThe expansion coefficients are extracted in the usual way:\n$\\smash{a_j = \\vec{d} \\cdot \\vec{\\psi}_j^*}$.\nNow require that these coefficients be statistically\nuncorrelated,\n$\\langle a_i a_j^* \\rangle = \\lambda_i \\delta_{ij}$\n(no sum on $i$). This gives\n$$\n\\vec{\\psi}_i^* \\cdot \\langle \\vec{d} \\, \\vec{d}^* \\rangle\n\\cdot \\vec{\\psi}_j = \\lambda_i \\delta_{ij},\n$$\nwhere the dyadic $\\langle \\vec{d} \\, \\vec{d}^* \\rangle$\nis $\\vec{\\vec{C}}$, the correlation matrix of the data vector: \n$(\\vec{d} \\, \\vec{d}^*)_{ij}\\equiv d_i d^*_j$.\nNow, the effect of operating this matrix on one of the\n$\\vec{\\psi}_i$ must be expandable in terms of the complete\nset, which shows that the $\\smash{\\vec{\\psi}_j}$ must be the eigenvectors\nof the correlation matrix:\n$$\n\\langle \\vec{d} \\, \\vec{d}^* \\rangle \\cdot\n\\vec{\\psi}_j = \\lambda_j \\vec{\\psi}_j.\n$$\n\nVogeley \\& Szalay further show that these uncorrelated modes are\noptimal for representing the data: if the modes are\narranged in order of decreasing $\\lambda$, and the\nseries expansion truncated after $n$ terms, the rms\ntruncation error is minimized for this choice of\neigenmodes. To prove this, consider\nthe truncation error\n$$\n\\vec\\epsilon = \\vec{d} - \\sum_{i=1}^n a_i \\vec{\\psi}_i = \n\\sum_{i=n+1}^\\infty a_i \\vec{\\psi}_i.\n$$\nThe square of this is\n$$\n\\langle \\epsilon^2 \\rangle = \\sum_{i=n+1}^\\infty \\langle \n|a_i|^2 \\rangle,\n$$\nwhere $\\langle \n|a_i|^2 \\rangle = \\vec{\\psi}_i^* \\cdot \\vec{\\vec{C}} \\cdot \\vec{\\psi}_i$,\nas before. We want to minimize $\\langle \\epsilon^2 \\rangle$\nby varying the $\\vec{\\psi}_i$, but we need to do this in\na way that preserves normalization. This is achieved\nby introducing a Lagrange multiplier, and minimizing\n$$\n\\sum \\vec{\\psi}_i^* \\cdot \\vec{\\vec{C}} \\cdot \\vec{\\psi}_i\n+ \\lambda (1-\\vec{\\psi}_i^* \\cdot \\vec{\\psi}_i).\n$$\nThis is easily solved if we consider the more general\nproblem where $\\vec{\\psi}_i^*$ and $\\vec{\\psi}_i$ are\nindependent vectors:\n$$\n\\vec{\\vec{C}} \\cdot \\vec{\\psi}_i = \\lambda \\psi_i.\n$$\nIn short, the eigenvectors of $\\vec{\\vec{C}}$\nare optimal in a least-squares sense for expanding the data.\nThe process of truncating the expansion is a form of\nlossy \\key{data compression}, since the size of the data vector\ncan be greatly reduced without significantly\naffecting the fidelity of the resulting representation of the universe.\n\n\nThe process of diagonalizing the covariance\nmatrix of a set of data also goes by the more\nfamiliar name of \\key{principal components analysis},\nso what is the difference between the KL\napproach and PCA? In the above discussion, they are identical,\nbut the idea of choosing an optimal\neigenbasis is more general than PCA.\nConsider the case where the covariance matrix\ncan be decomposed into a `signal' and a \n`noise' term:\n$$\n\\vec{\\vec{C}} =\n\\vec{\\vec{S}} +\n\\vec{\\vec{N}},\n$$\nwhere $\\vec{\\vec{S}}$ depends on cosmological\nparameters that we might wish to estimate,\nwhereas $\\vec{\\vec{N}}$ is some fixed property of\nthe experiment under consideration.\nIn the simplest imaginable case, $\\vec{\\vec{N}}$\nmight be a diagonal matrix, so PCA diagonalizes\nboth $\\vec{\\vec{S}}$ and $\\vec{\\vec{N}}$.\nIn this case, ranking the PCA modes by eigenvalue would \ncorrespond to ordering the modes according to\nsignal-to-noise ratio. Data compression by truncating\nthe mode expansion then does the sensible thing: it rejects\nall modes of low signal-to-noise ratio.\n\nHowever, in general these matrices will not commute, and \nthere will not be a single set of eigenfunctions that\nare common to the $\\vec{\\vec{S}}$ and $\\vec{\\vec{N}}$\nmatrices. Normally, this would be taken to mean that it\nis impossible to find a set of coordinates in which \nboth are diagonal. This conclusion can however be evaded, as follows.\nWhen considering the effect of coordinate transformations on\nvectors and matrices, we are normally forced to consider\nonly rotation-like transformations that preserve the norm of\na vector (e.g. in quantum mechanics, so that states stay normalized).\nThus, we write $\\vec{d}' = \\vec{\\vec{R}}\\cdot \\vec{d}$, where\n$\\vec{\\vec{R}}$ is unitary, so that $\\vec{\\vec{R}} \\cdot \\vec{\\vec{R}}^\\dagger =\n\\vec{\\vec{I}}$. If $\\vec{\\vec{R}}$ is chosen so that its columns are\nthe eigenvalues of $\\vec{\\vec{N}}$, then the transformed noise\nmatrix, $\\smash{\\vec{\\vec{R}} \\cdot \\vec{\\vec{N}} \\cdot \\vec{\\vec{R}}^\\dagger}$, \nis diagonal. Nevertheless, if the transformed $\\vec{\\vec{S}}$\nis not diagonal, the two will not commute. This apparently insuperable\nproblem can be solved by using the fact that the data vectors are\nentirely abstract at this stage. There is therefore no reason not to\nconsider the further transformation of scaling the data, so that\n$\\vec{\\vec{N}}$ becomes proportional to the identity matrix. This\nmeans that the transformation is no longer unitary -- but there is\nno physical reason to object to a change in the normalization\nof the data vectors.\n\nSuppose we therefore make a further transformation\n$$\n\\vec{d}'' = \\vec{\\vec{W}}\\cdot \\vec{d}'\n$$\nThe matrix $\\vec{\\vec{W}}$ is related to the rotated noise matrix:\n$$\n\\vec{\\vec{N}}' = {\\rm diag}\\, (n_1,n_2,\\dots) \\quad \\Rightarrow \\quad\n\\vec{\\vec{W}} = {\\rm diag}\\, (1/\\sqrt{n_1},1/\\sqrt{n_2},\\dots).\n$$\nThis transformation is termed \\key{prewhitening} by Vogeley \\& Szalay (1996),\nsince it converts the noise matrix to white noise,\nin which each pixel has a unit noise that is uncorrelated with\nother pixels. \nThe effect of this transformation on the full covariance matrix is\n$$\nC_{ij}'' \\equiv \\langle d_i'' d_j''{}^* \\rangle \\quad \\Rightarrow \\quad\n\\vec{\\vec{C}}'' = (\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}}) \\cdot \\vec{\\vec{C}} \\cdot\n(\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}})^\\dagger\n$$\nAfter this transformation, the noise and signal\nmatrices certainly do commute, and the optimal modes for\nexpanding the new data are once again the PCA\neigenmodes in the new coordinates:\n$$\n\\vec{\\vec{C}}''\\cdot \\vec{\\psi}_i'' = \\lambda \\vec{\\psi}_i''.\n$$\nThese eigenmodes must be expressible\nin terms of some modes in the original coordinates, $\\vec{e}_i$:\n$$\n\\vec{\\psi}_i'' = (\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}}) \\cdot \\vec{e}_i.\n$$\nIn these terms, the eigenproblem is \n$$\n(\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}}) \\cdot \\vec{\\vec{C}} \\cdot\n(\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}})^\\dagger \\cdot (\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}}) \\cdot \\vec{e}_i\n= \\lambda (\\vec{\\vec{W}}\\cdot \\vec{\\vec{R}}) \\cdot \\vec{e}_i.\n$$\nThis can be simplified using $\\vec{\\vec{W}}^\\dagger \\cdot \\vec{\\vec{W}} = \\vec{\\vec{N}}'{}^{-1}$\nand $\\vec{\\vec{N}}'{}^{-1} = \\vec{\\vec{R}} \\cdot \\vec{\\vec{N}}^{-1} \\vec{\\vec{R}}^\\dagger$,\nto give\n$$\n\\vec{\\vec{C}} \\cdot \\vec{\\vec{N}}^{-1} \\cdot \\vec{e}_i = \\lambda \\vec{e}_i,\n$$\nso the required modes are eigenmodes of $\\vec{\\vec{C}} \\cdot \\vec{\\vec{N}}^{-1}$.\nHowever, care is required when considering the orthonormality of the $\\vec{e}_i$:\n$\\smash{\\vec{\\psi}_i^\\dagger \\cdot \\vec{\\psi}_j = \\vec{e}_i^\\dagger \\cdot \\vec{\\vec{N}}^{-1} \\cdot \\vec{e}_j}$,\nso the $\\vec{e}_i$ are not orthonormal. If we write $\\vec{d} = \\sum_i a_i \\vec{e}_i$, then\n$$\na_i = (\\vec{\\vec{N}}^{-1} \\cdot \\vec{e}_i)^\\dagger \\cdot \\vec{d} \\equiv \\vec{\\psi}_i^\\dagger \\cdot \\vec{d}.\n$$ \nThus, the modes used to\nextract the compressed data by dot product satisfy\n$\\vec{\\vec{C}} \\cdot \\vec{\\psi} = \\lambda \\vec{\\vec{N}}\\cdot \\vec{\\psi}$, or finally\n$$\n\\vec{\\vec{S}}\n\\cdot \\vec{\\psi} = \\lambda\\, \\vec{\\vec{N}} \\cdot \\vec{\\psi},\n$$\ngiven a redefinition of $\\lambda$.\nThe optimal modes are thus eigenmodes of\n$\\vec{\\vec{N}}^{-1} \\cdot \\vec{\\vec{S}}$,\nhence the name \\key{signal-to-noise eigenmodes}\n(Bond 1995; Bunn 1996).\n\n\nIt is interesting to appreciate that the set of KL modes\njust discussed is also the `best'\nset of modes to choose from a completely different\npoint of view: they are the modes that\nare optimal for estimation of a parameter via\nmaximum likelihood.\nSuppose we write the compressed data vector, $\\vec{x}$, in terms of a\nnon-square matrix $\\vec{\\vec{A}}$ (whose rows are the basis\nvectors $\\vec{\\psi}_i^*$):\n$$\n\\vec{x}=\\vec{\\vec{A}}\\cdot \\vec{d}.\n$$\nThe transformed covariance matrix is\n$$\n\\vec{\\vec{D}} \\equiv \\langle \\vec{x}\\vec{x}^\\dagger \\rangle\n=\n\\vec{\\vec{A}} \\cdot \\vec{\\vec{C}} \\cdot \\vec{\\vec{A}}^\\dagger.\n$$\nFor the case where the original data obeyed Gaussian\nstatistics, this is true for the compressed data also, so the\nlikelihood is\n$$\n-2\\ln {\\cal L} = \\ln {\\rm det}\\, \\vec{\\vec{D}} + \n\\vec{x}^* \\cdot \\vec{\\vec{D}}^{-1} \\cdot \\vec{x} + {\\rm constant}\n$$\nThe normal variance on some parameter $p$ (on\nwhich the covariance matrix depends) is\n$$\n{1\\over \\sigma_p^2} = {d^2 [-2\\ln {\\cal L}] \\over dq^2}.\n$$\nWithout data, we don't know this, so it is common to use\nthe expectation value of the rhs as\nan estimate (recently, there has been a tendency to dub this\nthe `Fisher matrix').\n\nWe desire to optimize $\\sigma_p$ by an appropriate choice\nof data-compression vectors, $\\vec{\\psi}_i$.\nBy writing $\\sigma_p$ in terms of $\\vec{\\vec{A}}$,\n$\\vec{\\vec{C}}$ and $\\vec{d}$, it may eventually be\nshown that the desired optimal modes satisfy\n$$\n\\left({d\\over dp}\\, \\vec{\\vec{C}} \\right)\n\\cdot \\vec{\\psi} = \\lambda\\, \\vec{\\vec{C}} \\cdot \\vec{\\psi}.\n$$\nFor the case where the parameter of interest is\nthe cosmological power, the matrix on the lhs is \njust proportional to $\\vec{\\vec{S}}$, so we have to solve\nthe eigenproblem\n$$\n\\vec{\\vec{S}}\n\\cdot \\vec{\\psi} = \\lambda\\, \\vec{\\vec{C}} \\cdot \\vec{\\psi}.\n$$\nWith a redefinition of $\\lambda$, this becomes\n$$\n\\vec{\\vec{S}}\n\\cdot \\vec{\\psi} = \\lambda\\, \\vec{\\vec{N}} \\cdot \\vec{\\psi}.\n$$\nThe optimal modes for parameter estimation in the\nlinear case are thus identical to the PCA modes of the\nprewhitened data discussed above.\nThe more general expression was given by\nTegmark, Taylor \\& Heavens (1997), and it is\nonly in this case, where the covariance matrix\nis not necessarily linear in the parameter of interest, that\nthe KL method actually differs from PCA.\n\n\nThe reason for going to all this trouble is that the likelihood\ncan now be evaluated much more rapidly, using the compressed data.\nThis allows extensive model searches over large parameter spaces\nthat would be unfeasible with the original data (since inversion\nof an $N\\times N$ covariance matrix takes a time proportional\nto $N^3$). Note however that the price paid for this\nefficiency is that a different set of modes need to be\nchosen depending on the model of interest, and that these\nmodes will not in general be optimal for expanding the\ndataset itself.\nNevertheless, it may be expected that application of these methods will\ninevitably grow as datasets increase in size. Present applications\nmainly prove that the techniques work: see \nMatsubara, Szalay \\& Landy (1999) for application to the LCRS, or\nPadmanabhan, Tegmark \\& Hamilton (1999) for the UZC survey.\nThe next generation of experiments will probably be\nforced to resort to data compression of this sort,\nrather than using it as an elegant alternative method\nof analysis.\n\n\n\\sec{Redshift-space effects}\n\nPeculiar velocity fields are responsible for the\ndistortion of the clustering pattern in \nredshift space, as first clearly articulated\nby Kaiser (1987). \nFor a survey that subtends a small angle\n(i.e. in the \\key{distant-observer approximation}), a good approximation to\nthe anisotropic redshift-space Fourier spectrum is given\nby the Kaiser function together with a damping\nterm from nonlinear effects:\n$$\n\\delta_k^s=\\delta_k^r (1+\\beta\\mu^2)D(k\\sigma\\mu),\n$$\nwhere $\\beta=\\Omega_m^{0.6}/b$, $b$ being the\nlinear bias parameter of the galaxies under study,\nand $\\mu={\\bf \\hat k \\cdot \\hat r}$.\nFor an exponential distribution of relative\nsmall-scale peculiar velocities (as seen empirically),\nthe damping function is \n$D(y)\\simeq (1+y^2/2)^{-1/2}$, and $\\sigma\\simeq 400\\kms$\nis a reasonable estimate for the pairwise velocity dispersion of galaxies\n(e.g. Ballinger, Peacock \\& Heavens 1996).\n\nIn principle, this distortion should be a robust\nway to determine $\\Omega$ (or at least $\\beta$).\nIn practice, the effect has not been easy to see\nwith past datasets. This is mainly a question of\ndepth: a large survey is needed in order to beat down\nthe shot noise, but this tends to favour bright\nspectroscopic limits. This limits the result both because\nrelatively few modes in the linear regime are\nsampled, and also because local survey volumes\nwill tend to violate the small-angle approximation.\nStrauss \\& Willick (1995) and Hamilton (1997a) review\nthe practical application of redshift-space distortions.\nIn the next section, preliminary results are presented\nfrom the 2dF redshift survey, which shows the\ndistortion effect clearly for the first time.\n\n\n\\sec{The state of the art in LSS}\n\n\\ssec{The APM survey}\n\nIn the past few years, much attention has been attracted by\nthe estimate of the galaxy power spectrum from the APM\nsurvey (Baugh \\& Efstathiou 1993, 1994; Maddox et al. 1996).\nThe APM result was generated from\na catalogue of $\\sim 10^6$ galaxies derived from UK\nSchmidt Telescope photographic plates scanned with the\nCambridge Automatic Plate Measuring machine; because it is based\non a \\key{deprojection} of angular clustering, it is immune to the\ncomplicating effects of redshift-space distortions.\nThe difficulty, of course, is in ensuring that any\nlow-level systematics from e.g. spatial variations\nin magnitude zero point are sufficiently well\ncontrolled that they do not mask the cosmological\nsignal, which is of order $w(\\theta) \\ls 0.01$ \nat separations of a few degrees.\n\nThe best evidence that the\nAPM survey has the desired uniformity is the \\key{scaling test}, \nwhere the correlations in fainter magnitude slices are expected to \nmove to smaller scales and be reduced in amplitude.\nIf we increase the depth of the survey by some\nfactor $D$, the new angular correlation function will be\n$$\nw'(\\theta) = {1\\over D} \\, w(D\\theta).\n$$\nThe APM survey passes this test well; once the overall \nredshift distribution is known, it is possible to obtain\nthe spatial power spectrum by inverting a convolution integral:\n$$\nw(\\theta)= \\int_0^\\infty y^4\\phi^2\\, dy\\ \\int_0^\\infty\n \\pi\\, \\Delta^2(k)\\, J_0(ky\\theta)\\, dk/k^2\n$$\n(where zero spatial curvature is assumed).\nHere, $\\phi(y)$ is the comoving density at comoving\ndistance $y$, normalized so that $\\int y^2\\phi(y)\\, dy=1$.\n\nThis integral was inverted numerically by Baugh \\& Efstathiou\n(1993), and gives an impressively accurate determination\nof the power spectrum.\nThe error estimates are derived empirically from the scatter\nbetween independent regions of the sky, and so should be\nrealistic. If there are no undetected systematics, these\nerror bars say that the power is very accurately determined.\nThe APM result has been investigated\nin detail by a number of authors (e.g. \nGazta\\~naga \\& Baugh 1998; Eisenstein \\& Zaldarriaga 1999)\nand found to be robust;\nthis has significant implications if true.\n\n\n\\ssec{Past redshift surveys}\n\nBecause of the sheer number of galaxies, plus the large\nvolume surveyed, the APM survey outperforms redshift\nsurveys of the past, at least for the purpose of\ndetermining the power spectrum. The largest surveys\nof recent years (CfA: Huchra et al. 1990; \nLCRS: Shectman et al. 1996; PSCz: Saunders et al. 1999)\ncontain of order $10^4$ galaxy redshifts, and their\nstatistical errors are considerably larger than\nthose of the APM. On the other hand, it is of\ngreat importance to compare the results of deprojection\nwith clustering measured directly in 3D.\n\nThis comparison was carried out\nby Peacock \\& Dodds (1994; PD94).\nThe exercise is not straightforward, because the 3D\nresults are affected by redshift-space distortions;\nalso, different galaxy tracers can be biased to \ndifferent extents. The approach taken was to use each\ndataset to reconstruct an estimate of \nthe linear spectrum, allowing the relative bias factors\nto float in order to make these estimates agree\nas well as possible\n(figure 5). To within a scatter of perhaps a factor 1.5 in\npower, the results were consistent with a $\\Gamma\\simeq 0.25$ CDM model.\nEven though the subsequent sections will discuss some possible\ndisagreements with the CDM models at a higher level of\nprecision, the general existence of CDM-like curvature\nin the spectrum is likely to be an important clue to the\nnature of the dark matter.\n\n\\japfig{37}{117}{490}{749}{japfig5.eps}\n{The PD94 compilation of power-spectrum\nmeasurements. The upper panel shows raw\npower measurements; the lower shows these data\ncorrected for relative bias, nonlinear effects, and\nredshift-space effects.}\n\n\n\n\\ssec{The 2dF survey}\n\nThe proper resolution of many of the observational questions\nregarding the large-scale distribution of galaxies requires\nnew generations of redshift survey that push beyond\nthe $N=10^5$ barrier. Two groups are pursuing this\ngoal. The Sloan survey (e.g. Margon 1999) is using a\ndedicated 2.5-m telescope to measure redshifts for \napproximately 700,000 galaxies to $r=18.2$ in the North Galactic Cap.\nThe 2dF survey (e.g. Colless 1999) is using a fraction of the\ntime on the 3.9-m Anglo-Australian Telescope plus\nTwo-Degree Field spectrograph to measure 250,000 galaxies\nfrom the APM survey to $B_J=19.45$ in the South Galactic Cap.\nAt the time of writing, the Sloan spectroscopic\nsurvey has yet to commence. However, the 2dF project has measured 77,000\nredshifts, and some preliminary clustering results \nare given below.\nFor more details of the survey, particularly the team\nmembers whose hard work has made all this possible,\nsee\n{\\tt http://www.mso.anu.edu.au/2dFGRS/}.\n\n\n\n\\japfig{57}{211}{515}{588}{japfig6.eps}\n{A 4-degree thick slice of the Southern\nstrip of the 2dF redshift survey. This restricted region \nalone contains 16,419 galaxies.}\n\nOne of the advantages of 2dF is that it is a fully sampled survey,\nso that the space density out to the depth imposed by the\nmagnitude limit (median $z=0.12$) is as high as nature\nallows: apart from a tail of low surface brightness \ngalaxies (inevitably omitted from any spectroscopic survey),\nthe 2dF measure all the galaxies that exist over a\ncosmologically representative volume. It is the first to\nachieve this goal. The fidelity of the resulting map of\nthe galaxy distribution can be seen in figure 6, which shows\na small subset of the data: a slice of thickness 4\ndegrees, centred at declination $-27^\\circ$.\n\n\nAn issue with using the 2dF data in their current\nform is that the sky has to be divided into circular `tiles'\neach two degrees in diameter (`2dF' = `two-degree field', within\nwhich the AAT is able to measure 400 spectra simultaneously;\nsee {\\tt http://www.aao.gov.au/2df/} for details of the instrument).\nThe tiles are positioned adaptively, so that larger overlaps\noccur in regions of high galaxy density. It this way, it is\npossible to place a fibre on $>95\\%$ of all galaxies.\nHowever, while the survey is in progress, there exist parts\nof the sky where the overlapping tiles have not yet been observed,\nand so the effective sampling fraction is only $\\simeq 50\\%$.\nThese effects can be allowed for in two different ways.\nIn clustering analyses, we compare the counts of pairs\n(or $n$-tuplets) of galaxies in the data to the corresponding\ncounts involving an unclustered random catalogue. The\neffects of variable sampling can therefore be dealt with\neither by making the density of random points fluctuate\naccording to the sampling, or by weighting observed galaxies\nby the reciprocal of the sampling factor for the zone in\nwhich they lie. The former approach is better from the\npoint of view of shot noise, but the latter may be safer\nif there is any suspicion that the sampling fluctuations\nare correlated with real structure on the sky. In practice,\nboth strategies give identical answers for the results below.\n\nAt the two-point level, the most direct quantity to compute\nis the \\key{redshift-space correlation function}. This is an\nanisotropic function of the orientation of a galaxy \npair, owing to peculiar velocities. We therefore evaluate\n$\\xi$ as a function of 2D separation in terms of coordinates\nboth parallel and perpendicular to the line of sight.\nIf the comoving radii of two galaxies\nare $y_1$ and $y_2$ and their total separation is $r$, then\nwe define coordinates\n$$\n\\pi \\equiv |y_1-y_2|; \\quad\\quad \\sigma = \\sqrt{r^2-\\pi^2}.\n$$\nThe correlation function measured in these coordinates\nis shown in figure 7.\nIn evaluating $\\xi(\\sigma, \\pi)$, the optimal\nradial weight discussed above has been applied, so that\nthe noise at large $r$ should be representative of\ntrue cosmic scatter. \n\n\n\\begin{figure*}\n\\centering\\mbox{\\epsfxsize=0.45\\hsize\n\\epsfbox[38 123 521 658]{japfig7a.eps} \\quad\\quad\n\\raise 1.5em\\hbox{\n\\epsfxsize=0.45\\hsize\n\\epsfbox[60 211 511 633]{japfig7b.eps}\n}\n}\n\\caption[]{The redshift-space correlation function from the\n2dF data, $\\xi(\\sigma, \\pi)$, with a bin size of\n$0.6\\mpcoh$.\n$\\sigma$ is the pair separation transverse to the line\nof sight; $\\pi$ is the radial separation.\nThis plot clearly displays redshift distortions, with\n`fingers of God' at small scales and the coherent\nKaiser squashing at large $\\sigma$.\nThe distortions are quantified via the \nquadrupole-to-monopole ratio of $\\xi$ as a function\nof radius in the second panel. The contours are\nround at $r=7\\mpcoh$, but flatten progressively thereafter.\n}\n\\end{figure*}\n\nThe correlation-function results display very clearly\nthe two signatures of redshift-space distortions discussed\nabove. The \\key{fingers of God} from small-scale random\nvelocities are very clear, as indeed has been the case\nfrom the first redshift surveys (e.g. Davis \\& Peebles 1983).\nHowever, this is arguably the first time that the large-scale\nflattening from coherent infall has been really obvious in the\ndata.\n\nA good way to quantify the flattening is to analyze the\nclustering as a function of angle into Legendre polynomials:\n$$\n\\xi_\\ell(r) = {2\\ell+1\\over 2} \\int_{-1}^1 \\xi(\\sigma=r\\sin\\theta,\n\\pi=r\\cos\\theta)\\; P_\\ell(\\cos\\theta)\\; d\\cos\\theta.\n$$\nThe quadrupole-to-monopole ratio should be a clear indicator\nof coherent infall. In linear theory, it is given by\n$$ \n{\\xi_2\\over \\xi_0} = f(n) \\,\n{4\\beta/3 + 4\\beta^2/7 \\over\n1 + 2\\beta/3 + \\beta^2/5 },\n$$\nwhere $f(n)=(3+n)/n$ (Hamilton 1992). On small and intermediate\nscales, the effective spectral index is negative,\nso the quadrupole-to-monopole\nratio should be negative, as observed.\n\nHowever, it is clear that the results on the\nlargest scales are still significantly affected by\nfinger-of-God smearing. The best way to interpret the\nobserved effects is to calculate the same quantities\nfor a model. To achieve this, we use the observed\nAPM 3D power spectrum, plus the distortion model\ndiscussed above. This gives the plots shown in figure 8.\nThe free parameter is $\\beta$, and this is set at\na value of 0.5, approximately consistent with\nother arguments for a universe with $\\Omega=0.3$\nand little large-scale bias (e.g. Peacock 1997).\nAlthough a quantitative comparison has not yet\nbeen carried out, it is clear that this plot\nclosely resembles the observed data.\n\n\n\\begin{figure*}\n\\centering\\mbox{\\epsfxsize=0.45\\hsize\n\\epsfbox[38 123 521 658]{japfig8a.eps} \\quad\\quad\n\\raise 1.5em\\hbox{\n\\epsfxsize=0.45\\hsize\n\\epsfbox[60 211 511 633]{japfig8b.eps}\n}\n}\n\\caption[]{The redshift-space correlation function predicted from the\nreal-space APM power spectrum, assuming the model of\nBallinger, Peacock \\& Heavens (1996), with $\\beta=0.5$.}\n\\end{figure*}\n\n\nBy the end of 2001, the size of the 2dF survey should have expanded\nby a factor 3, increasing the pair counts tenfold. It should\nthen be possible to trace the correlations well beyond the present\nlimit, and follow the redshift-space distortion well into the\nlinear regime.\nHowever, the biggest advantage of a survey of this size and\nuniformity is the ability to subdivide it. All analyses to date\nhave lumped together very different kinds of galaxies, whereas\nwe know from morphological segregation that different classes\nof galaxy have spatial distributions that differ from each other.\nThe homogeneous 2dF data allow classification into\ndifferent galaxy types (representing, physically, a sequence\nof star-formation rates), from the spectra alone\n(Folkes et al. 1999). It will be a critical test to see if\nthe distortion signature can be picked up in each type\nindividually. Although the large-scale behaviour of each\ngalaxy type will probably be quite similar, differences in\nthe clustering properties will inevitably arise on smaller\nscales, giving important information about\nthe sequence of galaxy formation.\n\n\n\\sec{Small-scale clustering}\n\n\\ssec{History}\n\nOne of the earliest models to be used to interpret the\ngalaxy correlation function was to consider a density\nfield composed of randomly-placed independent clumps\nwith some universal density profile (Neyman, Scott \\& Shane 1953; Peebles 1974).\nSince the clumps are placed at random, the only correlations\narise from points in the same clump.\nThe correlations are easily deduced by using statistical\nisotropy: calculate the excess number of pairs separated\nby a distance $r$ in the $z$ direction (chosen as some arbitrary\npolar axis in a spherically-symmetric clump).\nFor power-law clumps, with $\\rho= n B r^{-\\epsilon}$, truncated at\n$r=R$, this model gives $\\xi\\propto r^{3-2\\epsilon}$\nin the limit $r\\ll R$, provided $3/2 < \\epsilon <3$.\nValues $\\epsilon >3$ are unphysical, and\nrequire a small-scale cutoff to the profile. There is no such objection\nto $\\epsilon < 3/2$, and the expression for $\\xi$ tends to a\nconstant for small $r$ in this case (see Yano \\& Gouda 1999).\n\nA long-standing problem for this model is that the\ncorrelation function in this case is much flatter than is\nobserved for galaxies: $\\xi \\propto r^{-1.8}$ is the\ncanonical slope, requiring $\\epsilon=2.4$.\nThe first reaction may be to say that the\nmodel is incredibly naive by comparison with our\nsophisticated present understanding of the nonlinear\nevolution of CDM density fields. However, as will\nbe shown below, it may after all contain more than a grain of\ntruth.\n\n\n\\ssec{The CDM clustering problems}\n\nA number of authors have pointed out that the detailed\nspectral shape inferred from galaxy data \nappears to be inconsistent with that of nonlinear\nevolution from CDM initial conditions.\n(e.g. Efstathiou, Sutherland \\& Maddox 1990;\nKlypin, Primack \\& Holtzman 1996; Peacock 1997).\nPerhaps the most detailed work was carried out by the\nVIRGO consortium, who carried out $N=256^3$ simulations of\na number of CDM models (Jenkins et al. 1998). Their results\nare shown in figure 9, which gives the nonlinear power\nspectrum at various times (cluster normalization is chosen\nfor $z=0$) and contrasts this with the APM data.\nThe lower small panels are the scale-dependent bias\nthat would required if the model did in fact describe the real universe,\ndefined as\n$$\nb(k)\\equiv \\left({\\Delta^2_{\\rm gals}(k)\\over\\Delta^2_{\\rm mass}}\\right)^{1/2}.\n$$\nIn all cases, the required bias is non-monotonic; it rises at\n$k\\gs 5\\mpcoh$, but also displays a bump around\n$k\\simeq 0.1\\mpcoh$.\nIf real, this feature seems impossible to understand as a\ngenuine feature of the mass power spectrum; certainly, it is not at\na scale where the effects of even a large baryon fraction\nwould be expected to act (Eisenstein et al. 1998; Meiksin, White\n\\& Peacock 1999).\n\n\\japfig{20}{75}{525}{700}{japfig9.eps}\n{The nonlinear evolution of various CDM\npower spectra, as determined by the Virgo\nconsortium (Jenkins et al. 1998).}\n\n\n\n\\sec{Bias}\n\nThe conclusions from the above discussion are either that\nthe physics of dark matter and structure formation are\nmore complex than in CDM models, or that the relation\nbetween galaxies and the overall matter distribution\nis sufficiently complicated that the effective bias is\nnot a simple slowly-varying monotonic function of position.\n\n\\ssec{Simple bias models}\n\nThe simplest assumption is that all the complicated physical effects \nleading to galaxy formation depend in a causal (but nonlinear) way on the\nlocal mass density, so that we write\n$$\n\\rho_{\\rm light}=f(\\rho_{\\rm mass}).\n$$\nColes (1993) showed that, under rather general assumptions, this\nequation would lead to an effective bias that was a monotonic\nfunction of scale. This issue was investigated in some detail\nby Mann, Peacock \\& Heavens (1998), who verified Coles'\nconclusion in practice for simple few-parameter forms for\n$f$, and found in all cases that the effective bias varied\nrather weakly with scale. The APM results thus are either inconsistent\nwith a CDM universe, or require non-local bias.\n\n\\japfig{0}{0}{484}{472}{japfig10.eps}\n{The projected correlation function from the\nLCRS fails to match CDM models when comparison is made to\njust the mass distribution. However, the agreement\nis excellent when allowance is made for a small\ndegree of scale-dependent antibias; galaxy formation\nis suppressed in the most massive haloes\n(Jing, Mo \\& B\\\"orner 1998).}\n\nA puzzle with regard to this conclusion is provided\nby the work of Jing, Mo \\& B\\\"orner (1998). They\nevaluated the projected real-space correlations\nfor the LCRS survey (see figure 10). This statistic also\nfails to match the prediction of CDM models, but this\ncan be amended by introducing a simple {\\it antibias\\/}\nscheme, in which galaxy formation is suppressed in the\nmost massive haloes. This scheme should in practice\nbe very similar to the Mann, Peacock \\& Heavens recipe\nof a simple weighting of particles as a function of the\nlocal density; indeed, the main effect is a change of\namplitude, rather than shape of the correlations.\nThe puzzle is this: if the APM power spectrum is used\nto predict the projected correlation function, the\nresult agrees almost exactly with the LCRS. Either\nprojected correlations are a rather\ninsensitive statistic, or perhaps the Baugh \\& Efstathiou\ndeconvolution procedure used to get $P(k)$ has\nexaggerated the significance of features in the spectrum.\nThe LCRS results are one reason for treating the apparent conflict \nbetween APM and CDM with caution.\n\n\n\\ssec{Halo correlations}\n\nIn reality, bias is unlikely to be completely causal,\nand this has led some workers to explore stochastic bias\nmodels, in which\n$$\n\\rho_{\\rm light}=f(\\rho_{\\rm mass}) + \\epsilon,\n$$\nwhere $\\epsilon$ is a random field that is uncorrelated with the\nmass density (Pen 1998; Dekel \\& Lahav 1999).\nAlthough truly stochastic effects are possible in galaxy formation,\na relation of the above form is expected when the\ngalaxy and mass densities are filtered on some scale\n(as they always are, in practice). Just averaging a \ngalaxy density that is a nonlinear\nfunction of the mass will lead to some scatter when comparing with the\naveraged mass field; a scatter will also arise when the\nrelation between mass and light is non-local, however, and this\nmay be the dominant effect.\n\nThe simplest and most important example of non-locality\nin the galaxy-formation process is to recognize that\ngalaxies will generally form where there are galaxy-scale\nhaloes of dark matter. In the past, it was\ngenerally believed that dissipative processes were\ncritically involved in galaxy formation, since pure\ncollisionless evolution would lead to the destruction\nof galaxy-scale haloes when they are absorbed into the\ncreation of a larger-scale nonlinear system such as a group\nor cluster. However, it turns out that this\n{\\it overmerging problem\\/} was only an artefact of\ninadequate resolution. When a simulation is carried out\nwith $\\sim 10^6$ particles in a rich cluster, the cores of\ngalaxy-scale haloes can still be identified after many crossing\ntimes (Ghigna et al. 1997). Furthermore, if catalogues of\nthese `sub-haloes' are created within a cosmological-sized\nsimulation, their correlation function is quite different from that\nof the mass, resembling the single power law seen in galaxies \n(e.g. Klypin et al. 1999; Ma 1999).\n\n\nThese are very important results, and they\nhold out the hope that many of the issues concerning\nwhere galaxies form in the cosmic density field can be settled\nwithin the domain of collisionless simulations. \nDissipative physics will still be needed to understand in\ndetail the star-formation history within a galaxy-scale\nhalo. Nevertheless, the idea that there may be a one-to-one correspondence\nbetween galaxies and galaxy-scale dark-matter haloes\nis clearly an enormous simplification -- and one that increases\nthe chance of making robust predictions of the statistical\nproperties of the galaxy population.\n\n\n\n\\ssec{Numerical galaxy formation}\n\nThe formation of galaxies must be a non-local process to\nsome extent. The modern paradigm was introduced by White \\& Rees (1978):\ngalaxies form through the cooling of baryonic material in\nvirialized haloes of dark matter. The virial radii of these\nsystems are in excess of 0.1~Mpc, so there is the potential\nfor large differences in the correlation properties of\ngalaxies and dark matter on these scales.\n\n\\japfig{18}{144}{574}{701}{japfig11.eps}\n{The correlation function of galaxies in the\nsemianalytical simulation of an LCDM\nuniverse by Benson et al. (1999).}\n\nA number of studies have indicated that the observed\ngalaxy correlations may indeed be reproduced by CDM models.\nThe most direct approach is a numerical simulation that\nincludes gas, and relevant dissipative processes.\nThis is challenging, but just starting to be feasible with\ncurrent computing power (Pearce et al. 1999). The alternative\nis `semianalytic' modelling, in which the merging history\nof dark-matter haloes is treated via the extended Press-Schechter\ntheory (Bond et al. 1991), and the location of galaxies within\nhaloes is estimated using dynamical-friction arguments\n(e.g. Cole et al. 1996; Kauffmann et al. 1996; \nSomerville \\& Primack 1997). Both these approaches\nhave yielded similar conclusions, and shown how CDM models\ncan match the galaxy data: specifically, the low-density\nflat $\\Lambda$CDM model that is favoured on other\ngrounds can yield a correlation function that is close to a\nsingle power law over $1000 \\gs \\xi \\gs 1$, even though the\nmass correlations show a marked curvature over this range\n(Pearce et al. 1999; Benson et al. 1999; see figure 11).\nThese results are impressive, yet it is frustrating to have a result\nof such fundamental importance emerge from a complicated\ncalculational apparatus. \nThere is thus some motivation for constructing a simpler\nheuristic model that captures the main processes at work in\nthe full semianalytic models. The following section\ndescribes an approach of this sort (Peacock \\& Smith,\nin preparation).\n\n\n\\ssec{Halo-ology and bias}\n\nWe mentioned above the early model of Neyman, Scott \\& Shane (1953),\nin which the nonlinear density field was taken to be a superposition\nof randomly-placed clumps. With our present knowledge\nabout the evolution of CDM universes, we can\nmake this idealised model considerably more realistic:\nhierarchical models are expected to\ncontain a distribution of masses of clumps, which\nhave density profiles that are more complicated than\nisothermal spheres. These issues are well\nstudied in $N$-body simulations, and highly accurate\nfitting formulae exist, both for the mass function and\nfor the density profiles. \nBriefly, we use the mass function of\nSheth \\& Tormen (1999; ST) and the halo profiles\nof Moore et al. (1999; M99).\n$$\n\\eqalign{\nf(\\nu) &= 0.21617[ 1 + (\\sqrt{2}/\\nu^2)^{0.3} ] \\exp[-\\nu^2/(2\\sqrt{2})] \\cr\n\\Rightarrow F(>\\nu) &= 0.32218[1-\\erf(\\nu/2^{3/4})] \\cr\n& + 0.14765 \\Gamma[0.2, \\nu^2/(2\\sqrt{2})], \\cr\n}\n$$\nwhere $\\Gamma$ is the incomplete gamma function. \n\nRecently, it has been claimed by Moore et al. (1999; M99) that the\ncommonly-adopted density profile of Navarro, Frenk \\& White\n(1996; NFW) is in error at small $r$. M99 proposed the\nalternative form\n$$\n\\rho/\\rho_b = {\\Delta_c \\over y^{3/2} (1+y^{3/2}) }; \\quad (r<r_{\\rm vir}); \\quad y\\equiv r/r_c.\n$$\nUsing this model,\nit is then possible to calculate the correlations\nof the nonlinear density field, neglecting only the\nlarge-scale correlations in halo positions. The\npower spectrum determined in this way is shown in figure 12,\nand turns out to agree very well with the\nexact nonlinear result on small and intermediate scales.\nThe lesson here is that a good deal of the\nnonlinear correlations of the dark matter field\ncan be understood as a distribution of random clumps,\nprovided these are given the correct distribution of\nmasses and mass-dependent density profiles.\n\n\n\\japfig{57}{211}{515}{588}{japfig12.eps}\n{The power spectrum for the $\\Lambda$CDM model.\nThe solid lines contrast the linear spectrum\nwith the nonlinear spectrum, calculated according to\nthe approximation of PD96. The spectrum according\nto randomly-placed haloes is denoted by open circles;\nif the linear power spectrum is added, the main\nfeatures of the nonlinear spectrum are well reproduced.}\n\nHow can we extend this model to understand how the\nclustering of galaxies can differ from that of the mass?\nThere are two distinct ways in which a degree of bias is inevitable:\n\n\\japitem{(1)} Halo occupation numbers. For low-mass haloes, the\nprobability of obtaining an $L^*$ galaxy must fall to zero.\nFor haloes with mass above this lower limit, the number of\ngalaxies will in general not scale with halo mass.\n\n\\japitem{(2)} Nonlocality. Galaxies can orbit within their\nhost haloes, so the probability of forming a galaxy depends\non the overall halo properties, not just the density at a point.\nAlso, the galaxies will end up at special places within\nthe haloes: for a halo containing only one galaxy, the\ngalaxy will clearly mark the halo centre. In general,\nwe expect one central galaxy and a number of satellites.\n\n\nThe numbers of galaxies that form in a halo of a\ngiven mass is the prime quantity that numerical models\nof galaxy formation aim to calculate.\nHowever, for a given assumed background cosmology, the\nanswer may be determined empirically.\nGalaxy redshift surveys have been analyzed via grouping\nalgorithms similar to the `friends-of-friends' method\nwidely employed to find virialized clumps in $N$-body\nsimulations. With an appropriate correction for the\nsurvey limiting magnitude, the observed number of galaxies in\na group can be converted to an estimate of the total\nstellar luminosity in a group. This allows a\ndetermination of the All Galaxy System (AGS)\nluminosity function: the distribution of virialized\nclumps of galaxies as a function of their total\nluminosity, from small systems like the Local Group to\nrich Abell clusters.\n\n\\japfig{57}{211}{515}{588}{japfig13.eps}\n{The empirical luminosity--mass relation\nrequired to reconcile the observed AGS luminosity function\nwith two variants of CDM. $L^*$ is the characteristic\nluminosity in the AGS luminosity function\n($L^* = 7.6\\times 10^{10}h^{-2} L_\\odot$).\nNote the rather flat slope around\n$M=10^{13}$ to $10^{14}h^{-1}M_\\odot$,\nespecially for $\\Lambda$CDM.}\n\n\nThe AGS function for the CfA survey was investigated by\nMoore, Frenk \\& White (1993), who found that the\nresult in blue light was well described by\n$$\nd\\phi = \\phi^*\\, \\left[ (L/L^*)^\\beta + (L/L^*)^\\gamma \\right]^{-1}\\;\ndL/L^*,\n$$\nwhere $\\phi^*=0.00126h^3\\rm Mpc^{-3}$, $\\beta=1.34$, $\\gamma=2.89$;\nthe characteristic luminosity is $M^*=-21.42 + 5\\log_{10}h$ in\nZwicky magnitudes, corresponding to $M_B^*=-21.71 + 5\\log_{10}h$,\nor $L^* = 7.6\\times 10^{10}h^{-2} L_\\odot$, assuming\n$M_B^\\odot=5.48$.\nOne notable feature of this function is that it is\nrather flat at low luminosities, in contrast to the\nmass function of dark-matter haloes (see Sheth \\& Tormen 1999).\nIt is therefore clear that any fictitious galaxy catalogue\ngenerated by randomly sampling the mass is unlikely to be a\ngood match to observation.\nThe simplest cure for this deficiency is to assume that the\nstellar luminosity per virialized halo is a monotonic, but nonlinear,\nfunction of halo mass. The required luminosity--mass\nrelation is then easily deduced by finding the luminosity\nat which the integrated AGS density $\\Phi(>L)$ matches the\nintegrated number density of haloes with mass $>M$.\nThe result is shown in figure 13.\n\nWe can now return to the halo-based galaxy power spectrum\nand use the correct occupation number, $N$, as a function of \nmass. This is needs a little care at small numbers,\nhowever, since the number of haloes with occupation number unity\naffects the correlation properties strongly. These\nhaloes contribute no correlated pairs, so they simply\ndilute the signal from the haloes with $N\\ge 2$. The existence\nof antibias on intermediate scales can probably be traced to\nthe fact that a large fraction of galaxy groups contain only\none $>L_*$ galaxy. Finally, we need to put the\ngalaxies in the correct location, as discussed above.\nIf one galaxy always occupies the halo centre, with others\nacting as satellites, the small-scale correlations automatically\nfollow the slope of the halo density profile, which keeps them\nsteep. The results of this exercise are shown in figure 14.\n\n\\japfig{57}{211}{515}{588}{japfig14.eps}\n{The power spectrum for a galaxy catalogue constructed from\nthe $\\Lambda$CDM model. A reasonable\nagreement with the APM data (solid line) is achieved by\nsimple empirical adjustment of the occupation number\nof galaxies as a function of halo mass, plus a\nscheme for placing the haloes non-randomly within the haloes.}\n\n\nAlthough it is encouraging that it is possible to find simple models in which\nit is possible to understand the observed correlation properties of galaxies, \nthere are other longstanding puzzles concerning the galaxy distribution.\nArguably the chief of these concerns the dynamical properties\nof galaxies, in particular the pairwise peculiar velocity dispersion. \nThis statistic has been the subject of debate, and preferred\nvalues have crept up in recent years, to perhaps 450 or $500 \\kms$\nat projected separations around 1~Mpc (e.g. Jing, Mo \\& B\\\"orner 1998),\nmost simple models predict a higher figure.\nClearly, the amplitude of peculiar velocities depends on the\nnormalization of the fluctuation spectrum; however, if this\nis set from the abundance of rich clusters, then Jenkins et al. (1998)\nfound that reasonable values were predicted for large-scale\nstreaming velocities, independent of $\\Omega$. However,\nJenkins et al. also found a robust prediction for the pairwise peculiar velocity dispersion\naround 1~Mpc of about $800\\kms$. The observed galaxy velocity\nfield appears to have a higher `cosmic Mach number' than the\npredicted dark-matter distribution.\n\nThis difficulty is also solved by the simple bias model\ndiscussed here. Two factors contribute: the variation of\noccupation number with mass downweights the contribution of more\nmassive groups, with larger velocity dispersions.\nAlso, where one galaxy is centred on a halo, it gains\na peculiar velocity which is that of the centre of mass of\nthe halo, but does not reflect the internal velocity dispersion\nof the halo. \nGiven a full $N$-body simulation, it is easy enough to predict what\nwould be expected for a realistic bias model: one needs to\nconstruct a halo catalogue, calculating the peculiar velocities\nand internal velocity dispersions of each halo. Knowing the\noccupation number as a function of mass, a montecarlo catalogue\nof `galaxies' complete with peculiar velocities can be generated.\nAs shown in figure 15, the effect of the empirical bias recipe\nadvocated here is sufficient\nto reduce the predicted dispersion into agreement with observation.\nThe simple model outlined here thus gives a consistent picture,\nand it is tempting to believe that it may capture some of the\nmain features of realistic models for galaxy bias.\n\n\\japfig{57}{211}{515}{588}{japfig15.eps}\n{The line-of-sight pairwise velocity dispersion for the $\\Lambda$CDM model.\nThe top curve shows the results for all the mass; the lower pair\nof curves shows the predicted galaxy results, with and without \nassuming that one galaxy occupies the halo centre (the former case gives\nthe lowest curve).}\n\n\n\\sec{Conclusions}\n\nIt should be clear from these lectures that large-scale structure has \nadvanced enormously as a field in the past two decades.\nMany of our long-standing ambitions have been realised;\nin some cases, much faster than we might have expected.\nOf course, solutions for old problems generate new difficulties.\nWe now have good measurements of the clustering\nspectrum and its evolution, and it is arguable that the\ndiscussion of section 7.4 captures the main features of the\nplacement of galaxies with respect to the mass.\nHowever, a fairly safe bet is that one of the\nmajor results from new large surveys such as 2dF and\nSloan will be a heightened appreciation of the subtleties\nof this problem.\n\nNevertheless, we should not be depressed if problems\nremain. Observationally, we are moving from an era of\n20\\% -- 50\\% accuracy in measures of large-scale\nstructure to a future of pinpoint precision. This\nmaturing of the subject will demand more careful\nanalysis and rejection of some of our existing tools\nand habits of working. The prize for rising to this\nchallenge will be the ability to claim a real understanding\nof the development of structure in the universe. We are\nnot there yet, but there is a real prospect that the next\n5--10 years may see this remarkable goal achieved.\n\n\n\\section*{Acknowledgements}\n\nI thank my colleagues in the 2dF Galaxy Redshift Survey\nfor permission to reproduce our joint results in section\n5.3, and Robert Smith for the joint work reported\nin section 7.4.\n\n\n\\section*{References}\n\n\\japref Ballinger W.E., Peacock J.A., Heavens A.F., 1996, MNRAS, 282, 877\n\\japref Baugh C.M., Efstathiou G., 1993, MNRAS, 265, 145\n\\japref Baugh C.M., Efstathiou G., 1994, MNRAS, 267, 323\n\\japref Benson A.J., Cole S., Frenk C.S., Baugh C.M., Lacey C.G., 1999, astro-ph/9903343\n\\japref Bond J.R., Cole S., Efstathiou G., Kaiser N., 1991, \\apj, 379, 440\n\\japref Bond J.R., 1995, \\prl, 74, 4369\n\\japref Bunn E.F., 1995, PhD thesis, Univ. of California, Berkeley\n\\japref Coles P., {1993}, {MNRAS}, {262}, {1065}\n\\japref Colless M., 1999, Phil. Trans. R. Soc. Lond. 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An extended multi-zone model for the MCG$-$6-30-15 warm absorber
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"author": "\\parbox[]{6.in} {R. Morales$^1$, A.C.~Fabian$^1$ and C.S. Reynolds$^2$"
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"author": "}"
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The variable warm absorber seen with {\em ASCA} in the X-ray spectrum of MCG$-$6-30-15 shows complex time behaviour in which the optical depth of OVIII anticorrelates with the flux whereas that of OVII is unchanging. The explanation in terms of a two zone absorber has since been challenged by {\em BeppoSAX} observations. These present a more complicated behaviour for the OVIII edge. We demonstrate here that the presence of a third, intermediate, zone can explain all the observations. In practice, warm absorbers are likely to be extended, multi-zone regions of which only part causes directly observable absorption edges at any given time.
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Morales$^1$, A.C.~Fabian$^1$ and C.S. Reynolds$^2$ \\\\\n\\footnotesize\n1. Institute of Astronomy, Madingley Road, Cambridge CB3 0HA \\\\\n2. JILA, University of Colorado, Campus Box 440, Boulder, CO\n80309-0440 USA\\\\ }} \n\\maketitle\n\n\\begin{abstract} \n The variable warm absorber seen with {\\em ASCA} in the X-ray\n spectrum of MCG$-$6-30-15 shows complex time behaviour in which the\n optical depth of OVIII anticorrelates with the flux whereas that of\n OVII is unchanging. The explanation in terms of a two zone absorber\n has since been challenged by {\\em BeppoSAX} observations. These\n present a more complicated behaviour for the OVIII edge. We\n demonstrate here that the presence of a third, intermediate, zone\n can explain all the observations. In practice, warm absorbers are\n likely to be extended, multi-zone regions of which only part causes\n directly observable absorption edges at any given time.\n\\end{abstract}\n\n\\begin{keywords} galaxies: active $-$ galaxies: individual:\n MCG$-$6-30-15 $-$ galaxies: Seyfert $-$ X-rays: galaxies.\n\\end{keywords}\n\n\\section{INTRODUCTION} \n\nX-ray absorption by partially ionized, optically thin material, along\nthe line of sight of the central engine, the so called {\\em warm\n absorber}, is one of the prominent features in the X-ray spectrum of\nmany AGN \\cite{reyno97}. The presence of such gas was first postulated\nin order to explain the unusual form of the X-ray spectrum of QSO MR\n2251-178 \\cite{hal84}. A direct confirmation of the existence of\ncircumnuclear ionized matter came from {\\em ASCA}, which for the first\ntime was able to resolve the OVII and OVIII absorption edges (at rest\nenergies of 0.74 and 0.87 \\keV, respectively) in the X-ray spectra of\nthe Seyfert 1 galaxy MCG$-$6-30-15 \\cite{fab94}. Systematic studies of\nwarm absorbers in Seyfert 1 galaxies with {\\em ASCA} have shown their\nubiquity, being detected in half of the sources \\cite{reyno97}.\n\nWarm absorbers were usually described by single zone, photoionization\nequilibrium models. Under this assumption, simple variability patterns\nwere expected: increasing ionization of the matter when the source\nbrightens. This was not found by Otani et al. \\shortcite{ota96} during\ntheir long-look {\\em ASCA} observation of the nearby (z=0.008) Seyfert\n1 galaxy MCG$-$6-30-15. The source varied with large amplitude on\nshort time scales ($10^4$ s or so). The depth of the OVII edge, on the\ncontrary, stayed almost constant, while that of the OVIII edge was\nanticorrelated with the flux. To explain the behaviour of the OVII and\nOVIII edges, the authors adopted a multizone model in which the OVII\nand OVIII edges originate from spatially distinct regions. OVII ions\nin the region responsible for the OVII edge, the outer absorber, have\na long recombination timescale (i.e. weeks or more), whereas the OVIII\nedge arises from more highly ionized material, the inner absorber, in\nwhich most oxygen is fully stripped. The recombination timescale for\nthe OIX ions in the inner absorber is of the order of $10^4 s$ or\nless. A decrease in the primary ionizing flux is then accompanied by\nthe recombination of OIX to OVIII, giving the observed variation in\nthe OVIII edge depth.\n\nOrr et al. \\shortcite{orr97} raised the possibility of a more complex\nwarm absorber. During their MCG$-$6-30-15 {\\em BeppoSAX} observation\nthe depth of the OVII edge was marginally consistent with being\nconstant, whereas the optical depth for OVIII, $\\tau(OVIII)$,\nexhibited significant variability. The authors claimed that its large\nvalue during epoch 1\\footnote{The epochs in the {\\em BeppoSAX}\n observation are chronologically numerated (i.e. number 1 corresponds\n to the first epoch of the observation, etc.).} ($1.7\\pm0.5$,\n$1\\sigma$ uncertainty) was inconsistent with the values at all other\nepochs. They also pointed out that the value of $\\tau(OVIII)$ during\nepoch 5 (a low luminosity state) did not show the expected\nanticorrelaction with the ionizing flux .\n\nIn both Otani et al. \\shortcite{ota96} and Orr et\nal.\\shortcite{orr97}, $\\tau(OVIII)$ was plotted versus count rate. In\norder to compare {\\em ASCA} and {\\em BeppoSAX} observations, these two\nobservational results for $\\tau(OVIII)$ have been plotted versus\nluminosity\\footnote{The conversion from count rate to luminosity has\n been obtained using $H_o=50$ \\kmpspMpc, $q_0=0$ and PIMMS\n (http://heasarc.gsfc.nasa.gov/Tools/w3pimms.html).} in 0.1-10 \\keV\nin figure 1 (instead of versus count rate). The conversion from count\nrate to luminosity is different for each apparatus and therefore, the\ncomparison can not be made using count rate, but luminosity.\n\\begin{figure}\n\\centerline{\\psfig{figure=fig1.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Comparison {\\em ASCA} (square) - {\\em BeppoSAX} (circle)\n observational results for the optical depth of OVIII, $\\tau(OVIII)$,\n versus luminosity in 0.1-10 \\keV. Note the only discrepant point in\n the {\\em BeppoSAX} observation labelled as 1 and the very good\n agreement for point 5.}\n\\end{figure}\nThe only discrepancy between both sets of data is the result for epoch\n1 (labelled 1 in figure 1)\\footnote{This epoch was at the very\n beginning of the {\\em BeppoSAX} observation. In a private\n communication, A. Orr notes that this high value for the\n optical depth for OVIII could not be due to instrumental effects,\n since no similar behaviour, neither at the beginning nor during the\n observation has been observed in any other {\\em BeppoSAX} target\n yet.}. Note also that there is no disagreement at all with any other\npoint (Orr et al. mentioned epoch 5 as problematic, but in this plot\nit appears consistent with the rest of the\nOtani et al. data).\n\nIn this paper we present a simple photoionization model that accounts\nfor the experimental results of both {\\em ASCA} and {\\em BeppoSAX}\nobservations. Section 2 describes the code used to model the inner\nwarm absorber. The application to the MCG$-$6-30-15 warm absorber is\npresented in Section 3. The extension of the multi-zone model for the\nwarm absorber (i. e. the third component) is addressed in Section\n4. Finally our conclusions are discussed in Section 5.\n\n\\section{TIME DEPENDENT PHOTOIONIZATION CODE}\n\nIn order to reproduce both {\\em ASCA} and {\\em BeppoSAX} observations,\nthe state of the inner absorber has been modelled using a time\ndependent photoionization code for oxygen \\cite{rey96}. This code treats the\nmaterial in the inner absorber as containing only ions of oxygen in an\notherwise completely ionized hydrogen plasma. A given oxygen ion is\nassumed to be in one of the 9 states corresponding to its ionization\nlevel. Different excitation levels of a given ionization state are not\ntreated. The total abundance of oxygen is fixed at $7.41\\times\n10^{-4}$\\cite{gre89} relative to hydrogen. Both ions and electrons are\nassumed to be in local thermal equilibrium (LTE) with a common\ntemperature T and the plasma is assumed to be strictly optically-thin\nat all frequencies (i.e. radiative transfer processes are not\nconsidered).\n\nA point source of ionizing radiation is placed at a distance $R$ from\nthis material with a frequency dependent luminosity $L_{\\nu}$ (total\nluminosity $L$). In the calculations presented here, the ionizing\ncontinuum is taken to be a power-law with a photon index $\\Gamma=2$\nextending from $\\nu_{min}$ to $\\nu_{max}$: i.e. we take\n\n\\begin{equation}\nL_{\\nu}=\\frac{L}{\\Lambda\\nu}\n\\end{equation}\nwhere $\\Lambda=\\ln(\\nu_{max}/\n\\nu_{min})$. The upper and lower cutoff frequencies are chosen such\nthat $h\\nu_{max}=100$ \\keV, and $\\Lambda=10$, corresponding to\n$h\\nu_{min}\\approx4.5$ \\eV.\n\nThe physical processes included in the code are: photoionization,\nAuger ionization, collisional ionization, radiative recombination,\ndielectronic recombination, bremsstrahlung, Compton scattering and\ncollisionally-excited O$\\lambda$1035 resonance line cooling. Given\nthese processes, the ionization and thermal structure of the plasma is\nevolved from an initial state assumed to have a temperature of\n$T=10^5$ \\K, and equal ionization fractions in each state.\n\nThe ionization structure of the oxygen is governed by 9 equations of\nthe form:\n\\begin{equation}\n\\frac{dn_i}{dt}=\\sum_{prod.}\\delta_{prod.}-\\sum_{dest.}\\delta_{dest.}\n\\end{equation}\nwhere $n_i$ is the number density of state-i, $\\delta$ stands for the\nionization/recombination rate per unit volume, the first summation on\nthe right hand side (RHS) is over all ionization and recombination\nmechanisms that produce state-i and the second summation is over all\nsuch mechanisms that destroy state-i.\n\nThe thermal evolution of the plasma is determined by the local\nheating/cooling rate and the macroscopic constraint. The net heating\nrate per unit volume is given by:\n\\begin{equation}\n\\frac{dQ}{dt}=\\sum_{heat}\\Delta_{heat}-\\sum_{cool}\\Delta_{cool}\n\\end{equation}\nwhere $\\Delta$ stands for the heating/cooling rate per unit volume,\nthe first summation on the RHS is over all heating processes and the\nsecond term is over all cooling processes. For a {\\em constant\n density} plasma, we have $du=dQ$ where $u$ is the internal energy\nper unit volume and is given by:\n\\begin{equation} \nu=\\frac{3}{2}n_ek_BT.\n\\end{equation}\nThus, the rate of change of temperature is related to the\nheating/cooling rate via:\n\\begin{equation}\n\\frac{dT}{dt}=\\frac{2}{3n_ek_B}\\frac{dQ}{dt}.\n\\end{equation}\n\nThe state of the plasma is evolved using the ionization equations\nrepresented by (2) and the energy equation (3). A simple step-by-step\nintegration of these differential equation is performed. The time step\nfor the integration process is allowed to dynamically change and is\nset to be $0.1\\times t_{sh}$ where $t_{sh}$ is the shortest relevant\ntimescale\\footnote{At each step the ionization, collisional and\n recombination timescales of each oxygen ionization state is\n calculated. The shortest of these timescales is taken to be\n $t_{sh}$.}. In the case of a constant ionizing luminosity, it is\nfound that the system always evolves to an equilibrium state, as\nexpected.\n\nThe model has been compared against the photoionization code {\\sc\n cloudy}\\cite{ferla96} (version 9004, \\cite{ferl98}) in the case of a\nplasma in photoionization equilibrium. Figures 2 and 3 report this\ncomparison.There is a qualitative agreement between the model (solid\nline) and {\\sc cloudy} (dashed line) in figure 2 for the case of a\npure hydrogen/oxygen plasma. The main goal of this paper is to\nreproduce the time variability of the oxygen edges, and, this figure\nshows how our model mirrors quite well the behavior of this element.\n{\\sc cloudy} includes many more physical processes and realistic\nelemental abundances and, as seen in\nfigure 3, the agreement is not so good when more elements are\nconsidered\\footnote{Realistic elemental abundances can be important\n both for the ionization structure and for the heating/cooling rate\n of the plasma, and since features of the\n stability curve result from peaks in the heating and cooling\n functions (which are in turn associated with particular ionic\n species), the comparison presented in figure 2 is expected to present\n a much better agreement. The consideration of realistic abundances\n is beyond the scope of this paper and is currently being studied.}.\n\\begin{figure}\n\\centerline{\\psfig{figure=fig2.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Comparison of the model (solid curve) with {\\sc cloudy}\n(dashed line) of a pure hydrogen/oxygen plasma.} \n\\end{figure}\n\\begin{figure}\n\\centerline{\\psfig{figure=fig3.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Comparison of the model (solid curve) with {\\sc cloudy}\n(dashed line).}\n\\end{figure}\nWe have also investigated the reaction of a constant density plasma to\nan inverted top hat function for the light-curve (i.e. initially\n$T=10^5$ \\K, equal ionization fractions in each state, the luminosity\nis $L=3\\times10^{43}$ \\ergps and held constant. The system is allowed\nto achieve an equilibrium at an ionization parameter\n$\\xi=\\frac{L}{nR^2}=75$ \\ergcmps, where $n$ is the density of the warm\nplasma and $R$ is the distance of the slab of the plasma from the\nionizing source of radiation with isotropic ionizing luminosity $L$.\nThe luminosity is then halved for a short period, $\\Delta t$, and then\nback to its initial value) . During these changes, the state of the\nplasma is recorded as a function of time. This choice of $\\xi$ places\nthe inner warm absorber a region where $f_{O8}\\propto L^{-1}$ (i.e. in\nthis regime $f_{O8}$ is expected to be inversely proportional to $\\xi$\nor equivalently to $L$). The investigation has been carried out for\ndifferent values of $n$ and $R$ keeping $n>2\\times10^7$ \\pcmcu and\n$R<1.4\\times10^{17}$ \\cm (i.e. the constraints given by Otani et\nal.\\shortcite{ota96} for the inner warm absorber). Fig. 4 shows an\nexample of the results obtained. As expected, $f_{O8}$ increases when\n$L$ is halved, showing a more noticeable increment when $L$ is halved\nover a longer period.\n\\begin{figure}\n\\centerline{\\psfig{figure=fig4.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Time behaviour of the ionization fraction for OVIII,\n $f_{O8}$, for different light-curves. The plasma has ionization\n parameter $\\xi=75$ \\ergcmps for luminosity $L=3\\times10^{43}$\n \\ergps, electron density $n_e=3\\times10^7$ \\pcmcu and it is situated\n at $1.15\\times10^{17}$ \\cm from the ionizing source. The luminosity\n $L$ is halved over an interval $\\Delta t$ equal to: 450(dashed\n line), 1350(solid line), 4500(dot line) and 13500(dot-dot-dot-dashed\n line) seconds. The corresponding ionization fraction, $f_{O8}$, is\n plotted below.}\n\\end{figure}\n\n\\section{APPLICATION TO THE MCG$-$6-30-15 WARM ABSORBER}\n\nTo reproduce the observational data using our model, it is required to\nobtain the value of the optical depth for OVIII once the ionization\nfraction $f_{O8}$ has been calculated by the code. Considering the\ncross section for OVIII, $\\sigma_8$, as constant along the\nline-of-sight and using the fact that the material contains only ions\nof oxygen in an otherwise completely ionized plasma, the optical depth\nfor OVIII, $\\tau(OVIII)$, can be written as:\n\\begin{equation}\n\\tau(OVIII)=\\frac{\\sigma_8f_{O8}\\Delta R n_e}{\\frac{1}{Abun}+\\sum\n\\limits_{i=1}^9 f_{Oi}\\times (i-1)}\n\\end{equation}\nwhere $\\sigma_8=10^{-19} cm^2$\n\\cite{ost89}, $\\Delta R$ is the line-of-sight\ndistance through the ionized plasma, $n_e$ is the electron density,\n$Abun$ is the oxygen abundance relative to hydrogen\\cite{gre89} and\n$f_{Oi}$ is the ionization fraction for i ionization species for oxygen.\n\nThe light-curve used to reproduced the {\\em ASCA} observation is given\nby Otani et al. \\shortcite{ota96}. For the {\\em BeppoSAX} observation,\nthe light-curve has been defined as a step function with a constant\nvalue for the luminosity $L$ over the different time periods given by\nOrr et al. \\shortcite{orr97}. The constant value for $L$ over each\nperiod is chosen to be that given in Orr et al. (1997, Fig.\n3)\\nocite{orr97} plus a period of $2\\times 10^4$ \\s previous to epoch\n1 with $L=1.8\\times10^{43}$ \\ergps (a standard value for the\nluminosity during the observation). Different parameters for the warm\nabsorber have been investigated using the constraints given by Otani\net al. \\shortcite{ota96}. With the only exception of point 1 (see\nfigure 1), a general good agreement for all other experimental points\nis found.\n\nFollowing a suggestion by Orr et al. \\shortcite{orr97}, we have\nmodified the light-curve for the {\\em BeppoSAX} observation including\na previous epoch to it for which the luminosity is much lower (the\nrange of values used is $10^{40}-10^{43}$ \\ergps)\\footnote{An example\n of a Seyfert 1 galaxy exhibiting an unusual low flux state (a\n decrease of more than one order of magnitude in luminosity) is\n presented in Uttley et al. \\shortcite{utt99}.}. The reason for using\nthis very low value for the luminosity is that in a regime for which\n$f_{O8}\\propto L^{-1}$, the highest values $f_{O8}$ are expected for\nlow values of $L$. However, the suggested explanation does not\nreproduce the high value of $\\tau (OVIII)$ for epoch 1 in the {\\em\n BeppoSAX} observation. Even for those values of $\\xi$ that give a\nmaximum for $f_{O8}$ (i.e. $\\xi\\approx 50$ \\ergcmps), the ionization\nfraction for O(VIII) is still too low to account for the high $\\tau\n(OVIII)$ value at epoch 1.\n\n\n\\section{A THIRD WARM ABSORBER COMPONENT}\n\nThe model we propose to explain both {\\em ASCA} and {\\em BeppoSAX}\nobservations incorporates a new zone for the warm absorber. Let warm\nabsorber 1 $\\equiv$ WA1 be the inner warm absorber which parameters\nare: $R<1.4\\times10^{17}$ \\cm, $n>2\\times10^7$ \\pcmcu and $\\Delta\nR\\simeq 10^{14}$ \\cm. The outer warm absorber will be warm absorber 2\n$\\equiv$ WA2 with parameters $R>3\\times10^{18}$ \\cm, $n<2\\times10^5$\n\\pcmcu and $\\Delta R\\simeq 10^{14}$ \\cm. In our model a warm absorber\n3 $\\equiv$ WA3 is situated between WA1 and WA2. The WA3 radius and\ndensity will have values between those of WA1 and WA2. Therefore,\nwhile WA1 and WA2 respond on timescales of hours and weeks\nrespectively, WA3 is expected to respond to variations in the ionizing\nflux on timescales of days. WA3 would have an ionization parameter\n$\\xi$ of the order of 500 \\ergcmps for $L=3\\times10^{43}$ \\ergps.\nHence the ionization fraction for this value of $L$ is too low to be\ndetected. Only when the luminosity of the source is sufficiently low\n(i.e. $\\xi\\approx 50$ \\ergcmps), WA3 reveals its presence by\ncontributing to the total optical depth for OVIII. The medium between\nWA1 and WA2 would be constituted by a continuum of warm absorbers:\nclouds with different densities situated at different radii. Only some\nof them happen to be at the radius and have densities that efficiently\nabsorbs the OVIII edge energy (i.e. most of them are undetectable). In\nBaldwin et al. \\shortcite{bal95} a model for the BLR is presented, in\nwhich individual BLR clouds can be thought of as machines for\nreprocessing radiation. As long as there are enough clouds at the\ncorrect radius and with the correct gas density to efficiently form a\ngiven line, the line will be formed with a relative strength which\nturns out to be very similar to the one observed. Similarly in our\nmodel, only WA1 and WA2 are detectable for the ordinary values of the\nionizing flux. Only for the case of a state of low luminosity, WA3\nwill be unmasked. Other zones, as yet unseen, may be present.\n\nAssuming then the presence of WA3 and also an epoch of low luminosity\nprevious to the {\\em BeppoSAX} observation, the expected WA3 behaviour\nwould be:\n\ni) when $L\\approx 0.4\\times10^{43}$ \\ergps (previous to epoch 1), the\nionization parameter $\\xi\\approx 50$ \\ergcmps, giving a high value for\n$f_{O8}$. This period lasts for approximately $10^5$ \\s, so the plasma\nhas time to recombine.\n\nii) when $L\\approx (1,5)\\times 10^{43}$ \\ergps (i.e. during the\nobservation), then $\\xi\\approx 150,750$ \\ergcmps. For these high\nvalues of $\\xi$, oxygen is practically fully stripped and therefore\nthere is a very small contribution to the optical depth for OVIII.\n\nThe range of parameters investigated for WA3 is $R=(2,8)\\times\n10^{17}$ cm, $n=5\\times10^5,10^7$ \\pcmcu and $\\Delta R$ in the\ninterval that gives a column density for WA3 approximately equal to\n$3\\times 10^{22}$ \\pcmcu. After taking into account the soft X-ray\nabsorption due to WA1, the response of WA3 has been calculated and an\nexample of the results obtained is presented in figures 5 and 6, where\nthe general good agreement is also extended to point 1. \n\nWA3 has also been modelled using {\\sc cloudy} and we found a drop in\nthe transmitted portion of the incident continuum at $\\approx 7.8$\n\\keV, of approximately $1\\%$ (i.e. undetectable for current\ninstruments). The coronal lines strength has also been checked using\n{\\sc cloudy}\\footnote{See Sect. 3.3 \\cite{Ferg97} for a discussion of\n the state of the coronal lines atomic data used in {\\sc cloudy}.}.\nThe ratio of the modelled to observed fluxes for WA3 are all below\n$0.1\\times f_c$, where $f_c$ is the covering fraction\\footnote{Porquet\n et al. \\shortcite{Porq99} give some restrictions on the density of\n the WA in order to avoid producing coronal line equivalent widths\n larger than observed. Although WA3 presents no problems at all for\n any $f_c$, WA2 does, unless a low value of $f_c$ is considered. This\n possibility is currently being investigated.}.\n\nFinally, the contribution to $\\tau$(OVII) from each component for our\nmodel has been calculated and, as expected, we found that WA2 is the\nmain responsible for the OVII edge (its contribution makes 96\\% of the\ntotal value of $\\tau$(OVII)). \n\\begin{figure}\n\\centerline{\\psfig{figure=fig5.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Comparison {\\em ASCA} data (square) with the model\n computations (star) for the following warm absorber parameters: WA1:\n distance to the ionizing source, $R=1.0\\times10^{17}$ \\cm,\n line-of-sight distance through the warm absorber, $\\Delta\n R=3.0\\times 10^{14}$ \\cm, and electron density $n_e=4.0\\times10^7$ \\pcmcu.\n WA3: $R=4.0\\times10^{17}$ \\cm, $\\Delta R=7.0\\times 10^{16}$ \\cm, and\n $n_e=5.0\\times 10^5$ \\pcmcu.}\n\\end{figure}\n\\begin{figure}\n\\centerline{\\psfig{figure=fig6.ps,width=0.50\\textwidth,angle=-90}}\n\\caption{Comparison {\\em BeppoSAX} data (square) with the model\n computations (star) for the following warm absorber parameters: WA1:\n distance to the ionizing source, $R=1.0\\times10^{17}$ \\cm,\n line-of-sight distance through the warm absorber, $\\Delta\n R=3.0\\times 10^{14}$ \\cm, and electron density $n_e=4.0\\times10^7$ \\pcmcu.\n WA3: $R=4.0\\times10^{17}$ \\cm, $\\Delta R=7.0\\times 10^{16}$ \\cm, and\n $n_e=5.0\\times 10^5$ \\pcmcu.}\n\\end{figure}\n\n\\section{DISCUSSION}\nWarm absorbers have been the subject of extensive studies during the\nlast decade. Such regions are not spatially resolved, and all the\navailable information about their geometry is obtained from analysis\nof the variability of the oxygen edges. The explanation we offer for\nthe time variability of the MCG$-$6-30-15 warm absorber during both\n{\\em ASCA} and {\\em BeppoSAX} observations does not invoke complex\nprocesses, but a very simple photoionization model together with the\npresence of a multi-zone warm absorber. This would be constituted by a\ncontinuum of clouds at different radii and different densities, such\nthat only some of them contribute to the total optical depth for OVIII\ndepending on the value of the luminosity.\n\nAs a final remark note how in our model WA3 is much more volume\nfilling than WA1 ($\\Delta R/R\\geq 0.1$ for WA3 while $\\Delta R/R\\leq 10^{-3}$\nfor WA1). This suggests that WA3 could be part of the inter-cloud\nmedium of WA1.\n\\section{ACKNOWLEDGMENTS}\nThis work has been supported by PPARC and Trinity College (R.M.) and by\nthe Royal Society (A.C.F.). C.S.R. thanks support from Hubble\nFellowship grant HF-01113.01-98A. This grant was awarded by the Space\nTelescope Institute, which is operated by the Association of\nUniversities for Research in Astronomy, Inc., for NASA under contract\nNAS 5-26555. C.S.R. also thanks support from NASA under LTSA grant\nNAG5-6337.\n\n\\bibliographystyle{mnras}\n%\\bibliography{paper,mnrasmnemonic}\n\\begin{thebibliography}{}\n \n\\bibitem[\\protect\\citename{Baldwin et al.}1995]{bal95}\n Baldwin J., Ferland G., Korista K., Verner D., 1995, \\apjl,\n 455, L119\n\n\\bibitem[\\protect\\citename{Fabian et al.}1994]{fab94}\nFabian A.~C. et~al., 1994, \\pasj, 46, L59\n\n\\bibitem[\\protect\\citename{Ferguson et al.}1997]{Ferg97} Ferguson\n J.W., Korista K.T., Baldwin J.A., Ferland G.J., 1997, \\apj, 487,\n 122\n \n\\bibitem[\\protect\\citename{Ferland}1996]{ferla96} Ferland G.F., 1996,\n Hazy, a Brief Introduction To Cloudy. \\newblock U. of Kentucky,\n Dept. of Physics and Astronomy Internal Report\n \n\\bibitem[\\protect\\citename{Ferland et~al.}1998]{ferl98} Ferland G.J.,\n Korista K.T., Verner D.A., Ferguson J.W., Kingdon J.B., Verner E.M.,\n 1998, \\pasp, 110, 761\n \n\\bibitem[\\protect\\citename{Grevesse}1989]{gre89} Grevesse E., N. \\&\n Anders, 1989, in Waddington C.J., ed, Cosmic Abundances of Matter,\n AIP Conference Proceedings 183. \\newblock AIP, New York\n\n\\bibitem[\\protect\\citename{Halpern}1984]{hal84}\nHalpern J.P., 1984, \\apj, 281, 90\n\n\\bibitem[\\protect\\citename{Orr et~al.}1997]{orr97}\nOrr A., Molendi S., Fiore F., Grandi P., Parmar A.N., Owens A.,\n 1997, \\aap, 324, L77\n\n\\bibitem[\\protect\\citename{Osterbrock}1989]{ost89}\nOsterbrock D., 1989, Kelly A., ed, Astrophysics of Gaseous Nebulae and Active\n Galactic Nuclei.\n\\newblock Univ. Science Books, Mill Valley, Ch.~11\n\n\\bibitem[\\protect\\citename{Otani et~al.}1996]{ota96}\nOtani C. et~al., 1996, \\pasj, 48, 211\n\n\\bibitem[\\protect\\citename{Porquet et~al.}1999]{Porq99}\n Porquet D., Dumont A.~M., Collin S., Mouchet M., 1999, \\aap,\n 341, 58\n\n\\bibitem[\\protect\\citename{Reynolds}1996]{rey96}\nReynolds C.~S., 1996, Ph.D. thesis, University of Cambridge\n\n\\bibitem[\\protect\\citename{Reynolds}1997]{reyno97}\n Reynolds C.~S., 1997, \\mnras, 286, 513\n\n\\bibitem[\\protect\\citename{Uttley et~al.}1999]{utt99}\nUttley P., McHardy I.~M., Papadakis I.~E., Guainazzi M., Fruscione\n A., 1999, \\mnras, accepted (astro-ph/9905104)\n\n\\end{thebibliography}\n\n\\end{document}"
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{
"name": "astro-ph0002015.extracted_bib",
"string": "\\begin{thebibliography}{}\n \n\\bibitem[\\protect\\citename{Baldwin et al.}1995]{bal95}\n Baldwin J., Ferland G., Korista K., Verner D., 1995, \\apjl,\n 455, L119\n\n\\bibitem[\\protect\\citename{Fabian et al.}1994]{fab94}\nFabian A.~C. et~al., 1994, \\pasj, 46, L59\n\n\\bibitem[\\protect\\citename{Ferguson et al.}1997]{Ferg97} Ferguson\n J.W., Korista K.T., Baldwin J.A., Ferland G.J., 1997, \\apj, 487,\n 122\n \n\\bibitem[\\protect\\citename{Ferland}1996]{ferla96} Ferland G.F., 1996,\n Hazy, a Brief Introduction To Cloudy. \\newblock U. of Kentucky,\n Dept. of Physics and Astronomy Internal Report\n \n\\bibitem[\\protect\\citename{Ferland et~al.}1998]{ferl98} Ferland G.J.,\n Korista K.T., Verner D.A., Ferguson J.W., Kingdon J.B., Verner E.M.,\n 1998, \\pasp, 110, 761\n \n\\bibitem[\\protect\\citename{Grevesse}1989]{gre89} Grevesse E., N. \\&\n Anders, 1989, in Waddington C.J., ed, Cosmic Abundances of Matter,\n AIP Conference Proceedings 183. \\newblock AIP, New York\n\n\\bibitem[\\protect\\citename{Halpern}1984]{hal84}\nHalpern J.P., 1984, \\apj, 281, 90\n\n\\bibitem[\\protect\\citename{Orr et~al.}1997]{orr97}\nOrr A., Molendi S., Fiore F., Grandi P., Parmar A.N., Owens A.,\n 1997, \\aap, 324, L77\n\n\\bibitem[\\protect\\citename{Osterbrock}1989]{ost89}\nOsterbrock D., 1989, Kelly A., ed, Astrophysics of Gaseous Nebulae and Active\n Galactic Nuclei.\n\\newblock Univ. Science Books, Mill Valley, Ch.~11\n\n\\bibitem[\\protect\\citename{Otani et~al.}1996]{ota96}\nOtani C. et~al., 1996, \\pasj, 48, 211\n\n\\bibitem[\\protect\\citename{Porquet et~al.}1999]{Porq99}\n Porquet D., Dumont A.~M., Collin S., Mouchet M., 1999, \\aap,\n 341, 58\n\n\\bibitem[\\protect\\citename{Reynolds}1996]{rey96}\nReynolds C.~S., 1996, Ph.D. thesis, University of Cambridge\n\n\\bibitem[\\protect\\citename{Reynolds}1997]{reyno97}\n Reynolds C.~S., 1997, \\mnras, 286, 513\n\n\\bibitem[\\protect\\citename{Uttley et~al.}1999]{utt99}\nUttley P., McHardy I.~M., Papadakis I.~E., Guainazzi M., Fruscione\n A., 1999, \\mnras, accepted (astro-ph/9905104)\n\n\\end{thebibliography}"
}
] |
astro-ph0002016
|
Understanding NLR in Seyfert Galaxies: numerical simulation of jet-cloud interaction
|
[
{
"author": "P.\\ Rossi\\inst{1}"
},
{
"author": "A.\\ Capetti \\inst{1}"
},
{
"author": "G.\\ Bodo\\inst{1}"
},
{
"author": "S.\\ Massaglia \\inst{2}"
},
{
"author": "A.\\ Ferrari\\inst{1,2}"
}
] |
Recent HST observations suggest that the NLR in Seyfert Galaxies can be the result of interaction between jet and external inhomogeneous medium; following this suggestion we perform numerical simulations considering the impact of a radiative jet on a dense cloud. We approach the problem adopting a hydrodynamical code, that consents us to study in detail the jet hydrodynamics, while we choose a more simplified treatment of radiative processes, in order to give a qualitatively good interpretation of the emission processes. Our three main purposes are: i) to reproduce in our simulations the physical conditions observed in the NLR of Seyfert Galaxies, ii) to obtain physical constraints of the jet parameters and iii) to study the jet capacity to photoionize the surrounding medium. We find that the jet-cloud interaction leads to clumps of matter with density, temperature and velocity that agree with observations. Conversely, the photoionizing flux radiated by the jet-induced shocks does not appear to be sufficient to account for the NLR line luminosity but it may produce local and transient effects on the NLR ionization balance. Finally, the observational requirements can be matched only if jets in Seyfert galaxies are relatively heavy, $\rho_{jet}\, \gapp 1 $ cm $^{-3}$, and with velocities smaller than $\lapp \, 50,000\,$km s$^{-1}$, very different from their counterparts in radio-galaxies. % \keywords{ Hydrodynamics -- ISM: jets and outflows -- NLR in Seyfert Galaxies}
|
[
{
"name": "seyfert.tex",
"string": "%\\documentstyle[psfig,referee]{l-aa} % for a referee version\n\\documentstyle[psfig]{l-aa}\n\n%\\usepackage{graphics}\n%\\input psfig.sty\n\\def\\lapp{\\mathbin{\\raise2pt \\hbox{$<$} \\hskip-9pt \\lower4pt\n\\hbox{$\\sim$}}}\n\\def\\gapp{\\mathbin{\\raise2pt \\hbox{$>$} \\hskip-9pt \\lower4pt\n\\hbox{$\\sim$}}}\n\n\\begin{document}\n\n\\thesaurus{02.08.1; 09.10.1; 11.19.1}\n\n\n\n\n\\title{Understanding NLR in Seyfert Galaxies: numerical simulation of \njet-cloud interaction}\n\\subtitle{} \n\n\\author{ P.\\ Rossi\\inst{1}\\and A.\\ Capetti \\inst{1} \\and G.\\ Bodo\\inst{1} \n\\and S.\\ Massaglia \\inst{2} \\and A.\\ Ferrari\\inst{1,2}} \n\n\\institute{Osservatorio Astronomico di Torino, I-10025 Pino Torinese, Italy\\\\\nemail: [email protected], [email protected], [email protected]\n\\and Dipartimento di Fisica Generale dell'Universit\\`a, Via Pietro\nGiuria 1, I-10125 Torino, Italy\\\\\nemail: [email protected], [email protected]} \n\n\\offprints{P. Rossi}\n%\\mail{[email protected]}\n%\n\\date{Received / Accepted}\n%\n%\\titlerunning{Jet-cloud interaction in Seyfert}\n%\\authorrunning{Rossi et al.}\n\\maketitle\n%\n\\begin{abstract}\nRecent HST observations suggest that the NLR in Seyfert Galaxies can be the \nresult \nof interaction between jet and external inhomogeneous medium; following this \nsuggestion we \nperform numerical simulations considering the impact of a radiative\njet on a dense cloud. We approach the problem adopting a \nhydrodynamical code, that consents us to study in detail \nthe jet hydrodynamics, while we choose a more simplified\ntreatment of \nradiative processes, in order to give a qualitatively good interpretation of \nthe emission processes. Our three main purposes are: \ni) to reproduce in our simulations the physical conditions observed in the NLR\nof Seyfert Galaxies, ii) to obtain \nphysical constraints of the jet parameters and iii) to study the jet \ncapacity to photoionize the surrounding medium.\n\nWe find that the jet-cloud interaction leads to clumps of matter with\ndensity, temperature and velocity that agree with observations.\nConversely, the \nphotoionizing flux radiated by the jet-induced shocks \ndoes not appear to be sufficient to account for the NLR line luminosity\nbut it may produce local and transient effects on the NLR ionization balance.\n\nFinally, the observational requirements can be matched only\nif jets in Seyfert galaxies are relatively heavy,\n$\\rho_{\\rm jet}\\, \\gapp 1 $ cm $^{-3}$, and with velocities smaller than \n$\\lapp \\, 50,000\\,$km s$^{-1}$, very different from \ntheir counterparts in radio-galaxies.\n\n%\n\\keywords{\nHydrodynamics -- ISM: jets and outflows \n-- NLR in Seyfert Galaxies}\n\\end{abstract}\n%\n\\thesaurus{}\n%\n\\section{Introduction}\n%\n\nExtensive HST emission-line imaging \nof Seyfert galaxies has for the first time\nresolved details of the structure of their Narrow Line Regions (NLR). \nIn several cases cone-like morphologies have been revealed, \nsimilar in shape to - but of much smaller linear extent than - \nthe Extended Narrow Line Regions (ENLR) seen\nin the lower resolution ground based images \n(Wilson \\& Tsvetanov, 1994 and references therein). \nIn the standard model of the NLR, the UV \nemission of the nucleus is responsible of photoionizing the\nInterstellar Medium (ISM) of the host galaxy. \nThese conical distributions of the ionized gas \nhave been interpreted as a confirmation\nof the anisotropy of the nuclear radiation field which, in the framework \nof the unified scheme for Seyfert galaxies (e.g. Antonucci 1993) is caused by\nthe shadowing of an obscuring circumnuclear torus. \nHowever, in galaxies with linear radio structures,\nthe morphology of the emission-line region appears to be directly \nrelated to that of the radio emission. In particular, in Seyferts with radio \njets (e.g. Mrk 3, Mrk 348, Mrk 6, Mrk\n1066, ES0 428-G14), the NLR itself appears jet-like and is\nspatially coincident with the radio jet, while\nthe emission-line region takes a different form when a radio lobe is\npresent (e.g. Mrk 573, Mrk 78, NGC 3393): \narc-like shells of emission, very reminiscent of bow-shocks, \nsurround the leading edge of the lobes \n(Capetti et al. 1995a, 1995b, 1996; Falcke et al. 1996, 1998).\nThis dichotomy in radio and\nemission-line morphology is reflected in their different scales: \nbow-shock structures cover several kiloparsecs,\nwhile the jet-like features extend only over a few hundred parsecs. \nThe simplest interpretation of this radio-to-optical correspondence is \nthat the radio emitting outflow creates an expanding and cooling gas halo.\nThe compression induced by the outflow causes the line emission to be \nhighly enhanced in the regions where the jet-cloud interactions occur.\nA clear confirmation of this scenario came recently from HST spectroscopy \nof Mrk 3 (Capetti et al. 1999): its NLR has velocity field characteristic \nof a cylindrical shell expanding at a rate of 1700 km/s. They\ninterpreted this as the consequence of the rapid expansion of a hot gas cocoon \nsurrounding the radio-jet, which \ncompresses and accelerates the ambient gas. \n\n%The ionization structure of the NLR provides additional evidence for the \n%importance. \nHST observations also provided\nevidence for spatial variations in the NLR ionization structure.\n%which require a fundamental change in the picture of the NLR\n%in which the source of ionization is solely the nuclear radiation.\nIn NGC 1068 the material located along the radio jet is in a much higher \nionization state than its surroundings. This might suggest the presence of a \nlocal source of ionization which dominates over the \nnuclear radiation field (Capetti, Axon and Macchetto 1997; Axon et al. 1998). \nIn other sources, too distant for such a detailed analysis, \nthe radial variations of the ionization parameter are generally much\nflatter than expected from pure nuclear photoionization on the basis of\nthe measured density gradients (Capetti et al. 1996, Allen et al. 1999) \nrequiring again a local source of ionizing photons. \nAn appealing possibility of interpreting these data is\nto invoke the ionizing effects of \nshocks, originated by jet-cloud interactions: \nif these shocks are fast enough (velocities $>$ a few \nhundred km s$^{-1}$) the hot, shocked gas could produce a significant flux \nof ionizing photons (Sutherland, Bicknell and Dopita 1993; \nDopita and Sutherland 1995, 1996). Direct evidence for this emission \nhas been found by\nAxon, Capetti and Macchetto (1999) who showed that the radio-jets \nin the Seyfert 2\ngalaxies Mrk 348 and Mrk 3 are associated with an extended linear\nstructure in UV and optical continua. \nIn this picture, the radio-jet would not only \ndetermine the morphology of the NLR but is physically involved in\nits ionization. \nA radio imaging survey of the CfA sample of Seyfert \n(Kukula et al. 1995) shows that\nradio linear structures are present in a large fraction of sources (more than \n50\\%) suggesting that such an interaction is likely to be a quite common\nphenomenon in this class of objects. \n\nThe jet interaction with the external medium is clearly \na complex physical problem which involves both a hydrodynamical study \nof the jet propagation as well as a detailed understanding of the \nmicrophysics of the induced shocks, which might also be magnetized, and of the \nradiative processes.\n\nIn the framework of Seyfert galaxies this issue has been tackled by several\nauthors (Dopita and Sutherland 1995, 1996,\nEvans et al. 1999, Wilson and Raymond 1999, Allen et al. 1999).\nTheir focus is however mainly on the shocks properties with a very \ndetailed treatment of the emission mechanisms, with simplifying assumptions\nabout the hydrodynamics (e.g. plane parallel \ngeometry, steady-state shock).\nThe comparison with the observations is \nbased on the emitted spectrum and in particular on \ndiagnostic line-ratios, particularly with the aim of distinguishing the \ndifferent signatures of nuclear versus local photoionization. \n\nIn this paper we follow a complementary,\nalbeit different, approach by studying in detail the \njet hydrodynamics, while adopting a simplified treatment of the radiative \nprocesses, as we employ an equilibrium cooling \nfunction in an optically thin approximation. \nThis approach allows us to compare\nthe results of simulations with\nthe observed properties of NLR, in particular their morphology, \nthe expansion velocities and the characteristic \nvalues of gas density and temperature. \nMore precisely we consider the interaction\nof the jet with an inhomogeneity in the external medium (cloud) and \n our aim is that of constraining\nthe jet and cloud physical parameters for which it is possible to \nreproduce the observed conditions.\nIn this way, in addition of getting a better understanding of the \nNLR physics, we can also obtain information on the \njet properties from the NLR data. Moreover, we can calculate the fraction of\nthe jet power converted in radiation by shocks, resulting from the\ninteraction of the jet with the environment. We then get from the global \ndynamics a conversion efficiency from kinetic to radiative power\n and we can determine whether\nthe jet itself, via shocks, can provide an {\\it in situ} \nphotoionization source for the NLR emitting material,\nas discussed above. \n\nSteffen et al. (1997a) have used a rather similar approach \nwith the main difference that they considered the jet \npropagating into a uniform medium. It seems that in this \nsituation it is impossible to reach the high densities typical of the \nNLR with jet-like emission (see discussion below) \non which we will focus in the present\npaper. This is because, at low density, radiation is not efficient enough to\ngive the needed compression factors.\nThe conditions of the emitting material obtained \nby Steffen et al. seem to be appropriated for the case of the more \nextended (lobe-like) line emission structure. \n\nSteffen et al. (1997b) considered also jet-cloud interactions\nmainly from an analytical point of view. They found that\nwhen a jet interacts with a large number of clouds the most relevant effects\non the NLR structure\nare due to the most massive clouds located along the jet path.\nThis lead us to our choice for the geometry of the simulation in which\nthe jet hits a single dense cloud.\n\nThe paper is structured as follows: In the next section (Sect. 2), we \ndescribe the basic physical problem and the observational constraints, \nwhile the equations used and the method \nof solution are examined in Sect. 3 and 4; the results of simulations are \ndiscussed in Sect. 5; conclusions are drawn in Section 6. \n%\n\\section{Observational data and astrophysical scenario}\n%\nObservational data provide us with quite detailed information on the physical\nconditions of the narrow line emitting regions, in particular HST observations\ncan now be used to determine the propertirties of individual NLR clouds:\n typically, densities are \nlarger than $10^3\\,$cm$^{-3}$, temperatures are of the order \nof $10^4 - 2\\times10^4\\,$ K, and \nvelocities are $\\sim 300 - 1000\\, {\\rm km \\ s}^{-1}$ (Caganoff et al. 1991,\nKraemer, Ruiz and Crenshaw 1998, Ferruit et al. 1999, Axon et al. 1998,\nCapetti et al. 1999). \n\nThese are the observational constraints that we try to match \nin our simulations.\nResults of simulations of a jet impinging on a uniform medium,\nwith properties typical of the ISM,\nhave shown that it is not possible to match, in this situation, the density\nvalues reported above (Steffen et al. 1997a, Rossi \\& Capetti 1998). \nWe will therefore consider throughout the rest of the \npaper the case of a jet impinging on pre-existing inhomegeneities. \nWe can identify such inhomogeneities with giant molecular clouds (GMCs), \nthat typically populate spiral galaxies.\nThese objects have typically mass $\\sim 10^5 - 10^6 \\ {\\rm M}_{\\odot}$, radius\n$\\lapp 100$ pc, and temperature $\\sim 10$ K (Blitz 1993). \nThe resulting particle densities\nspan from a few up to about hundred particles per cm$^3$. \n\nA supersonic\njet, of radius $\\sim 10$ pc, that bore its way through the interstellar medium\nhas a considerably good chance of impinging frontally upon a (much larger) GMC,\nand this is the case we will consider in our simulations. In any event, \nthis latter case, i.e. the head-on collision with a large cloud, can be considered \nthe most efficient \ncase of interaction, for the compression, acceleration and heating\nof the NLR material. \n\n\nAs discussed below the effects of the jet/cloud interaction last for a time \nconsiderably longer than the cloud crossing time.\nMoreover, the jet crosses the tenuous inter-cloud regions at a much higher \nspeed than while in a cloud. We therefore expect that more \nthan one cloud will be interacting at any given time\nand they will display simultaneously the different evolutionary stages\nof the interaction.\n\n\\section{ The physical problem} \n%\nWe study the evolution of a cylindrical fluid jet impinging upon a cold heavy \nsteady inhomogeneity, namely the cloud, in pressure equilibrium with the \nexternal medium. The relevant equations governing the jet evolution, \nfor mass, momentum conservation, and radiative losses, are \n$$ \n{{\\partial \\rho } \\over {\\partial t}} + \\nabla \\cdot (\\rho \\vec{v}) = 0 \n\\,, \n\\eqno (1{\\rm a}) \n$$ \n$$ \n{{\\partial \\rho v_r} \\over {\\partial t}} + \\nabla \\cdot { \n(\\rho v_r \\vec{v })} = - {{\\partial p}\\over {\\partial r}}\\,, \n%{{\\partial {\\vec{v }}} \\over {\\partial t}} + ({\\vec{v}} \\cdot \n%\\nabla){\\vec{v}} = -\\nabla p / \\rho\\,, \n\\eqno (1{\\rm b}) \n$$ \n$$ \n{{\\partial \\rho v_z} \\over {\\partial t}} + \\nabla \\cdot { \n(\\rho v_z \\vec{v })} = - {{\\partial p}\\over {\\partial z}}\\,, \n\\eqno (1{\\rm c}) \n$$ \n$$ \n{{\\partial E} \\over {\\partial t}} + {\\nabla \\cdot (E \\vec{v })} = \n- p \\nabla \\cdot \\vec{v } - {\\cal L}\\,,\n%{{\\partial p} \\over {\\partial t}} + ({\\vec{v}} \\cdot \\nabla) p - \n%\\Gamma{p \\over \\rho} \\left[ \n%{{\\partial \\rho} \\over {\\partial t}} + ({\\vec{v}} \\cdot \\nabla) \\rho \n%\\right] = (\\Gamma - 1) (H - {\\cal L}) \n\\eqno (1{\\rm d}) \n$$ \nwhere the fluid variables $p$, $\\rho$, $\\vec{v}$ and $E$\nare, as customary, pressure, density, velocity, and \nthermal energy ($p / (\\Gamma -1)$) respectively; \n$\\Gamma$ is the ratio of the specific heats; ${\\cal L}$ represents \nthe radiative energy loss term \n(energy per unit volume per unit time, \nRaymond and Smith 1977).\n \n \nThe jet occupies initially \na cylinder of length $L$. \nThe initial flow structure has the following form:\n$$\n%\\begin{displaymath}\nv_z(r) = \n\\left\\{ \\begin{array}{ll}\n {v_z(r=0)}\\over{\\cosh[(r/a)^m]} & \\qquad {z \\le L} \\\\\n &\\\\\n 0 & \\qquad {z > L}\n\\end{array} \\right.\n\\nonumber\n$$\n%\\end{displaymath}\nwhere $m$ is \na `steepness' parameter for the shear layer separating the jet from the\nexternal medium (see Fig. 1).\nThe choice of separating the jet's interior from the ambient medium with a \nsmooth \ntransition, instead of a sharp discontinuity, avoids numerical instabilities\nthat can develop at the interface between the\njet and the exteriors, especially at high Mach numbers.\n\nRegarding the cloud, we fix its initial density $\\rho_{\\rm cloud}$ and impose \npressure equilibrium with respect to external medium; for simplicity we \nconsider \na steady cloud, with a thickness equal to the jet diameter.\n%\n \\begin {figure}\n %{\\resizebox{\\hsize}{!}{\\includegraphics{figure1.eps}}\n \\psfig{file=figura1.ps,width=\\hsize}\n \\caption []\n {In panel a) the computational domain is sketched. The grid is finer on the\n region of jet/cloud interaction, while is coarser far from the region of our\n interest. In panel b) the physical domain is shown.\n }\n \\end{figure}\n %\n\n%\n\\section{ The numerical scheme } \n%\n \n\\subsection{Integration domain and boundary conditions}\nIntegration is performed in cylindrical geometry and\nthe domain of integration ($0 \\leq z \\leq D$, $0\n\\leq r \\leq R$) is covered by a grid of $ 1020 \\times 704$ grid points.\nThe axis of the beam is taken coincident with the bottom boundary\nof the domain ($r=0$), where symmetric (for $p$, $\\rho$ and $v_z$) or\nantisymmetric (for $v_r$) boundary conditions are assumed. At the top\nboundary ($r=R$) and right\nboundary ($z=D$) we choose free outflow conditions, imposing\nfor every variable $Q$ null gradient ($dQ/d(r,z)=0$). \nThe boundaries are placed\nas far as possible from the region of the jet where the most interesting\nevolutionary effects presumably take place by employing\na nonuniform grid both in the longitudinal $(z)$ and the radial $(r)$ \ndirections\n(Fig. 1, panel a)).\nIn the radial direction the grid is uniform over the first 500 points and\nthen \nthe\nmesh size is increased assuming $\\Delta r_{j+1} = 1.015 \\Delta r_{j}$. The\njet spans over 200 uniform meshes, while the external boundary is\nshifted to $r = 10a$ where $a$ is the jet radius.\nAs for the $z$--direction, we assume a constant fine grid in the\ncentral part of the domain, where the cloud is located, \ni.e. in a sub-domain of length $40 a$, between the grid points 180 and \n844; conversely, in the remaining part we consider an\nexpanded grid increasing the mesh\ndistance according to the scaling law $\\Delta z_{j \\pm 1} = 1.015\n\\Delta z_{j}$,\nwhere the minus sign applies in the first 180 grid points and the plus sign\nabove grid point 844. \n \n%\n\\subsection{ Integration method } \n%\n\n The basic equations (1a-d) have been integrated with a two-dimensional \nversion of the Piecewise Parabolic Method (PPM) of Colella \\& Woodward \n(1984) (for a discussion of the main characteristics of this code \n and its merits for this kind of problems see Bodo et al. 1995).\n Radiative losses are dealt with the operator splitting \n technique, following which we split a single time step into two parts. \n In the first part, we advance the dynamical quantities, \n by using the adiabatic equations. \nIn the second part we update the internal energy, \nkeeping all the other variables constant, by taking into account \nradiative losses. \n%We impose the \n%condition that the internal energy cannot vary \n%in a single time step more than 10\\%. Therefore we get two limits \n%on the maximum length of the time step, in addition to the Courant\n%condition. \n\n%\n\\subsection{ Physical parameters and Scaling} \n%\nThe physical problem that we are approaching is quite complex, \nwith three different \ninteracting and radiating media, i.e. jet, ambient medium\nand cloud, each one described by its density, \ntemperature, velocity and size.\nWe note that in the adiabatic simulations of propagating jets, \nby normalizing to the jet density, sound speed, jet radius and\n sound crossing time over the jet radius, we are\nleft with only two parameters, namely the density ratio between jet and \nexternal medium and the jet Mach number.\nThe presence of radiation complicates the matter (Rossi et al. 1997), in fact \ntemperature is not scale free, since the radiative loss function in \nEq. (1c) explicitly depends on its physical value and in addition to the \nsound crossing time ($t_{\\rm cr} = a/c_{\\rm s}$), we have another typical \n time scale of the system, i.e. the radiative \n time scale, defined as $t_{\\rm rad} = p/[(\\Gamma-1){\\cal L} ] $ which depends\non the density of the medium. Therefore in this case one has to consider\nfor each medium the value of density and temperature as independent parameters.\nIn addition, as we already noticed we are now considering three media. \nWhen the jet passes through the cloud, \nthe evolution of the compressed cloud material is completely \ndifferent with respect to the case of two media,\nwhere the jet continues to push \ndense material at the head and it does not\nhave any reaccelerations related to \nthe passage from a denser to lighter medium. We would like to stress that the \npresence of a inhomogeneity is fundamental, in fact only in this \ncase, as we show \nlater, it is possible to reach the proper density for the emitting material.\nIn conclusion, we must assign a large number of physical parameters for\ndefining the initial conditions of our simulations.\n\n\nA thorough investigation of such huge parameter space is unfeasible; however,\n not all the parameters are equally important and some of them can \nbe well constrained by observational considerations. As a first step \nwe will then fix criteria to minimize the number \nof free parameters.\n \n\nConcerning the external (uniform) medium, we have to fix $\\rho_{\\rm ext}$ and\n$T_{\\rm ext}$, having $v_{\\rm ext} = 0$. With respect to \n$\\rho_{\\rm ext}$, we can assume one particle per cubic centimeter, \na value which we know to be appropriate to the interstellar medium of our \nGalaxy (Cox \\& Reynolds, 1987). \nIn reference to $T_{\\rm ext}$, again its choice is not so crucial,\nsince the most \nimportant temperature for the emission processes is the shock temperature, \ndepending mainly on jet velocity, in any case observations tell us that \nthe external medium is completely ionized, which means temperatures\nlarger than $10^4$ K, and we assume $T_{\\rm ext} = 10^4$K. \n\nThe jet is physically described \nby its density $\\rho_{\\rm jet}$, temperature $T_{\\rm jet}$, \n initial velocity $v_{\\rm jet}$ and radius $a$. \nThe radius $a$ can be chosen as our length unit in order \nto scale the other lengths in the system, and following the radio\nobservational suggestions (Pedlar et al. 1993, Kukula et al. 1999) \nwe consider it to be $10$ pc. \nConcerning the jet density we do not have any tightening constraint, so in a \nfirst approach, we take it equal to $\\rho_{\\rm ext}$.\nRelatively to $T_{\\rm jet}$, looking at the loss function (Fig. 2) \nwe can immediately realize that its \ninitial value it is not so crucial, since cooling is fast \nand soon the jet temperature falls to $\\sim 10^4$ K. Anyway $T_{\\rm jet}$ in\nour simulations is taken to be $10^6$K.\nThe jet velocity will be instead an important parameter of our simulations.\n\nFinally we consider the cloud, its density $\\rho_{\\rm cloud}$ is the\nparameter on which \nwe will focus our investigation. $T_{\\rm cloud}$ will be fixed by imposing \npressure equilibrium with the\nexternal medium. Actually GMC's are not required to be in pressure equilibrium\nsince they might be autogravitating, however, as discussed for the external \ntemperature, the exact value of $T_{\\rm cloud}$ is not crucial for the\nresults of the simulations. For simplicity we consider a steady cloud\n($v_{\\rm cloud} = 0$). The cloud dimensions must lie in the range of\nGMCs, so we will fix the size longitudinal to the jet to 20 pc\n(i.e. $2a$), with\na indefinitely large (with respect to $a$) transversal size.\n\nIn summary, we have three control parameters, namely the initial cloud \ndensity, the initial \njet velocity and the initial jet density, that we fix equal to one\nparticle per cm$^{-3}$. So we will \ninvestigate in details the effects of adopting different values\nfor $v_{\\rm jet}$ and $\\rho_{\\rm cloud}$.\n\\begin {figure}\n %{\\resizebox{\\hsize}{!}{\\includegraphics{figure1.eps}}\n \\psfig{file=figura2.ps,width=\\hsize}\n \\caption []\n {Plot of the energy loss function {\\sl vs} temperature \n(Raymond \\& Smith 1977).}\n \\end{figure}\n %\n\n\n%\n\\section{ Results} \n%\n\nWe begin\nour discussion with a short general description of the complete evolution \nof the jet-cloud interaction, that can be summarized in three steps\n(see Fig. 3 for a visualization of the basic features of the three steps for\nthe case $\\rho_{\\rm cloud}=30\\, {\\rm cm}^{-3}$ and $v_{\\rm jet}=6500\\,\n{\\rm km \\ s}^{-1}$):\n%\n \\begin {figure*}\n %{\\resizebox{\\hsize}{!}{\\includegraphics{figure1.eps}}\n \\psfig{file=ntvimage_v.ps,width=\\hsize}\n \\caption []\n {Images of the density distribution showing the jet-cloud interaction \nand cuts of density, temperature and\nexpansion velocity, in the middle of the cloud, across the thin layer \nof compressed material for the case $\\rho_{\\rm cloud} =\n30\\,{\\rm cm}^{-3}$, $v_{\\rm jet} = \n6500\\,{\\rm km \\ s}^{-1}$, at different times. \nThe three columns correspond respectively to $t=1\\,t_{\\rm cc}$,\n$t=2\\,t_{\\rm cc}$ and \n $t=5\\,t_{\\rm cc}$.}\n \\end{figure*}\n %\n\n\\noindent\n{$\\bullet$} The jet hits the cloud, forming a strong shock, the post-shock \nregion becomes hot and blows up, because of its increasing pressure; the jet \nmaterial is conveyed in a back-flow that squeezes the jet itself. During this \nprocess the cloud material is compressed and heated by the shock, at the head \nthe temperature is very high ($> 10^8$ K), while on the jet sides it is lower \n$\\sim 10^7$ K, so that it can cool down, to reach the observed line emission \nconditions. It is in this region, forming a layer around the jet, that the \nnarrow line emission can originate. Our analysis \nwill therefore concentrate on the properties of this region. \nDuring this first phase, in which the jet \ncrosses the cloud, the layer is accelerated by the strong inside pressure\nand cools down, its density thereby increases \n(see the leftmost panels in Fig. 3).\n\n\\noindent\n{$\\bullet$} The second phase begins when the jet is completely out of the\ncloud, \nthe compressed emitting material reaches a quasi-steady state, during which \nthe emission is almost constant, the inside pressure begins to decay, but the\n emitting layer is still accelerated. From Fig. 3 (central panels), we \ncan see that the material in the layer has been compressed, its maximum \ndensity has increased, while its temperature has decreased. The maximum\ndensity is found now at temperatures around $10^4$ K, and its velocity \nhas also increased. \n\n\\noindent\n{$\\bullet$} In the third phase, the inside pressure has decayed and the \nemitting layer begins to slow down, the jet flows freely through the cloud and \nalso the emission decreases, eventually disappearing. \nFrom Fig. 3 (rightmost panels),\nwe see a decrease in density and velocity, while almost all the layer is found \nat $5 \\times 10^3 < T < 10^4$ K.\n\nThe efficient formation of the line emitting region will therefore depend on \nthe efficiency of radiation during the jet crossing of the \ncloud. We will then \nintroduce two typical timescales, the \n{\\it cloud crossing time} and the {\\it radiative time},\nwhose ratio will be a fundamental parameter for determining the evolution \nof the narrow line emitting layer. \nFollowing analytical treatments of the jet-ambient \ninteraction we \ndefine the cloud crossing time as \n$t_{\\rm cc} = d ( 1 +\\sqrt {\\rho_{\\rm cloud}/\\rho_{\\rm jet}})/{v_{\\rm jet}} $, \nwhere we have assumed, for the jet head velocity in the cloud,\nthe steady velocity obtained from the 1-D momentum balance in a medium \nwith $\\rho = \\rho_{\\rm cloud}$ (see, e.g., Cioffi and Blondin 1992,\n Norman et al.\\ 1982). In this way we are actually overestimating\nthe crossing time, since our situation is not steady, however this value\nis sufficiently accurate for our purposes.\nConcerning the radiative time, its definition is given in Section 4.3,\nhowever, we must notice \nthat for its evaluation we have to assume a value for the temperature,\nin the following considerations we have taken $T = 10^7$ K, that \nis the average of the typical post-shock \ntemperature in the region of our interest, this choice is properly done for \nall jets with $v_{\\rm jet} = 6500 \\ {\\rm km \\ s}^{-1}$ and \n$v_{\\rm jet} = 32500 \\ {\\rm km \\ s}^{-1}$, \nwhile it is overestimated for the low velocity cases, that means that \n$t_{\\rm rad}$ for those cases are shorter than the real ones. We have\nthen defined\n$\\tau \\equiv t_{\\rm cc} / t_{\\rm rad}$ as the ratio between crossing\nand radiative \ntime scales and this, as said before, is an important parameter for the \ninterpretation of the results.\n\nAs a first step in our analysis, we have performed an exploration of the\nparameter space. \nAs discussed before, we reduced our parameters to $\\rho_{\\rm cloud}$ and the \ninitial $v_{\\rm jet}$. In Table 1 we report, for each pair\nof their values, typical values of density, \nexpansion velocity and temperature of the emitting material\nand the value of $\\tau$. \nThe density is the median value of density distribution weighted on the \nemissivity function (that is proportional to $\\rho^2$), while velocity \nand temperature are those corresponding to this density value. \nAll the quantities are evaluated at $2\\,t_{\\rm cc}$, this choice is due to \nthe fact that during this period the expansion velocity of the emitting \nmaterial increases rapidly \nreaching a maximum and then decreases monotonically, so that, if the\nexpansion \nvelocity does not match the observational constraint within this time,\nit never will, and the case will not be of interest for our analysis.\nRadiation must therefore act efficiently during this time, in order to \ncreate the needed conditions for radiation, and this poses a lower limit \non the value of $\\tau$. On the basis of the values reported in this table \nwe choose the most promising cases for our investigation. \n\n\\noindent\n\\begin{table}\n\\caption{Parameters of the simulations}\n\\input tabella.tex\n\\end{table}\n\nConsidering the first column we can immediately realize that jets at low \nvelocity cannot reach conditions comparable to those observed. \nThe values of $\\tau$ for these simulations are high, meaning that radiation \nis very efficient. On the other hand, the jet momentum is low and \ncannot drive the emitting material at high velocities. For the case \n$\\rho_{\\rm cloud} = 30 \\ {\\rm cm}^{-3}$ we have, in fact, high densities in \naccord with the high \nvalue of $\\tau$, but very low velocities. For this reason we did not \nperform simulations for the other two cases\nof higher density, since jets \nwould produce stronger and cooler compression practically at \nrest, very far from the observational scenario. \n\nLooking at the high velocity case, we see that, in the case of small \ninhomogeneities, $\\tau$ has a very low value and, therefore, radiation is \ninefficient. The jet is very energetic and sweeps the \ncloud, before radiation becomes effective and so it does not form \nany condensation (the velocity reported for this case is therefore \nmeaningless). Increasing the cloud density, we increase also the value of \n$\\tau$: the maximum density increases, but it is still quite low. Only for \nthe high density cloud ($\\tau = 0.5$), we get values of density and velocity\nin agreement with observations.\n \nRegarding the intermediate velocity, the values of $\\tau$ are $> 0.3$: \n radiation is efficient and thus the emitting layer can reach sufficiently\nhigh densities. Only in the lighter \ncloud case, however, the velocity is comparable to the observed values.\n\nFrom this exploration of the parameter space we can conclude that the\nobserved \nconditions can be matched only for a narrow range of parameters and that \nthe properties of the emitting layer depend \nessentially only on one parameter, the ratio between the \nradiative timescale and the cloud crossing timescale $\\tau$.\nFor low values of $\\tau$ ($\\tau < 0.3$), radiation is inefficient and the \ndensities in the layer are too low. For higher values of $\\tau$ \n($\\tau > 0.55$) we find, on the other hand, that the velocity of the emitting\nlayer becomes too small. This is because the cloud density is high and the jet \nmomentum flux is too small to impart to it a large enough velocity. \nOnly for a narrow range of values of $\\tau$ \nwe can match the observed conditions and, in Table 2, we have\ntranslated these limits into limits on velocity range at different cloud\ndensities. \n\n\\begin{table}\n\\caption{Ranges of jet velocities that can match the observed properties}\n\\input tabella1.tex\n\\end{table}\n\\noindent\n%\n\\subsection{Case of $\\rho_{\\rm cloud}\\,=\\,120\\ {\\rm cm}^{-1}\\,,\\,v_{\\rm jet}\\,=\n\\,32500\\ {\\rm km \\ s}^{-1}$ \n} \n%\nIn this subsection we will discuss in more details the case that \nbest matches the \nobservational scenario. We begin our discussion showing, Fig. 4, \na gray-scale image with a snapshot of \nthe density distribution at $5t_{\\rm cc}$ and \nthree small panels showing enlargements of the region of interaction \nbetween jet and \ncloud referred to density, temperature and the expansion velocity of \nemitting gas. The proper physical condition for emission are \nreached in \na thin layer of compressed cloud material, whose width and mass grow \nin time as \nthe shocked cloud material cools down.\n\n\n\\begin {figure*}\n\\psfig{file=image.ps,width=\\hsize}\n\\caption []\n{The larger panel shows the image of the distribution of logarithm \nof density at \n$5t_{cc}$ for the case $\\rho_{\\rm cloud} =\n120\\,{\\rm cm}^{-3}$, $v_{\\rm jet} = \n32500\\,{\\rm km \\ s}^{-1}$. The other three small panels show, in enlargements\n of the interaction region, the distributions of the logarithm of density, \nthe logarithm of temperature and of velocity.}\n\\end{figure*}\n\n The detailed physical properties of this line emitting region\nare reported in Fig. 5, where we have represented the \nbehavior of density, temperature and velocity along\nradial cuts through this layer. We note that the proper conditions\nare matched in a layer of width $\\lapp \\,2$ pc. \n\n\n\\begin {figure}\n\\psfig{file=ntv.ps,width=\\hsize}\n%\\psfig{file=ntv.ps,width=11cm}\n\\caption []\n{The three panels present a transversal cut of \n density, temperature, and the expansion velocity, in the middle of cloud,\nacross the thin emitting layer for the same case of Fig. 4. Notice that the \ncoordinate $r$ measure the distance from the jet axis.}\n\\end {figure} \n \nHow the properties of the material contained in this thin layer \ncompare with the \nphysical conditions of gas of the NLR? \nTo answer the question we plot in\nFig. 6 the temporal behavior of the mean \nexpansion velocity (panel a) and mass (panel b) of the emitting \nmaterial shell at two different density limits. We see that from the time\nwhen the jet touches the cloud until \n$2t_{\\rm cc}$, when \n a strong interaction between the jet head and the cloud takes place, \nthe cloud material is accelerated and \nthe quantity of emitting material increases; \nafter this interval the jet flows, essentially freely, across the \ncloud without any further acceleration of the compressed material \nshell and the accelerated cloud material slows down monotonically.\n\\begin {figure} \n\\psfig{file=masvex.ps,width=\\hsize}\n%\\psfig{file=masvex.ps,width=11cm}\n\\caption []\n{In the two panels we plot the behavior of the mean expansion velocity of \nthe emitting material vs \ntime (panel a) and of the total emitting mass, in unit of solar masses, \nvs time (panel b). The solid \nlines refer to material denser than 400 particle per cube centimeter,while \nthe dashed line refers to material denser than 800 particle per cube \ncentimeter.}\n\\end{figure}\nNotice that the mean expansion velocity, relative to an observer, lies,\nfor the denser material, in the range\n $600-1200\\ {\\rm km \\ s}^{-1}$ \n(since one must consider twice the mean expansion velocity), that is in \ngood agreement with the velocity deduced by the line widths detected.\nLooking more in detail at the emitting mass,\n we see that its growth begins some time after the jet has initiated \nto drill its way\n into the cloud, and this delay corresponds to the cooling time of the \nshocked material. We also note that, after $t=2t_{\\rm cc}$, the jet \ncontinues to\nsweep out material laterally at a pace that is higher for the lighter\nmaterial, the total mass exceeds\n$3\\times 10^4 / {\\rm M}_{\\odot}$ at $t=35,000$ ys and this would correspond \nto an $H_\\beta$ luminosity of $\\sim 2 \\times 10^{40}$erg s$^{-1}$ which,\nconsidering also the possibility of having simultaneuously several active \nclouds, is consistent with the observed values.\n\nAs the interaction is effective over a timescale much longer than \n$t=t_{\\rm cc}$ the jet will quickly propagate into the low density inter-cloud\nmedium and it will reach any other cloud lying on its path. \nThus more than one cloud\nwill be effectively interacting with the jet at any time. Each will display\na behaviour typical of its evolutionary stage and the total emitting mass\nmust be considered as the total over all clouds. Furthermore, this will \nnaturally reproduce the jet-like morphology of the NLR.\n\n\\subsection{Energetics} \n% \n\\begin{table*}\n\\caption{High frequency radiative power and radiative efficiencies}\n\\input tabella2.tex\n\\end{table*}\n\nAs discussed in the Introduction, the source of ionization of the NLR \nis still matter of debate. While the NLR gas is certainly illuminated\nby the nuclear source, its interaction with the radio jet also produces\nregions of high temperature and density which radiates ionizing photons.\nIn this paragraph we derive the conversion efficiency of the jet kinetic\npower into energy radiated in ionizing photons. To estimate the \nionizing energy flux we integrated radiative losses over all regions where \n$T > 10^5$ K as above this temperature most of them \ncorrespond to the production of photons with energy higher than the\nhydrogen ionization threshold.\n\nIn Table 3 we summarize our results reporting the \nkinetic power referred to the three different velocities\n($P_{\\rm kin}=\\rho \\ v_{\\rm jet}^3 \\ A$,\nwhere $\\rho$, $v_{\\rm jet}$ and $A$ are respectively the density,\nthe velocity and the \ntransverse section of the jet) and the conversion \nefficiency at peak and after 2 $t_{cc}$ for all the cases considered.\n\nThe peak efficiency reaches in one case a value as high as 10 \\%\nbut it is usually 0.1 - 2 \\%. \nHowever, over the interaction, the typical value of $\\eta$ \n(well represented by its value after 2 $t_{cc}$) is much lower \n$\\eta \\sim 10^{-4} - 5. \\times 10^{-3}$. Faster jets have lower efficiency \nthan slower jets and this conspires in producing a very similar \namount of energy radiated in ionizing photons, \n$\\sim 10^{40} \\ {\\rm erg \\ s}^{-1}$, in all cases.\n \nIn Seyfert galaxies $L_{H\\beta} \\sim 10^{39} - 10^{42}\n{\\rm erg \\ s}^{-1}$ (Koski 1978).\nThe minimum ionizing photon luminosity required to \nproduce a given line emission luminosity corresponds to the limiting case in \nwhich all ionizing photons are absorbed\nand all photons have an energy\nvery close to the hydrogen ionization threshold $\\nu_{\\rm ion}$.\nIn this situation\n\n$ L_{\\rm ion,min} = \\frac{1}{p_{H\\beta}}\\frac{\\nu_{\\rm ion}}{\\nu_{H\\beta}} \n L_{H\\beta} \\sim 50 \\, L_{H\\beta} $\n\n\\noindent\nwhere $p_{H\\beta}\\approx 0.1$ is the probability that any recombination will \nresult in the emission of an H$\\beta$ photon.\n\nIt appears that, even in this most favourable scenario,\nthe radiation produced in shocks \ncan only represent a small fraction\nof the overall ionization budget of the NLR, particularly as sources with\nhigh radio luminosity (in which usually radio-jets are found)\nalso have the highest line luminosity (e.g. Whittle 1985).\n\nNonetheless, in the most promising case examined above\n($\\rho_{\\rm cloud}=120\\, {\\rm cm}^{-3}$ and $v_{\\rm jet}=32500\\,\n{\\rm km \\ s}^{-1}$)\nat the peak of the conversion efficiency the radiated energy \nis $3 \\times 10^{41} \\, {\\rm erg \\ s}^{-1}$ and it is substained over \na crossing time, $\\sim 10^4$ years. Shock ionization may thus produce\nimportant ionization effects which, however, can be only\nboth local and transient. \n\n\\section{Conclusions} \n\nWe have studied in detail the dynamics of the \ninteraction of a jet with a large cloud \npre-existing in the ISM in order to find the conditions for which it\nis possible to reproduce the main physical parameters of the NLR emitting\nmaterial. \n\nFollowing the suggestion by Steffen et al. (1997b) \nthat the most relevant effects of the interaction arise when a jet hits\ndense massive clouds, we adopted a quite simplified geometry of a single \ngas condensation with can be astrophysically identified with a giant \nmolecular cloud. \nAs the interaction last for a time \nconsiderably longer than the cloud crossing time \nmore than one cloud will be interacting at any given time\nand they will display simultaneously the different evolutionary stages\nof the interaction. Furthermore the characteristic jet-line structure \nof the NLR is thus reproduced. In any event, \nthis case, i.e. the head-on collision with a large cloud, is \nthe most efficient case of interaction, for the compression, acceleration \nand heating of the NLR material. \n\nWe concentrated our efforts on the exploration of\nthe parameter plane ($v_{\\rm jet}, \\ \\rho_{\\rm cloud})$, since the other \nparameters, on which the simulation depends, have little influence on\nthe properties of the optically emitting material. \nWe have found that the condition\nfor obtaining values of density, temperature and velocity in the observed\nrange can be translated in a condition on the parameter $\\tau$, \nwhich is the ratio of the cloud crossing timescale to the radiative timescale\n($0.3 < \\tau < 0.55$) and which depends on our two fundamental parameters\n$v_{\\rm jet}$ and $\\rho_{\\rm cloud}$. For small values of $\\tau$, radiation\nis inefficient and it is not possible to produce regions dense enough, while,\non the other hand, for large values of $\\tau$, the cloud is too dense \nand the obtained\nvelocities are too low. We have explored a range of cloud densities which \ncan be considered typical of GMCs and, for this range,\nthe jet velocities span an interval\nfrom $4000\\,$km s$^{-1}$ to $55,000\\,$km s$^{-1}$.\n\nThe jet kinetic power corresponding to these combinations of parameters \n(for a jet density of 1 cm$^{-3}$) ranges from\n$3.2 \\times 10^{41}$ to $8 \\times 10^{44}$ erg s$^{-1}$, in general agreement\nwith the estimates of Capetti et al. 1999 for Mrk 3. \nFor jet density much lower than 1 cm $^{-3}$, however, in order to\nmatch the observed NLR conditions we would need a correspondingly higher\nvelocity and therefore untenable requirements on the kinetic power\nwhich grows with $v_{\\rm jet}^3$. \nWe conclude that jets in Seyfert galaxies are unlikely to have densities\nmuch lower than 1 cm $^{-3}$ and velocities higher than \n$50,000\\,$km s$^{-1}$, and therefore they are very different from \ntheir counterparts in radio-galaxies in which densities are \nmuch lower and velocities are relativistic. \n\nConcerning radio-galaxies we can speculate\nthat with lower jet densities and higher velocities,\nthe gas postshock temperatures and radiative time \nwould be increased with respect to the case of Seyfert galaxies\nand therefore the conditions for having efficient \nline emission would be more difficult to meet. \nIn addition the different properties of the jet environment \nin the elliptical galaxies hosting radio-galaxies render\nencounters with gas condensations less likely to occur. \nThis probably explain why \nthe association between radio and line emission although \noften present in radio-galaxies (e.g. Baum and Heckman 1989)\nis not as strong as in Seyfert galaxies.\n\nFinally, the study of the global dynamics allowed us to have \nestimates of the overall efficiency of the conversion of kinetic\nto high frequency radiative power in the shocks that form in the interaction \nbetween jet and ambient medium. We have found that the efficiency is \nincreased by the presence of the cloud, its peak value is \n0.1 - 2 \\% , its typical value is much lower $\\sim 10^{-4} - 5 \\times 10^{-3}$\nand it decreases with the jet power. These results lead us to the conclusion\nthat radiation emitted in shocks can be only a small fraction of the\noverall ionization budget of the NLR, although it can have local and \ntransient important effects. \n \n\\begin{acknowledgements} \nWe thank CNAA (Consorzio Nazionale per l'Astronomia e Astrofisica) for\nsupporting the use of supercomputers at CINECA, .\n\\end{acknowledgements}\n\n\n\n\\begin{thebibliography}{} \n\n\\bibitem{}\nAllen M.G., Dopita M.A., Tsvetanov Z.I., Sutherland R.S., \n1999, ApJ 511, 686 \n\n\\bibitem{}\nAntonucci R.R.J., \n1993, ARA\\&A, 31, 473 \n\n\\bibitem{}\nAxon D.J., Capetti A., Macchetto, F.D., \n1999, ApJ submitted\n\n\\bibitem{}\nAxon D.J., Marconi A., Capetti A., Macchetto F.D., \nSchreier E., Robinson, A.,\n1998, ApJ 496, L75 \n\n\\bibitem{} \nBaum S.A., Heckman T., \n1989, ApJ 336, 702 \n\n%\\bibitem{}\n%Bicknell et al. 1998\n\\bibitem{}\nBlitz L., 1993,\nin Protostars and Planets III, eds. E.H. Levy and J.I. 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},
{
"name": "tabella.tex",
"string": " \n\n\\vspace{0.30cm}\n{\\centering \\begin{tabular}{|c|c|c|c|}\n\\hline \n&&&\\\\\n&$v_{jet} =$&$v_{jet} =$&$v_{jet} =$\\\\\n&&&\\\\\n&$1300\\,km\\,s^{-1}$&$6500\\,km\\,s^{-1}$&$32500\\,km\\,s^{-1}$\\\\\n&&&\\\\\n\\hline \n&&& \\\\ \n$\\rho_{cloud} = $&$430\\,cm^{-3}$&$1130\\,cm^{-3}$&$31\\,cm^{-3}$\\\\\n \n&$23\\,km\\,s^{-1}$&$335\\,km\\,s^{-1}$&$6\\,km\\,s^{-1}$\\\\\n \n$30\\,cm^{-3}$&$ 8,900\\,K$&$9,600\\,K$&$23,500\\,K$\\\\\n&$\\tau = 1.75$&$\\tau = 0.34$&$\\tau = 0.06$\\\\ \n&&&\\\\ \n\\hline \n&&&\\\\\n$\\rho_{cloud} =$&& $1170\\,cm^{-3}$ &$390\\,cm^{-3}$\\\\ \n \n& &$100\\,km\\,s^{-1}$ &$380\\,km\\,s^{-1}$ \\\\\n\n$60\\,cm^{-3}$& &$8,300\\,K$&$21,500\\,K$\\\\ \n&$\\tau = 4.65$&$\\tau = 0.93$&$\\tau = 0.17$\\\\ \n&&&\\\\\n\\hline \n&&$\\hfill $&\\\\\n$\\rho_{cloud} =$&&$1360\\,cm^{-3}$&$1690\\,cm^{-3}$\\\\ \n\n& &$170\\,km\\,s^{-1}$&$722\\,km\\,s^{-1}$\\\\\n\n$120\\,cm^{-3}$& &$ 10,500\\,K$&$ 11,300\\,K$\\\\ \n&$\\tau = 13.2$&$\\tau = 2.64$&$\\tau = 0.5$\\\\ \n&&&\\\\\n\\hline \n\\end{tabular}\\par}\n\\vspace{0.30cm}\n\n\n\n\n"
},
{
"name": "tabella1.tex",
"string": " \n \n{\\centering \\begin{tabular}{|c|c|c|c|}\n\\hline \n&\\\\\n&$0.3 < \\tau < 0.55 $\\\\\n&\\\\\n\\hline\n&\\\\ \n$\\rho_{cloud} = 30\\,cm^{-3}$&$4,000\\,km\\,s^{-1} < v_{jet} <7,500\\,km\\,s^{-1} $\\\\ \n&\\\\ \n\\hline\n&\\\\ \n$\\rho_{cloud} = 60\\,cm^{-3}$&$11,000\\,km\\,s^{-1} < v_{jet} <20,500\\,km\\,s^{-1} $\\\\ \n&\\\\ \n\\hline\n&\\\\ \n$\\rho_{cloud} = 120\\,cm^{-3}$&$30,000\\,km\\,s^{-1} < v_{jet} <55,500\\,km\\,s^{-1} $\\\\ \n&\\\\ \n\\hline\n\\end{tabular}\\par}\n\\vspace{0.30cm}\n\n \n\n"
},
{
"name": "tabella2.tex",
"string": " \n \n \n\\vspace{0.30cm}\n\\hspace{17.cm}\n{\\centering \\begin{tabular}{|c|c|c|c|}\n\\hline \n&&&\\\\\n &$v_{jet} = 1,300\\,km\\,s^{-1}$&$v_{jet} = 6,500\\,km\\,s^{-1}$&$v_{jet} = \n32,500\\,km\\,s^{-1}$\\\\\n &&&\\\\\n\\hline\n&&&\\\\\n$P_{kin}$ & $1.1\\,10^{40}\\,erg\\,s^{-1}$ & $1.38\\,10^{42}\\,erg\\,s^{-1}$ &\n$1.73\\,10^{44}\\,erg\\,s^{-1}$ \\\\\n&&&\\\\\n\\hline \n&&& \\\\ \n&${(P_{rad})}_{max} = 0.03\\,10^{40}\\,erg\\,s^{-1}$ & ${(P_{rad})}_{max} = \n0.02\\,10^{42}\\,erg\\,s^{-1}$&${(P_{rad})}_{max} = 0.07\\,10^{42}\\,erg\\,s^{-1}$ \\\\\n $\\rho_{cloud} = 30\\,cm^{-3}$& & &\\\\ \n &$\\eta_{max} = 2.7\\%,\\;\\eta_{2t_{cc}} = 0.08\\% $&$\\eta_{max} = \n1.6\\%,\\;\\eta_{2t_{cc}} = 0.4\\% $\n &$\\eta_{max} = 0.04\\%,\\;\\eta_{2t_{cc}} = 0.5\\,10^{-2}\\% $\\\\ \n&&&\\\\ \n\\hline \n&&&\\\\\n & & ${(P_{rad})}_{max} = 0.14\\,10^{42}\\,erg\\,s^{-1}$&${(P_{rad})}_{max} = \n0.15\\,10^{42}\\,erg\\,s^{-1}$ \\\\\n $\\rho_{cloud} = 60\\,cm^{-3}$& & &\\\\ \n & &$\\eta_{max} = 10.\\%,\\;\\eta_{2t_{cc}} = 0.5\\% $&$\\eta_{max} = \n0.09\\%\\,;\\eta_{2t_{cc}} = 4.\\,10^{-2}\\% $\\\\ \n&&&\\\\\n\\hline\n &&&\\\\\n & & ${(P_{rad})}_{max} = 0.02\\,10^{42}\\,erg\\,s^{-1}$&${(P_{rad})}_{max} = \n0.35\\,10^{42}\\,erg\\,s^{-1}$ \\\\\n $\\rho_{cloud} = 120\\,cm^{-3}$& & &\\\\ \n & &$\\eta_{max} = 1.4\\%,\\;\\eta_{2t_{cc}} = 0.5\\% $&$\\eta_{max} = \n0.2\\%,\\;\\eta_{2t_{cc}} = 1.\\,10^{-2}\\% $\\\\ \n&&&\\\\\n\\hline\n\\end{tabular}\\par}\n\\vspace{0.30cm}\n\n \n\n"
}
] |
[
{
"name": "astro-ph0002016.extracted_bib",
"string": "\\begin{thebibliography}{} \n\n\\bibitem{}\nAllen M.G., Dopita M.A., Tsvetanov Z.I., Sutherland R.S., \n1999, ApJ 511, 686 \n\n\\bibitem{}\nAntonucci R.R.J., \n1993, ARA\\&A, 31, 473 \n\n\\bibitem{}\nAxon D.J., Capetti A., Macchetto, F.D., \n1999, ApJ submitted\n\n\\bibitem{}\nAxon D.J., Marconi A., Capetti A., Macchetto F.D., \nSchreier E., Robinson, A.,\n1998, ApJ 496, L75 \n\n\\bibitem{} \nBaum S.A., Heckman T., \n1989, ApJ 336, 702 \n\n%\\bibitem{}\n%Bicknell et al. 1998\n\\bibitem{}\nBlitz L., 1993,\nin Protostars and Planets III, eds. E.H. Levy and J.I. Lunine,\nTucson: Univ. of Arizona Press, p. 125\n\n\\bibitem{} \nBodo G., Massaglia S., Rossi P., Rosner R., Malagoli A., Ferrari A.,\n1995, A\\&A 303, 281 \n\n%\\bibitem{}\n%Burns, Norman \\& Clarke 1991 \n\n\\bibitem{} \nCaganoff S., et al., \n1991, ApJ 377, L9 \n\n\\bibitem{}\nCapetti A., Axon D.J., Macchetto F.D., Marconi A., Winge C.,\n1999, ApJ, 516, 187\n\n\\bibitem{}\nCapetti A., Axon D.J., Macchetto F.D., \n1997, ApJ 487, 560 \n\n\\bibitem{}\nCapetti A., Axon D. J., Macchetto F.D., Sparks W.B., Boksenberg, A.\n1996, ApJ 469, 554 \n\n\\bibitem{}\nCapetti A., Macchetto F.D., Axon D.J., Sparks W.B., Boksenberg, A.\n1995, ApJ 448, 600 \n\n\\bibitem{}\nCapetti A., Axon D.J., Kukula M., Macchetto F.D., Pedlar A., \nSparks W.B., Boksenberg A. \n1995, ApJL 454, L85 \n\n\\bibitem{}\n Cioffi D. F., Blondin J. M., \n1992, ApJ 392, 458 \n\n\n\\bibitem{}\n Colella P., Woodward P.R.,\n 1984, J. Comp. Phys. 54, 174\n\n\\bibitem{}\nCox D.P., Reynolds R.J., \n1987, ARA\\&A 25, 303\n\n\\bibitem{}\nDopita M.A., \\& Sutherland R.S., \n1995, ApJ 455, 468 \n\n\\bibitem{}\nDopita M.A., \\& Sutherland R.S., \n1996, ApJS 102, 161 \n\n\\bibitem{} \nEvans I. , Koratkar A. , Allen M. , Dopita M., Tsvetanov Z.,\n 1999, ApJ 521, 531 \n\n\\bibitem{}\nFalcke H., Wilson A.S., Simpson C., Bower G.A., \n1996, ApJ 470, 31\n\n\\bibitem{}\nFalcke H., Wilson A.S., Simpson C.\n1998, ApJ 470, 31\n\n\\bibitem{} \nFerruit P. , Wilson A. S., Whittle M. , \nSimpson C. , Mulchaey J. S., Ferland G. J.,\n 1999, ApJ 523, 147 \n\n\n\\bibitem{} \nKoski A. T.,\n1978, ApJ 223, 56 \n\n\\bibitem{} \nKraemer S. B., Ruiz J. R., Crenshaw D. M.,\n1998, ApJ 508, 232 \n\n\\bibitem{}\nKukula M., Pedlar A., Baum S., O'Dea C.P.,\n1995, MNRAS 276, 1262\n\n\\bibitem{}\nKukula M., Ghosh T., Pedlar A., Schilizzi R.T., \n1999, ApJ 518, 117 \n\n\\bibitem{} \nNorman M. L., Winkler K. -H. A., Smarr L., Smith M. D., \n1982, A\\&A 113, 285 \n\n\\bibitem{}\nPedlar A., et al. \n1993, MNRAS 263, 471\n\n\\bibitem{} \nRaymond J. C., \\& Smith B. W., \n1977, ApJS 35, 419 \n\n\\bibitem{}\nRossi P. \\& Capetti A.,\n1998 in ``Astrophysical Jets: Open Problems'', eds. Massaglia S. \\& Bodo, G.,\nNew York: Gordon and Breach, p.139\n\n\\bibitem{} \nSteffen W., Gomez J. L., Williams R. J. R., Raga A. C., Pedlar A.,\n 1997a, MNRAS 286, 1032 \n\n\\bibitem{} \nSteffen W., Gomez J. L., Raga A. C., Williams R. J. R.,\n 1997b, ApJ 491, L73 \n\n\\bibitem{}\nSutherland R.S., Bicknell G.V., Dopita, M.A., \n1993, ApJ 414, 510 \n\n%\\bibitem{}\n%Wilson \\& Scheuer 1983)\n\n\\bibitem{} \nWhittle M.,\n 1985, MNRAS 213, 1 \n\n\\bibitem{}\nWilson A.S., \\& Tsvetanov Z.I.,\n1994, AJ 107, 1227\n\n\\bibitem{} \nWilson A. S., \\& Raymond J. C.,\n 1999, ApJ 513, L115 \n\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002017
|
X-Ray Wakes in Abell~160
|
[
{
"author": "Nick Drake"
},
{
"author": "$^{1}$ Michael R. Merrifield"
},
{
"author": "$^{2}$ Irini Sakelliou$^{3}$ and Jason C. Pinkney$^{4}$"
},
{
"author": "$^{1}$Department of Physics and Astronomy"
},
{
"author": "Highfield"
},
{
"author": "Southampton SO17 1BJ"
},
{
"author": "$^{2}$School of Physics and Astronomy"
},
{
"author": "Nottingham NG7 2RD"
},
{
"author": "$^{3}$Mullard Space Science Laboratory"
},
{
"author": "Holmbury St. Mary"
},
{
"author": "Dorking"
},
{
"author": "Surrey RH5 6NT"
},
{
"author": "$^{4}$Department of Astronomy"
},
{
"author": "Ann Arbor"
},
{
"author": "MI~48109--1090"
},
{
"author": "USA"
}
] |
`Wakes' of X-ray emission have now been detected trailing behind a few (at least seven) elliptical galaxies in clusters. To quantify how widespread this phenomenon is, and what its nature might be, we have obtained a deep (70~ksec) X-ray image of the poor cluster Abell~160 using the ROSAT~HRI. Combining the X-ray data with optical positions of confirmed cluster members, and applying a statistic designed to search for wake-like excesses, we confirm that this phenomenon is observed in galaxies in this cluster. The probability that the detections arise from chance is less than $3.8\times10^{-3}$. Further, the wakes are not randomly distributed in direction, but are preferentially oriented pointing away from the cluster centre. This arrangement can be explained by a simple model in which wakes arise from the stripping of their host galaxies' interstellar media due to ram pressure against the intracluster medium through which they travel.
|
[
{
"name": "a160.tex",
"string": "\\documentstyle[psfig]{mn}\n\\input epsf\n\n\\title[X-Ray Wakes in Abell~160]\n {X-Ray Wakes in Abell~160}\n\n\\author[N. Drake et al.]\n {Nick Drake,$^{1}$ Michael R. Merrifield,$^{2}$ Irini Sakelliou$^{3}$ \nand Jason C. Pinkney$^{4}$ \\\\ \n $^{1}$Department of Physics and Astronomy, University of Southampton,\n Highfield, Southampton SO17 1BJ \\\\ \n $^{2}$School of Physics and Astronomy, University Park, University of \n Nottingham, Nottingham NG7 2RD \\\\ \n $^{3}$Mullard Space Science Laboratory, University College \n London, Holmbury St. Mary, Dorking, Surrey RH5 6NT \\\\ \n $^{4}$Department of Astronomy, University of Michigan, \n Ann Arbor, MI~48109--1090, USA}\n\n\\date{Accepted . Received ; \n in original form }\n\n\\begin{document}\n\n\\maketitle\n\n% *** Abstract ***\n\\begin{abstract} \n\n`Wakes' of X-ray emission have now been detected trailing behind a few (at\nleast seven) elliptical galaxies in clusters. To quantify how widespread\nthis phenomenon is, and what its nature might be, we have obtained a deep\n(70~ksec) X-ray image of the poor cluster Abell~160 using the\n\\emph{ROSAT}~HRI. Combining the X-ray data with optical positions of\nconfirmed cluster members, and applying a statistic designed to search for\nwake-like excesses, we confirm that this phenomenon is observed in\ngalaxies in this cluster. The probability that the detections arise from\nchance is less than $3.8\\times10^{-3}$. Further, the wakes are not\nrandomly distributed in direction, but are preferentially oriented\npointing away from the cluster centre. This arrangement can be explained\nby a simple model in which wakes arise from the stripping of their host\ngalaxies' interstellar media due to ram pressure against the intracluster\nmedium through which they travel. \n\n\\end{abstract} \n\n\\begin{keywords}\n galaxies: clusters: individual (Abell~160) --- galaxies: kinematics and \ndynamics --- X-rays: galaxies\n\\end{keywords}\n\n\n% *** Section One ***\n\\section{Introduction}\n\\label{sec:introduction}\n\nWith the advent of satellite-based X-ray astronomy, it was discovered that\nelliptical galaxies can contain as much interstellar gas as their spiral\nkin [for example, see Forman et al.\\ (1979)]. In the case of ellipticals,\nhowever, this interstellar medium (ISM) predominantly takes the form of a\nhot plasma at a temperature of $\\sim 10^7\\,{\\rm K}$. The vast majority of\nelliptical galaxies are found in clusters, which themselves are permeated\nby very hot gas --- the intracluster medium (ICM) --- at a temperature of\n$\\sim 10^8\\,{\\rm K}$. The existence of these two gaseous phases raises\nthe question of how they interact with each other. The collisional nature\nof such material means that one might expect ram pressure to strip the ISM\nfrom cluster members. But since the ISM is continually replenished by\nmass loss from stellar winds, planetary nebulae, and supernovae, it is not\nevident \\emph{a priori} that galaxies will be entirely denuded of gas by\nthis process. \n\nObserving the X-ray emission from individual cluster galaxies is quite\nchallenging, since they are viewed against the bright background of the\nsurrounding ICM. Sakelliou \\& Merrifield (1998) used a deep \\emph{ROSAT}\nobservation to detect the X-ray emission from galaxies in the\nmoderately-rich cluster Abell~2634. They showed that the level of galaxy\nemission is consistent with the expected X-ray binary content of the\ngalaxies, and hence that there is no evidence of surviving ISM in this\nrich environment. \n\nWhen one looks in somewhat poorer environments, one does see evidence for\nsurviving interstellar gas, and for the stripping process itself. The\nbest-documented example is M86 in the Virgo Cluster which, when mapped in\nX-rays, reveals a tail or plume of hot gas apparently being stripped from\nthe galaxy by ram pressure [Rangarajan et al.\\ (1995), and references\ntherein]. A similar process appears to be happening to NGC~1404 in the\nFornax Cluster, which displays a clear wake of X-ray emission pointing\naway from the cluster centre (Jones et al.\\ 1997). Evidence for a\n`cooling wake' formed by gravitational accretion is found in the NGC~5044\ngroup where a soft, linear X-ray feature is seen trailing from NGC~5044\nitself (David et al. 1994). \n\nGiven the difficulty of detecting such faint wakes against the bright\nbackground of the ICM, it is quite possible that this phenomenon is\nwidespread amongst galaxies in poor clusters. This possibility is\nintriguing, since wakes indicate the direction of motion of galaxies on\nthe plane of the sky, and it has been shown that this information can be\ncombined with radial velocity data to solve for both the distribution of\ngalaxy orbits in a cluster and the form of the gravitational potential\n(Merrifield 1998). The existing isolated examples do not tell us,\nhowever, how common wake formation might be amongst cluster galaxies:\nalthough the observed wakes might represent the most blatant examples of\nwidespread on-going ISM stripping, the galaxies in question might have\nmerged with their current host clusters only recently, or be in some other\nway exceptional. \n\n\n% * Figure 1 *\n\\begin{figure*}\n \\begin{center}\n \\psfig{file=figures/fig1.eps,width=17.6cm,angle=0}\n \\end{center}\n \\caption{Greyscale \\emph{ROSAT} HRI image of Abell~160, smoothed using a \n Gaussian kernel with a dispersion of eight arcseconds. \n The positions of the 35 cluster galaxies with measured \n redshifts studied in this paper are marked with symbols \n such that the brightest 15 are \n marked with `$+$' and the fainter 20 with `$=$'. \n These subsamples are discussed later in the paper.} \n \\label{fig:overlay}\n\\end{figure*}\n\n\nIn order to obtain a more objective measure of the importance of ram\npressure stripping in poor clusters, and the frequency with which it\nproduces wakes behind galaxies, we need to look at a well-defined sample\nof cluster members within a single system. The cluster Abell~160 provides\nan ideal candidate for such a study. Its richness class of 0 makes it a\ntypical poor system. It lies at a redshift of $z=0.045$, and hence at a\ndistance of $270\\,{\\rm Mpc}$,\\footnote{We adopt a value for the Hubble\nconstant of $H_{0}=50\\,{\\rm km}\\,{\\rm s}^{-1}\\,{\\rm Mpc}^{-1}$ throughout\nthis paper.} which is sufficiently close to allow galactic-scale structure\nto be resolved in its X-ray emission and corresponds to a size scale of\n$\\sim79$~kpc~arcmin$^{-1}$. Furthermore, its Bautz-Morgan class of III\nmeans that it contains quite a number of comparably luminous galaxies, and\none might hope to detect ISM emission most readily from such a sample. In\naddition, its Rood-Sastry classification of C means that its members are\nconcentrated towards the centre of the cluster: galaxies lying in the\ncluster core, where the ICM density is high, will be most affected by ram\npressure stripping. Finally, Pinkney (1995) has obtained positions and\nredshifts for an almost complete, independently-defined set of galaxies in\nthe field of Abell~160, providing an objective sample of cluster members\nfor this study. \n\nWe therefore obtained a deep \\emph{ROSAT} HRI X-ray image of Abell~160 in\norder to investigate ISM stripping in this typical poor cluster. We use a\nGalactic H\\textsc{i} column density towards A160 of\n$4.38\\times10^{20}$~cm$^{-2}$ (Stark et al. 1992) throughout this paper. \nIn the next section, we present the X-ray observation and the redshift\ndata employed. Section~3 describes an objective method for detecting and\nquantifying wake features in the X-ray data, and Section~4 presents the\nresults of applying this approach to the Abell~160 data. We conclude in\nSection~5 with a discussion of the interpretation of the results. \n\n\n% * Table 1 *\n\\begin{table*}\n \\centering\n \\caption{\\emph{ROSAT}~HRI observations of Abell~160.}\n \\begin{tabular}{cccc} \\hline\n {\\em Observation Start Date} & {\\em Observation End Date} & {\\em \n Number of Used OBIs} & {\\em Total Time (s)} \\\\\n \\hline\n 1996~Dec~30 & 1997~Jan~19 & 14 & 36965 \\\\ \n 1997~Jul~01 & 1997~Jul~30 & 8 & 16501 \\\\ \n 1997~Dec~30 & 1998~Jan~07 & 10 & 16943 \\\\ \n \\hline \\\\\n \\end{tabular}\n \\protect\\label{tab:log}\n\\end{table*}\n\n\n\n% *** Section Two ***\n\\section{X-Ray data and Optical Redshifts}\n\\label{sec:data}\n\n\nAbell~160 was observed with the \\emph{ROSAT} HRI in three pointings\n(1997~January and July, and 1998~January) for a total integration time of\n70.4~ksec (see Table~\\ref{tab:log}). The data were reduced with the\n\\emph{ROSAT} Standard Analysis pipeline, with subsequent analysis\nperformed using the IRAF/PROS software package. \n \nPoint sources detected in the three X-ray observations were used to\nexamine the registration in relation to the nominal \\emph{ROSAT} pointing\nposition. A \\emph{Digitized Sky Survey} image of Abell~160 was employed\nto provide the optical reference frame. The second observation set was\nshifted $\\sim-0.9$ arcseconds east and $\\sim1.7$~arcsec south, and the\nthird set was shifted $\\sim0.3$~arcsec east and $\\sim1.8$~arcsec south. \nRegistration of all three sets of observations was then within\n0.5~arcseconds of the optical reference, tied down to five sources. A\ngreyscale image of the merged X-ray dataset is shown in\nFigure~\\ref{fig:overlay}. \n\nThe centroid of the diffuse X-ray emission in this image was\ncalculated by interpolating over any bright point sources, and\nprojecting the emission down on to two orthogonal axes. \nFitting a Gaussian to each of these one-dimensional distributions then \ngives a robust estimate for the centroid of the emission. \nThis procedure yielded a location of \n\\[ \\left. \n\\begin{array}{c} \n\\alpha_{2000.0}=01^{\\mathrm{h}}~13^{\\mathrm{m}}~05^{\\mathrm{s}} \n\\\\ \n\\delta_{2000.0}=+15^{\\circ}~29^{\\prime}~48^{\\prime\\prime} \n\\end{array} \n\\right\\} \n\\pm43~\\mathrm{arcsec}, \\]\nwhich was adopted as the cluster centre for the subsequent analysis. \n\nPinkney (1995) obtained redshifts for the 94 brightest galaxies in the\nfield of A160 using the MX~multi-object spectrograph on the Steward\nObservatory 2.3m telescope. Figure~\\ref{fig:veldist} shows the resulting\nvelocity distribution. In order to investigate the X-ray properties of\nnormal cluster members, we have excluded the central galaxy since it\ncontains a twin-jet radio source (Pinkney 1995), so its X-ray emission may\nwell contain a significant contribution from the central AGN. There are\n91 galaxies within 8,000~km~s$^{-1}$ of the twin-jet source\n($v_{\\mathrm{TJ}}=13,173\\pm100$~km~s~$^{-1}$); some of these form a\nbackground cluster detected at approximately 18,000~km~s$^{-1}$. After\nfurther eliminating galaxies outside the field of view of the HRI, we end\nup with a sample of 35 cluster members whose X-ray emission we wish to\nquantify. This subsample, highlighted in Figure~\\ref{fig:veldist}, has a\nline-of-sight velocity dispersion of 560~km~s$^{-1}$, directly comparable\nto other poor clusters. The locations of these galaxies are marked on\nFigure~\\ref{fig:overlay} where the different symbols indicate different\nsubsamples of galaxies based upon optical luminosity, as described in the\nfigure's caption. \n\n\n\n\n% *** Section Three ***\n\\section{Detecting Wakes}\n\\label{sec:wakedetect}\n\nHaving combined the optical cluster member locations with the X-ray data,\nwe now turn to trying to see whether there is X-ray emission associated\nwith any individual galaxy, and whether it takes the form of an X-ray\nwake. On examining Figure~\\ref{fig:overlay}, the eye is drawn to a number\nof cases where there is an enhancement in the X-ray emission near, but\noffset from, the optical galaxy position --- see, for example, the galaxy\nat RA~1:12:38, Dec~15:28:03. It would be tempting to ascribe these\nnear-coincidences to X-ray wakes. However, it is also clear from\nFigure~\\ref{fig:overlay} that there are many apparent enhancements in the\nX-ray emission that are totally unrelated to cluster members: some will be\nfrom foreground and background point sources, while others are probably\nsubstructure or noise associated with the ICM itself. What we need,\ntherefore, is some objective criterion for assessing the probability that\nany given wake is a true association rather than a chance superposition. \nFurther, even if we cannot unequivocally decide whether some particular\nfeature is real, we need to be able to show that there are too many\napparent wakes for all to be coincidences. \n\n\n% * Figure 2 *\n\\begin{figure}\n \\centering\n \\psfig{file=figures/fig2.eps,width=8cm,angle=270}\n \\caption{Histogram showing the distribution of velocities of galaxies\nin the field of Abell~160. The subsample of galaxies taken \nto be cluster members, and which are in the field of view of \n\\emph{ROSAT's} High Resolution Imager, is highlighted as a solid histogram.} \n \\label{fig:veldist}\n\\end{figure}\n\n\nThe test adopted to meet these requirements is as follows. First, for\neach galaxy we must seek to detect the most significant wake-like emission\nthat might be associated with it. We must therefore choose a range of\nradii from the centre of the galaxy in which to search for a wake. \nScaling the wakes previously detected in other clusters to the distance of\nAbell~160, we might expect enhanced X-ray emission at radii $r < 8\\,{\\rm\narcsec}$, equivalent to a galaxy distance of approximately 10~kpc. We\nalso want, as far as possible, to exclude emission from any faint central\nAGN component in the galaxy, so we only consider emission from radii $r >\n3\\,{\\rm arcsec}$. Balsara, Livio \\& O'Dea (1994) found wake-like\nstructure in high resolution, hydrodynamic simulations with a scalelength\nof $\\sim2$~arcseconds at the distance of Coma (see also Stevens, Acreman\n\\& Ponman 1999); in the poor environment of Abell~160 we expect wakes to\nbe longer as their formation should be dominated by ISM stripping. We\nadopt the annulus $3 < r < 8\\,{\\rm arcsec}$ to search for wakes: counts\nin annuli with larger inner and outer radii were also performed but did\nnot improve the statistical results described below. \n\nIn our chosen annulus, we search for the most significant emission feature\nby taking a wedge with an opening angle of 45 degrees, rotating about the\ncentre of the galaxy in 10 degree increments, and finding the angle that\nproduces the maximum number of counts in the intersection of the wedge and\nthe annulus. Finally, the contribution to the emission in this wedge from\nthe surrounding ICM is subtracted by calculating an average local\nbackground between radii $25 < r< 60\\,{\\rm arcsec}$, centered on the\ngalaxy and each comparison region at the same cluster radius (see below),\nto give a brightest wake flux, $f_{\\rm wake}$. \n\nTo provide a diagnostic as to the nature of this wake, its direction on\nthe plane of the sky, $\\Theta$, was also recorded. This angle was\nmeasured relative to the line joining the galaxy to the cluster centre, so\nthat $|\\Theta| = 0^{\\circ}$ corresponds to a wake pointing directly away\nfrom the cluster centre, while $|\\Theta|=180^{\\circ}$ indicates one\npointing directly toward the cluster centre.\\footnote{Under the assumption\nof approximately spherical symmetry in the cluster, there is no physical\ninformation in the sign of $\\Theta$.}\n\nHaving found this strongest wake feature, we must assess its significance. \nTo do so, we simply repeated the above procedure using\n$n_{\\mathrm{comp}}=100$ points for each galaxy at the same projected\ndistance from the cluster centre, but at randomly-selected azimuthal\nangles. These comparison points were chosen to lie at the same distance\nfrom the cluster centre so that the properties of the ICM and the amount\nof vignetting in the \\emph{ROSAT} image were directly comparable to that\nat the position of the real galaxy. As noted above, counts in `background\nannuli' were also acquired and all these counts were averaged together in\norder to obtain a value for the background to be subtracted from the\ncounts in each wedge region. Fewer comparison regions were used for the\n12 galaxies closest to the cluster centre, as otherwise the count regions\nwould overlap. \n\nThe comparison regions and real\ndata were then sorted by their values of $f_{\\rm wake}$, from faintest\nto brightest, and the rank of the galaxy (i.e. the position of the\nreal data in this ordered list), $\\mathrm{Rank}_{\\mathrm{gal}}$,\ncomputed. \nThe statistic\n\\begin{equation} \nk=\\frac{\\mathrm{Rank}_{\\mathrm{gal}}}{n_{\\mathrm{comp}}+1} \n\\label{eq:frank} \n\\end{equation} \nwas then calculated. \nClearly, if all the apparent galaxy wakes were\nspurious, then nothing would differentiate these regions from the\ncomparison regions, and we would expect $k$ to be uniformly\ndistributed between 0 and 1. \nFor significant wake features, on the\nother hand, we would expect the distribution of $k$ values to be\nskewed toward $k \\sim 1$. \n\nAs an additional comparison to the X-ray emission around galaxies in\nAbell~160 we performed the same analysis on 70.4~ksec of `blank field'\ndata, extracted from the \\emph{ROSAT} Deep Survey, which encompasses\n$\\sim1,320$~ksec of HRI pointings towards the Lockman Hole (see e.g. \nHasinger et al. 1998). We searched for wake-like features around 35\nrandom positions across this HRI field, using comparison regions for each\n`galaxy' as defined above. \n\n% *** Section Four ***\n\\section{Results}\n\\label{sec:results}\n\nWe have applied the above analysis to the confirmed cluster members using\nIRAF software packages and the merged QP datafile. Figure~\\ref{fig:khist}\nshows the distribution of the $k$ statistic for both the complete sample\nof 35 galaxies and the subsample of the 15 brightest galaxies. The full\nsample of A160 galaxies yields a reduced chi-squared value of\n$\\chi^{2}=1.617$ when fitted by a uniform distribution, which is\napproximately a $3\\sigma$ deviation; the probability of obtaining\n$\\chi^{2}\\geq1.617$ for 34 degrees of freedom is only\n$\\sim5.1\\times10^{-3}$. The full sample has $\\left<k\\right> = 0.628$ and\nthe subsample of the 15 brightest galaxies yields $\\left<k\\right> =\n0.741$; indeed, selecting subsamples of the 20 or so optically brightest\ngalaxies always gives $\\left<k\\right> > 0.7$ and the distributions are\nclearly skewed towards $k=1$. This suggests that we have detected\nsignificant wake-like excesses in these data. \n\n% * Figure 3 *\n\\begin{figure}\n \\centering\n \\psfig{file=figures/fig3.eps,width=8cm,angle=270}\n \\caption{Histogram of the values of the $k$ statistic derived for both the\n complete sample of 35 cluster members (dashed line) and for the \n subsample of the 15 brightest cluster members (solid line). }\n \\label{fig:khist}\n\\end{figure}\n\nKolmogorov-Smirnov tests were performed to compare the $k$ statistic\nresults to a uniform distribution. Figure~\\ref{fig:kspanels} presents\nthese test results for the complete sample of galaxies as well as the\nbrightest 15 subsample. The figure's annotation gives the values of the\nK-S statistic, $d$, which is simply the greatest distance between the\ndata's cumulative distribution and that of a uniform distribution, and\n\\emph{prob}, which is a measure of the level of significance of $d$. The\nprobability of the detected features arising from chance is less than\n$3.5\\times10^{-4}$ for the bright sample and $3.8\\times10^{-3}$ for the\nentire sample of 35 galaxies. It is clear from Figure~\\ref{fig:kspanels}\nthat the more luminous galaxies do not follow a uniform distribution in\n$k$-space. \n\n% * Figure 4 *\n\\begin{figure}\n \\centering\n \\psfig{file=figures/fig4.eps,width=8cm,angle=270}\n \\caption{Plot of the cumulative distributions of the Kolmogorov-Smirnov \ntest for the whole sample of 35 cluster galaxies (top panel) and for the \nsubsample of the 15 optically brightest galaxies (bottom panel). \n$d$ and \\emph{prob} are explained in the text.} \n \\label{fig:kspanels}\n\\end{figure}\n\nThe analysis applied to the Deep Survey `blank field' data yielded a mean\nvalue for the $k$ statistic of $\\left<k\\right>=0.48$ indicating that the\nresults are uniformly distributed in $k$-space and that we do not detect\n`wakes' in this comparison field. Indeed, assuming a uniform distribution\nfor $k$, the fit to the data has a chi-squared value of $\\chi^{2}=1.015$,\nimplying that the values of $k$ are uniformly distributed to high\nprecision. \n\nIn order to investigate the nature of the wake-like excesses in the A160\ndata, we now consider the distribution of their directions on the sky. \nFigure~\\ref{fig:directions} shows the directions of the strongest\nwake-like features found using the $k$ statistic analysis, for all 35\ncluster members. The lines on this figure represent the wakes and their\nlengths are drawn proportional to wake strength. \n\n% * Figure 5 *\n\\begin{figure}\n \\centering\n \\leavevmode\n \\epsfxsize 0.9\\hsize\n \\epsffile{figures/fig5.eps}\n% \\psfig{file=figures/fig5.eps,width=8cm,angle=270}\n \\caption{Directions of the wake-like features found for the 35 cluster \n galaxies in Abell~160. \n The positions of the galaxies are marked by crosses and the \n lines represent the wakes. \n Length of line is proportional to wake strength (as determined \n by the $k$ statistic). \n The centre of the cluster is also shown for reference. }\n \\label{fig:directions}\n\\end{figure}\n\nThe azimuthal distributions of the counts found in some of the\nhighest-ranked wakes are shown in Figure~\\ref{fig:wprofs}. The wake\nprofiles show wakes for these galaxies to be statistically significant\nwith a mean net count of $\\sim5$, corresponding to a mean net X-ray flux\nof $1.7\\times10^{-15}$erg~cm$^{-2}$~s$^{-1}$. The wake fluxes translate\ninto X-ray luminosities in the range $(1-2)\\times10^{40}$erg~s$^{-1}$. \nGrebenev et al. (1995) used a wavelet transform analysis to study the\nsmall-scale X-ray structure of the richness class 2 cluster Abell 1367: \nthey found 16 extended features of which nine were associated with\ngalaxies and had luminosities in the range\n$(3-30)\\times10^{40}$erg~s$^{-1}$. They concluded that the features could\nbe associated with small galaxy groups, as suggested by Canizares,\nFabbiano \\& Trinchieri (1987), rather than individual galaxies. The\nwake-like features we have detected have X-ray luminosities of the same\norder as individual galaxies in Abell 160, and the emission is clearly\nconfined to extensions in specific directions away from the galaxies. \nFurthermore, the features noted by Canizares, Fabbiano \\& Trinchieri\n(1987) have size scales $\\sim1^{\\prime}$, much larger than the expected\nwake size at the distance of A1367 and so not directly comparable with the\ncurrent work. \n\n\n% * Figure 6 *\n\\begin{figure*}\n \\centering\n \\psfig{file=figures/fig6.eps,width=17.6cm,angle=270}\n \\caption{Azimuthal distributions of the counts around four galaxies for \nwhich $k>0.9$. Here the azimuthal angle (with respect to the parent \ngalaxy) is defined such that $0^{\\circ}$ corresponds to north on the sky \nand the angle increases counter-clockwise. The values of $k$ for each \ngalaxy are noted in the panels. }\n \\label{fig:wprofs}\n\\end{figure*}\n\n\n\nFigure~\\ref{fig:scatter} shows the distribution of apparent wake angles as\na function of the galaxies' radii in the cluster, for different strengths\nof wake as quantified by the $k$ statistic. As we might expect, for low\nvalues of $k$ where the wake is almost certainly a noise feature, the\nvalues of $\\left|\\Theta\\right|$ are randomly distributed between\n$0^{\\circ}$ and $180^{\\circ}$. However, for values of $k>0.7$, which are\nunlikely to be attributable to noise, there is only one wake pointed at an\nangle of $\\left|\\Theta\\right|>135^\\circ$. If the distribution of wake\ndirections was intrinsically isotropic, the probability of finding only\none of the 12 most significant wakes in this range of angles is only 0.01. \nGiven the \\emph{a posteriori} nature of this statistical measure, its high\nformal significance should not be over-interpreted. Nonetheless, there\ndefinitely appears to be a deficit of wakes pointing toward the cluster\ncentre. \n\n\n\n% *** Section Five ***\n\\section{Discussion}\n\\label{sec:discussion}\n\nAs a first attempt at an objective determination of the frequency of wakes\nbehind cluster galaxies, we have found significant excesses of X-ray\nemission apparently offset from their host galaxies. Before exploring the\npossible astrophysical meaning of such features, we must rule out more\nprosaic possibilities. \n\nIf the X-ray emission were truly centred on the galaxies, we would still\ndetect offset X-ray emission if there were significant positional errors\nin the optical galaxy locations. The uncertainties on these positions,\nhowever, are much less than the radii at which we have detected the wakes,\nso this possibility can be excluded. Similarly, an overall mismatch\nbetween the optical and X-ray reference frames would produce offsets\nbetween X-ray and optical locations of coincident sources, but the\ndistribution of apparent offset directions shown in\nFigure~\\ref{fig:directions} is not consistent with the coherent pattern\nthat one would expect from either an offset or a rotation between the two\nframes. \n\n\n% * Figure 7 *\n\\begin{figure}\n \\centering\n \\psfig{file=figures/fig7.eps,width=8cm,angle=270}\n \\caption{Scatter plot of the projected angle\n $\\left|\\Theta\\right|$ of the 35 brightest wedge features as a \n function of distance from cluster centre. \n Larger point sizes reflect greater values of the \n $k$ statistic found for each galaxy, as \n given in the key to the figure. }\n \\label{fig:scatter}\n\\end{figure}\n\n\nWe could explain the excess of sources where the X-ray emission lies at\nlarger radii in the cluster than the optical position if the spatial scale\nof the optical data had been underestimated relative to that of the X-ray\ndata. But both the \\emph{ROSAT} and optical data image scales are\nextremely well calibrated. Further, if such mismatch in magnification\nwere responsible for the effect, one would expect the radial offsets to\nincrease with distance from the field centre, and Figure~\\ref{fig:scatter}\nprovides no evidence that the wakes become more radially oriented at large\ndistances from the cluster centre. \n\nA further possibility is that the distorted nature of the X-ray emission\ncould arise from an asymmetry in the \\emph{ROSAT} HRI point-spread\nfunction (PSF). Such asymmetries are documented [see, for example, Morse\net al.\\ (1995)], but the observed shape of the HRI PSF actually becomes\ntangentially extended at large off-axis angles, so one would expect the\nwakes to be oriented at angles of $|\\Theta| \\sim 90^\\circ$. The three\nwakes at very large radii and $|\\Theta| \\simeq70-120^\\circ$ in\nFigure~\\ref{fig:scatter} could well result from this phenomenon, but there\nis no evidence for any such effect at smaller radii. \n\nWe are therefore forced to return to trying to find an astrophysical\nexplanation for the bulk of the observed wakes. As discussed in the\nintroduction, an individual galaxy can emit at X-ray wavelengths due to\nboth its hot ISM component and its contingent of X-ray binaries. Such\nemission could extend to the radii where we have been searching for wakes,\nor appear to do so due to the blurring influence of the PSF, so we might\nexpect some wake-like features to appear simply due to this component. \nSuch asymmetric wake features could arise from Poisson noise on\nintrinsically symmetric emission, or it could reflect a real asymmetry in\nthe emission. For example, the emission from X-ray binaries could be\ndominated by one or two ultra-luminous sources in the outskirts of a\ngalaxy, leading to an offset in the net X-ray emission. Even the X-ray\nwake phenomenon that we are seeking to detect can be described as an\nasymmetric distortion in the normal ISM emission. How, then, are we to\ndistinguish between these possibilities? \n\nPerhaps the best clue as to the nature of the detected asymmetric emission\ncomes from the distribution of the angles at which it is detected,\n$\\Theta$. As we have described above, there is a deficit of wakes\npointing toward the cluster centre. It is hard to see how such a\nsystematic effect can be attributed to any of the more random processes\nsuch as Poisson noise on a symmetric component, or even the azimuthal\ndistribution of X-ray binaries within the galaxy. It therefore seems\nhighly probable that we are witnessing the more systematic wake phenomenon\nthat we seek. If a wake indicates the direction of motion of the galaxy,\nthen the deficit of detections at large values of $|\\Theta|$ implies that\nthe production mechanism becomes ineffective when a galaxy is travelling\nout from the cluster centre. This conclusion has a simple physical\nexplanation: if a galaxy is travelling on a reasonably eccentric orbit, by\nconservation of angular momentum it will spend a large fraction of its\ntime close to the orbit's apocentre. During this period, its velocity is\nslow and the ICM it encounters is tenuous, so it is able to retain its\nISM. In fact, continued mass loss from stellar winds and planetary\nnebulae means that the amount of gas in its ISM will increase. \nUltimately, however, its orbit will carry it inward toward the core of the\ncluster. At this point, the galaxy is travelling more rapidly, and\nencounters the higher density gas near the centre of the cluster, so ram\npressure stripping becomes more efficient, and a wake of stripped ISM\nmaterial will be seen behind the infalling galaxy. By the time the galaxy\npasses the pericentre of its orbit, the ISM will have been stripped away\nto the extent that the outgoing galaxy does not contain the raw material\nto create a measurable wake, explaining the lack of detected wakes at\nlarge values of $|\\Theta|$. \n\nThis simple picture seems to fit the data on Abell~160 rather well; a\nsimilar scenario was invoked by McHardy (1979) to explain the locations of\nweak radio sources in clusters. It is also notable that the beautiful\nwake feature behind NGC~1404 in the Fornax Cluster detected by Jones et\nal.\\ (1997) is oriented such that it points radially away from the cluster\ncentre. Clearly, though, more deep X-ray observations of clusters are\nrequired if we are to confirm the widespread applicability of this\nscenario. \n\n\n% ** Acknowledgements **\n\\subsection*{Acknowledgements}\nThe authors are grateful to the referee for helpful comments and \nsuggestions, and to Ian McHardy for several fruitful discussions. \nND acknowledges receipt of a PPARC Studentship. \nThis research has made use of data obtained from the Leicester Database \nand Archive Service at the Department of Physics and Astronomy, Leicester \nUniversity, UK. \n\n% *** References ***\n\\begin{thebibliography}{}\n\n \\bibitem[\\protect\\citename{Balsara et al. }1994]{balsara94}\n Balsara D., Livio M., O'Dea C. P., 1994, ApJ, 437, 83 \n \\bibitem[\\protect\\citename{Canizares, Fabbiano \\& Trinchieri \n}1987]{canizares87} \n Canizares C., Fabbiano G., Trinchieri G., 1987, ApJ, 312, 503 \n \\bibitem[\\protect\\citename{David et al. }1994]{david94} \n David L. P., Jones C., Forman W., Daines S., 1994, ApJ, 428, 544 \n \\bibitem[\\protect\\citename{Forman et al. }1979]{forman79}\n Forman W., Schwarz J., Jones C., Liller W., Fabian A. C., 1979, ApJ, \n 234, L27 \n \\bibitem[\\protect\\citename{Grebenev et al. }1995]{grebenev95} \n Grebenev S. A., Forman W., Jones C., Murray S., 1995, ApJ, 445, 607 \n \\bibitem[\\protect\\citename{Hasinger et al. }1998]{hasinger98}\n Hasinger G., Burg R., Giacconi R., Schmidt M., Tr\\\"{u}mper J., Zamorani \n G., 1998, A\\&A, 329, 482 \n \\bibitem[\\protect\\citename{Jones et al. }1997]{jones97}\n Jones C., Stern C., Forman W., Breen J., David L., Tucker W., Franx M., \n 1997, ApJ, 482, 143 \n \\bibitem[\\protect\\citename{McHardy }1979]{mchardy79}\n McHardy I. M., 1979, MNRAS, 188, 495 \n \\bibitem[\\protect\\citename{Merrifield }1998]{merrifield98}\n Merrifield M. R., 1998, MNRAS, 294, 347 \n \\bibitem[\\protect\\citename{Morse et al. }1995]{morse95}\n Morse J. A., Wilson A. S., Elvis M., Weaver K. A., 1995, ApJ, 439, 121 \n \\bibitem[\\protect\\citename{Pinkney }1995]{pinkney95}\n Pinkney J. C., 1995, PhD Thesis. New Mexico State University \n \\bibitem[\\protect\\citename{Rangarajan et al. }1995]{rangarajan95}\n Rangarajan F. V. N., White D. A., Ebeling H., Fabian A. C., 1995, MNRAS, \n 277, 1047 \n \\bibitem[\\protect\\citename{Sakelliou \\& Merrifield }1998]{sakelliou98}\n Sakelliou I., Merrifield M. R., 1998, MNRAS, 293, 489 \n \\bibitem[\\protect\\citename{Stark et al. }1992]{stark92}\n Stark A. A., Gammie C. F., Wilson R. W., Bally J., Linke R. A., Heiles \n C., Hurwitz M., 1992, ApJS, 79, 77 \n \\bibitem[\\protect\\citename{Stevens, Acreman \\& Ponman }1999]{stevens99}\n Stevens I. R., Acreman D. M., Ponman T. J., 1999, MNRAS, 310, 663 \n\n\\end{thebibliography}\n\n\\bsp\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002017.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n \\bibitem[\\protect\\citename{Balsara et al. }1994]{balsara94}\n Balsara D., Livio M., O'Dea C. P., 1994, ApJ, 437, 83 \n \\bibitem[\\protect\\citename{Canizares, Fabbiano \\& Trinchieri \n}1987]{canizares87} \n Canizares C., Fabbiano G., Trinchieri G., 1987, ApJ, 312, 503 \n \\bibitem[\\protect\\citename{David et al. }1994]{david94} \n David L. P., Jones C., Forman W., Daines S., 1994, ApJ, 428, 544 \n \\bibitem[\\protect\\citename{Forman et al. }1979]{forman79}\n Forman W., Schwarz J., Jones C., Liller W., Fabian A. C., 1979, ApJ, \n 234, L27 \n \\bibitem[\\protect\\citename{Grebenev et al. }1995]{grebenev95} \n Grebenev S. A., Forman W., Jones C., Murray S., 1995, ApJ, 445, 607 \n \\bibitem[\\protect\\citename{Hasinger et al. }1998]{hasinger98}\n Hasinger G., Burg R., Giacconi R., Schmidt M., Tr\\\"{u}mper J., Zamorani \n G., 1998, A\\&A, 329, 482 \n \\bibitem[\\protect\\citename{Jones et al. }1997]{jones97}\n Jones C., Stern C., Forman W., Breen J., David L., Tucker W., Franx M., \n 1997, ApJ, 482, 143 \n \\bibitem[\\protect\\citename{McHardy }1979]{mchardy79}\n McHardy I. M., 1979, MNRAS, 188, 495 \n \\bibitem[\\protect\\citename{Merrifield }1998]{merrifield98}\n Merrifield M. R., 1998, MNRAS, 294, 347 \n \\bibitem[\\protect\\citename{Morse et al. }1995]{morse95}\n Morse J. A., Wilson A. S., Elvis M., Weaver K. A., 1995, ApJ, 439, 121 \n \\bibitem[\\protect\\citename{Pinkney }1995]{pinkney95}\n Pinkney J. C., 1995, PhD Thesis. New Mexico State University \n \\bibitem[\\protect\\citename{Rangarajan et al. }1995]{rangarajan95}\n Rangarajan F. V. N., White D. A., Ebeling H., Fabian A. C., 1995, MNRAS, \n 277, 1047 \n \\bibitem[\\protect\\citename{Sakelliou \\& Merrifield }1998]{sakelliou98}\n Sakelliou I., Merrifield M. R., 1998, MNRAS, 293, 489 \n \\bibitem[\\protect\\citename{Stark et al. }1992]{stark92}\n Stark A. A., Gammie C. F., Wilson R. W., Bally J., Linke R. A., Heiles \n C., Hurwitz M., 1992, ApJS, 79, 77 \n \\bibitem[\\protect\\citename{Stevens, Acreman \\& Ponman }1999]{stevens99}\n Stevens I. R., Acreman D. M., Ponman T. J., 1999, MNRAS, 310, 663 \n\n\\end{thebibliography}"
}
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astro-ph0002018
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The HST view of the FR~I / FR~II dichotomy \thanks{Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555 and by STScI grant GO-3594.01-91A}
|
[
{
"author": "M. Chiaberge \\inst{1}"
},
{
"author": "A. Capetti \\inst{2}"
},
{
"author": "A. Celotti \\inst{1}"
}
] |
In order to explore how the FR~I / FR~II dichotomy is related to the nuclear properties of radio galaxies, we studied a complete sample of 26 nearby FR~II radio galaxies using Hubble Space Telescope (HST) images and compared them with a sample of FR~I previously analyzed. FR~I nuclei lie in the radio-optical luminosity plane along a tight linear correlation, which argues for a common synchrotron origin. FR~II show a more complex behavior, which is however clearly related to their optical spectral classification. Broad line FR~II radio galaxies (BLRG) are located overall well above the FR~I correlation, suggesting that a contribution from thermal (disc) emission is present. Three narrow line (NLRG) and one weak line radio galaxy (WLRG), in which no nuclear source is seen, can be interpreted as the obscured counter-parts of BLRG, in agreement with the current unification schemes. Conversely, in 5 sources of the sample, all of them NLRG or WLRG, optical cores are located on the same correlation defined by FR~I and with similar radio and optical luminosities. This suggests that, in analogy to FR~I, the emission is dominated by synchrotron radiation and represents the optical counter-part of the non--thermal radio cores. Interestingly, all these galaxies are located in clusters, an environment typical of FR~I. These results imply that, at least at low redshifts, the FR~II population is not homogeneous. Furthermore, the traditional dichotomy between edge darkened and brightened radio morphology is not univocally connected with the innermost nuclear structure, as we find FR~II with FR~I--like nuclei and this has interesting bearings from the point of view of the AGN unified models. \keywords{galaxies: active - galaxies: elliptical and lenticular, cD - galaxies: jets - galaxies: nuclei}
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[
{
"name": "chiab.tex",
"string": "%\\documentclass[referee]{aa} % for a referee version\n\\documentclass{aa} \n\\usepackage{graphics} \n\\input psfig.sty \n\\newcommand{\\ltsima} {$\\; \\buildrel < \\over \\sim \\;$} \n\\newcommand{\\gtsima} {$\\; \\buildrel > \\over \\sim \\;$} \n\\newcommand{\\lta} {\\lower.5ex\\hbox{\\ltsima}} \n\\newcommand{\\gta} {\\lower.5ex\\hbox{\\gtsima}} \n \n%\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}} \n% \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}} \n%\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}} \n% \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}} \n \n\\begin{document} \n \n\\thesaurus{03(11.01.2; 11.05.1; 11.10.1; 11.14.1)} \n\\title{The HST view of the FR~I / FR~II dichotomy \n\\thanks{Based on observations with the NASA/ESA \nHubble Space Telescope, obtained at the Space Telescope Science \nInstitute, which is operated by AURA, Inc., under NASA contract NAS \n5-26555 and by STScI grant GO-3594.01-91A}} \n \n\\author{M. Chiaberge \\inst{1}, A. Capetti \\inst{2} \\and \nA. Celotti \\inst{1}} \n \n\\offprints{M. Chiaberge} \n \n\\institute{SISSA/ISAS, Via Beirut 2-4, I-34014 Trieste, Italy ([email protected])\n\\and \nOsservatorio Astronomico di Torino, Strada Osservatorio 20, I-10025 \nPino Torinese (TO), Italy } \n \n\\date{Received 17 June 1999; accepted 21 December 1999} \n \n\\titlerunning{HST view of the FR~I and FR~II dichotomy} \n\\authorrunning{Chiaberge et al.} \\maketitle \n \n\\begin{abstract} \nIn order to explore how the FR~I / FR~II dichotomy is related to \nthe nuclear properties of radio galaxies, we studied a complete sample \nof 26 nearby FR~II radio galaxies using Hubble Space Telescope \n(HST) images and compared them with a sample of FR~I \npreviously analyzed. FR~I nuclei lie in the radio-optical \nluminosity plane along a tight linear correlation, which argues for a \ncommon synchrotron origin. FR~II show a more complex behavior, which \nis however clearly related to their optical spectral classification. \n \nBroad line FR~II radio galaxies (BLRG) are located overall well \nabove the FR~I correlation, suggesting that a contribution from thermal \n(disc) emission is present. Three narrow line (NLRG) and one \nweak line radio galaxy (WLRG), in which no nuclear source is \nseen, can be interpreted as the obscured counter-parts of BLRG, in \nagreement with the current unification schemes. \n \nConversely, in 5 sources of the sample, all of them NLRG or WLRG, \noptical cores are located on the same correlation defined by FR~I and \nwith similar radio and optical luminosities. This suggests that, \nin analogy to FR~I, the emission is dominated by synchrotron \nradiation and represents the optical counter-part of the \nnon--thermal radio cores. Interestingly, all these galaxies are \nlocated in clusters, an environment typical of FR~I. \n \nThese results imply that, at least at low redshifts, the FR~II \npopulation is not homogeneous. Furthermore, the traditional dichotomy \nbetween edge darkened and brightened radio morphology is not \nunivocally connected with the innermost nuclear structure, as we \nfind FR~II with FR~I--like nuclei\nand this has interesting bearings from the point of \nview of the AGN unified models.\n \n\\keywords{galaxies: active - galaxies: elliptical and lenticular, cD - galaxies: \njets - galaxies: nuclei} \n \n\\end{abstract} \n \n\\section{Introduction} \n\\label{intro} \nThe original classification of extended radio galaxies by Fanaroff \\& \nRiley (\\cite{fr}) is based on a morphological criterion, i.e. edge \ndarkened (FR~I) vs edge brightened (FR~II) radio structure. It was \nlater discovered that this dichotomy corresponds to a (continuous) \ntransition in total radio luminosity (at 178 MHz) which formally \noccurs at $L_{178}= 2\\times 10^{33}$ erg s$^{-1}$ Hz$^{-1}$. The \npresence of radio sources with intermediate morphology, in which \ntypical FR~I structures (such as extended plumes and tails) are seen \ntogether with features characteristics of FR~II sources (narrow jets \nand hot spots) (see e.g. Parma et al. \\cite{parm87}, Capetti et \nal. \\cite{capetti95}) argues in favour of a continuity between the two \nclasses. \n \nFrom the optical point of view both FR~I and FR~II are associated with \nvarious sub-classes of elliptical-like galaxies, but \nstatistically their populations are different \n(Zirbel \\cite{zirb96}). Owen (\\cite{owen93}) found that \nthe FR~I/FR~II division is also linked to the optical magnitude of the \nhost galaxy, possibly suggesting that the environment plays an \nimportant role in producing different extended radio morphologies. \nMoreover, FR~II are generally found in regions of lower galaxy density \nand are more often associated with galaxy interactions with respect to \nFR~I (Prestage \\& Peacock \\cite{pp}, Zirbel \n\\cite{zirb97}). Differences are also observed in the optical \nspectra: while FR~I are generally classified as weak-lined radio \ngalaxies, strong (narrow and broad) emission lines are often found in \nFR~II (Morganti et al. \\cite{morg92}, Zirbel \\& Baum \\cite{zirb95}), \nalthough a sub-class of weak-lined FR~II is also present (Hine \\& Longair \n\\cite{hine}). \n \nWithin the unification scheme for radio-loud AGN (for a review, see \nUrry \\& Padovani \\cite{urry95}), FR~I and FR~II radio galaxies are \nthought to represent the parent population of BL Lac objects and \nradio-loud quasars, respectively (Antonucci \\& Ulvestad \\cite{anto85},\nBarthel \\cite{bart89}). In order to \nexplain the lack of broad lines in the ``mis-oriented'' (narrow-lined) \nFR~II--type objects, obscuration by a thick torus is invoked. A \ncombination of obscuration and beaming is therefore necessary at least \nfor the FR~II-quasars unification (e.g. Antonucci \\& Barvainis \\cite{anto90}). \nHowever, there is evidence that \nthis simple picture is probably inadequate: some \nradio--selected BL Lacs - among the most powerful sources in the class \n- display an extended radio structure and luminosity typical of FR~II \n(Kollgaard et al. \\cite{koll92}, Murphy et al. \\cite{murphy93}) \nand broad - although weak - lines have been observed in some BL Lacs. \nMoreover, Owen et al. \\cite{owen96} noted that the \nlack of BL Lacs in a sample of radio galaxies located in Abell clusters \ncan be an effect of their selection criteria if the parent population of \nBL Lacs includes both FR~I and FR~II. This idea is also consistent with \na recently proposed modification of the unification scheme, which claim \nthat the weak-lined FR~II are indeed associated with BL Lac objects \n(Jackson \\& Wall \\cite{jackson}).\nThese observations can be however reconciled with the unification \nscenario once continuity between the weak and powerful radio--loud \nsources is allowed and thus transition objects are expected. \n\nIn Chiaberge et al. (\\cite{pap1}, hereafter Paper~I) we studied HST \nimages of all FR~I radio galaxies belonging to the 3CR catalogue, \nfinding that unresolved nuclear sources are commonly present in these \nobjects. A strong linear correlation is found between this optical and \nthe radio core emission, extending over four orders of magnitude in \nluminosity. This, together with spectral information, strongly argues \nfor a common non-thermal origin, and suggests that the optical cores \ncan be identified with synchrotron radiation produced in a \nrelativistic jet, qualitatively supporting the unifying model for FR~I \nand BL Lacs. \nFurthermore, the high rate detection (\\gta 85 \\%) of optical cores in \nthe complete sample indicates that a standard pc--scale geometrically \nthick torus is not present in these low-luminosity radio galaxies. Any \nabsorption structure, if present, must be geometrically thin, \nand thus the lack of broad lines in FR~I cannot be attributed to \nobscuration. Alternatively, thick tori are present only in a minority of FR~I.\nGiven the dominance of non-thermal emission, the optical \ncore luminosity also represents a firm upper limit to any thermal \ncomponent, suggesting that accretion might take place in a low \nefficiency radiative regime. \n \nThe picture which emerges from this analysis is that FR~Is lack \nsubstantial thermal (disc) emission, Broad Line Regions and obscuring \ntori, which are usually associated with radio-quiet and powerful \nradio--loud AGN.\n \nAs a natural extension of Paper~I, here we study the HST images \nof a sample of low redshift FR~II radio galaxies, in order to explore \nhow the differences in radio morphology are related to the optical \nnuclear properties. In particular, one of the most important questions \nis whether the FR~I/FR~II dichotomy is generated by two different \nmanifestations of the same astrophysical phenomenon, and the \ntransition between the two classes is indeed continuous, or instead it \nreflects fundamental differences in the innermost structure of the \ncentral engine. \n \nThe selection of the sample is presented and discussed in \nSect. \\ref{thesample}, while in Sect. \\ref{hstobs} we describe the HST \nobservations. In Sect. \\ref{CCCII} we focus on the detection and \nphotometry of the optical cores. Finally, in Sect. \\ref{discussion} we \ndiscuss our findings. \n \n\\section{The sample} \n\\label{thesample} \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig1.ps}} \n\\caption{Total radio luminosity (at 178 MHz) vs redshift diagram for \nthe FR~I (empty circles) and FR~II (filled circles) samples.} \n\\label{lumz} \n\\end{figure} \n\n\\input tab1.tex \n\n\nThe sample considered here comprises all radio galaxies belonging to \nthe 3CR catalogue (Spinrad \\cite{spinrad}) with redshift $z<0.1$, \nmorphologically classified as FR~II. We directly checked their \nclassification for erroneous or doubtful identifications by \nsearching the literature for the most recent radio maps. The final \nlist (see Table \\ref{tabfr2}) constitutes a complete, flux and \nredshift limited sample of 26 FR~II radio galaxies. \n \nWe searched for optical spectral classification and/or optical \nspectra, in order to differentiate our sources on the basis of the \npresence of broad or narrow emission lines. For only one source \n(namely 3C~136.1) we could not find spectral information in the \nliterature. All spectral types usually associated with FR~II galaxies \nare represented in the sample: five objects are BLRG, fifteen are \nclassified as NLRG, while four show only weak lines in their \noptical spectrum (WLRG). The remaining source, namely \\object{3C~371},\nhas been classified as a BL Lac object. In Table \n\\ref{tabfr2} redshifts and radio data are reported, as taken from the \nliterature, together with the optical spectral classifications. \n \nIn Fig. \\ref{lumz} \nwe show the redshift vs total radio luminosity diagram for the sample \nof FR~II galaxies, together with the sample of FR~I discussed in \nPaper~I, but limited to sources with $z<0.1$ for coherence with the \nFR~II sample. FR~II have a median redshift $z=0.06$, and total radio \nluminosities at 178 MHz are between $10^{32}$ and 10$^{34}$ erg s$^{-1}$ \nHz$^{-1}$ ($H_0= 75$ km s$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$ are adopted \nhereafter). Notice that whereas the two samples are selected at the \nsame limits of redshift and flux, FR~II are, on average, more \nluminous and distant than FR~I. \n \n \n\\section{HST observations} \n\\label{hstobs} \n\n\nHST observations of the FR~II sources are available in the public \narchive (up to April 1999) for 25 out of the 26 sources (only \n\\object{3C~33} and \\object{3C~105} have not been observed). The HST \nimages were taken using the Wide Field and Planetary Camera 2 \n(WFPC2). The whole sample was observed using the F702W \nfilter as part of the HST snapshot survey of 3C radio galaxies (Martel \net al. \\cite{martel}, De Koff et al. \\cite{De Koff}). \nFor 3C~192 we used a F555W image, as this source was not observed with the \nF702W filter. Exposure times are in the range 140--300 s. The \ndata have been processed through the standard PODPS (Post Observation \nData Processing System) pipeline for bias removal and flat fielding \n(Biretta et al. \\cite{biretta}). Individual exposures in each filter \nwere combined to remove cosmic rays events. \n \n\\section{Optical cores in FR~II} \n\\label{CCCII} \n \n\\begin{figure*} \n\\centerline{\\psfig{figure=fig2.eps,width=0.95\\textwidth,angle=0}} \n\\caption{HST/WFPC2 broad band images of three FR~II: \\object{3C~192} is a NLRG \nshowing a diffuse nucleus; \\object{3C~388} is a NLRG with an \noptical core; 3C~390.3 is a BLRG.} \n\\label{figurine} \n\\end{figure*} \n\nIn Paper~I we have adopted a simple operative approach, based on the\nanalysis of the nuclear brightness profile, in order to establish\nwhen an optical core is present in a radio galaxy. \nAs in the case of FR~I sources, \nthe FWHM fall into two very distinct regimes:\nin 11 cases we measured a \nFWHM = 0.05$^{\\prime\\prime}$ -- 0.08$^{\\prime\\prime}$,\ni.e. indicative of the presence of an unresolved source at the HST\nresolution, while in 8 cases we found widths larger than \n0.2$^{\\prime\\prime}$. We therefore believe that \nno ambiguity exists on whether or not a central unresolved source is\npresent.\n\nIn three sources (3C~382, 3C~390.3 and 3C~445)\nthe central regions are saturated. While, on the one hand, this \nprevents us from deriving \ntheir brightness profile, on the other is by itself a clear indication \nof a point-like source. In fact diffuse emission would produce saturation \nwith our instrument configuration and exposure times only for surface \nbrightness $< 13$ mag arcsec$^{-2}$ in the R band, much larger than \ntypically observed\nin the central regions of radio-galaxies at this redshift. Furthermore\nin all these sources we observe diffraction rings and spikes,\nthe characteristic hallmarks of the HST Point Spread Function.\n\nWe performed aperture photometry of these components. \nThe background \nlevel is evaluated, as in Paper I, by measuring the intensity at a \ndistance of $\\sim 5$ pixels ($\\sim 0.23^{\\prime\\prime}$) from the center.\nThe dominant \nphotometric error is thus the determination of the background in regions of \nsteep brightness gradients, especially for the faintest cores, \nresulting in a typical error of $\\sim 10\\%$.\nFor the saturated cores we evaluated their fluxes by comparing the \nPSF wings with those of several bright stars seen in archival HST images\ntaken with the same filter. This method leads to a somewhat larger \nuncertainties, 25 \\% as estimated from the scatter of measures obtained \nwith different reference stars, \nwhich arise from the time dependent structure of the HST PSF.\nIn Table \\ref{tabfr2} we report fluxes and luminosities of \nthe optical cores. \n\nAll of the images were taken using broad band filters, which include \nemission lines. In particular, the F702W transmission curve covers the\nwavelength range $5900-8200$ \\AA ~and thus within our redshift range\nincludes the H$\\alpha$ and [N II] emission lines.\nUnfortunately, no HST narrow band images are available for \nthe NLRG and WLRG, however, we expect the line contamination \nto be small, due to the wide spectral region \ncovered by the filters used ($\\sim$ 2000 \\AA)\nwith respect to typical lines equivalent width. \nWe correct the broad band fluxes only in the case of BLRG, where the \nemission of broad lines is probably co-spatial to the optical core, \nusing ground-based data taken from the literature (Zirbel \\& Baum \n\\cite{zirbel}). The resulting emission line contribution \nis typically $25- 30 \\%$ of the total flux measured in the F702W filter.\n\nIn 8 cases the nuclear regions only show diffuse emission: for such \ngalaxies we estimate upper limits to a possible central component \nevaluating the light excess of the central 3x3 pixels with respect to \nthe surrounding galaxy background. The remaining 3 sources show \ncomplex morphologies, e.g. with dust lanes obscuring the central \nregions, and no photometry was performed. \n \n\\medskip \nFR~II cores span a wide range of optical luminosities $L_o$ \n(from $10^{25.5}$ up to $10^{30}$ erg s$^{-1}$ Hz$^{-1}$). In \nFig. \\ref{lum} we report the optical core versus radio (5 GHz) core \nluminosity for the FR~II sample, superimposed to the data (as from \nPaper~I) for FR~I galaxies limiting ourselves, for consistency, to \nthose with redshift $z<0.1$. \nFR~II show a complex behavior, which however seems to \nbe related to their optical spectral classification. \n \nLet us firstly consider the blazar, \\object{3C~371}. \nAs one might expect, since its emission is \ndominated by beamed synchrotron radiation, it is among the \nbrightest source both in the radio and in the optical band (see \nFig. \\ref{lum}). In the $L_r$ vs $L_o$ plane it falls in the low \nluminosity end of the region defined by radio selected blazars \n(Chiaberge et al., in preparation).\n \nThe second group of sources is represented by the BLRG \n(\\object{3C~111}, \\object{3C~227}, \\object{3C~382}, \\object{3C~390.3} \nand \\object{3C~445}): all of them have very luminous optical cores \n($L_o > 10^{28}$ erg s$^{-1}$ Hz$^{-1}$) being -- together with \n\\object{3C~371} -- the most powerful objects of the sample and clearly \nseparating from the other FR~II in the diagram. Notice that they \nhave an optical excess (or radio deficiency) of up to 2 orders of \nmagnitude with respect to the radio-optical core luminosity \ncorrelation found for FR~I. \n \nIn 5 WLRG and NLRG, namely \\object{3C~88}, \\object{3C~285}, \n\\object{3C~388}, \\object{3C~402} and \\object{3C~403}, we detected \noptical cores which share the same region in the luminosity plane as \nFR~I sources with luminosities between $L_o=10^{25.5}$ up to \nmore than $10^{27.5}$ erg s$^{-1}$ Hz$^{-1}$. \n \nThe 8 upper limits, all associated with WLRG or NLRG, are also \nplotted. Four objects (\\object{3C~35}, \\object{3C~98}, \n\\object{3C~192} and \\object{3C~326}) lie close to the correlation \ndefined by FR~I. Conversely, \\object{3C~15}, \\object{3C~353}, \n\\object{3C~452} and \\object{3C~236} present an optical luminosity \ndeficit of one to two orders of magnitude given their radio core \nemission with respect to FR~I. \n \nNo radio core data have been found in the literature for \n\\object{3C~136.1}, \\object{3C~198} and \\object{3C~318.1}. \n\n\\begin{figure}[h] \n\\resizebox{\\hsize}{!}{\\includegraphics{fig3.ps}} \n\\caption{Optical nuclear luminosity versus radio (5 GHz) core \nluminosity for both the FR~I (open circles) and FR~II (filled circles) \nsamples. Different symbols are used to identify different spectral \nclassifications. The dashed line is the correlation found in the case \nof FR~I galaxies (see Paper~I).} \n\\label{lum} \n\\end{figure} \n \n \n\n \n\\section{Discussion} \n\\label{discussion} \n \nIn the 24 nearby FR~II \nradio galaxies (out of a complete sample of 26) studied in this paper, \n13 show an unresolved optical core, in 8 cases we can only set an \nupper limit to their luminosity, while 3 sources present a \ncomplex nuclear morphology. The location in the optical-radio core \nluminosity plane is clearly connected to the optical spectral \nclassification. \n \nConversely, cores in FR~I radio galaxies show a linear correlation \nbetween their radio and optical luminosity, which strongly argues for \na common non-thermal origin. The presence of such correlation \nprovides a useful benchmark to investigate the origin of optical cores \nin FR~II. \n \nIn the following we consider each FR~II group separately. \n \n\\subsection{Broad Line Radio Galaxies} \n \nLet us first focus on BLRG. These sources present, overall, \na strong optical excess (or radio deficit), of up to two orders of \nmagnitude, with respect to the correlation defined by the FR~I cores \n(see Fig. \\ref{lum}). Note that in the sample of nearby FR~I, the \nonly source lying well above the radio-optical correlation is 3C~386, \nwhich also shows a broad H$\\alpha$ line. \n \nBLRG are objects in which the innermost nuclear regions are thought to \nbe unobscured along our line of sight (Barthel \\cite{bart89}). We \ntherefore expect the presence of a thermal/disc component: \nindeed this might dominate over any synchrotron jet radiation and thus \nbe responsible for the observed emission. The idea that we see \ndirectly an accretion disc is supported by several observations: \nin the case of \\object{3C~390.3}, a bump in the spectral energy \ndistribution has been interpreted as radiation emitted by a disc \ncomponent with intermediate inclination (Edelson \\& Malkan \n\\cite{edelson86}). Furthermore, the broad and double peaked H$\\beta$ \nline observed in this source as well as in other BLRG (see \ne.g. Eracleous \\& Halpern \\cite{eracl94}), can be accounted for \nwithin a relativistic accretion disc model (Perez et al. \n\\cite{perez88}). \n \nThe location of 3C~111 is puzzling, as it lies along the correlation. \nHowever, several pieces of evidence point to the idea that beamed \nradiation from the relativistic jet significantly contributes in this \nsource: it has the largest core dominance among the BLRG of our \nsample; superluminal motions with apparent speed $v \\sim 3.4c$ \\ have \nbeen revealed in the inner jet (Vermeulen \\& Cohen \\cite{vermu}), \nimplying that the angle between the line of sight and the jet axis is \nsmaller than $\\sim 30^{\\circ}$; the radio core is strongly variable \nand polarized (Leahy et al. \\cite{leahy}). Furthermore a broad \nK$\\alpha$ iron line is detected in the X--ray band, but with a \nrelatively small equivalent width which can be explained if the \ncontinuum emission is diluted by a beamed component (Reynolds et \nal. \\cite{reynolds}). However, its total radio extent of $\\sim$ 250 \nkpc argues against a viewing angle typical of blazars. Thus \n\\object{3C~111} appears to be a transition source between \nradio-galaxies and blazars, seen at an angle sufficiently small that \nthe jet beaming already affects its nuclear properties. \n \n\\subsection{WLRG and NLRG with optical cores} \n \nLet us now concentrate on the NLRG and WLRG in which we detected \noptical cores. These objects (2 WLRG and 3 NLRG), all with FR~II radio \nmorphology, have cores with radio and optical emission properties that \nare {\\it completely consistent with those found in FR~I}. This \nsuggests that in these sources the nuclear emission is \nsimilarly dominated by synchrotron radiation from the inner jet. \n \nIn the case of FR~I, based on the high fraction of detected nuclei, we \nsuggested that any obscuring material must be geometrically thin \nand thus the absence of broad lines and the \nrelative weakness of any thermal (disc) component with respect to the \nsynchrotron emission cannot be ascribed to extinction. \n \nFor FR~II with FR~I--like nuclei -- of which we do not have \nenough statistics -- there is an alternative possibility, namely \nthat the optical core (jet) emission is produced outside the obscuring \ntorus (and thus outside the BLR). In this sense they would represent \ntransition objects seen at an intermediate angle between the \ncompletely obscured and unobscured ones. \nHowever, VLBI observations \nshow that radio cores are unresolved on scale of $\\sim$ 0.1 pc \nin nearby radio galaxies and this suggests that their optical \ncounter--parts have a similar extent, as already discussed in Paper~I. \nFurthermore, \na symmetric jet-counter jet structure has been observed in several \nradio sources, implying that they lie essentially in the \nplane of the sky (Giovannini et al. \\cite{giovannini98}). If the core \nemission is indeed produced outside the torus, at a distance of, say, \n$\\sim$1 pc from the central black hole, a clear separation \nbetween the two sides of the jet (and no stationary core) should be \nobserved in these highly misoriented objects \n(although, at present, symmetric jets have been found only in FR~I). \nThis ad hoc geometrical model \ndoes not seem to be viable, but a conclusive test requires \nspectropolarimetry looking for polarized scattered broad lines. \nA further indication could be obtained from the comparison\nof the nuclear infrared (reprocessed?) luminosity of FR~Is and FR~IIs with\nFR~I--like nuclei of similar optical luminosity.\n \nWe conclude that these FR~II are intrinsically narrow-lined objects \nwhich are in every aspect, except their extended radio-morphology, \nsimilar to FR~I. Note that the presence of an FR~I-like nucleus \nin a FR~II does not seem to be connected with the total (radio) \nluminosity or redshift of the galaxy. In fact, the total power of such \nsources spans the range $L_{178}= 10^{32}-10^{33.5}$ erg s$^{-1}$ \nHz$^{-1}$ and the redshifts are between $z=0.025-0.091$, completely \noverlapping with the entire sample and not limited, as one might \nexpect, to the low luminosity end. \n \nConversely, it appears that a possible relationship exists between the \noccurrence of FR~I-like nuclei in FR~II and the environment, as all \nthese 5 galaxies reside in clusters. This result can be particularly \nimportant, as it is known that FR~I and FR~II inhabit different \nenvironments, with FR~II generally avoiding rich groups, especially at \nlow redshifts (Zirbel \\cite{zirb97}), while FR~I are usually located \nin rich clusters. However, before any firm conclusion can be drawn \nabout this issue, a larger sample of objects has to be considered. \n \n\\subsection{WLRG and NLRG without optical cores} \n \nIn 8 galaxies, all WLRG or NLRG, we do not detect the presence of an \nunresolved nuclear component. \nFour sources are located above or very close to the FR~I \ncorrelation. They are consistent with being objects in which an \noptical counter--part to the radio core is present, \nbut it is too faint \nto be seen against the bright background of the host galaxy. \n \nThe remaining 4 objects (3 NLRG and 1 WLRG) are certainly more \ninteresting, since they lie 1 - 2 orders of magnitude below the \ncorrelation. Therefore they lack not only of a BLR, but also of the \nexpected optical counterpart of the radio core. \nHowever, note that these sources have radio core luminosities which cover \nthe same range of BLRG. According to the prescriptions of the \nunification schemes, they can well be the obscured \ncounter--parts of BLRG. Noticeably, excluding the blazar\n\\object{3C~371}, BLRG and these obscured sources clearly \ndistinguish themselves for having the brightest radio cores among FR~II. \n \n\\section{Conclusions} \n \n \nIn Chiaberge et al. (\\cite{pap1}) we discovered that FR~I nuclei lie \nin the radio-optical luminosity plane along a tight linear \ncorrelation. We argued that this is due to a common synchrotron \norigin for both the radio and optical emission. FR~I nuclei must \nalso be unobscured and intrinsically lacking of BLR and of \nsignificant thermal emission from any powerful accretion disc. \n\nIn order to explore how the differences in radio morphology are \nrelated to the optical nuclear properties, we analyzed HST images of \n24 extended radio-galaxies morphologically classified as FR~II, \nbelonging to the 3C catalog and with $z<0.1$. \nWe detected optical cores in 13 sources, which implies that the\ncovering fraction of any obscuring material is less than $\\sim 0.54$, or\nequivalently, the torus has an opening angle of $\\sim 63^{\\circ}$.\nThis can be even larger if at least some of the upper limits\nare actually just below the detection threshold. \nNotice that our determination of \nthis critical angle is inconsistent with the division\nbetween higher redshift ($0.5 < z < 1$) 3CR quasars and radio galaxies, which\nhas been found to be $\\theta \\sim 45^{\\circ}$ (Barthel \\cite{bart89}).\nThis might be a problem, however the low redshift selection of our\nsources does not allow to derive any firm conclusion. We are currently \nstudying a larger and higher redshift sample in order to further investigate \nthis issue (Chiaberge et al. in preparation).\n\nOur results suggest that the radio morphology is not univocally connected with \nthe optical properties of the innermost structure of radio \ngalaxies. In fact, at least at low redshifts, there is not a single \nhomogeneous population of FR~II: unlike FR~I, they show a complex \nbehavior, which is however clearly related to their optical spectral \nclassification. \n \nIn BLRG optical nuclei are likely to be dominated by thermal (disc) \nemission. As discussed above, line emission contamination\ncannot account for this excess.\nIn agreement with the current unification scheme of radio \nloud AGNs, we also identify their possible obscured counter--parts. \nIt seems that broad lines and obscuring tori are closely linked and \nboth are present only associated to radiatively efficient accretion. \n \nWe also find five FR~II sources, spectrally \nidentified as narrow lined objects, which harbor nuclei \nessentially indistinguishable from those seen in FR~I. \nBy analogy with FR~I, we argue that their optical nuclear\nemission is produced primarily by synchrotron radiation,\nthey are not obscured to our line of sight and therefore \nintrinsically lack a BLR.\n\nClearly, a classification based on the optical nuclear \nproperties, as seen in these HST images, is more likely to reflect \ntrue similarities (or differences) on the nature of the central \nengine (such as, e.g., the rate of radiative dissipation in the \naccretion disc) than the traditional dichotomy of radio morphology. \n \nFrom our data and within the limits of the available statistics, \nwe find no evidence of a continuous transition between \nthe two classes (FR~I and FR~II),\nas they are well separated in the $L_r$ vs $L_o$ \nplane. At this stage we only point out that sources with cores below \n$L_o < 10^{27.5}$ erg s$^{-1}$ Hz$^{-1}$ (or equivalently $L_r < \n10^{31}$ erg s$^{-1}$ Hz$^{-1}$) have FR~I like nuclei, while FR~II \nstart above this threshold. \n \nIt is of particular interest that a significant fraction of FR~II \n(at least 30 \\%, but can be as large as 50 \\% depending on the nature \nof the sources without detected optical nuclei) have FR~I--like \nnuclei. The fact that all of these are located in clusters, an \nenvironment typical of FR~I, might represent an important hint on the \norigin of the different flavours of radio galaxies, worth exploring \nthrough the study of a larger sample of objects. \n \nThese results have also interesting bearings from the point of \nview of the unified models. In fact, this picture argues \nagainst the idea that all FR~II radio galaxies constitute the parent \npopulation of radio-loud quasars. We propose instead that \ngalaxies with FR~II morphology and an FR~I-like core are possibly \nmis-aligned counter--parts of BL Lac objects. \nThis can account for the observation that some \nradio-selected-type BL Lacs show radio morphologies more consistent \nwith FR~II than with FR~I (e.g. Kollgaard et al. \\cite{koll92}). \n \nTo conclude, we note that all of the galaxies included in our sample \nare low redshift objects with total radio powers not exceeding \n$L_{178} \\sim 10^{27}$ erg s$^{-1}$ Hz$^{-1}$: thus a crucial \nobservational issue is to understand whether these results hold \nto higher power/redshift samples or they are limited to low \nluminosities FR~II. This will be explored in a forthcoming paper. \n \n\\begin{acknowledgements} \nWe thank Jim Pringle for insightful suggestions and Edo Trussoni \nfor useful comments on the manuscript.\nThe authors acknowledge the Italian MURST for financial support.\nThis research was supported in part by the \nNational Science Foundation under Grant No. PHY94-07194 (A. Celotti).\\\\ \nThis research has made use of the NASA/IPAC Extragalactic Database \n(NED) which is operated by the Jet Propulsion Laboratory, California \nInstitute of Technology, under contract with the National Aeronautics \nand Space Administration.\\\\ \n\\end{acknowledgements} \n \n\\begin{thebibliography}{} \n\\bibitem[1985]{anto85} Antonucci R., Ulvestad J.S. 1985, ApJ 294, 158 \n\\bibitem[1985]{anto90} Antonucci R., Barvainis R. 1990, ApJ 363, L17 \n\\bibitem[1989]{bart89} Barthel P.D. 1989, ApJ 336, 606 \n\\bibitem[1996]{biretta} Biretta J.A., Burrows C.J., Holtzman J.A. \net al. 1996, Wide Field and \nPlanetary Camera 2 Instrument handbook, ed. J.A. Biretta (Baltimore:STScI) \n\\bibitem[1995]{capetti95} Capetti A., Fanti R., Parma P. 1995, \nA\\&A 300, 643 \n\\bibitem[1999]{pap1} Chiaberge M., Capetti A., Celotti A. 1999, A\\&A 349, 77\n\\bibitem[1996]{De Koff} De Koff S., Baum S. A., Sparks W. 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P. 1995, \nApJ 451, 88 \n\\end{thebibliography} \n\\end{document} \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nExamples for figures using psfig and epsf respectively \n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% Figure up to 8.8cm (use the vertical space and the horizontal space to \n% place the figure in the right place, top and left of page) \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n\\vspace{0cm} \n\\hspace{0cm}\\psfig{figure=994f9.ps,width=8..8cm} \n\\vspace{0cm} \n \n\\vspace{0cm} \n\\hspace{0cm}\\epsfxsize=8.8cm \\epsfbox{file.ps} \n\\vspace{0cm} \n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% 2 figures side by side \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n\\vspace{0cm} \n\\hbox{\\hspace{0cm}\\psfig{figure=994f9.ps,width=14.8cm}\\hspace{0cm} \n\\psfig{figure=994f9.ps,width=14.8cm}} \n\\vspace{0cm} \n \n\\vspace{0cm} \n\\hbox{\\hspace{0cm}\\epsfxsize=7.5cm \\epsfbox{file.ps} \n\\epsfxsize=7.5cm \\epsfbox{file.ps}} \n\\vspace{0cm} \n \n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% Figure with caption on the right side (0.5cm place between the figure \n% and the legend) \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n\\vbox{\\psfig{figure=file.ps,width=12.0cm}\\vspace{-3cm}} \n\\hfill\\parbox[b]{5.5cm}{\\caption[]{}} \n \n\\vbox{\\epsfxsize=12cm \\epsfbox{file.ps}\\vspace{-3cm}} \n\\hfill\\parbox[b]{5.5cm}{\\caption[]{}} \n \n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% working with epsf.sty and rotate.sty to rotate figures (the figure \n% will be rotated out of the paper thats why you have to use big \n% hspaces and vspaces to put the figure in the right position) \n% but first try it with the psfig-macro (angle-command) \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n\\psfig{figure=file.ps,width=8.8cm,angle=-90} \n \n\\vbox{\\vspace{-5.2cm}\\hbox{\\hspace{8.5cm}\\epsfxsize=5.9cm \n\\rotate[l]{\\epsfbox{file.ps}}}} \n\\vspace{5.4cm} \n \n \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n% to cut somthing from the top, bottom, right and left of the figure \n% change the Bounding Box of the figure with the folowing parameters \n% or use the command clip= (in epsf: \\epsfclipon) \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n \n\\psfig{figure=file.ps,width=8.8cm,bbllx=20pt,bblly=20pt,% \n bburx=365pt,bbury=567pt} \n \n\\psfig{figure=file.ps,width=8.8cm,clip=} \n \n\\epsfxsize=8.8cm \\epsfbox[20 20 300 300]{aa2283.f1} \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n"
},
{
"name": "tab1.tex",
"string": "\n\\begin{table*} \n\\caption{Summary of FR~II radio and optical data.}\n\\hspace{0.5cm} \n\\begin{tabular}{l c c c c c c} \\hline\n\n\n\nName & Redshift & Spectral & Log $L_{178}$ & Log $L_r$ (5GHz) & $F_o$ (7000 \\AA) & Log $L_o$ (7000 \\AA)\\\\\n & z & class. & erg s$^{-1}$ Hz$^{-1}$ & erg s$^{-1}$ Hz$^{-1}$ & erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$ & erg s$^{-1}$ Hz $^{-1}$\\\\ \n\\hline\n\t\t\t\t\t\t\t\t\t \n 3C15 & 0.073 & NLRG & 33.16 & 31.54 & $ <$--28.12 & $ <$26.85 \\\\\n 3C33 & 0.059 & NLRG & 33.51 & 30.27 & \\multicolumn{2}{c}{no HST observations} \\\\\n 3C35 & 0.067 & NLRG & 32.75 & 30.27 & $ <$--28.47 & $ <$26.42 \\\\\n 3C40 & 0.018 & WLRG & 32.24 & 30.60 & $ $ -- & $ $ -- \\\\\n 3C88 & 0.030 & WLRG & 32.46 & 30.50 & $ $~~--27.64 & $ $~~26.57 \\\\\n 3C98 & 0.030 & NLRG & 32.78 & 29.25 & $ <$--28.58 & $ <$25.64 \\\\\n 3C105 & 0.089 & NLRG & 33.38 & 30.36 & \\multicolumn{2}{c}{no HST observations} \\\\\n 3C111 & 0.049 & BLRG & 33.18 & 31.69 & $ $~~--26.51 & $ $~~28.12 \\\\\n 3C136.1 & 0.064 & - & 33.00 & --\t & $ $ -- & $ $ -- \\\\\n 3C192 & 0.060 & NLRG & 33.16 & 29.73 & $ <$--27.86 & $ <$26.94 \\\\\n 3C198 & 0.082 & NLRG & 33.31 & --\t & $ $~~--27.10 & $ $~~27.96 \\\\\n 3C227 & 0.086 & BLRG & 33.57 & 30.48 & $ $~~--26.27 & $ $~~28.83 \\\\\n 3C236 & 0.099 & WLRG & 33.52 & 31.51 & $ <$--28.26 & $ <$26.95 \\\\\n 3C285 & 0.079 & NLRG & 32.80 & 29.93 & $ $~~--29.44 & $ $~~25.58 \\\\\n 3C318.1 & 0.046 & NLRG & 32.66 & --\t & $ $~~--28.94 & $ $~~25.63 \\\\\n 3C321 & 0.096 & NLRG & 33.23 & 30.78 & $ $ -- & $ $ -- \\\\\n 3C326 & 0.089 & NLRG & 33.02 & 30.34 & $ <$--28.11 & $ <$27.02 \\\\\n 3C353 & 0.030 & NLRG & 33.56 & 30.54 & $ <$--28.71 & $ <$25.51 \\\\\n 3C371 & 0.050 & BL Lac & 32.37 & 31.89 & $ $~~--25.56 & $ $~~29.09 \\\\\n 3C382$^{*}$ & 0.058 & BLRG & 32.95 & 31.13 & $ $~~--25.11$^{*}$ & $ $~~29.66$^{*}$ \\\\\n 3C388 & 0.091 & WLRG & 33.49 & 31.04 & $ $~~--27.96 & $ $~~27.18 \\\\\n 3C390.3$^{*}$ & 0.056 & BLRG & 33.46 & 31.38 & $ $~~--25.91$^{*}$ & $ $~~28.83$^{*}$ \\\\\n 3C402 & 0.025 & NLRG & 32.01 & 29.73 & $ $~~--27.49 & $ $~~26.57 \\\\\n 3C403 & 0.059 & NLRG & 33.23 & 29.87 & $ $~~--28.19 & $ $~~26.60 \\\\\n 3C445$^{*}$ & 0.057 & BLRG & 33.13 & 31.34 & $ $~~--25.56$^{*}$ & $ $~~29.20$^{*}$ \\\\\n 3C452 & 0.081 & NLRG & 33.81 & 31.24 & $ <$--28.22 & $ <$26.83 \\\\\n\n\n\\hline\n\n\\end{tabular}\n\\label{tabfr2}\n\n\n\\medskip\n$L_{178}$ and $L_r$ are the total (at 178 MHz) and core radio luminosities, \ntaken from the literature. $F_o$ is the flux of the optical core.\nTotal radio luminosities are calculated from K\\\"uhr et al. (\\cite{kuhr}) or Gower et al. \n(\\cite{gower}). Radio core luminosities are taken from Zirbel \\& Baum (\\cite{zirbel}).\n``$<$'' indicate upper limits, i.e. not detected optical cores, ``*'' \nindicate objects in which the optical core saturates, ``--'' in the $F_o$ and $L_o$ colums\nmark objects with complex nuclear morphologies for which we do not estimate the core flux and\n ``--'' in the $L_r$ column indicate unavailable radio core data in the literature.\n\n\\end{table*}\t\t\t\t \n \n \n \n \n"
}
] |
[
{
"name": "astro-ph0002018.extracted_bib",
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}
] |
astro-ph0002019
|
Magnetized Atmospheres around Neutron Stars \\ Accreting at Low Rates
|
[
{
"author": "Silvia Zane"
}
] |
We present a detailed investigation of atmospheres around accreting neutron stars with high magnetic field ($B\gtrsim 10^{12}$ G) and low luminosity ($L\lesssim 10^{33}$ erg/s). We compute the atmospheric structure, intensity and emergent spectrum for a plane--parallel, pure hydrogen medium by solving the transfer equations for the normal modes coupled to the hydrostatic and energy balance equations. The hard tail found in previous investigations for accreting, non--magnetic neutron stars with comparable luminosity is suppressed and the X--ray spectrum, although still harder than a blackbody at the star effective temperature, is nearly planckian in shape. Spectra from accreting atmospheres, both with high and low fields, are found to exhibit a significant excess at optical wavelengths above the Rayleigh--Jeans tail of the X--ray continuum.
|
[
{
"name": "paper.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%\n% Preamble\n%%%%%%%%%\n%\\documentstyle[12pt,aasms4]{article} % <=== manuscript\n%\\documentstyle[11pt,aaspp4]{article} % <=== 1 column\n\\documentstyle[11pt,aaspp4,epsfig,psfig]{article} % <=== 1 column\n%%%%%%%%%\n\n%\\received{ }\n%\\accepted{ }\n%\\journalid{ }{ }\n%\\articleid{ }{ }\n\n%%%%%%%%%\n\\newcommand{\\sy}{{\\rm {s\\,\\,yr^{-1}}}}\n\\newcommand{\\etal}{{\\it et al.\\/}}\n\\newcommand{\\be}{\\begin{equation} }\n\\newcommand{\\ee}{\\end{equation} }\n\\newcommand{\\bea}{\\begin{eqnarray} }\n\\newcommand{\\eea}{\\end{eqnarray} }\n% \\der{f}{x} ====> derivata parziale df/dx\n\\def\\der#1#2{{\\partial#1\\over\\partial#2}}\n% \\ders{f}{x}{y} ====> derivata parziale seconda d2f/dxdy\n\\def\\ders#1#2#3{{\\partial^2#1\\over\\partial#2\\partial#3}}\n% \\derss{f}{x} ====> derivata parziale seconda d2f/dx2\n\\def\\derss#1#2{{\\partial^2#1\\over\\partial#2^2}}\n% \\dert{f}{x} ====> derivata totale df/dx\n\\def\\dert#1#2{{{d#1}\\over{d#2}}}\n\\newcommand{\\kes}{\\kappa_{es}}\n\\newcommand{\\kff}{\\kappa_{ff}}\n\n%%%%%%%%%\n\n\\lefthead{Zane, Turolla, \\& Treves}\n\\righthead{MAGNETIZED ATMOSPHERES AROUND ACCRETING NEUTRON STARS}\n\n%%%%%%%%%\n% Begin Text\n%%%%%%%%%\n\n\\begin{document}\n\n\\title{Magnetized Atmospheres around Neutron Stars \\\\ Accreting at\nLow Rates}\n\n\\author{Silvia Zane}\n\\affil{Nuclear and Astrophysics Laboratory,\nUniversity of Oxford, \\\\ Keble Road, Oxford OX1 3RH, England\\\\\ne--mail: [email protected]}\n\\author{Roberto Turolla}\n\\affil{Dept. of Physics, University of Padova, \\\\ Via Marzolo 8, 35131 Padova,\nItaly \\\\ e--mail: [email protected]}\n\\and\n\\author{Aldo Treves}\n\\affil{Dept. of Sciences, University of Insubria, \\\\\nVia Lucini 3,\n22100, Como, Italy \\\\ e--mail: [email protected]}\n\n\\begin{abstract}\n\nWe present a detailed investigation of atmospheres around\naccreting neutron stars with high\nmagnetic field ($B\\gtrsim 10^{12}$ G) and low luminosity ($L\\lesssim\n10^{33}$ erg/s). We compute the\natmospheric structure, intensity and emergent spectrum for a\nplane--parallel, pure hydrogen medium by solving the transfer equations\nfor the normal\nmodes coupled to the hydrostatic and energy balance equations. \nThe hard tail found in previous investigations for accreting,\nnon--magnetic neutron stars with comparable luminosity is suppressed and\nthe X--ray spectrum, although still harder than a blackbody at the star\neffective temperature, is nearly planckian in shape. Spectra from\naccreting atmospheres, both with high and low fields, are found to exhibit\na significant excess at optical wavelengths above the Rayleigh--Jeans tail\nof the X--ray continuum.\n\n\n\\end{abstract}\n\n\\keywords{Accretion, accretion disks --- radiative transfer ---\nstars: magnetic fields --- stars: neutron --- X--rays: stars}\n\n\n\\section{Introduction}\\label{intro}\n\nThe problem of investigating the properties of radiation emitted\nby neutron stars (NSs) accreting at low rates, $\\dot M\\approx\n10^{10}-10^{14}$ g/s, became of interest after it was realized\nthat the Galaxy may contain a large population of low luminosity\nmagnetic accretors (see e.g. Nelson, Wang, Salpeter, \\& Wasserman\n\\cite{nel95:1995}). The Galaxy should harbor more than $10^3$\nBe/X--ray binaries with an accreting NS shining at $\\approx\n10^{32}-10^{34}$ erg/s (Rappaport, \\& van den Heuvel\n\\cite{rvdh82:1982}; van den Heuvel, \\& Rappaport\n\\cite{vdhr86:1986}). Moreover, assuming a supernova birth rate of\n10--100 yr$^{-1}$, $\\sim 10^8-10^9$ old, isolated NSs (ONSs)\nshould be present in the Galaxy. Accretion onto a strongly\nmagnetized, moving neutron star may be severely hindered for\ndifferent reasons, but there is the possibility that a small,\nalbeit non--negligible, fraction of ONSs may be accreting directly\nfrom the interstellar medium and some of them might be above the\nsensitivity threshold of ROSAT (e.g. Treves, \\& Colpi\n\\cite{tc91:1991}; Blaes, \\& Madau \\cite{bm93:1993}; see Treves,\nTurolla, Zane, \\& Colpi \\cite{review:1999} for a review).\n\nAt variance with neutron stars accreting at high rates, e.g. in X--ray\npulsators, in low--luminosity sources the interaction of the escaping\nradiation with the inflowing material is of little importance, so they\nprovide a much simpler case for investigating the physics of accretion in a\nstrongly magnetized environment. For luminosities far below the Eddington\nlimit, the accretion problem becomes\ngermane to that of calculating\nthe spectrum emerging from static atmospheres around cooling NSs.\nSpectra from cooling NSs have been widely investigated by a number of\nauthors in connection with the X--ray emission from young, millisecond\npulsars and isolated NSs, both for low\nand high magnetic fields and for different chemical compositions (see e.g.\nRomani \\cite{rom87:1987}; Shibanov, Zavlin, Pavlov \\& Ventura\n\\cite{sh92:1992}; Rajagopal, \\& Romani \\cite{rr96:1996};\nPavlov, Zavlin, Tr\\\"umper,\n\\& Neuh\\\"auser \\cite{pztn96:1996}). Emerging\nspectra are not very different from a blackbody at the star effective\ntemperature, the\ndistinctive hardening present at low fields ($B\\lesssim 10^9$ G) becoming\nless pronounced when the magnetic field is $\\sim\n10^{12}-10^{13}$ G. Similar conclusions were reached for the\nspectrum emitted by low--luminosity, low--field, accreting NSs by\nZampieri, Turolla, Zane, \\& Treves (\\cite{ztzt95:1995}, hereafter\nZTZT) for a pure hydrogen atmospheric composition.\n\nThe search of isolated neutron stars with ROSAT produced in recent\nyears half a dozen promising candidates (Walter, Wolk, \\& Ne\\\"uhauser\n\\cite{wwn96:1996}; Haberl \\etal \\ \\cite{ha97:1997}; Haberl, Motch \\&\nPietsch \\cite{hmp98:1998};\nSchwope \\etal \\ \\cite{sch99:1999}; Motch \\etal \\ \\cite{mo99:1999};\nHaberl, Pietsch \\& Motch \\cite{hpm99:1999}). All\nof\nthem show a soft, thermal X--ray spectrum, with typical energies\n$\\sim 100$ eV, and have an exceedingly large X--ray to optical flux ratio,\n$\\gtrsim 10^4$. Although their association with isolated neutron stars is\nfirmly established, their interpretation in terms of an accreting or\na cooling object is still a matter of lively debate.\nPresent models predict rather similar spectral distributions\nin both cases, especially in the X--ray band. It is therefore of\nparticular importance\nto improve our theoretical understanding of these two classes of sources,\nlooking, in particular, for spectral signatures which can enable us to\ndiscriminate between them.\n\nIn this paper we present a first detailed calculation of spectra\nemitted by strongly magnetized ($B\\gtrsim 10^{12}$ G), accreting neutron\nstars, focusing our attention\non low luminosities, $L \\sim 10^{30}$--$10^{33}$ erg/s, such as those expected\nfrom old neutrons stars accreting the interstellar medium.\nSpectral distributions are computed\nsolving the transfer equations for the normal modes coupled to the\nhydrostatic equilibrium and\nthe energy balance for different values of the accretion\nrate and the magnetic field.\n\nWe find that spectra emerging from magnetized, accretion\natmospheres are blackbody--like in the X--ray band, in close\nagreement with the known results for cooling, magnetized\natmospheres. However, accretion spectra show a new and distinctive\nfeature at low energies, being characterized by an excess over the\nRaleigh--Jeans tail of the X--ray continuum below $\\sim 10$ eV.\nThe same behaviour is found in accretion atmospheres around\nunmagnetized neutron stars, but, as already pointed out by ZTZT,\nthe X--ray spectrum is sensibly harder in this case. This result\nmay be relevant in connection with the isolated neutron star\ncandidate RX J18563.5-3754. Multiwavelength observations of this\nsource indicate that, while ROSAT data are well fitted by a\nblackbody at $T_{eff}\\sim 60$ eV, HST points lie above the\nextrapolation of the fit in the optical (Walter, \\& Matthews\n\\cite{wm97:1997}).\n\n\nThe plan of the paper is as follows. The input physics relevant to\nour model is presented in \\S \\ref{model}: radiative transfer in a\nmagnetized plasma is discussed in \\S \\ref{model-radtra} and the\nstructure of an accreting, magnetized atmosphere in \\S\n\\ref{model-struct}. Computed spectra are presented in \\S\n\\ref{results}. Discussion and conclusions follow in \\S\n\\ref{discuss}.\n\n\\section{The Model}\\label{model}\n\n\\subsection{Radiation Transfer}\\label{model-radtra}\n\nIn this paper we consider a magnetized, nondegenerate, pure\nhydrogen, cold plasma, in which the main radiative processes are\nfree--free emission/absorption and Thomson scattering. The plasma\nis in local thermal equilibrium (LTE) at temperature $T$. We\nconsider a plane--parallel geometry with normal ${\\bf n}$ parallel\nto the magnetic field ${\\bf B}$ and to the $z$--direction. The\nstratification of the atmosphere is described by using as a\nparameter the scattering depth $\\tau$, as defined for an\nunmagnetized medium \\be \\tau = \\kes \\int_z^{\\infty} \\rho\\, dz \\ee\nwhere $z$ is the coordinate variable, $\\rho$ is the plasma\ndensity, $\\kes = \\sigma_T/m_p$ is the Thomson opacity and\n$\\sigma_T$ is the Thomson cross section.\n\nIn the following, we neglect collective plasma effects and consider only\nthe limit $\\omega_p^2/\\omega^2 \\ll 1$, where $\\omega_p = (4 \\pi n_e e^2\n/m_e)^{1/2}$\nis the plasma frequency and $n_e$ electron density.\nWe also consider only frequencies lower than the\nelectron\ncyclotron frequency, $\\omega_{c,e} = eB/m_ec$, so the semitransverse\napproximation can be assumed to hold. Since, for $\\tau \\gtrsim 0.01$, the\ntemperature in the\natmosphere is always\n$\\lesssim 10^7$ K (see \\S \\ref{model-struct} and ZTZT) and\nscattering dominates over true absorption only for\n$\\tau\\sim 1$, Comptonization\nis negligible. For this reason, similarly to what is done for cooling,\nmagnetized\natmospheres (see e.g. Shibanov, \\etal \\ \\cite{sh92:1992}), only\nconservative scattering is\naccounted for in the transfer equations (see, however, the discussion in\n\\S \\ref{model-struct} for the role of Compton heating/cooling in\nthe energy balance\nof the external atmospheric layers).\n\nUnder these assumptions, the coupled equations for the transfer of the\ntwo normal modes take the form (see e.g. Gnedin \\& Pavlov\n\\cite{gp74:1974}; Yahel \\cite{y80:1980})\n\\bea\n\\label{tr1}\n- y_G \\mu \\dert{f^1}{\\tau} & = &\n\\int K_s^{11} f^{1'} d \\mu'\n+ \\int K_s^{21} f^{2'} d \\mu' -\n k_s^{1} f^1\n+ k_{ab}^1 \\left ( { 1 \\over 2} b_\\nu - f^1 \\right )\\nonumber\\\\\n- y_G \\mu \\dert{f^2}{\\tau} &=&\n\\int K_s^{22} f^{2'} d \\mu'\n+ \\int K_s^{12} f^{1'} d \\mu' -\n k_s^{2} f^2\n+ k_{ab}^2 \\left ( { 1 \\over 2} b_\\nu - f^2 \\right )\n\\eea\nwhere $y_G = \\sqrt{1 - 2GM/Rc^2}$ is the gravitational redshift\nfactor, $R$ and $M$ are the star mass and radius,\n$\\mu = {\\bf n}\\cdot{\\bf s}=\\cos \\theta$, $f^i \\left ( \\tau,\n\\mu, \\nu \\right )= c^2 I^i/2h^4\\nu^3$ denotes the photon occupation number\nfor the ordinary ($i =1$) and extraordinary ($i=2$) mode, $I^i$ is the\nspecific intensity, $b_\\nu =\nc^2B_\\nu/2h^4\\nu^3 $, and $B_\\nu$\nis the Planck function.\nIn equations (\\ref{tr1}) $k_{ab}^i$ is the total free--free opacity,\n\\be\nk_s^i(\\mu,\\nu) = \\sum_{j=1}^2 \\int K_s^{ij}\\, d\\mu'\n\\ee\nand $K_s^{ij}(\\mu,\\mu',\\nu)$ is the probability that an incident photon, which\nhas polarization $\\hat e^i$ and propagates in the direction $\\mu$,\nscatters into a direction $\\mu'$ and polarization $\\hat e^j$.\nAll the quantities appearing in equations (\\ref{tr1}) are referred to the\nlocal observer, at rest on the star surface; the photon energy measured by\nan observer at infinity is given by $h\\nu_\\infty = y_Gh\\nu$.\nThe integral\nterms appearing into equations (\\ref{tr1}) account for the scattering\nemissivities, and\nall opacity/emissivity coefficients are normalized to $\\kes$.\nThe expressions for the opacities\nrelevant to the present calculation are reported in appendix\n\\ref{appa}.\n\n\\subsection{Atmospheric Structure}\\label{model-struct}\n\nAccretion atmosphere models are constructed by solving the transfer\nequations (\\ref{tr1}) coupled to the hydrostatic equilibrium and\nthe energy equation.\nThe hydrostatic balance is simply expressed as\n\\be\n\\label{pre}\n\\dert{P} {\\tau } = {GM \\over y_G^2 R^2 \\kes } \\, ,\n\\ee\nwhere $P = k \\rho T/\\mu_em_p$ ($\\mu_e\\sim 1/2$ for completely\n ionized hydrogen)\n is the gas pressure and we consider only the case $L/L_{Edd} \\ll 1$,\nwhere\n $L=L(\\tau)$ is the luminosity measured by the local observer. Since in\n all our models the ram pressure of the accreting material, $1/2 \\rho\nv^2$,\n turns out to be much smaller than the thermal pressure, it has\n been neglected, together with the radiative force. In this \n limit equation (\\ref{pre}) is\n immediately integrated, and gives the density as a function of depth\n \\be\\label{dens}\n \\rho = \\frac{GMm_p}{2 y_G^2 R^2\\kes}\\frac{\\tau}{kT(\\tau)}\\,.\n \\ee\n\nThe energy balance just states that the net radiative cooling must\nequate the heating $W_H$ supplied by accretion. The radiative\nenergy exchange is obtained adding equations (\\ref{tr1}) together,\nafter multiplying them by $(\\hbar\\omega)^3$, and integrating over\nangles and energies. Since we assumed conservative scattering, its\ncontribution to the energy balance clearly vanishes. However, as\ndiscussed in previous investigations (Alme, \\& Wilson\n\\cite{aw73:1973}; ZTZT), Comptonization is ineffective in\nmodifying the spectrum, but plays a crucial role in determining\nthe temperature in the external, optically thin layers. Contrary\nto what happens in cooling atmospheres, the temperature profile\nshows a sudden rise (or ``jump'') in the external, low--density\nlayers where the heating produced by the incoming protons is\nmainly balanced by Compton cooling. Including Compton\nheating/cooling the energy equation becomes\n\\be\n\\label{en2}\nk_P \\left ( \\frac{aT^4}{2} - {k_{am}^1 \\over k_P } U^1\n- {k_{am}^2 \\over k_P } U^2 \\right ) + \\left\n(\\Gamma - \\Lambda \\right)_C\n= {W_H \\over c \\kes}\n\\ee\nwhere $U^i$ is the radiation energy density of mode $i$ and $k_P$,\n$k^i_{am}$ are defined in strict analogy with the Planck and absorption\nmean opacities in the unmagnetized case.\nIn evaluating the previous expression the approximated formula by Arons,\nKlein, \\& Lea (\\cite{akl87:1987}) for the Compton rate in a magnetized\nplasma, $(\\Gamma - \\Lambda)_C$, has been used.\n\nThe detailed expressions for the heating rate $W_H$ and the stopping depth\n$\\tau_B$ in a magnetized atmosphere are presented in appendix \\ref{appb}.\n\n\n\\section{Results}\\label{results}\n\n\\subsection{Numerical Method}\\label{numeth}\n\n\nThe numerical calculation was performed adapting\nto radiative transfer in a magnetized medium the tangent--ray\ncode developed by Zane,\nTurolla, Nobili, \\& Erna (\\cite{crm:1996}) for\none--dimensional, general--relativistic radiation transfer. The method\nperforms an ordinary $\\Lambda$--iteration for computing the scattering\nintegrals.\nSchematically, the calculation proceeds as follows.\nFirst an initial temperature profile is specified (usually that of an\nunmagnetized model with similar parameters calculated by ZTZT) and the\nzero--th order approximation for $f^1$, $f^2$ is computed solving\nequations (\\ref{tr1}) with no scattering emissivity.\nThe boundary conditions for ingoing ($\\mu < 0$) trajectories are\n$f^i = 0$ at $\\tau = \\tau_{min}$\nwhile diffusive boundary conditions at $\\tau = \\tau_{max}$ were used for\noutgoing ($\\mu > 0$) trajectories.\nThe computed intensities are then used to evaluate the scattering\nintegrals and the whole procedure is repeated,\nkeeping the temperature profile unchanged. As soon as corrections on\nthe intensities are small enough, new temperature and density profiles\nare obtained solving equations (\\ref{en2}) and (\\ref{dens}). The whole\nscheme is then iterated to convergence. Each model is\ncompletely characterized by the\nmagnetic field strength, the total luminosity and the luminosity at\n$\\tau_B$, or, equivalently, by $B$ and the heating rate $W_H$ (see\nappendix \\ref{appb}). Since the code solves the full transfer\nproblem, it allows for the complete determination of the\nradiation field, including its angular dependence. This ensures a more\naccurate treatment of\nnon--anisotropic radiative process with respect to angle--averaged,\ndiffusion approximations. Owing to\nthe gravitational redshift, the total accretion luminosity measured at\ninfinity is related to the local luminosity at the top of the\natmosphere by $L_\\infty = y_G^2 L(0)$.\n\nModels presented below were computed using a logarithmic grid with\n300 equally--spaced depth points, 20 equally--spaced angular points and\n48 energies. We explored a wide\nrange of luminosities and considered\ntwo representative values of the magnetic field, $B= 10^{12}$ and\n$10^{13}$ G. The model parameters are reported in Table 1, together with\nthe accretion rate\n\\be\n\\dot M = L(0) { \\left [ 1 - L(\\tau_B)/L(0) \\right ] \\over \\eta\nc^2}\\,;\n\\ee\nhere $\\eta= 1 - y_G$ is the relativistic efficiency.\nSince\nthe values of $\\tau_B$ and $\\omega_{c,e,p}$ depend on $B$, the adopted\nboundaries in depth and energy\nvary from model to model.\nTypical values are $\\tau_{max} \\sim 10^2$ and $\\tau_{min}\n\\sim 10^{-6}-10^{-8}$; the energy range goes from 0.16 eV to 5.45 keV.\nThe angle--averaged effective depth is always $\\gtrsim 100$ at\n$\\tau_{max}$ and $\\sim 10^{-5}$ at $\\tau_{min}$.\n\nConvergence was generally achieved after 20--30 iterations with a\nfractional accuracy\n$\\sim 0.01$ both in the hydrodynamical variables and in the radiation\nfield.\nAs a further check on the accuracy of our solutions,\nthe luminosity evaluated numerically was compared with\n\\be\n\\label{lumi}\nL(\\tau) \\approx L(0) - \\left [ L(0) - L ( \\tau_B ) \\right ]\n{{1 - [1 - (1-v_{th}^4/v_{ff}^4)(\\tau/\\tau_B)]^{1/2}}\\over{1 -\nv_{th}^4/v_{ff}^4}}\n\\ee\nwhich follows integrating the first gray moment equation\n\\be\n\\dert { L} {\\tau} = - { 4\\pi R^2 f_A W_H\n\\over\ny_G \\kes }\n\\ee\nand provides an analytical expression for $L$ at $\\tau < \\tau_B$ (see\nappendix \\ref{appb} for notation). Within\nthe range of validity of equation (\\ref{lumi}), the two values of $L$ differ\nby less\nthan 4\\%.\n\nIn all models $M= 1 M_\\odot$, $R = 6 GM/c^2\\simeq 0.89 \\times 10^6$ cm\nwhich correspond to $\\tau_s \\simeq 3.3$ (see equation [\\ref{taus}]). Only\nmodel A5, the unmagnetized one, was computed with $\\tau_s \\simeq 8$. One\nof the largest complication introduced by the presence of the magnetic\nfield is the large--scale pattern of the accretion flow. In particular,\nwhen the accretion rate is small the way the spherically symmetric\ninfalling plasma enters the magnetosphere is not fully understood as yet\n(see e.g. Blaes, \\& Madau \\cite{bm93:1993}, Arons \\& Lea\n\\cite{al80:1980}). In order to bracket uncertainties, we assume a fiducial\nvalue for the fraction of the star surface covered by accretion, $f_A =\n0.01$. We stress that this choice has no effect on the spectral properties\nof the emitted radiation and affects only the total luminosity, which\nscales linearly with $f_A$.\n\n\n\\subsection{Emerging Spectra}\\label{spectra}\n\nThe emergent spectra for models A1--A2 and A3--A4 are\nshown in figures \\ref{spe12} and \\ref{spe13}, together with the blackbody at\nthe NS effective\ntemperature, $T_{eff}$. An unmagnetized model (A5) with similar\nluminosity is shown in\nfigure \\ref{spe0}. The corresponding temperature profiles are\nplotted in figure \\ref{tempfig}. Note that in all the plots the photon\nenergy is already corrected for the gravitational redshift, so the\nspectral distribution is shown as a function of the energy as observed\nat Earth. As it is apparent comparing the different curves (see also\nthe solutions computed by ZTZT)\nthe thermal stratification of the atmosphere shows the same general\nfeatures (inner layers in LTE, outer region dominated by Comptonization)\nindependently of $B$.\n\nThe sudden growth of $T$ (up to $10^7-10^8$ K) that appears in the\nexternal layers is basically due to the fact that\nfree--free cooling can not balance the heating produced by\naccretion at low densities. The temperature then rises until it\nreaches a value at which Compton cooling becomes efficient. This\neffect has been discussed by ZTZT and Zane, Turolla, \\& Treves\n(1998) in connection with unmagnetized atmospheres and they have\nshown that the temperature jump is located at the depth where the\nfree--free and Compton thermal timescales become comparable,\n$t_{ff}\\sim t_C$. In the magnetized case the situation is very\nsimilar, but now there are two relevant free--free timescales,\n$t^{(1)}_{ff}$ and $t^{(2)}_{ff}$, one for each mode. Comptonization\nbecomes the dominant cooling process for $\nt_C\\lesssim \\min(t^{(1)}_{ff}, t^{(2)}_{ff})$\nand gives rise to\nthe large jump present in all accretion models. For some values of the\nmodel parameters, the\nregion where $ \\rho = \\rho_{vac}$ coincides with the photospheric\nregion for both modes (see appendix \\ref{vacuum}). In this case,\nvacuum effects can produce the\npeculiar ``double jump'' structure present in model A1, with the\nfirst (small) jump located at a depth where $t^{(1)}_{ff}/\nt^{(2)}_{ff}\\sim 1$.\n\nIn order to compare our results with models available in the\nliterature, some cooling atmospheres have been also computed\nsetting $W_H = 0$ in equation (\\ref{en2}); accordingly, the\nluminosity is now a constant. The emergent spectra for two such\nmodels (C1 and C2, see Table 1) show a good agreement with those\ncomputed by Shibanov \\etal \\ (\\cite{sh92:1992}) using the\ndiffusion approximation.\n\nWe find that the spectral hardening at low luminosities, typical of\nunmagnetized atmospheres, is far less pronounced but still present up to\nfield strengths $\\sim 10^{13}$ G and tends to\ndisappear at large enough luminosities. For comparison, with $L\n\\sim 4 \\times 10^{33}$ erg/s, the magnetized ($B=10^{12}$ G) spectrum has\nnegligible hardening while the hardening ratio is still $\\sim 1.6$ in\nunmagnetized\nmodels of similar luminosity (ZTZT). The overall dependence of\nthe continuum is not particularly sensitive to\nthe value of the magnetic field, although the absorption feature at the\nproton cyclotron energy becomes more prominent with increasing $B$.\n\n\n\\subsection{The Optical Excess}\\label{excess}\n\nThe most striking result emerging from our computations is that,\nalthough spectra from cooling and accreting H atmospheres are\nrather similar in the X--rays, they differ substantially at low\nenergies. Below $\\sim 10$ eV spectra from accreting atmospheres\nexhibit a soft excess with respect to the blackbody spectrum which\nis not shared by the cooling models. This feature, which is\npresent also in the unmagnetized case, can be viewed as a\ndistinctive spectral signature of a low--luminosity, accreting\nneutron star. The fact that it was not reported by ZTZT (and by\nprevious investigators, see e.g. Alme, \\& Wilson \\cite{aw73:1973})\nis because they were mainly interested in the shape of the X--ray\ncontinuum and their energy range was not large enough to cover the\noptical band; besides, some numerical problems, related to the\nmoment formalism used to solve the transfer, prevented ZTZT to\nreach very low frequencies. The evidence of the soft excess is\neven more apparent in figures \\ref{spe12fit}, \\ref{spe13fit} and\n\\ref{spe0fit} where synthetic spectra are plotted together with\nthe best fitting blackbody in the X--ray band. The excess at two\nselected optical wavelengths ($\\lambda = 3000\\,, 6060$ A, see\ndiscussion below), together with the temperature $T_{fit}$ of the\nbest--fitting blackbody in the X--ray band, are reported in Table\n2.\n\nThe appearance of an optical excess in accreting\nmodels is related to the behaviour of the\ntemperature, which is different from that of cooling models.\nThe external layers are now\nhotter because Comptonization dominates the thermal balance there.\nThe low energy tail of the spectrum decouples at a depth that corresponds\nto the (relatively) high temperatures near the jump, and emerges at\ninfinity as a planckian at a temperature higher than $T_{eff}$. By\ndecreasing the luminosity, the temperature jump moves at lower\nscattering depth and the frequency\nbelow which the spectrum exceeds the blackbody at $T_{eff}$ becomes\nlower.\n\nThe presence of an optical excess has been reported in the\nspectrum of a few isolated, nearby pulsars (Pavlov, Stringfellow,\n\\& C\\'ordova \\cite{psc96:1996}) and, at lower luminosities, in the\nspectrum of the ONSs candidate RX J18563.5-3754. RX J18563.5-3754\nwas observed in the X--ray band with ROSAT (Walter, Wolk, \\&\nNeuh\\\"auser \\cite{wwn96:1996}) and by HST at $\\lambda = 3000$ and\n6060 A (Walter, \\& Matthews \\cite{wm97:1997}). These\nmultiwavelength observations made evident that the spectrum of RX\nJ18563.5-3754 is more complex than a simple blackbody. The\nblackbody fit to PSPC data underpredicts the optical fluxes\n$f_{3000}$ and $f_{6060}$ by a factor 2.4 and 3.7 respectively\n(Walter, \\& Matthews \\cite{wm97:1997}; see also Pavlov \\etal \\\n\\cite{pztn96:1996}). Models of cooling atmospheres based on\ndifferent chemical compositions also underestimate the optical\nfluxes (Pavlov \\etal \\ \\cite{psc96:1996}), while models with two\nblackbody components or with a surface temperature variation may\nfit the $f_{3000}$ flux.\nRecent spectra from non--magnetic atmospheres with Fe or Si--ash\ncompositions (see Walter, \\& An \\cite{wa98:1998}) may also provide\na fit of both the X--ray and optical data, although these spectral\nmodels agree with those of Rajagopal, \\& Romani (\\cite{rr96:1996})\nbut not with those of Pavlov \\etal \\ (\\cite{pztn96:1996}). Given\nthe considerable latitude of the unknown parameters $f_A$, $L$,\n$B$, however, results presented here indicate that the full spectral\nenergy distribution\nmay be consistent with the picture of an accreting NS. We want\nalso to note that all models computed here have a blackbody\ntemperature higher than that required to fit the X--ray spectrum\nof RX~J18563.5-3754 (see Table 2) and, although we are far from\nhaving explored the model parameter space, present results\nindicate that the excess decreases for decresing luminosities.\nAlthough the optical identification of another isolated NS\ncandidate, RX J0720.4-3125, still lacks a definite confirmation,\nit is interesting to note that the counterpart proposed by\nKulkarni \\& van Kerkwijk (\\cite{kvk98:1998}) also shows a similar\nexcess.\n\n\\subsection{Fraction of Polarization}\\label{polariz}\n\nThe fraction of polarization strongly depends on the energy band\nand, in the presence of a temperature and density gradient, shows\na variety of different behaviours (see figure \\ref{polfig}). Its\nsign is determined by the competition between plasma and vacuum\nproperties in the photospheric layers. However, independently of\nthe model parameters, the degree of polarization crosses zero at\nthe very vicinity of the proton cyclotron energy (see eq.\n[\\ref{criticion}]), where the mode absorption coefficients cross\neach other. The bulk of the thermal emission from low--luminosity\naccreting NSs falls in the extreme UV/soft X--ray band, which is\nsubject to strong interstellar absorption, making difficult their\nidentification. It has been suggested that the detection of the\nnon--thermal cyclotron emission feature at highest energies may be\na distinguishing signature for most of these low--luminosity\nsources (Nelson, \\etal \\ \\cite{nel95:1995}). Our results show that\nobservations of the proton cyclotron line combined with measures of\npolarization may also provide a powerful tool to determine the\nmagnetic field of the source, even in the absence of pulsations.\n\n\n\\section{Discussion and Conclusions}\\label{discuss}\n\nWe have discussed the spectral distribution of the radiation\nemitted by a static, plane--parallel atmosphere around a strongly\nmagnetized neutron star which is heated by\naccretion. Synthetic spectra have been computed solving the full\ntransfer problem in a magnetoactive plasma for several values of the\naccretion luminosity and of the star magnetic field. In particular, we\nexplored the low luminosities ($L\\sim 10^{30}$--$10^{33}$ erg/s),\ntypical e.g. of isolated accreting NSs, and found that model spectra show\na distinctive excess at low energies over the blackbody distribution which\nbest--fits the X--rays. The energy $\\hbar\\omega_{ex}$ at which the spectrum\nrises\ndepends both on the field strength and the luminosity, but for\n$B\\approx\n10^{12}$--$10^{13}$ G $\\hbar\\omega_{ex}\\sim 10$ eV, so that the optical\nemission of an\naccreting, NS is enhanced with respect to what is expected\nextrapolating the X--ray spectrum to optical wavelengths. The presence of\nan optical/UV bump is due to the fact that the low--frequency radiation\ndecouples at\nvery low values of the scattering depth in layers where the gas is kept at\nlarger temperatures by Compton heating.\nSince a hot outer zone is exhibited by accreting and not by cooling\natmospheres, the optical excess becomes a\ndistinctive spectral feature of NSs accreting at low rates.\n\nDespite present results are useful in shedding some light on the emission\nproperties of accreting, magnetized neutron stars, many\npoints still need further\nclarification before the problem is fully\nunderstood and some of the assumptions on which our investigation was\nbased deserve a further discussion.\nIn this paper we have considered only fully\nionized, pure hydrogen atmospheres. In the case of cooling NSs, the\nemitted spectra are strongly influenced by\nthe chemical composition of the surface layers which results\nfrom the supernova explosion and the subsequent envelope\nfallback. Present uncertainties motivated several authors to\ncompute cooling spectra for different abundances (see e.g. Miller,\n\\& Neuh\\\"auser \\cite{mn91:1991}; Miller \\cite{mil92:1992}; Pavlov,\n\\etal \\ \\cite{pszm95:1995}; Rajagopal, Romani,\n\\& Miller \\cite{rrm97:1997}) and led to the\nsuggestion that the comparison between observed and synthetic X--ray\nspectra may probe the chemistry of the NS crust (Pavlov, \\etal \\\n\\cite{pztn96:1996}).\nThe assumption of a pure hydrogen atmosphere, although crude, is not\nunreasonable for an accretion atmosphere. In this case, in fact,\nincoming protons and spallation by energetic particles in the\nmagnetosphere may enrich the NS surface with light elements (mainly H)\nand, owing to the rapid\nsedimentation, these elements should dominate the photospheric layers\n(Bildsten, Salpeter, \\& Wasserman \\cite{bsw92:1992}).\n\nEven in this simplified picture, however, the\nassumption of complete ionization may not provide an entirely\nrealistic description.\nIn a strongly magnetized plasma atomic binding is greatly enhanced, mainly\nfor light elements. For a typical field of $\\sim 10^{12}$ G,\nthe ionization potentials for the hydrogen ground state are $\\sim 100-300$\neV, moving the photoionization thresholds into the soft X--rays\n(see e.g. Ruderman \\cite{r72:1972}; Shibanov\n\\etal \\ \\cite{sh92:1992}). The role of photoionization and of pressure\nionization in a magnetized hydrogen atmosphere has been investigated by a\nnumber of authors (e.g Ventura, Herold, Ruder, \\& Geyer \\cite{vhrg92:1992};\nPotekhin, \\& Pavlov \\cite{pp97:1997}; Potekhin,\nShibanov, \\& Ventura \\cite{psv98:1998}). The neutral fraction, $f_H$,\nreaches a peak at\ndensities $\\approx 1 \\ {\\rm g/cm}^3$ then decreases due to\npressure ionization and turns out to be highly\ndependent on the temperature. While $f_H$ never\nexceeds a few percent at $T = 10^6$ K, it becomes as large as\n$\\sim 80 \\%$ for $T = 10^{5.5}$ K and $B=10^{13}$ G.\nAlthough in the models we presented here such low temperatures are only\nreached in relatively low--density layers (see figure \\ref{tempfig}),\nhydrogen ionization equilibrium should be properly included in a more\ndetailed analysis.\n\nThe effects of different orientations of the magnetic field through the\natmosphere have been also neglected by keeping $\\bf{B}\\, ||\\, \\bf{n}$, a\nkey simplifying assumption which allowed us to solve the transfer problem\nin one spatial dimension. Clearly, such\nan approximate description is valid only if the size of the\nemitting caps is small.\nDue to the intrinsic anisotropy of a magnetized medium,\nthe emerging flux is expected to depend on the angle $\\theta_B$ between\nthe magnetic field and the normal to the surface. Shibanov \\etal \\\n(\\cite{sh92:1992}) estimated that in a cooling atmosphere the flux at 1\nkeV from a surface element perpendicular to the field may exceed that\nof an element parallel to ${\\bf B}$ by nearly 50\\%.\nThis result shows that a\nnon--uniform magnetic\nfield may lead to a significant distortion in the emerging spectra.\nMoreover, if the orientation of $B$ varies along the atmosphere,\ntangential components of the radiative flux may induce some meridional\ncirculation to maintain the heat balance (Kaminker, Pavlov, \\& Shibanov\n\\cite{kps82:1982}).\n\nWhen the finite size of the emitting regions is accounted for, the problem\ncan not reduced to a plane--parallel geometry and its\nsolution necessarily demands for multidimensional transfer\nalgorithms (e.g. Burnard, Klein, \\& Arons \\cite{bka88:1988},\n\\cite{bka90:1990}; Hsu, Arons, \\& Klein \\cite{hak97:1997}).\nCalculations performed so far were\naimed to the solution of the\nfrequency--dependent radiative problem on a fixed background\nor of the full\nradiation hydrodynamical problem in the frequency--integrated case.\nNumerical codes for the solution of the full transfer problem in\naxially symmetric media under general conditions are now\navailable, see e.g. ZEUS (Stone, \\& Norman \\cite{sn92:1992}),\nALTAIR (Dykema, Castor, \\& Klein \\cite{dck96:1996})\nand RADICAL (Dullemond, \\& Turolla \\cite{dt99:1999}). Their\napplication to the transfer of radiation in accretion atmospheres around\nmagnetized NSs can add new insights on the properties of the emitted\nspectra.\n\n\n\\acknowledgments\n\nWe are grateful to G.G. Pavlov and to V.E. Zavlin for several very\nhelpful discussions,\nand to A.Y. Potekhin for providing us with the expressions for the ion\nopacities. We also\nthank S. Rappaport for calling our attention to some useful references.\n\n\\appendix\n\\section{Radiative Processes in a Magnetized Medium}\\label{appa}\n\\subsection{Electron Scattering}\n\nThe electron contribution to the scattering source terms has been\nevaluated using the expression of the differential cross\nsection, $d\\sigma^{ij}/d \\Omega$, discussed by Ventura (\\cite{v79:1979})\nand\nKaminker, Pavlov, \\& Shibanov (\\cite{kps82:1982}).\nThe electron contribution to $K_s^{ij}$\ncan be simply written as\n\\be\n\\label{emi}\nK_{s,e}^{ij} = { 1 \\over m_p \\kes } \\int d \\phi'\n\\dert{\\sigma^{ij}}{\\Omega } \\approx { 3 \\over 4}\n\\sum_{\\alpha=-1}^1\n\\left | e^{j'}_{\\alpha} \\right |^2\n\\left | e^{i}_{\\alpha} \\right |^2 { 1 \\over \\left ( 1 +\\alpha u^{1/2}\n\\right )^2 + \\gamma_r^2 } \\, .\n\\ee\nwhere $u = \\omega_{c,e}^2/\\omega^2$, the $\\ e^{i}_{\\alpha}$ are\nthe components of the normal mode\nunit polarization vector in a coordinate frame with the\n$z$--axis\nalong $\\bf B$ and $\\gamma_r=(2/3)(e^2/m_ec^3) \\omega$ is the radiation\ndamping.\nFurther integration over $\\theta'$ gives the total\nopacities\n\\be\nk_{s,e}^i = \\sum_{j=1}^2 \\int K_{s,e}^{ij}\\, d\\mu'\n\\approx\n\\sum_{\\alpha=-1}^1\n\\left | e^{i}_{\\alpha} \\right |^2 { 1 \\over \\left ( 1 +\\alpha u^{1/2}\n\\right )^2 + \\gamma_r^2 } \\, .\n\\ee\n\nFor energies near the proton cyclotron frequency $\\omega_{c,p} =\n(m_e/m_p) \\omega_{c,e}$, Thomson scattering on ions becomes\nimportant. The corresponding opacity has been derived by Pavlov\n\\etal \\ (\\cite{pszm95:1995}) in a relaxation--time approximation\nand it is\n\\be\nK_{s,p}^{ij} \\approx { 3 \\over 4} \\mu_m^2\n\\sum_{\\alpha=-1}^1\n\\left | e^{j'}_{\\alpha} \\right |^2\n\\left | e^{i}_{\\alpha} \\right |^2 { 1 \\over \\left ( 1 - \\alpha u_p^{1/2}\n\\right )^2 + \\mu_m^2 \\gamma_r^2 } \\, .\n\\ee\n\\be\nk_{s,p}^i \\approx \\mu_m^2 \\sum_{\\alpha=-1}^1 \\left |\ne^{i}_{\\alpha} \\right |^2 { 1 \\over \\left ( 1 - \\alpha u_p^{1/2}\n\\right )^2 + \\mu_m^2 \\gamma_r^2 } \\, , \\ee where $\\mu_m =\nm_e/m_p$ and $u_p = \\omega_{c,p}^2/\\omega^2$. The total opacities\n$K^{ij}_s$ and $k_s^i$ appearing in equations (\\ref{tr1}) are then\nevaluated by adding the contributions of the two species.\n\n\\subsection{Bremsstrahlung}\\label{brem}\n\nThe electron and proton contributions to free--free opacity have a\nstructure similar to that discussed for scattering. In a pure\nhydrogen plasma, they are given by (see Pavlov, \\& Panov\n\\cite{pp76:1976}; M\\'esz\\'aros \\cite{mes92:1992}; Pavlov \\etal \\\n\\cite{pszm95:1995})\n\\be\nk_{ab,e}^i \\approx {\\kff \\over \\kes}\n\\sum_{\\alpha=-1}^1\n\\left | e^{i}_{\\alpha} \\right |^2 { g_{\\alpha} \\over \\left ( 1 +\\alpha\nu^{1/2}\n\\right )^2 + \\gamma_r^2 }\n \\, ,\n\\ee\n\\be\nk_{ab,p}^i \\approx {\\kff \\over \\kes} \\mu_m^2 \\sum_{\\alpha=-1}^1\n\\left | e^{i}_{\\alpha} \\right |^2 { g_{\\alpha} \\over \\left ( 1 -\n\\alpha u^{1/2} \\right )^2 + \\mu_m^2 \\gamma_r^2 } \\ee\nwhere\n\\be\n\\kff = 4 \\pi^2 \\alpha_F^3 {\\hbar^2 c^2 \\over m_e^2} {n_e^2 \\over v_T\n\\omega^3} \\left [ 1 - \\exp \\left ( - \\hbar \\omega / k T \\right )\n\\right ] \\, ,\n\\ee\n$g_{0} = g_{||}$, $g_{-1} = g_{+1} = g_{\\perp}$, and $g_{||}$,\n$g_{\\perp}$ are the modified Gaunt factors, which account for the\nanisotropy induced by the magnetic field. The quantity\n$\\kff$ is the free--free opacity of a non--magnetic plasma apart\nfrom a factor $(4 \\pi /3 \\sqrt 3)g$, where $g$ is the unmagnetized Gaunt\nfactor.\nThe total absorption opacity can be then evaluated by summing over the\ntwo species.\n\nThe modified Gaunt factors were computed evaluating numerically\ntheir integral form as given by Pavlov, \\& Panov\n(\\cite{pp76:1976}). At low temperatures and small frequencies ($u\n\\gg 1$), where direct numerical quadrature becomes troublesome,\nthe Gaunt factors have been obtained from the simpler formulas by\nNagel (\\cite{n80:1980}; see also M\\'esz\\'aros \\cite{mes92:1992};\nRajagopal, Romani, \\& Miller \\cite{rrm97:1997} and references\ntherein). In order to decrease the computational time, the Gaunt\nfactors have been evaluated once for all over a sufficiently large\ngrid of temperatures and frequencies. In the transfer calculation\nthey are then obtained at the required values of $T$ and $\\omega$\nby polynomial interpolation.\n\n\\subsection{Vacuum Effects and Mode Switching}\\label{vacuum}\n\nThe opacities of a real plasma\nstart to change, due to the vacuum corrections in the\npolarization eigenmodes, when the field approaches the critical value\n$B_c=m_e^2c^3/\\hbar e \\simeq 4.41\n\\times 10^{13}$ G. The vacuum contribution has ben included modifying\nthe expressions for the $e_{\\alpha}^i$ as discussed by Kaminker, Pavlov,\n\\& Shibanov (\\cite{kps82:1982}), and is controlled by\nthe vacuum parameter $W$\n\\be\nW = \\left({ 3 \\times 10^{28} \\, {\\rm cm^{-3}} \\over n_e }\\right) \\left (\n{B \\over B_c }\\right )^4 \\, .\n\\ee\n\nThe inclusion of vacuum and of the protons produces the breakdown\nof the NM approximation near the mode collapse points (MCPs; see\ne.g. Pavlov, \\& Shibanov \\cite{ps79:1979}; M\\'esz\\'aros\n\\cite{mes92:1992} and references therein). For $W>4$, or $\\rho <\n\\rho_{vac} = 3.3\\times 10^{-3}(B/10^{12}\\, {\\rm G})^4 \\ {\\rm\ng/cm}^3$, the MCPs appear at the two critical frequencies\n\n\\be\\label{critic} \\omega_{c1,2}^2 = { 1 \\over 2}\n\\omega_{c,e}^2\\left[1\\pm \\left(1-\\frac{4}{W}\\right)^{1/2}\\right]\\,\n. \\ee MCPs play an important role in the transfer of radiation\nthrough a magnetized medium, since the absorption coefficients of\nthe two modes either cross each other or have a close approach,\ndepending on the angle. Following the discussion by Pavlov, \\&\nShibanov (\\cite{ps79:1979}), under the typical conditions at hand\nmode switching is likely to occur at nearly all values of $\\mu$.\nFor this reason and for the sake of simplicity, in the present\ncalculation we assumed mode switching for any value of $\\mu$ at\nthe two vacuum critical frequencies.\n\nAs shown by Bulik, \\& Pavlov (\\cite{bp96:1996}) in a fully ionized\nhydrogen plasma the presence of protons introduces (even in the absence\nof vacuum) a new MCP at\n\\be\\label{criticion}\n\\omega_{c,3} = \\frac{\\omega_{c,p}}{\\sqrt{1-\\omega_{c,p}/\\omega_{c,e}+\n\\omega_{c,p}^2/\\omega_{c,e}^2}}\\simeq\n\\omega_{c,p}\\left(1+\\frac{m_e}{2m_p}\\right)\\,.\n\\ee\nAt $\\omega=\\omega_{c,3}$ the opacity coefficients cross (Zavlin,\nprivate communication), and the MCP related to the proton contribution is\nagain a mode switching point. Although we are aware of no detailed\ncalculation of the\npolarization modes in a ``protons + electrons + vacuum'' plasma, it seems\nnatural to assume that, at least if $\\omega_{c,2} > \\omega_{c,3}$, the\nproton contribution to the ``vacuum'' term\nmay be safely neglected, being a function of the ratio\n$m_e/m_p$.\n\n\\section{Stopping Depth and Heating Rate in a Magnetized Atmosphere}\n\\label{appb}\n\nIn the unmagnetized case, under the assumption that all the\nproton stopping power is converted into electromagnetic radiation\nwithin the atmosphere, $W_H$ can be approximated as (Alme, \\&\nWilson \\cite{aw73:1973}; ZTZT) \\be\\label{wh} W_H \\approx\n\\cases{\\displaystyle { {y_G\\kes} \\over 8\\pi R^2 \\tau_s f_A} \\left\n[L(0) - L(\\tau_s) \\right ] {{f(x_e)}\\over{[1 -\n(1-v_{th}^4/v_{ff}^4)(\\tau/\\tau_s)]^{1/2}}}& $\\tau < \\tau_s$\\cr\n&\\cr 0 & $\\tau \\geq \\tau_s$\\cr} \\ee where $f_A$ is the fraction\nof the star surface covered by accretion, $\\tau_s$ is the proton\nstopping depth and $v_{th}^2/v_{ff}^2 = 3kT(\\tau_s) R/(2 m_p G M)$\nis the squared ratio of the proton thermal velocity to the\nfree--fall velocity. For cold atmospheres in which the proton\nkinetic energy is much larger than the thermal energy, $f(x_e)$\ncan be safely taken to be unity for all practical purposes.\n\nInfalling protons loose their energy to electrons via Coulomb\ncollisions and the generation of collective plasma oscillations\nand $\\tau_s$ can be approximated as (e.g. Zel'dovich, \\& Shakura\n\\cite{zs69:1969}; Nelson, Salpeter, \\& Wasserman\n\\cite{nel93:1993}) \\be\\label{taus} \\tau_s\\approx\n\\frac{1}{6}\\frac{m_p}{m_e}\\frac{v_{ff}^4}{c^4\\ln\\Lambda_c}\\simeq\n2.6 \\, \\left(\\frac{M}{M_\\odot}\\right)^2\\left(\\frac{R}{10^6\\, {\\rm\ncm}}\\right)^{-2} \\left(\\frac{10}{\\ln\\Lambda_c}\\right) \\ee where\n$\\ln\\Lambda_c$ is a (constant) Coulomb logarithm.\n\nThe proton stopping process in strongly magnetized atmospheres\npresents a few differences, and has been discussed in detail by\nNelson, Salpeter, \\& Wasserman (\\cite{nel93:1993}). Now the proton\nstopping depth, $\\tau_B$, is larger than $\\tau_s$, essentially\nbecause the magnetic field reduces the effective Coulomb logarithm\nperpendicular to the field. The expression for the proton stopping\npower retains, nevertheless, the same form as in the unmagnetized\ncase. In the present calculation we used their approximate\nexpression which relates $\\tau_B$ to $\\tau_s$ at different field\nstrengths \\be\\label{taub} \\frac{\\tau_B}{\\tau_s} \\approx\n\\cases{\\displaystyle {\\frac{\\ln\\Lambda_c}{\\ln(2n_{max})} }&\n$n_{max}\\gtrsim 1$\\cr &\\cr 2\\ln(m_p/m_e)\\simeq 15 &\n$n_{max}\\lesssim 1$\\cr} \\ee $n_{max}=\nm_ev_{ff}^2/(2\\hbar\\omega_{c,e})\\simeq$ $ 6.4\\,\n(M/M_\\odot)(R/10^6\\, {\\rm cm})^{-1} (B/10^{12}\\, {\\rm G})^{-1}$.\nSince proton--proton interactions limit the stopping length to the\nmean--free path for nuclear collisions, which corresponds to\n$\\tau_{pp} \\sim 22$ (M\\'esz\\'aros \\cite{mes92:1992}), if the value\nof $\\tau_B$ which follows form equation (\\ref{taub}) exceeds\n$\\tau_{pp}$, the latter is used instead.\n\nIn the very strong field limit ($n_{max}\\lesssim 1$), expression\n(\\ref{wh}) for the heating rate is still valid, provided that\n$\\tau_s$ is replaced by $\\tau_B$. The situation is more\ncomplicated in the moderate field limit ($n_{max}\\gtrsim 1$). In\nthis case, not only $\\tau_s$ must be replaced by $\\tau_B$, but a\nfurther effect must be accounted for. Now a sizeable fraction,\n$\\sim 1 - 1/\\ln(2n_{max}$), of the initial proton energy goes into\nexcitations of electrons Landau levels. The cyclotron photons\nproduced by radiative deexcitation will be partly thermalized by\nabsorption and Compton scattering while the remaining ones escape\nforming a broad cyclotron emission feature (Nelson, \\etal \\\n\\cite{nel95:1995}). To account for this we take in the moderate\nfield limit, \\be\\label{wmf} W_{MF} = (1-f)W_H +\nfW_H(\\Delta\\epsilon/\\epsilon) \\ee where $f$ is the fraction of the\ninitial proton energy which goes into Landau excitations and\n\\be\\label{fracgain} \\frac{\\Delta\\epsilon}{\\epsilon}\\approx\n\\frac{(\\hbar\\omega_{c,e}/m_ec^2)\\tau^2}{1+(\\hbar\\omega_{c,e}/m_ec^2)\\tau^2}\n\\ee is the electron fractional energy gain due to repeated\nscatterings. Strictly speaking, equation (\\ref{fracgain}) is valid\nonly for photons produced below $\\tau_C\\sim\n(\\hbar\\omega_{c,e}/m_ec^2)^{-1/2}\\simeq 7\\, (B/10^{12}\\, {\\rm\nG})^{-1/2}$, because only these photons loose a significant\nfraction of their energy in Compton collisions with electrons. We\nhave also to take into account that cyclotron photons produced at\ndepths greater than the thermalization depth, $\\tau_{th}\\sim 16\\,\n(B/10^{12}\\, {\\rm G})^{7/6}(M/M_\\odot)^{1/3}(R/10^{6}\\, {\\rm\ncm})^{2/3} (T/10^{7}\\, {\\rm K})^{1/3}$, are absorbed. In our\nmodels, however, $\\tau_B$ is always less than $\\tau_{th}$, so we\ndo not need to worry about free--free absorption in (\\ref{wmf}). A\nparabolic fit to the sum of first two curves ($0\\to 1$ and $0\\to\n2$ Landau transitions) in figure 4 of Nelson, Salpeter, \\&\nWasserman (\\cite{nel93:1993}) is very accurate and gives\n\\be\\label{ffit} f(\\tau ) = 6.1\\times 10^{-4} + 6.5\\times\n10^{-2}(\\tau/\\tau_s) + 8.7\\times 10^{-3}(\\tau/\\tau_s)^2\\, . \\ee\n\n\n\\clearpage\n\n\\begin{deluxetable}{cccccc}\n\\tablecolumns{6}\n\\tablewidth{0pc}\n\\tablecaption{Model Parameters\\label{table1}}\n\\tablenum{1}\n\\tablehead{\n\\colhead{Model}&\n\\colhead{$B$} &\n\\colhead{$L_\\infty$} &\n\\colhead{$L(\\tau_B)/L(0)$} &\n\\colhead{$\\dot M$} &\n\\colhead{$f_A$} \\\\\n\\colhead{} &\n\\colhead{$10^{12}$ G} &\n\\colhead{$10^{33}$ erg s$^{-1}$} &\n\\colhead{} &\n\\colhead{$10^{12}$ g s$^{-1}$} &\n\\colhead{}\n}\n\\startdata\n A1 & 1 & 0.1 & 0.17 & 0.75 & 0.01\\\\\n A2 & 1 & 3.7 & 0.25 & 25 & 0.01\\\\\n A3 & 10 & 0.2 & 0.28 & 0.13 & 0.01\\\\\n A4 & 10 & 6.3 & 0.33 & 38 & 0.01\\\\\n A5 & 0 & 4.3 & 0.29 & 28 & 0.01\\\\\n C1 & 1 & 0.2 & 1 & 0 & 1\\\\\n C2 & 9 & 0.52 & 1 & 0 & 1\\\\\n\n\\tablecomments{The first letter in the model identifier refers to\naccretion (``A'') or cooling (``C'') atmospheres.}\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n\\tablecolumns{4}\n\\tablewidth{0pc}\n\\tablecaption{Predicted Excess \\label{table2}}\n\\tablenum{2}\n\\tablehead{\n\\colhead{Model}&\n\\colhead{$\\displaystyle{F_{6060}}\\over \\displaystyle{F^{bb}_{6060}}$} &\n\\colhead{$\\displaystyle{F_{3000}}\\over \\displaystyle{F^{bb}_{3000}}$} &\n\\colhead{$T^{bb}_{fit}$ (keV)} \\\\\n}\n\\startdata\n A1 & 1.60 & 1.36 & 0.25 \\\\\n A2 & 3.05 & 1.44 & 0.43 \\\\\n A3 & 1.12 & 1.06 & 0.25 \\\\\n A4 & 3.44 & 2.21 & 0.57 \\\\\n A5 & 3.49 & 2.16 & 0.52 \\\\\n\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\n\n\\bibitem[1973]{aw73:1973}\nAlme, W.L., \\& Wilson, J.R. 1973, \\apj, 186, 1015\n\n\\bibitem[1980]{al80:1980}\nArons, J., \\& Lea, S.M. 1980, \\apj, 235, 1016 \n\n\\bibitem[1987]{akl87:1987}\nArons, J., Klein, R.I., \\& Lea, S.M. 1987, \\apj, 312, 666\n\n\\bibitem[1992]{bsw92:1992}\nBildsten, L., Salpeter, E.E., \\& Wasserman, I. 1992, \\apj, 384, 143\n\n\\bibitem[1993]{bm93:1993}\nBlaes, O., \\& Madau, P. 1993, \\apj, 403, 690\n\n\\bibitem[1996]{bp96:1996}\nBulik, T., \\& Pavlov, G.G. 1996, \\apj, 469, 373\n\n\\bibitem[1988]{bka88:1988}\nBurnard, D.J., Klein, R.I., \\& Arons, J. 1988, \\apj, 324, 1001\n\n\\bibitem[1990]{bka90:1990}\nBurnard, D.J., Klein, R.I., \\& Arons, J. 1990, \\apj, 349, 262\n\n\\bibitem[1999]{dt99:1999}\nDullemond, C.P., \\& Turolla, R. 1999, \\mnras, submitted\n\n\\bibitem[1996]{dck96:1996}\nDykema, P.G., Klein, R.I., \\& Castor, J.I. 1996, \\apj, 457, 892\n\n\\bibitem[1974]{gp74:1974}\nGnedin, Yu.N., \\& Pavlov, G.G. 1974, Sov. 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S., \\& Colpi, M. 1999, \\pasp, submitted\n\n\\bibitem[1986]{vdhr86:1986}\nvan den Heuvel, E.P.J., \\& Rappaport, S. 1986,\nPhysics of Be Stars, A. Slettebak \\& T. Snow eds. (Cambridge: Cambridge\nUniversity Press)\n\n\\bibitem[1979]{v79:1979}\nVentura, J. 1979, \\prd, 19, 1684\n\n\\bibitem[1992]{vhrg92:1992}\nVentura, J., Herold, H., Ruder, H. \\& Geyer, F. 1992, \\aap, 261, 235\n\n\\bibitem[1996]{wwn96:1996}\nWalter, F.M., Wolk, S.J., \\& Neuh\\\"auser, R. 1996, \\nat, 379, 233\n\n\\bibitem[1997]{wm97:1997}\nWalter, F.M., \\& Matthews, L.D. 1997, \\nat, 389, 358\n\n\\bibitem[1998]{wa98:1998}\nWalter, F.M., \\& An, P. 1998, $192^{nd}$ AAS meeting, invited talk\n\n\\bibitem[1980]{y80:1980}\nYahel, R.Z. 1980, \\apj, 236, 911\n\n\\bibitem[1995]{ztzt95:1995}\nZampieri, L., Turolla, R., Zane, S., \\& Treves, A. 1995, \\apj, 439, 849 (ZTZT)\n\n\\bibitem[1996]{crm:1996}\nZane, S., Turolla, R., Nobili, L., \\& Erna, M. 1996, \\apj, 466, 871\n\n\\bibitem[1998]{hot:1998}\nZane, S., Turolla, R., \\& Treves, A. 1998, \\apj, 501, 258\n\n\\bibitem[1969]{zs69:1969}\nZel'dovich, Ya., \\& Shakura, N. 1969, Soviet Astron.--AJ, 13, 175\n\n\\end{thebibliography}\n\n\\clearpage\n\n\n\\begin{figure}\n\\centering\n\\psfig{file=f1.ps,width=10cm}\n\\caption{Emergent spectra for models A1 and A2 (full lines),\ntogether with the\nblackbody spectra at the neutron star effective temperature (dash--dotted\nlines).\n\\label{spe12}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f2.ps,width=10cm}\n\\caption{Same as in\nfigure \\ref{spe12} for models A3 and A4.\n\\label{spe13}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f3.ps,width=10cm}\n\\caption\n{Same as in figure \\ref{spe12} for $B = 0$ (model A5).\n\\label{spe0}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f4.ps,width=10cm}\n\\caption\n{The run of the gas temperature in the atmosphere for the models of\nfigures \\ref{spe12},\n\\ref{spe13} and \\ref{spe0}; solid lines correspond to $B =\n10^{12}$ G, dash--dotted lines to $B = 10^{13}$\nG and dotted lines to $B=0$.\\label{tempfig}}\n\\end{figure}\n\n\n\\begin{figure}\n\\centering\n\\psfig{file=f5.ps,width=10cm}\n\\caption\n{Same models as in figure \\ref{spe12},\ntogether with the two blackbody functions which best--fit the X--ray\nspectra in the 0.03--4.5 keV interval (dashed lines). The arrows mark\nthe 3000--7500 A band. \\label{spe12fit}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f6.ps,width=10cm}\n\\caption\n{Same as in figure \\ref{spe12fit}, for the models with\n$B=10^{13}$ G; here the fit is computed in the 0.19--3.4/4.5 keV\nband for the two solutions.\n\\label{spe13fit}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f7.ps,width=10cm}\n\\caption\n{Same as in figure \\ref{spe12fit}, for the models with\n$B=0$; here the fit is computed in the 0.02--3.3 keV\nband. \\label{spe0fit}}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\psfig{file=f8.ps,width=10cm}\n\\caption\n{Fraction of polarization\nfor the same models as in figures \\ref{spe12} and \\ref{spe13}. Solid\nline: model A1; dash--dotted\nline: A2; dotted line: A3;\ndashed line: A4.\n\\label{polfig}}\n\\end{figure}\n\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002019.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\n\\bibitem[1973]{aw73:1973}\nAlme, W.L., \\& Wilson, J.R. 1973, \\apj, 186, 1015\n\n\\bibitem[1980]{al80:1980}\nArons, J., \\& Lea, S.M. 1980, \\apj, 235, 1016 \n\n\\bibitem[1987]{akl87:1987}\nArons, J., Klein, R.I., \\& Lea, S.M. 1987, \\apj, 312, 666\n\n\\bibitem[1992]{bsw92:1992}\nBildsten, L., Salpeter, E.E., \\& Wasserman, I. 1992, \\apj, 384, 143\n\n\\bibitem[1993]{bm93:1993}\nBlaes, O., \\& Madau, P. 1993, \\apj, 403, 690\n\n\\bibitem[1996]{bp96:1996}\nBulik, T., \\& Pavlov, G.G. 1996, \\apj, 469, 373\n\n\\bibitem[1988]{bka88:1988}\nBurnard, D.J., Klein, R.I., \\& Arons, J. 1988, \\apj, 324, 1001\n\n\\bibitem[1990]{bka90:1990}\nBurnard, D.J., Klein, R.I., \\& Arons, J. 1990, \\apj, 349, 262\n\n\\bibitem[1999]{dt99:1999}\nDullemond, C.P., \\& Turolla, R. 1999, \\mnras, submitted\n\n\\bibitem[1996]{dck96:1996}\nDykema, P.G., Klein, R.I., \\& Castor, J.I. 1996, \\apj, 457, 892\n\n\\bibitem[1974]{gp74:1974}\nGnedin, Yu.N., \\& Pavlov, G.G. 1974, Sov. Phys. JETP, 38, 903\n\n\\bibitem[1997]{ha97:1997} Haberl, F., \\etal \\ 1997, \\aap, 326, 662\n\n\\bibitem[1998]{hmp98:1998} Haberl, F., Motch, C., \\&\nPietsch, W. 1998, Astron. Nachr., 319, 97\n\n\\bibitem[1999]{hpm99:1999} Haberl, F., Pietsch, W., \\& Motch, C. 1999,\n\\aap, in the press (astro--ph/9911159)\n\n\\bibitem[1997]{hak97:1997}\nHsu, J.J.L., Arons, J., \\& Klein, R.I. 1997, \\apj, 478, 663\n\n\\bibitem[1982]{kps82:1982}\nKaminker, A.D., Pavlov, G.G., \\& Shibanov, Yu.A. 1982, \\apss, 86, 249\n\n\\bibitem[1998]{kvk98:1998}\nKulkarni, S.R., \\& van Kerkwijk, M.H. 1998, \\apjl, 507, L49\n\n\\bibitem[1991]{mn91:1991}\nMiller, M.C., \\& Neuh\\\"auser, D. 1991, \\mnras, 253, 107\n\n\\bibitem[1992]{mil92:1992}\nMiller, M.C. 1992, \\mnras, 255, 129\n\n\\bibitem[1992]{mes92:1992}\nM\\'esz\\'aros, P. 1992, High--Energy Radiation from\nMagnetized Neutron Stars (Chicago: The University of Chicago Press)\n\n\\bibitem[1999]{mo99:1999} Motch, C., \\etal \\ 1999, \\aap, in the\npress (astro--ph/9907306)\n\n\\bibitem[1980]{n80:1980}\nNagel, W. 1980, \\apj, 236, 904\n\n\\bibitem[1993]{nel93:1993}\nNelson, R.W., Salpeter, E.E., \\& Wasserman, I. 1993, \\apj, 418, 874\n\n\\bibitem[1995]{nel95:1995}\nNelson, R.W., Wang, C.L., Salpeter, E.E., \\& Wasserman, I. 1995, \\apj, 438, L99\n\n\\bibitem[1976]{pp76:1976}\nPavlov, G.G., \\& Panov, A.N. 1976, Sov. Phys. JETP, 44, 300\n\n\\bibitem[1979]{ps79:1979}\nPavlov, G.G., \\& Shibanov, Yu.A. 1979, Sov. Phys. JETP, 49, 741\n\n\\bibitem[1995]{pszm95:1995}\nPavlov, G.G., Shibanov, Yu.A., Zavlin, V.E., \\& Meyer,\nR.D. 1995, in The Lives of Neutron Stars, M.A. Alpar, et al. eds.\n(Dordrecht: Kluwers)\n\n\\bibitem[1996]{psc96:1996}\nPavlov, G.G., Stringfellow, G.S., \\& C\\'ordova, F.A.\n1996, \\apj, 467, 370\n\n\\bibitem[1996]{pztn96:1996}\nPavlov, G.G., Zavlin, V.E., Tr\\\"umper, J., \\&\nNeuh\\\"auser, R. 1996, \\apjl, 472, L33\n\n\\bibitem[1993]{pp93:1993}\nPotekhin, A.Y., \\& Pavlov, G.G 1993, \\apj, 407, 330\n\n\\bibitem[1997]{pp97:1997}\nPotekhin, A.Y., \\& Pavlov, G.G 1997, \\apj, 483, 414\n\n\\bibitem[1998]{psv98:1998}\nPotekhin, A.Y., Shibanov, Yu.A., \\& Ventura, J. 1998,\nin Neutron Stars and Pulsars, N. Shibazaki, et al. eds.\n(Tokyo: Universal Academy Press)\n\n\\bibitem[1996]{rr96:1996}\nRajagopal, M., \\& Romani, R.W. 1996, \\apj, 461, 327\n\n\\bibitem[1997]{rrm97:1997}\nRajagopal, M., Romani, R.W., \\& Miller, M.C. 1997, \\apj, 479, 347\n\n\\bibitem[1982]{rvdh82:1982}\nRappaport, S., \\& van den Heuvel, E.P.J. 1982,\nBe Stars, M. Jaschek \\& H.G. Groth eds. (Dordrecht: Reidel)\n\n\\bibitem[1987]{rom87:1987}\nRomani, R.W. 1987, \\apj, 313, 718\n\n\\bibitem[1972]{r72:1972}\nRuderman, M.A. 1972, IAU Symposium 53, The Physics of Dense\nMatter, Boulder, CO\n\n\\bibitem[1999]{sch99:1999}\nSchwope, A.D., \\etal \\ 1999, \\aap, 341, L51\n\n\\bibitem[1992]{sh92:1992}\nShibanov, Yu.A., Zavlin, V.E., Pavlov, G.G., \\& Ventura, J.\n1992, \\aap, 266, 313\n\n\\bibitem[1992]{sn92:1992}\nStone, J.M., \\& Norman, M.L. 1992, \\apjs, 80, 753\n\n\\bibitem[1991]{tc91:1991}\nTreves, A., \\& Colpi, M. 1991, \\aap, 241, 107\n\n\\bibitem[1999]{review:1999}\nTreves, A., Turolla, R., Zane. S., \\& Colpi, M. 1999, \\pasp, submitted\n\n\\bibitem[1986]{vdhr86:1986}\nvan den Heuvel, E.P.J., \\& Rappaport, S. 1986,\nPhysics of Be Stars, A. Slettebak \\& T. Snow eds. (Cambridge: Cambridge\nUniversity Press)\n\n\\bibitem[1979]{v79:1979}\nVentura, J. 1979, \\prd, 19, 1684\n\n\\bibitem[1992]{vhrg92:1992}\nVentura, J., Herold, H., Ruder, H. \\& Geyer, F. 1992, \\aap, 261, 235\n\n\\bibitem[1996]{wwn96:1996}\nWalter, F.M., Wolk, S.J., \\& Neuh\\\"auser, R. 1996, \\nat, 379, 233\n\n\\bibitem[1997]{wm97:1997}\nWalter, F.M., \\& Matthews, L.D. 1997, \\nat, 389, 358\n\n\\bibitem[1998]{wa98:1998}\nWalter, F.M., \\& An, P. 1998, $192^{nd}$ AAS meeting, invited talk\n\n\\bibitem[1980]{y80:1980}\nYahel, R.Z. 1980, \\apj, 236, 911\n\n\\bibitem[1995]{ztzt95:1995}\nZampieri, L., Turolla, R., Zane, S., \\& Treves, A. 1995, \\apj, 439, 849 (ZTZT)\n\n\\bibitem[1996]{crm:1996}\nZane, S., Turolla, R., Nobili, L., \\& Erna, M. 1996, \\apj, 466, 871\n\n\\bibitem[1998]{hot:1998}\nZane, S., Turolla, R., \\& Treves, A. 1998, \\apj, 501, 258\n\n\\bibitem[1969]{zs69:1969}\nZel'dovich, Ya., \\& Shakura, N. 1969, Soviet Astron.--AJ, 13, 175\n\n\\end{thebibliography}"
}
] |
astro-ph0002020
|
The ages of quasar host galaxies.
|
[
{
"author": "L.A. Nolan$^{1}$"
},
{
"author": "J.S. Dunlop$^{1}$"
},
{
"author": "M.J. Kukula$^{1}$"
},
{
"author": "D. H. Hughes$^{1,2}$"
},
{
"author": "T. Boroson$^{3}$ $\\&$ R. Jimenez$^{1}$."
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh"
},
{
"author": "EH9~3HJ"
},
{
"author": "$^{2}$INOAE"
},
{
"author": "Apartado Postal 51 y 216"
},
{
"author": "72000"
},
{
"author": "Puebla"
},
{
"author": "Pue."
},
{
"author": "Mexico."
},
{
"author": "$^{3}$NOAO"
},
{
"author": "PO Box 26732"
},
{
"author": "Tucson"
},
{
"author": "Arizona 85726$-$6732"
},
{
"author": "U.S.A."
}
] |
We present the results of fitting deep off-nuclear optical spectra of radio-quiet quasars, radio-loud quasars and radio galaxies at $z \simeq 0.2$ with evolutionary synthesis models of galaxy evolution. Our aim was to determine the age of the dynamically dominant stellar populations in the host galaxies of these three classes of powerful AGN. Some of our spectra display residual nuclear contamination at the shortest wavelengths, but the detailed quality of the fits longward of the 4000\AA\ break provide unequivocal proof, if further proof were needed, that quasars lie in massive galaxies with (at least at $z \simeq 0.2$) evolved stellar populations. By fitting a two-component model we have separated the very blue (starburst and/or AGN contamination) from the redder underlying spectral energy distribution, and find that the hosts of all three classes of AGN are dominated by old stars of age $8 - 14$ Gyr. If the blue component is attributed to young stars, we find that, at most, 1\% of the visible baryonic mass of these galaxies is involved in star-formation activity at the epoch of observation, at least over the region sampled by our spectroscopic observations. These results strongly support the conclusion reached by McLure et al. (1999) that the host galaxies of luminous quasars are massive ellipticals which have formed by the epoch of peak quasar activity at $z \simeq 2.5$.
|
[
{
"name": "AGNhost.tex",
"string": "\\documentstyle[epsfig,graphics]{mn}\n\n\n\\def\\ls{{\\tiny \\( \\stackrel{<}{\\sim}\\)}} \n\\def\\gs{{\\tiny \\( \\stackrel{>}{\\sim}\\)}} \n\n\n\\begin{document}\n\n\\newcommand{\\etal}{{\\em et al.}\\ } % puts et al. in italics.\n\\newcommand{\\ie}{{\\em i.e. }}\n\\newcommand{\\eg}{{\\em e.g. }}\n\\newcommand{\\micron}{\\mbox{\\,${\\mu}$m} } % microns\n\\newcommand{\\Msolar}{\\mbox{\\,$\\rm M_{\\odot}$}} % solar mass\n\\newcommand{\\Lsolar}{\\mbox{\\,$\\rm L_{\\odot}$}} % solar luminosity\n\\newcommand{\\asec}{^{\\prime\\prime}}\n\\newcommand{\\h}{{\\sc hst\\,}}\n\\newcommand{\\irc}{{\\sc ircam3\\,}}\n\\newcommand{\\wf}{{\\sc wfpc2\\,}}\n\\newcommand{\\psf}{{\\sc psf\\,}}\n\\hyphenation{infra-red} \n\\hyphenation{inter-stellar}\n\\renewcommand{\\baselinestretch}{1.5}\n%------------------------------------------------------------------------------\n\\newcommand{\\spsc}[2]{\\mbox{$\\rm #1^{#2}$}} % superscript in text\n\\newcommand{\\sbsc}[2]{\\mbox{$\\rm #1_{#2}$}} % subscript in text\n\\newcommand{\\ang}{\\mbox{$\\rm \\AA$}}\n\\newcommand{\\unit}[1]{\\; \\rm #1}\n\n\\newcommand{\\xs}{$\\chi^{2}$}\n\n%\\begin{document}\n\n\\title[The ages of quasar host galaxies.]{The ages of quasar host galaxies.}\n\\author[L.A. Nolan \\etal.]\n{L.A. Nolan$^{1}$, J.S. Dunlop$^{1}$, M.J. Kukula$^{1}$, D. H.\nHughes$^{1,2}$, T. Boroson$^{3}$ $\\&$ R. Jimenez$^{1}$. \n\\\\\n$^{1}$Institute for Astronomy, University of Edinburgh, Blackford Hill,\nEdinburgh, EH9~3HJ\\\\\n$^{2}$INOAE, Apartado Postal 51 y 216, 72000, Puebla, Pue., Mexico.\\\\\n$^{3}$NOAO, PO Box 26732, Tucson, Arizona 85726$-$6732, U.S.A.}\n\n\\date{Submitted for publication in MNRAS}\n\n\n\n\\maketitle\n \n\\begin{abstract}\n\n\nWe present the results of fitting deep off-nuclear optical spectra of\nradio-quiet quasars, radio-loud quasars and radio galaxies at $z \\simeq\n0.2$ with evolutionary synthesis models of galaxy evolution. Our aim was\nto determine the age of the dynamically dominant stellar populations in the host\ngalaxies of these three classes of powerful AGN. Some of our spectra\ndisplay residual nuclear contamination at the shortest wavelengths, but\nthe detailed quality of the fits longward of the 4000\\AA\\ break provide\nunequivocal proof, if further proof were needed, that quasars lie in\nmassive galaxies with (at least at $z \\simeq 0.2$) evolved stellar\npopulations. By fitting a two-component model we have separated the very\nblue (starburst and/or AGN contamination) from the redder underlying\nspectral energy distribution, and find that the hosts of all three\nclasses of AGN are dominated by old stars of age $8 - 14$ Gyr. If the blue\ncomponent is attributed to young stars, we find that, at most, 1\\% of the\nvisible baryonic mass of these galaxies is involved in star-formation activity at the epoch\nof observation, at least over the region sampled by our spectroscopic\nobservations. \nThese results strongly support the conclusion reached\nby McLure et al. (1999) that the\nhost galaxies of luminous quasars are massive ellipticals which have formed\nby the epoch of peak quasar activity at $z \\simeq 2.5$.\n\n\n\n\\end{abstract}\n\n\\begin{keywords}\n\tgalaxies: active -- galaxies: evolution -- galaxies: stellar content -- quasars: general\n\\end{keywords}\n\n\\section{Introduction}\n\nDetermining the nature of the host galaxies of powerful active galactic \nnuclei (AGN) is of importance not only for improving our understanding \nof different manifestations of AGN activity, but also for \nexploring possible relationships between nuclear activity and the \nevolution of massive galaxies. The recent affirmation that black-hole mass\nappears approximately proportional to spheroid mass in nearby inactive glaxies\n(Maggorian et al. 1998) has further strengthened the motivation for \nexploring the link between active AGN and the dynamical and spectral \nproperties of their hosts. \n\nOver the last few years, improvements in imaging resolution offered by\nboth space-based and ground-based optical/infrared telescopes has stimulated \na great deal of research activity aimed at determining the basic structural \nparameters ({\\it i.e.} luminosity, size and morphological type) of the hosts \nof radio-loud quasars, radio-quiet quasars, and lower-luminosity X-ray-selected\nand optically-selected AGN ({\\it e.g.} Disney et al. 1995; \nHutchings \\& Morris 1995; Bahcall et al. 1997; Hooper et al. 1997; \nMcLure et al. 1999, Schade et al. 2000). However, relatively little corresponding effort has been invested in spectroscopic investigations of AGN \nhosts, despite the fact that this offers an independent way of classifying \nthese galaxies, as well as a means of estimating the age of their \nstellar populations.\n\nOur own work in this field to date has focussed on the investigation of\nthe hosts of matched samples of radio-quiet quasars (RQQs), radio-loud quasars\n(RLQs) and radio galaxies (RGs) at relatively modest redshift ($z = 0.2$).\nDetails of these samples can be found in Dunlop et al. (1993). In\nbrief, the sub-samples of quasars (i.e. RQQs and RLQs) have been selected\nto be indistinguishable in terms of their two-dimensional distribution\non the $V-z$ plane, while the sub-samples of radio-loud AGN (i.e. RLQs\nand RGs) have been selected to be indistinguishable in terms of their\ntwo-dimensional distribution on the $P_{5GHz} - z$ plane (as well as\nhaving indistinguishable spectral-index distributions).\nDeep infrared imaging of these samples (Dunlop et al. 1993; Taylor et al. 1996)\nhas recently been complemented by deep WFPC2 HST optical imaging (McLure\net al. 1999), the final results of which are reported by Dunlop et al. \n(2000). As well as demonstrating that, dynamically, the hosts of all three\ntypes of luminous AGN appear indistinguishable from normal ellipticals, this \nwork has enabled us to deduce crude spectral information on the host galaxies\nin the form of optical-infrared colours. However, broad-baseline colour\ninformation can clearly be most powerfully exploited if combined with \ndetailed optical spectroscopy.\nOver the past few years we have therefore attempted to complement \nour imaging studies with a programme of \ndeep optical off-nuclear spectroscopy of this same sample of AGN.\n\nDetails of the observed samples, spectroscopic observations, and the \nbasic properties of the observed off-nuclear spectra are given in a companion\npaper (Hughes et al. 2000). As discussed by Hughes et al. (2000), the key \nfeature of this study (other than its size, depth, and sample control) is \nthat we have endeavoured to obtain spectra from positions further off-nucleus \n($\\simeq 5$ arcsec) than previous workers, in an attempt to better \nminimize the need for accurate subtraction of contaminating nuclear light. \nThis approach was made possible by our deep infrared imaging data, which \nallowed us to select slit positions $\\simeq 5$ arcsec off-nucleus \nwhich still intercepted the brighter isophotes of the host galaxies (slit\npositions are shown, superimposed on the infrared images, in Hughes et al.\n2000).\n\n\nIn this paper we present the results of attempting to fit the\nresulting off-nuclear\nspectra with evolutionary synthesis models of galaxy evolution. Our \nprimary aim was to determine whether, in each host galaxy, the optical\nspectrum could be explained by the same model as the optical-infrared\ncolour, and, if so, to derive an estimate of the age of the dynamically \ndominant stellar population. However, this study also offered the prospect\nof determining whether the hosts of different classes of AGN differ \nin terms of their more recent star-formation activity. \n\nIt is worth noting that our off-nuclear spectroscopy obviously does not\nenable us to say anything about the level of star-formation activity in\nthe nucleus of a given host galaxy. Rather, any derived estimates of the\nlevel of star-formation activity refer to the region probed by our\nobservations $\\simeq 5$ arcsec off-nucleus. However, given the large\nscalelengths of the hosts, their relatively modest redshift, and the fact\nthat our spectra are derived from long-slit observations, it is\nreasonable to regard our conclusions as applying to fairly typical\nregions, still located well within the bulk of the host galaxies under\ninvestigation.\n \nThe layout of this paper is as follows. In section 2 we provide details of \nthe adopted models, and how they have been fitted to the data. The results are\npresented in section 3, along with detailed notes on the fitting of \nindividual spectra. The implications of the model fits are then discussed \nin section 4, focussing on a comparison of the typical derived host-galaxy \nages in the three AGN subsamples. Finally our conclusions are summarized \nin section 5. \nThe detailed model fits, along with corresponding chi-squared plots are \npresented in Appendix A.\n\n\\section{Spectral fitting.}\n\nThe stellar population synthesis models adopted for age-dating the AGN host \ngalaxy stellar populations are the solar metallicity, instantaneous starburst \nmodels of Jimenez et al. (2000). We have endeavoured to fit each off-nuclear\nhost galaxy optical spectrum by a combination of two single starburst \ncomponents. For the first component, age is fitted as a free\nparameter, while for the second component the age is fixed at 0.1 Gyr,\nand the normalization relative to the first component is the only free\nparameter. This dual-component approach was adopted because single-age\nmodels are not able to adequately represent the data, and because it allows\nthe age of the dynamically dominant component to be determined in a way which\nis not overly reliant on the level of ultraviolet flux which might be\ncontributed either by a recent burst of star-formation, or by\ncontamination of the slit by scattered light from the quasar nucleus.\nAfter experimentation it was found that the spectral shape of the \nblue light was better represented by the 0.1 Gyr-old (solar metallicity) model \nof Jimenez than by models of greater (intermediate) age (e.g. 1 Gyr). \nMoreover, the further addition of a third intermediate age component, \n$\\simeq$ 1 Gyr, did not significantly improve the quality of the fits\nachieved.\n\nIn general, our data are of insufficient quality to tell whether the\ncomponent which dominates at $\\lambda \\simeq 3000$\\AA\\ really is due to\nyoung stars, or is produced by direct or scattered quasar light. However, \nwhile the origin of the blue light is obviously of some interest, it has little\nimpact on the main results presented in this paper, which refer to the\nage of the dynamically dominant stellar population which dominates the\nspectrum from longward of the 4000\\AA\\ break through to the near infrared. The robustness of the age determination of the dominant population is demonstrated by comparing the results of the two stellar-population model fit with the results of a fit allowi\nng for a nuclear contribution as well as the two stellar populations. \n\n\nThe model parameters determined were therefore \nthe age of the dominant stellar population, \nwhich we can reasonably call the age of the galaxy, and the fraction, by \n(visible) baryonic mass, of the 0.1 Gyr component. For the fit including a nuclear contribution, the fraction of the total flux contributed by quasar light was a third parameter. The red end of each SED was further \nconstrained by fitting $R-K$ colour simultaneously with the optical\nspectral energy distribution. The fitting process is described below.\n\nFirst, the observed off-nuclear spectra were corrected for redshift and transformed to the rest frame. They were then rebinned to the \nspectral resolution of the model spectra. The rebinned flux is then the mean \nflux per unit wavelength in the new bin and the statistical error on each \nnew bin is the standard error in this mean. The data were normalised to a \nmean flux per unit wavelength of unity across the wavelength range 5020 $-$ \n5500 \\ang.\n\nThe two-component model was built from the instantaneous-burst stellar-population synthesis model SEDs, so that\n $$\tF_{\\lambda,age,\\alpha} = const (\\alpha f_{\\lambda,0.1} + (1-\\alpha)f_{\\lambda,age}) $$\nwhere $f_{\\lambda,age}$ is the mean flux per unit wavelength in the bin \ncentred on wavelength $\\lambda$ for a single burst model of $age$ \nGyr, $\\alpha$ is the fraction by mass of the young (0.1 Gyr) component, \nand $F_{\\lambda,age,\\alpha}$ is then the new, mean twin stellar-population \nflux per unit wavelength in the bin centred on wavelength $\\lambda$ for a \nmodel of $age$ Gyr. \nThis composite spectrum was then normalised in the same way as the observed \nspectra.\n\nA \\xs\\ fit was used to determine the age of the older stellar population and \nthe mass-fraction, $\\alpha$, of the younger population, for each host galaxy \nin the sample. The whole parameter space was searched, with the best-fit \nvalues quoted being those parameter values at the point on the grid with the \nminimum calculated \\xs . The normalization of the model spectra was\nallowed to float during the fitting \nprocess, to allow the best-fitting continuum shape to be determined in an\nunbiased way.\n\nThe models were fitted across the observed (rest-frame) spectral range, within the wavelength ranges listed in Table 1. \nAs a result of the optimisation of the instruments with which the objects \nwere observed, some of the galaxy spectra contain a `splice' region where \nthe red and blue end of the spectrum have been observed separately and then \njoined together (see Hughes \\etal (2000) for details). These splice \nregions, defined in Table 1, were masked out of the fit in order to guard\nagainst the fitting procedure being dominated by data-points whose flux\ncalibration was potentially less robust. The main emission \nlines, present due to nuclear light contamination or nebular emission\nfrom within the host, were also masked out, over the wavelength ranges \ngiven in Table 2.\n\nThe fit including a nuclear component was carried out in the same way, with the model flux in this case being\n $$\tF_{\\lambda,age,\\alpha,\\eta} = const (\\alpha f_{\\lambda,0.1} + (1-\\alpha)f_{\\lambda,age} + \\eta f0054_{\\lambda}) $$\nwhere $\\eta$ is the fraction contributed to the total model flux by the nucleus, and \n$f0054_{\\lambda}$ is the observed flux of the nucleus of the radio quiet quasar 0054+144. $\\alpha$ is the fraction by mass of the total stellar population contributed by the 0.1 Gyr population. The wavelength range of the observed nuclear flux of 0054+144\n is 3890$-$6950 \\ang. This was extended to 3500$-$8500 \\ang\\ by smooth extrapolation over the wavelength ranges 3500$-$3890 \\ang\\ and 6950$-$8500 \\ang\\ in order to carry out the \\xs\\ fit across the full wavelength range of the observed off-nuclear spectr\na.\n\n\\begin{table*}\n\n\\caption{Wavelength ranges of observed spectra, and splice regions which\nwere excluded from the fitting process. All wavelengths are in the observed \nframe. M4M denotes the Mayall 4m Telescope at Kitt Peak, and WHT denotes \nthe 4.2m William Herschel Telescope on La Palma (see Hughes \\etal (2000)\nfor observational details).}\n\n\\begin{tabular}{lccc}\n\n\n\\hline\n\n\n IAU name & Telescope & Wavelength range / \\ang & Masked splice region / \\ang \\\\\n\n\n\\hline\n\n\n\\multicolumn{4}{c}{ \\large \\it Radio Loud Quasars}\t \\\\ \n \t\n\\hline\n\n 0137+012 & M4M & 3890$-$6950 &\t \t\\\\ \n 0736+017 & M4M & 3890$-$6950 &\t\t\\\\ \n\t & WHT & 3500$-$8000 & 6050$-$6150 \\\\\n 1004+130 & WHT & 3500$-$8000 & 6050$-$6150\t\\\\ \n 1020$-$103 & M4M & 3890$-$6950 &\t\t\\\\ \n 1217+023 & WHT & 3500$-$7500 & 6000$-$6100\t\\\\ \n 2135$-$147 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 2141+175 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 2247+140 & M4M & 3890$-$6950 &\t\t\\\\ \n\t & WHT & 3500$-$7500 & 6050$-$6150\t\\\\\n 2349$-$014 & WHT & 3500$-$8300 & 6000$-$6100 \\\\\t\n\n\\hline\n\n\n\\multicolumn{4}{c}{ \\large \\it Radio Quiet Quasars} \t\\\\\n\n\\hline\n\n\n 0054+144 & M4M & 3890$-$6950 &\t\t\\\\\n\t & WHT & 3500$-$8000 & 6000$-$6100\t\\\\\n 0157+001 & M4M & 3890$-$6950 &\t\t\\\\\n \t & WHT & 3500$-$8000 & 6050$-$6150 \\\\\n 0204+292 & WHT & 3500$-$8000 & 6050$-$6150 \\\\\n 0244+194 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 0923+201 & WHT & 3500$-$7000 &\t\t\\\\\n 1549+203 & WHT & 3500$-$8000 & 6050$-$6150\t\\\\ \n 1635+119 & WHT & 3500$-$7800 & 6000$-$6100\t\\\\ \n 2215$-$037 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 2344+184 & M4M & 3890$-$6950 &\t\t\\\\\n\t & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n\n\n\\hline\n\n\n\\multicolumn{4}{c}{\\large \\it Radio Galaxies} \\\\\n\n\\hline\n\n\n 0230$-$027 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 0345+337 & WHT & 3500$-$8500 & 6000$-$6100\t\\\\ \n 0917+459 & WHT & 3500$-$8500 & 6050$-$6150\t\\\\ \n 1215$-$033 & WHT & 3500$-$7500 & 6000$-$6100\t\\\\ \n 1330+022 & M4M & 3890$-$6950 &\t\t\\\\ \n 2141+279 & M4M & 3890$-$6950 &\t\t\\\\\n\n\\hline\n\n\\end{tabular}\n\n\\end{table*}\n\n\n$R-K$ colour was fitted in both cases with a typical error of a few\npercent.\nThe observed $R-K$ colours for the host galaxies are obtained from \n{\\sc ukirt\\,} and \\h images (McLure \\etal, 1999, Dunlop \\etal, 2000), \nand define the basic shape of the host galaxy SED out to $\\lambda \\simeq \n2 \\mu m$. The composite model spectra were appropriately red-shifted before \ncalculating the colour, so that they could be compared to the observed \ncolours without introducing uncertainties in k-correction. The $R$ band was \nsimulated using the filter function, including system response and CCD \nquantum efficiency, for the \\h \\wf F675W filter, and the K band was \nreproduced using the filter data for the \\irc K Ocli filter at 77K combined \nwith Mauna Kea atmosphere. \n\n\\section{Results}\n\nThe plots showing fits to individual spectra and \\xs \nas a function of fitted age are given in Appendix A. The plots for the two-component fit are presented in Figure A1, and those for the two stellar-component plus nuclear contribution are in Figure A2. \nThe results for each object are summarized below, under their IAU names, \nwith alternative names given in parentheses.\nObjects are listed in order of increasing right ascension, within each AGN \nclass (radio loud quasars, radio quiet quasars and radio galaxies). \nThe telescopes with which the spectra were obtained are also noted; \nM4M denotes the Mayall 4m Telescope at Kitt Peak, and WHT denotes the 4.2m \nWilliam Herschel Telescope on La Palma. Where there are two spectra, the \nfirst plot is for the spectrum observed with the Mayall 4m Telescope, and \nthe second is for the spectrum taken with the William Herschel Telescope.\n\n\n\\subsection{Notes on individual objects}\n\n\\subsubsection{Radio loud quasars}\n\n{\\bf 0137+012} (L1093) M4M\\\\\nThe models give a good fit at 13 Gyr, which is clearly improved by the \ninclusion of a small percentage (0.25\\%) of young stars. There is no significant nuclear contribution to the spectrum.\nHST imaging has shown that this host galaxy is a large elliptical, with a\nhalf-light radius $r_e = 13$ kpc (McLure et al. 1999).\\\\\n{\\bf 0736+017} (S0736+01, OI061) M4M,WHT\\\\\n0736+017 has been observed with both telescopes, and fits to the \ntwo observed spectra are in good agreement. Both indicate an age of 12 Gyr. \nThe M4M spectrum requires a somewhat larger young blue population\n(0.75\\%) than the WHT spectrum (0.125\\%). This may be due to poorer seeing \nat Kitt Peak leading to slightly more nuclear contamination of the slit,\nor to the use of slightly different slit positions at the two telescopes.\nHowever, this difference between the observed spectra shortward of \n4000\\AA\\ leaves the basic form of $\\chi^2$ versus age, and the best-fitting \nage of 12 Gyr unaffected. Inclusion of a nuclear component gives a much better fit to the blue end of the M4M spectrum, without changing the age estimation. The size of the fitted young populations are in much better agreement in this case. \nHST imaging has shown that morphologically this host galaxy is a large elliptical, with \na half-light radius $r_e = 13$ kpc (McLure et al. 1999).\\\\\n{\\bf 1004+130} (S1004+13, OL107.7, 4C13.41) WHT\\\\\nThe spectrum of this luminous quasar certainly appears to display significant nuclear contamination below the 4000\\ang\\ break. As a result\na relatively large young population is required to attempt (not\ncompletely successfully) to reproduce the blue end of the spectrum . \nHowever, the models predict that the underlying stellar population is old \n(12 Gyr). Allowing a nuclear component to be fit reproduces the blue end of the spectrum much more successfully, without changing the best-fit age estimation.\nHST $R$-band imaging indicates the morphology of the host galaxy is dominated by a large\n($r_e = 8$ kpc) spheroidal component, but subtraction of this best-fit\nmodel reveals two spiral-arm-type features on either side of the nucleus\n(McLure et al. 1999), which may be associated with the young stellar\ncomponent required to explain the spectrum.\\\\\n{\\bf 1020$-$103} (S1020$-$103, OL133) M4M\\\\\nThis object has the second bluest $R-K$ of this sample, which leads to a \nmuch younger inferred age than the majority of the rest of the sample\n(5 Gyr), despite the presence of a rather clear 4000\\AA\\ break in the\noptical spectrum. Ages greater than $\\simeq$10 Gyr are rejected by Jimenez' \nmodels, primarily on the basis of $R-K$ colour.\nHST imaging has shown that this host has an elliptical morphology, and a\nhalf-light radius of $r_e = 7$ kpc. (Dunlop et al. 2000).\\\\\n{\\bf 1217+023} (S1217+02, UM492) WHT\\\\\nNuclear contamination can again be seen bluewards of 4000\\ang, \nwith a correspondingly large young population prediction for the purely stellar population model, which still\nfails to account for the very steep rise towards 3000\\AA. Hence, a large nuclear contribution is required to reproduce the blue end of the spectrum. The fit achieved \nby the models suggests that the dominant population is old, with a best-fit \nage of 12 Gyr.\nHST imaging has shown that this host has an elliptical morphology, and a\nhalf-light radius of $r_e = 11$ kpc. (Dunlop et al. 2000).\\\\\n{\\bf 2135+147} (S2135$-$14, PHL1657) WHT\\\\\n2135+147 has a very noisy spectrum, but a constrained fit has still been \nachieved, and an old population is preferred. 2135+147 requires a large $\\alpha$, even when a nuclear contribution is fitted.\nHST imaging has shown that this host has an elliptical morphology, and a\nhalf-light radius of $r_e = 12$ kpc. (Dunlop et al. 2000).\\\\\n{\\bf 2141+175} (OX169) WHT\\\\\nThis is another noisy spectrum, which has a relatively large quasar light contribution. An old population is again indicated by the model\nfits.\n>From optical and infrared imaging this object is known to be complex, but\nHST images indicate that it is dominated by a moderate sized ($r_e = 4$\nkpc) elliptical component\n(see McLure et al. (1999) for further details).\\\\\n{\\bf 2247+140} (PKS2247+14, 4C14.82) M4M,WHT\\\\\n2247+140 has been observed with both telescopes. The model fitting indicates \nan old population is required by both spectra - although the two \nobservations do not agree precisely, the general level of agreement is\nvery good, the two $\\chi^2$ plots have a very similar form,\nand the difference in \\xs\\ between the alternative \nbest-fitting ages of 8 Gyr and 12 Gyr is very small. No significant nuclear contribution to the flux is present.\nHST imaging has shown that this host has an elliptical morphology, and a\nhalf-light radius of $r_e = 14$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 2349$-$014} (PKS2349$-$01, PB5564) WHT\\\\\nThis is a very good fit to a good-quality spectrum, \nshowing an obvious improvement when the low-level young population is added. \nJimenez' models clearly predict that the dominant population is old, \nwith a well-constrained age of 12 Gyr. A very small nuclear contribution \n($\\eta$ = 0.050) does not significantly change the results.\nHST imaging of this object strongly suggests that it is involved in a\nmajor interaction, with a massive tidal tail extending to the north of\nthe galaxy. However, the dominant morphological component is a spheroid\nwith a half-light radius of $r_e = 18$ kpc (McLure et al. 1999).\\\\\n\n\n\\subsubsection{Radio quiet quasars}\n\n{\\bf 0054+144} (PHL909) M4M,WHT\\\\\nThere is evidence of relatively large contamination from nuclear emission in \nthe spectrum of this luminous quasar taken on both telescopes, and \nthe age is not well-constrained, although the fit to the WHT spectrum derived \nfrom the models again suggests an old age. The $\\chi^2$ plots serve to\nemphasize how similar the two spectra of this object actually are (as\nalso discussed by Hughes \\etal 2000). Inclusion of a nuclear component in the model better constrains the age and improves the goodness of the fit.\nHST imaging of this object has shown that, morphologically, it is\nundoubtedly an elliptical galaxy, with a half-light radius $r_e = 8$ kpc\n(McLure et al. 1999).\\\\\n{\\bf 0157+001} (Mrk 1014) M4M,WHT\\\\\nThe age inferred from both the M4M and WHT spectrum of 0157+001 is again \n12 Gyr. The apparently more nuclear-contaminated WHT spectrum does not give \nsuch a good fit, but 0157+001 is a complex object known to have extended\nregions of nebular emission, and the slit positions used for the two\nobservations were not identical (Hughes \\etal 2000). The age is much better\nconstrained from the more passive M4M spectrum, to which Jimenez' models \nprovide a very good fit. Again, it seems that the nuclear contamination does \nnot have a great influence on the predicted age of the old population, \nalthough the fit to the WHT spectrum is greatly improved by including a \nnuclear component in the model. Despite its apparent complexity in both\nground-based and HST images, this host galaxy does again seem to be\ndominated by a large spheroidal component, of half-light radius $r_e =\n8$ kpc (McLure et al. 1999).\\\\\n{\\bf 0204+292} (3C59) WHT\\\\\nJimenez' models fit the spectrum of this object well, indicating an old underlying stellar \npopulation ($> 6$Gyr), with a best-fit age of 13 Gyr for the stellar population plus nuclear component model, and a very small young population.\nHST imaging has shown this galaxy to be an elliptical, with half-light\nradius $r_e = 9$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 0244+194} (MS 02448+19) WHT\\\\\nThe colour derived from the optical and infrared imaging of this host\ngalaxy is rather blue ($(R-K)_{obs}$ = 2.34) and this in part leads to a \nfairly young (5 Gyr) age prediction. However, the spectrum is very noisy, \nand, as indicated by the very flat $\\chi^2$ plot, the age is not \nstrongly constrained. No nuclear flux contamination is fitted.\nHST imaging has shown this galaxy to have an elliptical morphology, with half-light\nradius $r_e = 9$ kpc (McLure et al. 1999).\\\\\n{\\bf 0923+201} WHT\\\\\nThe spectrum of 0923+201 is noisy, and it also appears to have some nuclear \ncontamination. The fit is therefore improved by inclusion of a nuclear \ncomponent. An old age is strongly preferred\nby the form of the \\xs\\ / age plot, with a best-fit value of 12 Gyr.\nHST imaging has shown this galaxy to have an elliptical morphology, with half-light\nradius $r_e = 8$ kpc (McLure et al. 1999).\\\\\n{\\bf 1549+203} (1E15498+203, LB906, MS 15498+20) WHT\\\\\nThis is a good fit, which is clearly improved by the addition of the younger \npopulation. The slope of the \\xs\\ / age plot strongly indicates \nan old dominant population, with a best-fit age of 12 Gyr. There is very little evidence of nuclear contamination.\nHST imaging has shown this galaxy to be a moderate-sized elliptical\n$r_e = 5$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 1635+119} (MC1635+119, MC2) WHT\\\\\nThis is another very successful fit. An old age (12 Gyr) is inferred.\nAgain, HST imaging has shown this galaxy to be a moderate-sized elliptical\n$r_e = 6$ kpc (McLure et al. 1999).\\\\\n{\\bf 2215$-$037} (MS 22152$-$03, EX2215$-$037) WHT\\\\\n2215$-$037 has a noisy spectrum, to which an acceptable fit has nevertheless been \npossible. Jimenez' models suggest an old population, with a best-fitting age \nof 14 Gyr, but this age is not well constrained. This is the only object \nwhere the inclusion of a nuclear contribution to the fitted spectrum substantially \nchanges the age predicted of the dominant stellar population. However, the \n$\\chi^2$ plots are very flat after an age of 5 Gyr, and the age is not \nstrongly constrained in either case.\nHST imaging has shown this galaxy to have an elliptical morphology, with\n$r_e = 7$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 2344+184} (E2344+184) M4M,WHT\\\\\n2344+184 has been observed with both telescopes, and the fits to both \nspectra are in good agreement $-$ although, formally, \ntwo different ages are predicted. This is because \nthe \\xs\\ / age plots are fairly flat after about 8 Gyr.\nThe fits to both observations suggest an old dominant population, with a \nsmall young blue population improving the fit. There is no \nsignificant change in the predictions when a nuclear flux component is \nincluded in the model.\nHST imaging has shown this to be one of the few host galaxies in the\ncurrent sample to be disc-dominated. However, the nuclear component is in\nfact sufficiently weak that this object should really be classified as a\nSeyfert galaxy rather than an RQQ (McLure et al. 1999).\\\\\n\n\n\\subsubsection{Radio galaxies}\n\\begin{table}\n\n\\caption{Rest frame emission lines masked out in the \\xs\\ fit.}\n\n\\begin{tabular}{cl}\n\n\t\\hline\n\tMasked region / \\ang & Emission line\t\t\t\\\\\n\t\\hline\n\t3720 $-$ 3735 & OII 3727 \t\t\t\t\t\\\\\n\n\t3860 $-$ 3880 & NeIII 3869 \t\t\t\t\\\\\n\n\t4840 $-$ 5020 & OIII 4959, OIII 5007, H$_{\\beta}$ 4861 \t\\\\\n\n\t\\hline\n\n\\end{tabular}\n\n\\end{table}\n\n{\\bf 0230$-$027} (PKS0230$-$027) WHT\\\\\n0230$-$027 has a very noisy spectrum, and the colour of the host as\nderived from optical and infrared imaging is very blue \n($(R-K)_{obs}$ = 2.09). Consequently the best-fitting age derived using \nthe models is 1 Gyr, with no younger component, but it is clear that\nlittle reliance can be placed on the accuracy of this result. Allowing for a contribution from quasar light does not improve the fit.\nHST imaging has shown this galaxy to have an elliptical morphology, with\n$r_e = 8$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 0345+337} (3C93.1) WHT\\\\\n0345+337 requires no young component or nuclear flux contribution at all, and an old age, of 12 Gyr, \nis clearly indicated by the models.\nHST imaging has shown this galaxy to be a large elliptical, with\n$r_e = 13$ kpc (McLure et al. 1999).\\\\\n{\\bf 0917+459} (3C219, 3C219.0) WHT\\\\\nThis is an excellent fit, with an old age produced by the models (12 Gyr), \ntogether with a very small young population.\nHST imaging has shown this galaxy to be a large elliptical, with\n$r_e = 11$ kpc (McLure et al. 1999).\\\\\n{\\bf 1215$-$033} WHT\\\\\nJimenez' models suggest that the population of 1215$-$033 is universally \nold (best-fit age, 13 Gyr), with no young component or nuclear contribution required.\nHST imaging has shown this galaxy to be a large elliptical, with\n$r_e = 9$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 1330+022} (3C287.1) M4M\\\\\nAn excellent fit to the data is produced by Jimenez' models, \nindicating that the dominant population is old, with a best-fit age of 8 Gyr.\nHST imaging has shown this galaxy to be a large elliptical, with\n$r_e = 16$ kpc (Dunlop et al. 2000).\\\\\n{\\bf 2141+279} (3C436) M4M,WHT\\\\\nThis is another very successful, and well-constrained fit,\nwith an inferred age of 12 Gyr.\nHST imaging has shown this galaxy to be a large elliptical, with\n$r_e = 21$ kpc (McLure et al. 1999).\\\\\n\n \n\\subsection{Sample overview}\n\nThe results illustrated in Appendix A are summarised in Table 3. \nIt should be noted that the 4000\\ang\\ break typical of evolved stellar \npopulations is present in the majority of the observed spectra\n(see Appendix A and Hughes \\etal 2000), so we can be \nconfident in fitting stellar population models to the data. \nThe plots clearly show that the addition of even a very small amount of \nsecondary star formation to the simple, near-instantaneous star-burst models \nreproduces the blue end of the observed host galaxy spectra much more \nsuccessfully (and in most cases very well) \nthan does a single stellar population. Including a nuclear component further improves the fit to the blue end, especially for those spectra not well fit by purely stellar light. At the same time, the red end of the \nspectra, plus the observed $R-K$ colours generally require that the underlying \nstellar populations are old. \n\n\n\\begin{table*}\n\n\\centerline{\\epsfig{file=table.ps,width=18cm,angle=0,clip=}}\n\n\n\\setcounter{table}{2}\n\n\\caption{Results from the simultaneous fitting to the AGN host sample of the two-component model spectra (using the solar metallicity models of Jimenez et al. 2000) and $R-K$ colour. $\\alpha$ is the percentage young population, by mass. Results are also p\nresented for the fits including the subtraction of a nuclear component from the observed spectrum. $\\eta$ is the fraction of nuclear flux subtracted, and the corresponding results are denoted by the subscript $\\eta$.} \\label{tbl-3}\n\n\n\\end{table*}\n\n\nThe most meaningful output from the model fitting is a constraint\non the minimum age of the host galaxies; \nthe \\xs\\ plots show that often the best-fit age is not strongly constrained \nbut the trend is clearly towards old ($\\geq$ 8 Gyr) stellar populations. In general, young populations are strongly excluded.\n\nThe peaks and troughs in \\xs\\ as a function of model age \nappear to be the result of real features of the population evolution\nsynthesis, rather than being due to, for example, poor sampling\n(Jimenez, private communication).\n\n\\begin{figure*}\n\\centerline{\\epsfig{file=QSOagehist.ps,width=9cm,angle=-90,clip=}}\n \\caption{The age distribution of the dominant stellar populations of the sample host galaxies. These are the best-fitting results from Jimenez' solar metallicity models. On the left, results are shown for the fits to the data using a two-component\n model. The results on the right are those for the two-component model plus a nuclear contribution. The populations are predominantly old (12-14 Gyr) in both cases.}\n\t\\vspace{0.3in}\n\\centerline{\\epsfig{file=QSOperchist.ps,width=9cm,angle=-90,clip=}}\n \\caption{The distribution of $\\alpha$, the percentage \ncontribution (by mass) of the 0.1 Gyr component. \nWhere results have been obtained from two spectra for one object, the \nbest-fitting result has been adopted. Again, the results on the left are for \nfits using the two-component model, and those on the right are for fits with the \ntwo-component model plus a nuclear contribution. Allowing for the\npossibility of a nuclear contribution means that a \nsmaller $\\alpha$ is required to fit the blue end of the spectrum, and the \napparent difference between the radio galaxies and radio-loud and quiet \nquasars is reduced to a statistically insignificant level.}\n\n\n\\end{figure*}\n\n\n\\section{Discussion}\n\nFigure 1 shows the distribution of best-fit ages estimated using Jimenez' \nmodels. The left-hand panel shows the ages of the dominant stellar\ncomponent which result from fitting the two-component (stars only) model, while the right-hand\npanel shows the ages of the dominant stellar component in the case of the \n3 component model (i.e. two stellar components + a contribution from \nscattered nuclear light). The host galaxies of the AGN in each sample \nare predominantly old, and this result is unaffected by whether or not\none chooses to include some nuclear contribution to assist in fitting the\nblue end of the spectrum. \nThis general result also appears to be relatively unaffected by the \nprecise choice \nof stellar population model;\nthe models of Bruzual and Charlot (2000), fitted to the host galaxies \nwith the same process, reproduce the results for Jimenez' models to \nwithin a typical accuracy of 1-3 Gyr. We have not attempted to fit the stellar population models of Yi et al. (2000), because of problems we have found in their MS rate of evolution (Nolan et al., 2000).\n\nInclusion of a nuclear contribution in the 3-component models obviously\nraises the question of whether a young stellar population component\nis really necessary at all. We thus also explored the results of \nfitting a two-component model consisting of a single stellar population \nplus nuclear contribution. Such a model adequately reproduces the \ntwo-population-plus-nuclear-component results \nfor the {\\it redder} galaxies, but in fact the \nspectra of the bluest galaxies cannot be adequately reproduced by these \nmodels; the resulting serious increase in minimum \\xs\\ demonstrates \nthat inclusion of a young population component is necessary \nto achieve a statistically acceptable fit to these data.\n\nFigure 2 shows the distribution of percentage contribution (by mass),\n$\\alpha$, of\nthe young (0.1 Gyr) component to the spectra of the hosts.\nThe left-hand panel shows the values of $\\alpha$ as derived from \nfitting the two-component (stars only) model, while the right-hand\npanel shows the values of $\\alpha$ produced by the \n3 component model (i.e. two stellar components + a contribution from \nscattered nuclear light).\n\nWhere two spectra of the same object have been obtained with alternative\ntelescopes/instruments, the derived ages\nof the dominant stellar componenets are reproduced \nreassuringly well. There are, however, small discrepancies in the \nestimated percentage of young population present (see Table 3). \nThis effect is suggestive that at least some of the blue light might be\ndue to a scattered nuclear contribution, the strength of which would be\nhighly dependent on the seeing at the time of observation, and on the\nprecise repeatability of slit placement relative to the galaxy core.\nInterestingly, when a nuclear component is included \nwith the stellar flux model, an even smaller percentage of 0.1 Gyr \nstellar population is required to fit the blue end of the spectra, and \n(more importantly) the difference in $\\alpha$ between two spectra of the same object is\ngenerally reduced. This provides further support for the suggestion that\nsome of the bluest quasar host spectra remain contaminated by quasar\nlight at the shortest wavelengths, and indicates that the right-hand\npanel of Figure 2 provides a more realistic estimate of the level of\non-going star-formation in the host galaxies. While this figure still\nappears to suggest that at least some quasar hosts display higher levels\nof ongoing star-fomration activity than do radio galaxies, statistically\nthis `result' is not significant.\n\n\nThere are three galaxies which have very low age estimates, namely 0230$-$027, \n0244+1944 and 1020$-$103. These objects have the bluest observed \n$R-K$ colours, so it may be expected that the fitted ages would be \nyounger than the rest \nof the sample, and that these populations are genuinely young. As \ndiscussed above, it may be that these objects are bluer because of scattered \nnuclear light contaminating the host galaxy spectrum. However, it seems \nunlikely that their fitted ages are low simply because of this, \nbecause elsewhere in our sample, where \ntwo spectra have been obtained of the same object, the amount of nuclear \ncontamination present does not significantly affect the age estimation \n({\\em e.g.} 0736+017 and 0157+001). Moreover, the inclusion of a nuclear \ncomponent to the fit does not change the estimated age distribution of the \nhost galaxies. If these ages are in error, then a more likely \nexplanation, supported by the relative\ncompactness of these particular host galaxies, is that nuclear and host\ncontributions have been imperfectly separated in the $K$-band images,\nleading to an under-estimate of the near-infrared luminosity of the host.\n\nThe result of the three-component fitting process which also allows a contribution from\nscattered nuclear light is that there are in fact only 3 host galaxies in \nthe sample for which there is evidence that $\\alpha > 0.5$. One of these\nis the host of a radio-loud quasar (2135$-$147) but, as can be\nseen from Fig A2, this spectrum is one of the poorest (along with\n0230$-$027, \nthe only apparently young radio galaxy) in the entire dataset.\nThe 2 convincing cases are both the hosts of radio-quiet quasars,\nnamely 0157$+$001 and 2344$+$184.\n\n\nWithin the somewhat larger sample of 13 RQQs imaged with the HST by McLure\net al. (1999) and Dunlop et al. (2000), 4 objects showed evidence for a\ndisk component in addition to a bulge, namely 0052+251, 0157+001,\n0257+024, and 2344+184. Since we do not possess spectra of 0052+251\nand 0257+024 this means that there is a 1:1 correspondence\nbetween the objects which we have identified on the basis of this\nspectroscopic study as having recent star-formation activity, and those\nwhich would be highlighted on the basis of HST imaging as possessing a\nsignificant disk component. This straightforward match clearly\nprovides us with considerable confidence that the spectral decomposition \nattempted here has been effective and robust.\nFinally we note that it is almost certainly significant that 0157+001, \nwhich has the largest starburst component ($\\alpha = 1.1$) based on this \nspectroscopic analysis, is also the only IRAS source in the sample.\n\n\n\\section{Conclusions}\n\n\nWe conclude that the hosts of all three major classes of AGN contain \npredominantly old stellar populations ($\\simeq 11$ Gyr) by $z \\simeq 0.2$.\nThis agrees well with the results of McLure \\etal (1999), and Dunlop\n\\etal (2000) who compare host \ngalaxy morphologies, luminosities, scale lengths and colours in the same \nsample, and conclude that the hosts are, to first order,\nindistinguishable from `normal' quiescent giant elliptical galaxies.\n\nThe best-fitting age of the dominant stellar population is {\\it not} a function\nof AGN class. For the purely stellar models, the fitted percentage contribution of the blue component is,\nhowever, greater in the quasar hosts than in the radio galaxies; the median\nvalues are 0.6\\% for the 9 radio-loud quasars, 0.6\\% for the 9\nradio-quiet quasars, and 0.05\\% for the 6 radio galaxies. However, when a nuclear component is included, the median\nvalues are 0.3\\% for the radio-loud quasars, 0.3\\% for the radio-quiet quasars, and 0.00\\% for the radio galaxies. Performing a Kolmogorov-Smirnov test on these results \nyields a probability greater than 0.2 that the percentage of young \nstellar population in host galaxies is in fact also not a function of AGN class.\n\n\nThese results strongly support the conclusion that the host galaxies of all \nthree major classes of AGN are massive ellipticals, dominated by old stellar \npopulations.\n \\\\\n \\\\\n \\\\\n{\\bf ACKNOWLEDGEMENTS}\\\\\n \\\\\nLouisa Nolan acknowledges the support provided by the award of a PPARC\nStudentship. Marek Kukula and David Hughes acknowledge the support\nprovided by the award PPARC PDRAs, while Raul Jimenez acknowledges the award \nof a PPARC Advanced Fellowship. We thank an anonymous referee for\nperceptive comments which helped to clarify the robustness of our results\nand improved the clarity of the paper.\n \\\\\n{\\bf REFERENCES}\\\\\n \\\\\nBahcall J.N., Kirhakos S., Saxe D.H., Schneider D.P., 1997, ApJ, 479, 642\\\\\nBruzual A.G., Charlot S., 2000, in preparation\\\\\nDisney M.J. et al., 1995, Nat, 376, 150\\\\\nDunlop J.S., 2000, In: `The Hy-Redshift Universe: Galaxy Formation and\nEvolution at High Redshift', ASP Conf. Ser., Vol 193, eds. A.J. Bunker \\&\nW.J.M. van Breugel, in press, (astro-ph/9912380)\\\\\nDunlop J.S., McLure R.J., Kukula M.J., Baum S.A., O'Dea C.P., Hughes D.H., 2000, MNRAS, in press\\\\ \nDunlop J.S., Taylor G.L., Hughes D.H., Robson E.I., 1993, MNRAS, 264, 455\\\\\nHooper E.J., Impey C.D., Foltz C.B., 1997, ApJ, 480, L95\\\\\nHughes D. H., Kukula M.J., Dunlop J.S., Boroson T., 2000, MNRAS, in press\\\\\nHutchings J.B., Morris S.C., 1995, AJ, 109, 1541\\\\\nJimenez R., Dunlop J.S., Peacock J.A., Padoan P., MacDonald J., J$\\o$rgensen U.G., 2000, MNRAS, in press\\\\\nJimenez R., Padoan P., Matteucci F., Heavens A.F., 1998, MNRAS, 299, 123\\\\\nMagorrian J., et al., 1998, AJ, 115, 2285\\\\\nMcLure R.J., Kukula M.J., Dunlop J.S., Baum S.A., O'Dea C.P., Hughes D.H., 1999, MNRAS, in press, (astro-ph/9809030)\\\\\nNolan L.A., Dunlop J.S., Jimenez R., 2000, MNRAS, submitted, (astro-ph/0004325)\nSchade, D.J., Boyle, B.J., Letawsky, M., 2000, MNRAS, in press\\\\\nTaylor G.T., Dunlop J.S., Hughes D.H., Robson E.I., 1996, \nMNRAS, 283, 930\\\\\nYi S., Brown T.M., Heap S., Hubeny I., Landsman W., Lanz T., Sweigart A., 2000, ApJ, submitted\\\\\n\n\n\n\\appendix\n\n\\section{Spectra and \\xs\\ plots}\nThe fits for all the off-nuclear spectra are given. In Fig A1, the rest frame spectra are in the first column (black), with the best-fitting two-component model spectra (Jimenez et al., 2000) superimposed (green). The spectra of the single-aged old popula\ntion (red) is given for comparison. In Fig A2, the fits allowing for an additional contribution to the flux from the nucleus are presented. The key is the same as in A1, with the additional blue line representing the best-fitting two-component model flux\n plus the nuclear flux contribution. \n\nThe second column of plots shows the \\xs evolution with age for the dominant older population. The third column shows the best-fit \\xs as a function of percentage young population, $\\alpha$, for fixed ages of the dominant component. The models have solar \nmetallicity. The subscript $\\eta$ denotes results obtained by including the nuclear contribution.\n\nWhere there are two spectra of the same object, the spectrum given first is the one observed on the Mayall 4m Telescope, and the second is that observed using the William Herschel Telescope.The data for the following objects have been smoothed using a Han\nning function: 2135+147 (RLQ), 2141+175 (RLQ), 0244+194 (RQQ), 0923+201 (RQQ), 1549+203 (RQQ), 2215-037 (RQQ), 0230-027 (RG) and 0345+337 (RG).\n\n\n\n\\newpage\n\\begin{figure*}\n\\centerline{ {\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl1.ps,width=15cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, for\neach object, with the corresponding $\\chi^{2}$ plots. The rest-frame \nhost-galaxy spectra are in the first column (lightest grey), with the \nbest-fitting two-component model spectra (Jimenez et al., 2000) superimposed (black). \nThe spectra of the single-aged old population (mid-grey, lowest line) is given \nfor comparison. The second column shows the \\xs evolution with age for the \ndominant older population and the third column shows the best-fit \\xs\\ as a \nfunction of percentage young population, $\\alpha$, for fixed ages of the \ndominant component. All models have solar metallicity. Where there are two \nspectra of the same object, the spectrum given first is the one observed on \nthe Mayall 4m Telescope, and the second is that observed using the \nWilliam Herschel Telescope.\nThe data for the following \nobjects have been smoothed using a Hanning function: 2135+147 (RLQ), 2141+175 (RLQ), 0244+194 \n(RQQ), 0923+201 (RQQ), 1549+203 (RQQ), 2215$-$037 (RQQ), 0230$-$027 (RG) \nand 0345+337 (RG).}\n\\end{figure*}\n \n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{{\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl2.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl3.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-6.0cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl4.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl5.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl6.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Galaxies}} }\n\\centerline{\\epsfig{file=pl7.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{0}\n\\centerline{ {\\LARGE {\\em Radio Galaxies}} }\n\\centerline{\\epsfig{file=pl8.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-11cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, continued. }\n\\end{figure*}\n\n\n\n\n\n\n\n%%%%%\n%%%%%\n\n\n\\begin{figure*}\n\\centerline{{\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl1_nuc.ps,width=15cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \t\\caption{ Model fits to the off-nuclear rest frame spectra,\nincluding the modelling of a nuclear contribution, for each object, with the corresponding $\\chi^{2}$ plots. The rest frame \nhost galaxy spectra are in the first column (light grey), with the \nbest-fitting two-component model flux plus the nuclear flux contribution (black) \nand the best-fitting two-component model spectra (Jimenez et al. 2000) \nsuperimposed (mid grey). As in Fig A1, the spectra of the single-aged old \npopulation (dotted line) is given for comparison. The second column shows \nthe \\xs evolution with age for the dominant older population and the third \ncolumn shows the best-fit \\xs\\ as a function of percentage young population, $\\alpha$, \nfor fixed ages of the dominant component. The subscript $\\eta$ denotes \nresults obtained by including the nuclear contribution. All models have \nsolar metallicity. Where there are two spectra of the same object, the \nspectrum given first is the one observed on the Mayall 4m Telescope, and \nthe second is that observed using the William Herschel Telescope.\nThe data for the following objects have been smoothed using a Hanning \nfunction: 2135+147 (RLQ), 2141+175 (RLQ), 0244+194 (RQQ), 0923+201 (RQQ), 1549+203 \n(RQQ), 2215$-$037 (RQQ), 0230$-$027 (RG) and 0345+337 (RG).}\n\\end{figure*}\n \t\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl2_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Loud Quasars}} }\n\\centerline{\\epsfig{file=pl3_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-6cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl4_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl5_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Quiet Quasars}} }\n\\centerline{\\epsfig{file=pl6_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Galaxies}} }\n\\centerline{\\epsfig{file=pl7_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-1.5cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\centerline{{\\LARGE {\\em Radio Galaxies}} }\n\\centerline{\\epsfig{file=pl8_nuc.ps,width=16cm,angle=0,clip=}}\n\t\\vspace{-11cm}\n \\caption{Model fits to the off-nuclear rest frame spectra, including the modelling of a nuclear contribution, continued. }\n\\end{figure*}\n\n\n\n\n\n\\end{document}\n\n\n\n\n\n\n"
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astro-ph0002021
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Optical off-nuclear spectra of quasar hosts and radio galaxies
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[
{
"author": "David~H.~Hughes$^{1}$\\thanks{current address: INAOE, Apartado Postal 51 y 216, 7200, Puebla, Pue., Mexico}"
},
{
"author": "Marek~J.~Kukula$^{1}$"
},
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"author": "James~S.~Dunlop$^{1}$ and Todd Boroson$^{2}$"
},
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"author": "Department of Physics and Astronomy"
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"author": "Blackford Hill"
},
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"author": "Edinburgh EH9 3HJ"
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"author": "U.K."
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"author": "3700 San Martin Drive"
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"author": "Baltimore MD 21218"
},
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"author": "U.S.A."
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{
"author": "$^{2}$~NOAO"
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"author": "PO Box 26732"
},
{
"author": "Tucson"
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"author": "Arizona 85726-6732"
}
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%\baselineskip=20pt We present optical ($\sim 3200$\AA~ to $\sim9000$\AA~) off-nuclear spectra of 26 powerful active galaxies in the redshift range $0.1 \leq z \leq 0.3$, obtained with the Mayall and William Herschel 4-meter class telescopes. The sample consists of radio-quiet quasars, radio-loud quasars (all with $-23 \geq M_{V} \geq -26$) and radio galaxies of Fanaroff \& Riley Type II (with extended radio luminosities and spectral indices comparable to those of the radio-loud quasars). The spectra were all taken approximately 5 arcseconds off-nucleus, with offsets carefully selected so as to maximise the amount of galaxy light falling into the slit, whilst simultaneously minimising the amount of scattered nuclear light. The majority of the resulting spectra appear to be dominated by the integrated stellar continuum of the underlying galaxies rather than by light from the non-stellar processes occurring in the active nuclei, and in many cases a 4000\AA~break feature can be identified. The individual spectra are described in detail, and the importance of the various spectral components is discussed. Stellar population synthesis modelling of the spectra will follow in a subsequent paper (Nolan et al. 2000).
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"name": "mz862.tex",
"string": "\\documentstyle{mn}\n%\\documentstyle[referee]{mn}\n\n\\title[Quasar host galaxy spectra]{Optical off-nuclear spectra of quasar hosts and radio galaxies}\n\n\\author[D. H. Hughes et al.]\n{David~H.~Hughes$^{1}$\\thanks{current address: INAOE, Apartado Postal 51 y 216, 7200, Puebla, Pue., Mexico}, Marek~J.~Kukula$^{1}$, James~S.~Dunlop$^{1}$ and Todd Boroson$^{2}$\\\\\n$^{1}$~Institute for Astronomy, Department of Physics and Astronomy,\nUniversity of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, U.K. \\\\\n%$^2$~Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD 21218, U.S.A. \\\\\n$^{2}$~NOAO, PO Box 26732, Tucson, Arizona 85726-6732, U.S.A. \\\\}\n\n\\date{}\n\n\\begin{document}\n%\\baselineskip=20pt\n\\maketitle\n\n\\begin{abstract}\n%\\baselineskip=20pt\n\nWe present optical ($\\sim 3200$\\AA~ to $\\sim9000$\\AA~) off-nuclear\nspectra of 26 powerful active galaxies in the redshift range $0.1 \\leq\nz \\leq 0.3$, obtained with the Mayall and William Herschel 4-meter\nclass telescopes. The sample consists of radio-quiet quasars,\nradio-loud quasars (all with $-23 \\geq M_{V} \\geq -26$) and radio\ngalaxies of Fanaroff \\& Riley Type II (with extended radio\nluminosities and spectral indices comparable to those of the\nradio-loud quasars). The spectra were all taken approximately 5\narcseconds off-nucleus, with offsets carefully selected so as to\nmaximise the amount of galaxy light falling into the slit, whilst\nsimultaneously minimising the amount of scattered nuclear light. The\nmajority of the resulting spectra appear to be dominated by the\nintegrated stellar continuum of the underlying galaxies rather than by\nlight from the non-stellar processes occurring in the active nuclei,\nand in many cases a 4000\\AA~break feature can be identified. The\nindividual spectra are described in detail, and the importance of the\nvarious spectral components is discussed. Stellar population\nsynthesis modelling of the spectra will follow in a subsequent paper\n(Nolan et al. 2000).\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: stellar content -- galaxies: active -- quasars: general\n\\end{keywords}\n\n\\section{Introduction}\n\nUnderstanding the host galaxies of active galactic nuclei (AGN) is now\nrecognised as an important step on the path towards reaching an\nunderstanding of AGN themselves - how they form, how they are fuelled\nand how the differences between the various classes of object\narise. In two areas in particular the nature of the host galaxy gives\nus a direct insight into the workings of the AGN: galaxy properties\nseem to play a role in determining the radio loudness of the central\nengine (powerful radio sources are almost never found in spiral or\ndisc-dominated systems -- though see McHardy et al. 1994); and amongst\nradio-loud objects the host galaxies offer a powerful,\norientation-independent means of testing models which attempt to unify\ndifferent types of AGN via beaming and viewing angle effects ({\\it eg}\nUrry \\& Padovani 1995). The observations presented here attempt to\naddress both of these issues by comparing the galaxies associated with\nthe three main types of powerful AGN: radio-quiet quasars (RQQs),\nradio-loud quasars (RLQs) and radio galaxies (RGs) of Fanaroff \\&\nRiley Type II.\n\n\\subsection{Quasar hosts}\n\nOnly once the problem of separating the diffuse galaxy emission from\nthe wings of the quasar point spread function (PSF) has been overcome\ncan one can begin to describe and classify the morphologies,\nbrightness profiles and interaction histories of the quasar hosts.\nOver the last decade improvements in ground-based techniques and the\nadvent of the Hubble Space Telescope (HST) have revolutionised our\nunderstanding of quasar host galaxies.\n\nEvidence for mergers or interactions in the form of morphological\ndisturbances and close companions is a common feature of these images,\nbut a significant number of quasars are also found in what appear to\nbe undisturbed hosts. In addition, the idea that radio-loudness is a\nstraightforward consequence of the host galaxy type has had to be\nabandoned. Although some radio-quiet quasars are found in spirals\n({\\it eg} Hutchings et al. 1994; \\\"{O}rndahl, R\\\"{o}nnback \\& van\nGroningen 1997) in general the hosts of both radio-loud and\nradio-quiet quasars tend to have properties consistent with early-type\ngalaxies ({\\it eg} V\\'{e}ron-Cetty \\& Woltjer 1990; Disney et\nal. 1995, Hutchings \\& Morris 1995, Bahcall et al. 1997, McLeod, Rieke\n\\& Storrie-Lombardi 1999) and typically have luminosities $> L^{*}$\n({\\it eg} Dunlop et al. 1993, Bahcall, Kirhakos \\& Schneider 1994,\n1995ab, 1996; Hutchings et al. 1994, Boyce et al. 1998, Hooper, Impey\n\\& Foltz 1997) and in many cases are comparable in mass to brightest\ncluster galaxies (BCGs).\n\nMeanwhile, McLeod \\& Rieke (1995a) find evidence for a {\\it lower}\nlimit on the $H$-band luminosities (and hence the mass of the red,\nestablished stellar populations) of galaxies hosting radio-quiet AGN,\nwhich appears to increase as the nuclear luminosity increases,\nimplying that the nuclear activity is closely linked to the mass of\nthe bulge component of the host. This impression has been reinforced\nby McLure et al. (1999), who find that {\\it all} the RQQs with\n$M_{R}\\leq -24$ in their HST sample occur in massive elliptical\ngalaxies, with only the least luminous radio-quiet objects lying in\ndisc-dominated hosts.\n\nMany long-held views about the triggering of nuclear activity and the\norigins of radio loudness are currently being reassessed in the light\nof these imaging studies, but images cannot tell the whole story. A\ncompletely independent way of characterising the host galaxies of AGN\nis via analysis and classification of their stellar populations and\nstarformation histories. The aim of the observations described in this\npaper was to obtain high signal-to-noise spectra of quasar hosts and\nradio galaxies for use in spectrophotometric modelling to determine\nthe nature and history of their stelllar constituents.\n\n\\subsection{Spectroscopy of quasar hosts}\n \nPrevious off-nuclear spectroscopy of the host galaxies of quasars has\nproduced mixed results. Boroson \\& Oke (1982) were the first to detect\nan unequivocably stellar continuum from the nebulosity surrounding the\nradio-loud quasar 3C48 and subsequent studies revealed stellar\ncontinua and emission/absorption features around several other quasars\n(Boroson, Oke \\& Green 1982; Boroson \\& Oke 1984; Boroson, Persson \\&\nOke 1985; Hickson \\& Hutchings 1987; Hutchings \\& Crampton\n1990). However, except for the general result that there appeared to\nbe systematic differences between the spectra of radio-loud and\nradio-quiet quasar hosts, these studies produced little advance in our\nunderstanding of the relationship between RQQs, RLQs and RGs for the\nreasons outlined below.\n\nIn general the quasar targets were chosen virtually at random,\noften for the sole reason that they were `interesting' and/or\nunusual. Until now a programme of off-nuclear spectroscopy for\nstatistically useful and properly matched samples of RQQs and RLQs has\nnever been carried out, nor has any attempt been made to compare the\noff-nuclear spectra of RLQs with equivalent {\\it off-nuclear} spectra\nof radio galaxies. \n\nThe early work also focussed mostly on emission-line activity, with\ndiscussion of the stellar continuum being confined to classification\nas red or blue, and the identification of a few stellar features. Only\nlimited attempts were made to use the form of the spectrum to\ninvestigate the composition and evolution of the stellar population.\n\nFinally, few of the host galaxy spectra were taken sufficiently\noff-nucleus - {\\it eg} the spectra taken by Boroson and collaborators\nwere taken only 3$''$ from the quasar. This was done in the belief\nthat any further off-nucleus the host galaxy would be too faint for a\nreasonable spectrum to be obtained, but inevitably resulted in\nsignificant contamination of the host galaxy spectrum by scattered\nlight from the quasar nucleus. A scaled version of the quasar spectrum\nhad therefore to be subtracted from the off-nuclear spectrum to reveal\nthe spectrum of the underlying host, but the extra noise and\nsystematic errors introduced by this process severely limited the\nquality of the final spectra.\n\nThus, the main obstacles in these previous attempts to classify the\nhosts of powerful AGN were the difficulty in separating the underlying\nstarlight from the glare of the quasar and - less immediately, but\nstill of some importance - the lack of well-defined samples of a\nsufficient size to carry out straightforward statistical comparisons.\n\nAs far as possible, the design of the current study was intended to\ncircumvent both these problems with the goal of obtaining clean\nspectra of the stellar component of radio-loud and radio-quiet quasar\nhosts and radio galaxies, which could then be used to search for\nsystematic differences and similarities between the stellar\npopulations and of the galaxies hosting each type of activity. Despite\nthat fact that the radio galaxies lack bright nuclear point sources we\nwere careful to adopt exactly the same observing strategy as used for\nthe quasars to ensure that the data would be directly comparable.\n\nIn this paper we describe the observations and present the spectra. A\nsecond paper (Nolan et al. 2000) will describe the results of\nspectrophotometric modelling to estimate the ages and starformation\nhistories of the galaxies (preliminary results have already been\nreported by Kukula et al. 1997). The current paper is organised as\nfollows. Section~2 describes the samples used and Section~3 details\nthe observing and data reduction strategies chosen to optimise the\namount of starlight collected by the various instruments employed\nthroughout the study. Section~4 gives an overview of the data obtained\nand Sections~5 and 6 contain more detailed information on the\nindividual spectra.\n\n\n\\section{Sample selection}\n\nDunlop et al. (1993) and Taylor et al. (1996) observed a sample of\nintermediate-redshift ($0.1 \\leq z\\leq 0.3$) radio-loud and -quiet\nquasars\\footnote{Dunlop et al. define `radio quiet' objects as those with\n$L_{5GHz} < 10^{24}$W~Hz$^{-1}$sr$^{-1}$.} and Fanaroff-Riley Type II\nradio galaxies (RGs) in the near infrared ($K$-band:2.2$\\mu$m) in\norder to compare the luminosities and morphologies of the galaxies\nassociated with these three main types of powerful active nucleus. The\nchoice of waveband was informed by the low quasar:host ratio in the\nnear infrared, which allowed accurate determination of the galaxy\nproperties from the ground with the minimum amount of confusion from\nthe point spread function of the central quasar. Their sample was\ncarefully constructed to ensure that the different types of object\ncould be compared directly with one another: the radio-loud and -quiet\nquasars both have the same distribution of optical luminosities ($-23\n\\geq M_{V} \\geq -26$) and both the radio-loud quasars and the radio\ngalaxies have similar extended radio luminosities and morphologies and\nsteep radio spectra. The sample is therefore ideal for investigating\nthe influence of galaxy properties on the `radio loudness' of\notherwise very similar quasars, and also for testing unified models of\nRLQs and RGs which predict that the properties of their hosts should\nbe identical. A substantial subset of the sample has also formed the\nbasis for an $R$-band imaging study using HST (Kukula et al. 1999,\nMcLure et al. 1999, Dunlop et al. 2000), in which the enhanced angular\nresolution of HST has allowed both unambiguous identification of the\nhost morphology and identification of detailed substructure in the\nquasar hosts and radio galaxies.\n\nThis sample provides an ideal starting point for a spectroscopic\nstudy of host galaxies because, in addition to the careful selection\ncriteria, the existence of deep near-infrared images of every object\nprovides us with a unique opportunity to minimise the contamination of\nthe galaxy spectra by quasar light. Armed with knowledge of the\nextent and orientation of the host galaxy on the sky one is able to\nchoose a slit position which is far enough from the nucleus to avoid\nthe worst excesses of scattered quasar light, but which simultaneously\nmaximises the amount of galaxy light falling onto the slit.\n\nOut of the the 40 objects in the original Taylor et al. sample a total\nof 26 objects were observed in the current study (9 RQQs, 10 RLQs and\n7 RGs). Details are listed in Table~1. Note that the radio source 3C59\nhas been shown by Meurs \\& Unger (1991) to consist of three separate\nsources, of which only the weakest appears to be associated with the\nquasar 0204+292. As a result, the radio luminosity of 0204+292 places\nit below our dividing line of $L_{5GHz} = 10^{24}$W~Hz$^{-1}$sr$^{-1}$\nand we classify it as an RQQ.\n\n\\begin{table*}\n%\\vspace{-1.5cm}\n\\caption{Objects discussed in the current paper. Column 6 lists the\ntelescope with which the object's spectrum was obtained: M4M denotes\nthe Mayall 4-m Telescope at Kitt Peak; WHT denotes the 4.2-m William\nHerschel Telescope on La Palma.}\n\n\n\\begin{tabular}{cllcccl}\n\n\\hline\n\\footnotesize\nIAU & \\multicolumn{2}{c}{Optical position (J2000)}& V & $z$ & Telescope & Alternative \\\\\nname & RA ($h~m~s$) & Dec ($^{\\circ}~'~''$) & & & & names \\\\ \\hline\n\\multicolumn{7}{c}{\\it Radio-Quiet Quasars} \\\\ \\hline\n0007$+$106 & 00 10 30.98 &$+$10 58 28.4 & 15.40 & 0.089 & M4M & III Zw 2 \\\\ \n0054$+$144 & 00 57 09.92 &$+$14 46 11.0 & 15.71 & 0.171 & M4M/WHT& PHL909 \\\\ \n0157$+$001 & 01 59 49.72 &$+$00 23 41.0 & 15.69 & 0.164 & M4M/WHT& Mrk 1014 \\\\ \n0204$+$292 & 02 07 02.16 &$+$29 30 45.4 & 16.00 & 0.109 & WHT & 3C59 \\\\ \n0244$+$194 & 02 47 41.22 &$+$19 40 53.6 & 16.66 & 0.176 & WHT & MS 02448+19 \\\\\n1549$+$203 & 15 52 02.28 &$+$20 14 01.6 & 16.50 & 0.250 & WHT & 1E15498+203, LB906, MS 15498+20\\\\ \n1635$+$119 & 16 37 46.54 &$+$11 49 49.8 & 16.50 & 0.146 & WHT & MC1635+119, MC 2 \\\\ \n2215$-$037 & 22 17 47.35 &$-$03 32 48.4 & 17.20 & 0.241 & WHT & MS 22152-03, EX2215-037\\\\\n2344$+$184 & 23 47 25.71 &$+$18 44 58.4 & 15.90 & 0.138 & M4M/WHT& E2344+184\\\\ \\hline \n\\multicolumn{7}{c}{\\it Radio-Loud Quasars} \\\\ \\hline\n0137$+$012 & 01 39 57.24 &$+$01 31 46.8 & 17.07 & 0.258 & M4M & PHL1093 \\\\ \n0736$+$017 & 07 39 18.01 &$+$01 37 04.6 & 16.47 & 0.191 & M4M/WHT& S0736+01, OI061 \\\\ \n1004$+$130 & 10 07 26.12 &$+$12 48 56.4 & 15.15 & 0.240 & WHT & S1004+13, OL107.7, 4C13.41\\\\ \n1020$-$103 & 10 22 32.79 &$-$10 37 44.2 & 16.11 & 0.197 & M4M & S1020-103, OL133 \\\\ \n1217$+$023 & 12 20 11.90 &$+$02 03 42.3 & 16.53 & 0.240 & WHT & S1217+02, UM492 \\\\ \n2135$-$147 & 21 37 45.24 &$-$14 32 55.6 & 15.53 & 0.200 & WHT & S2135-14, PHL1657\\\\ \n2141$+$175 & 21 43 35.56 &$+$17 43 49.1 & 15.73 & 0.213 & WHT & OX169 \\\\\n2201$+$315 & 22 03 15.00 &$+$31 45 38.3 & 15.58 & 0.298 & M4M & B2 2201+31A, 4C31.63\\\\ \n2247$+$140 & 22 50 25.40 &$+$14 19 49.9 & 15.33 & 0.237 & M4M/WHT& PKS2247+14, 4C14.82\\\\ \n2349$-$014 & 23 51 56.14 &$-$01 09 12.8 & 15.33 & 0.173 & WHT & PKS2349-01, PB5564\\\\ \\hline \n\\multicolumn{7}{c}{\\it Radio Galaxies} \\\\ \\hline\n0230$-$027 & 02 32 43.14 &$-$02 33 34.1 & 19.20 & 0.239 & WHT & PKS0230-027 \\\\ \n0345$+$337 & 03 48 46.9 &$+$33 53 16 & 19.00 & 0.244 & WHT & 3C93.1 \\\\ \n%0410$+$110 & 04 13 40.38 &$+$11 12 15 & 18.01 & 0.306 & WHT & 3C109.0 \\\\ \n0917$+$459 & 09 21 08.95 &$+$45 38 55.8 & 17.22 & 0.174 & WHT & 3C219.0 \\\\ \n1215$-$033 & 12 17 55.3 &$-$03 37 23 & 18.90 & 0.184 & WHT & \\\\\n1330$+$022 & 13 32 53.27 &$+$02 00 45.0 & 18.27 & 0.215 & M4M & 3C287.1 \\\\ \n1334$+$008 & 13 37 31.38 &$+$00 35 29.0 & 19.00 & 0.299 & WHT & \\\\ \n2141$+$279 & 21 44 11.66 &$+$28 10 18.9 & 18.15 & 0.215 & M4M/WHT& 3C436 \\\\ \\hline \n\n\n\\end{tabular}\n\\end{table*}\n\n\n\n\\begin{table*}\n%\\vspace{-1.5cm}\n\\small\n\\caption{Objects observed on the Mayall 4-m Telescope at Kitt\nPeak. The detector used was a Tek T2KB chip. Columns are as follows:\n(1) source name, listed in RA order; (2) type of spectrum, `G' $=$\noff-nuclear (galaxy) spectrum, `N' $=$ nuclear spectrum; (3) redshift;\n(4) date of observation (dd/mm/yy); (5) average airmass during\nobservation; (6) average seeing during observation (arcsec); (7)\nnumber and length (in seconds) of consecutive exposures; (8) slit\nwidth (set to $3''$ throughout); (9) wavelength range determined by\ngrating setting; (10) positional offset of slit centre from\nquasar/galaxy centroid, and PA of slit (measured East from North).}\n\n\\begin{tabular}{lcccccrccl}\n\n\\hline\n\\footnotesize\nSource & Type & z &Date&Airmass&Seeing&Exposure&Slit &$\\lambda$-range&\\multicolumn{1}{c}{Slit offset}\\\\\n & & & & &($''$)& (sec) &width&(\\AA) &\\multicolumn{1}{c}{\\& PA} \\\\ \\hline\n\\multicolumn{10}{c}{\\it Radio-Quiet Quasars} \\\\ \\hline\n0007+106 & G & 0.089& 25/09/92 & 1.10 & 1.7 & 5$\\times$1800& 3$''$&3665-7121 &5$''$N, 90$^{\\circ}$ \\\\ \n & N & 0.089& 25/09/92 & 1.13 & 1.6 & 1$\\times$1800& 3$''$&3665-7121 &zero offset \\\\ \n0054+144 & G & 0.171& 26/09/92 & 1.19 & 1.8 & 6$\\times$1800& 3$''$&3659-7121 &3$''$S, 4$''$E, 15$^{\\circ}$ \\\\\n & N & 0.171& 26/09/92 & 1.60 & 1.6 & 1$\\times$900& 3$''$&3659-7121 &zero offset \\\\\n0157+001 & G & 0.164& 25/09/92 & 1.26 & 1.8 & 5$\\times$1800& 3$''$&3662-7121 &5$''$N, 90$^{\\circ}$\t\t \\\\\n & N & 0.164& 25/09/92 & 1.55 & 1.9 & $1\\times1200$& 3$''$&3662-7121 &zero offset \\\\\n2344+184 & G & 0.138& 24/09/92 & 1.05 & 1.9 & 5$\\times$1800& 3$''$&3665-7124 &5$''$E, 177$^{\\circ}$ \t \\\\\n & N & 0.138& 24/09/92 & 1.15 & 2.5 & 1$\\times$1800& 3$''$&3662-7121 &zero offset \\\\ \\hline \n\\multicolumn{10}{c}{\\it Radio-Loud Quasars} \\\\ \\hline\n0137+012 & G & 0.258& 24/09/92 & 1.34 & 2.0 & 5$\\times$1800& 3$''$&3662-7121 &5$''$E, 155$^{\\circ}$\t \t \\\\\n & N & 0.258& 26/09/92 & 1.70 & 1.8 & 1$\\times$900& 3$''$&3659-7121 &zero offset \t \\\\\n0736+017 & G & 0.191& 19/03/93 & 1.20 & 2.9 & 5$\\times$1800& 3$''$&3530-7004 &5$''$S, 90$^{\\circ}$\t \\\\\n & G & 0.191& 20/03/93 & 1.19 & 1.4 & 4$\\times$1800& 3$''$&3530-7004 &5$''$S, 90$^{\\circ}$\t \\\\\n & N & 0.191& 19/03/93 & 1.40 & 3.1 & 1$\\times$900& 3$''$&3530-6989 &zero offset \\\\ \n & N & 0.191& 20/03/93 & 1.17 & 1.4 & 1$\\times$1200& 3$''$&3530-6989 &zero offset\t \\\\\n1020$-$103& G & 0.197& 19/03/93 & 1.41 & 2.9 & 3$\\times$1800& 3$''$&3530-7004 &3.5$''$W, 3.5$''$N, 45$^{\\circ}$ \t \\\\\n & G & 0.197& 20/03/93 & 1.38 & 1.4 & 4$\\times$1800& 3$''$&3530-7004 &3.5$''$W, 3.5$''$N, 45$^{\\circ}$ \t \\\\\n & N & 0.197& 19/03/93 & 1.36 & 2.9 & 1$\\times$900& 3$''$&3530-6989 &zero offset \t \\\\\n2201+315 & G & 0.298& 25/09/92 & 1.09 & 1.8 & 5$\\times$1800& 3$''$&3665-7121 &5$''$N, 84$^{\\circ}$\t \\\\\n & N & 0.298& 25/09/92 & 1.00 & 1.8 & 1$\\times$1800& 3$''$&3665-7121 &zero offset \t \t \\\\\n2247+140 & G & 0.237& 24/09/92 & 1.26 & 1.2 & 5$\\times$1800& 3$''$&3665-7124 &4$''$E, 3$''$S, 38.7$^{\\circ}$ \t \\\\\n & N & 0.237& 24/09/92 & 1.06 & 1.2 & 1$\\times$1800& 3$''$&3665-7124 &zero offset \\\\ \\hline\n\\multicolumn{10}{c}{\\it Radio Galaxies} \\\\ \\hline\n1330+022 & G & 0.215& 20/03/93 & 1.18 & 1.4 & 5$\\times$1800& 3$''$&3548-7004 &2.5$''$N, 2.5$''$E, 135$^{\\circ}$ \t \\\\\n & N & 0.215& 19/03/93 & 1.18 & 3.1 & 2$\\times$1800& 3$''$&3548-7004 &zero offset \t \\\\\n2141+279 & G & 0.215& 26/09/92 & 1.03 & 1.8 & 4$\\times$1800& 3$''$&3542-7124 &4$''$E, 0$^{\\circ}$ \t \t \\\\\n & N & 0.215& 26/09/92 & 1.13 & 1.6 & 4$\\times$1800& 3$''$&3542-7124 &zero offset \t \\\\ \\hline\n\n\\end{tabular}\n\\end{table*}\n\n\n%\\newpage\n\n\\begin{table*}\n%\\vspace{-1.5cm}\n\\small\n\\caption{Galaxies observed with ISIS on the 4.2~m William Herschel\nTelescope on La Palma. Unlike the observations at Kitt Peak, nuclear\nspectra were not obtained for all objects observed with the WHT. Where\nsuch spectra are available, either from Kitt Peak or WHT observations,\nthey are listed here and displayed in Figure~2 along with the\noff-nuclear (galaxy) spectrum. `M4M' denotes that the nuclear spectrum\nwas taken with the Mayall 4-m Telescope at Kitt Peak and `WHT' that\nthe spectrum was obtained using ISIS on the William Herschel\nTelescope. Columns are as follows: (1) source name, listed in RA\norder; (2) type of spectrum, `G' $=$ off-nuclear (galaxy) spectrum,\n`N' $=$ nuclear spectrum; (3) redshift; (4) date of observation\n(dd/mm/yy); (5) average airmass during integration period; (6) average\nseeing during observations (arcsec); (7) number and length (in\nseconds) of consecutive exposures; (8) slit width ($2''$ for all data\nexcept the six nuclear spectra obtained at Kitt Peak); (9) wavelength\nrange determined by grating settings; (10) `join' wavelength at which\nred and blue spectra have been spliced together; (11) positional\noffset of slit centre from quasar/galaxy centroid and PA of slit\n(measured East from North).}\n\n\\begin{tabular}{lcccccrcccl}\n\n\\hline\n\\footnotesize\nSource &Type&z&Date&Airmass&Seeing&Exposure&Slit &$\\lambda$-range&$\\lambda$ join&\\multicolumn{1}{c}{Slit offset} \\\\\n & & & & &($''$)&(sec) &width&(\\AA) &(\\AA) &\\multicolumn{1}{c}{\\& PA} \\\\ \\hline\n\\multicolumn{11}{c}{\\it Radio-Quiet Quasars} \\\\ \\hline\n0054+144 & G & 0.171 & 01/09/94& 1.30 &0.9 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &3.5$''$N, 4$''$W, 228$^{\\circ}$ \\\\\n &N(M4M)& 0.171 & 26/09/92& 1.60 &1.6 & 1$\\times$900& 3$''$& 3659-7121& -- &zero offset \\\\\n0157+001 & G & 0.164 & 16/11/93& 1.15 &1.6 & 4$\\times$1800& 2$''$& 3456-9060& 6100 &5$''$N, 107.5$^{\\circ}$ \\\\\n &N(M4M)& 0.164 & 25/09/92& 1.55 &1.9 & 1$\\times$1200& 3$''$& 3662-7121& -- &zero offset \\\\\n0204+292 & G & 0.109 & 17/11/93& 1.03 &1.0 & 5$\\times$1800& 2$''$& 3456-9060& 6100 &4.5$''$W, 0$^{\\circ}$ \\\\\n0244+194 & G & 0.176 & 02/09/94& 1.06 &1.7 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &5$''$W, 180$^{\\circ}$ \\\\\n1549+203 & G & 0.250 & 30/03/95& 1.05 &1.2 & 4$\\times$1800& 2$''$& 3450-8991& 6100 &4$''$W, 3$''$N, 228$^{\\circ}$ \\\\\n1635+119 & G & 0.146 & 13/05/94& 1.12 &1.3 & 5$\\times$1800& 2$''$& 3240-8700& 6050 &4.75$''$W, 1$''$S, 172$^{\\circ}$ \\\\\n2215$-$037& G & 0.241 & 01/09/94& 1.60 &0.9 & 3$\\times$1800& 2$''$& 3240-8700& 6050 &4.25$''$W, 3$''$N, 210$^{\\circ}$ \\\\\n2344+184 & G & 0.138 & 02/09/94& 1.20 &1.6 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &3$''$N, 4$''$W, 215$^{\\circ}$ \\\\\n &N(M4M)& 0.138 & 24/09/92& 1.15 &2.5 & 1$\\times$1800& 3$''$& 3662-7121& -- &zero offset \\\\ \\hline\n\\multicolumn{11}{c}{\\it Radio-Loud Quasars} \\\\ \\hline\n0736+017 & G & 0.191 & 16/11/93& 1.14 &1.0 & 5$\\times$1800& 2$''$& 3456-9060& 6100 &3.5$''$S, 3.5$''$W, 135$^{\\circ}$ \\\\\n &N(M4M)& 0.191 & 19/03/93& 1.40 &3.1 & 1$\\times$900& 3$''$& 3530-6989& -- &zero offset \\\\\n1004+130 & G & 0.240 & 30/03/95& 1.20 &1.5 & 4$\\times$1800& 2$''$& 3450-8991& 6100 &3.5$''$N, 3.5$''$W, 43$^{\\circ}$ \\\\\n1217+023 & G & 0.240 & 11/05/94& 1.20 &0.8 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &4$''$E, 3$''$N, 334$^{\\circ}$ \\\\\n2135$-$147& G & 0.200 & 02/09/94& 1.60 &1.2 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &3.5$''$W, 3.5$''$S, 315$^{\\circ}$ \\\\\n2141+175 & G & 0.213 & 13/05/94& 1.60 &1.0 & 3$\\times$1800& 2$''$& 3240-8700& 6050 &5$''$N, 290$^{\\circ}$ \\\\\n &N(WHT)& 0.213 & 13/05/94& 1.30 &1.1 & 1$\\times$900& 2$''$& 3240-8700& 6050 &zero offset \\\\\n2247+140 & G & 0.237 & 16/11/93& 1.04 &1.6 & 2$\\times$1800& 2$''$& 3456-9060& 6100 &4$''$E, 3$''$S, 38.7$^{\\circ}$ \\\\\n &N(M4M)& 0.237 & 24/09/92& 1.06 &1.2 & 1$\\times$1800& 3$''$& 3665-7124& -- &zero offset \\\\\n2349$-$014& G & 0.173 & 04/09/94& 1.35 &0.7 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &1$''$S, 5$''$W, 324$^{\\circ}$ \\\\ \\hline\n\\multicolumn{11}{c}{\\it Radio Galaxies} \\\\ \\hline\n0230$-$027& G & 0.239 & 02/09/94& 1.30 &2.0 & 2$\\times$1800& 2$''$& 3240-8700& 6050 &3.5$''$S, 3.5$''$W, 320$^{\\circ}$ \\\\\n &N(WHT)& 0.239 & 01/09/94& 1.20 &1.5 & 1$\\times$1800& 2$''$& 3240-8700& 6050 &zero offset \\\\\n0345+337 & G & 0.244 & 02/09/94& 1.30 &3.0 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &5$''$N, 0.5$''$W, 265$^{\\circ}$ \\\\\n%0410+110& G & 0.306 & 17/11/93& 1.13 &1.5 & 3$\\times$1200& 2$''$& 3456-9060& 6100 &4.5$''$W, 253$^{\\circ}$ \\\\\n0917+459 & G & 0.174 & 19/11/93& 1.10 &1.7 & 5$\\times$1800& 2$''$& 3456-9060& 6100 &5$''$N, 90$^{\\circ}$ \t \\\\\n1215$-$033& G & 0.184 & 13/05/94& 1.19 &0.9 & 3$\\times$1800& 2$''$& 3240-8700& 6050 &4$''$S, 3$''$E, 50$^{\\circ}$ \\\\\n1334+008 & G & 0.299 & 30/03/95& 1.60 &2.0 & 2$\\times$1800& 2$''$& 3450-8991& 6100 &3.5$''$W, 3.5$''$S, 135$^{\\circ}$ \\\\\n2141+279 & G & 0.215 & 02/09/94& 1.20 &1.0 & 4$\\times$1800& 2$''$& 3240-8700& 6050 &4.5$''$N, 2$''$E, 296$^{\\circ}$ \\\\\n &N(M4M)& 0.215 & 26/09/92& 1.13 &1.6 & 4$\\times$1800& 3$''$& 3542-7124& -- &zero offset \\\\ \\hline\n\n\\end{tabular}\n\\end{table*}\n\n\n\\section{Observations} \n\nIn order to asssess the feasibility of our observing strategy initial\nobservations of 11 of the nearest and brightest objects in the sample\nwere carried out using the Mayall 4-m Telescope at Kitt Peak National\nObservatory. This was followed by a larger programme of observations\nusing the 4.2-m William Herschel Telescope (WHT), part of the Isaac\nNewton Group of telescopes on La Palma.\n\nTables 2 and 3 list the observations made on the Mayall 4-m Telescope\nand the WHT respectively. Six objects (0054$+$144, 0157$+$001,\n0736$+$017, 2141$+$279, 2247$+$140 and 2344$+$184) were observed with\nboth telescopes in order to provide a check for consistency between\nthe two sets of observations. The spectra for these objects are\ndiscussed in more detail in Section~6.\n\n\\subsection{The Mayall 4-m Telescope}\n\nObservations of 11 objects were carried out with the\nR. C. Spectrograph on the Mayall 4-m Telescope at Kitt Peak in 1992\nSeptember and 1993 March (Table~1). The long-slit spectrograph uses a\nTektronix $2048\\times2048$ chip with 24-$\\mu$m pixels, designated\nT2KB. The slit width was set to 3$''$ and the instrument was\nconfigured to give a spectral resolution of 1.9\\AA/pixel and a spatial\nresolution of 0.69$''$/pixel.\n\nThe slit was first centred on the quasar (or, if the object was a\nradio galaxy, on the galaxy centroid), before being rotated and offset\nto the desired position, usually 5~arcseconds off-nucleus. \n\nTo allow the removal of cosmic rays five 1800-second off-nuclear\nexposures were obtained for each object, along with a shorter exposure\nof the quasar itself. The spectra typically spanned wavelengths from\n3500\\AA~ to 6000\\AA, although the precise range varied from object to\nobject according to redshift; details for individual objects are given\nin Table~2. Data reduction was carried out using standard {\\sc iraf}\nroutines.\n\n\\subsection{Observations with ISIS on the WHT}\n\nAfter the two runs at Kitt Peak had demonstrated that galaxy light\ncould indeed be separated from that of the quasar and that useful\nspectra could be obtained, further observations were made of 22\nobjects (6 of which had already been observed at Kitt Peak) with the\nIntermediate Dispersion Spectroscopic and Imaging System (ISIS) at the\n4.2~m William Herschel Telescope (WHT) on La Palma. ISIS uses a\ndichroic mirror to split the incoming light into red and blue beams\nwhich are then treated separately in spectrographs which have been\noptimised for the appropriate wavelength ranges\n($3000\\rightarrow6000$\\AA~ for the blue arm and\n$5000\\rightarrow10000$\\AA~ for the red). This arrangement allows a\nlarger wavelength coverage than is possible with the single\nspectrograph on the Mayall 4-m, enabling us to extend our spectra\nfurther into the red and thus giving greater scope for constraining\nmodels of spectrophotometric evolution.\n\nThe data were obtained in four separate observing runs in 1993\nNovember, 1994 May, 1994 September and 1995 March. The instrumental\nset-up differed slightly between the runs, resulting in variations in\nthe wavength ranges obtained. For the two sessions in 1994 the detectors\nin both the blue and red arms were Tektronix (`Tek') CCDs, with 24-$\\mu$m\npixels. In November 1993 and March 1996 the Tektronix chip in the red arm\nwas replaced by an EEV~P88300 chip, with 22.5-$\\mu$m pixels, which\nallowed a slightly larger wavelength coverage. R158 gratings were\nused in each arm, giving a spectral resolution of 2.88\\AA~pixel$^{-1}$\nfor the blue Tek chip and 2.90 (Tek) or 2.72\\AA~pixel$^{-1}$ (EEV) for\nthe red chips.\n\nAs with the observations at Kitt Peak the slit was first centred on\nthe quasar nucleus, or the optical peak of the radio galaxy, and then\noffset to the desired position, 5$''$ from the quasar, and rotated to\nbe at right angles to the direction of the offset. The slit width was\nset to 2$''$, placing the inner edge of the slit at least 4$''$ from\nthe quasar position. \n\nOnce again exposures were limited to 1800 seconds duration. Whenever\npossible we aimed to obtain five such frames per object, giving a\ntotal on-source exposure time of 2.5 hours. On-nuclear quasar spectra\nwere also taken when time permitted. Data reduction was carried out\nusing the {\\sc figaro} package, part of the Starlink suite of\nastronomical software.\n\n\n\\subsubsection{Calibration and splicing of red and blue spectra}\n\nThe galaxies observed with the WHT tend to be fainter and/or at\ngreater redshifts than those observed on the Mayall 4-m at Kitt Peak,\nand so additional care needed to be taken during the reduction of the\nWHT spectra. In particular, the procedure employed to optimize the\nextraction of the off-nuclear spectrum from the CCD frame means that\nthe final flux calibration is only relative and not absolute -\ncomparisons with the absolute fluxes obtained on the Mayall 4-m are\ntherefore not meaningful.\n\nThe use of the red and blue arms of ISIS, whilst extending the\nwavelength coverage significantly, also introduces its own special\nproblems. The large wavelength range made available by ISIS means\nthat the spectra are affected by several prominent atmospheric\nemission features (Figure~1) which must be removed. Of these the\nstrongest are the two oxygen lines at 5577 and 6300\\AA, the sodium D\nline at 5890\\AA, and the series of OH bands at wavelengths\n$>6500$\\AA. Sky lines were removed by fitting a third order polynomial\nto two empty strips of sky on either side of the target spectrum but\nthe removal process sometimes left a residual imprint of these\nfeatures and this constitutes a major source of noise in some of the\nfainter spectra in our sample. Where this is the case the affected\nregions are mentioned in the description of the individual spectrum.\n\n\n\\begin{figure}\n\\setcounter{figure}{0}\n\\vspace{4.5cm}\n\\special{psfile=figures/spectra/spec_sky_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=-30 voffset=300}\n\n\\caption{Sky spectrum obtained at the WHT in September 1994. For the\nfainter targets in the sample the process of sky subtraction often\nleads to residuals around the positions of strong sky emission\nfeatures such as the two lines of neutral oxygen at 5577 and 6300\\AA,\nthe sodium D line at 5890\\AA, and the series of OH bands at wavelengths\n$>6500$\\AA. }\n\\end{figure}\n\nA second problem involves the splicing together of the two spectra\nfrom the red and blue arms of the instrument to give continuous\nwavelength coverage from 3200\\AA~ to 9000\\AA. \n\nThe reflection and transmission responses of the ISIS dichroic cross\nat $\\sim6100$\\AA~ and the instrument settings were designed to ensure\na large overlap between the wavelength coverages of the two arms so\nthat the full reflection/transmission curves could be followed in the\nblue and the red spectra respectively. However, the faintness of many\nof the spectra effectively causes the flux calibration to fail at the\nred end of the blue spectrum and the blue end of the red, producing an\nartificial `lump' in the spliced spectrum at the crossover point\n(6100\\AA~ or 6050\\AA, depending on the exact instrumental settings at\nthe time of the observations - see column~8 in Table~3).\n\nAccordingly, in plotting the WHT spectra in Figure~2 we have blanked out\nthe data points for 100\\AA~ on either side of the join region and\nreplaced them with an averaged bridging section. We have masked out\nthis section of the data in all subsequent modelling due to its\ninherrent unreliability (see Nolan et al. 2000). \n\nDue to the luminosity of the quasars themselves the on-nuclear spectra\nobtained with the WHT do not suffer from this problem and the\nred and blue sections have been spliced together directly with no\nnoticeable discontinuity in flux at the join.\n\n\\section{Results}\n\nThe galaxy spectra themselves are displayed in Figure~2 along with\nnuclear spectra for the same object, where such are available. All the\ndata have been smoothed to 10-\\AA~ bins, and the WHT data are\ndisplayed with the region linking the individual red and blue spectra\nblanked out as described above. The expected position of various\nstellar absorption features, including the 4000\\AA~ break are\nindicated by dotted lines in the off-nuclear spectra and the\nwavelengths of redshifted [O{\\sc iii}]$\\lambda5007$ and H$\\alpha$ are\nalso marked.\n\n\n\\subsection{Data quality}\n\nA cursory examination of Figure~2 is enough to show that the quality\nof the off-nuclear spectra varies considerably from object to\nobject. In the two initial observing runs at Kitt Peak priority was\ngiven to nearby objects with bright, prominent host galaxies, and the\neleven spectra obtained with the Mayall 4-m enjoy a high\nsignal-to-noise ratio. By contrast, the objects observed in later runs\non the WHT tend to have larger redshifts and the signal-to-noise in\nmany of these spectra is correspondingly lower due to the rapid\nreduction in surface brightness and increase in galactocentric radius\nwith $z$.\n\n\\subsection{Degree of quasar contamination}\n\nThe primary goal of the observing program - to obtain spectra from the\nstellar component of the host whilst avoiding scattered emission from\nthe active nucleus - appears to have been satisfied to a large\nextent. This can be demonstrated most easily by comparing the\noff-nuclear (galaxy) and nuclear spectra for the same object in Figure\n2. The quasar spectra show prominent broad lines, notably those of\nH$\\alpha~\\lambda 6563$ and H$\\beta~\\lambda 4861$ , with an increase in\nflux towards shorter wavelengths (particularly when the `blue bump'\ncontinuum feature begins to emerge at $\\lambda_{rest} \\leq 5000$\\AA).\n\nWhilst emission lines do occur in the off-nuclear spectra, they tend\nto be relatively narrow forbidden lines such as [O{\\sc\niii}]$\\lambda \\lambda \\lambda 4363,4959,5007$. Where permitted lines\noccur, they lack the extremely broad profiles seen in the quasar\nnuclei, and are thus unlikely to result from scattering-induced\ncontamination by nuclear light. In many cases the line ratios in the\noff-nuclear spectra also differ from those measured in the quasars,\nindicating that the emission arises under different conditions than\nthose prevailing in the active nucleus.\n\nHowever, in spectra obtained under conditions of poor seeing, there is\nlikely to be some degree of nuclear contamination and this will be\nexacerbated if the object was observed far from the zenith, where\ndifferential atmospheric refraction may also lead to signifcantly more\ncontamination at the blue end of our wavelength range than in the\nred. Although the extent of such contamination is difficult to measure\ndirectly, Tables 2 and 3 list the atmospheric seeing and airmass at\nthe time each spectrum was obtained, to allow a rough assessment of\nthe problem to be made.\n\n\\subsection{Spectral features}\n\n\\begin{table}\n%\\vspace{-1.5cm}\n\\caption{Strength of the 4000\\AA~break feature in the host galaxy\nspectra (defined as the ratio of the flux density between 4050 and\n4250\\AA~ to that between 3750 and 3950\\AA~ in the object's rest frame,\nand measured in terms of $F_{\\nu}$). M4M denotes the Mayall 4-m Telescope\nat Kitt Peak; WHT denotes the 4.2-m William Herschel Telescope on La\nPalma. 3-sigma errors were estimated from the scatter in the flux\ndensity across the two reference regions.}\n\n\\begin{tabular}{ccc}\n\n\\hline\n\\footnotesize\nIAU & Telescope & Break \\\\\nname & & strength \\\\ \\hline\n\\multicolumn{3}{c}{\\it Radio-Quiet Quasars} \\\\ \\hline\n0007$+$106 & M4M & $ 1.4 \\pm 0.1$ \\\\ \n0054$+$144 & M4M & $ 1.3 \\pm 0.1$ \\\\ \n & WHT & $ 1.3 \\pm 0.1$ \\\\ \n0157$+$001 & M4M & $ 1.3 \\pm 0.1$ \\\\ \n & WHT & $ 1.3 \\pm 0.1$ \\\\ \n0204$+$292 & WHT & $ 1.6 \\pm 0.1$ \\\\ \n0244$+$194 & WHT & $ 0.8 \\pm 0.2$ \\\\ \n1549$+$203 & WHT & $ 2.0 \\pm 0.1$ \\\\ \n1635$+$119 & WHT & $ 1.7 \\pm 0.1$ \\\\ \n2215$-$037 & WHT & $ 1.4 \\pm 0.1$ \\\\ \n2344$+$184 & M4M & $ 1.7 \\pm 0.1$ \\\\ \n & WHT & $ 1.4 \\pm 0.1$ \\\\ \\hline \n\\multicolumn{3}{c}{\\it Radio-Loud Quasars} \\\\ \\hline\n0137$+$012 & M4M & $ 1.7 \\pm 0.1$ \\\\ \n0736$+$017 & M4M & $ 1.4 \\pm 0.1$ \\\\ \n & WHT & $ 1.8 \\pm 0.1$ \\\\\n1004$+$130 & WHT & $ 1.1 \\pm 0.1$ \\\\ \n1020$-$103 & M4M & $ 1.7 \\pm 0.1$ \\\\ \n1217$+$023 & WHT & $ 1.1 \\pm 0.1$ \\\\ \n2135$-$147 & WHT & $ 2.0 \\pm 0.3$ \\\\ \n2141$+$175 & WHT & $ 0.9 \\pm 0.2$ \\\\\n2201$+$315 & M4M & $ 1.4 \\pm 0.1$ \\\\ \n2247$+$140 & M4M & $ 1.9 \\pm 0.1$ \\\\ \n & WHT & $ 2.0 \\pm 0.1$ \\\\\n2349$-$014 & WHT & $ 1.5 \\pm 0.1$ \\\\ \\hline \n\\multicolumn{3}{c}{\\it Radio Galaxies} \\\\ \\hline\n0230$-$027 & WHT & $ 1.9 \\pm 0.4$ \\\\ \n0345$+$337 & WHT & $ 1.7 \\pm 0.4$ \\\\ \n0917$+$459 & WHT & $ 2.0 \\pm 0.1$ \\\\ \n1215$-$033 & WHT & $ 1.9 \\pm 0.2$ \\\\\n1330$+$022 & M4M & $ 1.6 \\pm 0.1$ \\\\ \n1334$+$008 & WHT & $ 1.1 \\pm 0.2$ \\\\ \n2141$+$279 & M4M & $ 2.2 \\pm 0.1$ \\\\\n & WHT & $ 1.3 \\pm 0.2$ \\\\ \\hline \n\n\\end{tabular}\n\\end{table}\n\n\n\nThe characteristic shape of the stellar continuum, including features\nsuch as the 4000\\AA~ break and various stellar absorption lines, is\neasily recognisable in most cases. The 4000\\AA~ break is particularly\nimportant for comparison between data and models of the stellar\npopulation. Since it covers a large wavelength interval it is\nrelatively insensitive to the effects of instrument resolution and\nnoise (Hamilton 1985). The break amplitude (defined as the ratio of\nthe average flux density between rest-frame 4050 and 4250\\AA~ to that\nbetween 3750 and 3950\\AA) is therefore widely used as a tracer of\nspectral evolution ({\\it eg} Bruzual 1983). The discontinuity results\nfrom the combined effect, shortwards of 4000\\AA, of lines of several\nelements heavier than helium, in a variety of ionization states, along\nwith the crowding of higher order Balmer lines. If a significant\npopulation of massive young stars is present the enhanced degree of\nionization causes the feature to weaken; it is most prominent in the\nspectrum of a well-established stellar population in which the most\nmassive stars have had time to evolve away from the main sequence.\nHence the 4000\\AA~break is sensitive to both spectral type and\nmetallicity, although if we assume a constant metallicity (a\nreasonable assumption for a particular galaxy at a fixed radius) it\nbecomes a good indicator of the mean age of the local stellar\npopulation. The strength of this feature, as measured in each of the\ncurrent spectra, is listed in Table~4. Other stellar absorption\nfeatures, such as G band (4300 to 4320\\AA) and the Mg Ib (5173\\AA) and\nFe$\\lambda5270$ lines, are also clearly present in many of the\nspectra.\n\nSeveral of the off-nuclear spectra ({\\it eg} 0054+144, 2201+315),\ndespite showing a clear break at 4000\\AA~ and a continuum longwards of\nthis wavelength which can be fitted extremely well by a passively\nageing stellar population (Nolan et al. 2000), also display a\ncontribution from a component which rises steeply towards the\nblue. The slope of this feature closely resembles that of a quasar\nSED, and its presence is often (but not always) accompanied by\nemission lines characteristic of quasar nuclei, suggesting that it is\nin fact scattered light from the quasar itself, the result either of\natmospheric scattering or (since the feature is not always\ncorrelated with poor observing conditions) of scattering within the\nISM of the host galaxy. Another possibility is that the blue excess\nindicates the presence of a substantial population of young stars\nwithin the host galaxy. If this latter case were true then it would\npose a serious problem for the unification of RLQs and RGs since none\nof the radio galaxies display such a component. The issue of excess\nblue continuum is raised on a case-by-case basis in the following\nsection, but a full discussion in the light of detailed stellar\npopulation synthesis modelling is deferred to the companion paper by\nNolan et al. (2000).\n\nThe average values of the 4000\\AA~break strength for the three types\nof object in the sample are 1.4 (RQQ hosts), 1.5 (RLQ hosts) and 1.7\n(RGs). These are all somewhat lower than the value of $\\sim\n2.0$ measured for local inactive elliptical galaxies by Hamilton\n(1985), but we note that there is a wide scatter in our sample and\nthat the lowest values are all associated either with spectra in which\nthe signal to noise is particularly poor ({\\it eg} 0244+292, 1004+130,\n1334+008) or those which clearly show an extra source of continuum\nemission at short wavelengths ({\\it eg} the quasars 0054+144,\n1217+023, 2141+175). The cleanest spectra generally have break\nstrengths which are consistent with those seen in `normal'\nwell-established galaxies.\n\nAs a final caveat we note that these spectra tell us only about the\nstellar composition of the region of the galaxy covered by the slit -\nwe cannot, for example, rule out the presence of a significantly\ndifferent stellar population closer to the nucleus, or concentrated in\nclumps which the slit happens to avoid. However, the slit has a width\nof at least 2~arcsec and, as can be seen from the contour plots in\nFigure 2, its length cuts across a significant fraction of the galaxy\nin the transverse direction. The area covered often amounts to several\nsquare arcseconds (equivalent to several tens of square kiloparsecs at\ntypical redshifts) and therefore represents a good general sample of\nthe outer regions of the host.\n\n\\section{Individual objects}\n\nObjects are listed under their IAU names (alternative names are listed\nin Table~1), in order of increasing right ascension. The\nclassification of each object as either an RQQ, an RLQ or a radio\ngalaxy is indicated in parentheses, along with the name(s) of the\ntelescope(s) on which off-nuclear spectra were obtained. The form of\nthe spectrum is described, noting any peculiar features as well as the\npresence or otherwise of a 4000\\AA~ break at the expected observed\nwavelength ($\\lambda_{obs}$). We also note the morphology of the\ngalaxy (disc or elliptical) based on its surface brightness profile in\nthe $K$ or $R$-band continuum images by Taylor et al. (1996)\n($K$-band; UKIRT) or McLure et al. (1999) and Dunlop et al. (2000)\n($R$-band; HST). For a more detailed description of previous imaging\nstudies of the host galaxies see Dunlop et al. (1993) (RLQs and RQQs)\nor Taylor et al. (1996) (RGs).\n\n\\noindent\n{\\bf 0007$+$106 (RQQ; M4M):} the nuclear spectrum of this radio-quiet\nquasar shows prominent broad H$\\alpha \\lambda 6583$ and H$\\beta\n\\lambda 4861$ emission as well as narrower forbidden line emission\nfrom species including [0{\\sc iii}] and [Fe{\\sc vii}]. The off-nuclear\nspectrum of the host galaxy has a high signal-to-noise and displays\nlittle sign of contamination from the quasar: the contribution from\nemission lines is very small, and the 4000\\AA~ break is clearly\nvisible (redshifted to 4356\\AA) despite the rapid increase in quasar\nflux towards the blue end of the spectrum, which would tend to mask\nthe break if scattering were significant. G band and Mg {\\sc i}b\nabsorption are also present. We note that the slit crosses the optical\narc-like structure to the north of the quasar which Hutchings et\nal. (1984) suggest may be a spiral arm. Previous spectroscopy of this\nregion by Green, Williams \\& Morton (1978) showed narrow emission\nlines (with different line ratios from those in the nucleus) and a red\ncontinuum which they attribute to starlight. However, this region only\nconstitutes a small fraction of the galaxy light intercepted by the\nslit in the current observations. Taylor et al. (1996) find that an\nexponential disc profile provides a good fit to the NIR surface\nbrightness distribution of the galaxy. (Morphology: disc; Taylor et\nal. 1996.)\n\n\\noindent\n{\\bf 0054$+$144 (RQQ; M4M \\& WHT):} quasar continuum emission\ndominates the nuclear spectrum of this RQQ, although H$\\beta \\lambda\n4861$ and [O{\\sc iii}]$\\lambda\\lambda\\lambda 4363,4959,5007$ lines are\nvisible. These lines are not prominent in either the Mayall 4-m or WHT\noff-nuclear spectra of the host (particularly the latter spectrum) but\nbluewards of the (relatively weak) 4000\\AA~ break (at $\\lambda_{obs} =\n4684$\\AA) the galaxy spectrum displays a marked increase in flux, very\nsimilar in form to that displayed by the quasar itself. This component\nis seen in both off-nuclear spectra, which were taken at different\ntimes, under different seeing conditions, and used different slit\npositions, so it is not clear whether we are seeing quasar light which\nis being scattered into our line of sight either by the atmosphere or\nby the interstellar medium of the host galaxy, or whether the blue\nexcess is due to a population of young stars. G band, Mg {\\sc i}b and\nFe5270 absorption features appear in the Mayall 4-m spectrum. McLure\net al. (1999) classify the galaxy as an elliptical: its light profile\nis very well described by an $r^{1/4}$ law and the galaxy itself is\nquite red ($R-K=3.14$), but a tidal interaction with a nearby\ncompanion is suggested by the extension to the NW of the nucleus\n(Dunlop et al. 1993). (Morphology: elliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 0137$+$012 (RLQ; M4M):} the 4000\\AA~ break in this object is quite\nclear (at $\\lambda_{obs} = 5032$\\AA) and there is little evidence of\nnuclear emission lines. (Morphology: elliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 0157$+$001 (RQQ; M4M \\& WHT):} the off-nuclear spectrum obtained\nwith the Mayall 4-m does not appear to be strongly contaminated by\nemission from the nucleus and the 4000\\AA~ break is visible at\n$\\lambda_{obs} = 4656$\\AA. The G band absorption feature is also\npresent. However, in the spectrum taken with the WHT using a similar\nslit position, there appears to be a significant contribution from the\nquasar continuum bluewards of the break. The signal:noise ratio in the\nWHT spectrum is much reduced longwards of 7500\\AA~ due to residuals\nfrom the subtracted OH bands. In both cases the slit intercepts the\nprominent tidal arm which extends north and NW of the nucleus\n(MacKenty \\& Stockton 1984) and is known to contain several emission\nline regions (Stockton \\& MacKenty 1987), although emission lines are\nnot strongly evident in the integrated spectra presented\nhere. Previous spectroscopy of this structure by Heckman et al. (1984)\nshowed a velocity difference of $300\\pm200$~km~s$^{-1}$ between the\narm and the quasar itself. McLure et al. (1999) find that the\nunderlying smooth $R$-band continuum light is well described by an\n$r^{1/4}$-law, though conceivably this might be another result of the\ntidal interaction. (Morphology: elliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 0204$+$292 (RQQ; WHT):} the 4000\\AA~break ($\\lambda_{obs}\n=4436$\\AA) is quite strong in this WHT spectrum, but residuals from\noxygen and OH features from the sky spectrum are also present.\n(Morphology: disc; Taylor et al. 1996)\n\n\\noindent\n{\\bf 0230$-$027 (RG; WHT):} the off-nuclear spectrum of this small, faint\nradio galaxy suffers from low signal to noise and residual sky\nfeatures are visible. However a break can be seen at $\\lambda_{obs} =\n4952$\\AA. The nuclear spectrum of this object is also dominated by\nstarlight, although narrow emission lines are present.\n(Morphology: elliptical; Dunlop et al. 2000.)\n\n\\noindent\n{\\bf 0244$+$194 (RQQ; WHT):} the signal to noise in this off-nuclear\nspectrum is very low. Apart from residual sky features there is some\nevidence for a drop in the continuum level around $\\lambda_{obs} =\n4704$\\AA~ (the expected position of the 4000\\AA~break), but also for a\nblue component shortwards of this, perhaps indicative of nuclear\ncontamination. (Morphology: elliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 0345$+$337 (RG; WHT):} the spectrum is noisy, but a break feature\nappears to be present at $\\lambda_{obs} =4936$\\AA. The WHT slit\nintercepts a bright knot NW of the quasar which Taylor et al. (1996)\nsuggest may be an embedded companion galaxy. (Morphology: elliptical;\nMcLure et al. 1999.)\n\n\\noindent\n{\\bf 0736$+$017 (RLQ; M4M \\& WHT):} the WHT spectrum, though noisier\nand suffering from OH-band residuals at long wavelengths, agrees well\nwith the spectrum obtained previously at Kitt Peak. The 4000\\AA~break\nis quite clear at $\\lambda_{obs} =4764$\\AA~ and weak [O{\\sc iii}],\nH$\\alpha$ and H$\\beta$ features can also be seen, though they appear\nto be narrower than those in the nuclear spectrum. The galaxy itself\nis highly disturbed, but McLure et al. (1999) fit an $r^{1/4}$-law\nprofile to the smooth component of the $R$-band continuum. (Morphology: \nelliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 0917$+$459 (RG; WHT):} the off-nuclear spectrum is pure stellar\ncontinuum, with a strong break at $\\lambda_{obs} =4696$\\AA. The galaxy\nisophotes are complex but McLure et al. (1999) find the underlying\ndistribution to be well described by an $r^{1/4}$-law. (Morphology:\nelliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 1004$+$130 (RLQ; WHT):} OH-band residuals are the only prominent\nfeature of this off-nuclear spectrum, with little evidence for either\nemission lines or a 4000\\AA~break (at $\\lambda_{obs} =4960$\\AA). The\nabsence of a strong break may reflect the fact that the elliptical\nhost galaxy of this quasar is known to possess unusual `spiral'\nfeatures close to the nucleus (McLure et al. 1999), perhaps\nindicating the presence of a significant population of young\nstars. Stockton \\& MacKenty (1987) note that there is no significant\nextended [O{\\sc iii}] emission in this object. (Morphology:\nelliptical; McLure et al. 1999.)\n\n\n\\noindent\n{\\bf 1020$-$103 (RLQ; M4M):} despite the presence of stellar\nabsorption features such as G band and a 4000\\AA~break at\n$\\lambda_{obs} =4788$\\AA, the off-nuclear spectrum also contains many\nemission lines as well as a blue excess, which may indicate a\nsignificant contribution from scattered quasar light (the seeing was\nquite poor for much of the observations). Dunlop et al. (1993) note\nthat the quasar is off-centre and that the galaxy isophotes appear to\nbe swept back towards the SW, providing evidence for disturbance in\nthis object. (Morphology: elliptical; Dunlop et al. 1999.)\n\n\n\\noindent\n{\\bf 1215$-$033 (RG; WHT):} this spectrum displays only a weak break at\n$\\lambda_{obs} =4736$\\AA~. OH-band residuals dominate longwards of\n7500\\AA. (Morphology: elliptical; Dunlop et al. 2000.)\n\n\\noindent\n{\\bf 1217$+$023 (RLQ; WHT):} a weak break feature is present at\n$\\lambda_{obs} =4960$\\AA~ but shortwards of this the spectrum is\ndominated by a component which rises towards the blue possibly\nindicating scattered nuclear continuum (there is however little\nevidence for accompaning nuclear line emission, and the seeing during\nthe observations was excellent). At the red end, poor subtraction of OH\nbands has reduced the signal to noise ratio of the spectrum.\n(Morphology: elliptical; Dunlop et al. 2000.)\n\n\\noindent\n{\\bf 1330$+$022 (RG; M4M):} weak [O{\\sc iii}] lines occur in the\noff-nuclear spectrum of this radio galaxy and the stellar continuum\nshows G band absorption and a strong 4000\\AA~break feature at\n$\\lambda_{obs} =4860$\\AA. By contrast, the nuclear spectrum shows\nevidence for broad H$\\beta \\lambda 4861$ and the less prominent break\nmay indicate a contribution from a quasar-type continuum or perhaps a\nnuclear starburst region. (Morphology: elliptical; Dunlop et\nal. 2000.)\n\n\\noindent\n{\\bf 1334$+$008 (RG; WHT):} a very noisy spectrum obtained under poor\nconditions, the underlying continuum is confused by many residual sky\nfeatures. The apparent increase in flux shortwards of 4500\\AA~ almost\ncertainly reflects a failure of the flux calibration at very low light\nlevels. However, there is some evidence for a break at the expected\nwavelength of $\\lambda_{obs} =5196$\\AA. The slit intercepts one of the\nsecondary nuclei reported by Taylor et al. (1996). (Morphology:\nelliptical; Taylor et al. 1996.)\n\n\\noindent\n{\\bf 1549$+$203 (RQQ; WHT):} the extended nebulosity around this RQQ,\nthough confused by a foreground galaxy cluster, shows a strong break\nfeature at the expected wavelength of $\\lambda_{obs} =5000$\\AA~ and\nlittle evidence for emission lines. OH-band residuals add to the noise\nlevels at long wavelengths. (Morphology: elliptical; Dunlop et al. 2000.)\n\n\\noindent\n{\\bf 1635$+$119 (RQQ; WHT):} the 4000\\AA~break is clearly visible at\n$\\lambda_{obs} =4584$\\AA, but residual sky features degrade the\nquality of the spectrum towards the red end. (Morphology: elliptical;\nMcLure et al. 1999.)\n\n\\noindent\n{\\bf 2135$-$147 (RLQ; WHT):} generally low signal to noise with\nprominent residuals due to sky features. However, there is weak\nevidence for a break at $\\lambda_{obs} =4800$\\AA. The galaxy appears\nto be disturbed and possesses a secondary nucleus to the SE of the\nquasar (Stockton 1982) which may also be active (Hickson \\& Hutchings\n1987). The WHT slit intercepts a region to the SW of the quasar at\nwhich Stockton \\& MacKenty (1987) report extended [O{\\sc iii}]\nemission. Narrow H$\\alpha$ is present in the current spectrum but the\n[O{\\sc iii}] lines fall within the join region where the signal is\nunreliable. (Morphology: elliptical; Dunlop et al. 2000.)\n\n\\noindent\n{\\bf 2141$+$175 (RLQ; WHT):} low signal to noise and the presence of a\nstrong blue component may serve to mask any evidence of a\n4000\\AA~break in this object (expected at $\\lambda_{obs}\n=4852$\\AA). The idea that this blue component originates as scattered\nquasar light is bolstered by the possible presence of the H$\\alpha$\nline, but the issue is confused by strong sky residuals (although the\nseeing was good, the airmass during the observations was relatively\nhigh, so differential refraction might explain the presence of quasar\ncontamination at shorter wavelengths without requiring the presence of\na strong H$\\alpha$ line). The elongated appearance of the galaxy is\napparently the result of an edge-on tidal arm consisting of old stars\n(Stockton \\& Farnham 1991). However, the WHT slit crosses the galaxy\nto the NE of the quasar, where the starlight appears to follow a\nbulge-dominated $r^{1/4}$-law (McLure et al. 1999a). (Morphology:\nelliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 2141$+$279 (RG; M4M \\& WHT):} the off-nuclear spectrum taken at\nKitt Peak shows a weak [O{\\sc iii}]$\\lambda 5007$ line, a break\nfeature at $\\lambda_{obs} =4860$\\AA and Mg {\\sc i}b absorption. The\nWHT spectrum is much noisier, but generally consistent with the\nfeatures in the earlier data. The nuclear spectrum of this radio\ngalaxy is also dominated by starlight, although prominent narrow lines\nare present. (Morphology: elliptical; McLure et al. 1999.)\n\n\\noindent\n{\\bf 2201$+$315 (RLQ; M4M):} this object shows prominent G band\nabsorption but only a weak 4000\\AA~break at $\\lambda_{obs}\n=5192$\\AA, along with low-equivalent-width [O{\\sc iii}] lines. A blue\ncomponent shortwards of the break is consistent with scattering of the\nnuclear quasar continuum. (Morphology: ambiguous; Taylor et al. 1996.)\n\n\\noindent\n{\\bf 2215$-$037 (RQQ; WHT):} the spectrum is relatively noisy with\nprominent residuals from all the bright sky features. The apparent\n`hump' at $\\sim 6000$\\AA~ is an artifact that results from the sodium\nD sky line coinciding with the beginning of the masking region that\nlinks the red and blue halves of the the spectra from ISIS. There is\nlittle evidence for a prominent break at the expected wavelength of\n$\\lambda_{obs} =4964$\\AA. Both Hutchings et al. (1989) and McLure et\nal. (1999b) classify the galaxy as a non-interacting elliptical\nsystem. (Morphology: elliptical; Dunlop et al. 2000.)\n\n\n\\noindent\n{\\bf 2247$+$140 (RLQ; M4M \\& WHT):} the galaxy's 4000\\AA~break is\nvisible at $\\lambda_{obs} =4948$\\AA~ in the Mayall 4-m spectrum, along\nwith G band absorption. The data obtained on the WHT are consistent\nwith this, although residual sky features from oxygen and sodium D\nlines and the OH bands are also present. (Morphology: elliptical;\nMcLure et al. 1999.)\n\n\\noindent\n{\\bf 2344$+$184 (RQQ; M4M \\& WHT):} both the Mayall 4-m and WHT\nspectra show a break at $\\lambda_{obs} =4552$\\AA~ as well as G band\nabsorption and are generally consistent with one another despite their\ndiffering slit positions. The nuclear spectrum of this object is also\ndominated by starlight; 2344$+$184 is one of the least powerful\nquasars in the current study and technically qualifies as a Type 1\nSeyfert galaxy. The surface brightness profile is that of a disc\ngalaxy, although a bulge dominates in the central regions (McLure et\nal. 1999) and there is also evidence for a bar (Hutchings, Janson \\&\nNeff 1989). (Morphology: disc; McLure et al. 1999.)\n\n\\noindent\n{\\bf 2349$-$014 (RLQ; WHT):} there is a weak break feature at\n$\\lambda_{obs} =4692$\\AA~ and also evidence for weak H$\\beta$, [O{\\sc\niii}]$\\lambda 5007$ and H$\\alpha$ lines. The red end of the spectrum\nis dominated by residual atmospheric OH band emission. (Morphology:\nelliptical; McLure et al. 1999.)\n\n\\section{Comparison of Mayall 4-m and WHT results}\n\nSix objects in the current sample (the RQQs 0054$+$144, 0157$+$001 and\n2344$+$184, the RLQs 0736$+$017 and 2247$+$140, and the radio galaxy\n2141$+$279) were observed with both the Mayall 4-m Telescope and the\nWHT. This duplication allows us to check for systematic differences\nbetween the spectra obtained with each instrument and to this end the\nare replotted one above the other in Figure~3. Since the observations\nwere often made under different atmospheric conditions they also\nprovide a means of assessing the degree to which any contamination by\nnuclear light can be attributed to either the airmass and seeing\nconditions at the time of the observations or scattering within the\nhost galaxy itself. Where a different slit position was used, the two\nspectra allow us to examine the degree of homogeneity in the stellar\ncomposition of the galaxy.\n\nIt should be noted that due to the optimization method used to extract\nthe WHT spectra, their flux calibration can only be considered as\nrelative, not absolute. Different slit widths were also used on the\ntwo instruments. Comparisons of the flux densities obtained on the\ntwo telescopes are therefore not meaningful.\n\n\\noindent\n{\\bf 0054$+$144 (RQQ):} different slit positions were used for the\nMayall 4-m and WHT observations. The spectrum obtained with the Mayall\n4-m shows a contribution from H$\\beta$/[O{\\sc iii}] at $\\lambda_{obs}\n\\sim5800$\\AA, which is lacking in the WHT data. However, the\nunderlying continuum is very similar in both spectra and the measured\ndepth of the (weak) 4000\\AA~break is very similar in each. This\nimplies that the emission lines detected in the Mayall 4-m spectrum\nare a local feature, produced {\\it in situ} rather than being due to\nscattered light from emission-line regions in the nucleus, since they\ndo not appear to be accompanied by a corresponding amount of scattered\nnuclear continuum. The consistency in the strength of the\n4000\\AA~break at the two observing epochs, along with its relative\nweakness, suggests the presence of a significant population of young\nstars in the host galaxy. McLure et al. (1999) report a tidal feature\nvisible in their $R$-band HST image of the elliptical host galaxy\nwhich may be linked to the origin of this young stellar population.\n\n\\noindent\n{\\bf 0157$+$001 (RQQ):} the slit positions used in the two sets of\nobservations were essentially the same. However, the WHT spectrum\nshows excess blue continuum shortwards of this feature. The two\nspectra were taken under what were ostensibly very similar atmospheric\nconditions, but we note that a very good approximation of the WHT\nspectrum can be obtained simply by adding a scaled version of the\nnuclear spectrum to the off-nuclear Mayall 4-m data. This suggests\nthat atmospheric scattering is to blame for the blue excess in the WHT\nspectra.\n\n\\noindent\n{\\bf 0736$+$017 (RLQ):} the two spectra were both taken under good\natmospheric conditions and using the same slit position. The agreement\nbetween the two is excellent.\n\n\\noindent\n{\\bf 2141$+$279 (RG):} the WHT spectrum has a much lower signal:noise\nratio than the Mayall 4-m spectrum, and uses a different slit\nposition. However, the overall continuum shape is in good agreement\nwith the earlier data. Both slits intercept an extension to the NE of\nthe nucleus which may be a tidal feature caused by interaction with a\nnorthern companion.\n\n\\noindent\n{\\bf 2247$+$140 (RLQ):} the same slit position was used for both\nspectra, although the seeing during the WHT run was quite poor ($\\sim\n1.6''$). The two datasets are consistent with one another, with a\nrelatively strong 4000\\AA~break and little sign of an additional blue\ncontinuum component from either young stars or scattered quasar\nlight. \n\n\\noindent\n{\\bf 2344$+$184 (RQQ):} different slit positions were used on the two\ndifferent instruments, and the WHT spectrum shows an excess of blue\nemission and a correspondingly weaker 4000\\AA~break. The seeing\nconditions were actually worse during the M4M observations, making\natmospheric scattering of quasar light an unlikely culprit. Moreover,\nwe note that the nuclear spectrum of this low-luminosity quasar is not\nparticularly blue and itself shows prominent stellar continuum\nfeatures (see Figure 2). More likely is that the WHT slit crossed a\nregion of the galaxy containing a large number of young stars. The\nhost of 2344$+$184 is a disc galaxy, with a central bulge and\nprominent spiral arms (McLure et al. 1999). (Hutchings et al. (1989)\nalso suggest the presence of a bar.)\n\n%Thus, although it is not always possible to quantify the amount of\n%contamination by quasar light in an individual spectrum, the\n%duplicated observations demonstrate that our detection of stellar\n%continuum features is robust, whether or not scattered nuclear\n%continuum is present. \n\n\n\\section{Summary}\n\nWe describe and present optical spectra of 26 galaxies hosting\npowerful nuclear activity. The sample contains carefully matched\nsubsamples of all three types of powerful AGN - radio-quiet and\nradio-loud quasars, and FR{\\sc ii} radio galaxies - enabling us to\ninvestigate the relationship between the host galaxy and the radio\nproperties of the resident AGN and also to test unified models for\nradio-loud objects.\n\nThe spectra were taken 5~arcsec {\\it off-nucleus} and, via a careful\nchoice of slit position, aim to maximise the amount of galaxy light\nentering the instrument whilst avoiding contamination from the active\nnucleus. In the majority of cases this approach appears to have been\nsuccessful; the continuum is clearly overwhelmingly stellar in origin\nand even when the presence of scattered nuclear emission is suspected,\nfeatures such as the 4000\\AA~break are still clearly discernable. In\nalmost all objects we detect at least some stellar signatures.\n\nA second paper (Nolan et al. 2000) will discuss spectrophotometric\nmodelling of the galaxy spectra in order to determine the ages and\nstarformation histories of their constituent stellar populations.\n\n\n\\section*{Acknowledgments}\n\nThe authors would like to thank the staff at KPNO and the ING for\ntheir assistance during the observations, and the anonymous referee\nwhose comments and suggestions resulted in several improvements in the\nfinal paper. DHH and MJK acknowledge PPARC support. This research has\nmade use of the NASA/IPAC Extragalactic Database (NED), which is\noperated by the Jet Propulsion Laboratory, California Institute of\nTechnology, under contract with the National Aeronautics and Space\nAdministration.\n\n\\section*{References}\n \n\n\\noindent\nBahcall J. N., Kirhakos S. \\& Schneider D. P., 1994, ApJ, 435, L11\n \n\\noindent\nBahcall J. N., Kirhakos S. \\& Schneider D. 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M. \\& Padovani P., PASP, 107, 803\n\n\\noindent\nV\\'{e}ron-Cetty M. -P. \\& Woltjer L., 1990, A\\&A, 236, 69\n\n\\clearpage\n\n% Plots of spectra + slit positions follow\n\n\n\\begin{figure*}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec0007_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=695}\n\\special{psfile=figures/slits/0007m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec0054_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/0054m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec0054_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/0054wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{Spectra obtained on the Mayall 4-m Telescope (M4M) at Kitt\nPeak and the Willliam Herschel Telescope (WHT) on La Palma, in order\nof increasing right ascension. The spectra are plotted at the\nobserved wavelength in units of $F_{\\lambda}$. In each case the lower\npanel shows the off-nuclear (host galaxy) spectrum and the upper panel\nthe nuclear (quasar) spectrum where available. The expected positions\nof various stellar absorption features are marked by vertical dotted\nlines in the off-nuclear spectra: (a) the 4000\\AA~break; (b) G band\n($\\lambda_{rest} = 4300 \\rightarrow 4320$\\AA); (c) Mg Ib\n($\\lambda_{rest} = 5173$\\AA); (d) Fe$\\lambda5270$. The redshifted\nwavelengths of the [O{\\sc iii}]$\\lambda5007$ and H$\\alpha$ emission\nlines are also indicated. The side panels show the slit position and\norientation for the off-nuclear data superimposed on the near-infrared\n(2.2$\\mu$m) contours of the object from Taylor et al. (1996) (each\npanel is $30\\times30$~arcsec$^{2}$).}\n\n\\end{figure*}\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec0137_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=695}\n\\special{psfile=figures/slits/0137m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec0157_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/0157m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec0157_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/0157wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec0204_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/0204wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec0230_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/0230wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec0244_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=335}\n\\special{psfile=figures/slits/0244wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec0345_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/0345wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec0736_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/0736m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec0736_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/0736wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec0917_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/0917wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec1004_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=535}\n\\special{psfile=figures/slits/1004wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec1020_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/1020m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec1215_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/1215wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec1217_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=535}\n\\special{psfile=figures/slits/1217wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec1330_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/1330m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec1334_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/1334wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec1549_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=535}\n\\special{psfile=figures/slits/1549wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec1635_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=335}\n\\special{psfile=figures/slits/1635wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec2135_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=735}\n\\special{psfile=figures/slits/2135wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec2141+175_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/2141+175wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec2141+279_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/2141+279m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec2141+279_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=695}\n\\special{psfile=figures/slits/2141+279wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec2201_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/2201m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec2215_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=335}\n\\special{psfile=figures/slits/2215wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{21.0cm}\n\\special{psfile=figures/spectra/spec2247_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=695}\n\\special{psfile=figures/slits/2247m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=430}\n\n\\special{psfile=figures/spectra/spec2247_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/2247wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec2344_m4m.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=295}\n\\special{psfile=figures/slits/2344m4m_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\\begin{figure*}\n\\setcounter{figure}{1}\n\\vspace{14.0cm}\n\\special{psfile=figures/spectra/spec2344_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=495}\n\\special{psfile=figures/slits/2344wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=230}\n\n\\special{psfile=figures/spectra/spec2349_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=220 voffset=335}\n\\special{psfile=figures/slits/2349wht_slit.eps\n hscale=70 vscale=70 angle=0 hoffset=50 voffset=30}\n\n\\caption{continued.}\n\n\\end{figure*}\n\n\n\n\\begin{figure*}\n\\setcounter{figure}{2}\n\\vspace{21.0cm}\n\\special{psfile=figures/compare/spec0054_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=-10 voffset=700}\n\\special{psfile=figures/compare/spec0157_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=240 voffset=700}\n\n\\special{psfile=figures/compare/spec0736_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=-10 voffset=500}\n\\special{psfile=figures/compare/spec2141+279_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=240 voffset=500}\n\n\\special{psfile=figures/compare/spec2247_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=-10 voffset=300}\n\\special{psfile=figures/compare/spec2344_m4m_wht.ps\n hscale=50 vscale=50 angle=-90 hoffset=240 voffset=300}\n\n\\caption{A comparison of off-nuclear (host galaxy) spectra obtained on\nthe Mayall 4-m Telescope at Kitt Peak (upper panel) with those\nobtained with the 4.2m WHT (lower panel). The spectra are plotted at\nthe observed wavelength in units of $F_{\\lambda}$. The expected\npositions of various stellar absoption features are shown as vertical\ndotted lines: (a) the 4000\\AA~break; (b) G band ($\\lambda_{rest} =\n4300 \\rightarrow 4320$\\AA); (c) Mg Ib ($\\lambda_{rest} = 5173$\\AA);\n(d) Fe$\\lambda5270$. The redshifted wavelengths of the [O{\\sc\niii}]$\\lambda5007$ and H$\\alpha$ emission lines are also\nmarked. Different slit widths were used on the two instruments and the\nflux callibration for the WHT spectra is relative rather than\nabsolute, so the flux values from the two telescopes are not directly\ncomparable.}\n\n\\end{figure*}\n\n\n\\end{document}\n\n\n\n"
}
] |
[] |
astro-ph0002022
|
The power spectral properties of the Z source GX~340+0
|
[
{
"author": "Peter G. Jonker\\altaffilmark{1}"
},
{
"author": "Michiel van der Klis\\altaffilmark{1}"
},
{
"author": "Rudy Wijnands\\altaffilmark{1}$^{,}$\\altaffilmark{2}"
},
{
"author": "Jeroen Homan\\altaffilmark{1}"
},
{
"author": "Jan van Paradijs\\altaffilmark{1}$^{,}$\\altaffilmark{3}"
},
{
"author": "Mariano M\\'endez\\altaffilmark{1,4}"
},
{
"author": "Eric C. Ford\\altaffilmark{1}"
},
{
"author": "Erik Kuulkers\\altaffilmark{5,6}"
},
{
"author": "Frederick K. Lamb\\altaffilmark{7}"
}
] |
\noindent We present an analysis of $\sim$390 ksec of data of the Z source GX~340+0 taken during 24 observations with the {\em Rossi\,X\,-ray\,Timing\,Explorer} satellite. We report the discovery of a new broad component in the power spectra. The frequency of this component varied between 9 and 14 Hz, and remained close to half that of the horizontal branch quasi-periodic oscillations (HBO). Its rms amplitude was consistent with being constant around $\sim$5\%, while its FWHM increased with frequency from 7 to 18 Hz. If this sub-HBO component is the fundamental frequency, then the HBO and its second harmonic are the second and fourth harmonic component, while the third harmonic was not detected. This is similar to what was recently found for the black hole candidate XTE~J1550--564. The profiles of both the horizontal- and the normal branch quasi-periodic oscillation peaks were asymmetric when they were strongest. We describe this in terms of a shoulder component at the high frequency side of the quasi-periodic oscillation peak, whose rms amplitudes were approximately constant at $\sim$4\% and $\sim$3\%, respectively. The peak separation between the twin kHz quasi-periodic oscillations was consistent with being constant at 339$\pm$8 Hz but a trend similar to that seen in, e.g. Sco~X--1 could not be excluded. We discuss our results within the framework of the various models which have been proposed for the kHz QPOs and low frequency peaks.
|
[
{
"name": "ms.tex",
"string": "\\documentstyle[psfig,11pt,emulateapj]{article}\n\n\\begin{document}\n\\title{The power spectral properties of the Z source GX~340+0}\n\\author{Peter G. Jonker\\altaffilmark{1}, Michiel van der\nKlis\\altaffilmark{1}, Rudy\nWijnands\\altaffilmark{1}$^{,}$\\altaffilmark{2}, Jeroen\nHoman\\altaffilmark{1}, Jan van\nParadijs\\altaffilmark{1}$^{,}$\\altaffilmark{3}, Mariano\nM\\'endez\\altaffilmark{1,4}, Eric C. Ford\\altaffilmark{1}, Erik\nKuulkers\\altaffilmark{5,6}, Frederick K. Lamb\\altaffilmark{7}}\n\n\\altaffiltext{1}{Astronomical Institute ``Anton Pannekoek'',\nUniversity of Amsterdam, and Center for High-Energy Astrophysics,\nKruislaan 403, 1098 SJ Amsterdam; [email protected],\[email protected], [email protected], [email protected],\[email protected]} \\altaffiltext{2}{MIT, Center\nfor Space Research, Cambridge, MA 02139, Chandra Fellow; [email protected]}\n\\altaffiltext{3}{University of Alabama, Huntsville}\n\\altaffiltext{4}{Facultad de Ciencias Astron\\'omicas y\nGeof\\'{\\i}sicas, Universidad Nacional de La Plata, Paseo del Bosque\nS/N, 1900 La Plata, Argentina} \\altaffiltext{5}{Space Research\nOrganization Netherlands, Sorbonnelaan 2, 3584 CA Utrecht, The\nNetherlands; [email protected]} \\altaffiltext{6}{Astronomical\nInstitute, Utrecht University, P.O. Box 80000, 3507 TA Utrecht, The\nNetherlands} \\altaffiltext{7}{Department of Physics and Astronomy,\nUniversity of Illinois at Urbana-Champaign, Urbana, IL 61801;\[email protected]}\n\n\\begin{abstract}\n\\noindent\nWe present an analysis of $\\sim$390 ksec of data of the Z source\nGX~340+0 taken during 24 observations with the {\\em\nRossi\\,X\\,-ray\\,Timing\\,Explorer} satellite. We report the discovery\nof a new broad component in the power spectra. The frequency of this\ncomponent varied between 9 and 14 Hz, and remained close to half that\nof the horizontal branch quasi-periodic oscillations (HBO). Its rms\namplitude was consistent with being constant around $\\sim$5\\%, while\nits FWHM increased with frequency from 7 to 18 Hz. If this sub-HBO\ncomponent is the fundamental frequency, then the HBO and its second\nharmonic are the second and fourth harmonic component, while the third\nharmonic was not detected. This is similar to what was recently found\nfor the black hole candidate XTE~J1550--564. The profiles of both the\nhorizontal- and the normal branch quasi-periodic oscillation peaks\nwere asymmetric when they were strongest. We describe this in terms of\na shoulder component at the high frequency side of the quasi-periodic\noscillation peak, whose rms amplitudes were approximately constant at\n$\\sim$4\\% and $\\sim$3\\%, respectively. The peak separation between\nthe twin kHz quasi-periodic oscillations was consistent with being\nconstant at 339$\\pm$8 Hz but a trend similar to that seen in,\ne.g. Sco~X--1 could not be excluded. We discuss our results within the\nframework of the various models which have been proposed for the kHz\nQPOs and low frequency peaks.\n\n\\end{abstract}\n\n\\subjectheadings{accretion, accretion disks --- stars: individual\n(GX\\,340+0) --- stars: neutron --- X-rays: stars}\n\n\\section{Introduction}\n\\label{intro}\n\\noindent\nGX\\,340+0 is a bright low-mass X-ray binary (LMXB) and a Z source\n(Hasinger \\& van der Klis 1989). The Z-shaped track traced out by Z\nsources in the X-ray color-color diagram or hardness-intensity diagram\n(HID) is divided into three branches: the horizontal branch (HB), the\nnormal branch (NB), and the flaring branch (FB). The power spectral\nproperties and the HID of GX\\,340+0 were previously described by van\nParadijs et al. (1988) and Kuulkers \\& van der Klis (1996) using data\nobtained with the EXOSAT satellite, by Penninx et al. (1991) using\ndata obtained with the Ginga satellite, and by Jonker et al. (1998)\nusing data obtained with the {\\em Rossi\\,X\\,-ray\\,Timing\\,Explorer}\n{\\em(RXTE)} satellite. An extra branch trailing the FB in the HID has\nbeen described by Penninx et al. (1991) and Jonker et al. (1998).\nWhen the source is on the HB or on the upper part of the NB,\nquasi-periodic oscillations (QPOs) occur with frequencies varying from\n20--50 Hz: the horizontal branch quasi-periodic oscillations or HBOs\n(Penninx et al. 1991; Kuulkers \\& van der Klis 1996; Jonker et\nal. 1998). Second harmonics of these HBOs were detected by Kuulkers \\&\nvan der Klis (1996) and Jonker et al. (1998) in the frequency range\n73--76 Hz and 38--69 Hz, respectively. In the middle of the NB, van\nParadijs et al. (1988) found normal branch oscillations (NBOs) with a\nfrequency of 5.6 Hz. Recently, Jonker et al. (1998) discovered twin\nkHz QPOs in GX\\,340+0. These QPOs have now been seen in all six\noriginally identified Z sources (Sco~X--1, van der Klis et al. 1996;\nCyg X--2, Wijnands et al 1998a; GX~17+2, Wijnands et al. 1997b;\nGX~349+2, Zhang et al. 1998; GX~340+0, Jonker et al. 1998; GX~5--1,\nWijnands et al. 1998b; see van der Klis 1997, 1999 for reviews), but\nnot in Cir~X--1, which combines Z source and atoll source\ncharacteristics (Oosterbroek et al. 1995; Shirey, Bradt, and Levine\n1999; see also Psaltis, Belloni, \\& van der Klis 1999). \\par\n\\noindent\nIn the other class of LMXBs, the atoll sources (Hasinger \\& van der\nKlis 1989), kHz QPOs are observed as well (see van der Klis 1997, 1999\nfor reviews). Recently, also HBO-like features have been identified\nin a number of atoll sources (4U\\,1728--34, Strohmayer et al. 1996,\nFord \\& van der Klis 1998, Di Salvo et al. 1999; GX13+1, Homan et\nal. 1998; 4U~1735--44, Wijnands et al. 1998c; 4U~1705--44, Ford, van\nder Klis, \\& Kaaret 1998; 4U\\,1915--05, Boirin et al. 1999;\n4U~0614+09, van Straaten et al. 1999; see Psaltis, Belloni, \\& van der\nKlis 1999 for a summary). Furthermore, at the highest inferred mass\naccretion rates, QPOs with frequencies near 6 Hz have been discovered\nin the atoll sources 4U\\,1820--30 (Wijnands, van der Klis, \\&\nRijkhorst 1999c), and XTE~J1806--246 (Wijnands \\& van der Klis 1998e,\n1999b; Revnivtsev, Borozdin, \\& Emelyanov 1999), which might have a\nsimilar origin as the Z source NBOs. \\par\n\\noindent\nAt low mass accretion rates the power spectra of black hole\ncandidates, atoll, and Z sources show similar characteristics (van der\nKlis 1994a,b). Wijnands \\& van der Klis (1999a) found that the break\nfrequency of the broken power law which describes the broad-band power\nspectrum, correlates well with the frequency of peaked noise\ncomponents (and sometimes narrow QPO peaks) observed in atoll sources\n(including the millisecond X-ray pulsar SAX\\,J1808.4--3658; Wijnands\n\\& van der Klis 1998d, Chakrabarty \\& Morgan 1998), and black hole\ncandidates. The Z sources followed a slightly different correlation.\nIn a similar analysis, Psaltis, Belloni, \\& van der Klis (1999) have\npointed out correlations between the frequencies of some of these QPOs\nand other noise components in atoll sources, Z sources, and black hole\ncandidates, which suggests these phenomena may be closely related\nacross these various source types, or at least depend on a third\nphenomenon in the same manner. Because of these correlations, models\ndescribing the kHz QPOs which also predict QPOs or noise components in\nthe low-frequency part of the power spectrum can be tested by\ninvestigating this low-frequency part. \\par\n\\noindent\nIn this paper, we study the full power spectral range of the bright\nLMXB and Z source GX~340+0 in order to further investigate the\nsimilarities between the atoll sources and the Z sources, and to help\nconstrain models concerning the formation of the different QPOs. We\nreport on the discovery of two new components in the power spectra of\nGX~340+0 with frequencies less than 40 Hz when the source is on the\nleft part of the HB. We also discuss the properties of the NBO, and\nthose of the kHz QPOs.\n\n\n\\section{Observations and analysis}\n\\label{analysis}\n\\noindent\nThe Z source GX\\,340+0 was observed 24 times in 1997 and 1998 with the\nproportional counter array (PCA; Jahoda et al. 1996) on board the {\\em\nRXTE} satellite (Bradt, Rothschild \\& Swank 1993). A log of the\nobservations is presented in Table \\ref{obs_log}. Part of these data\n(observations 1, 9--18) was used by Jonker et al. (1998) in the\ndiscovery of the kHz QPOs in GX~340+0. The total amount of good data\nobtained was $\\sim$390 ksec. During $\\sim$19\\% of the time only 3 or 4\nof the 5 PCA detectors were active. \n\\begin{deluxetable}{lllll}\n\\tablecaption{Log of the observations. \\label{obs_log}}\n\\startdata\n\nNumber & Observation & Date \\& & Total on source \\nl\n & ID & Start time (UTC) & observing time (ksec.)\\nl \n\\tableline\n1 & 20054-04-01-00 & 1997-04-17 13:26:21 & 19.8\\nl\n\\tableline\n2 & 20059-01-01-00 & 1997-06-06 06:05:07 & 34.7\\nl\n3 & 20059-01-01-01 & 1997-06-06 21:39:06 & 8.1 \\nl\n4 & 20059-01-01-02 & 1997-06-07 11:15:05 & 22.1 \\nl\n5 & 20059-01-01-03 & 1997-06-07 23:48:56 & 21.6 \\nl\n6 & 20059-01-01-04 & 1997-06-08 07:51:04 & 22.9 \\nl\n7 & 20059-01-01-05 & 1997-06-09 00:09:03 & 17.5 \\nl\n8 & 20059-01-01-06 & 1997-06-10 01:22:46 & 22.0\\nl\n\\tableline\n9 & 20053-05-01-00 & 1997-09-21 01:04:06 & 17.5\\nl\n10 & 20053-05-01-01 & 1997-09-23 04:09:30 & 11.5\\nl\n11 & 20053-05-01-02 & 1997-09-25 01:30:29 & 8.4 \\nl\n12 & 20053-05-01-03 & 1997-09-25 09:37:51 & 19.3 \\nl\n13 & 20053-05-02-00 & 1997-11-01 22:38:58 & 9.5\\nl\n14 & 20053-05-02-01 & 1997-11-02 03:32:07 & 9.0\\nl\n15 & 20053-05-02-02 & 1997-11-02 19:42:00 & 12.7\\nl\n16 & 20053-05-02-03 & 1997-11-03 01:50:07 & 13.9\\nl\n17 & 20053-05-02-04 & 1997-11-04 01:59:34 & 11.1\\nl\n18 & 20053-05-02-05 & 1997-11-04 16:18:27 & 7.2\\nl\n\\tableline\n19 & 30040-04-01-00 & 1998-11-13 23:52:00 & 16.7\\nl\n20 & 30040-04-01-01 & 1998-11-14 13:55:00 & 17.3 \\nl\n21 & 30040-04-01-02 & 1998-11-14 21:03:00 & 28.1 \\nl\n22 & 30040-04-01-03 & 1998-11-15 13:48:00 & 17.1 \\nl\n23 & 30040-04-01-04 & 1998-11-15 20:57:00 & 17.0\\nl\n24 & 30040-04-01-05 & 1998-11-15 09:53:00 & 2.6\\nl\n\\enddata\n\\end{deluxetable}\n\\par\n\\noindent\nThe data were obtained in various modes, of which the Standard 1 and\nStandard 2 modes were always active. The Standard 1 mode has a\ntime resolution of 1/8 s in one energy band (2--60 keV). The\nStandard 2 mode has a time resolution of 16 s and the effective 2--60\nkeV PCA energy range is covered by 129 energy channels. In addition, high\ntime resolution data (with a resolution of 244 $\\mu$s or better for the\n2--5.0 keV band and with a resolution of 122 $\\mu$s or better for the\n5.0--60 keV range) were obtained for all observations. \\par\n\\noindent\nFor all observations except observation 1, which had only 4 broad\nenergy bands, and observation 22, for which technical problems with\nthe data occurred, we computed power spectra in five broad energy\nbands (2--5.0, 5.0--6.4, 6.4--8.6, 8.6--13.0, 13.0--60 keV) with a\nNyquist frequency of 256 Hz dividing the data in segments of 16 s length\neach. We also computed power spectra for all observations using 16 s\ndata segments in one combined broad energy band ranging from 5.0--60\nkeV with a Nyquist frequency of 4096 Hz. \\par\n\\noindent\nTo characterize the properties of the low-frequency part (1/16--256\nHz) of the power spectrum we experimented with several fit functions\n(see Section ~\\ref{result}) but finally settled on a fit function that\nconsisted of the sum of a constant to represent the Poisson noise, one\nto four Lorentzians describing the QPOs, an exponentially cut-off\npower law component, $P\\propto\\nu^{-\\alpha} exp(-\\nu/\\nu_{cut})$ to\ndescribe the low frequency noise (LFN), and a power law component to\nrepresent the very low frequency noise (VLFN) when the source was on\nthe NB. \\par\n\\noindent\nTo describe the high frequency part (128 to 4096 Hz or 256 to 4096 Hz)\nof the power spectrum we used a fit function which consisted of the\nsum of a constant and a broad sinusoid to represent the dead-time\nmodified Poisson noise (Zhang et al. 1995), one or two Lorentzian\npeaks to represent the kHz QPOs, and sometimes a power law to fit the\nlowest frequency part ($<$ 150 Hz). The PCA setting concerning the\nvery large event window (Zhang et al. 1995; van der Klis et al. 1997)\nwas set to 55 $\\mu$s. Therefore, its effect on the Poisson noise was\nsmall and it could be incorporated into the broad sinusoid. The\nerrors on the fit parameters were determined using $\\Delta\\chi^2$=1.0\n($1 \\sigma$ single parameter). The 95\\% confidence upper limits were\ndetermined using $\\Delta\\chi^2$=2.71. \\par\n\\noindent\nWe used the Standard 2 data to compute hardnesses and intensities from\nthe three detectors that were always active. Figure ~\\ref{fig_HIDs}\nshows three HIDs; one (A) for observations 1 and 9--18 combined (data\nset A), one (B) for observation 2--8 combined (data set B), and one\n(C) for observation 19--24 combined (data set C). The observations\nwere subdivided in this way because the hard vertex, defined as the\nHB--NB intersection, is at higher intensities in data set C than in\ndata set A. The hard vertex of data set B falls at an intermediate\nintensity level. \n\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=3HIDs_3datasets_apart.ps}}\n\\figcaption{Hardness-intensity diagrams for observations 1 and 9--18\n(A), 2--8 (B), and 19--24 (C) (see Table \\ref{obs_log}). The hard\ncolor is defined as the logarithm of the 9.7--16.0/6.4--9.7 keV count\nrate ratio. The intensity is defined as the three-detector count rate\nmeasured in the 2--16.0 keV band. The data were background subtracted\nbut no dead-time correction was applied. The dead-time correction\nfactor was less than 1.5\\%.\n\\label{fig_HIDs}}\n\\end{figure*}\n\\par\n\\noindent\nWe assigned a value to each power spectrum according to the position\nof the source along the Z track using the $\\rm{S_z}$ parameterization\n(Dieters \\& van der Klis 1999, Wijnands et al. 1997) applied to each\nHID separately. In this parametrization, the hard vertex (defined as\nthe HB-NB intersection) is assigned the value $\\rm{S_z}$ = 1.0 and the\nsoft vertex (defined as the NB--FB intersection) is assigned\n$\\rm{S_z}$ = 2.0. Thus, the distance between the hard and soft vertex\ndefines the length scale along each branch. Since for HID C we only\nobserved part of the Z track, we used the position of the soft vertex\nof HID A in HID C. From the fact that the soft vertex of the HID B was\nconsistent with that from HID A, we conclude that the error introduced\nby this is small.\\par\n\\noindent\nThe shifts in the position of the hard vertex prevented us from\nselecting the power spectra according to their position in an HID of\nall data combined. We selected the power spectra according to the\n$\\rm{S_z}$ value in each of the three separate Z tracks, since Jonker\net al. (1998) showed that for GX~340+0 the frequency of the HBO is\nbetter correlated to the position of the source relative to the\ninstantaneous Z track than to its position in terms of coordinates in\nthe HID. The power spectra corresponding to each $\\rm{S_z}$ interval\nwere averaged. However, employing this method yielded artificially\nbroadened HBO peaks, and sometimes the HBO profile even displayed\ndouble peaks. The reason for this is that in a typical $\\rm{S_z}$\nselection interval of 0.05 the dispersion in HBO frequencies well\nexceeds the statistical one, as shown in Figure ~\\ref{HBO_vs_Sz}.\nWhile the relation between $\\rm{S_z}$ and HBO frequency is roughly\nlinear, the spread is large.\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=HBO_vs_Sz.ps,width=15cm,height=15cm,angle=270}}\n\\figcaption{The $\\rm{S_z}$ value of $\\sim $150 individual 16 s length\npower spectra from observation 1 plotted against their fitted HBO\nfrequency. The line represents the best linear fit. The $\\chi^2_{red}$\nis 1.75 for 144 degrees of freedom, the linear-correlation\ncoefficient is 0.83.\n\\label{HBO_vs_Sz}}\n\\end{figure*}\n\\par\n\\noindent\nFor this reason, when the HBO was detectable in the 5.0--60 keV power\nspectra, we selected those power spectra according to HBO frequency\nrather than on $\\rm{S_z}$ value. In practice, this was possible for\nall data on the HB. To determine the energy dependence of the\ncomponents, the 2--5.0, 5.0--6.4, 6.4--8.6, 8.6--13.0, 13.0--60 keV\npower spectra were selected according to the frequency of the HBO peak\nin the 2--60 keV power spectrum, when detectable. \\par\n\\noindent\nThe HBO frequency selection proceeded as follows. For each observation\nwe constructed a dynamical power spectrum using the 5--60 keV or 2--60\nkeV data (see above), showing the time evolution of the power spectra\n(see Fig.~\\ref{dynspec}). Using this method, we were able to trace the\nHBO frequency in each observation as a function of time. We determined\nthe maximum power in 0.5 Hz bins over a range of 2 Hz around the\nmanually identified QPO frequency for each power spectrum, and adopted\nthe frequency at which this maximum occurred as the HBO frequency in\nthat power spectrum. This was done for each observation in which the\nHBO could be detected. \n\\begin{figure*}[]\n\\centerline{\\psfig{figure=dynspecA.ps,width=15cm,height=15cm,angle=270}}\n\\figcaption{The dynamical power spectrum of part of observation 1\nshowing the 1/16--60 Hz range, with a frequency resolution of 0.5 Hz\nin the energy band 5--60 keV. The grey scale represents the Leahy\nnormalized power (Leahy et al. 1983). Data gaps have been omitted for\nclarity. Clearly visible is the HBO at $\\sim18$ to $\\sim50$ Hz and the\nLFN component at low ($<10$ Hz) frequencies.\n\\label{dynspec}}\n\\end{figure*}\n\\par\n\\noindent\nThe 18--52 Hz frequency range over which the HBO was detected was\ndivided in 16 selection bins with widths of 2 or 4 Hz, depending on\nthe signal to noise level. For each selection interval the power\nspectra were averaged, and a mean $\\rm{S_z}$ value was determined.\\par\n\\noindent\nThe HBO selection criteria were applied to all data along the HB and\nnear the hard vertex. When the source was near the hard vertex, on the\nNB, or the FB, we selected the power spectra according to the\n$\\rm{S_z}$ value. An overlap between the two methods occurred for data\nnear the hard vertex; both selection methods yielded the same results\nfor the fit parameters to well within the statistical errors (see\nSection \\ref{result}). Separately, for each set of observations (A,B,\nand C) we also determined the kHz QPO properties according to the\n$\\rm{S_z}$ method.\n\n\\section{Results}\n\\label{result}\n\\label{fitf}\n\\noindent\nUsing the fit function described by Jonker et al. (1998) which\nconsisted of two Lorentzians to describe the HBO and the second\nharmonic of the HBO, and a cut-off power law to describe the LFN noise\ncomponent, we obtained poor fits. Compared with Jonker et al. (1998)\nwe combined more data, resulting in a higher signal to noise\nratio. First we included a peaked noise component (called sub-HBO\ncomponent) at frequencies below the HBO, since a similar component was\nfound by van der Klis et al. (1997) in Sco~X--1. This improved the\n$\\chi^2_{red}$ of the fit. Remaining problems were that the frequency\nof the second harmonic was not equal to twice the HBO frequency\n(similar problems fitting the power spectra on the HB of Cyg~X--2 were\nreported by Kuulkers, Wijnands, \\& van der Klis 1999), and the\nfrequency of the sub-HBO component varied erratically along the\nHB. Inspecting the fit showed that both the fit to the high frequency\ntail of the HBO, and the fit to its second harmonic did not represent\nthe data points very well. Including an additional component in the\nfit function representing the high frequency tail of the HBO (called\nshoulder component after Belloni et al. [1997] who used this name)\nresulted in a better fit to the HBO peak, a centroid frequency of the\nHBO second harmonic more nearly equal to twice the HBO frequency, and\na more consistent behavior of the frequency of the sub-HBO component\n(which sometimes apparently fitted the shoulder when no shoulder\ncomponent was present in the fit function).\\par\n\\noindent\nWe also experimented with several other fit function components to\ndescribe the average power spectra which were used by other authors to\ndescribe the power spectra of other LMXBs. Using a fit function built\nup out of a broken power law, to fit the LFN component, and several\nLorentzians to fit the QPOs after Wijnands et al. (1999a) results in\nsignificantly higher $\\chi^2_{red}$ values than when the fit function\ndescribed in Section~\\ref{analysis} was used ($\\chi^2_{red}$= 1.66 for\n205 degrees of freedom (d.o.f.) versus a $\\chi^2_{red}$= 1.28 with 204\nd.o.f.). We also fitted the power spectra using the same fit function\nas described in Section~\\ref{analysis} but with the frequency of the\nsub-HBO component fixed at 0 Hz, in order to test whether or not an\nextra LFN-like component centred around 0 Hz was a good representation\nof the extra sub-HBO component. Finally, we tested a fit function\nbuilt up out of two cut-off power laws; one describing the LFN and one\neither describing the sub-HBO component or the shoulder component, and\nthree Lorentzians, describing the HBO, its second harmonic, and either\nthe sub-HBO or shoulder component when not fitted with the cut-off\npower law. But in all cases the $\\chi^2_{red}$ values obtained using\nthese fit functions were significantly higher (for the 24--26 Hz\nselection range values of 1.52 for 205 d.o.f., 1.62 for 204 d.o.f.,\nand 2.00 for 205 d.o.f. were obtained, respectively). \\par\n\\noindent\nSettling on the fit function already described in\nSection~\\ref{analysis}, we applied an F-test (Bevington \\& Robinson\n1992) to the $\\chi^2$ of the fits with and without the extra\nLorentzian components to test their significance. We derived a\nsignificance of more than 8 $\\sigma$ for the sub-HBO component, and a\nsignificance of more than 6.5 $\\sigma$ for the shoulder component, in\nthe average selected power spectrum corresponding to HBO frequencies\nof 24 to 26 Hz. In Figure~\\ref{separate_comps} we show the\ncontribution of all the components used to obtain the best fit in this\npower spectrum.\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=separate_comps.ps,width=15cm,height=15cm}}\n\\figcaption{Leahy normalized power spectrum showing the different\ncomponents used to fit the 5.0--60 keV power spectrum. The full line\nrepresents the LFN component, and the constant arising in the power\nspectrum due to the Poisson counting noise; the dashed line represents\nthe sub-HBO component; the dotted line represents the HBO; the\ndashed-dotted line represents the shoulder component; and the\ndash-three dots-dash line represents the harmonic of the\nHBO.\n\\label{separate_comps}}\n\\end{figure*}\n\\par\n\\noindent\nThe properties of all the components used in describing the\nlow-frequency part of the average power spectra along the HB are given\nin Fig.~\\ref{all_low_freq_prop} as a function of $\\rm{S_z}$. When the\nHBO frequency was higher than 32 Hz, the sub-HBO and shoulder\ncomponent were not significant. We therefore decided to exclude these\ntwo components from the fit function in the HBO frequency selections\nof 32 Hz and higher. When this affected the parameters determined for\nthe remaining components in the fit function, we mention so. Splitting\nthe total counts into different photon energies reduced the signal to\nnoise in each energy band and therefore these effects were more\nimportant in the fits performed to determine the energy dependence of\nthe parameters.\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=all_low_freq_prop.ps,width=15cm,height=12cm}}\n\\figcaption{(A) Rms amplitude of the low-frequency noise (LFN); (B)\npower law index of the LFN; (C) cut-off frequency of the LFN; (D) rms\namplitude of the noise component at frequencies below the HBO\nfrequency (sub-HBO component); (E) FWHM of the sub-HBO component; (F)\nfrequency of the sub-HBO component; (G) rms amplitude of the HBO; (H)\nFWHM of the HBO; (I) frequency of the HBO; (J) rms amplitude of the\nshoulder component used to describe the HBO; (K) FWHM of the shoulder\ncomponent; (L) frequency of the shoulder component; (M) rms amplitude\nof the harmonic of the HBO; (N) FWHM of the harmonic; (O) frequency of\nthe harmonic. The points represent data selected according to the HBO\nselection method and the bullets represent the data selected according\nto the $\\rm{S_z}$ selection method (parameters measured in the 5.0--60\nkeV band, see text). The two methods overlap starting around\n$\\rm{S_z}\\sim$1.0.\n\\label{all_low_freq_prop}}\n\\end{figure*}\n\n\\subsection{The LFN component}\n\\noindent\nThe fractional rms amplitude of the LFN decreased as a function of\n$\\rm{S_z}$ (Fig~\\ref{all_low_freq_prop} A), with values ranging from\n10\\% to 2.2\\% (5.0--60 keV). Upper limits on the LFN component were\ncalculated by fixing the power law index at 0.0. The power law index\nof the LFN component increased from $\\sim$ 0 at $\\rm{S_z} \\sim$ 0.5 to\n$\\sim$ 0.4 around $\\rm{S_z}$= 0.9; when the source moved on to the NB\nthe index of the power law decreased to values slightly below 0.0\n(Fig~\\ref{all_low_freq_prop} B). The cut-off frequency of the LFN\ncomponent increased as a function of $\\rm{S_z}$. For $\\rm{S_z}> 1.0$\nthe cut-off frequency could not be determined with high accuracy\n(Fig~\\ref{all_low_freq_prop} C). \\par\n\\noindent\nThe LFN fractional rms amplitude depended strongly on photon energy\nall across the selected frequency range. The rms amplitude increased\nfrom 5\\% at 2--5.0 keV to more than 15\\% at 13.0--60 keV\n($\\rm{S_z}$=0.48). The power law index, $\\alpha$, of the LFN\ncomponent was higher at lower photon energies (changing from 0.3--0.5\nalong the HB at 2--5.0 keV) than at higher photon energies (changing\nfrom $-$0.2--0.2 along the HB at 13.0--60 keV). The cut-off frequency\nof the LFN component did not change as a function of photon energy.\n\n\\subsection{The HBO component}\n\\noindent\nThe fractional rms amplitude of the HBO decreased as a function of\n$\\rm{S_z}$ (Fig~\\ref{all_low_freq_prop} G), with values ranging from\n10\\% to 1.7\\% over the detected range (5.0--60 keV). Upper limits on\nthe HBO component were determined using a fixed FWHM of 15 Hz. The\nfrequency of the HBO increased as a function of $\\rm{S_z}$ but for\n$\\rm{S_z}>$1.0 it was consistent with being constant around 50 Hz\n(Fig~\\ref{all_low_freq_prop} I). \\par\n\\noindent\nThe ratio of the rms amplitudes of the LFN and the HBO component, of\ninterest in beat frequency models (see Shibazaki \\& Lamb 1987)\ndecreased from $\\sim$ 1 at an $\\rm{S_z}$ value of 0.48 to $\\sim 0.6$\nat $\\rm{S_z}$ values of 0.8--1.0. The ratio increased again to a value\nof $\\sim$ 0.9 at $\\rm{S_z}=$1.05 when the source was on the NB.\\par\n\\noindent\nThe HBO rms amplitude depended strongly on photon energy all across\nthe selected frequency range. The rms amplitude increased from 5\\% at\n2--5.0 keV to $\\sim$ 16\\% at 13.0--60 keV (at $\\rm{S_z}$=0.48) (see\nFigure~\\ref{en_dep} [dots] for the HBO energy dependence in the 26--28\nHz range). The increase in fractional rms amplitude of the HBO towards\nhigher photon energies became less as the frequency of the HBO\nincreased. At the highest HBO frequencies the HBO is relatively\nstronger in the 8.4--13.0 keV band than in the 13.0--60 keV band. The\nratio between the fractional rms amplitude as a function of photon\nenergy of the HBO at lower frequencies and the fractional rms\namplitude as a function of photon energy of the HBO at higher\nfrequencies is consistent with a straight line with a positive\nslope. The exact fit parameters depend on the HBO frequencies at which\nthe ratios were taken. This behavior was also present in absolute rms\namplitude ($\\equiv \\rm{fractional\\,rms\\,amplitude} * I_{x}$, where\n$\\rm{I_{x}}$ is the count rate), see Fig.~\\ref{rmsratio}. So, this\nbehavior is caused by actual changes in the QPO spectrum, not by\nchanges in the time-averaged spectrum by which the QPO spectrum is\ndivided to calculate the fractional rms spectrum of the HBO. The FWHM\nand the frequency of the HBO were the same in each energy band.\n\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=en_dep.ps,width=15cm}}\n\\figcaption{The figure shows the typical energy dependence of the rms\namplitude of the HBO (bullets) and NBO (squares) as measured in the\nfrequency range 26--28 Hz for the HBO, and as measured in the\n$\\rm{S_z}$ 1.0--1.9 range for the NBO.\n\\label{en_dep}}\n\\end{figure*}\n\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=abs_ratio_rmsenHBO_20Hz_49Hz.ps,width=15cm,height=15cm}}\n\\figcaption{The absolute rms amplitude of the HBO at $\\sim$20 Hz\ndivided by the absolute rms amplitude of the HBO at $\\sim$50 Hz as a\nfunction of the photon energy.\n\\label{rmsratio}}\n\\end{figure*}\n\n\\subsection{The second harmonic of the HBO}\n\\noindent\nThe rms amplitude of the second harmonic of the HBO decreased as a\nfunction of $\\rm{S_z}$ (Fig~\\ref{all_low_freq_prop} M) from 5.2\\% to\n3.6\\% (5.0--60 keV). Upper limits on the second harmonic of the HBO\nwere derived using a fixed FWHM of 25 Hz. The frequency of the second\nharmonic of the HBO was consistent with being twice the HBO frequency\nwhen the sub-HBO and the shoulder component were strong enough to be\nmeasured (see Fig~\\ref{all_low_freq_prop} O, and\nFig.~\\ref{freqs}). When these two extra components could not be\ndetermined significantly, due to the limited signal to noise, and we\ntherefore omitted them from the fit function (as explained above),\nthe frequency of the second harmonic of the HBO was clearly less than\ntwice the HBO frequency (see Fig.~\\ref{freqs}).\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=freqs_lijns2e.ps}}\n\\figcaption{The frequencies of the four Lorentzian components used to\ndescribe the average 5.0--60 keV power spectra, as a function of the\nHBO frequency. Shown are from low frequencies to high frequencies; the\nsub-HBO component (stars), the HBO (bullets), the shoulder component\n(open circles), and the second harmonic of the HBO (squares). The\nsolid line represents the relation $\\nu = 0.5 * \\nu_{HBO}$, the\ndashed-dotted line represents $\\nu = 1.0 * \\nu_{HBO}$, and the dotted\nline represents $\\nu = 2.0 * \\nu_{HBO}$. Errors in the HBO frequency\nare in some cases smaller than the symbols.\n\\label{freqs}}\n\\end{figure*}\n\\par\n\\noindent\nThe rms amplitude of the second harmonic of the HBO was also energy\ndependent. Its rms amplitude increased from less than 4\\% in the\n2--5.0 keV, to more than 9\\% in the 8.6--13 keV band. The FWHM of the\nsecond harmonic varied erratically in the range of 10--50 Hz. This is\nnot necessarily a property of the second harmonic since the HBO\nshoulder component which was not significant by themselve was omitted\nfrom the fit function. This may have influenced the fit to the FWHM of\nthe second harmonic when it was weak. Its frequency was consistent\nwith being the same in each energy band.\n\n\\subsection{The sub-HBO component}\n\\noindent\nThe centroid frequency (Fig~\\ref{all_low_freq_prop} F) and FWHM\n(Fig~\\ref{all_low_freq_prop} E) of the Lorentzian at sub-HBO\nfrequencies increased from 9.3$\\pm$0.3 Hz to 13.6$\\pm$1.0 Hz and from\n7.1$\\pm$0.6 Hz to 18$\\pm$3 Hz, respectively, as the source moved up\nthe HB from $\\rm{S_z}=$ 0.48 to 0.67. The rms amplitude of this\ncomponent did not show a clear relation with $\\rm{S_z}$; its value was\nconsistent with being constant around 5\\% (Fig~\\ref{all_low_freq_prop}\nD). Upper limits on the sub-HBO component were determined using a\nfixed FWHM of 15 Hz. The frequency of the sub-HBO component is close\nto half the frequency of the HBO component. The fact that the ratio\nbetween the HBO frequency and the sub-HBO frequency is not exactly 2\nbut $\\sim2.2$ may be accounted for by the complexity of the data\nand therefore its description. \\par\n\\noindent\nWe detected the sub-HBO component in the three highest energy bands\nthat we defined over an $\\rm{S_z}$ range from 0.48--0.65. Its rms\namplitude is higher in the highest energy band ($\\sim$7\\% in 13.0--60\nkeV, and less than 5\\% in 6.4--8.6 keV) and decreased as a function of\n$\\rm{S_z}$, while the FWHM and the frequency increased from 6--12 Hz,\nand 9--15 Hz, respectively.\n\n\\subsection{The HBO shoulder component}\n\\noindent\nAt an $\\rm{S_z}$ value of 0.48 (the left most part of the HB) the\nfrequency of the shoulder component was higher than the frequency of\nthe HBO, and the frequency separation between them was largest\n(Fig~\\ref{all_low_freq_prop} L and Fig.~\\ref{freqs}). Both the\nfrequency of the shoulder and the HBO increased when the source moved\nalong the HB, but the frequency difference decreased. The FWHM of the\nshoulder component increased from 7$\\pm$2 Hz to 17$\\pm$3 Hz and then\ndecreased again to 8.6$\\pm$1.0 Hz as the frequency of the HBO peak\nincreased from 25.7$\\pm$0.7 Hz to 30.9$\\pm$0.4 Hz\n(Fig~\\ref{all_low_freq_prop} K). From an $\\rm{S_z}$ value of 0.61 to\n0.67 the frequency was consistent with being constant at a value of 32\nHz. The rms amplitude was consistent with being constant around 4\\%\n(5.0--60 keV), over the total range where this component could be\ndetected (Fig~\\ref{all_low_freq_prop} J), but the data is also\nconsistent with an increase of fractional rms amplitude with\nincreasing HBO frequency. Upper limits on the HBO shoulder component\nwere determined using a fixed FWHM of 7 Hz. \\par\n\\noindent\nIn the various energy bands the HBO shoulder component was detected\nseven times in total; once in the 2--5.0 keV band, three times in the\n6.4--8.6 keV band, and three times in the in the 8.6--13.0 keV band,\nwith rms amplitudes increasing from $\\sim$3\\% in the 2--5.0 keV band\nto $\\sim$6\\% in the 8.6--13.0 keV band, and a FWHM of $\\sim$10\nHz. Upper limits of the order of 3\\%--4\\%, and of 5\\%--7\\% were\nderived in the two lowest and three highest energy bands considered,\nrespectively. These are comparable with or higher than the rms\namplitudes of this component determined in the 5--60 keV band.\n\n\\subsection{The NBO component}\n\\noindent\nThe NBOs were not observed when the source was on the HB, with an\nupper limit of 0.5\\% just before the hard vertex (for an $\\rm{S_z}$\nvalue of 0.96). They were detected along the entire NB and they\nevolved into a broad noise component on the FB. The properties are\nlisted in Table~\\ref{nbo_tab}. The rms amplitude of the NBO gradually\nincreased while the source moved from the upper NB to the middle part\nof the NB where the rms amplitude is highest. On the lower part of the\nNB the NBO rms amplitude gradually decreased. Upper limits on the NBO\ncomponents were determined using a fixed FWHM of 5 Hz.\n\\begin{table*}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}{lllllllll}\n\\tableline\n\\tableline\n & NBO & & & shoulder & & & Total &\\\\\n\\tableline\n$\\rm{S_z}$ & $\\nu_{NBO}$ & FWHM & Rms &\n$\\nu_{shoulder}$& FWHM & Rms & $\\nu_{weighted}$ & Total rms\\\\\n & (Hz) & (Hz) & (\\%) & \n(Hz) & (Hz) & (\\%) & (Hz) & (\\%)\\\\\n\\tableline\n$0.96\\pm0.03$ & $8^{\\em a}$ & $5^{\\em a}$ & $<0.5$ & -- & -- & --& --& -- \\\\\n$1.04\\pm0.03$ & $6.2\\pm0.4$ & $10\\pm2$ & $1.8\\pm0.2$& $8^{\\em a}$\n& $5^{\\em a}$ & $<1$ & -- & --\\\\\n$1.14\\pm0.03$ & $5.74\\pm0.07$ & $6.3\\pm0.3$ & $3.4\\pm0.1$ & $8^{\\em\na}$ & $5^{\\em a}$ & $<2$& -- & --\\\\\n$1.25\\pm0.03$ & $4.98\\pm0.07$ & $2.2\\pm0.2$ & $2.8\\pm0.3$ &\n$6.7\\pm0.3$ & $5.0\\pm0.4$ & $3.1\\pm0.3$& $5.27\\pm0.07$ & $4.2\\pm0.8$ \\\\\n$1.35\\pm0.03$ & $5.40\\pm0.05$ & $2.2\\pm0.2$ & $4.1\\pm0.3$ &\n$7.5\\pm0.7$ & $5.4\\pm0.7$ & $2.6\\pm0.4$ &\n$5.74\\pm0.05$ & $4.9\\pm1.0$ \\\\\n$1.46\\pm0.03$ & $5.65\\pm0.05$ & $2.5\\pm0.2$ & $4.0\\pm0.2$ &\n$8.4\\pm1.1$ & $8.5\\pm1.7$ & $2.5\\pm0.4$ &\n$5.87\\pm0.05$ & $4.7\\pm0.9$ \\\\\n$1.54\\pm0.03$ & $5.67\\pm0.12$ & $2.9\\pm0.5$ &\n$3.3\\pm0.5$ & $7.5^{+1.4}_{-0.8}$ & $9^{+5}_{-2}$ &\n$2.8\\pm0.6$ & $5.83\\pm0.18$ & $4.3\\pm1.6$ \\\\\n$1.65\\pm0.03$ & $5.9\\pm0.2$ & $5.3\\pm0.7$ & $3.2\\pm0.1$ & $8^{\\em a}$\n& $5^{\\em a}$& $<2.3$ & -- & --\\\\\n$1.75\\pm0.03$ & $6.1\\pm0.3$ & $5.2\\pm0.9$ &\n$2.4\\pm0.2$ & -- & -- & -- & -- & --\\\\\n$1.85\\pm0.04$ & $7.1\\pm0.8$& $6.7\\pm1.6$ & $2.1\\pm0.2$& -- & -- & --& -- & --\\\\\n$1.95\\pm0.04$ & $6.3\\pm0.9$ & $5\\pm3$ & $1.7\\pm0.3$ & --& -- & --& -- & --\\\\\n$2.05\\pm0.03$ & $5.6\\pm1.4$ & $12\\pm4$&$2.6\\pm0.4$& -- & -- & --& -- & --\\\\\n$2.15\\pm0.03$ & $ 4^{+3}_{-10}$ & $22^{+15}_{-8}$ &\n$3.2^{+1.6}_{-0.5}$& -- & -- & --& -- & --\\\\ \n\\tableline\n\\end{tabular}\n\\end{center}\n\\tablenotetext{a}{Parameter fixed at this value}\n\\caption{Properties of the NBO fitted using one or two Lorentzians, as\na function of $\\rm{S_z}$ in the 5.0--60 keV band.\\label{nbo_tab}}\n\\end{table*}\n\\par\n\\noindent\nAs the NBO got stronger towards the middle of the NB the profile of\nthe NBO became detectably asymmetric (see Fig.~\\ref{NBO_asym});\nbetween $\\rm{S_z}$=1.25 and 1.54 the NBO was fitted using two\nLorentzians. The FWHM of the NBO as a function of the position along\nthe NB was first decreasing from $~\\sim$10 Hz at $\\rm{S_z}$=1.038 to\naround 2.5 Hz on the middle part of the NB ($\\rm{S_z}$ values from\n1.25--1.54), and then increased again to $~\\sim$ 5 Hz on the lowest\npart of the NB.\n\\begin{figure*}[]\n\\centerline{\\psfig{figure=NBO_asym.ps,width=15cm}}\n\\figcaption{Typical Leahy normalized power spectrum on the NB showing\nthe NBO in the energy band 5.0--60 keV (in the $\\rm{S_z}$ 1.2--1.5\nrange). The asymmetry of the profile is clearly visible; the drawn\nline represents the best fit model, using two Lorentzian peaks. The\ndotted line and the dash-dotted line represent the two\nLorentzians.\n\\label{NBO_asym}}\n\\end{figure*}\n\\par\n\\noindent\nDue to the fact that the NBO profiles had to be fitted using two\nLorentzians in part of the data, the behavior of the NBO frequency as a\nfunction of $\\rm{S_z}$ is also not determined\nunambiguously. Therefore, we weighted the frequencies of these two\nLorentzians according to one over the square of the FWHM. The FWHM\nweighted average of the two centroid frequencies of the two\nLorentzians used to describe the NBO was consistent with a small\nincrease as a function of $\\rm{S_z}$ from $5.27\\pm0.07$ Hz at\n$\\rm{S_z}$=1.25 to $5.83\\pm0.18$ Hz at $\\rm{S_z}$=1.54.\\par\n\\noindent\nWe combined all power spectra with an $\\rm{S_z}$ between 1.0 and 1.9\nin order to investigate the energy dependence of the NBO. The rms\namplitude of the NBO increased as of function of photon energy (see\nFigure~\\ref{en_dep} [squares]). \n\n\\subsection{KHz QPOs} \n\\label{khz_res}\n\\noindent\nUsing the HBO frequency selection method in all data combined, the\nfrequency of the kHz QPO peaks increased from $197^{+26}_{-70}$ Hz to\n$565^{+9}_{-14}$ Hz and from $535^{+85}_{-48}$ Hz to $840\\pm21$\nHz for the lower and upper peak, respectively, while the frequency of\nthe HBO increased from $20.55\\pm0.02$ Hz to $48.15\\pm0.08$ Hz. Using\nthe $\\rm{S_z}$ selection method on the three data sets we defined in\nSection~\\ref{analysis} (Figure~\\ref{fig_HIDs}), we found that the\nrelation between the kHz QPO and the HBO is consistent with being the\nsame in all three data sets (Fig.~\\ref{kHz_vs_HBO_two_selection} upper\npanel). The same relation was found when we combined all data and\nselected the power spectra according to the HBO frequency. \n\\begin{figure*}[]\n\\centerline{\\psfig{figure=kHz_vs_HBO_delta_vs_upper.ps}}\n\\figcaption{Upper panel: Relation between the lower and upper kHz QPO\npeak frequencies and the HBO frequency, as measured using all the data\nselected according to their HBO frequency in the 5--60 keV energy band\n(filled large squares), and using data from observations 1, and 9--18\ncombined (bullets; see Jonker et al. 1998), data from observations\n2--8 combined (stars), and data from observations 19--25 combined\n(diamonds) selected according to the $\\rm{S_z}$ selection method. The\nerror bars on the HBO frequency are small compared to the size of the\ndata points, and are therefore omitted. Lower panel: The peak\nseparation vs. upper kHz QPO frequency as measured when selected\naccording to HBO frequency. The solid, dashed, and dash-dotted lines\nrepresent the predicted relations between the peak separation and the\nKeplerian frequency in the Stella \\& Vietri (1999) model for a neutron\nstar mass of 1.4, 2.0, and 2.2 $M_{\\odot}$,\nrespectively.\n\\label{kHz_vs_HBO_two_selection}}\n\\end{figure*}\n\\par\n\\noindent\nUpper limits on the kHz QPOs were determined with the FWHM fixed at\n150 Hz. When only one of the two kHz QPO peaks was detected the upper\nlimit on the other peak was determined by fixing the frequency at the\nfrequency of the detected peak plus or minus the mean difference\nfrequency between the two peaks, depending on whether the lower or the\nupper peak was detected. The properties of the kHz QPOs as determined\nin all data combined when selected according to the HBO frequency are\nlisted in Table ~\\ref{khztable}.\n\\begin{table*}\n\\footnotesize\n\\begin{center}\n\\begin{tabular}{lllllll}\n\\tableline\n\\tableline\n$\\nu_{HBO}$ (Hz) & Upper & FWHM upper & Rms upper & Lower & FWHM lower &\nRms lower \\\\\n & kHz $\\nu$ (Hz) & peak (Hz) & peak (\\%) & kHz $\\nu$ (Hz) & peak (Hz)\n& peak (\\%) \\\\\n\\tableline\n$20.55\\pm0.02$ & $535^{+85}_{-48}$ & $334^{+103}_{-172}$ &\n$4.2^{+0.8}_{-1.2}$ & $197^{+26}_{-70}$ & $171^{+377}_{-94}$ &\n$3.1^{+3.7}_{-0.8}$ \\\\\n$23.16\\pm0.02$ & $552\\pm20$ & $176\\pm43$& $3.3\\pm0.4$ &\n$252\\pm17$ & $125\\pm58$ & $2.7\\pm0.5$ \\\\\n$25.02\\pm0.02$ & $605\\pm14$ & $170\\pm34$ &\n$3.6\\pm0.4$ & $246\\pm40$ & $208^{+151}_{-85}$ &\n$2.8^{+1.0}_{-0.5}$ \\\\\n$27.04\\pm0.02$ & $ 625\\pm12$ & $156\\pm36$ & $3.3\\pm0.3$ &\n$269\\pm11$ & $63\\pm25$ & $2.0\\pm0.3$\\\\\n$28.81\\pm0.03$ & $614\\pm27$ & $229^{+118}_{-80}$ &\n$3.1\\pm0.6$ & $275^{\\em a}$ & $150^{\\em a}$ & $<1.4$ \\\\\n$30.94\\pm0.04$ & $709\\pm17$ & $189\\pm50$ &\n$3.4\\pm0.4$ & $296\\pm12$ & $100\\pm38$ & $2.5\\pm0.4$\\\\\n$31.8\\pm0.3$ & $702\\pm7$ & $83\\pm18$ & $2.7\\pm0.2$ &\n$351\\pm19$ & $152^{+92}_{-52}$ & $2.4\\pm0.5$ \\\\\n$33.09\\pm0.02$ & $729\\pm13$ & $119\\pm31$ & $2.7\\pm0.3$ &\n$390^{\\em a}$ & $150^{\\em a}$ & $<2.4$ \\\\\n$36.82\\pm0.05$ & $720^{+17}_{-69}$ & $209^{+389}_{-71}$ &\n$3.5^{+2.7}_{-0.5}$ & $382^{\\em a}$ & $150^{\\em a}$ & $<2.4$ \\\\\n$40.00\\pm0.06$ & $809\\pm14$ & $86\\pm49$ &\n$1.9^{+0.2}_{-0.4}$ & $452\\pm7$ & $35\\pm27$ & $1.2\\pm0.3$\\\\\n$43.81\\pm0.07$ & $802\\pm6$ & $62^{+30}_{-18}$ &\n$1.8\\pm0.3$ & $500\\pm18$ & $73\\pm31$ & $1.3\\pm0.2$\\\\\n$48.15\\pm0.08$ & $840\\pm21$ & $109\\pm61$ &\n$1.2\\pm0.3$ & $565\\pm12$ & $69^{+46}_{-29}$ & $1.1\\pm0.2$\\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\tablenotetext{a}{Parameter fixed at this value}\n\\caption{Properties of the kHz QPOs as determined in all 5.0--60 keV\ndata combined, selected according to the HBO\nfrequency.\\label{khztable}}\n\\end{table*}\n\\par\n\\noindent\nThe kHz QPO peak separation was consistent with being constant at\n339$\\pm$8 Hz over the observed kHz QPO range\n(Fig.~\\ref{kHz_vs_HBO_two_selection} lower panel), but a decrease\ntowards higher upper peak frequencies similar to that found in\nSco~X--1 (van der Klis et al. 1997), 4U~1608--52 (M\\'endez et\nal. 1998), 4U~1735--44 (Ford et al. 1998), 4U~1702--429 (Markwardt,\nStrohmayer, \\& Swank 1999), and 4U~1728--34 (M\\'endez \\& van der Klis\n1999) cannot be excluded. The FWHM of neither the lower nor the higher\nfrequency kHz QPO peak showed a clear relation with frequency. The rms\namplitude of the lower and upper kHz QPO peak decreased from 3.1\\% to\n1.1\\%, and from 4.2\\% to 1.2\\%, respectively when the HBO frequency\nincreased from 20.55 to 48.15 Hz.\n\n\\section{Discussion}\n\\noindent\nIn the present work we combined all {\\em RXTE} data presently\navailable for the Z source GX~340+0 using our new selection method\nbased on the frequency of the HBO peak. This allowed us to distinguish\ntwo new components in the low-frequency part of the power\nspectrum. \\par\n\\noindent\nThese two extra components were strongest when the source was at the\nlowest count rates on the HB (see Fig.~\\ref{fig_HIDs}), between\n$\\rm{S_z}=$ 0.48--0.73, i.e., at the lowest inferred $\\dot{M}$. The\nfrequency of one of these components, the sub-HBO component, is close\nto half the frequency of the HBO component. The frequency ratio was\nconsistent with being constant when the frequency of the sub-HBO\nchanged from 9 to 14 Hz. A similar feature at sub-HBO frequencies has\nbeen reported by van der Klis et al. (1997) in Sco\\,X--1. Since the\nfrequency of this component is close to twice the predicted\nLense-Thirring (LT) precession frequency for rapidly rotating neutron\nstars (Stella \\& Vietri 1998), we shall discuss the properties of this\ncomponent within this framework. \\par\n\\noindent\nThe other component we discovered, the HBO shoulder component, was\nused to describe the strong excess in power in the HBO profile towards\nhigher frequencies. If this shoulder component is related to the HBO\nand not to a completely different mechanism which by chance results in\nfrequencies close to the frequency of the HBO, it can be used to\nconstrain the formation models of the HBO peak. We demonstrated that\nboth the HBO and the NBO have a similar asymmetric profile. In the NBO\nthis was previously noted by Priedhorsky et al. (1986) in Sco~X--1. We\nshall consider the hypothesis that the formation of this shoulder is a\ncommon feature of the two different QPO phenomena, even if the two\npeaks themselves perhaps occur due to completely different physical\nreasons. \\par\n\\noindent\nOur results on the kHz QPOs based on more extensive data sets at three\ndifferent epochs and using the new HBO selection method are consistent\nwith those of Jonker et al. (1998). We discuss the properties of the\nkHz QPOs within the framework of precessing Keplerian flows (Stella \\&\nVietri 1999), the sonic point model (Miller, Lamb, \\& Psaltis\n1998), and the transition layer model described by Osherovich \\&\nTitarchuk (1999), and Titarchuk, Osherovich, \\& Kuznetsov (1999).\n\n\\subsection{Comparison with other observations}\n\\noindent\nIn various LMXBs, QPOs have been found whose profiles are clearly not\nsymmetric. Belloni et al. (1997) showed that for the black hole\ncandidate (BHC) GS~1124--68 the QPO profiles are asymmetric, with a\nhigh frequency shoulder. Dieters et al. (1998) reported that the 2.67\nHz QPO of the BHC 4U~1630--47 was also asymmetric with a high\nfrequency shoulder. In the Z source Sco~X--1 the NBO profile was also\nfound to be asymmetric (Priedhorsky et al. 1986). It is clear that\nasymmetric shapes of the QPO profiles are frequently observed in LMXBs\nand are not restricted to either the black hole candidates or the\nneutron star systems.\\par\n\\noindent\nIn the BHCs GS~1124--68 (Belloni et al. 1997) and XTE~J1550--564\n(Homan et al. 1999) several QPOs were discovered which seem to be\nharmonically related in the same way as we report for GX~340+0,\ni.e. the third harmonic is not detected, while the first, the second\nand the fourth harmonic are. If this implies that these QPOs are the\nsame, models involving the magnetic field of the neutron star for\ntheir origin could be ruled out. The time lag properties of the\nharmonic components of the QPOs in XTE~J1550--564 are complex and\nquite distinctive (Wijnands, Homan, \\& van der Klis 1999). In GX~340+0\nno time lags of the harmonic components could be measured, but the\ntime lags measured in the HBO in the similar Z source GX~5--1 (Vaughan\net al. 1994) are quite different. \\par\n\\noindent\nIn order to study in more detail the relationship found by Wijnands \\&\nvan der Klis (1999) between the QPOs and the noise break frequency in\nthe power spectrum of LMXBs, we fitted the LFN component using a\nbroken power law. To determine the value for the break frequency we\nfixed the parameters of all other components to the values found when\nusing a cut-off power law to describe the LFN. Wijnands \\& van der\nKlis (1999a) reported that the Z sources did not fall on the relation\nbetween the break and QPO frequency established by atoll sources and\nblack hole candidates. They suggested that the Z source LFN is not\nsimilar to the atoll HFN but the noise component found in Sco~X--1 at\nsub-HBO frequencies is. By using the centroid frequency of that peaked\nnoise component as the break frequency instead of the LFN break\nfrequency, the HBO frequencies did fall on the reported relation. On\nthe other hand, we find that using the sub-HBO frequency instead of\nthe HBO frequency together with the LFN break frequency, the Z source\nGX~340+0 also falls exactly on the relation. Therefore, the\nsuggestion made by Wijnands \\& van der Klis (1999a) that the strong\nband-limited noise in atoll and Z sources have a different origin is\nonly one of the two possible solutions to the observed\ndiscrepancy. Our proposed alternative solution is that the Z and atoll\nnoise components are the same, but that it is the sub-HBO in Z sources\nwhich corresponds to the QPO in atoll sources. An argument in favour\nof the noise components in Z and atoll sources being the same is that\nthe cut-off frequency of the LFN component increased as a function of\n$\\rm{S_z}$, in a similar fashion as the frequency associated with the\natoll high frequency noise (van der Klis 1995, Ford \\& van der Klis\n1998, van Straaten et al. 1999). \\par\n\\noindent\nFollowing Psaltis, Belloni, \\& van der Klis (1999) we plotted the\nsub-HBO frequency against the frequency of the lower-frequency kHz\nQPO. The sub-HBO does not fall on the relation found by Psaltis,\nBelloni, \\& van der Klis (1999) between the frequency of the HBO and\nthe lower-frequency kHz QPO frequency. Instead the data points fall\nbetween the two branches defined by the HBO-like QPO frequencies\nvs. the lower kHz QPO frequency at high frequencies (see Psaltis,\nBelloni, \\& van der Klis 1999).\n\n\\subsection{HBO -- kHz QPO relations}\n\\subsubsection{Lense-Thirring precession frequency}\n\\noindent\nStella \\& Vietri (1998) recently considered the possibility that the\nHBO is formed due to the LT precession of the nodal points of sligthly\ntilted orbits in the inner accretion disk, but as they already\nmentioned the Z sources GX~5--1 and GX~17+2 did not seem to fit in\nthis scheme. For reasonable values of I/M, the neutron star moment of\ninertia divided by its mass, the observed frequencies were larger by a\nfactor of $\\sim$2 than the predicted ones. Jonker et al. (1998) showed\nthat for GX~340+0 the predicted frequency is too small by a factor of\n3, if one assumes that the higher frequency peak of the kHz QPOs\nreflects the Keplerian frequency of matter in orbit around the neutron\nstar, and that the mean peak separation reflects the neutron star spin\nfrequency. Using the same assumptions Psaltis et al. (1999) also\nconcluded that a simple LT precession frequency model is unable to\nexplain the formation of HBOs in Z sources. \\par\n\\noindent\nDetailed calculations of Morsink \\& Stella (1999) even worsen the\nsituation, since their calculations lower the predicted LT\nfrequencies. They find that the LT precession frequencies are\napproximately a factor of two too low to explain the noise components\nat frequencies $\\sim$20--35 Hz observed in atoll sources (4U~1735--44,\nWijnands \\& van der Klis 1998c; 4U~1728--34, Strohmayer et al 1996,\nFord \\& van der Klis 1998). Stella \\& Vietri (1998) already put\nforward the suggestion that a modulation can be produced at twice the\nLT precession frequency if the modulation is produced by the two\npoints where the inclined orbit intersects the disk plane (although\nthey initially used this for explaining the discrepancy of a factor of\ntwo between the predicted and the observed LT precession frequencies\nfor the Z sources). \\par\n\\noindent\nThe sub-HBO peaked noise component we discovered could be harmonically\nrelated to the HBO component. If the sub-HBO is the second harmonic of\nthe fundamental LT precession frequency, as needed to explain the\nfrequencies in the framework of the LT precession model where the\nneutron star spin frequency is approximately equal to the frequency of\nthe kHz QPO peak separation, the HBO must be the fourth and the\nharmonic of the HBO must be the eighth harmonic component, whereas the\nsixth and uneven harmonics must be much weaker. This poses strong\n(geometrical) constraints on the LT precession process. On the other\nhand, if the HBO frequency is twice the LT precession frequency, which\nimplies a neutron star spin frequency of $\\sim$900 Hz (see Morsink \\&\nStella 1999), the frequency of the sub-HBO component is the LT\nprecession frequency, and the frequency of the second harmonic of the\nHBO is four times the LT precession frequency. In that case only even\nharmonics and the LT precession frequency are observed.\n\n\\subsubsection{Magnetospheric beat frequency and radial-flow models}\n\\label{random}\n\\noindent\nIn this section, we discuss our findings concerning the QPOs and the\nLFN component in terms of the magnetic beat frequency model where the\nQPOs are described by harmonic series (e.g. Shibazaki \\& Lamb\n1987). \\par\n\\noindent\nIf the sub-HBO frequency is proven not to be harmonically related to\nthe HBO, the sub-HBO peak might be explained as an effect of\nfluctuations entering the magnetospheric boundary layer\nperiodically. Such an effect will be strongest at low HBO frequencies\nsince its power density will be proportional to the power density of\nthe LFN (Shibazaki \\& Lamb 1987). If it is the fundamental frequency\nand the HBO its first overtone then the magnetospheric beat frequency\nmodel proposed to explain the HBO formation (Alpar \\& Shaham 1985;\nLamb et al. 1985) is not strongly constrained. \\par\n\\noindent\nWithin the beat frequency model the high frequency shoulder of the HBO\npeak can be explained as a sign of radial drift of the blobs as they\nspiral in after crossing the magnetospheric boundary layer (Shibazaki\n\\& Lamb 1987). Shibazaki \\& Lamb (1987) describe another mechanism\nwhich may produce a high frequency shoulder. Interference between the\nLFN and the QPO caused by a non uniform phase distribution of the\nblobs will also cause the QPO to become asymmetric. This effect will\nbe strongest when the LFN and the QPO components overlap, as\nobserved. Finally, an asymmetric initial distribution of frequencies\nof the blobs when entering the magnetospheric boundary layer may also\nform an asymmetric HBO peak. \\par\n\\noindent\nThe changes in the power law index of the LFN as a function of photon\nenergy can be explained by varying the width or the steepness of the\nlifetime distribution of the blobs entering the magnetic boundary\nlayer (Shibazaki \\& Lamb 1987). The decrease in increase of both the\nfractional and absolute rms amplitude of the HBO as a function of\nenergy towards higher frequencies (Fig.~\\ref{rmsratio}) also\nconstrains the detailed physical interactions occurring in the\nboundary layer. \\par\n\\noindent\nFortner et al. (1989) proposed that the NBO is caused by oscillations\nin the electron scattering optical depth at the critical Eddington\nmass accretion rate. How a high frequency shoulder can be produced\nwithin this model is not clear. Both the HBO and the NBO shoulder\ncomponents were detected when the rms amplitude of the HBO and the NBO\nwas highest. In case of the NBO, this may be a result of the higher\nsignal to noise. Since the rms amplitude of the NBO shoulder component\nis consistent with being $\\sim$2/3 of the NBO rms amplitude (see\nTable~\\ref{nbo_tab}), combining more observations should increase the\nrange over which this shoulder component is detected, if this ratio is\nconstant along $\\rm{S_z}$. In case of the HBO the two components seem\nto merge. While the fractional rms amplitude of the HBO shoulder\ncomponent increased that of the HBO decreased. When the fractional rms\namplitudes were comparable, the HBO was fitted with one\nLorentzian. The rms amplitude of both shoulder components increased in\na similar way as the rms amplitudes of the NBO and the HBO with photon\nenergy. So, the formation of these shoulder components seems a common\nfeature of both QPO forming mechanisms.\n\n\\subsubsection{Radial oscillations in a viscous layer}\nIn Sco~X--1, Titarchuk, Osherovich, \\& Kuznetsov (1999) interpreted\nthe extra noise component in the power spectra (van der Klis et\nal. 1997) as due to radial oscillations in a viscous boundary layer\n(Titarchuk \\& Osherovich 1999). If the noise component in Sco~X--1 is\nthe sub-HBO component in GX~340+0, the model of Titarchuk \\&\nOsherovich (1999) can be applied to the frequencies and dependencies\nwe found for the sub-HBO component in GX~340+0. Fitting our data to\nthe relation between the frequency of the extra noise component and\nthe Keplerian frequency, using the parameters and parametrization\ngiven by Titarchuk, Osherovich, \\& Kuznetsov (1999), we obtained a\nvalue of $C_N=15$ for GX~340+0. This value is much larger than the\nvalue obtained for Sco~X--1 (9.76). According to Titarchuk \\&\nOsherovich (1999) a higher $C_N$ value implies a higher viscosity for\nthe same Reynold's number.\n\n\\subsection{KHz QPOs and their peak separation}\n\\noindent\nRecently, Stella \\& Vietri (1999) have put forward a model in which\nthe formation of the lower kHz QPO is due to the relativistic\nperiastron precession (apsidal motion) of matter in (near) Keplerian\norbits. The frequency of the upper kHz QPO peaks is the Keplerian\nfrequency of this material. The peak separation is then equal to the\nradial frequency of matter in a nearly circular Keplerian orbit, and\nis predicted to decrease as the Keplerian frequency increases and\napproaches the predicted frequency at the marginally stable circular\norbit. This model can explain the decrease in peak separation as\nobserved in various sources (see Section~\\ref{khz_res}). \\par\n\\noindent\nBeat frequency models stating that the upper kHz QPO peak is formed by\nKeplerian motion at a preferred radius in the disk (e.g. the sonic\npoint radius, Miller, Lamb, \\& Psaltis 1998), whereas the lower kHz\nQPO peak formed at the frequency of the beat between the neutron star\nspin frequency and this Keplerian frequency, cannot in their original\nform explain the decrease in peak separation in these two sources. A\nrelatively small extension of the model (Lamb, Miller, \\& Psaltis\n1998) can, however, produce the observed decrease in peak\nseparation.\\par\n\\noindent\nOsherovich \\& Titarchuk (1999) developed a model in which the kHz QPOs\narise due to radial oscillations of blobs of accreting material at the\nmagnetospheric boundary. The lower kHz QPO frequency is in their\nmodel identified with the Keplerian frequency. Besides this QPO\ntwo eigenmodes are identified whose frequencies coincide with the\nupper kHz QPO peak frequency and the frequency of the HBO component in\nthe power spectra of Sco~X--1 (Titarchuk \\& Osherovich\n1999). Interpreting our findings within this framework did not result in\nstringent constraints on the model. \\par\n\\noindent\nWe found that the peak separation is consistent with being constant\n(Fig.~\\ref{kHz_vs_HBO_two_selection} A and B), but neither a decrease\ntowards higher $\\dot{M}$ as in Sco~X--1, 4U~1608--52, 4U~1735--44,\n4U~1702--429, and 4U~1728--34 nor a decrease towards lower $\\dot{M}$,\nas predicted by Stella \\& Vietri (1999) can be ruled out. If the model\nof Stella \\& Vietri turns out to be the right one the mass of the\nneutron star most likely is in the range of 1.8 to 2.2 $M_{\\odot}$\n(see Fig.~\\ref{kHz_vs_HBO_two_selection} B). This is in agreement with\nthe mass of Cyg~X--2 derived by Orosz \\& Kuulkers (1999), and with the\nmasses of the neutron stars derived when interpreting the highest\nobserved kHz QPO frequencies as due to motion at or near the\nmarginally stable orbit (Kaaret, Ford, \\& Chen 1997; Zhang,\nStrohmayer, \\& Swank 1997).\n\n\n\\acknowledgments This work was supported in part by the Netherlands\nOrganization for Scientific Research (NWO) grant 614-51-002. This\nresearch has made use of data obtained through the High Energy\nAstrophysics Science Archive Research Center Online Service, provided\nby the NASA/Goddard Space Flight Center. This work was supported by\nNWO Spinoza grant 08-0 to E.P.J.van den Heuvel. MM is a fellow of the\nConsejo Nacional de Investigaciones Cient\\'{\\i}ficas y T\\'ecnicas de\nla Rep\\'ublica Argentina. 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ApJ, 512, L125\n\\bibitem[M\\'endez 1998]{mendez} M\\'endez, M., et al. 1998, ApJ, 494,\nL65\n\\bibitem[M\\'endez \\& van der Klis 1999]{mendez1999} M\\'endez, M.. \\&\nvan der Klis, M. 1999, ApJ, 517, L51\n\\bibitem[Miller, Lamb, \\& Psaltis 1998]{millersp} Miller, M.C., Lamb,\nF.K., Psaltis, D. 1998, ApJ, 508, 791\n\\bibitem[Oosterbroek et al. 1995]{oosterbroek} Oosterbroek, T., van\nder Klis, M., Kuulkers, E., van Paradijs, J., \\& Lewin, W.H.G., 1995,\nA\\&A, 297, 141 \n\\bibitem[Orosz \\& Kuulkers 1999]{orosz} Orosz, J.A., Kuulkers,\nE. 1999, MNRAS, 305, 1320\n\\bibitem[Osherovich Titarchuk\\& 1999]{osherovich} Osherovich, V.,\nTitarchuk, L. 1999, ApJ, 522, L113\n\\bibitem[Penninx et al. 1991]{penninx} Penninx, W., Lewin, W.H.G.,\nTan, J., Mitsuda, K., van der Klis, M., \\& van Paradijs, J. 1991,\nM.N.R.A.S., 249, 113\n\\bibitem[Priedhorsky et al. 1986]{priedhorsjky} Priedhorsky, W.,\nHasinger, G., Lewin, W.H.G., Middleditch, J., Parmar, A., Stella, L.,\n\\& White, N., 1986, ApJ, 306, L91\n\\bibitem[Psaltis et al. 1999]{hbo-lt_psaltis} Psaltis, D., Wijnands,\nR., Homan, J., Jonker, P.G., van der Klis, M., Miller, M.C., Lamb,\nF.K., Kuulkers, E., van Paradijs, J., \\& Lewin, W.H.G., 1999, ApJ,\n520, 763\n\\bibitem[Psaltis, Belloni, \\& van der Klis 1999]{psaltis} Psaltis, D.,\nBelloni, T., van der Klis, M. 1999, ApJ, 520, 262\n\\bibitem[Revnivtsev, Borozdin, \\& Emelyanov 1999]{rev} Revnivtsev, M.,\nBorozdin, K., Emelyanov, A. 1999, A\\&A, \n\\bibitem[Shirey, Bradt, and Levine (1999)]{shirey} Shirey, R.E.,\nBradt, H.V., \\& Levine, A.M. 1999, ApJ, 517, 472\n\\bibitem[Stella, \\& Vietri (1998)]{stella98} Stella, L., Vietri,\nM. 1998, ApJ, 492, L59\n\\bibitem[Stella, \\& Vietri (1999)]{stella99} Stella, L., Vietri,\nM. 1999, Phys. Rev Lett, 82, 17\n\\bibitem[Stella, Vietri, \\& Morsink 1999]{stella_lt} Stella, L.,\nVietri, M., Morsink, S.M., 1999, ApJ, 524, L63\n\\bibitem[Shibazaki, \\& Lamb (1987)]{shibazaki} Shibazaki, N., Lamb,\nF.K. 1987, ApJ, 318, 767\n\\bibitem[Strohmayer et al. (1996)]{strohmayer} Strohmayer, T.E.,\nZhang, W., Swank, J.H., Smale, A., Titarchuk, L., \\& Day, C. 1996,\nApJ, 469, L9\n%\\bibitem[Terrell, N.J., 1972]{terrell} Terrell, N.J. 1972, ApJ, 174, L35\n\\bibitem[Titarchuk \\& Osherovich 1999]{titarchuk99} Titarchuk,\nL., Osherovich, V., 1999, ApJ, 518, L95\n\\bibitem[Titarchuk, Osherovich, \\& Kuznetsov]{titarchuk} Titarchuk,\nL., Osherovich, V., Kuznetsov, S. 1999, submitted to ApJ\n\\bibitem[van Paradijs et al. 1988]{jvp} van Paradijs, J., Hasinger,\nG., Lewin, W.H.G., van der Klis, M., Sztajno, M., Schulz, N., \\&\nJansen, F. 1988, M.N.R.A.S., 231, 379\n\\bibitem[van der Klis 1994a]{michiel94a} van der Klis, M., 1994a, A\\&A,\n283, 469\n\\bibitem[van der Klis 1994b]{michiel94b} van der Klis M., 1994b,\nApJSuppl, 92, 511\n%\\bibitem[van der Klis 1994c]{michiel94} van der Klis, M. 1994c, ``Lives\n%of the Neutron stars''\n\\bibitem[van der Klis 1995]{michiel95} van der Klis, M, 1995 pag. 252\nin X-Ray Binaries, ed. W.H.G. Lewin, J. van Paradijs, \\& E.P.J. van\nder Heuvel (Cambridge: Cambridge Univ. Press) \n\\bibitem[van der Klis 1997]{scomichiel} van der Klis, M., Wijnands,\nR.A.D., Horne, K., \\& Chen, W. 1997, ApJ, 481, L97\n\\bibitem[van der Klis 1998]{michiel98} van der Klis, M. 1998, in 'The\nmany faces of Neutron Stars', R. Buccheri, J. van Paradijs \\&\nM.A. Alpar (Eds), NATO ASI Series C, Vol. 515, pp. 337-368 (Kluwer\nAcademic Publishers)\n\\bibitem[van der Klis, 1999]{vanderKlis1999} van der Klis, M.,\nProc. of the Third William Fairbank Meeting, in press, astro-ph/9812395 \n\\bibitem[van Straaten et al. 1999]{straaten} van Straaten, S., et\nal. 1999, ApJ, submitted\n\\bibitem[Vaughan et al. 1994]{vaughan} Vaughan, B., van der Klis, M.,\nLewin, W.H.G., Wijers, R.A.M.J., van Paradijs, J., Dotani, T., \\&\nMitsuda, K. 1994, ApJ, 421, 738\n\\bibitem[Wijnands et al. 1997a]{wijn1997a} Wijnands, R.A.D., van der\nKlis, M., Kuulkers, E., Asai, K., \\& Hasinger, G. 1997a, A\\&A, 323, 399\n\\bibitem[Wijnands et al. 1997b]{wijn1997b} Wijnands, R. et al. 1997b,\nApJ, 490, L157\n\\bibitem[Wijnands et al. 1998a]{wijn1998a} Wijnands, R. et al. 1998a,\nApJ, 493, L87\n\\bibitem[Wijnands et al. 1998b]{wijn1998b} Wijnands, R., M\\'endez, M.,\nvan der Klis, M., Psaltis, D., Kuulkers, E., \\& Lamb, F. 1998b, ApJ,\n504, L35\n\\bibitem[Wijnands et al. 1998c]{wijn1998c} Wijnands, R., van der Klis,\nM., M\\'endez, M., van Paradijs, J., Lewin , W.H.G., Lamb, F.K.,\nVaughan, B., Kuulkers, E. 1998c, ApJ, 495, L39\n\\bibitem[Wijnands \\& van der Klis 1998d]{wijnnature} Wijnands, R.,\nvan der Klis, M. 1998d, Nature, 394, 344\n\\bibitem[Wijnands \\& van der Klis 1998e]{atelwijn98e} Wijnands, R.,\n\\& van der Klis, M., 1998e, ATel, 17, 1\n\\bibitem[Wijnands \\& van der Klis 1999a]{wijnands1999a} Wijnands, R.,\n\\& van der Klis 1999a, ApJ, 514, 939\n\\bibitem[Wijnands \\& van der Klis 1999b]{wijnands1999b} Wijnands, R.,\n\\& van der Klis, 1999, ApJ, 512, L39\n\\bibitem[Wijnands, van der Klis, \\& Rijkhorst 1999c]{wijnandsetal}\nWijnands, R., van der Klis, \\& Rijkhorst E. 1999, ApJ, in press\n\\bibitem[Wijnands, Homan, \\& van der Klis 1999]{wijnands1550}\nWijnands, R., Homan, J., \\& van der Klis, M., 1999, ApJ, 526, in press\n\\bibitem[Zhang 1995]{Zhang1} Zhang, W. 1995, XTE/PCA Internal Memo\n\\bibitem[Zhang et al. 1995]{Zhang2} Zhang, W., Jahoda, K., Swank, J.H.,\nMorgan, E.H., \\& Giles, A.B. 1995, ApJ, 449, 930 \n\\bibitem[Zhang, Strohmayer, \\& Swank 1997]{zhang97} Zhang, W.,\nStrohmayer, T.E., Swank, J.H. 1997, ApJ, 482, L167\n\\bibitem[Zhang Strohmayer, \\& Swank 1999]{zhang} Zhang, W.,\nStrohmayer, T.E., Swank, J.H. 1998, ApJ, 500, L167\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002022.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem[Alpar \\& Shaham 1985]{alpar} Alpar, M.A., Shaham, J. 1985,\nNature 316, 239 \n\\bibitem[Belloni et al. (1997)]{belloni} Belloni, T., van der Klis,\nM., Lewin, W.H.G., van Paradijs, J., Dotani, T., Mitsuda, K., \\&\nMiyamoto, S. 1997, A\\&A, 322, 857 \n\\bibitem[Bevington,\\& Robinson (1992)]{bevington} Bevington, P.R., \\&\nRobinson, D.K. 1992, ``Data reduction and error analysis for the\nphysical sciences''\n\\bibitem[Boirin et al. 1999]{boirin} Boirin, L., Barret, D., Olive,\nJ.F., Grindlay, J.E., Bloser, P.F., in ``Broad band spectra of cosmic\nX-ray sources'', proc. of the 32nd COSPAR Meeting, Advances in Space\nResearch, in press, astro-ph/9902237\n\\bibitem[Bradt, Rothschild \\& Swank 1993]{bradtetal} Bradt, H.V.,\nRothschild, R.E., Swank, J.H. 1993, A\\&AS, 97, 355\n\\bibitem[Chakrabarty \\& Morgan 1998]{chakrabarty} Chakrabarty, D. \\&\nMorgan, E. 1998, Nature, 394, 346\n\\bibitem[Dieters et al. (1998)]{dieters} Dieters, S., Belloni, T.,\nKuulkers, E., Harmon, A., Sood, R. 1998, AIU, 6823\n\\bibitem[Dieters \\& van der Klis 1999]{dieters_sco} Dieters, S., van\nder Klis, M., 1999, in press MNRAS\n\\bibitem[Di Salvo et al. 1999]{disalvo} Di Salvo, T., M\\'endez, M.,\nvan der Klis, M., Ford, E.C., Robba, N.R., in prep.\n\\bibitem[Ford, \\& van der Klis 1998]{ford} Ford, E.C., van der Klis,\nM. 1998, ApJ, 506, L39\n\\bibitem[Ford, van der Klis, Kaaret 1998]{ford2} Ford, E.C., van der Klis,\nM., Kaaret, P 1998, ApJ, 498, 41\n\\bibitem[Ford et al. 1998]{ford98} Ford, E.C., van der Klis,\nM., van Paradijs, J., M\\'endez, M., Wijnands, R., Kaaret, P. 1998,\nApJ, 508, L155\n\\bibitem[Fortner et al. 1989]{fortner} Fortner, B., Lamb, F.K.,\nMiller, G.S., 1989, Nature, 342, 775\n\\bibitem[Hasinger \\& van der Klis (1989)]{hasinger} Hasinger, G., \\&\nvan der Klis, M. 1989, A\\&A, 225, 79\n\\bibitem[Homan et al. 1998]{homan} Homan, J., van der Klis, M.,\nWijnands, R., Vaughan, B., \\& Kuulkers, E. 1998, ApJ, 499, 41 \n\\bibitem[Jahoda et al. 1996]{jahoda} Jahoda, K., Swank, J.H., Giles,\nA.B., Stark, M.J., Strohmayer, T., Zhang, W., Morgan, E.H. 1996,\nSPIE, 2808, 59\n\\bibitem[Jonker et al. 1998]{Jonker} Jonker, P.G., Wijnands, R., van\nder Klis, M., Psaltis, D., Kuulkers, E., \\& Lamb, F.K. 1998, ApJ,\n499, L191\n\\bibitem[Kaaret, Ford, \\& Chen 1997]{Kaaret} Kaaret, P., Ford, E.C.,\nChen, K. 1997, ApJ, 480, L27\n\\bibitem[Kuulkers \\& van der Klis 1996]{kuulkers} Kuulkers, E., \\& van der\nKlis, M. 1996, A\\&A, 314, 567\n\\bibitem[Kuulkers et al. 1999]{kuulkercygx2} Kuulkers, E., Wijnands,\nR., \\& van der Klis, M. 1999, MNRAS, 308, 485\n\\bibitem[Lamb et al. 1985]{Lamb85} Lamb, F.K., Shibazaki, N., Alpar,\nM.A., Shaham, J. 1985, Nature, 317, 681\n\\bibitem[Lamb, Miller, \\& Psaltis 1998]{lamb_deltanu} Lamb, F.K.,\nMiller, M.C., Psaltis, D. 1999, proc. of the HEAD meeting, 31, 10.05\n\\bibitem[Leahy et al. 1983]{leahy} Leahy, D.A., Darbro, W., Elsner,\nR.F., Weisskopf, M.C., Sutherland, P.G., Kahn, S., \\& Grindlay, J.E.\n1983, ApJ, 266, 160 \n\\bibitem[Markwardt, Strohmayer, \\& Swank 1999]{markwardt} Markwardt,\nC.B., Strohmayer, T.E., \\& Swank, J.H. ApJ, 512, L125\n\\bibitem[M\\'endez 1998]{mendez} M\\'endez, M., et al. 1998, ApJ, 494,\nL65\n\\bibitem[M\\'endez \\& van der Klis 1999]{mendez1999} M\\'endez, M.. \\&\nvan der Klis, M. 1999, ApJ, 517, L51\n\\bibitem[Miller, Lamb, \\& Psaltis 1998]{millersp} Miller, M.C., Lamb,\nF.K., Psaltis, D. 1998, ApJ, 508, 791\n\\bibitem[Oosterbroek et al. 1995]{oosterbroek} Oosterbroek, T., van\nder Klis, M., Kuulkers, E., van Paradijs, J., \\& Lewin, W.H.G., 1995,\nA\\&A, 297, 141 \n\\bibitem[Orosz \\& Kuulkers 1999]{orosz} Orosz, J.A., Kuulkers,\nE. 1999, MNRAS, 305, 1320\n\\bibitem[Osherovich Titarchuk\\& 1999]{osherovich} Osherovich, V.,\nTitarchuk, L. 1999, ApJ, 522, L113\n\\bibitem[Penninx et al. 1991]{penninx} Penninx, W., Lewin, W.H.G.,\nTan, J., Mitsuda, K., van der Klis, M., \\& van Paradijs, J. 1991,\nM.N.R.A.S., 249, 113\n\\bibitem[Priedhorsky et al. 1986]{priedhorsjky} Priedhorsky, W.,\nHasinger, G., Lewin, W.H.G., Middleditch, J., Parmar, A., Stella, L.,\n\\& White, N., 1986, ApJ, 306, L91\n\\bibitem[Psaltis et al. 1999]{hbo-lt_psaltis} Psaltis, D., Wijnands,\nR., Homan, J., Jonker, P.G., van der Klis, M., Miller, M.C., Lamb,\nF.K., Kuulkers, E., van Paradijs, J., \\& Lewin, W.H.G., 1999, ApJ,\n520, 763\n\\bibitem[Psaltis, Belloni, \\& van der Klis 1999]{psaltis} Psaltis, D.,\nBelloni, T., van der Klis, M. 1999, ApJ, 520, 262\n\\bibitem[Revnivtsev, Borozdin, \\& Emelyanov 1999]{rev} Revnivtsev, M.,\nBorozdin, K., Emelyanov, A. 1999, A\\&A, \n\\bibitem[Shirey, Bradt, and Levine (1999)]{shirey} Shirey, R.E.,\nBradt, H.V., \\& Levine, A.M. 1999, ApJ, 517, 472\n\\bibitem[Stella, \\& Vietri (1998)]{stella98} Stella, L., Vietri,\nM. 1998, ApJ, 492, L59\n\\bibitem[Stella, \\& Vietri (1999)]{stella99} Stella, L., Vietri,\nM. 1999, Phys. Rev Lett, 82, 17\n\\bibitem[Stella, Vietri, \\& Morsink 1999]{stella_lt} Stella, L.,\nVietri, M., Morsink, S.M., 1999, ApJ, 524, L63\n\\bibitem[Shibazaki, \\& Lamb (1987)]{shibazaki} Shibazaki, N., Lamb,\nF.K. 1987, ApJ, 318, 767\n\\bibitem[Strohmayer et al. (1996)]{strohmayer} Strohmayer, T.E.,\nZhang, W., Swank, J.H., Smale, A., Titarchuk, L., \\& Day, C. 1996,\nApJ, 469, L9\n%\\bibitem[Terrell, N.J., 1972]{terrell} Terrell, N.J. 1972, ApJ, 174, L35\n\\bibitem[Titarchuk \\& Osherovich 1999]{titarchuk99} Titarchuk,\nL., Osherovich, V., 1999, ApJ, 518, L95\n\\bibitem[Titarchuk, Osherovich, \\& Kuznetsov]{titarchuk} Titarchuk,\nL., Osherovich, V., Kuznetsov, S. 1999, submitted to ApJ\n\\bibitem[van Paradijs et al. 1988]{jvp} van Paradijs, J., Hasinger,\nG., Lewin, W.H.G., van der Klis, M., Sztajno, M., Schulz, N., \\&\nJansen, F. 1988, M.N.R.A.S., 231, 379\n\\bibitem[van der Klis 1994a]{michiel94a} van der Klis, M., 1994a, A\\&A,\n283, 469\n\\bibitem[van der Klis 1994b]{michiel94b} van der Klis M., 1994b,\nApJSuppl, 92, 511\n%\\bibitem[van der Klis 1994c]{michiel94} van der Klis, M. 1994c, ``Lives\n%of the Neutron stars''\n\\bibitem[van der Klis 1995]{michiel95} van der Klis, M, 1995 pag. 252\nin X-Ray Binaries, ed. W.H.G. Lewin, J. van Paradijs, \\& E.P.J. van\nder Heuvel (Cambridge: Cambridge Univ. Press) \n\\bibitem[van der Klis 1997]{scomichiel} van der Klis, M., Wijnands,\nR.A.D., Horne, K., \\& Chen, W. 1997, ApJ, 481, L97\n\\bibitem[van der Klis 1998]{michiel98} van der Klis, M. 1998, in 'The\nmany faces of Neutron Stars', R. Buccheri, J. van Paradijs \\&\nM.A. Alpar (Eds), NATO ASI Series C, Vol. 515, pp. 337-368 (Kluwer\nAcademic Publishers)\n\\bibitem[van der Klis, 1999]{vanderKlis1999} van der Klis, M.,\nProc. of the Third William Fairbank Meeting, in press, astro-ph/9812395 \n\\bibitem[van Straaten et al. 1999]{straaten} van Straaten, S., et\nal. 1999, ApJ, submitted\n\\bibitem[Vaughan et al. 1994]{vaughan} Vaughan, B., van der Klis, M.,\nLewin, W.H.G., Wijers, R.A.M.J., van Paradijs, J., Dotani, T., \\&\nMitsuda, K. 1994, ApJ, 421, 738\n\\bibitem[Wijnands et al. 1997a]{wijn1997a} Wijnands, R.A.D., van der\nKlis, M., Kuulkers, E., Asai, K., \\& Hasinger, G. 1997a, A\\&A, 323, 399\n\\bibitem[Wijnands et al. 1997b]{wijn1997b} Wijnands, R. et al. 1997b,\nApJ, 490, L157\n\\bibitem[Wijnands et al. 1998a]{wijn1998a} Wijnands, R. et al. 1998a,\nApJ, 493, L87\n\\bibitem[Wijnands et al. 1998b]{wijn1998b} Wijnands, R., M\\'endez, M.,\nvan der Klis, M., Psaltis, D., Kuulkers, E., \\& Lamb, F. 1998b, ApJ,\n504, L35\n\\bibitem[Wijnands et al. 1998c]{wijn1998c} Wijnands, R., van der Klis,\nM., M\\'endez, M., van Paradijs, J., Lewin , W.H.G., Lamb, F.K.,\nVaughan, B., Kuulkers, E. 1998c, ApJ, 495, L39\n\\bibitem[Wijnands \\& van der Klis 1998d]{wijnnature} Wijnands, R.,\nvan der Klis, M. 1998d, Nature, 394, 344\n\\bibitem[Wijnands \\& van der Klis 1998e]{atelwijn98e} Wijnands, R.,\n\\& van der Klis, M., 1998e, ATel, 17, 1\n\\bibitem[Wijnands \\& van der Klis 1999a]{wijnands1999a} Wijnands, R.,\n\\& van der Klis 1999a, ApJ, 514, 939\n\\bibitem[Wijnands \\& van der Klis 1999b]{wijnands1999b} Wijnands, R.,\n\\& van der Klis, 1999, ApJ, 512, L39\n\\bibitem[Wijnands, van der Klis, \\& Rijkhorst 1999c]{wijnandsetal}\nWijnands, R., van der Klis, \\& Rijkhorst E. 1999, ApJ, in press\n\\bibitem[Wijnands, Homan, \\& van der Klis 1999]{wijnands1550}\nWijnands, R., Homan, J., \\& van der Klis, M., 1999, ApJ, 526, in press\n\\bibitem[Zhang 1995]{Zhang1} Zhang, W. 1995, XTE/PCA Internal Memo\n\\bibitem[Zhang et al. 1995]{Zhang2} Zhang, W., Jahoda, K., Swank, J.H.,\nMorgan, E.H., \\& Giles, A.B. 1995, ApJ, 449, 930 \n\\bibitem[Zhang, Strohmayer, \\& Swank 1997]{zhang97} Zhang, W.,\nStrohmayer, T.E., Swank, J.H. 1997, ApJ, 482, L167\n\\bibitem[Zhang Strohmayer, \\& Swank 1999]{zhang} Zhang, W.,\nStrohmayer, T.E., Swank, J.H. 1998, ApJ, 500, L167\n\\end{thebibliography}"
}
] |
astro-ph0002023
|
The relativistic iron line profile in the Seyfert 1 Galaxy IC4329a
|
[
{
"author": "C. Done$^1$"
},
{
"author": "G.M. Madejski$^2$"
},
{
"author": "P.T. \\.{Z}ycki$^3$"
}
] |
We present simultaneous ASCA and RXTE data on the bright Seyfert 1 galaxy IC4329a. The iron line is significantly broadened, but not to the extent expected from an accretion disk which extends down to the last stable orbit around a black hole. We marginally detect a narrow line component, presumably from the molecular torus, but even including this gives a line profile from the accretion disk which is significantly narrower that that seen in MCG--6--30--15, and is much more like that seen from the low/hard state galactic black hole candidates. This is consistent with the inner disk being truncated before the last stable orbit, forming a hot flow at small radii as in the ADAF models. However, we cannot rule out the presence of an inner disk which does not contribute to the reflected spectrum, either because of extreme ionisation suppressing the characteristic atomic features of the reflected spectrum or because the X--ray source is intrinsically anisotropic, so it does not illuminate the inner disk. The source was monitored by RXTE every 2 days for 2 months, and these snapshot spectra show that there is intrinsic spectral variability. The data are good enough to disentangle the power law from the reflected continuum and we see that the power law softens as the source brightens. The lack of a corresponding increase in the observed reflected spectrum implies that either the changes in disk inner radial extent/ionisation structure are small, or that the variability is actually driven by changes in the seed photons which are decoupled from the hard X--ray mechanism.
|
[
{
"name": "ms.tex",
"string": "%&latex209 \n%\\documentstyle[epsf,emulateapj]{article}\n\\documentstyle[11pt,epsf,aaspp4]{article}\n\\def\\Rin{R_{\\rm in}}\n\\def\\Rg{R_{\\rm g}}\n\\def\\Rs{R_{\\rm s}}\n\\def\\mdot{{\\dot m}}\n\\def\\mdcrit{{\\dot m}_{\\rm crit}}\n\\def\\msun{M_{\\odot}}\n\\def\\dm{{\\dot m}}\n\\def\\ref{{\\hang\\noindent}}\n\n\\def\\plotone#1{\\centering \\leavevmode\n\\epsfxsize=0.45\\textwidth \\epsfbox{#1}}\n\\def\\plottwo#1#2{{\\centering \\leavevmode\n\\epsfxsize=0.45\\textwidth \\epsfbox{#1}} \\centering \\leavevmode\n\\epsfxsize=0.45\\textwidth \\epsfbox{#2}}\n\n\n\\righthead{}\n\\lefthead{}\n\n\\begin{document}\n\n\\title{The relativistic iron line profile in the Seyfert 1 Galaxy IC4329a}\n\n\\author{C. Done$^1$, G.M. Madejski$^2$, P.T. \\.{Z}ycki$^3$}\n\\affil{$^1$ Department of Physics, University of Durham, South Road,\n\tDurham DH1 3LE, England; [email protected]}\n\\affil{$^2$ NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA; [email protected]}\n\\affil{ $^3$ Nicolaus Copernicus Astronomical Center, Bartycka 18,\n 00-716 Warsaw, Poland; [email protected]}\n\n\n\\begin{abstract}\n\nWe present simultaneous ASCA and RXTE data on the bright Seyfert 1\ngalaxy IC4329a. The iron line is significantly broadened, but not to\nthe extent expected from an accretion disk which extends down to the\nlast stable orbit around a black hole. We marginally detect a narrow\nline component, presumably from the molecular torus, but even\nincluding this gives a line profile from the accretion disk which is\nsignificantly narrower that that seen in MCG--6--30--15, and is much\nmore like that seen from the low/hard state galactic black hole\ncandidates. This is consistent with the inner disk being\ntruncated before the last stable orbit, forming a hot flow at\nsmall radii as in the ADAF models. However, we cannot rule out the\npresence of an inner disk which does not contribute to the reflected\nspectrum, either because of extreme ionisation suppressing the\ncharacteristic atomic features of the reflected spectrum or because\nthe X--ray source is intrinsically anisotropic, so it does not\nilluminate the inner disk.\n\nThe source was monitored by RXTE every 2 days for 2 months, and these\nsnapshot spectra show that there is intrinsic spectral variability.\nThe data are good enough to disentangle the power law from the\nreflected continuum and we see that the power law softens as the\nsource brightens. The lack of a corresponding increase in the\nobserved reflected spectrum implies that either the changes in disk\ninner radial extent/ionisation structure are small, or that the\nvariability is actually driven by changes in the seed photons which\nare decoupled from the hard X--ray mechanism.\n\n\\end{abstract}\n\n\\keywords{accretion, accretion disks -- black hole physics -- galaxies:\nindividual (IC4329a) -- galaxies: Seyfert -- X-rays: galaxies}\n\n\n\\section{INTRODUCTION}\n\nAccretion of material onto a black hole is known to produce hard\nX--ray ($E \\ge 2$ keV) emission: satellite observations over the last 30 \nyears have\nconclusively shown this to be the case for both stellar mass black\nholes in our own Galaxy, and the supermassive black holes which power\nthe Active Galactic Nuclei (AGN). However, it is still the case that\nthe mechanism by which the gravitational potential energy is converted\ninto high energy radiation is not understood. Standard models of an\naccretion disk (Shakura \\& Sunyaev 1973, hereafter SS) produce copious\nUV and even soft X--ray radiation, but are completely unable to\nexplain the observed higher energy X--ray emission which extends from \nthe disk spectrum out to 200 keV. Clearly something other\nthan the standard model is required, and the two currently favored\ncandidates are either magnetic reconnection above an accretion disk\n(e.g. Galeev, Rosner \\& Vaiana 1979; Haardt, Maraschi \\& Ghisellini\n1994; di Matteo 1998), or that some part of the accretion flow is not\ngiven by the standard disk configuration.\n\nThe recent rediscovery of another stable solution of the accretion\nflow equations lent plausibility to this second possibility. The\nstandard SS accretion disk model derives the accretion flow structure\nin the limit where the gravitational energy released is radiated\nlocally in an optically thick, geometrically thin disk. This contrasts\nwith the new accretion models, where below some critical mass\naccretion rate, $\\dm\\le \\mdcrit$, the material is not dense enough to\nthermalise and locally radiate all the gravitational potential energy\nwhich is released. Instead the energy can be carried along with the\nflow (advected), eventually disappearing into the black hole. These\nsolutions give an X--ray hot, optically thin, quasi--spherical flow\n(Narayan \\& Yi 1995; Esin, McClintock \\& Narayan 1997).\n\nClearly it would be nice to know which (if any!) of these models for\nthe hard X--ray emission is correct. In its most general form the\nproblem comes down to understanding the geometry of the cool,\noptically thick accretion flow. If this extends down to the last\nstable orbit around the black hole then it is unlikely that the\nadvective flow can exist (e.g.\\ Janiuk, \\.{Z}ycki \\& Czerny 1999). \nConversely, if the optically thick disk\ntruncates before this point then a composite model with an outer disk\nand inner, hot, advective flow (ADAF) may be favored. \n\nThe accretion flow can be tracked via X--ray spectroscopy. Wherever hard\nX--rays illuminate optically thick material then this gives rise to a Compton\nreflected continuum and associated iron K$\\alpha$ fluorescence line (e.g.\\\nLightman \\& White 1988; George \\& Fabian 1991; Matt, Perola \\& Piro 1991). The\namplitude of the line and reflected continuum is dependent on the solid angle\nsubtended by the disk to the X--ray source (as well as on elemental \nabundances, inclination and ionisation). The two models outlined above \ncan then be distinguished by the amount of reflection and line, since \nan untruncated disk should subtend a rather larger solid angle \nthan a truncated one. \n\nA survey of AGN showed that Seyfert 1 spectra are consistent with a\npower law X--ray spectrum illuminating an optically thick, (nearly)\nneutral disk, which subtends a solid angle of $\\sim 2\\pi$ (Pounds et\nal. 1990; Nandra \\& Pounds 1994). This then seems to favor the\nmagnetic reconnection picture. However, this contrasts with the\nsituation in the Galactic Black Hole Candidates (GBHC). These are also\nthought to be powered by accretion via a disk onto a black hole, and,\nin their low/hard state, show broad band spectra which are rather\nsimilar to those from AGN, but have an apparently rather smaller\namount of reflection (e.g. Gierli\\'{n}ski et al. 1997; Done \\&\n\\.{Z}ycki 1999). One potential drawback of this comparison\nis that AGN inhabit a more complex environment than the GBHC.\nUnification schemes for Seyfert galaxies propose that there is a\nmolecular torus which enshrouds the nucleus. The molecular torus can\nalso contribute to the reflected spectrum, perhaps distorting our view\nof the very innermost regions in AGN.\n\nThese two potential sites for the reflected component can be distinguished\nspectrally: any features from the accretion disk should be strongly smeared by\nthe combination of special and general relativistic effects expected from the\nhigh orbital velocities in the vicinity of a black hole (Fabian et al. 1989),\nwhereas the molecular torus is at much larger distances so its reflected\nfeatures should be {\\it narrow}. The seminal ASCA observation of the AGN\nMCG--6--30--15 showed that the line is so broad that it requires that the\naccretion disk extends down to {\\it at least} the last stable\norbit in a Schwarzschild metric, with {\\it no} narrow component from the\nmolecular torus (Tanaka et al. 1995; Iwasawa et al. 1996), and that the\nrelativistically smeared material subtended a solid angle of $\\sim 2\\pi$ with\nrespect to the X--ray source. This very clear cut result then seems\nto rule out the advective flows, at least in their simplest form. \n\nHowever, the GBHC again show a rather different picture: they have a\nline which is detectably broad, but not so broad as might be expected\nfor a disk extending all the way down to 3 Schwarzschild radii \n($R_{\\rm Schw} = 2 G M/c^2$; \n\\.{Z}ycki, Done, \\& Smith 1997, 1998, 1999; Done \\& \\.{Z}ycki 1999). This\n{\\it is} consistent with the truncated disk geometry, and so perhaps\nwith the advective flow models. Only in the soft/high state do the\nGBHC seem to show the extreme relativistic smearing and large amount\nof reflection seen in the MCG--6--30--15 spectra (\\.{Z}ycki et al. 1998,\nGierli\\'{n}ski et al. 1999).\n\nIs there a real difference in accretion geometry between GBHC and AGN,\npointing to a difference in radiation mechanism ? This seems unlikely,\nsince both classes are ultimately accreting black holes. Are subtle\nionisation effects masking the derived disk parameters in the GBHC\n(Ross, Fabian \\& Young 1999). Or is MCG--6--30--15 unusual among AGN\n(and GBHC) in having such a relativistic disk? Perhaps MCG--6--30--15\nis an AGN in a state which corresponds to the soft state GBHC?\n\nOne factor supporting the latter is a recent study by Zdziarski, \nLubi\\'{n}ski, \\& Smith (1999) which showed that there is a \ncorrelation between the intrinsic spectral slope, $\\Gamma$, and \nthe solid angle subtended by the reflecting material, \n$\\Omega/2\\pi$. In their plots, MCG--6--30--15 is the \nAGN with the steepest spectrum, and highest amount of reflection. \nThis correlation also holds for individual objects (such as NGC 5548 \nfor AGN and Nova Muscae for the GBHC), where the intrinsic \nspectrum hardens as the amount of reflection decreases. This \nsuggests that there is a universal physical mechanism and/or \ngeometry for both classes, with perhaps a single parameter \ndetermining the state of a given source through a feedback between the\ngeometry and physical conditions in the X--ray emitting region. \nSuch a feedback could be provided by e.g.\\ soft photons from \nthe thermalized fraction of the hard X--rays intercepted by the \nreprocessing medium, and the parameter could be the inner disk \nradius. Perhaps for MCG--6--30--15 (and other soft AGN and the\nsoft state GBHC) the cool accretion disk extends down to the innermost \nstable orbit around the black hole with the X--rays being powered \nby magnetic reconnection above the disk, while for harder spectra \nAGN (and the low state GBHC) the inner disk recedes outwards, \nbeing replaced by an X--ray hot (advective ?) flow. As\nthe disk recedes it subtends a smaller solid angle, so \nthere is less reflection (and less relativistic smearing), but \nthere are also fewer seed photons from the disk (both from\nintrinsic emission and by reprocessing) for Compton scattering \ninto the intrinsic power law, giving a harder intrinsic power \nlaw (\\.{Z}ycki et al. 1999; Zdziarski et al. 1999).\n\nIf this is true, then this clearly predicts that the Fe K$\\alpha$ \nline {\\it in AGN} is not always as broad as in the extreme case of \nMCG-6-30-15 (Tanaka et al.\\ 1995). Previous ASCA studies \non a sample of objects (Nandra et al.\\ 1997) hint towards such a \npossibility, since a whole range of geometries were inferred for\nvarious objects. \n \nHere we test this idea using ASCA, XTE and OSSE data from IC 4329a, \nthe brightest 'typical' Seyfert 1 in the X--ray band (cf. Madejski et\nal. 1995). It lies towards the middle of the $\\Gamma-\\Omega/2\\pi$ plot \nof Zdziarski et al. (1999), and (consequently) has a spectrum very \nclose to that of the mean Seyfert 1 spectrum compiled by Zdziarski \net al. (1995). IC 4329a may then be used as a template for\nSeyfert galaxies as a class, unlike MCG--6--30--15 which has a rather steep\nX--ray spectral index. \n\n\\section{DATA REDUCTION}\n\n\\subsection{ASCA}\n\nThe 1997 campaign for IC 4329a included\nfour ASCA pointings, on August 7, 10, 12, and 16, each\nnominally providing 20 ks of data. The resulting data were extracted\nusing the standard screening procedures, yielding total exposures of\n61 ks for SIS0 and SIS1 (using the {\\tt BRIGHT2} mode), and 78 ks for \nGIS2 and GIS3. The source data were\nextracted from circular regions with radii of 3 arc min for the SISs\nand 4 arc min for the GISs, while background was taken from a\nsource-free regions of the same images. \nThe source showed a clear variability between the\nfour pointings, with GIS2 counting rates of $1.77 \\pm 0.009$, \n$1.27 \\pm 0.008$, $1.53 \\pm 0.009$, and $1.78 \\pm 0.009$, matching the \nvariability seen in the simultaneous RXTE data (see below and Fig. 1). \nThe PHA data were then grouped so as to have more than 20 counts per \nbin. \n\n\\subsection{RXTE: PCA}\n\nIC4329a was observed a total of 66 times over a period of 58 days with\nRXTE. The PCA standard 2 data were extracted from all layers of\ndetectors 0,1 and 2, using standard selection criteria (Earth\nelevation angle $> 10^\\circ$, offset between the source and the\nsatellite pointing direction $< 0.02^\\circ$, electron rates in each\ndetector $< 0.1$, excluding data taken within 30 minutes of the SAA\npassage). This gave a total of 73 ks of good data. The background for\nthese data were then modeled using the 'L7' model (see Zhang et\nal. 1993; Madejski et al. 1999; and Jahoda et al. 2000, in preparation), and\nthe corresponding response matrix for each observation was generated\nusing version 3.0 of the channel to energy conversion file. We use\ndata from 3--20 keV, since lower energies are affected by response\nmatrix uncertainties and the background may not be well modeled above\n20 keV. A 1\\% systematic error is applied to data in all PHA\nchannels. \n\n\\subsection{RXTE: HEXTE}\n\nThe HEXTE instrument onboard RXTE (cf. Rothschild et al. 1998)\nconsists of two scintillator modules, sensitive in the hard X--ray\nband. The background is measured via \nchopping the detectors to off-axis, source free locations every \n16 seconds. The HEXTE data were extracted using standard data \nreduction procedures, which, after appropriate dead-time correction, \nyielded a total net exposure of $\\sim 24$ ks. The source was \nclearly detected in each pointing over the range of 15 -- 100 keV\nrange, at a level consistent with \nthe PCA, but the statistical errors in each pointing were too\nlarge to study variability. The resultant data were binned such that \nchannels 17--28 (16.9-28.3 keV) \nwere grouped by a factor 3, 29--48 (28.3--47.8 keV) by a factor 4 and\n49--120 (47.8--123.4 keV)\nby a factor 6. The effective area of both HEXTE clusters was\nscaled by 0.7, the current best normalization to the Crab spectrum. \n\n\\subsection{OSSE}\n\nOSSE pointed at IC~4329a during the CGRO viewing period 625, over the\nepoch of 1997 August 8 to 18, with the total exposure of 567 ks. \nThe data were reduced in a standard manner (see Johnson et al. 1997 and\nreferences therein), resulting in a net counting rate of $0.18 \\pm\n0.08$ counts s$^{-1}$ over the 50 -- 500 keV range. The resulting \ndata were binned such that channels 9--18 were grouped by a factor \n5, while 19--48 were grouped by a factor 10. \n\n\\subsection{Lightcurves}\n\nFigure 1 shows the 2--10 keV light curve obtained from the RXTE PCA\ndata. The source is clearly variable on timescales of a few days, with \nan {\\it r.m.s} variation of 13\\%. There is no significant \nshort timescale variability within each observations. These typically\nhave 3$\\sigma$ upper limits of 0.06 to the fractional {\\it r.m.s}\nvariability of the 1000--2000 second lightcurve binned on 16 seconds.\nThe horizontal lines on Figure 1 mark the times at which ASCA and OSSE \ndata were taken.\n\n\\begin{figure*}\n\\plotone{figure1.ps}\n\\figcaption{XTE PCA count rate showing the variability throughout the \nmonitoring campaign. The times of the ASCA and OSSE observations are \nmarked by the horizontal lines}\n\\end{figure*}\n\n\n\\section{SPECTRAL FITTING}\n\nThe data were fitted using XSPEC v10.0, with errors quoted as 90\\%\nconfidence intervals ($\\Delta\\chi^2=2.7$). We use elemental \nabundances and cross-sections of Morrison \\& McCammon (1983).\n\n\\subsection{ASCA SIS and GIS}\n\nData from SIS0 and SIS1 \nare showing increasing divergence with time from the GIS2 and GIS3 (and\nfrom each other) at low energies. The reasons for this are not yet\nwell understood (Weaver \\& Gelbord 1999, in preparation). A\ncurrent pragmatic approach is to allow excess absorption in the SIS\ndetectors to account for this effect to zeroth order. \n\nAnother source of low energy complexity is the partially ionized\nabsorber, first seen in the ROSAT PSPC spectrum (Madejski et al. 1995). \nA previous ASCA observation has shown that in IC4329a this complex\nabsorption is better modeled by two edges (corresponding to H and\nHe--like Oxygen at rest energies of 0.739 and 0.871 keV, respectively) rather\nthan a full ionized absorber code (Cappi et al. 1996; Reynolds 1997\nsee also the discussion in George et al. 1998). We\nuse this description here, but we caution that the determination of this\nabsorption in our data will be somewhat dependent on the way the low energy\ncalibration problems are treated.\n\nWe first use a\nphenomenological model for the ASCA data, consisting of an underlying\npower law and its reflected continuum from a neutral disk ({\\tt\npexrav}: Magdziarz \\& Zdziarski 1995) \ninclined at $30^\\circ$, together with a separate Gaussian\niron line, with the two edge description for the warm absorber. \nThis model gives a good fit to the data ($\\chi^2_\\nu=2533/2392$), \nfor an intrinsic power law spectrum of $\\Gamma=1.85\\pm 0.03$, \nand reflector solid angle (for an inclination of\n$30^\\circ$) of $\\Omega/2\\pi=0.48_{-0.31}^{+0.34}$. \nThe associated iron K$\\alpha$\nfluorescence line is at a (rest frame) energy of $6.37\\pm 0.06$ keV, \nwith equivalent width of $180\\pm 50$ eV and intrinsic width of\n$\\sigma = 0.39\\pm 0.10$ keV (hereafter all intrinsic line widths are \nthe gaussian $\\sigma$).\n\nThe iron line physical width is similar to that seen in a previous \nobservation of this \nAGN (Mushotzky et al. 1995; Cappi et al. 1996; Reynolds 1997), but is\nmuch smaller than that seen from the archetypal\nrelativistically smeared line in MCG--6--30--15 (Tanaka et al. 1995).\nOne way to show this is to fit the spectrum in the 2.5--10 keV band (where the\neffects of the ionised absorption is much less) with a simple power law and its\nexpected reflected continuum (with solar abundances, and fixed solid angle\n$\\Omega/2\\pi=1$ at $30^\\circ$ inclination). The fit excludes the 5--7 keV iron\nline range. Figure 2a shows the resulting shape of the line residuals from\nIC4329a, while figure 2b shows those from MCG--6--30--15 for comparison.\n\n\\begin{figure*}\n\\plottwo{figure2a.ps}{figure2b.ps}\n\\figcaption{Residuals of a continuum fit to a power law plus its Compton\nreflected component over the 2.5--10 keV bandpass, excluding the iron line range\nof 5--7 keV. (a) shows the residuals to the ASCA IC4329a data presented here,\nwhile (b) shows residuals to the ASCA long look observation of MCG--6--30--15 of\nTanaka et al (1995). The line is clearly broader and skewed towards\nlower energies in MCG--6--30--15 than in IC4329a.\n}\n\\end{figure*}\n\nReplacing the Gaussian line with a {\\tt diskline} relativistic model (fixing the\ndisk inclination at $30^\\circ$ and line emissivity at $\\propto r^{-\\beta}$ with\n$\\beta=3$) gives that the smearing implies an inner disk radius of\n$48_{-20}^{+33} \\Rg$ ($\\chi^2_\\nu=2540/2392$: a slightly worse fit than the\nsimple broad Gaussian line). This is significantly larger than the last stable\norbit at $6R_g$ ($\\Rg=GM/c^2$, so the last stable orbit at 3 Schwarzchild radii\nis at $6\\Rg$). The derived radius is dependent on the form of the emissivity,\nbut fits to two separate observations of MCG--6--30--15 require $\\beta=3.4_{-0.8}^{+1.3}$ and\n$\\beta=4.4_{-1.1}^{+3.0}$, respectively (Nandra et al 1997), showing that\nthe line emission is strongly weighted towards the innermost radii. We might\nalso expect this on theoretical arguments. The\nenergy emitted per unit area of a disk goes as $r^{-3}$, so this should\ngive the time averaged emissivity from a magnetic corona, as well as being a\ngood approximation to the illumination expected from a central spherical source\n(see appendix A in \\.{Z}ycki\\ et al 1999). Thus we fix $\\beta=3$ in all our \nfits,\nwhich gives $\\Delta\\chi^2 > 20$ for an inner radius equal to the last stable\norbit at {\\it any} inclination.\n \nThe reflection description used above has several drawbacks. Firstly it allows\nthe line to vary in intensity (and energy) without reference to the reflected\ncontinuum. Secondly, the relativistic smearing is only applied to the iron\nline, and not to the reflected continuum also. We replace these components with\nthe reflection model described by \\.{Z}ycki et al. (1999), {\\tt rel-repr}, which\ncalculates the self--consistent line associated with the reflected continuum,\nand then applies the relativistic smearing (including gravitational light\nbending) to this total reprocessed spectrum. The ionisation state is a free\nparameter, and the models are calculated for iron abundance between $1-2\\times$\nsolar. The reprocessor in AGN is generally assumed to be neutral but an\naccretion disk temperature of $\\sim 10$ eV can give a thermal population\ndominated by ions with ionization potential $\\sim 10-30 \\times kT$ (Rybicki \\&\nLightman 1979) i.e. between Fe V -- FeX, which in our model corresponds to $0.3\n< \\xi < 20$. Photo--ionisation by the X--ray source can increase these estimates\nconsiderably.\n\nWe replace the {\\tt pexrav} and {\\tt diskline} components with our\ncombined model for the reprocessed component. We allow the ionisation,\niron abundance, and inner disk radius to be fit parameters, for a fixed\ninclination of $30^\\circ$, and for a fixed line emissivity of $\\propto r^{-3}$.\nThis again gave a disk inner radius of $45_{-18}^{+32} \\Rg$\n($\\chi^2_\\nu=2540/2392$).\n\n\\subsection{ASCA--XTE Simultaneous Data}\n\nWe extracted RXTE data which were taken exactly simultaneously with\nthe ASCA observation (datasets 4,5,6,11,12,13,16,16--01,18,19 and 20),\ngiving a total PCA exposure of 13 ks. The corresponding HEXTE data\nover this short time interval have very low signal to noise so do not\nadd any appreciable constraints. Figure 3a shows the residuals\nresulting from an absorbed power law fit to the PCA data, showing the classic\nsignature of Compton reflection and its associated iron fluorescence\nline ($\\chi^2_\\nu=162.3/42$). Figure 3b shows residuals including a\nbroad gaussian line in the fit. Clearly there are still systematic\nresiduals, with a decrement at the expected energy of the iron edge\nand a rise to higher energies ($\\chi^2_\\nu=50.5/39$). Including a\nreflected continuum component (the {\\tt pexrav} model in xspec,\nassuming solar abundances and inclination of $30^\\circ$) gives\n$\\chi^2_\\nu=11.7/38$, showing that the reflected {\\it continuum }\ncomponent is significantly detected independently of the iron line.\n\n\\begin{figure*}\n\\plottwo{figure3a.ps}{figure3b.ps}\n\\figcaption{XTE data: (a) shows residuals to a simple power law, showing the\nclassic reflection signature. (b) shows the remaining residuals including a\nbroad gaussian line. Plainly the reflected continuum is detected independently\nof the iron line.\n}\n\\end{figure*}\n\nSince the data are simultaneous, we can \nfix the absorption (warm and cold) \nto that seen in the GIS for the same model fit to the ASCA data. This gives \nan excellent fit to the data with $\\chi^2_\\nu=12.6/39$\n(rather too good in fact, showing that the\nstatistics are dominated by the 1 per cent systematic error)\nfor an intrinsic power law spectrum of\n$\\Gamma=1.94\\pm 0.04$,\nand reflector solid angle (for an inclination of\n$30^\\circ$) of \n$\\Omega/2\\pi=0.49^{+0.17}_{-0.14}$. The associated iron K$\\alpha$\nfluorescence line is at a (rest frame) energy of $6.33\\pm 0.13$ keV,\nwith equivalent width of $210 \\pm 45$ eV and intrinsic width (gaussian\n$\\sigma$) of\n$0.49^{+0.19}_{-0.18}$ keV. The PCA 2--10 keV flux is 25 per cent higher than\nthat from ASCA due to absolute flux calibration problems in both instruments:\nASCA gives a Crab 2--10 keV flux of $1.8\\times 10^{-8}$ ergs s$^{-1}$\n(Makishima et al., 1996), while RXTE gives $2.4\\times 10^{-8}$ \nergs s$^{-1}$ (see PCA Crab spectrum at\nhttp://lheawww.gsfc.nasa.gov/users/keith/pcarmf.html) \nand the original Crab calibration is $\\sim 2.15\\times 10^{-8}$ ergs s$^{-1}$ (Toor\n\\& Seward 1974). A more serious discrepancy is in the spectral index, which is\n$\\Delta\\alpha\\sim 0.1$ steeper than that seen in ASCA. \nIt is known that the current RXTE PCA calibration gives\nresults for the Crab which are roughly $\\Delta\\alpha\\sim 0.1$ steeper than the\nindex assumed for the calibration of other instruments (K. Jahoda, private\ncommunication). However, reassuringly, the relative amount of reflection\nequivalent width, energy and intrinsic width of the line \nare consistent with those from the ASCA data, though of course the absolute\nnormalisations are different due to the calibration discrepancies.\nTieing the absorption across the two datasets, together with the \nrelative reflection parameters (the reflector solid angle, its \ninner radius and ionisation state, and the iron line\nenergy, width and equivalent width)\ngives $\\chi^2_\\nu=2548/2435$, not significantly different\nfrom the $\\chi^2_\\nu=2546/2432$ obtained from the separate fits. Thus in what follows we\ntie the relative reflection (and absorber) parameters across the two datasets, and \nlet only the power law spectral index and normalization be free.\n\nWe replace the {\\tt pexrav} and broad Gaussian line with our {\\tt rel-repr}\nmodel. Table 1 shows the results of a joint fit to the ASCA and RXTE PCA data\nfor inclination angles of $30$, $60$ and $72^\\circ$ and for iron abundances of\n$1$ and $2\\times$ solar. \nThe derived inner disk radius is highly correlated with the assumed inclination.\nHigh inclination angles give stronger Doppler effects and so a broader line.\nThe inner disk radius then has to be larger to match the observed line width.\nHowever, {\\it none} of the fits allow the disk to extend down to the innermost\nstable orbit, irrespective of inclination. This also means that \nthe data are not very sensitive to the\ninclination ($\\Delta\\chi^2\\sim 4$, i.e. marginally significant preference for\nhigher inclinations). It is only the broadest components from the very innermost disk\nwhich significantly change the skewness of the line profile (as opposed to its\nwidth) as function of inclination.\n\nThe data {\\it are} sensitive to the iron abundance. They significantly \nprefer supersolar abundances ($\\Delta\\chi^2\\ge 7$), as would be expected from measurements of \nradial abundance gradients in spiral galaxies (e.g. Henry \\& Worthey 1999). \nAnother way to see this is\nthe phenomenological fits give a line equivalent with of $180$ eV, as expected\nfor a solar abundance slab subtending a solid angle of $2\\pi$ (e.g. George \\&\nFabian 1991), yet the solid angle of the reflected continuum in these fits is \napproximately half of this. Figure 4 shows the best fit joint RXTE and ASCA \ndata fit to a disk model with $2\\times$ solar abundance, inclined at $30^\\circ$.\n\n\\begin{figure*}\n\\plotone{figure4.ps}\n\\figcaption{ASCA and simultaneous RXTE data fit to a model in which the\nrelativistic reprocessor is assumed to have twice solar iron abundance, and is\ninclined at $30^\\circ$. The ASCA and RXTE intrinsic power law index is not tied\nbetween the two instruments due to calibration uncertainties.}\n\\end{figure*}\n\n\\begin{deluxetable}{lccccccc}\n \\footnotesize\n \\tablewidth{0pt}\n \\tablecaption{ASCA and simultaneous XTE PCA data fit to the {\\tt rel-repr}\n model }\n \\tablehead{\n\\colhead{${\\rm A_{Fe}}$\\tablenotemark{a}} &\n \\colhead{Inclination} &\n \\colhead{$\\Gamma$\\tablenotemark{b}} &\n \\colhead{Norm at 1 keV} & \n \\colhead{$\\Omega/2\\pi$\\tablenotemark{c}} &\n \\colhead{$\\xi$\\tablenotemark{d} } &\n \\colhead{$\\Rin$\\tablenotemark{e}\\ ($\\Rg$)} &\n\\colhead{$\\chi^2_\\nu$} \\nl\n& & \\colhead{ASCA, XTE} & \\colhead{ASCA, XTE}\\nl\n}\n\\startdata\n\n1 & 30 & $1.87\\pm 0.02$, $1.99_{-0.04}^{+0.03}$ & $0.031, 0.049$ & $0.62^{+0.11}_{-0.13}$\n & $21_{-13}^{+45}$ & $35_{-15}^{+20}$ & 2567/2436 \\nl\n1 & 60 & $1.88\\pm 0.02$, $2.00_{-0.02}^{+0.04}$ & $0.031, 0.05$ & $0.85^{+0.16}_{-0.10}$\n & $12^{+10}_{-8}$ & $90^{+60}_{-30}$ & 2575/2436 \\nl\n1 & 72 & $1.89\\pm 0.02$, $2.02\\pm 0.04$ & $0.031, 0.051$ & $1.25^{+0.23}_{-0.20}$ \n & $7^{+10}_{-5}$ & $110^{+80}_{-38}$ & 2576/2436 \\nl\n2 & 30 & $1.85\\pm 0.02$, $1.94_{-0.02}^{+0.03}$ & $0.030, 0.046$ & $0.55\\pm 0.10$ \n & $4_{-3.95}^{+11}$ & $35^{+16}_{-12}$ & 2562/2436 \\nl\n2 & 60 & $1.86_{-0.02}^{+0.01}$, $1.97\\pm 0.02$ & $0.030, 0.048$ & $0.88\\pm 0.11$ \n & $0.01_{-0.01}^{+0.8}$ & $75_{-23}^{+45}$ & 2560/2436 \\nl\n2 & 72 & $1.86\\pm 0.02$, $1.95^{+0.03}_{-0.02}$ & $0.030, 0.048$ & $1.20^{+0.13}_{-0.10}$\n & $0.005_{-0.005}^{+0.3}$ & $90_{-25}^{+40}$ & 2558/2436 \\nl\n\n\\enddata\n\\tablenotetext{a}{Iron abundance of reflector relative to solar}\n\\tablenotetext{b}{Photon spectral index}\n\\tablenotetext{c}{Solid angle subtended by the reprocessor with respect to the\nX--ray source}\n\\tablenotetext{d}{Ionization parameter of the reprocessor}\n\\tablenotetext{e}{Inner radius of the accretion disk}\n\n\\end{deluxetable}\n\nSince IC4329a is a Seyfert 1 there could be a contribution\nto the line/reflected continuum from \na molecular torus as well as from the accretion disk (Ghisellini, Haardt \\& \nMatt 1994; Krolik, Madau \\& \\.{Z}ycki 1994). \nTable 2 shows the results obtained including a\nneutral, unsmeared reflector, with assumed mean inclination of $60^\\circ$.\nOnly the parameters of the two reflectors are included, since the continuum\nis similar to that derived before. This gives a {\\it significantly} better fit to the data,\ngenerally with $\\Delta\\chi^2\\ge 9$ for the addition of 1 extra free parameter\n(the amount of non--relativistic reflection). \n\nThe double reprocessing model now gives a fit which is as good as or even\nbetter than those from the phenomenological (i.e. unphysical) broad Gaussian\nline/{\\tt pexrav} model. The observed line is fairly broad but also fairly\nsymmetric, contrary to the predictions of a line from an accretion disk which\n{\\it must} also be skewed if it is broad. Adding the second neutral,\nnon--smeared reprocessor gives a narrow core to the line, while the line\nfrom the relativistic reprocessor then fills in a broad (and skewed) line\nwing. The presence of the narrow component means that the relativistic effects\nhave to be more marked than in the single reflector fits in order to make the\ntotal line as broad as before. Thus the derived\ninner disk radius is always rather smaller than before {\\it but still never\nconsistent with the 3 Schwarzschild radii}. The smaller inner radius means that\nthe lower inclination reflected spectra are significantly gravitationally\nredshifted, so requiring the reflector to be somewhat ionized to compensate for\nthis.\n\nThe above discussion assumed that the torus was Compton thick,\ni.e. with $N_H \\gg 10^{24}$ cm$^{-2}$. However, it can still produce\nsubstantial line emission, without the accompanying strong reflected\ncomponent if the torus column is $\\sim 10^{23-24}$\ncm$^{-2}$. Replacing the unsmeared, neutral reflected component by a\nnarrow 6.4 keV line gives a similar series of fits as those shown in Table\n2. In particular, the fits {\\it never} allow the amount of smearing to\nbe as large as expected from the innermost stable orbit of an\naccretion disk, and they show the same preference for twice solar iron\nabundance and inclination angles $> 30^\\circ$.\n\n\\begin{deluxetable}{lccccccc}\n \\footnotesize\n \\tablewidth{0pt}\n \\tablecaption{ASCA and simultaneous XTE PCA data fit to the {\\tt rel-repr}\n model, with relativistic disk and neutral, unsmeared reflection }\n \\tablehead{\n\\colhead{${\\rm A_{Fe}}$\\tablenotemark{a}} &\n \\colhead{Inclination} &\n \\colhead{$\\Omega/2\\pi$\\tablenotemark{b}} &\n \\colhead{$\\Omega/2\\pi$\\tablenotemark{c}} &\n \\colhead{$\\xi$\\tablenotemark{d} } &\n \\colhead{$\\Rin$\\tablenotemark{e}\\ ($\\Rg$)} &\n\\colhead{$\\chi^2_\\nu$} \\nl\n}\n\\startdata\n\n1 & 30 & $0.40\\pm 0.14$ & $0.25_{-0.07}^{+0.09}$ & $120_{-50}^{+110}$ \n & $18_{-6}^{+10}$ & 2550/2435\\nl\n1 & 60 & $0.52_{-0.14}^{+0.13}$ & $0.33_{-0.09}^{+0.14}$ & \n$100_{-55}^{+90}$ \n & $42_{-18}^{+25}$ & 2551/2435\\nl\n1 & 72 & $0.53_{-0.14}^{+0.13}$ & $0.46_{-0.14}^{+0.24}$ & $90_{-55}^{+70}$ \n & $55^{+30}_{-24}$ & 2551/2435\\nl\n2 & 30 & $0.29\\pm 0.11$ & $0.25_{-0.09}^{+0.15}$ \n & $60^{+100}_{-50}$ & $16_{-5}^{+10}$ & 2552/2435 \\nl\n2 & 60 & $0.33_{-0.11}^{+0.10}$ & $0.51^{+0.23}_{-0.18}$ & $5_{-5}^{+40}$ \n & $32_{-10}^{+21}$ & 2545/2435 \\nl\n2 & 72 & $0.31\\pm 0.12$ & $0.85_{-0.35}^{+0.21}$ & $0.06_{-0.06}^{+25}$ \n & $40_{-12}^{+28}$ & 2544/2435 \\nl\n\n\\enddata\n\\tablenotetext{a}{Iron abundance of reflector relative to solar}\n\\tablenotetext{b}{Solid angle subtended by the neutral, unsmeared reprocessor\n(assumed mean inclination of $60^\\circ$) with respect to the\nX--ray source}\n\\tablenotetext{c}{Solid angle subtended by the relativistic reprocessor with respect to the\nX--ray source}\n\\tablenotetext{d}{Ionization parameter of the relativistic reprocessor}\n\\tablenotetext{e}{Inner radius of the relativistic accretion disk}\n\n\\end{deluxetable}\n\nThe series of fits above show that the best physical description of the data is\nwith two reprocessed components, one which is relativistically smeared and\npossibly ionized from the accretion disk, and one which is neutral and \nunsmeared (and possibly consisting of just line rather than line and \nreflected continuum)\nfrom the molecular torus. A similar composite line is seen in the Seyfert\nMCG--5--23-16 (Weaver et al.\\ 1997; see also Weaver \\& Reynolds 1998). \nThe data prefer \nmodels with twice solar abundances, and inclinations of $> 30^\\circ$,\nand these solutions have the advantage that the\nderived ionisation of reflector is generally rather low, consistent\nwith that expected (see section 2). However, there is a further constraint\non the inclination, since the extra reprocessor cannot be along our line\nof sight to the nucleus. IC4329a is classified optically as a Seyfert 1\nand the X--ray spectrum is not heavily absorbed. \nFor a disk inclined at $72^\\circ$ then for our line of sight not to\nintercept the molecular torus severely restricts its scale height, and so the\npossible solid angle it can subtend. Thus while the range of double reflector\nfits given in Table 2 are statistically indistinguishable, these consistency\narguments lead us to favor viewing angles to the accretion disk of $\\sim\n45^\\circ$ and supersolar abundances.\n\nAll these models assumed that the ionisation state of the disk was\nconstant with radius. A more physical picture might be one where the\nionisation varies as a function of radius (e.g. Matt et al. 1993). In\nsuch models, the inner disk might be so ionized that it produces no\nspectral features. The observed reflected spectrum would then arise\nfrom further out in the disk, and so not contain the highly smeared\ncomponents. This might provide an alternative explanation to a\ntruncated disk as to why the relativistic smearing observed is not\ncompatible with a disk extending down to the last stable orbit. We\ntest this by dividing the disk into 10 radial zones, with ionisation \n$\\xi(r)\\propto r^{-4}$ as described in Done \\& \\.{Z}ycki (1999). \nWith the inner radius fixed at $6\\Rg$, and allowing for a narrow component from \nthe molecular torus we are never able to obtain fits within \n$\\Delta\\chi^2\\sim 20$ of those in Table 2.\n\n\\subsection{RXTE PCA Variability}\n\nThere is clear intensity variability during the RXTE campaign, and also\nspectral variability in the sense that the spectrum becomes softer as\nthe source brightens. This could be due to either\nintrinsic change in the power law spectral index, or a change in the\nrelative contribution of the reflected spectrum (or both). \n\nWe can attempt to disentangle the power law from the reflected spectrum\nby fitting these components to the individual spectra from each orbit\n(including a 1 per cent systematic uncertainty), fixing the absorption\nat $3\\times 10^{21}$ cm$^{-2}$. The reflected spectrum is assumed to\nhave twice solar iron abundance, be inclined at $60^\\circ$ and have\nfixed negligible ionisation ($\\xi=0.01$, see table 1). Thus the free\nparameters are the power law index and normalization, the solid angle\nsubtended by the relativistic reflector and its inner radius. Figure\n5a shows these derived parameters as a function of time. Clearly the\ninner radius cannot be constrained, but the index and the solid angle\nof the reflector show some possible trend. Fitting these with\na constant gives $\\chi^2_\\nu=36.0/58$ and $13.4/58$ respectively\ni.e. they are statistically consistent with a constant value. Figure\n5b shows these plotted against the 2--10 keV flux, and a linear\nregression (taking errors in both $x$ and $y$ into account: Press et\nal.\\ 1992) shows that the power law index is {\\it significantly}\ncorrelated with flux, since it gives $\\chi^2_\\nu=25.7/57$. \nThis corresponds to an F value of $10.3/(25.7/57)= 22.8$, \nsignificant at $\\ge 99.9$ per cent. \nEven using just the difference in $\\chi^2$ between the two fits \ngives $F=10.3$, significant \nat $\\ge 99.5$ per cent, so the correlation is clearly\npresent. IC4329a then becomes only the second Seyfert 1 where there is\nclear {\\it intrinsic} spectral variability (the other is NGC 5548:\nMagdziarz et al. 1998), where underlying continuum changes can be\nunambiguously disentangled from changes in the reflected spectrum. \n\nWe use the same procedure to look for variability in the amount of reflection\nas a function of flux. The linear regression\ngives $\\chi^2_\\nu=10.6/57$ \nwhere the fractional amount of reflection relative to the\npower law {\\it decreases} as the flux increases. \nThis is significant at $> 99.9$ per cent confidence on an F test,\nbut is only 90 per cent significant using just the change in \n$\\chi^2$. \n\n\n\\begin{figure*}\n\\plottwo{figure5a.ps}{figure5b.ps} \n\\figcaption{Results for\nfitting a simple power law and its relativistic reflection with\nabsorption fixed at $3\\times 10^{21}$ cm$^{-2}$ to the 3--20 keV\nindividual snapshot PCA spectra. (a) shows the inferred 2--10 keV\nflux, spectral index and derived inner disk radius as a function of\ntime, while (b) shows the spectral index and amount of reflection as a\nfunction of 2--10 keV flux. The power law becomes intrinsically\nsteeper as the source brightens, while the reflected fraction marginally\ndecreases.}\n\\end{figure*}\n\nTo illustrate these points we co--add spectra when the source was at\nits lowest and highest intensity level (see Figure 1), and fit these\nspectra with a power law and single relativistically smeared reflector\n(with reflector parameters fixed as above, and with the disk inner\nradius fixed at $60\\Rg$). The spectral index changes from $1.92\\pm 0.04$\nto $2.00\\pm 0.02$, for the low\nand high state, respectively. Figure 6 shows the unfolded spectra, with\nthe model extrapolated out to 100 keV. The thick and thin lines show\nthe model components for the high and low state data, respectively.\nThe underlying continuum is brighter at all energies $\\le 100$ keV \nin the high state despite it being steeper, with an integrated 0.01--300 keV\nflux of $6.2$ to $10.7 \\times 10^{-10}$ ergs cm$^{-2}$ s$^{-1}$ for\nthe low and high state, respectively. This behaviour is fairly\neasy to reproduce in comptonisation models in which the seed photons\nvary (see discussion), but the (marginally significant) \nlack of change in the absolute amount\nof reflection (so that the relative reflected fraction in the low\nstate is larger than in the high state) is harder to explain.\nClearly a model in which the reflected flux is produced at large\ndistances from the source would be viable, but the\nreflected spectrum is broadened,\nso does contain at least some contribution from the relativistically\nsmeared inner disk. For a $10^8\\msun$ black hole, then the inner 100\nSchwarzschild radii are on scales of $3\\times 10^{15}$ cm, i.e. less\nthan 1 lightday. The spectra are taken at intervals of a day or more,\nso the relativistically smeared reprocessed component should not be\nappreciably lagged behind the source variability.\n\n\\begin{figure*}\n\\plotone{figure6.ps}\n\\figcaption{The high and low state PCA spectra fit to a simple power\nlaw and its relativistic reflection with absorption fixed at $3\\times\n10^{21}$ cm$^{-2}$. The best fit model components are shown in thick\nand thin lines for the high and low state spectra, respectively, where\nthe spectral index and relative amount of reflection are $\\alpha=\n2.00\\pm 0.02$, $1.92\\pm 0.04$, and $\\Omega/2\\pi=\n0.74\\pm 0.13$, $1.07^{+0.25}_{-0.22}$. \nThe model is extrapolated out to 100 keV, showing that the high\nstate power law has higher intensity at all energies of importance for\nthe formation of the reflected continuum, despite being\nsteeper (the pivot energy is at $\\sim 1$ MeV).\n}\n\\end{figure*}\n\nOne possibility is that this anti--correlation of relative reflected\nfraction with flux is intrinsic to the\nsource, that the geometry changes in such a way as to produce less\nreflection as the source brightens and steepens. However, it is very\nhard to see how this can be the case. A brighter, steeper source\nimplies that there are more seed photons for the Compton scattering\n(see Figure 6 and the Discussion),\ni.e. that the geometry is such that more disk photons are intercepted\nby the source. Thus we can easily explain more reflected flux as the\nsource steepens, but not less. A {\\it correlation} of reflected solid\nangle with spectral index is indeed seen in both Galactic Black Hole\nCandidates (e.g. \\.{Z}ycki et al. 1999) and AGN (Zdziarski et al. 1999). It\nseems much more likely that the (marginal) {\\it anti--correlation} is an\nartifact of there being a second reflector at much larger distances\nfrom the source. The light travel time delay then means that the\ndistant reprocessor does not have time to respond to rapid flux\nvariations, so that as the source dims the relative contribution of\nthe reflected spectrum from the distant reprocessor increases.\n\nWe include a reprocessed component from a torus, fixing its parameters\nto the best fit XTE values from the joint ASCA--RXTE fit (see table 2,\nagain assuming twice solar abundance and inclination of $60^\\circ$,\nbut this time also fixing the inner edge of the disk to $60 \\Rg$). The\nsignificance of the correlation of the spectral index with flux is\nunchanged ($\\chi^2_\\nu=44.7/58$ for a constant while adding the linear\nterm gives $\\chi^2_\\nu=29.4/57$), while the flux/accretion disk\nreflection variability is now consistent with a constant solid angle\n($\\chi^2_\\nu=12.4/58$): adding a linear term gives an insignificant\nchange ($\\chi^2_\\nu=11.4/58$). The results are similar for a fixed\nGaussian line rather than a full reprocessed spectrum.\n\nWe illustrate this again by fits to the high and low state spectra.\nFigure 7a shows the confidence contours for the power law spectral\nindex, while Figure 7b shows the derived solid angle of the\nrelativistic reflector. The diagonal lines denote solutions where the\npower law index and reflected fraction remain constant between the two\ndatasets. The power law index is clearly variable between the high and\nlow flux level datasets irrespective of how the reprocessor is\nmodelled. With a single reprocessor then the relative amount of\nreflection is only consistent with remaining constant at the $<90$ per\ncent confidence level. The data prefer a larger contribution of\nreflected flux relative to the power law in the low state spectrum\ni.e. that the absolute normalization of the reflected flux is\nconstant. The dashed and dotted lines show the same contours for a\nmodel including an unsmeared, neutral reprocessed spectrum and\nGaussian line from the molecular torus, respectively. The reflected\nfraction is then consistent with a constant value.\n\n\n\\begin{figure*}\n\\plottwo{figure7a.ps}{figure7b.ps}\n\\figcaption{Confidence contours for (a) the power law spectral index\nand (b) the reflected fraction in the high and low state spectra.\nSolid contours denote a spectral model where the reprocessing is from\nan accretion disk, while the dashed contours include a fixed\ncontribution from reflection from a molecular torus and the dotted\ncontours include a fixed Gaussian line. In (a) the solid straight line\ndenotes constant spectral index. This is plainly outside all the\nmodel contours, strongly requiring that the intrinsic power law index\nchanges. In (b) the solid straight line indicates a constant reflected\nfraction, while the dashed line shows a constant absolute\nnormalisation of the reflected component. Modeling the accretion disk\nalone gives confidence contours which are only marginally consistent\nat the 90 per cent confidence level with a constant reflected\nfraction. Instead the data prefer a constant absolute normalisation\nof the reflected component. Including a constant component (line or\nfull reprocessed spectrum) shifts the derived contours for the\naccretion disk, allowing a constant reflected fraction at higher\nconfidence level. }\n\\end{figure*}\n\n\\subsection{PCA, HEXTE and OSSE Total Spectrum}\n\nAll the RXTE PCA data were co--added to form a single spectrum (with 1\nper cent systematic uncertainty added) and fit together with the HEXTE\nand OSSE data to give a broad band spectrum. Current consensus is that\nthe continuum is formed by Compton scattering of soft seed photons by\nhot electrons. Such a Comptonised continuum can be approximated by a\npower law with exponential cutoff, but this becomes inaccurate if the\nspectrum extends close to the energies of either the seed photons or\nhot electrons. The seed photons are presumably from the accretion\ndisk, with expected temperatures of $\\sim 10$ eV, so the spectral\ncurvature here is not an issue. However, the inclusion of the OSSE\ndata means that the shape of the spectral cutoff from the electron\ntemperature becomes important. Thus we use an analytical approximation\nto a Comptonised spectrum based on solutions of the Kompaneets\nequation (Lightman \\& Zdziarski 1987), where the shape of the high\nenergy cutoff is sharper than an exponential rollover.\n\nThe relativistic reflection and line from this incident continuum are\ncalculated, and included in the model fit. The results are detailed in\nTable 3 for inclinations of the relativistic reprocessor of $30, 60$\nand $72^\\circ$ and iron abundances of $1$ and $2\\times$ solar. We see\nthe same trend as in Table 1 in terms of the spectra preferring higher\niron abundance, and these solutions constrain the electron temperature\nto be $kT_e\\sim 40-100$ keV (corresponding to an exponential e-folding\nenergy of $\\sim 120-300$ keV). Figure 8 shows the best fit solution\nfor twice solar abundance, inclined at $60^\\circ$. However, the poor\nsignal--to--noise of the data at the highest energies means that this\ntemperature is dependent on details of the reflection spectrum. For\nsolar abundances the temperature is generally unconstrained.\n\n\\begin{figure*}\n\\plotone{figure8.ps}\n\\figcaption{The total PCA (crosses), HEXTE (filled squares) and OSSE \n(open squares) spectra, fit to a comptonised\ncontinuum model with $kT_e\\sim 50$ keV, together with its relativistic\nreflection component for an assumed inclination of $60^\\circ$ and twice solar\niron abundance}\n\\end{figure*}\n\n\\begin{deluxetable}{lccccccccc}\n \\footnotesize\n \\tablewidth{0pt}\n \\tablecaption{Total XTE PCA, RXTE HEXTE and CGRO OSSE data fit to an approximate\n comptonised continuum and its relativistically smeared reflection}\n \\tablehead{\n\\colhead{${\\rm A_{Fe}}$\\tablenotemark{a}} &\n \\colhead{Inclination} &\n \\colhead{$\\Gamma$\\tablenotemark{b}} &\n\t\t \\colhead{$kT_e$ (keV)} &\n \\colhead{Norm at 1 keV} & \n \\colhead{$\\Omega/2\\pi$\\tablenotemark{c}} &\n \\colhead{$\\xi$\\tablenotemark{d} } &\n \\colhead{$\\Rin$\\tablenotemark{e}\\ ($\\Rg$)} &\n\\colhead{$\\chi^2_\\nu$} \\nl\n}\n\\startdata\n\n1 & 30 & $1.97\\pm 0.03$ & $90_{-40}^{+360}$ & $0.053$ & $0.48\\pm 0.10$\n & $45_{-30}^{+45}$ & $23_{-14}^{+50}$ & 62.8/91 \\nl\n1 & 60 & $2.00\\pm 0.03$ & $110^{+\\infty}_{-57}$ & $0.055$ & $0.77^\n{+0.17}_{-0.16}$\n & $13_{-8}^{+17}$ & $150^{+\\infty}_{-100}$ & 68.2/91 \\nl\n1 & 72 & $2.01\\pm 0.03$ & $140_{-80}^{+\\infty}$ & $0.056$ &\n $1.20^{+0.33}_{-0.25}$ \n & $8_{-6}^{+11}$ & $160^{+\\infty}_{-100}$ & 68.4/91 \\nl\n2 & 30 & $1.94\\pm 0.02$ & $50_{-15}^{+40}$ & $0.052$ & $0.48^{+0.10}_{-0.09}$ \n & $10_{-9}^{+25}$ & $25^{+75}_{-14}$ & 59.6/91 \\nl\n2 & 60 & $1.96 \\pm 0.03$ & $52^{+46}_{-17}$ & $0.053$ & \n$0.75\\pm 0.16$ \n & $0.7_{-0.7}^{+8}$ & $110_{-55}^{+\\infty}$ & 61.8/91 \\nl\n2 & 72 & $1.97\\pm 0.02$ & $55_{-20}^{+60}$ & $0.054$ & \n$1.14^{+0.21}_{-0.23}$\n & $0.01_{-0.01}^{+3}$ & $100_{-55}^{+\\infty}$ & 60.3/91 \\nl\n\n\\enddata\n\\tablenotetext{a}{Iron abundance of reflector relative to solar}\n\\tablenotetext{b}{Photon spectral index}\n\\tablenotetext{c}{Solid angle subtended by the reprocessor with respect to the\nX--ray source}\n\\tablenotetext{d}{Ionization parameter of the reprocessor}\n\\tablenotetext{e}{Inner radius of the accretion disk}\n\n\\end{deluxetable}\n\nWe note that these data are consistent with previous observations of\nthis source (Madejski et al.\\ 1995), and with the mean Seyfert spectrum\nat high energies (Zdziarski et al.\\ 1995). However, the \ntemperatures of the Comptonizing medium \nderived from these data by Zdziarski et al. 1994) \nare rather higher ($kT\\sim 250$ keV), due to their\nassumption of an exponential rollover as an approximation to a\nComptonised cutoff. This also means that the derived plasma optical\ndepths in these previous papers of $\\tau\\sim 0.1$ are too low.\nModelling the spectrum with more accurate comptonised \nspectra gives $kT\\sim 130$ keV and $\\tau\\sim 1$ (Zdziarski et al. 1996).\n\n\\section{DISCUSSION}\n\n\\subsection{Fe K Line and Overall Spectral Shape}\n\nFirstly, we clearly see that not all AGN are consistent with a\nsubstantial solid angle of extreme, relativistically smeared\nreflection. The reprocessed component seen in MGC--6--30--15 is not\nnecessarily typical of AGN in general. A similar result is seen in a\nrecent analysis of the ASCA spectrum of NGC 5548 (Chiang et al.\\ 1999), \nwhere the line is broad, but not so broad as expected from a disk which \nextends down to the last stable orbit around a black hole (for the June 15th\ndata set they obtain $\\Rin = 18.7^{+29.1}_{-9.5}\\,\\Rg$ for emissivity \n$\\propto r^{-3}$; J.\\ Chiang, private communication). \nCrucially, our data\nallow us to constrain a reflected component from a molecular torus. A\ntorus with column $\\ge 10^{23}$ cm$^{-2}$ can produce a strong, narrow\n6.4 keV line, accompanied by a reflected continuum for columns $\\ge\n10^{24}$ cm$^{-2}$. We do significantly detect such a contribution to\nthe iron K$\\alpha$ line, which may also be accompanied by a reflected\ncontinuum. However, even with a narrow line from the torus, the\nremaining line from the accretion is not as broad as that seen in\nMCG--6--30--15.\n\nThe amount of relativistically smeared reflection is rather less than\nunity for any inclination $\\le 60^\\circ$. Larger inclinations are not\nexpected since this object is classified as a Seyfert 1 and no strong\nabsorption from the torus is seen in the X--ray spectrum. Thus the\nreflection from the accretion disk in IC4329a looks very like that\nseen in the low state spectra of the galactic black hole systems\n(\\.{Z}ycki et al. 1998; Done \\& \\.{Z}ycki 1999) in having $\\Omega/2\\pi < 1$,\nrelativistically smeared by velocities which are inconsistent with the\nreflecting material extending down to 3 Schwarzschild radii. There is\nthen no intrinsic difference between the Galactic and extragalactic\naccreting black holes, but there is a spread in source properties in\nboth classes (intrinsic spectral index, amount of reflection and\namount of relativistic smearing). The AGN results to date show that\nsteep spectra have a larger amount of reflection (Zdziarski et al.\n1999) and more relativistic smearing. This is exactly the sequence\nseen in the Galactic Black Hole Candidate Nova Muscae 1991 (\\.{Z}ycki et al.\n1998; \\.{Z}ycki et al. 1999) as a function of decreasing mass accretion rate.\n\nThere are currently two ways to explain the lack of extreme\nrelativistic line. The first is to say that the inner accretion disk\nis simply not present, that it has been replaced by an X--ray hot\nflow. These composite truncated disk/hot X--ray source models were\nfirst proposed by Shapiro, Lightman and Eardley (1976) when they\ndiscovered a hot, two temperature, optically thin solution to the\naccretion flow equations, though this was subsequently shown to be\nunstable. Such models were given new impetus by the rediscovery of a\nrelated {\\it stable} solution of the accretion flow equations (Narayan\n\\& Yi 1995), which include advective as well as radiative cooling\n(ADAFs). These ideas are clearly consistent with our results.\n\nThe alternative is that the inner disk is present, \nas required by the magnetic reconnection models for the X--ray flux,\nbut that it cannot be seen\nin the reflected spectrum. One way to do this is if the \nupper layers of the disk are so ionized that they produce almost no atomic\nspectral features (Ross et al. 1999). \nSimple models for this, where the ionisation state of the disk varies as a\nsmooth function of radius, do not match the data. However, the ionisation\nstructure could be highly complex, with rapid transition between complete \nionisation and relatively cool material (R\\'{o}\\.{z}a\\'{n}ska 1999; \nS. Nayakshin, private communication).\nAlternatively, if the X--ray source is moving away from the disk\nat transrelativistic velocities, perhaps because of plasma ejection \nfrom expanding magnetic loops, then its radiation pattern \ndoes not strongly illuminate the inner disk (Beloborodov 1999).\n\nIt is currently very difficult to distinguish observationally between\nthese models, and all have some remaining theoretical problems. For\nthe ADAF solutions, it is not yet known whether the fundamental assumptions\nunderlying the solutions can hold, or how a transition from the cool\ndisk to a hot flow can occur, while for the disk--corona geometry the\nuncertainties are mainly in the detailed outcome of magnetic\nreconnection, and in the ionisation structure of the illuminated disk.\n\n\\subsection{Spectral Variability}\n\nOur data sample the source variability, which gives another way to\ninvestigate the underlying radiation mechanisms. This is only the second \nAGN where the reflected\nand intrinsic spectrum can be disentangled (the other is NGC 5548:\nMagdziarz et al.\\ 1998; Chiang et al.\\ 1999). The results show\nthat the power law itself clearly gets intrinsically steeper as the\nsource brightens, which allows to constrain\nthe variability process. If there were merely more dissipation in\nthe X--ray hot corona without an accompanying change in soft seed\nphoton flux then the spectrum would harden as it got brighter (e.g.\\\nGhisellini \\& Haardt 1994). Thus\nthe observed spectral index--flux correlation implies that the soft\nseed photons also increase, and by somewhat more than the increase in\nthe hard flux. Seed photons are thought to arise primarily through\nreprocessing, since the hard X--rays illuminating the disk which are\nnot reflected are thermalised, emerging as soft photons. In this\nmodel the change in soft photons is commensurate with the change\nin flux dissipated in the hot corona. To change the seed photons by\n{\\it more} than the change in hard dissipation requires either a\nchange in geometry, such that the hard X--ray source intercepts a\nlarger fraction of the disk radiation, or a decrease in reflection\nalbedo, so that more of the incident hard X--ray radiation is\nthermalised rather than reflected. The former can be linked to the\ncomposite hot flow/cool accretion disk models as a result of varying\nthe inner disk edge, while the latter could be produced in the\ndisk--corona models if the ionisation state of the disk\ndecreases for steeper spectra, so that the reflection albedo decreases\nand the thermalised soft flux increases. However, recent simultaneous\nobservations of EUV and X--ray variability cast doubt on the simple\nscenario where the EUV seed photon flux is primarily reprocessed\n(Nandra et al.\\ 1998; Chiang et al.\\ 1999). The variability that we see\ncould equally well be the result of a variable soft photon flux\nirradiating the X--ray region.\n\nThese three possibilities predict some differences in the behavior of\nthe reflected continuum. If the disk geometry is changing to give more\nsoft seed photons then we expect more solid angle of reflection as the\nspectrum steepens (as seen in the AGN/XRB compilation of Zdziarski et\nal.\\ 1999). If the increased soft photons are from increasing\nthermalisation in the disk due to decreasing ionisation, then we should\nalso see more cold reflection (as opposed to unobservable, completely\nionized reflection) for steeper spectra. If it is simply the\nirradiating soft flux which is changing, without changing disk\ngeometry then the reflected fraction should remain constant.\n\nWhat we see is marginally (90 per cent confidence contour) consistent\nwith a constant reflected fraction, although the data prefer that the\nrelative amount of reflection {\\it decreases} as the source increases\nand steepens. The resulting spectrum is consistent with the absolute\nnormalisation of the reflected spectrum remaining constant as the\nsource changes. Some part of the reflected spectrum could be\ncontaminated by a line or reprocessed component from a molecular\ntorus, which would be constant due to light travel time delays on the\ntimescales of the monitoring campaign. Allowing for this results in\nthe reflected fraction from the accretion disk being more convincingly\nconsistent with a constant value, but still does not permit much \nof an increase with increasing flux or spectral index. The data then\nsupport the idea of a variable soft flux which is {\\it not} reprocessed\nas the driver for the hard X--ray variability, but could also allow \n{\\it small} changes in reflection geometry/ionisation. \n\nWe speculate that {\\it both} variability mechanisms operate in Seyferts\ni.e. that there are spectral changes linked to changes in the \ngeometry/ionisation (such as seen by Zdziarski et al. 1999), but that the\nsoft seed photons can also vary independently of these changes, giving a \nsecond, subtly different source of spectral variability. \n\n\\section{CONCLUSIONS}\n\n$\\bullet$ Not all AGN have the extreme relativistic line profiles\nexpected from a disk extending down to the innermost stable orbit\naround a black hole. \nThis is consistent with either the inner disk\nbeing truncated before the last stable orbit, or with an inner disk\nwhich produces no significant reflected features either through\nanisotropic illumination or extreme ionisation. Simple\nphoto--ionisation models, where the ionisation varies smoothly as a\nfunction of radius can be ruled out by the data, but these may differ\nsubstantially from more detailed models of the ionisation structure.\n\n$\\bullet$ There is intrinsic spectral variability, where the power law\nsoftens as the source brightens. This implies that the soft seed\nphotons are increasing faster than the increase of the hard X--ray\nluminosity. The lack of a corresponding increase in the observed\nreflected spectrum implies that either the changes in disk inner\nradial extent/ionisation structure are small, or that the variability\nis actually driven by changes in the seed photons which are decoupled\nfrom the hard X--ray mechanism.\n\n\\section{ACKNOWLEDGEMENTS}\n\nThis research was supported in part by grant 2P03D01816 of the Polish\nState Committee for Scientific Research (KBN) and by NASA grant\nNAG 54106. We thank James Chiang for discussing with us their results on\nNGC 5548. We acknowledge the help of the OSSE team in reducing the\nOSSE data, and the RXTE Guest Observer Facility (and in particular,\nTess Jaffe) for providing the PCA data reduction script {\\tt rex}. \n\n\\section{REFERENCES}\n\n\\ref Beloborodov A.M. 1999, ApJ, 510, L123\n\n\\ref Cappi M., Mihara T., Matsuoka M., Hayashida K., Weaver K.A., Otani C. \n1996, ApJ, 458, 149\n\n\\ref Chiang J., Reynolds C.S., Blaes O.M., Nowak M.A., Murray N.,\nMadejski G.M., Marshall H.L., Magdziarz P. 1999, ApJ, in press\n\n\\ref di Matteo T. 1998, MNRAS, 299, 15\n\n\\ref Done C., \\.{Z}ycki P.T. 1999, MNRAS, 305, 457\n\n\\ref Esin A. 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H, Morgan, E.M. 1993,\nin ``EUV, X--ray, and Gamma-ray Instrumentation for Astronomy IV,'' SPIE\nProceedings, O. Siegmund ed., 2006, 324\n\n\\ref \\.{Z}ycki P.T., Done C., Smith D.A. 1997, ApJ, 488, L113\n\n\\ref \\.{Z}ycki P.T., Done C., Smith D.A. 1998, ApJ, 496, L25\n\n\\ref \\.{Z}ycki P.T., Done C., Smith D.A. 1999, MNRAS, 305, 231\n\n\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002024
|
ISO-LWS spectroscopy of Centaurus A: extended star formation
|
[
{
"author": "S. J. Unger \\inst{1}"
},
{
"author": "P. E. Clegg \\inst{1}"
},
{
"author": "G. J. Stacey \\inst{2}"
},
{
"author": "P. Cox \\inst{3}"
},
{
"author": "J. Fischer \\inst{4}"
},
{
"author": "M. Greenhouse \\inst{5}"
},
{
"author": "S. D. Lord \\inst{6}"
},
{
"author": "M. L. Luhman \\inst{4} %"
},
{
"author": "M. A. Malkan \\inst{7}"
},
{
"author": "S. Satyapal \\inst{5}"
},
{
"author": "H. A. Smith \\inst{7}"
},
{
"author": "L. Spinoglio \\inst{8}"
},
{
"author": "M. Wolfire \\inst{9}"
}
] |
We present the first full FIR spectrum of Centaurus A (NGC 5128) from 43 - 196.7 $\mu$m. The data was obtained with the ISO Long Wavelength Spectrometer (LWS). We conclude that the FIR emission in a 70~\arcsec~beam centred on the nucleus is dominated by star formation rather than AGN activity. The flux in the far-infrared lines is $\sim$ 1 \% of the total FIR: the \cii line flux is $\sim$ 0.4 \% FIR and the \oi line is $\sim$ 0.2 \%, with the remainder arising from \oiiinb, \nii and \niii lines. These are typical values for starburst galaxies. The ratio of the \niii / \nii line intensities from the HII regions in the dust lane corresponds to an effective temperature, T$_{\mathrm{eff}}$ $\sim$ $35\,500$ K, implying that the tip of the main sequence is headed by O8.5 stars and that the starburst is $\sim$ 6 $\times 10^6$ years old. This suggests that the galaxy underwent either a recent merger or a merger which triggered a series of bursts. The N/O abundance ratio is consistent with the range of $\sim$ 0.2 - 0.3 found for Galactic HII regions. We estimate that $<$ 5 \% of the observed \cii arises in the cold neutral medium (CNM) and that $\sim$ 10 \% arises in the warm ionized medium (WIM). The main contributors to the \cii emission are the PDRs, which are located throughout the dust lane and in regions beyond where the bulk of the molecular material lies. On scales of $\sim$ 1 kpc the average physical properties of the PDRs are modelled with a gas density, n $\sim$ $10^3$ cm$^{-3}$, an incident far-UV field, G $\sim$ $10^2$ times the local Galactic field, and a gas temperature of $\sim$ 250 K. \keywords{Galaxies: individual: Centaurus A = NGC 5128 -- Infrared: galaxies -- Galaxies: active, ISM, starburst}
|
[
{
"name": "h1733.tex",
"string": "%\\documentstyle[referee,epsfig]{l-aa}\n\\documentstyle[epsfig]{l-aa}\n% some abbreviations\n%\n\\def\\ha{H$\\alpha$ }\n\\def\\eg{{\\it e.g.\\ }}\n\\def\\ie{{\\it i.e.\\ }}\n%\\def\\etal{{\\it et al.\\ }}\n\\def\\h0{{\\rm H_0}}\n\\def\\mum{\\mu {\\rm\\,m}}\n\\def\\pm{^+_-}\n\n\\def\\oiii{[O\\kern.2em{\\sc iii}] }\n\\def\\oiiinb{[O\\kern.2em{\\sc iii}]}\n\\def\\oiiif{[O\\kern.2em{\\sc iii}] \\kern.2em{3p2-3p1}}\n\\def\\oiiie{[O\\kern.2em{\\sc iii}] \\kern.2em{3p1-3p0}}\n\\def\\oiv{[O\\kern.2em{\\sc iv}] } \n\\def\\oivt{[O\\kern.2em{\\sc iv}] \\kern.2em{2p$\\frac{3}{2}$-2p$\\frac{1}{2}$} } \n\\def\\oi{[O\\kern.2em{\\sc i}] } \n\\def\\ois{[O\\kern.2em{\\sc i}] \\kern.2em{3p1-3p2}} \n\\def\\oio{[O\\kern.2em{\\sc i}] \\kern.2em{3p0-3p1}} \n\n\\def\\cii{[C\\kern.2em{\\sc ii}] }\n\\def\\ciio{[C\\kern.2em{\\sc ii}] \\kern.2em{2p$\\frac{3}{2}$-2p$\\frac{1}{2}$}}\n\n\\def\\ariii{[Ar\\kern.2em{\\sc iii}] } \n\\def\\ariiin{[Ar\\kern.2em{\\sc iii}] \\kern.2em{3p1-3p2}} \n\\def\\arii{[Ar\\kern.2em{\\sc ii}] } \n\\def\\ariis{[Ar\\kern.2em{\\sc ii}] \\kern.2em{2p$\\frac{1}{2}$-2p$\\frac{3}{2}$} } \n\n\\def\\neii{[Ne\\kern.2em{\\sc ii}] }\n\\def\\neiit{[Ne\\kern.2em{\\sc ii}] \\kern.2em{2p$\\frac{1}{2}$-2p$\\frac{3}{2}$} }\n\\def\\neiii{[Ne\\kern.2em{\\sc iii}] } \n\\def\\neiiif{[Ne\\kern.2em{\\sc iii}] \\kern.2em{3p1-3p0}} \n\n\\def\\niii{[N\\kern.2em{\\sc iii}] } \n\\def\\niiif{[N\\kern.2em{\\sc iii}] \\kern.2em{2p$\\frac{3}{2}$-2p$\\frac{1}{2}$} }\n\\def\\nii{[N\\kern.2em{\\sc ii}] } \n\\def\\niif{[N\\kern.2em{\\sc ii}] \\kern.2em{3p2-3p1}} \n\n\n\\def\\siii{[S\\kern.2em{\\sc iii}] } \n\\def\\siiie{[S\\kern.2em{\\sc iii}] \\kern.2em{3p2-3p1}}\n\\def\\siiit{[S\\kern.2em{\\sc iii}] \\kern.2em{3p1-3p0}}\n\\def\\siv{[S\\kern.2em{\\sc iv}] } \n\\def\\sivt{[S\\kern.2em{\\sc iv}] \\kern.2em{2p$\\frac{3}{2}$-2p$\\frac{1}{2}$} } \n\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%\\newcommand{\\DXDYCZ}[3]{\\left( \\frac{ \\partial #1 }{ \\partial #2 }\\right)_{#3L}}\n\\begin{document}\n\n\n%\n% \\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\n% (03.11.1; % Cosmogony,\n% 16.06.1; % Planets and satellites: general,\n% 19.06.1; % Solar system: general,\n% 19.37.1; % Stars: formation of,\n% 19.53.1; % Stars: oscillations of,\n% 19.63.1)} % Stars: structure of.\n\n%name, infrared galaxies; galaxies:starburst; galaxies:ism; galaxies:active\n\\thesaurus{03(11.09.1 Centaurus A = NGC 5128; 13.09.1;11.09.4; 11.19.3,11.01.2)}\n\\title{ISO-LWS spectroscopy of Centaurus A: extended star formation}\n\n\\author{ S. J. Unger \\inst{1} \n\\and P. E. Clegg \\inst{1}\n\\and G. J. Stacey \\inst{2}\n\\and P. Cox \\inst{3}\n\\and J. Fischer \\inst{4} \n\\and M. Greenhouse \\inst{5} \n\\and S. D. Lord \\inst{6}\n\\and M. L. Luhman \\inst{4} \n%\\and M. A. Malkan \\inst{7}\n\\and S. Satyapal \\inst{5} \n\\and H. A. Smith \\inst{7}\n\\and L. Spinoglio \\inst{8}\n\\and M. Wolfire \\inst{9} }\n\n\\offprints{[email protected]}\n\n\\institute{Physics Dept., Queen Mary \\& Westfield College, University of \nLondon, London E1 4NS, U.K.\n\\and Cornell University, Ithaca, NY, USA\n\\and Institut d'Astrophysique Spatiale, Orsay, France\n\\and Naval Research Laboratory, Washington, USA \n\\and NASA Goddard, Greenbelt, USA\n\\and IPAC, California Institute of Technology, Pasadena, USA\n%\\and University of California, Los Angeles, USA\n\\and Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA\n\\and Istituto di Fisica dello Spazio Interplanetario-CNR, Roma, Italy\n\\and University of Maryland, College Park, MD, USA }\n\n\\date{Received ;Accepted}\n\n\\maketitle\n\n\\begin{abstract}\nWe present the first full FIR spectrum of Centaurus A (NGC 5128)\nfrom 43 - 196.7 $\\mu$m. The data was obtained with the ISO Long Wavelength\nSpectrometer (LWS). We conclude that the FIR emission in a \n70~\\arcsec~beam centred on the nucleus is dominated by star formation\nrather than AGN activity. The flux in the \nfar-infrared lines is $\\sim$ 1 \\% of the total FIR: \nthe \\cii line flux is $\\sim$ 0.4 \\% FIR and the \\oi line is \n$\\sim$ 0.2 \\%, with the remainder arising from \\oiiinb, \\nii and\n\\niii lines. These are typical values for starburst galaxies.\n\nThe ratio of the \\niii / \\nii line intensities from the HII regions in\nthe dust lane corresponds to an effective temperature, \nT$_{\\mathrm{eff}}$ $\\sim$ $35\\,500$ K, implying that the tip of the \nmain sequence is headed by O8.5 stars and that the starburst is \n$\\sim$ 6 $\\times 10^6$ years old. This suggests that the galaxy\nunderwent either a recent merger or a \nmerger which triggered a series of bursts. The N/O abundance ratio is\nconsistent with the range of $\\sim$ 0.2 - 0.3 found for Galactic HII regions. \n\nWe estimate that $<$ 5 \\% of the observed \\cii arises in the cold\nneutral medium (CNM) and\nthat $\\sim$ 10 \\% arises in the warm ionized medium (WIM). The main\ncontributors to the \n\\cii emission are the PDRs, which\nare located throughout the dust lane and in regions beyond where the bulk of\nthe molecular material lies. On scales of $\\sim$ 1 kpc the average physical \nproperties of the PDRs are modelled with a gas density, \nn $\\sim$ $10^3$ cm$^{-3}$, an incident far-UV field, G $\\sim$ $10^2$\ntimes the local Galactic field, and a \ngas temperature of $\\sim$ 250 K. \n\\keywords{Galaxies: individual: Centaurus A = NGC 5128 -- Infrared: \ngalaxies -- Galaxies: active, ISM, starburst} \n\\end{abstract}\n\n\\section{Introduction}\n\nCentaurus A (NGC 5128) is the nearest (d = 3.5 Mpc; 1 \\arcsec $\\sim$17~pc, Hui \net al. 1993) example of a giant elliptical galaxy associated with a powerful \nradio source. The large-scale radio morphology consists of twin radio\nlobes separated by\n$\\sim$ 5 degrees on the sky. The compact ($\\sim$ milliarcsecond) radio \nnucleus is variable and has a strong jet extending \n$\\sim$ 4 arcminutes towards the \nnortheast lobe. The spectacular optical appearance is that of a \ngiant elliptical galaxy that appears enveloped in a nearly edge on, warped \ndust lane. There is also a series of faint optical shells.\nThe stellar population in the dominant elliptical structure is old, whilst \nthat of the twisted dust lane is young, sporadically punctuated by HII \nregions, \ndust and gas (Graham 1979). The overall structure of Cen A resembles\nthat of a recent ($< 4 \\times 10^8$ years, Tubbs 1980) merger, \nbetween a spiral and a large elliptical galaxy. The dust lane is the source \nof most (90 \\%) of the far-infrared luminosity (L$_{\\mathrm{FIR}} \\sim 3 \n\\times 10^{9}$ L$_{\\odot}$) and is thought to be re-radiated starlight \nfrom young stars in the dusty disk (Joy et al. 1988).\n\nIn Sect. 2 we describe the observations and data analysis. Sect. 3 looks at\nthe general FIR properties and proceeds to model the\nHII regions and the PDRs in the dust lane. Sect. 4 summarises the results\nand presents our conclusions.\n\n\\section{Observations}\n\nCen A was observed with the LWS grating \n($R=\\lambda/\\Delta\\lambda \\sim 200$) as part of the LWS consortium's\nguaranteed time extragalactic programme. A full grating observation \n(43 - 196.7 $\\mu$m) was taken of the nucleus at the centre of the dust\nlane and a series of line observations were taken at two positions in\nthe SE and NW regions of the dust lane. \nA short \\cii~157 $\\mu$m line observation was taken off-source at\nposition \\#4 (see Table 1) to estimate the Galactic emission near the \nsource. Position \\#1 was intended to provide a deeper integration \ncoincident with position \\#2, but was accidently offset.\n\nA series of half-second integration ramps were taken at each grating\nposition with four samples per resolution element ($\\Delta\\lambda =\n0.29~\\mu$m $\\lambda\\lambda 43 - 93~\\mu$m and $\\Delta\\lambda = 0.6~\\mu$m \n$\\lambda\\lambda 84 - 196~\\mu$m). The total integration time per\nresolution element and per pointing were:\nposition \\#1 88~s for the \\oiii 52~$\\mu$m and 34~s for the \n\\niii 57~$\\mu$m; \nposition \\#2 (the centre), 30~s for the range 43--196 $\\mu$m; \npositions NW and SE (2 point raster\nmap) 22~s for the the \\oi 63~$\\mu$m, 14~s for the \\oiii 88~$\\mu$m, \n12~s for the \\nii 122~$\\mu$m, 28~s for the \\oi 145~$\\mu$m and 12~s for\nthe \\cii 158~$\\mu$m; \nposition \\#4 12~s for the \\cii 158~$\\mu$m.\n\nThe data were processed with RAL pipeline 7 and analysed using the LIA\nand ISAP packages. \nThe LWS flux calibration and relative spectral response function (RSRF)\nwere derived from\nobservations of Uranus (Swinyard et al. 1998). The full grating spectrum at\nthe centre enabled us to estimate the relative flux uncertainty\nbetween individual detectors arising from \nuncertainties in the relative responsivity and the \ndark-current subtraction. \nThe offsets between the detectors (excluding detector\nSW1) was $\\leq 10$ \\%. The \\oiii 88 $\\mu$m line on detectors SW5 and LW1 \nhad a 15 \\%\nsystematic uncertainty and the \\cii line on detectors LW3 and LW4 had a \n10 \\% systematic uncertainty. We therefore adopt a relative flux uncertainty \nof $\\sim$ 15\\%. Because we only took spectra of individual lines at the\nNW and SE positions there is no corresponding overlap in wavelength\ncoverage at these positions. One indicator of relative flux uncertainty \nis a discrete step down in flux, of $\\sim$ 25 \\%, \nat $\\sim$ 125~$\\mu$m at \nthe SE position. The relative flux uncertainty is assumed to be\n$\\le$ 25 \\% at these positions.\n\nThe absolute flux calibration w.r.t. Uranus for point like objects \nobserved on axis is better than 15 \\% (Swinyard et al. 1998). However, extended\nsources give rise either to channel fringes or to a\nspectrum that is not a smooth function of wavelength. This is still a\ncalibration issue. For example, in \nFig. 2, detectors SW5, LW1, LW2 have slopes that differ from those of\ntheir neighbours in the overlap region. This may account for the\ncontinuum shape, which is\ndiscussed in Sect. 3.1.\nThe LWS beam profile is known to be asymmetric and is still under\ninvestigation. We therefore adopt a value for the FWHM of 70~\\arcsec~at\nall wavelengths, believing that a more sophisticated treatment would not\nsignificantly affect our conclusions. We also note that there is good \ncross calibration between the ISO-LWS results and the Far-infrared Imaging\nFabry-Perot Interferometer (FIFI) (Madden et al. 1995); \nthe \\cii peak fluxes agree to within $\\sim$ 10 \\%.\n\n\n\\begin{table}\n\\begin{center}\n\\caption{ Observation Log}\n\\vspace*{0.3cm}\n\\begin{tabular}{l|r|r|l}\n{Position}&{Offset in RA}&{Offset in Dec}&{Date/AOT}\\\\\n&arcsec&arcsec&\\\\\n\\hline\n&&&\\\\\n\\#1&+ 29&- 12 &1996 Aug 23 L02\\\\\n\\#2 Centre&0&0&1997 Aug 11 L01\\\\ \n\\#3 (map)&& &1997 Feb 12 L02\\\\\nNW&- 53&+ 27&\\\\ \nSE&+ 110&- 49&\\\\\n\\#4 (off)&- 2 & + 600&1997 Feb 12 L02\\\\\n\\end{tabular}\n\nOffsets w.r.t. 13h 25m 27.6s -43d 01 \\arcmin 08.6 \\arcsec J2000\\\\\n\\end{center}\n\\end{table}\n\\normalsize\n\n\\begin{figure}[h]\n \\begin{center}\n \\leavevmode\n \\centerline{\\epsfig{file=h1733f1.ps,width=8.0cm,angle=0}}\n \\end{center}\n \\caption{\\rm Cen A digital sky survey image overlaid with the LWS beam\n positions}\n \\label{fig:sample1}\n\\end{figure}\n\n\\section{Results and discussion}\n\n\n\n\\subsection{\\rm General FIR properties}\n\nThe far-infrared continuum at each position is modelled with a\nsingle-temperature blackbody spectrum of the form F$_{\\lambda}$ $\\alpha$ \n$\\Omega$ B$_{\\lambda}$(T)(1-e$^{-\\tau_{\\mathrm{dust}}}$), where the\nsolid angle,\n$\\Omega$, is constrained to equal the LWS beam, B$_{\\lambda}$(T) is the \nPlanck function at temperature T and $\\tau_{\\mathrm{dust}}$ $\\alpha$ \n$\\lambda^{-1.5}$. The result for the central position is shown as the\ndashed curve in Fig. 2. Although the observed continuum is not a\nsimple function of wavelength and the single temperature blackbody is\nnot an especially good fit, particularly at wavelengths $> 100 \\mu$m, a\nbetter calibration of straylight and the beam profile is required for\nanything more sophisticated. The best FIR temperature at each position\nis $\\sim$ 30 K.\n\n\n\\begin{figure}[h]\n \\begin{center}\n \\leavevmode\n \\centerline{\\epsfig{file=h1733f2.ps,width=7.cm,angle=90}}\n \\end{center}\n \\caption{\\rm LWS spectrum of the central region of the dust lane\n(dashed line is the blackbody fit)}\n \\label{fig:saple1}\n\\end{figure}\n\nThe luminosities quoted here are derived from the line fluxes listed in\nTable 2. At the central position, the total luminosity in all of the \nfar-infrared lines \nis 2.6 $\\times 10^7$ L$_{\\odot}$, which is $\\sim$ 1 \\% of the total FIR \nluminosity (L$_{43-197 \\mu m} = 3.2 \\times 10^9$ L$_{\\odot}$). \nThe \\cii luminosity is \n1.1 $\\times 10^7$ L$_{\\odot}$ (0.4 \\% FIR) and the \\oi luminosity is \n7.5 $\\times 10^6$ L$_{\\odot}$ (0.2 \\% FIR). \nBecause full spectra are not available at the NW and SE positions we \nestimate the FIR continuum luminosity by integrating under the \nsingle-temperature blackbody fit\nto the data.\nAt the NW position the total FIR luminosity,\nL$_{43-197 \\mu m} = 2.2 \\times 10^9$ L$_{\\odot}$. The \\cii luminosity is \n9.3 $\\times 10^6$ L$_{\\odot}$ (0.4 \\% FIR) and the \\oi luminosity is \n3.4 $\\times 10^6$ L$_{\\odot}$ (0.2 \\% FIR).\nAt the SE position the total FIR luminosity,\nL$_{43-197 \\mu m} = 8.7 \\times 10^8$ L$_{\\odot}$. The \\cii luminosity is \n3.5 $\\times 10^6$ L$_{\\odot}$ (0.4 \\% FIR) and the \\oi luminosity is \n2.0 $\\times 10^6$ L$_{\\odot}$ (0.2 \\% FIR). These are typical values\nfor starburst galaxies (c.f. Lord et al. 1996).\n \n\n\n\\begin{table*}\n\\begin{center}\n\\caption{Line Fluxes}\n\\vspace*{0.3cm}\n\\begin{tabular}{l|l|l|l|l|l}\n{Line}&{$\\lambda_{\\rm{rest}}$}&{\\#1}&{Centre}&{NW}&{SE}\\\\\n&$\\mu$m&Flux&Flux&Flux&Flux\\\\\n\\hline\n&&&&&\\\\\n\\oiiif&51.815&0.31&0.72&-&-\\\\\n\\niiif&57.3170&0.16&0.24&-&-\\\\\n\\ois&63.184&-&1.96&0.90&0.51\\\\\n\\oiiie&88.356&-&0.70&0.6&0.2\\\\\n\\niif&121.898&-&0.15&0.15&$\\le$0.15\\\\\n\\oio&145.525&-&0.11&0.08&$\\le$0.03\\\\\n\\ciio&157.741&-&2.91&2.43&0.92\\\\\n\\end{tabular}\n\n\\normalsize\nFlux $ \\times10^{-18}$ W cm$^{-2}$\\\\\n- wavelength range not covered\\\\\nupper limits are 3 x rms residuals from a fit to the continuum \\\\\n\\cii~157~$\\mu$m flux at \\#4 (off) is 0.04 \\\\\n\\end{center}\n\\end{table*}\n\\normalsize\n\n\n\\subsection{\\rm Ionized gas lines}\n\nPhotons of energy 35.12, 29.60 and 14.53 eV are required to form \nO++, N++ and N+, \nrespectively, so that the observed \\oiii, \\niii and \\nii \nemission must originate in or around HII regions. The \\oiii line ratio\nis a sensitive \nfunction of density in the range $\\sim 30 - 10^4$ cm$^{-3}$.\nFor the central position this ratio is $\\sim$ 0.9, corresponding\nto an electron density, n$_{\\mathrm{e}} \\sim$ 100 cm$^{-3}$ (Rubin et\nal. 1994). \nThe \\oiii lines indicate a higher electron density, \nn$_{\\mathrm{e}} \\sim$ 250 cm$^{-3}$, for the starburst nuclei of M82 \n(Colbert et \nal. 1999) and M83 (Stacey et al. 1999). In contrast, the \\nii \n205 $\\mu$m / 122 $\\mu$m line intensity ratio for the Galaxy gives\nan average electron density, of only $\\sim$ 3 cm$^{-3}$ \n(Petuchowski \\& Bennett 1993).\nThe {\\it thermal pressure} of the ionized material in the Cen A dust \nlane is therefore closer to that of starburst galaxies than to that of the \nMilky Way.\n\nSince the \\niii 57 $\\mu$m and the \\nii 122 $\\mu$m lines arise from \ndifferent ionization states of the same element, the line intensity \nratio is sensitive to the hardness of the interstellar UV field and\ntherefore to the spectral type of the hottest main sequence star. \nFor the central \nposition \\niii / \\nii $\\sim$ 1.6. This is larger \nthan the value of $\\sim$ 0.9 for M83 (Stacey et al. 1999) but smaller\nthan the value of $\\sim$ 2.1 for M82 (Colbert et al. 1999). \nAssuming that the region \nis ionization bounded, with an electron density, n$_e$ $\\sim$ 100 cm$^{-3}$\nthe \\niii / \\nii line intensity \nratio for Cen A corresponds to an abundance ratio N++/N+ of $\\sim$ 0.3; this \ncorresponds to an effective temperature, T$_{\\mathrm{eff}} \\sim 35\\,500$ K \n(Rubin et al. 1994). Applying the same \ncorrections to M82 and M83 with n$_e$ $\\sim$ 250 cm$^{-3}$ implies an\neffective temperature, T$_{\\mathrm{eff}} \\sim 34\\,500$ K for M83 and \nT$_{\\mathrm{eff}} \\sim$ 35\\,500 K for M82. If the effective temperature\nin Cen A corresponds to the tip of the main sequence formed in a single\nstarburst, we are observing O8.5 stars and the burst is \n$\\sim$ 6 $\\times 10^6$ years old.\nIf the burst was triggered by the spiral-elliptical galaxy merger \nthen its occurance was very recent. Alternatively, the merger triggered \na series of bursts of star formation, of which we are witnessing the most\nrecent.\n\nThe N++ and O++ coexist in roughly the same ionization zones, and the\n\\oiii 52 $\\mu$m and \\niii 57 $\\mu$m lines have roughly the same critical \ndensity. As a result the ratio of these lines is an indicator, to within\n$\\sim 50$~\\%, of the N++/O++ \nabundance ratio, which itself, is nearly equal to the N/O ratio in the hard UV \nfield environments we are seeing here (Rubin et al. 1988). \nThe line ratio we observe at \nthe centre of the dust lane is $\\sim$ 0.3 - the same as found in the\nnucleus of M82 (Colbert et al. 1999), but much smaller than that found for \nthe nucleus of M83 ($\\sim$ 0.67 Stacey et al. 1999). \n \nA more precise determination of the abundance ratio requires the \nobserved line ratio to be divided by the volume emissivity ratio. The latter \nratio is dependent on the electron \ndensity because the two lines have slightly different critical densities.\nUsing our value for the electron density $\\sim$ 100 cm$^{-3}$ and \nFig. 3 of Lester et al. (1987) we estimate that the N/O abundance\nratio to be $\\sim$ 0.2 in Cen A. This value is consistent with the range of \n$\\sim$ 0.2 - 0.3 found for Galactic HII regions (Rubin et al. 1988). The\nnitrogen to oxygen abundance ratio is a \nmeasure of the chemical evolution and we expect it to increase with time \n(cf. the solar value of $\\sim$ 0.12).\n\n\\subsection{\\rm Neutral gas lines}\n\nCarbon has a low ionization potential (11.4 eV), which is less than that\nof hydrogen. \\cii 157~$\\mu$m line emission\nis therefore observed from both neutral and ionized hydrogen clouds. We\nmodel the \\cii line emission with three components:\nPhotodissociation regions (PDRs) on the surfaces of UV exposed\nmolecular clouds; cold (T $\\sim$ 100 K) HI clouds (i.e. the cold neutral \nmedium (CNM) Kulkarni \\& Heiles 1987, Wolfire et al. 1995); and\ndiffuse HII regions (i.e. the warm ionized medium (WIM) Heiles 1994).\n\n\n\n\n\\subsubsection{\\rm HI clouds}\n\nIt can be shown that the intensity in the \\cii line emitted from gas clouds \nwith density, n(H) and temperature (T) is given by (c.f. Madden et al. 1993)\n\n\\begin{equation}\n\\mathrm\nI_{c^+} = 2.35 \\times 10^{-21} \\big[ \\frac{2exp(\\frac{-91.3}{T})}{1 + 2exp(\\frac{-91.3}{T}) + \\frac{n_{crit}}{n_H}} \\big] X_{c^+}N(HI)\n\\end{equation}\n\nwhere the critical density for collisions with H, n$_{\\mathrm{crit}} \n\\sim 3000$ cm$^{-3}$ (Launay \\& Roueff 1977) and the fractional C$^+$ \nrelative to hydrogen is $\\mathrm{X_{c^+} \\sim X_{c} = 1.4 \\times\n10^{-4}} $ (Sofia et al. 1997).\n\nN(HI) is estimated from the HI 21cm map of Van Gorkom et al. (1990) to be\n18.8 $\\times 10^{20}$ atom cm$^{-2}$ at the SE position. The central and\nNW positions are difficult to estimate due to HI absorption against the\nnuclear continuum. There may be a central hole in the HI and the column\ndensity is certainly not higher than the peak observed in the SE region \nof the dust lane (Van Gorkom et al. 1990) \n\nAssuming typical Galactic values for the temperature, T\n$\\sim$ 80 K, and hydrogen density, n $\\sim$ 30 cm$^{-3}$, results in an\nestimated \\cii flux of $3.5 \\times 10^{-20}$ W cm$^{-2}$ in a\n70~\\arcsec~LWS beam at the SE position. This corresponds to 4 \\%, 1 \\%\nand 1 \\%\nof the observed \\cii flux at positions SE, Centre and NW respectively.\nThe peak HI emission line flux corresponds to \n$1.9 \\times 10^{-19}$ W cm$^{-2}$ which is only 6~\\% and 8~\\% of the \n\\cii flux at the centre and NW positions respectively. We conclude that\nthere is very little \\cii emission in our beams from HI clouds. \n\n\n\\subsubsection{\\rm Diffuse HII regions}\n\nIonized carbon can be found in both neutral gas and ionized gas clouds, \nand is an important coolant for each. We detected \\oiii 88 $\\mu$m in all 3 \nbeam positions so there is an ionized gas component in each\nbeam. Using the constant density HII region model of Rubin (1985) with the \nKurucz abundances, 10$^{49}$ ionizing photons per second and our derived\ndensity, n$_e \\sim$ 100 cm$^{-3}$ and effective \ntemperature, T$_{\\mathrm{eff}} \\sim$ 35\\,500 K we can estimate the \n\\cii emission\nfrom the HII regions. Applying the model \\oiii 88\n$\\mu$m / \\cii 158 $\\mu$m line ratio of 0.35 to the observed \\oiii 88\n$\\mu$m line flux at each position results in $\\sim$ 10 \\% contribution\nto the observed \\cii line flux in each beam. Scaling the model fluxes to\nthe distance of Cen A gives $\\sim$ 3000 HII regions in the central and\nNW regions and $\\sim$ 1000 HII regions in the SE region. \n\nThe estimate above assumes that the observed lines have the same filling\nfactor in the large LWS beam. If, alternatively, we were to assume that\nthe ionized component was instead dominated by a contribution \nfrom an extended low density warm ionized medium (ELDWIM) with \nn$_e \\sim$ 3 cm$^{-3}$, then the \\cii flux can be\nestimated from the ratio of the \\cii/\\nii lines to be $\\sim$ 18 \\% at\nthe central position. The observations of the \\nii 121.9~$\\mu$m line at\nthe NW and SE positions (with lower signal to noise)\nindicate a similar fractional component (21 \\% and $\\le 56$ \\%, respectively).\n\nWe have estimated the density in the HII regions in the centre of \nCen A to be $\\sim$ 100 cm$^{-3}$ with an effective temperature, \nT$_{\\mathrm{eff}} \\sim 35\\,500$ K. Based on the HII region models of\nRubin (1985) we estimate that $\\sim$ 10 \\% of the observed \\cii arises\nin the WIM. \n\n\\begin{figure}[h]\n \\begin{center}\n \\leavevmode\n \\centerline{\\epsfig{file=h1733f3.ps,width=7.0cm,angle=90}}\n \\end{center}\n \\caption{\\rm PDR Lines (Flux Density $\\times 10^{17}$ W cm$^{-2}$\n $\\mu$m$^{-1}$). Note the \\cii lines are the total observed flux density\n i.e. PDR + CNM + WIM}\n \\label{fig:saple1}\n\\end{figure}\n\n\\subsubsection{\\rm PDRs}\n\nFar-UV photons (6 eV $<$ h$\\nu \\leq$ 13.6 eV) from either O/B stars or\nan AGN will photo-dissociate H$_2$ and CO molecules and photo-ionize\nelements with ionization potentials less than the Lyman limit\n(e.g. C$^+$ ionization potential = 11.26 eV). The gas heating in these \nphotodissociation regions (PDRs) is dominated by electrons ejected from \ngrains due to the\nphotoelectric effect. Gas cooling is dominated by the emission of\n\\oi~63~$\\mu$m and \\cii~158~$\\mu$m emission.\nObservations of these lines,\nthe \\oi~146~$\\mu$m and CO~(J=1-0) 2.6 mm lines and the FIR continuum can be\nused to model the average physical properties of the neutral\ninterstellar medium (Wolfire et al. 1990). Kaufman et al. (1999) have\ncomputed PDR models over a wide range of physical conditions. The new\ncode accounts for gas heating by\nsmall grains/PAHs and large molecules, and uses a lower,\ngas phase carbon abundance (X$_{\\mathrm{C}}$ = 1.4x10$^{-4}$, Sofia et\nal. 1997)\nand oxygen abundance (X$_{\\mathrm{O}}$ = 3.0x10$^{-4}$, Meyer et al. 1998).\nThe \\oi 63 $\\mu$m / \\cii 158 $\\mu$m line ratio and either the \\oi 146 $\\mu$m\n/ \\oi 63 $\\mu$m line ratio or the (\\oi 63 $\\mu$m + \\cii 158 $\\mu$m) /\nFIR continuum can be used as PDR diagnostics to determine the \naverage gas density (i.e the proton density,\nn cm$^{-3}$), the average incident far-UV flux (in units of the Milky Way\nflux, G$_o$ = 1.6 $\\times 10^{-3}$~erg cm$^{-2}$ s$^{-1}$) and\nthe gas temperature. \n\nWe assume that the measured \\cii flux at each position should have \n$\\sim$ 10 \\% subtracted, due to the HI and WIM components, before it is used \nto model the PDRs (if, alternatively, a 20 \\% ELDWIM contribution is \nsubtracted it would not significantly affect the PDR parameters derived \nbelow). The PDR lines are plotted in Fig. 3 and the line intensity\nratios are given in Table 3.\n\n\n\\begin{table}\n\\begin{center}\n\\caption{PDR diagnostic line intensity ratios}\n\\vspace*{0.3cm}\n\\begin{tabular}{l|l|l|l}\n{Line Ratio}&{Centre}&{NW}&{SE}\\\\\n\\hline\n&&&\\\\\n\\oi 63~$\\mu$m / \\cii 158~$\\mu$m &0.7&0.4&0.6\\\\\n\\oi 146~$\\mu$m / \\oi 63~$\\mu$m &0.06&0.09&$\\le$ 0.06\\\\\n(\\oi 63~$\\mu$m + \\cii 158~$\\mu$m )/FIR&0.006&0.005&0.006\\\\\n\\end{tabular}\n\\normalsize\n\\end{center}\n\\end{table}\n\\normalsize\n\n%Table 4 lists the derived PDR parameters at the three\n%positions. \n\nThe results for the three regions are\nconsistent with each other, having a gas\ndensity, n $\\sim$ 10$^3$ cm$^{-3}$, and an incident far-UV field, \nG $\\sim$ 10$^2$. \n\nAt the NW position, only the combination of the \\oi 63 $\\mu$m / \n\\cii 158 $\\mu$m ratio and the\n(\\oi 63 $\\mu$m + \\cii 158 $\\mu$m) /FIR continuum ratio gives a \nmeaningful solution for G and n. The \\oi 146 $\\mu$m line is clearly detected\nbut with a very rippled baseline due to channel fringes. \nThe observed \\oi 146 $\\mu$m line\nflux would need to be reduced by $\\sim$ 60 \\% in order\nto obtain a consistent result with the \\oi 146 $\\mu$m / \\oi 63 $\\mu$m\nline ratio predicted by the PDR model. \n\n%\\begin{table}\n%\\begin{center}\n%\\caption{PDR Parameters}\n%\\vspace*{0.3cm}\n%\\begin{tabular}{l r r r}\n%{Position}&{log n}&{log G}&{T}\\\\\n%&&{$1.6\\times10^{-3}$}&\\\\\n%&{cm$^{-3}$}&{erg~cm$^{-2}$~s$^{-1}$}&{K}\\\\\n%&&&\\\\\n%centre&3.0(3.0)&2.2(2.2)&250(250)\\\\\n%NW&(2.6)&(2.1)&(200)\\\\\n%SE&$\\ge$2.4(2.7)&$\\le$2.3(2.1)&250(200)\\\\\n%\\end{tabular}\n%Numbers in parentheses derived using FIR continuum.\n%\\end{center}\n%\\end{table}\n%\\normalsize\n\nThe LWS results for the nucleus confirm those previously derived from\nIR, submm and CO observations. \nThe consistent set of derived PDR conditions for all three positions \nsuggest that the observed FIR emission\nin a 70~\\arcsec~beam centred on the nucleus is dominated by star formation\nand not AGN activity. Joy et al. (1988) mapped Cen A at 50 and 100\n$\\mu$m on the KAO. They concluded that the extended FIR\nemission was from dust grains heated by massive\nyoung stars distributed throughout the dust lane, not the \ncompact nucleus. Hawarden et al. (1993)\nmapped Cen A at 800 $\\mu$m and 450 $\\mu$m with a resolution of \n$\\sim$10 \\arcsec. \nThey attribute the large scale 800 $\\mu$m emission to thermal emission\nfrom regions of star formation embedded in the dust lane.\nThey note that the H$_2$ emission within a few arcseconds of the nucleus,\nobserved by Israel et al. (1990), indicates that significant UV\nradiation from the nucleus does not reach large radii in the plane of\nthe dust lane i.e. the nuclear contribution to exciting the extended gas and \ndust disk is small.\n\nEckart et al. (1990) and Wild et al. (1997)\nmapped Cen A in $^{12}$CO J=1-0, \n$^{12}$CO J=2-1 and $^{13}$CO J=1-0. All three maps have two peaks\nseparated by $\\sim$ 90 \\arcsec centred on the nucleus.\nIt is interesting to note that our SE position only clips the lowest\ncontours of the CO (1-0) and CO (2-1) maps of Wild et\nal. (1997). In spite of this the derived PDR parameters are consistent with\nthose encompassing the bulk of the molecular emission. There must be\nextended low level CO (1-0) emission beyond the sensitivity limits of\nthe Wild et al. (1997) maps. The lowest contour is 17.5 K kms$^{-1}$,\ncorresponding to M$_{\\mathrm{H}_2}$ $\\sim$ 10$^{8}$ M$_{\\odot}$ if the material\nfilled the LWS beam.\n\n\n\n\n\n\\section{Summary and conclusions}\n\nWe present the first full FIR spectrum from 43 - 196.7 $\\mu$m of Cen A.\nWe detect seven fine structure lines (see Table 2), the strongest being \nthose generated in PDRs.\nAt the central position, the total flux in the far-infrared lines \nis $\\sim$ 1 \\% of the total FIR luminosity \n(L$_{43-197 \\mu m} = 3.2 \\times 10^9$ L$_{\\odot}$ for a distance of 3.5 Mpc). \nThe \\cii line flux is $\\sim$0.4 \\% FIR and the \\oi line flux is \n$\\sim$ 0.2 \\% FIR. These are typical values for starburst galaxies (Lord \net al. 1996). The \\oiii 52 $\\mu$m / \\oiii 88 $\\mu$m line \nintensity ratio is $\\sim$ 0.9, which corresponds to an electron density, \nn$_{\\mathrm{e}} \\sim$ 100 cm$^{-3}$ (Rubin et al. 1994). \nThe {\\it thermal pressure} of the ionized medium in the Cen A dust \nlane is closer to that of starburst galaxies (n$_e \\sim$ 250 cm$^{-3}$ in \nM82 (Colbert et al. 1999) and M83 (Stacey et al. 1999)) than that of the \nMilky Way (n$_e \\sim$ 3 cm$^{-3}$ (Pettuchowski \\& Bennett 1993)).\n\n\nThe \\niii / \\nii line intensity \nratio is $\\sim$ 1.6, giving an abundance ratio N++/N+ $\\sim$ 0.3, which \ncorresponds to an effective temperature, T$_{\\mathrm{eff}} \\sim$ 35\\,500 K \n(Rubin et al. 1994). Assuming a coeval \nstarburst, then the tip of the main sequence is headed by O8.5\nstars, and the starburst is $\\sim$ 6 $\\times 10^6$ \nyears old. \nIf the burst in Cen A was triggered by the spiral-elliptical galaxy merger \nthen its occurance was very recent. Alternatively, the merger triggered \na series of bursts of star formation and we are witnessing the most recent \nactivity. \n\nWe estimate that the N/O abundance ratio is $\\sim$ 0.2 in the HII regions in \nCen A. This value is consistent with the range of \n$\\sim$ 0.2 - 0.3 found for Galactic HII regions (Rubin et al. 1988). N/O is a \nmeasure of the chemical evolution and we expect it to increase with time\n(c.f. the solar value of $\\sim$ 0.12).\n\nWe estimate that $\\sim$ 10 \\% of the observed \\cii arises in the \nWIM. The CNM contributes very little ($< 5$ \\%) \\cii emission at our\nbeam positions. The bulk of the emission is from the PDRs.\n\nWe derive the average physical conditions for the PDRs in Cen A for\nthe first time. There is active star formation throughout the dust lane\nand in regions beyond the bulk of the molecular material. The FIR emission in \nthe 70~\\arcsec~LWS beam at the nucleus is dominated by emission from \nstar formation rather than AGN activity. On scales of\n$\\sim$ 1 kpc the average\nphysical properties of the PDRs are modelled with a gas\ndensity, n $\\sim$ 10$^3$ cm$^{-3}$, an incident far-UV field, \nG $\\sim$ 10$^2$ and a gas temperature of $\\sim$ 250 K.\n\n\n\n\\section*{Acknowledgements}\nMany thanks to the dedicated efforts of the LWS instrument team. The ISO \nSpectral Analysis Package (ISAP) is a joint development by the\nLWS and SWS Instrument Teams and Data Centers. Contributing institutes\nare CESR, IAS, IPAC, MPE, QMW, RAL and SRON.\n\n\n%\\begin{thebibliography}{}\n\\section*{References}\n\nColbert J.W., Malkan M.A., Clegg P.E., et al., 1999, ApJ 511, 721 \\\\\n%Cunningham C.T., Ade, P.A.R., Robson, E.I. et al.,\n%1984, MNRAS 211, 543\\\\\nEckart A., Cameron M., Rothermel H., et al., 1990, ApJ 363, 451\\\\\nGraham J., 1979, ApJ 232, 60\\\\\nHawarden T.G., Sandell G., Matthews H.E., et\nal., 1993, MNRAS 260, 844\\\\\nHeiles C., 1994, ApJ 436, 720\\\\\nHui X., Ford H.C., Ciardillo R., et al., 1993, ApJ 414, 463\\\\\nIsrael F.P., van Dishoeck E.F., Baas F. et al.,\n1990, A\\&A 227, 342\\\\\nJoy M., Lester D.F., Harvey P.M., et al., 1988, ApJ 326, 662\\\\\nKaufman M.J., Wolfire M.G., Hollenbach D., et al., 1999, ApJ in press\\\\\nKulkarni S.R., Heiles C., 1987, in Hollenbach, D., Thronson Jr, H.A. \n(eds.) Interstellar Processes. Reidel, Dordrecht, p. 87\\\\\nLaunay J.M., Roueff E., 1977, JPhysB 10, 879\\\\\nLester D.F., Dinnerstein H.L., Werner M.W., et al., 1987, ApJ 320, 573\\\\\nLord S.D., Malhotra S., Lim T.L., et al., 1996, A\\&A 315, L117\\\\\nMadden S.C., Geis N., Genzel R., et al, 1993, ApJ 407, 579\\\\\nMadden S., Geis N., Townes C.H.et al., 1995, Airbourne Astronomy\nSymposium on the Galactic Ecosystem, ASP Conf. Series 73, 181. \\\\\n%Meyer et al., 1997, ApJ 490, L103\\\\\n%MEYER, DAVID M.; CARDELLI, JASON A.;\n% SOFIA, ULYSSES J.\n%nitrogen abundance\nMeyer D.M., Jura M., Cardelli J.A., 1998, ApJ 493, 222\\\\\n%Mirabel et al. 1999, AA 341, 667 \\\\\nPetuchowski S.J., Bennett C.L., 1993, ApJ 405, 591\\\\\n%Quillen et al., 1993, ApJ 412, 550\\\\\nRubin R.H., 1985, ApJS 57, 349\\\\\nRubin R.H., Simpson J.P., Erickson E.F., et al., 1988, ApJ 327, 377\\\\\nRubin R.H., Simpson J.P., Lord S.D., et al., 1994, ApJ 420, 772 \\\\\nSofia U.J., Cardelli J.A., Guerin K.P., et al., 1997, ApJ 482, L105\\\\\nStacey G.J., Swain M.R., Bradford C.M., et al., 1999, \nThe Universe as seen by ISO, ESA SP-427 p973\\\\\nSwinyard B.M., Burgdorf M.J., Clegg P.E et al., 1998, SPIE 3354 \\\\\n%, Burgdorf, M.J., Clegg, P.E. et al.,\n%, Davis, G.R., Griffin, M.J.,\n%Gry, C., Leeks, S.J., Lim, T.L., Pezzuto, S., Tommasi, E.,\n%`In-Orbit performance of the ISO Long Wavelength Spectrometer'\n%in Infrared Astronomical Instrumentation SPIE vol 3354, 1998.\\\\\nTubbs A.D., 1980, ApJ 241, 969\\\\\nvan Gorkom J.H., van der Hulst J.M., Haschick A.D., \net al., 1990 AJ 99, 1781\\\\\nWild W., Eckart A., Wilkind T., 1997, A\\&A 322, 419\\\\\nWolfire M.G., Tielens A.G.G.M., Hollenbach D., 1990, ApJ 358,\n116\\\\\nWolfire M.G., Tielens A.G.G.M., Hollenbach D., 1995, ApJ 443, 152\\\\\n\n%\\end{thebibliography}\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002024.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\section*{References}\n\nColbert J.W., Malkan M.A., Clegg P.E., et al., 1999, ApJ 511, 721 \\\\\n%Cunningham C.T., Ade, P.A.R., Robson, E.I. et al.,\n%1984, MNRAS 211, 543\\\\\nEckart A., Cameron M., Rothermel H., et al., 1990, ApJ 363, 451\\\\\nGraham J., 1979, ApJ 232, 60\\\\\nHawarden T.G., Sandell G., Matthews H.E., et\nal., 1993, MNRAS 260, 844\\\\\nHeiles C., 1994, ApJ 436, 720\\\\\nHui X., Ford H.C., Ciardillo R., et al., 1993, ApJ 414, 463\\\\\nIsrael F.P., van Dishoeck E.F., Baas F. et al.,\n1990, A\\&A 227, 342\\\\\nJoy M., Lester D.F., Harvey P.M., et al., 1988, ApJ 326, 662\\\\\nKaufman M.J., Wolfire M.G., Hollenbach D., et al., 1999, ApJ in press\\\\\nKulkarni S.R., Heiles C., 1987, in Hollenbach, D., Thronson Jr, H.A. \n(eds.) Interstellar Processes. Reidel, Dordrecht, p. 87\\\\\nLaunay J.M., Roueff E., 1977, JPhysB 10, 879\\\\\nLester D.F., Dinnerstein H.L., Werner M.W., et al., 1987, ApJ 320, 573\\\\\nLord S.D., Malhotra S., Lim T.L., et al., 1996, A\\&A 315, L117\\\\\nMadden S.C., Geis N., Genzel R., et al, 1993, ApJ 407, 579\\\\\nMadden S., Geis N., Townes C.H.et al., 1995, Airbourne Astronomy\nSymposium on the Galactic Ecosystem, ASP Conf. Series 73, 181. \\\\\n%Meyer et al., 1997, ApJ 490, L103\\\\\n%MEYER, DAVID M.; CARDELLI, JASON A.;\n% SOFIA, ULYSSES J.\n%nitrogen abundance\nMeyer D.M., Jura M., Cardelli J.A., 1998, ApJ 493, 222\\\\\n%Mirabel et al. 1999, AA 341, 667 \\\\\nPetuchowski S.J., Bennett C.L., 1993, ApJ 405, 591\\\\\n%Quillen et al., 1993, ApJ 412, 550\\\\\nRubin R.H., 1985, ApJS 57, 349\\\\\nRubin R.H., Simpson J.P., Erickson E.F., et al., 1988, ApJ 327, 377\\\\\nRubin R.H., Simpson J.P., Lord S.D., et al., 1994, ApJ 420, 772 \\\\\nSofia U.J., Cardelli J.A., Guerin K.P., et al., 1997, ApJ 482, L105\\\\\nStacey G.J., Swain M.R., Bradford C.M., et al., 1999, \nThe Universe as seen by ISO, ESA SP-427 p973\\\\\nSwinyard B.M., Burgdorf M.J., Clegg P.E et al., 1998, SPIE 3354 \\\\\n%, Burgdorf, M.J., Clegg, P.E. et al.,\n%, Davis, G.R., Griffin, M.J.,\n%Gry, C., Leeks, S.J., Lim, T.L., Pezzuto, S., Tommasi, E.,\n%`In-Orbit performance of the ISO Long Wavelength Spectrometer'\n%in Infrared Astronomical Instrumentation SPIE vol 3354, 1998.\\\\\nTubbs A.D., 1980, ApJ 241, 969\\\\\nvan Gorkom J.H., van der Hulst J.M., Haschick A.D., \net al., 1990 AJ 99, 1781\\\\\nWild W., Eckart A., Wilkind T., 1997, A\\&A 322, 419\\\\\nWolfire M.G., Tielens A.G.G.M., Hollenbach D., 1990, ApJ 358,\n116\\\\\nWolfire M.G., Tielens A.G.G.M., Hollenbach D., 1995, ApJ 443, 152\\\\\n\n%\\end{thebibliography}"
}
] |
astro-ph0002025
|
First results of the air shower experiment KASCADE
|
[
{
"author": "T.~Antoni$^{a}$"
},
{
"author": "W.D.~Apel$^{a}$"
},
{
"author": "K.~Bekk$^{a}$"
},
{
"author": "K. Bernl{\\\"o}hr$^{a}$"
},
{
"author": "H.~Bl\\\"umer$^{a,d}$"
},
{
"author": "E.~Bollmann$^{a}$"
},
{
"author": "H.~Bozdog$^{b}$"
},
{
"author": "I.M.~Brancus$^{b}$"
},
{
"author": "C.~B\\\"uttner$^{a}$"
},
{
"author": "K.~Daumiller\\address{Institut f{\\\"u}r Experimentelle Kernphysik"
},
{
"author": "Universit{\\\"a}t Karlsruhe, D--76021 Karlsruhe, Germany}"
},
{
"author": "P.~Doll$^{a}$"
},
{
"author": "J.~Engler$^{a}$"
},
{
"author": "F.~Fe{\\ss}ler$^{a}$"
},
{
"author": "H.J.~Gils$^{a}$"
},
{
"author": "R.~Glasstetter$^{d}$"
},
{
"author": "R.~Haeusler$^{a}$"
},
{
"author": "W.~Hafemann$^{a}$"
},
{
"author": "D.~Heck$^{a}$"
},
{
"author": "T.~Holst$^{a}$"
},
{
"author": "K.--H.~Kampert$^{a,d}$"
},
{
"author": "H.~Keim$^{a}$"
},
{
"author": "H.O.~Klages$^{a}$"
},
{
"author": "D.~Martello$^{d}$"
},
{
"author": "H.J.~Mathes$^{a}$"
},
{
"author": "P.~Matussek$^{a}$"
},
{
"author": "H.J.~Mayer$^{a}$"
},
{
"author": "J.~Milke$^{a}$"
},
{
"author": "D.~M{\\\"u}hlenberg$^{a}$"
},
{
"author": "J.~Oehlschl{\\\"a}ger$^{a}$"
},
{
"author": "M.~Petcu$^{b}$"
},
{
"author": "H.~Rebel$^{a}$"
},
{
"author": "M.~Risse$^{a}$"
},
{
"author": "M.~Roth$^{a}$"
},
{
"author": "G.~Schatz$^{a}$"
},
{
"author": "F.K.~Schmidt$^{a}$"
},
{
"author": "T.~Thouw$^{a}$"
},
{
"author": "H.~Ulrich$^{a}$"
},
{
"author": "A.~Vardanyan$^{c}$"
},
{
"author": "B.~Vulpescu$^{b}$"
},
{
"author": "J.H.~Weber$^{a}$"
},
{
"author": "J.~Wentz$^{a}$"
},
{
"author": "T.~Wiegert$^{a}$"
},
{
"author": "J.~Wochele$^{a}$"
},
{
"author": "S.~Zagromski$^{a}$"
}
] |
The main goals of the KASCADE (KArlsruhe Shower Core and Array DEtector) experiment are the determination of the energy spectrum and elemental composition of the charged cosmic rays in the energy range around the knee at $\approx 5\,$PeV. Due to the large number of measured observables per single shower a variety of different approaches are applied to the data, preferably on an event-by-event basis. First results are presented and the influence of the high-energy interaction models underlying the analyses is discussed. \vspace{1pc} \vspace{-1.pc}
|
[
{
"name": "taup.tex",
"string": "\\documentclass[twoside]{article}\n\\usepackage{fleqn,espcrc2}\n\\usepackage{graphicx}\n\\hyphenation{author another created financial paper \nre-commend-ed Post-Script CORSIKA KASCADE SIBYLL\nForschungs-zentrum}\n\\renewcommand{\\bottomfraction}{0.999}\n\\renewcommand{\\topfraction}{0.999}\n\\renewcommand{\\textfraction}{0.001}\n\\parindent0pc\n\n\\title{First results of the air shower experiment KASCADE}\n\n\\author{A.~Haungs\\address{Institut f{\\\"u}r Kernphysik, \n Forschungszentrum Karlsruhe, P.O. Box 3640, \n\t D--76021 Karlsruhe, Germany}\\thanks{corresponding \n\t author, e-mail: [email protected]},\n\tT.~Antoni$^{\\rm a}$, \n\tW.D.~Apel$^{\\rm a}$, \n F.~Badea\\address{Institute of Physics and Nuclear \n\tEngineering, RO--7690 Bucharest, Romania},\n\tK.~Bekk$^{\\rm a}$, \n\tK. Bernl{\\\"o}hr$^{\\rm a}$,\n\tH.~Bl\\\"umer$^{\\rm a,d}$, \n\tE.~Bollmann$^{\\rm a}$, \n\tH.~Bozdog$^{\\rm b}$, \n\tI.M.~Brancus$^{\\rm b}$, \n\tC.~B\\\"uttner$^{\\rm a}$,\n A.~Chilingarian\\address{Cosmic Ray Division, Yerevan Physics \n\t Institute, Yerevan 36, Armenia},\n\tK.~Daumiller\\address{Institut f{\\\"u}r Experimentelle \n Kernphysik, Universit{\\\"a}t Karlsruhe, \n D--76021 Karlsruhe, Germany}, \n P.~Doll$^{\\rm a}$, \n\tJ.~Engler$^{\\rm a}$, \n\tF.~Fe{\\ss}ler$^{\\rm a}$, \n\tH.J.~Gils$^{\\rm a}$, \n\tR.~Glasstetter$^{\\rm d}$, \n\tR.~Haeusler$^{\\rm a}$,\n\tW.~Hafemann$^{\\rm a}$, \n\tD.~Heck$^{\\rm a}$, \n\tJ.R.~H{\\\"o}randel$^{\\rm d}$\\thanks{now at: University of \n\t Chicago, Chicago, IL 60637},\n T.~Holst$^{\\rm a}$, \n\tK.--H.~Kampert$^{\\rm a,d}$, \n\tH.~Keim$^{\\rm a}$, \n\tJ.~Kempa\\address{Department of Experimental Physics, \n\t University of Lodz, PL--90236 Lodz, Poland},\n\tH.O.~Klages$^{\\rm a}$, \n J.~Knapp$^{\\rm d}$\\thanks{now at: University of Leeds, \n\t Leeds LS2 9JT, U.K.},\n\tD.~Martello$^{\\rm d}$,\n H.J.~Mathes$^{\\rm a}$,\n\tP.~Matussek$^{\\rm a}$, \n\tH.J.~Mayer$^{\\rm a}$, \n\tJ.~Milke$^{\\rm a}$, \n\tD.~M{\\\"u}hlenberg$^{\\rm a}$, \n\tJ.~Oehlschl{\\\"a}ger$^{\\rm a}$,\n\tM.~Petcu$^{\\rm b}$, \n H.~Rebel$^{\\rm a}$, \n\tM.~Risse$^{\\rm a}$, \n\tM.~Roth$^{\\rm a}$, \n\tG.~Schatz$^{\\rm a}$, \n\tF.K.~Schmidt$^{\\rm a}$, \n T.~Thouw$^{\\rm a}$, \n\tH.~Ulrich$^{\\rm a}$, \n\tA.~Vardanyan$^{\\rm c}$,\n\tB.~Vulpescu$^{\\rm b}$, \n\tJ.H.~Weber$^{\\rm a}$, \n\tJ.~Wentz$^{\\rm a}$, \n\tT.~Wiegert$^{\\rm a}$, \n J.~Wochele$^{\\rm a}$,\n\tJ.~Zabierowski\\address{Soltan Institute for Nuclear Studies, \n\t\t\t PL--90950 Lodz, Poland},\n\tS.~Zagromski$^{\\rm a}$ }\n \n\\begin{document}\n\n\\begin{abstract}\nThe main goals of the KASCADE (KArlsruhe Shower Core and \nArray DEtector) experiment are the determination of the\nenergy spectrum and elemental composition of the charged\ncosmic rays in the energy range around the knee at \n$\\approx 5\\,$PeV. Due to the large number of measured\nobservables per single shower a variety of different approaches\nare applied to the data, preferably on an event-by-event basis.\nFirst results are presented and the influence of\nthe high-energy interaction models underlying the \nanalyses is discussed. \n\\vspace{1pc}\n\\vspace{-1.pc}\n\\end{abstract}\n\n% typeset front matter (including abstract)\n\\maketitle\n\n\\section{INTRODUCTION}\nThe air shower experiment \nKASCADE \\cite{klages} aims at the investigation of the knee \nregion of the charged cosmic rays. It is built up as\na multidetector setup for measuring simultaneously a large \nnumber of observables in the different particle (electromagnetic,\nmuonic and hadronic) components of the extended air shower (EAS). \nThis enables to \nperform a multivariate multiparameter analysis for the\nregistered EAS on an event-by-event basis to account for the non\nparametric, stochastic processes of the EAS development in the\natmosphere.\nIn parallel the KASCADE collaboration tries to improve the \ntools for the Monte Carlo simulations with the relevant\nphysics. The code CORSIKA \\cite{cors} allows not only \nthe detailed three dimensional simulation of the shower \ndevelopment in all particle components (including neutrinos) \ndown to the observation level,\nbut it has been implemented several high-energy\ninteraction models. \nAs the basic physics of these models in the relevant energy region\nand in the extreme forward direction cannot be tested at \npresent days' accelerators, the test of these models emerged as one of the\ngoals of the KASCADE experiment. \nThe following overview is based on results presented at the 26$^{\\rm\nth}$ International Cosmic Ray Conference in Salt Lake City, Utah \n1999 \\cite{slc}. \n \n\\section{THE KASCADE EXPERIMENT}\nThe KASCADE array consists of 252 detector \nstations in a $200 \\times 200\\,$m$^2$ \nrectangular grid containing unshielded liquid \nscintillation detectors ($e/\\gamma$-detectors) and below 10 cm \nlead and 4 cm steel plastic scintillators as muon-detectors.\nThe total sensitive areas are $490\\,$m$^2$ for the $e/\\gamma$-\nand $622\\,$m$^2$ for the muon-detectors. \nIn the center of the array a hadron calorimeter \n($16 \\times 20\\,$m$^2$) is built up, consisting \nof more than 40,000 liquid ionisation chambers in 8 layers with \na trigger layer consisting of 456 scintillation detectors \nin between.\nBelow the calorimeter a setup of position sensitive multiwire \nproportional chambers (MWPC) in two layers measures \nhigh-energy muons ($E_\\mu > 2\\,$GeV) of the EAS. \\\\\nFor each single shower a large number of observables \nare reconstructed with small uncertainties.\nFor example, the errors for the so-called shower sizes, \ni.e. total numbers of electrons $N_e$ \nand number of muons in the range of the core distance \n$40-200\\,$m $N_\\mu^{tr}$, are smaller than 10$\\%$. \\\\\nThe resulting frequency spectra of the sizes\n(inclusive the spectra of the hadron number and muon density \nspectra at different core distances)\nshow kinks at same integral fluxes. This is a strong hint\nfor an astrophysical source of the knee phenomenon based on pure\nexperimental data, since same intensity of the flux corresponds\nto equal primary energy. \\\\ \nBut for the reconstruction of the primary energy spectrum and\nthe chemical composition detailed Monte Carlo simulations are\nindispensable due to the unknown initial parameters\nand the large intrinsic fluctuations of the stochastic process of \nthe shower development in the atmosphere. The usage of a larger\nnumber of less correlated observables in a multivariate analysis\nparallel to independent tests of the simulation models\ntries to find the solution of this dilemma. \n\n\\section{ANALYSES AND RESULTS}\nIn the air shower simulation program CORSIKA several \nhigh-energy interaction models are embedded including \nVENUS, QGSJET and SIBYLL (Refs. see in \\cite{cors}). \nThe models are based on the Gribov-Regge-theory and QCD \nin accordance with accelerator data. \nExtrapolations for the EAS physics in the knee region\nare necessary due to the high interaction energy and for\n%\n\\begin{figure}[htb]\n \\begin{center}\n \\includegraphics[width=16pc]{trig.wert.eps}\n \\end{center}\n\\vspace*{-1.25cm}\n\\caption{Comparison of simulated and measured integral muon \ntrigger and hadron rates. Uncertainties of the elements' absolute\nfluxes of the relevant energy range is indicated by dotted lines.}\n\\label{fig:rate}\n\\vspace*{-.5cm}\n\\end{figure}\n%\nthe extreme forward direction. \nTo compare KASCADE data with Monte Carlo expectations\na detector simulation by\nGEANT is performed for each CORSIKA simulated shower. \\\\\nOne test is the comparison of simulated integral muon trigger and\nhadron rates with the measurements. This test is sensitive \nto the energy spectrum of the hadrons which are produced \nin the forward direction at primary energies around 10 TeV, where the\nchemical composition is roughly known (Fig.\\ref{fig:rate}). \nFor higher primary energies the hadronic part of the interaction\nmodels are tested by comparisons of different hadronic \nobservables in ranges of shower sizes \\cite{antoni}. \nIn general it is seen that the high-energy \ninteraction models predict\na too large number of hadrons at sea level compared with the\nmeasurements. \\\\\nNonparametric multivariate methods like ``Neural Networks''\nor analyses based on the ``Bayesian decision rules'' \nare applied to the KASCADE data for the estimation of the \nenergy and mass of the cosmic rays on an event-by-event basis. \nThe necessary ``a-priori'' information in form of \nprobability density distributions are won by detailed Monte Carlo \nsimulations with large statistics. \\\\\nFor the energy reconstruction the shower sizes $N_e$ and \n$N_\\mu^{tr}$ as parameters are used in a neural network analyses\n(Fig.\\ref{fig:spec}). \nA parametric approach to the same data \nleads to compatible results (Fig.\\ref{fig:spec}):\n%\n\\begin{figure}[htb]\n\\vspace*{0.1cm}\n \\begin{center}\n \\includegraphics[width=17pc]{energy.eps}\n \\end{center}\n\\vspace*{-1.2cm}\n\\caption{The primary cosmic ray energy spectrum from KASCADE\nand other experiments. The spectral index changes from $\\approx\n\\!-2.7$ to $\\approx \\!-3.1$ at the knee position of $\\approx 5\\cdot\n10^6\\,$GeV.}\n\\label{fig:spec}\n\\vspace*{-.5cm}\n\\end{figure}\n%\nhere a simultaneous fit to the $N_e$ and $N_\\mu^{tr}$\nsize spectra is performed.\nThe kernel function of this fit contains the size-energy \ncorrelations for two primary masses (proton and iron)\nobtained by Monte Carlo simulations. \\\\\nAn analysis of the size-ratio $\\lg (N_\\mu^{tr})/ \\lg (N_e)$ \ncalculated for each single event leads to results of the \nelemental composition for different energy ranges \n(Fig.\\ref{fig:comp}). \nThe measured distribution of these ratios is assumed to be a \nsuperposition of simulated distributions for different primary \nmasses. \nThe large iron sampling calorimeter of KASCADE \nallows to investigate\nthe hadronic part of EAS in terms of the chemical\ncomposition. For six different hadronic observables \n(won by spatial and energy distributions of the hadrons) \nthe deviations of the mean values \nto expectations of pure proton and iron primaries \nin certain energy ranges are calculated. \\\\\nBesides the use of global parameters like the shower sizes, \nsets of different parameters are used for neural network and \nBayesian decision analyses. \nExamples of such observables are the number of reconstructed hadrons\nin the calorimeter, their reconstructed energy sum, \nnumber of muons in the shower center, or\nparameters obtained by a fractal analysis of the hit pattern of \nmuons and secondaries at the MWPC.\n%\n\\begin{figure}[htb]\n \\begin{center}\n\\vspace*{-.cm}\n \\includegraphics[width=16.5pc]{comp.eps}\n \\end{center}\n\\vspace*{-1.3cm}\n\\caption{The chemical composition estimated with the KASCADE data, \nusing different methods and observables from different particle\ncomponents.}\n\\label{fig:comp}\n\\vspace*{-.5cm}\n\\end{figure}\n%\nThe latter ones are sensitive to the structure of the shower core\nwhich is mass sensitive due to different shower developments\nof light and heavy particles in the atmosphere.\nIn Figure \\ref{fig:comp} results of a Bayesian analyses \nand of a separate neural net analysis using the fractal parameters \nare shown. \\\\\nAs the tendency of the results of each described method is \nconsistent with a heavier primary mass after the knee region, but\nthe absolute scale strongly depends on the particle component\nof which the observables are constructed from, the syllogism\nis that the balance of the energy and number of particles \nbetween the muonic, electromagnetic and hadronic part in the EAS \ndiffers for simulations and the real shower development. \n \n\\section{CONCLUSIONS}\nFirst results of the KASCADE experiment \ncan be summarized by following statements:\nAll secondary particle components of the showers display a kink \nin the size spectra. \nThis strongly supports an astrophysical origin of the ``knee'', \nrather than effects of the interaction of the primaries in the \natmosphere.\nThe knee is sharper for the light primary component than\nfor the heavy one. \nThis result follows from the measurement as an increasing average \nmass of the primary cosmic rays above the observed kink, together \nwith the energy dependent mass classification of single air showers.\nBut none of the high-energy interaction models en vogue is \nable to fit the data of all observables consistently. \n\n\n\\begin{thebibliography}{9}\n\\bibitem{klages} \nH.O. Klages et al. -- KASCADE collaboration, \nNucl. Phys. B (Proc. Suppl.) 52B (1997) 92. \n\\bibitem{cors}\nD. Heck et al., FZKA 6019, Forschungszentrum Karlsruhe (1998).\n\\bibitem{slc}\nT. Antoni et al. -- KASCADE collaboration, \nProc. 26$^{\\rm th}$ ICRC, Salt Lake City, Utah 1999; \npublished as: K.H. Kampert (Editor), FZKA 6345, \nForschungszentrum Karlsruhe (1999). \n\\bibitem{antoni}\nT. Antoni et al. -- KASCADE collaboration, J. Phys. G: Nucl. \nPart. Phys. 25 (1999) 2161.\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002025.extracted_bib",
"string": "\\begin{thebibliography}{9}\n\\bibitem{klages} \nH.O. Klages et al. -- KASCADE collaboration, \nNucl. Phys. B (Proc. Suppl.) 52B (1997) 92. \n\\bibitem{cors}\nD. Heck et al., FZKA 6019, Forschungszentrum Karlsruhe (1998).\n\\bibitem{slc}\nT. Antoni et al. -- KASCADE collaboration, \nProc. 26$^{\\rm th}$ ICRC, Salt Lake City, Utah 1999; \npublished as: K.H. Kampert (Editor), FZKA 6345, \nForschungszentrum Karlsruhe (1999). \n\\bibitem{antoni}\nT. Antoni et al. -- KASCADE collaboration, J. Phys. G: Nucl. \nPart. Phys. 25 (1999) 2161.\n\\end{thebibliography}"
}
] |
astro-ph0002026
|
Mass-loss induced instabilities in fast rotating stars
|
[
{
"author": "F. Ligni\\`eres \\inst{1,} \\inst{2}"
},
{
"author": "C. Catala \\inst{3}"
},
{
"author": "A. Mangeney \\inst{2}"
}
] |
To explain the origin of Herbig Ae/Be stars activity, it has been recently proposed that strong mass-losses trigger rotational instabilities in the envelope of fast rotating stars. The kinetic energy transferred to turbulent motions would then be the energy source of the active phenomena observed in the outer atmosphere of Herbig Ae/Be stars (Vigneron et al. 1990; Ligni\`eres et al. 1996). In this paper, we present a one-dimensional model of angular momentum transport which allows to estimate the degree of differential rotation induced by mass-loss. Gradients of angular velocity are very close to $- 2 \Omega / R$ ($\Omega$ being the surface rotation rate and $R$ the stellar radius). For strong mass-loss, this process occurs in a short time scale as compared to other processes of angular momentum transport. Application of existing stability criteria indicates that rotational instabilities should develop for fast rotating star. Thus, in fast rotating stars with strong winds, shear instabilities are expected to develop and to generate subphotospheric turbulent motions. Albeit very simple, this model gives strong support to the assumption made by Vigneron et al. 1990 and Ligni\`eres et al. 1996. \keywords{Instabilities -- Stars: mass-loss -- rotation}
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[
{
"name": "rot.soum.tex",
"string": "\\documentclass{aa}\n%\\documentclass{aa}\n\\usepackage{graphics}\n\\begin{document}\n \n\\thesaurus{02.(02.09.1)08.(08.13.2;08.18.1)}\n \n\\title{Mass-loss induced\ninstabilities\nin fast rotating stars}\n\\author{F. Ligni\\`eres \\inst{1,} \\inst{2} \\and C. Catala \\inst{3}\n\\and A. Mangeney \\inst{2}}\n\\institute{Astronomy Unit, Queen Mary \\& Westfield College, Mile\nEnd Road, London E14NS, UK \\and\nD\\'epartement de Recherche Spatiale et Unit\\'e de Recherche\nassoci\\'ee au CNRS 264, Observatoire de Paris-Meudon, F-92195\nMeudon Cedex, France \\and\nLaboratoire d'Astrophysique de Toulouse et Unit\\'e de Recherche associ\\'ee\nau CNRS 285, Observatoire Midi-Pyr\\'en\\'ees, 14 avenue Edouard Belin, 31400\nToulouse, France}\n\\offprints{F. Ligni\\`eres}\n\\mail{[email protected]}\n\\date{Received ?? / Accepted ??}\n\\authorrunning\n\\titlerunning\n\\maketitle\n\\begin{abstract}\nTo explain the origin of Herbig Ae/Be stars activity,\nit has been recently proposed\nthat strong mass-losses trigger \nrotational instabilities in the envelope\nof fast rotating stars.\nThe kinetic energy transferred to turbulent motions\nwould then be the energy\nsource of the active phenomena observed\nin the outer atmosphere of Herbig Ae/Be stars \n(Vigneron et al. 1990; Ligni\\`eres et al. 1996).\n \nIn this paper, we present a one-dimensional model \nof angular momentum transport\nwhich allows to estimate the degree of \ndifferential rotation \ninduced by mass-loss. \nGradients of\nangular velocity are very close to $- 2 \\Omega / R$ \n($\\Omega$ being the surface rotation rate and $R$\nthe stellar radius). \nFor strong mass-loss,\nthis process occurs in a short time\nscale as compared to other processes\nof angular momentum transport.\nApplication of existing stability criteria indicates that\nrotational instabilities should develop for fast rotating star.\nThus, in fast rotating\nstars with strong winds,\nshear instabilities are expected\nto develop and to generate\nsubphotospheric turbulent motions.\nAlbeit very simple, this model gives strong support to\nthe assumption made by Vigneron et al. 1990 and Ligni\\`eres et al. 1996.\n\n\\keywords{Instabilities -- Stars:\nmass-loss -- rotation}\n\\end{abstract}\n\n\\section{Introduction}\n\nAlthough far from complete, the overall picture describing\nthe angular momentum \nevolution of\nsolar type stars \nis well established. Despite modest mass-loss rates,\n$\\dot{M} = 10^{-14} {\\rm M}_{\\sun} {\\rm yr}^{-1}$ for the sun, \nmagnetised stellar winds\nstrongly brake the rotation of the star.\nThe decrease of the angular velocity then\nreacts back on the magnetic field by reducing the efficiency of\nthe dynamo process.\nThis picture cannot be applied as such to early-type stars. First of all, the \nhistory of stellar rotation at intermediate and high masses is\ngenerally still poorly known; besides, the presence of magnetic fields\nin early-type stars has not been established, except for some categories\nof chemically peculiar stars, as well as for a couple of particular cases\n(Donati et al. 1997; Henrichs et al. 2000).\nOn the other hand, \nwe know that early type stars \ncan experience strong angular momentum losses\nas\nstellar winds with very large mass loss rate have been observed\n($\\dot{M} \\approx 10^{-5} - 10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$). \nIn this paper, we investigate how such\nangular momentum losses will affect the stellar rotation, assuming\nmagnetic fields are not dynamically relevant.\n\nThis question has not yet received much attention although it might\nhave important consequences for stellar structure and evolution\nas well as for the understanding of early-type stars activity.\nIn the context of stellar evolution, the effect of mass-loss on\nrotation has to be investigated since the rotation strongly\ninfluences the stellar structure. However, current models \nof stellar evolution with rotation do not take this effect\ninto account (Talon et al. 1997, Denissenkov et al. 1999). \nAs explained below, we have been confronted to the same question\nwhile investigating the origin\nof the very strong activity of Herbig Ae/Be stars, a class of \npre-main-sequence stars with masses ranging from $2$ to $5 {\\rm M}_{\\sun}$.\n\nA significant fraction of these objects is known to possess extended chromospheres, \nwinds, and to show high levels of spectral variability. In addition, the presence of \nmagnetic fields, first suggested by the rotational modulation of certain spectral lines\n(Catala et al. 1986), has been recently supported by a direct detection at the surface of \nthe Herbig Ae star, HD 104237 (Donati et al. 1997).\nDetailed estimates of the non-radiative heating in the outer atmosphere of Herbig Ae/Be \nstars (Catala 1989, Bouret et al. 1998) \ncompared to observational constraints on the available energy \nsources strongly suggest that the rotation of the star is the only \nenergy source capable of powering such activity\n(see discussion in F.Ligni\\`eres et al. 1996).\nThis led\nVigneron et al. (1990)\nto propose a scenario whereby\nthe braking torque exerted by the stellar wind\nforces turbulent motions in a differentially rotating layer\nbelow the stellar surface. Then, by invoking\nan analogy with stellar\nconvection zones,\nthese turbulent motions could generate a magnetic field\nwhich would transfer and dissipate the turbulent kinetic\nenergy into the outer layers of the star.\n\nUnlike Herbig stars, there is at present no observational evidence of\nnon-radiative energy input in the atmosphere of OB stars. \nTheir radiatively-driven \nwinds\ndo not require any additional \nacceleration mechanism and an eventual non-radiative heating\nwould be very difficult to detect because most lines are saturated.\nHowever, they show various forms of spectral variability. \nRecent observations\nseem to indicate that these phenomena\nare not due to an intrinsic variability of the wind\nbut are instead\ncaused by co-rotating features on the stellar surface (Massa et al. 1995). \nAs proposed in the literature (Howarth et al. 1995; Kaper et al. 1996), \nthese corotating features could be due to a magnetic structuration of the wind.\nSince OB stars rotate fast and possess strong winds, \nthe Vigneron et al. scenario might\nalso explain these phenomena.\nThe recent direct detection of a magnetic field in an early Be star,\n$\\beta$~Cep, adds some credit to this hypothesis (Henrichs et al. 2000).\n\nIn this paper, we shall investigate the starting assumption of\nthe Vigneron et al. scenario namely that\nthe braking torque of an\nunmagnetised wind generates strong enough velocity shear \nto trigger an instability in the subphotospheric layers.\nThis is a crucial step in the scenario since the onset of the instability \nallows to transfer kinetic energy from rotational motions to turbulent\nmotions. \n\nThe possible connection between mass-loss and instability had been already \nsuggested by \nSchatzman (1981). However, the onset of the instability is not really\nconsidered in this study since it is assumed from the start that\nthe wind driven angular momentum losses induce\na turbulent flux of angular momentum. \nHere, we propose a simple model of angular momentum transport by a purely radial\nmass flux in order \nto estimate the angular velocity gradients induced by mass loss.\nThen, the stability of these gradients\nis studied according to existing stability criteria.\nNote that, as\nwe neglect latitudinal flows,\nour model is best regarded as an equatorial model.\n\nIn the absence of magnetic fields, the braking effect\nof a stellar wind is simply due to\nthe fact that matter\ngoing away from the rotation\naxis has to slow down to preserve its angular momentum.\nThus, for the star's surface to be significantly braked,\nfluid parcels coming from deep layers inside the star have \nto reach the surface. Since radial velocities induced by\nmass-loss are very small deep inside the star,\nthis is expected to take a relatively long time, not \nvery different from the\nmass-loss time scale.\nBy contrast, we shall see that the formation of \nunstable angular velocity gradients near the surface take place \nin a very short time, much smaller than the braking time scale.\n\nThe paper is organised as follows: first, we estimate the time\nscale\ncharacterising the braking of the stellar surface and relate it\nto the mass loss time scale (Sect. 2). Then, we show that radial\noutflows in stellar envelopes generate differential rotation\nand we estimate the time scale of this process (Sect. 3). \nThe stability of these angular velocity gradients is considered\n(Sect. 4)\nand the results are summarised and discussed (Sect. 5).\n\n\\section{Braking of mass-losing stars}\n\nGenerally speaking, the braking of\nthe star's surface\ndepends\non the mass-loss mechanism and on the efficiency\nof angular momentum transfer inside\nthe star. In this section, we shall\nmake assumptions regarding these processes in order to estimate\nthe braking time scale.\nHowever, before we consider these particular assumptions,\nit is interesting to \nshow that the simple fact that the star adjusts\nits hydrostatic structure to its decreasing mass\nalready implies\nthat the star slows down as it loses mass.\n\nIndeed, according to models of pre-main-sequence\nevolution (Palla \\& Stahler 1993),\na $2 M_{\\sun}$ pre-main-sequence star\nlosing mass at a rate of the order of $\\dot{M} =\n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$\nwill have lost about one percent of its mass \nwhen it arrives on the main sequence.\nBecause mass is concentrated in the core of stars,\none percent of the total mass corresponds to \na significant fraction of the envelope. \nFor pre-main-sequence models of $2$ to $5 M_{\\sun}$,\nthis means\nthat all the matter initially located above \nthe radius $R_I \\approx 0.63 R_*$\nis expelled during the pre-main-sequence evolution.\nBut, during this mass-loss process, \nthe star continuously adjusts its structure to its decreasing mass\nand, from the point of view of stellar structure,\nthe loss of 1 percent of mass has a negligible effect\non the stellar radius.\nThus,\nas represented on Fig.1, the sphere\ncontaining 99 \\% of the initial mass must have expanded\nsignificantly during its pre-main-sequence evolution.\nIts moment of inertia has\nincreased and, due to angular momentum conservation, its mean \nangular velocity has been reduced.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig1.eps}}\n\\caption{One percent mass loss generates an expansion of the sphere containing\n$99$ percents of the stellar mass through readjustment of the stellar \nhydrostatic\nstructure. This expansion must be associated with a decrease of the mean\nrotation rate}\n\\end{figure}\n\nThus, we conclude that the hydrodynamic adjustment of stars ensures that\nmass loss is accompanied by a \nmean braking of the remaining matter.\nNow, if one wants to estimate the actual braking of the stellar surface,\nassumptions have to be\nmade on the mass-loss process and\non the efficiency of angular momentum transfer inside the star.\nIn order to obtain the order of magnitude of the braking time scale, \nwe assume that mass-loss is isotropic and constant in time and\nwe\nconsider two extreme assumptions regarding the efficiency of angular momentum transfer.\n\nFirst, we assume that the transfer of angular momentum is only due to\nradial expansion. Then, \nangular momentum conservation \nstates that \nthe angular velocity $\\Omega_I$ of a fluid parcel \nlocated at a radius $r=R_I$ will have decreased by $(R_I/R)^2$\nwhen it reaches the stellar surface. This occurs when\nall the matter above $r=R_I$ has been expelled so that\nthe decrease of the surface angular velocity can be related to the mass-loss.\nWe used the density structure of a $2 M_{\\sun}$ pre-main-sequence model (Palla \\& Stahler 1993)\nfor the following calculation.\n\nSecond, we assume that an unspecified transfer mechanism enforces solid\nbody rotation throughout the star so that angular momentum losses are \ndistributed over the whole star and the braking of the stellar surface \nis less effective. In this case, \nglobal angular momentum conservation reads\n\\begin{equation}\n\\frac{dJ}{J} = \\frac{2}{3} \n\\frac{M R^2}{I} \\frac{dM}{M},\n\\end{equation}\n\\noindent\nwhere $J = I \\Omega$ is the total angular momentum.\nAccording to stellar structure models\nof $2$ to $5 M_{\\sun}$ pre-main-sequence stars, the \nradius of gyration,\n$I / M R^2$ is close to $0.05$ so that\nthe \nangular velocity\ndecrease is approximatively given by \n\\begin{equation}\n\\frac{\\Omega_f}{\\Omega_i} = \\frac{I_i}{I_f} \n\\left(\\frac{M_f}{M_i}\\right)^{40/3} \n\\end{equation}\n\\noindent\nTo simply relate the braking to the mass-loss, we also assumed\nthat the \ndecrease of the moment of inertia is proportional to the mass decrease,\nor equivalently\nthat mass-loss induces an uniform density decrease \nthroughout the star.\nAlbeit rough, this assumption is not critical for the conclusion drawn in \nthis section. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig2.eps}}\n\\caption{Braking of the stellar surface as a function of the percentage\nof mass lost assuming\nsolid body rotation (solid line) or\npurely radial expansion (dashed line)}\n\\end{figure}\n\nStarting with an uniformly rotating star, \nFig. 2 presents the braking of the stellar surface as a function\nof the percentage of mass lost assuming \nsolid body rotation (solid line) and \nradial\nexpansion (dashed line). \nThis shows that, in the case of solid body rotation,\nthe braking time scale is about ten times smaller than the mass loss time scale,\nwhereas, it is hundred times smaller in the case of radial expansion \n(the braking time scale is defined as the time required to decrease the surface\nangular velocity by a factor $e$). We\ntherefore conclude that the braking time scale is significantly smaller \nthan the mass-loss time scale although both time scales\ndoes not differ by many orders of \nmagnitude.\n\nIn the next section, we study \nthe formation of angular velocity gradients in a stellar envelope\nassuming the transport of angular momentum is only due\nto a radial mass flux. We shall see\nthat this process generates strong near surface gradients in a time scale \nsmaller by many orders of magnitude than the mass-loss time scale.\n\n\\section{Radial advection of angular momentum across\na stellar surface}\n\nNon-uniform radial expansion tends to generate \ndifferential rotation and \nthis is particularly true across the stellar surface where\nthe steep density increase has to be accompanied by\na steep decrease of the radial velocity.\nTo show this let us follow the expansion of two \nspherical layers located at different depths in the star's envelope,\nand rotating at the same rate.\nAfter a given time,\nthe outer layer will have travelled a much larger distance\nthan the inner one so that its\nangular velocity will have decreased \nmore than \nthat of the inner\nlayer. \nA gradient of angular velocity has then appeared between both layers.\n\nTo estimate the gradient generated by this non-uniform expansion,\nwe write down the angular momentum conservation assuming the\ntransport of angular momentum is only due to a radial flow.\nConsequently, angular momentum transfers by viscous stresses, \nmeridional circulation, gravity waves or turbulence are neglected all together. \nAlthough latitudinal inhomogeneities\nin the mass-loss mechanism or Eddington-Sweet circulation\nare expected to induce latitudinal flows, we note that\nthe present assumption would be still justified in the\nequatorial plane if the meridional\ncirculation is symmetric with respect to the equatorial plane.\n\nIn the context of our simplified model, the angular momentum balance reads\n\\begin{equation}{\\label{eq:momcin}}\n\\frac{\\partial}{\\partial t}(\\omega)+v(r,t)\n\\frac{\\partial}{\\partial r} (\\omega)=0,\n\\end{equation}\n\\noindent\nwhere $\\omega$ is the specific angular momentum and\n$v(r,t)$ is the radial velocity. Up to mass loss rates\nof the order of $10^{-6} {\\rm M}_{\\sun} {\\rm yr}^{-1}$,\nradial velocities\ncarrying out a time-independent and isotropic mass-loss\nare much smaller than the local sound speed. Consequently\nthe star is always very close to hydrostatic equilibrium\nand continuously adjusts its structure to its decreasing mass.\nThis means in particular that the temporal variations\nof the density near the surface are small, because the effect of \nmass-loss\nis distributed over the whole star through hydrostatic equilibrium. \nAccordingly, temporal \nvariations of the radial velocities\nare small and we shall \nneglect them as their inclusion would\nnot \nmodify our conclusions.\nThen, the radial outflows satisfies\n\\begin{equation}{\\label{eq:mass}}\n4 \\pi r^2 \\varrho(r) v(r) = \\dot{M},\n\\end{equation}\n\\noindent\nwhere $\\varrho(r)$ is given by stellar structure models.\n\nWith the above assumptions, the specific angular momentum evolves\nlike a passive scalar advected in a one dimensional stationary \nflow $v(r)$. The mathematical problem can be readily solved and we will do\nso in the following for\na radial flow corresponding to\na $2 M_{\\sun}$ star with\na mass loss rate of $\\dot{M} =\n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$.\nBut first we derive useful properties by studying the evolution \nof the angular momentum gradient in the general case.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig3.eps}}\n\\caption{Gradients smoothing in an accelerated flow}\n\\end{figure}\n\nExcept when\n$\\omega$ or $v$ are uniform in space, advection\nalways modifies the distribution of the conserved quantity.\nWhile decelerated flows tend to sharpen $\\omega$-gradients,\naccelerated flows smooth them out.\nTo illustrate the process of gradient smoothing in an accelerated\nflow, the\nangular momentum evolution of two neighbouring fluid \nelements $A$\nand $B$ has been represented\nin Fig.3. Following the motions, \nthe angular momentum gradient between these two points decreases \nbecause their separation $\\Delta r$ increases while \nthe angular momentum difference $\\Delta \\omega$ is conserved.\n\nThis simple sketch can also be used to quantify the \ngradient decrease. We first note that $A$ and $B$ \ntravel the distance separating $r_1 + \\Delta r_1$ from $r_2$\nin the same time. Thus, the time interval \nrequired by A to go from $r_1$ to $r_1 + \\Delta r_1$ is\nthe same as the one used by $B$ to go from\n$r_2$ to $r_2 + \\Delta r_2$.\nThis is expressed by,\n$\\Delta r_2 / v(r_{2}) = \\Delta r_1 / v(r_{1})$, and then,\n\\begin{equation} \\label{eq:mi0}\nv(r_{1}) \\frac{\\Delta \\omega}{\\Delta r_1} = v(r_{2})\n\\frac{\\Delta \\omega}{\\Delta r_2}.\n\\end{equation}\n\\noindent\nTaking the limit of vanishing separation between $A$ and $B$,\nwe conclude \nthat the product $v(r) \\partial \\omega/\\partial r$ is\nconserved following the motions, a property which can\nbe readily\nverified by calculating \nthe Lagrangian derivative of \n$v \\partial\\omega/\\partial r$.\n\nThis property implies that\nangular momentum gradients \ncan be completely smoothed out if they are advected in a \nstrongly enough accelerated flow.\nThis is particularly relevant near stellar surfaces\nwhere steep density gradients\ninduce steep radial velocity gradients.\n\nTo specify this effect we express the conservation of\n$v \\partial \\omega / \\partial r$\nfor the radial outflow given by Eq. (\\ref{eq:mass}).\nThen, the evolution of the logarithmic\ngradients of the angular velocity following the flow\nbetween radii $r_1$ and $r_2$ reads\n\\begin{equation}\n\\frac{\\partial \\ln \\Omega}{\\partial \\ln r}(r_2) = -2 +\n\\frac{\\varrho(r_2)}{\\varrho(r_1)} {\\left(\\frac{r_2}{r_1}\\right)}^{3}\n\\left(\\frac{\\partial \\ln \\Omega}{\\partial \\ln r}(r_1) +2 \\right), \n\\end{equation}\n\\noindent\nwhere the quantity\n$\\frac{\\partial \\ln \\Omega}{\\partial \\ln r} + 2$ measures\ndepartures from uniform\nspecific angular momentum.\n\nIn this expression,\n$\\varrho(r) r^3$ decreases almost like $\\varrho(r)$\nin the vicinity of the\nphotosphere since the density decreases considerably\nover distances small compared to the stellar radius.\nThen, the above expression shows that \nany departure from constant\nspecific angular momentum will have decreased by a factor $e^n$\nafter crossing $n$ density scale heights.\nMoreover, initial departures can not be too large otherwise\nthe corresponding differential rotation would be subjected\nto powerful instabilities. Then, for any realistic values of the\ninitial angular velocity gradients, fluid elements reaching the surface\nwill have an angular velocity gradient close to $- 2 \\Omega/R$.\n \nWe confirmed the validity of this simple picture by solving the advection\nproblem for the density profile corresponding to the stellar structure\nmodel\nof a pre-main-sequence \n$2 M_{\\sun}$ star\n(Palla \\& Stahler 1993). \nAgain,\nthe mass-loss rate\nhas been fixed to $\\dot{M} = \n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$.\nStarting from a solid body rotation, the evolution of the rotation profile\nin the vicinity of the\nstellar surface is presented in Fig.4.\nThe different curves correspond to increasing advection times, \n$10^{-1}$, $1$, $10$,\n$10^{2}$, $10^{3}$ and $10^{4}$ years, respectively.\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig4.eps}}\n\\caption{Rotation rate profiles\nin the stellar envelope\nof a 2 $M_{\\sun}$ star as a result of the advection\nby a radial flow with a constant mass flux \n$\\dot{M} = \n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$.\nThe initial rotation rate is uniform and its evolution \nis shown after \n$10^{-1}$, $1$, $10$,\n$10^{2}$, $10^{3}$ and $10^{4}$ years, respectively}\n\\end{figure}\n\nWe observe that the evolution is first rapid and then\nmuch slower. This is because the evolution starts with\nthe rapid expansion of the outer layers\nwhich tends to set-up a profile of \nuniform specific angular momentum\n$\\Omega \\propto 1/ r^2$.\nOnce this is done,\nthe evolution takes place on much larger time scales\nas it involves \nthe much slowly expanding inner layers.\nThe gradual set-up of the $\\Omega \\propto 1/r^2$ profile is confirmed by \nthe evolution of the\nangular velocity logarithmic gradients. As shown on \nFig.5, specific angular momentum gradients are rapidly\nsmoothed out in the outer layers while the inner ones become\naffected after a long time. \n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{fig5.eps}}\n\\caption[ ]{\nLogarithmic derivative of the rotation rate. The initial derivative\nvanishes uniformly \nand its evolution is shown after $10^{-1}$, $1$, $10$,\n$10^{2}$, $10^{3}$ and $10^{4}$ years, respectively}\n\\end{figure}\n\nWe can therefore conclude that starting with\nany realistic angular velocity profile\nin a stellar envelope,\nradial expansion will generate angular velocity gradients very close to \n$-2 \\Omega / R$ near the surface.\n\nWhether such gradients are actually present in the subphotospheric\nlayers of mass-losing\nstars depends on how the characteristic time for the formation \nof these gradients\ncompares with the time\nscales of other angular momentum transport processes.\nThe angular velocity gradients being produced by radial acceleration,\nthe associated time scale is\n\\begin{equation}\nt_G = \\frac{1}{\\frac{\\partial v}{\\partial r}} = \\frac{H_{\\varrho}}{v(r)} =\n\\frac{4 \\pi r^2 \\varrho(r) H_{\\varrho}}{M} t_{\\rm M},\n\\end{equation}\n\\noindent\nwhere $H_{\\varrho}$ is the density scale height and $t_{\\rm M} = M / {\\dot M}$\nis the mass-loss time scale.\nFig.5 shows that no more than one month is necessary to form gradients\nof the order of ${\\Omega} / R$ for a mass loss\nrate\nequal to\n$\\dot{M} =\n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$. \nThis time scale is smaller by many orders of\nmagnitude than the mass-loss\ntime\nscale or the braking time scale. This is because the formation\nof gradients requires radial displacements corresponding to\na density scale height\nwhereas a significant braking requires radial displacements\nof the order of the stellar radius.\n\n\\section{Stability of the angular velocity gradients} \n\nIn this section, we investigate whether the\ndifferential rotation induced by the radial mass-loss\nis sufficient to trigger a hydrodynamical instability.\n\nThe\nuniform angular momentum profile being marginally stable with\nrespect to Rayleigh-Taylor instability, we\nconsider its stability with respect to shear instabilities.\nWhen, as it is the case here,\nthe vorticity associated with the velocity profile does not possess \nextrema, the study of shear instabilities is much complicated by the fact\nthat\nfinite amplitude perturbations involving non-linear effects\nhave to be taken into account.\nExisting stability criteria for such velocity profiles \nrely on laboratory experiments which\nshows critical Reynolds numbers above \nwhich destabilization occurs.\nAlthough the critical Reynolds number depends on the particular\nflow configuration,\nits value is generally of order of \n$1000$.\n\nJ.P. Zahn (1974) proposed the following instability criterion\n\\begin{equation} \n\\frac{\\partial\\Omega}{\\partial r} > {\\left(Pr Re^ \n{\\rm crit}\\right)}^{1/2}\\frac{N}{r}, \\label{eq:stab} \n\\end{equation}\n\\noindent\nwhere $Re^{\\rm crit}$ is the critical Reynolds number, $Pr=\\nu/\\kappa$\nis the Prandtl number comparing the thermal diffusivity $\\kappa$\nto the\nviscosity $\\nu$ and $N$ is the Brunt-V\\\"{a}is\\\"{a}l\\\"{a}\nfrequency\nwhich measures the strength of stable stratification in radiative interiors.\nThe combined effect of the stable\nstratification and the thermal diffusion has been derived on\nphenomenological grounds. However, the way\nthe criterion\ndepends on this effect has\nbeen recently supported in the context of the linear stability theory\n(Ligni\\`eres et al. 1999).\n\nApplying the criterion to an uniform angular momentum profile, we find that\ninstability occurs if the rotation period at the surface is smaller than\n\\begin{equation}\nP \\leq 18.4 \\; \\frac{g_{\\sun}}{g} {\\rm days},\n\\end{equation}\n\\noindent\nwhere the actual temperature gradient has been taken equal to\n$\\nabla = 0.25$, a typical value for\nradiative envelopes according to Cox (1968), and the\nradiative viscosity has been assumed to dominate the molecular one\nwhich is true in the envelope of intermediate mass stars.\nNote also that this expression holds for a mono-atomic completely ionised gas \nin a chemically homogeneous\nstar. When radiation pressure is taken into account, the upper limit of the rotation\nperiod has to be multiplied\nby $1/\\sqrt{4-3\\beta}$,\nwhere $\\beta$ is the ratio between the gas pressure and the total pressure. This\nfactor remains very close to one for pre-main-sequence models from \n$2$ to $5 M_{\\sun}$.\n\nThe above instability condition being easily met by early type stars, we \nconclude that\nmass-loss tends\nto impose an unstable differential rotation\nbelow the surface of early-type stars.\n\n\\section{Discussion and conclusion}\n\nWe have studied the effect of mass-loss on the rotation of stellar envelopes \nin the simplified context of an unmagnetised spherically symmetric outflow.\nIn the same way as an inhomogeneous distribution\nof a passive scalar\ntends to be\nsmoothed out in a expanding flows, the radial gradients of specific\nangular momentum are smoothed out by radial expansion in stellar envelopes.\nThis process becomes more and more effective as one approaches the surface\nbecause expansion becomes stronger and stronger. As shown\nin Figs 4 and 5, a profile\nof uniform angular momentum, $\\Omega \\propto 1/r^2$ is rapidly\nset-up in the outermost layers of the star and then\npervades towards the interior on much larger time scales.\nThese time scales being proportional to the mass-loss time\nscale, they vary very much from stars to stars. For a typical\nHerbig star ($\\dot{M} =\n10^{-8} {\\rm M}_{\\sun} {\\rm yr}^{-1}$),\nan angular velocity gradient close to $-2 {\\Omega}/R$ appears\nin one month. By contrast, for a solar-type mass-loss rate, $\\dot{M} =\n10^{-14} {\\rm M}_{\\sun} {\\rm yr}^{-1}$, it would be $10^6$ times longer\nto reach the same level of differential rotation.\nAccording to existing stability criteria, the uniform angular momentum\nprofile is subjected to shear instabilities provided the rotation period\nis shorter than $18.4 \\; g_{\\sun}/g$ days.\n\nThe present one-dimensional model is admittedly\nnot realistic at least because\nlatitudinal variations occur in rotating\nstars and\ngive rise to a meridional circulation. Nevertheless, as already mentioned,\nneglecting latitudinal flows may be justified in the equatorial plane.\nIn the following \nwe discuss to which extent the neglected processes\ncan prevent the\nformation of turbulent differentially rotating layers\nbelow the surface of rapidly rotating mass-losing stars.\nWe first consider the angular momentum transport and \nthen the stability problem.\n\nLatitudinal variations could be inherent to the mass-loss mechanism\nas proposed for radiatively driven wind emitted from\nfast rotating stars (Owocki \\& Gayley 1997).\nSuch variations are\nlikely to generate a meridional circulation (Maeder 1999)\nbut,\nat the latitudes where outflows occur,\nwe still expect radial expansion \nto play a major role in shaping the angular velocity\nprofile.\n\nThe Eddington-Sweet circulation driven by departure from sphericity\noperates on time scale larger than the Kelvin-Helmholtz time scale of the star. \nThis time scale is of the order of the order of $10^7$ years for a\n$2 M_{\\sun}$ Herbig stars. \nConsequently the Eddington-Sweet circulation is unlikely to prevent the formation\nof the differentially rotating subphotospheric layer for strong mass-loss rate.\n\nTurbulent motions like those generated in thermal convection zones\nmight prevent the formation of the differentially rotating layer.\nIn radiative envelopes however, it is not clear whether turbulent motions\n(not generated by the mass-loss process)\nwould be vigorous enough.\n\nStrong magnetic fields could in principle\nprevent the formation of these gradients.\nNote that\nthis objection is not relevant in\nthe context of the Vigneron et al. scenario where\nthe shear layer is first produced by an unmagnetised wind.\n\nFinally, we also neglected the effect of pre-main-sequence contraction.\nThis is justified because\nthe negative radial velocities associated with\nthe contraction are much smaller than the positive radial\nvelocities induced by mass-loss in the vicinity of the stellar surface.\n\nIn what concerns the stability of the uniform angular momentum\nprofile, one has to remind that the stability criterion results\nfrom an extrapolation of laboratory experiments results.\nDespite recent numerical simulations which contradict\nthe validity of this extrapolation for a differential\nrotation stable with respect to the Rayleigh-Taylor instability (Balbus et al.\n1996), analysis of the experimental results\nreveal that for large values of the Reynolds number\nthe properties of the turbulent flow do not depend on\nits stability or instability with respect to the Rayleigh-Taylor criterion \n(Richard \\& Zahn 1999). The solution of this debate would have to wait numerical \nsimulations with higher resolution or specifically designed laboratory experiments.\n\nThe fact that the shear layer is embedded in an expanding flow may also\naffect the stability because expansion is known to suppress the turbulence.\nFor example, this phenomenon is observed in numerical simulations\nof turbulent convection near the solar surface\n(Stein \\& Nordlund 1998). However, the growth time scale of the instability\nbeing of the order of the rotation period ($\\approx 1$ day for Herbig stars), \nwe do not expect \nthe expansion to be rapid enough to \nsuppress shear turbulence.\n\nWe conclude that the present model of angular momentum advection by a radial flow\nsupports the assumption made by Vigneron et al. (1990) and F. Ligni\\`eres et al. \n(1996) that unmagnetised winds tend to force an unstable differential rotation in the \nsubphotospheric layers of Herbig Ae/Be stars. Note that this work is part of an ongoing \neffort to assess the viability of the Vigneron et al. scenario. F. Ligni\\`eres et al (1996) \nand F.Ligni\\`eres et al. (1998) have already studied the step further, once turbulent motions \nare generated at the top of the radiative envelope, their work pointing towards the formation \nand inwards expansion of a differentially rotating turbulent layer. In addition, \nthree-dimensional numerical simulations are being performed to investigate whether \nmagnetic fields can be generated in such a layer.\n\n\\begin{acknowledgements}\nWe are very grateful to F. Palla and S.W. Stahler for making the results\nof their stellar evolution code available to us.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\\bibitem {1} Bouret J.-C., Catala C., 1998, A\\&A 340, 163\n\\bibitem {2} Balbus S.A., Hawley J.F., Stone J.M., 1996, ApJ 467, 76\n\\bibitem {6} Catala C., Felenbok P., Czarny J., Talavera A., \nBoesgaard A.M., 1986, ApJ 308, 791\n\\bibitem {6bis} Catala, C., 1989, In: \nPh. Delache, S. Laloe, C. Magnan, J., et al. (eds.)\n$4^{\\rm th}$ IAP meeting,\nModeling The Stellar Environment: How and\nWhy? Paris, p. 207\n\\bibitem {7} Cox J.P., 1968, In: Gordon and Breach Science Publishers (eds.),\nPrinciples of Stellar Structure, p. 587\n\\bibitem {7bis} Denissenkov P.A., Ivanova N.S., Weiss A., 1999, A\\&A 341, 181\n\\bibitem {8} Donati J.-F., Semel M., Carter B.D., Rees D.E., Cameron A.C., 1997, MNRAS\n291, 658\n\\bibitem {20} Henrichs H.F., de Jong J.A., Donati J.F., Catala C., Shorlin S.L.S.,\nWade G.A., Veen P.M., Nichols J.S., Verdugo E., Talavera A., Kaper L.,\n2000, A\\&A in press\n\\bibitem {21} Kaper L., Henrichs H.F., Nichols J.S., Snoek L.C., Volten H., Zwarthoed G.A.A.,\n1996, A\\&AS 116, 257\n\\bibitem [1999]{peg} Ligni\\`eres F., Catala C., Mangeney A., 1996, A\\&A 314, 465\n\\bibitem [1999]{tog} Ligni\\`eres F., Califano F., Mangeney A., 1998, Geophys. Astrophys.\nFluid Dyn. 88, 81\n\\bibitem [1999]{lig} Ligni\\`eres F., 1999, A\\&A 349, 1027\n\\bibitem {24} Maeder A., 1999, A\\&A 347, 185\n\\bibitem {22} Massa D., Fullerton A.W., Nichols J.S., Owocki S.P., Prinja R.K., St-Louis N., \nWillis A.J., Altner B., Bolton C.T., Cassinelli J.P., Cohen D., Cooper R.G., Feldmeier A., \nGayley K.G., Harries T., Heap S.R., Henriksen R.N., Howarth I.D., Hubeny I., Kambe E., Kaper L.,\nKoenigsberger G., Marchenko S., McCandliss S.R., Moffat A.F.J.,\nNugis T., Puls J., Robert C., Schulte-Ladbeck R.E., Smith L.J., Smith M.A., Waldron W.L., \nWhite R. L., 1995, ApJL 452, 53\n\\bibitem {25} Owocki S.P., Gayley K.G., 1997, \nIn: Nota A., amers H. (eds.) Luminous Blue Variables: \nMassive Stars in Transition. ASP Conf. Ser., p. 121\n\\bibitem {26} Palla F., Stahler S.W., 1993, ApJ 418, 414\n\\bibitem {27} Richard D., Zahn J.-P., 1999, A\\&A 347, 734\n\\bibitem {27bis} Schatzman E., 1981, In: G.E.V.O.N. and Sterken C. (eds.) \nProceedings of the workshop on pulsating\nB stars (Nice, 1-5 June 1981), p. 347\n\\bibitem {28} Stein R.F., Nordlund A., 1998, ApJ 499, 914\n\\bibitem {29} Talon S., Zahn J.-P., Maeder A.,\n Meynet G., 1997, A\\&A 322, 209 \n\\bibitem {41} Vigneron, C., Mangeney, A., Catala, C., Schatzman, E., 1990, Sol.\nPhys. 128, 287\n\\bibitem [1974]{zan} Zahn J.-P., 1974, In:\nLedoux et al. (eds.), Stellar instability and evolution, p. 185\n\\end{thebibliography}\n\\end{document}\n"
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"string": "\\begin{thebibliography}{}\n\\bibitem {1} Bouret J.-C., Catala C., 1998, A\\&A 340, 163\n\\bibitem {2} Balbus S.A., Hawley J.F., Stone J.M., 1996, ApJ 467, 76\n\\bibitem {6} Catala C., Felenbok P., Czarny J., Talavera A., \nBoesgaard A.M., 1986, ApJ 308, 791\n\\bibitem {6bis} Catala, C., 1989, In: \nPh. Delache, S. Laloe, C. Magnan, J., et al. (eds.)\n$4^{\\rm th}$ IAP meeting,\nModeling The Stellar Environment: How and\nWhy? Paris, p. 207\n\\bibitem {7} Cox J.P., 1968, In: Gordon and Breach Science Publishers (eds.),\nPrinciples of Stellar Structure, p. 587\n\\bibitem {7bis} Denissenkov P.A., Ivanova N.S., Weiss A., 1999, A\\&A 341, 181\n\\bibitem {8} Donati J.-F., Semel M., Carter B.D., Rees D.E., Cameron A.C., 1997, MNRAS\n291, 658\n\\bibitem {20} Henrichs H.F., de Jong J.A., Donati J.F., Catala C., Shorlin S.L.S.,\nWade G.A., Veen P.M., Nichols J.S., Verdugo E., Talavera A., Kaper L.,\n2000, A\\&A in press\n\\bibitem {21} Kaper L., Henrichs H.F., Nichols J.S., Snoek L.C., Volten H., Zwarthoed G.A.A.,\n1996, A\\&AS 116, 257\n\\bibitem [1999]{peg} Ligni\\`eres F., Catala C., Mangeney A., 1996, A\\&A 314, 465\n\\bibitem [1999]{tog} Ligni\\`eres F., Califano F., Mangeney A., 1998, Geophys. Astrophys.\nFluid Dyn. 88, 81\n\\bibitem [1999]{lig} Ligni\\`eres F., 1999, A\\&A 349, 1027\n\\bibitem {24} Maeder A., 1999, A\\&A 347, 185\n\\bibitem {22} Massa D., Fullerton A.W., Nichols J.S., Owocki S.P., Prinja R.K., St-Louis N., \nWillis A.J., Altner B., Bolton C.T., Cassinelli J.P., Cohen D., Cooper R.G., Feldmeier A., \nGayley K.G., Harries T., Heap S.R., Henriksen R.N., Howarth I.D., Hubeny I., Kambe E., Kaper L.,\nKoenigsberger G., Marchenko S., McCandliss S.R., Moffat A.F.J.,\nNugis T., Puls J., Robert C., Schulte-Ladbeck R.E., Smith L.J., Smith M.A., Waldron W.L., \nWhite R. L., 1995, ApJL 452, 53\n\\bibitem {25} Owocki S.P., Gayley K.G., 1997, \nIn: Nota A., amers H. (eds.) Luminous Blue Variables: \nMassive Stars in Transition. ASP Conf. Ser., p. 121\n\\bibitem {26} Palla F., Stahler S.W., 1993, ApJ 418, 414\n\\bibitem {27} Richard D., Zahn J.-P., 1999, A\\&A 347, 734\n\\bibitem {27bis} Schatzman E., 1981, In: G.E.V.O.N. and Sterken C. (eds.) \nProceedings of the workshop on pulsating\nB stars (Nice, 1-5 June 1981), p. 347\n\\bibitem {28} Stein R.F., Nordlund A., 1998, ApJ 499, 914\n\\bibitem {29} Talon S., Zahn J.-P., Maeder A.,\n Meynet G., 1997, A\\&A 322, 209 \n\\bibitem {41} Vigneron, C., Mangeney, A., Catala, C., Schatzman, E., 1990, Sol.\nPhys. 128, 287\n\\bibitem [1974]{zan} Zahn J.-P., 1974, In:\nLedoux et al. (eds.), Stellar instability and evolution, p. 185\n\\end{thebibliography}"
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% \bgroup \vskip 20pt% \leftskip 11pc\rightskip\z@ \noindent{\ninebf ABSTRACT}\par \tenpoint \Fullout \noindent #1\par \egroup
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\\magstep3\n\\font\\seventeensf=cmss10 scaled \\magstep3\n%\n\\fi\n\n\\def\\hexnumber#1{\\ifcase#1 0\\or1\\or2\\or3\\or4\\or5\\or6\\or7\\or8\\or9\\or\n A\\or B\\or C\\or D\\or E\\or F\\fi}\n\n\\def\\makestrut{%\n \\setbox\\strutbox=\\hbox{%\n \\vrule height.7\\baselineskip depth.3\\baselineskip width \\z@}%\n}\n\n\\def\\baselinestretch{1}\n\\newskip\\tmp@bls\n\n\\def\\b@ls#1{% set baseline using \\baselinestretch as a scale factor\n \\tmp@bls=#1\\relax\n \\baselineskip=#1\\relax\\makestrut\n \\normalbaselineskip=\\baselinestretch\\tmp@bls\n \\normalbaselines\n}\n\n\\def\\nostb@ls#1{% set baseline skip ignoring \\baselinestretch\n \\normalbaselineskip=#1\\relax\n \\normalbaselines\n \\makestrut\n}\n\n\n% families \\itfam, \\slfam, \\bffam, \\ttfam defined in PLAIN.\n%\n% \\itfam is \\fam4\n% \\slfam is \\fam5\n% \\bffam is \\fam6\n% \\ttfam is \\fam7\n\n\\newfam\\scfam % \\fam8\n\\newfam\\sffam % \\fam9\n\n\\def\\mit{\\fam\\@ne}\n\\def\\cal{\\fam\\tw@}\n\\def\\em{\\ifdim\\fontdimen1\\font>\\z@ \\rm\\else\\it\\fi}\n\n\\textfont3=\\tenex\n\\scriptfont3=\\tenex\n\\scriptscriptfont3=\\tenex\n\n\\setbox0=\\hbox{\\tenex B} \\p@renwd=\\wd0 % width of the big left (\n\n\\def\\eightpoint{% 8^6^5 on 10pt\n \\def\\rm{\\fam0\\eightrm}%\n \\textfont0=\\eightrm \\scriptfont0=\\sixrm \\scriptscriptfont0=\\fiverm%\n \\textfont1=\\eighti \\scriptfont1=\\sixi \\scriptscriptfont1=\\fivei%\n \\textfont2=\\eightsy \\scriptfont2=\\sixsy \\scriptscriptfont2=\\fivesy%\n \\textfont\\itfam=\\eightit\\def\\it{\\fam\\itfam\\eightit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\sixit\n \\scriptscriptfont\\itfam=\\fiveit\n \\else\n \\scriptfont\\itfam=\\eightit\n \\scriptscriptfont\\itfam=\\eightit\n \\fi\n \\textfont\\bffam=\\eightbf%\n \\scriptfont\\bffam=\\sixbf%\n \\scriptscriptfont\\bffam=\\fivebf%\n \\def\\bf{\\fam\\bffam\\eightbf}%\n \\textfont\\slfam=\\eightsl\\def\\sl{\\fam\\slfam\\eightsl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\sixsl\n \\scriptscriptfont\\slfam=\\fivesl\n \\else\n \\scriptfont\\slfam=\\eightsl\n \\scriptscriptfont\\slfam=\\eightsl\n \\fi\n \\textfont\\ttfam=\\eighttt\\def\\tt{\\fam\\ttfam\\eighttt}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\sixtt\n \\scriptscriptfont\\ttfam=\\fivett\n \\else\n \\scriptfont\\ttfam=\\eighttt\n \\scriptscriptfont\\ttfam=\\eighttt\n \\fi\n \\textfont\\scfam=\\eightcsc\\def\\sc{\\fam\\scfam\\eightcsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\sixcsc\n \\scriptscriptfont\\scfam=\\fivecsc\n \\else\n \\scriptfont\\scfam=\\eightcsc\n \\scriptscriptfont\\scfam=\\eightcsc\n \\fi\n \\textfont\\sffam=\\eightsf\\def\\sf{\\fam\\sffam\\eightsf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\sixsf\n \\scriptscriptfont\\sffam=\\fivesf\n \\else\n \\scriptfont\\sffam=\\eightsf\n \\scriptscriptfont\\sffam=\\eightsf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\eighti}%\n \\b@ls{10pt}\\rm\\@viiipt%\n}\n\\def\\@viiipt{}\n\n\\def\\ninepoint{% 9^6^5 on 11pt (two col) / 12 (single col)\n \\def\\rm{\\fam0\\ninerm}%\n \\textfont0=\\ninerm \\scriptfont0=\\sixrm \\scriptscriptfont0=\\fiverm%\n \\textfont1=\\ninei \\scriptfont1=\\sixi \\scriptscriptfont1=\\fivei%\n \\textfont2=\\ninesy \\scriptfont2=\\sixsy \\scriptscriptfont2=\\fivesy%\n \\textfont\\itfam=\\nineit\\def\\it{\\fam\\itfam\\nineit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\sixit\n \\scriptscriptfont\\itfam=\\fiveit\n \\else\n \\scriptfont\\itfam=\\nineit\n \\scriptscriptfont\\itfam=\\nineit\n \\fi\n \\textfont\\bffam=\\ninebf%\n \\scriptfont\\bffam=\\sixbf%\n \\scriptscriptfont\\bffam=\\fivebf%\n \\def\\bf{\\fam\\bffam\\ninebf}%\n \\textfont\\slfam=\\ninesl\\def\\sl{\\fam\\slfam\\ninesl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\sixsl\n \\scriptscriptfont\\slfam=\\fivesl\n \\else\n \\scriptfont\\slfam=\\ninesl\n \\scriptscriptfont\\slfam=\\ninesl\n \\fi\n \\textfont\\ttfam=\\ninett\\def\\tt{\\fam\\ttfam\\ninett}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\sixtt\n \\scriptscriptfont\\ttfam=\\fivett\n \\else\n \\scriptfont\\ttfam=\\ninett\n \\scriptscriptfont\\ttfam=\\ninett\n \\fi\n \\textfont\\scfam=\\ninecsc\\def\\sc{\\fam\\scfam\\ninecsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\sixcsc\n \\scriptscriptfont\\scfam=\\fivecsc\n \\else\n \\scriptfont\\scfam=\\ninecsc\n \\scriptscriptfont\\scfam=\\ninecsc\n \\fi\n \\textfont\\sffam=\\ninesf\\def\\sf{\\fam\\sffam\\ninesf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\sixsf\n \\scriptscriptfont\\sffam=\\fivesf\n \\else\n \\scriptfont\\sffam=\\ninesf\n \\scriptscriptfont\\sffam=\\ninesf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\ninei}%\n \\b@ls{\\TextLeading plus \\Feathering}\\rm\\@ixpt%\n}\n\\def\\@ixpt{}\n\n\\def\\tenpoint{% 10^7^5 on 11pt\n \\def\\rm{\\fam0\\tenrm}%\n \\textfont0=\\tenrm \\scriptfont0=\\sevenrm \\scriptscriptfont0=\\fiverm%\n \\textfont1=\\teni \\scriptfont1=\\seveni \\scriptscriptfont1=\\fivei%\n \\textfont2=\\tensy \\scriptfont2=\\sevensy \\scriptscriptfont2=\\fivesy%\n \\textfont\\itfam=\\tenit\\def\\it{\\fam\\itfam\\tenit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\sevenit\n \\scriptscriptfont\\itfam=\\fiveit\n \\else\n \\scriptfont\\itfam=\\tenit\n \\scriptscriptfont\\itfam=\\tenit\n \\fi\n \\textfont\\bffam=\\tenbf%\n \\scriptfont\\bffam=\\sevenbf%\n \\scriptscriptfont\\bffam=\\fivebf%\n \\def\\bf{\\fam\\bffam\\tenbf}%\n \\textfont\\slfam=\\tensl\\def\\sl{\\fam\\slfam\\tensl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\sevensl\n \\scriptscriptfont\\slfam=\\fivesl\n \\else\n \\scriptfont\\slfam=\\tensl\n \\scriptscriptfont\\slfam=\\tensl\n \\fi\n \\textfont\\ttfam=\\tentt\\def\\tt{\\fam\\ttfam\\tentt}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\seventt\n \\scriptscriptfont\\ttfam=\\fivett\n \\else\n \\scriptfont\\ttfam=\\tentt\n \\scriptscriptfont\\ttfam=\\tentt\n \\fi\n \\textfont\\scfam=\\tencsc\\def\\sc{\\fam\\scfam\\tencsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\sevencsc\n \\scriptscriptfont\\scfam=\\fivecsc\n \\else\n \\scriptfont\\scfam=\\tencsc\n \\scriptscriptfont\\scfam=\\tencsc\n \\fi\n \\textfont\\sffam=\\tensf\\def\\sf{\\fam\\sffam\\tensf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\sevensf\n \\scriptscriptfont\\sffam=\\fivesf\n \\else\n \\scriptfont\\sffam=\\tensf\n \\scriptscriptfont\\sffam=\\tensf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\teni}%\n \\b@ls{11pt}\\rm\\@xpt%\n}\n\\def\\@xpt{}\n\n\\def\\elevenpoint{% 11^8^6 on 13pt\n \\def\\rm{\\fam0\\elevenrm}%\n \\textfont0=\\elevenrm \\scriptfont0=\\eightrm \\scriptscriptfont0=\\sixrm%\n \\textfont1=\\eleveni \\scriptfont1=\\eighti \\scriptscriptfont1=\\sixi%\n \\textfont2=\\elevensy \\scriptfont2=\\eightsy \\scriptscriptfont2=\\sixsy%\n \\textfont\\itfam=\\elevenit\\def\\it{\\fam\\itfam\\elevenit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\eightit\n \\scriptscriptfont\\itfam=\\sixit\n \\else\n \\scriptfont\\itfam=\\elevenit\n \\scriptscriptfont\\itfam=\\elevenit\n \\fi\n \\textfont\\bffam=\\elevenbf%\n \\scriptfont\\bffam=\\eightbf%\n \\scriptscriptfont\\bffam=\\sixbf%\n \\def\\bf{\\fam\\bffam\\elevenbf}%\n \\textfont\\slfam=\\elevensl\\def\\sl{\\fam\\slfam\\elevensl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\eightsl\n \\scriptscriptfont\\slfam=\\sixsl\n \\else\n \\scriptfont\\slfam=\\elevensl\n \\scriptscriptfont\\slfam=\\elevensl\n \\fi\n \\textfont\\ttfam=\\eleventt\\def\\tt{\\fam\\ttfam\\eleventt}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\eighttt\n \\scriptscriptfont\\ttfam=\\sixtt\n \\else\n \\scriptfont\\ttfam=\\eleventt\n \\scriptscriptfont\\ttfam=\\eleventt\n \\fi\n \\textfont\\scfam=\\elevencsc\\def\\sc{\\fam\\scfam\\elevencsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\eightcsc\n \\scriptscriptfont\\scfam=\\sixcsc\n \\else\n \\scriptfont\\scfam=\\elevencsc\n \\scriptscriptfont\\scfam=\\elevencsc\n \\fi\n \\textfont\\sffam=\\elevensf\\def\\sf{\\fam\\sffam\\elevensf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\eightsf\n \\scriptscriptfont\\sffam=\\sixsf\n \\else\n \\scriptfont\\sffam=\\elevensf\n \\scriptscriptfont\\sffam=\\elevensf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\eleveni}%\n \\b@ls{13pt}\\rm\\@xipt%\n}\n\\def\\@xipt{}\n\n\\def\\fourteenpoint{% 14^10^7 on 17pt\n \\def\\rm{\\fam0\\fourteenrm}%\n \\textfont0\\fourteenrm \\scriptfont0\\tenrm \\scriptscriptfont0\\sevenrm%\n \\textfont1\\fourteeni \\scriptfont1\\teni \\scriptscriptfont1\\seveni%\n \\textfont2\\fourteensy \\scriptfont2\\tensy \\scriptscriptfont2\\sevensy%\n \\textfont\\itfam=\\fourteenit\\def\\it{\\fam\\itfam\\fourteenit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\tenit\n \\scriptscriptfont\\itfam=\\sevenit\n \\else\n \\scriptfont\\itfam=\\fourteenit\n \\scriptscriptfont\\itfam=\\fourteenit\n \\fi\n \\textfont\\bffam=\\fourteenbf%\n \\scriptfont\\bffam=\\tenbf%\n \\scriptscriptfont\\bffam=\\sevenbf%\n \\def\\bf{\\fam\\bffam\\fourteenbf}%\n \\textfont\\slfam=\\fourteensl\\def\\sl{\\fam\\slfam\\fourteensl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\tensl\n \\scriptscriptfont\\slfam=\\sevensl\n \\else\n \\scriptfont\\slfam=\\fourteensl\n \\scriptscriptfont\\slfam=\\fourteensl\n \\fi\n \\textfont\\ttfam=\\fourteentt\\def\\tt{\\fam\\ttfam\\fourteentt}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\tentt\n \\scriptscriptfont\\ttfam=\\seventt\n \\else\n \\scriptfont\\ttfam=\\fourteentt\n \\scriptscriptfont\\ttfam=\\fourteentt\n \\fi\n \\textfont\\scfam=\\fourteencsc\\def\\sc{\\fam\\scfam\\fourteencsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\tencsc\n \\scriptscriptfont\\scfam=\\sevencsc\n \\else\n \\scriptfont\\scfam=\\fourteencsc\n \\scriptscriptfont\\scfam=\\fourteencsc\n \\fi\n \\textfont\\sffam=\\fourteensf\\def\\sf{\\fam\\sffam\\fourteensf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\tensf\n \\scriptscriptfont\\sffam=\\sevensf\n \\else\n \\scriptfont\\sffam=\\fourteensf\n \\scriptscriptfont\\sffam=\\fourteensf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\fourteeni}%\n \\b@ls{17pt}\\rm\\@xivpt%\n}\n\\def\\@xivpt{}\n\n\\def\\seventeenpoint{% 17^12^10 on 20pt\n \\def\\rm{\\fam0\\seventeenrm}%\n \\textfont0\\seventeenrm \\scriptfont0\\twelverm \\scriptscriptfont0\\tenrm%\n \\textfont1\\seventeeni \\scriptfont1\\twelvei \\scriptscriptfont1\\teni%\n \\textfont2\\seventeensy \\scriptfont2\\twelvesy \\scriptscriptfont2\\tensy%\n \\textfont\\itfam=\\seventeenit\\def\\it{\\fam\\itfam\\seventeenit}%\n \\ifprod@font\n \\scriptfont\\itfam=\\twelveit\n \\scriptscriptfont\\itfam=\\tenit\n \\else\n \\scriptfont\\itfam=\\seventeenit\n \\scriptscriptfont\\itfam=\\seventeenit\n \\fi\n \\textfont\\bffam=\\seventeenbf%\n \\scriptfont\\bffam=\\twelvebf%\n \\scriptscriptfont\\bffam=\\tenbf%\n \\def\\bf{\\fam\\bffam\\seventeenbf}%\n \\textfont\\slfam=\\seventeensl\\def\\sl{\\fam\\slfam\\seventeensl}%\n \\ifprod@font\n \\scriptfont\\slfam=\\twelvesl\n \\scriptscriptfont\\slfam=\\tensl\n \\else\n \\scriptfont\\slfam=\\seventeensl\n \\scriptscriptfont\\slfam=\\seventeensl\n \\fi\n \\textfont\\ttfam=\\seventeentt\\def\\tt{\\fam\\ttfam\\seventeentt}%\n \\ifprod@font\n \\scriptfont\\ttfam=\\twelvett\n \\scriptscriptfont\\ttfam=\\tentt\n \\else\n \\scriptfont\\ttfam=\\seventeentt\n \\scriptscriptfont\\ttfam=\\seventeentt\n \\fi\n \\textfont\\scfam=\\seventeencsc\\def\\sc{\\fam\\scfam\\seventeencsc}%\n \\ifprod@font\n \\scriptfont\\scfam=\\twelvecsc\n \\scriptscriptfont\\scfam=\\tencsc\n \\else\n \\scriptfont\\scfam=\\seventeencsc\n \\scriptscriptfont\\scfam=\\seventeencsc\n \\fi\n \\textfont\\sffam=\\seventeensf\\def\\sf{\\fam\\sffam\\seventeensf}%\n \\ifprod@font\n \\scriptfont\\sffam=\\twelvesf\n \\scriptscriptfont\\sffam=\\tensf\n \\else\n \\scriptfont\\sffam=\\seventeensf\n \\scriptscriptfont\\sffam=\\seventeensf\n \\fi\n \\def\\oldstyle{\\fam\\@ne\\seventeeni}%\n \\b@ls{20pt}\\rm\\@xviipt%\n}\n\\def\\@xviipt{}\n\n\\lineskip=1pt \\normallineskip=\\lineskip\n\\lineskiplimit=\\z@ \\normallineskiplimit=\\lineskiplimit\n\n\n% BOLD MATH SYMBOLS\n\n\\def\\loadboldmathnames{%\n \\def\\balpha{{\\bmath{\\alpha}}}%\n \\def\\bbeta{{\\bmath{\\beta}}}%\n \\def\\bgamma{{\\bmath{\\gamma}}}%\n \\def\\bdelta{{\\bmath{\\delta}}}%\n \\def\\bepsilon{{\\bmath{\\epsilon}}}%\n \\def\\bzeta{{\\bmath{\\zeta}}}%\n \\def\\boldeta{{\\bmath{\\eta}}}%\n \\def\\btheta{{\\bmath{\\theta}}}%\n \\def\\biota{{\\bmath{\\iota}}}%\n \\def\\bkappa{{\\bmath{\\kappa}}}%\n \\def\\blambda{{\\bmath{\\lambda}}}%\n \\def\\bmu{{\\bmath{\\mu}}}%\n \\def\\bnu{{\\bmath{\\nu}}}%\n \\def\\bxi{{\\bmath{\\xi}}}%\n \\def\\bpi{{\\bmath{\\pi}}}%\n \\def\\brho{{\\bmath{\\rho}}}%\n \\def\\bsigma{{\\bmath{\\sigma}}}%\n \\def\\btau{{\\bmath{\\tau}}}%\n \\def\\bupsilon{{\\bmath{\\upsilon}}}%\n \\def\\bphi{{\\bmath{\\phi}}}%\n \\def\\bchi{{\\bmath{\\chi}}}%\n \\def\\bpsi{{\\bmath{\\psi}}}%\n \\def\\bomega{{\\bmath{\\omega}}}%\n \\def\\bvarepsilon{{\\bmath{\\varepsilon}}}%\n \\def\\bvartheta{{\\bmath{\\vartheta}}}%\n \\def\\bvarpi{{\\bmath{\\varpi}}}%\n \\def\\bvarrho{{\\bmath{\\varrho}}}%\n \\def\\bvarsigma{{\\bmath{\\varsigma}}}%\n \\def\\bvarphi{{\\bmath{\\varphi}}}%\n \\def\\baleph{{\\bmath{\\aleph}}}%\n \\def\\bimath{{\\bmath{\\imath}}}%\n \\def\\bjmath{{\\bmath{\\jmath}}}%\n \\def\\bell{{\\bmath{\\ell}}}%\n \\def\\bwp{{\\bmath{\\wp}}}%\n \\def\\bRe{{\\bmath{\\Re}}}%\n \\def\\bIm{{\\bmath{\\Im}}}%\n \\def\\bpartial{{\\bmath{\\partial}}}%\n \\def\\binfty{{\\bmath{\\infty}}}%\n \\def\\bprime{{\\bmath{\\prime}}}%\n \\def\\bemptyset{{\\bmath{\\emptyset}}}%\n \\def\\bnabla{{\\bmath{\\nabla}}}%\n \\def\\btop{{\\bmath{\\top}}}%\n \\def\\bbot{{\\bmath{\\bot}}}%\n \\def\\btriangle{{\\bmath{\\triangle}}}%\n \\def\\bforall{{\\bmath{\\forall}}}%\n \\def\\bexists{{\\bmath{\\exists}}}%\n \\def\\bneg{{\\bmath{\\neg}}}%\n \\def\\bflat{{\\bmath{\\flat}}}%\n \\def\\bnatural{{\\bmath{\\natural}}}%\n \\def\\bsharp{{\\bmath{\\sharp}}}%\n \\def\\bclubsuit{{\\bmath{\\clubsuit}}}%\n \\def\\bdiamondsuit{{\\bmath{\\diamondsuit}}}%\n \\def\\bheartsuit{{\\bmath{\\heartsuit}}}%\n \\def\\bspadesuit{{\\bmath{\\spadesuit}}}%\n \\def\\bsmallint{{\\bmath{\\smallint}}}%\n \\def\\btriangleleft{{\\bmath{\\triangleleft}}}%\n \\def\\btriangleright{{\\bmath{\\triangleright}}}%\n \\def\\bbigtriangleup{{\\bmath{\\bigtriangleup}}}%\n \\def\\bbigtriangledown{{\\bmath{\\bigtriangledown}}}%\n \\def\\bwedge{{\\bmath{\\wedge}}}%\n \\def\\bvee{{\\bmath{\\vee}}}%\n \\def\\bcap{{\\bmath{\\cap}}}%\n \\def\\bcup{{\\bmath{\\cup}}}%\n \\def\\bddagger{{\\bmath{\\ddagger}}}%\n \\def\\bdagger{{\\bmath{\\dagger}}}%\n \\def\\bsqcap{{\\bmath{\\sqcap}}}%\n \\def\\bsqcup{{\\bmath{\\sqcup}}}%\n \\def\\buplus{{\\bmath{\\uplus}}}%\n \\def\\bamalg{{\\bmath{\\amalg}}}%\n \\def\\bdiamond{{\\bmath{\\diamond}}}%\n \\def\\bbullet{{\\bmath{\\bullet}}}%\n \\def\\bwr{{\\bmath{\\wr}}}%\n \\def\\bdiv{{\\bmath{\\div}}}%\n \\def\\bodot{{\\bmath{\\odot}}}%\n \\def\\boslash{{\\bmath{\\oslash}}}%\n \\def\\botimes{{\\bmath{\\otimes}}}%\n \\def\\bominus{{\\bmath{\\ominus}}}%\n \\def\\boplus{{\\bmath{\\oplus}}}%\n \\def\\bmp{{\\bmath{\\mp}}}%\n \\def\\bpm{{\\bmath{\\pm}}}%\n \\def\\bcirc{{\\bmath{\\circ}}}%\n \\def\\bbigcirc{{\\bmath{\\bigcirc}}}%\n \\def\\bsetminus{{\\bmath{\\setminus}}}%\n \\def\\bcdot{{\\bmath{\\cdot}}}%\n \\def\\bast{{\\bmath{\\ast}}}%\n \\def\\btimes{{\\bmath{\\times}}}%\n \\def\\bstar{{\\bmath{\\star}}}%\n \\def\\bpropto{{\\bmath{\\propto}}}%\n \\def\\bsqsubseteq{{\\bmath{\\sqsubseteq}}}%\n \\def\\bsqsupseteq{{\\bmath{\\sqsupseteq}}}%\n \\def\\bparallel{{\\bmath{\\parallel}}}%\n \\def\\bmid{{\\bmath{\\mid}}}%\n \\def\\bdashv{{\\bmath{\\dashv}}}%\n \\def\\bvdash{{\\bmath{\\vdash}}}%\n \\def\\bnearrow{{\\bmath{\\nearrow}}}%\n \\def\\bsearrow{{\\bmath{\\searrow}}}%\n \\def\\bnwarrow{{\\bmath{\\nwarrow}}}%\n \\def\\bswarrow{{\\bmath{\\swarrow}}}%\n \\def\\bLeftrightarrow{{\\bmath{\\Leftrightarrow}}}%\n \\def\\bLeftarrow{{\\bmath{\\Leftarrow}}}%\n \\def\\bRightarrow{{\\bmath{\\Rightarrow}}}%\n \\def\\bleq{{\\bmath{\\leq}}}%\n \\def\\bgeq{{\\bmath{\\geq}}}%\n \\def\\bsucc{{\\bmath{\\succ}}}%\n \\def\\bprec{{\\bmath{\\prec}}}%\n \\def\\bapprox{{\\bmath{\\approx}}}%\n \\def\\bsucceq{{\\bmath{\\succeq}}}%\n \\def\\bpreceq{{\\bmath{\\preceq}}}%\n \\def\\bsupset{{\\bmath{\\supset}}}%\n \\def\\bsubset{{\\bmath{\\subset}}}%\n \\def\\bsupseteq{{\\bmath{\\supseteq}}}%\n \\def\\bsubseteq{{\\bmath{\\subseteq}}}%\n \\def\\bin{{\\bmath{\\in}}}%\n \\def\\bni{{\\bmath{\\ni}}}%\n \\def\\bgg{{\\bmath{\\gg}}}%\n \\def\\bll{{\\bmath{\\ll}}}%\n \\def\\bnot{{\\bmath{\\not}}}%\n \\def\\bleftrightarrow{{\\bmath{\\leftrightarrow}}}%\n \\def\\bleftarrow{{\\bmath{\\leftarrow}}}%\n \\def\\brightarrow{{\\bmath{\\rightarrow}}}%\n \\def\\bmapstochar{{\\bmath{\\mapstochar}}}%\n \\def\\bsim{{\\bmath{\\sim}}}%\n \\def\\bsimeq{{\\bmath{\\simeq}}}%\n \\def\\bperp{{\\bmath{\\perp}}}%\n \\def\\bequiv{{\\bmath{\\equiv}}}%\n \\def\\basymp{{\\bmath{\\asymp}}}%\n \\def\\bsmile{{\\bmath{\\smile}}}%\n \\def\\bfrown{{\\bmath{\\frown}}}%\n \\def\\bleftharpoonup{{\\bmath{\\leftharpoonup}}}%\n \\def\\bleftharpoondown{{\\bmath{\\leftharpoondown}}}%\n \\def\\brightharpoonup{{\\bmath{\\rightharpoonup}}}%\n \\def\\brightharpoondown{{\\bmath{\\rightharpoondown}}}%\n \\def\\blhook{{\\bmath{\\lhook}}}%\n \\def\\brhook{{\\bmath{\\rhook}}}%\n \\def\\bldotp{{\\bmath{\\ldotp}}}%\n \\def\\bcdotp{{\\bmath{\\cdotp}}}%\n}\n\n% Make \\, work in non-math mode\n\\def\\,{\\relax\\ifmmode \\mskip\\thinmuskip\\else \\thinspace\\fi}\n\\let\\protect=\\relax\n\n\\long\\def\\@ifundefined#1#2#3{\\expandafter\\ifx\\csname\n #1\\endcsname\\relax#2\\else#3\\fi}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n% NewFont.sty: ALPHA VERSION patchlevel 8, 16th August 1994, M. Reed\n\n% \\addtom@thgroup{math font loading info}\n% Adds to internal \\math@groups definition, which is executed at the end\n% of each size changing command. It is called by \\NewSymbolFont.\n\n\\newtoks\\math@groups \\math@groups={}\n\\def\\addtom@thgroup#1#2{#1\\expandafter{\\the#1#2}} % \\mac={new\\the\\mac}\n\n\n% Make TeX change the values of \\s@ze, \\ss@ze, \\sss@ze when \\@npt is\n% executed. This makes it possible for math characters to be loaded\n% at the correct size automatically when the size is changed.\n\n% \\addtosizeh@ok{x}{10}{7}{5}\n\n\\def\\addtosizeh@ok#1#2#3#4{%\n \\expandafter\\def\\csname @#1pt\\endcsname{%\n \\def\\s@ze{#2}\\def\\ss@ze{#3}\\def\\sss@ze{#4}\\the\\math@groups%\n }%\n}\n\n\n% \\resetsizehook allows the size parameters to be reset after \\addtosizeh@ok\n% has been called (it re-defines \\@npt).\n% e.g JFM which requires \\xpt to have 10.5pt instead of 10pt.\n% Note: \\resetsizehook must be used in the preamble BEFORE any\n% \\New... commands.\n\n% e.g. \\resetsizehook{x}{10.5}{7}{5}\n\n\\let\\resetsizehook=\\addtosizeh@ok\n\n\n% Standard LaTeX sizes\n\n\\ifprod@font\n% \\addtosizeh@ok{v} {5} {5} {5}\n% \\addtosizeh@ok{vi} {6} {6} {6}\n% \\addtosizeh@ok{vii} {7} {6} {5}\n \\addtosizeh@ok{viii} {8} {6} {5}\n \\addtosizeh@ok{ix} {9} {6} {5}\n \\addtosizeh@ok{x} {10}{7} {5}\n \\addtosizeh@ok{xi} {11}{8} {6}\n% \\addtosizeh@ok{xii} {12}{8} {6}\n \\addtosizeh@ok{xiv} {14}{10} {7}\n \\addtosizeh@ok{xvii} {17}{12}{10}\n% \\addtosizeh@ok{xx} {20}{14}{12}\n% \\addtosizeh@ok{xxv} {25}{20}{17}\n\\else\n% \\addtosizeh@ok{v} {5} {5} {5}\n% \\addtosizeh@ok{vi} {6} {6} {6}\n% \\addtosizeh@ok{vii} {7} {6} {5}\n \\addtosizeh@ok{viii} {8} {6} {5}\n \\addtosizeh@ok{ix} {9} {6} {5}\n \\addtosizeh@ok{x} {10} {7} {5}\n \\addtosizeh@ok{xi} {10.95} {8} {6}\n% \\addtosizeh@ok{xii} {12} {8} {6}\n \\addtosizeh@ok{xiv} {14.4} {10} {7}\n \\addtosizeh@ok{xvii} {17.28} {12} {10}\n% \\addtosizeh@ok{xx} {20.74} {14.4} {12}\n% \\addtosizeh@ok{xxv} {24.88} {20.74} {17.28}\n\\fi\n\n\n\\def\\get@font#1#2#3{%\n \\edef\\fonts@ze{\\romannumeral#3}% 10 -> x\n \\edef\\fontn@me{\\fonts@ze#1}% AMSa -> xAMSa\n \\@ifundefined{\\fontn@me}%\n {%%\\typeout{defining \\fontn@me}%\n \\global\\expandafter\\font\\csname \\fontn@me\\endcsname=#2 at #3pt}%\n {}%\n}\n\n\\def\\ass@tfont#1#2{%\n \\xdef\\fam@name{\\csname #1\\endcsname}%\n \\xdef\\font@name{\\csname #2\\endcsname}%\n \\let\\textfont@name\\font@name\n \\textfont\\fam@name\\textfont@name\n}\n\n\\def\\ass@sfont#1#2{%\n \\xdef\\fam@name{\\csname #1\\endcsname}%\n \\xdef\\font@name{\\csname #2\\endcsname}%\n \\let\\textfont@name\\font@name\n \\scriptfont\\fam@name\\textfont@name\n}\n\n\\def\\ass@ssfont#1#2{%\n \\xdef\\fam@name{\\csname #1\\endcsname}%\n \\xdef\\font@name{\\csname #2\\endcsname}%\n \\let\\textfont@name\\font@name\n \\scriptscriptfont\\fam@name\\textfont@name\n}\n\n\n% fam name base font (allocates a \\newfam)\n% \\NewSymbolFont {AMSa} {mtxm10}\n\n\\def\\NewSymbolFont#1#2{%\n \\expandafter\\ifx\\csname sym#1fam\\endcsname\\relax % if not defined\n \\expandafter\\newfam\\csname sym#1fam\\endcsname\n \\expandafter\\edef\\csname sym#1fam\\endcsname{\\the\\allocationnumber}%\n \\addtom@thgroup\\math@groups{%\n \\get@font{#1}{#2}{\\s@ze}%\n \\ass@tfont{sym#1fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\ss@ze}%\n \\ass@sfont{sym#1fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\sss@ze}%\n \\ass@ssfont{sym#1fam}{\\fontn@me}%\n }%\n \\else\n \\errmessage{Family `#1' already defined}%\n \\fi\n}\n\n\n% symbol type fam pos (hex)\n% \\NewMathSymbol {\\blacksquare} {0} {AMSa} {04}\n\n\\def\\NewMathSymbol#1#2#3#4{%\n \\edef\\f@mly{\\expandafter\\hexnumber{\\csname sym#3fam\\endcsname}}%\n \\mathchardef#1=\"#2\\f@mly#4\\relax\n}\n\n\n% macro name type fam1 pos fam2 pos\n% \\NewMathDelimiter{\\ulcorner} {4} {AMSa} {70} {AMSb} {70}\n\n\\newif\\ifd@f\n\n\\def\\NewMathDelimiter#1#2#3#4#5#6{%\n \\d@ftrue\n \\expandafter\\ifx\\csname sym#3fam\\endcsname\\relax\n \\d@ffalse \\errmessage{Family `#3' is not defined}%\n \\fi\n \\expandafter\\ifx\\csname sym#5fam\\endcsname\\relax\n \\d@ffalse \\errmessage{Family `#5' is not defined}%\n \\fi\n \\ifd@f\n \\edef\\f@mly{\\expandafter\\hexnumber{\\csname sym#3fam\\endcsname}}%\n \\edef\\f@mlytw@{\\expandafter\\hexnumber{\\csname sym#5fam\\endcsname}}%\n \\xdef#1{\\delimiter\"#2\\f@mly #4\\f@mlytw@ #6\\relax}%\n \\fi\n}\n\n\n% macro name base font skewchar setting e.g '60 (octal)\n% \\NewMathAlphabet {mathbssi} {mtmisb10} {}\n\n\\def\\setboxz@h{\\setbox\\z@\\hbox}\n\\def\\wdz@{\\wd\\z@}\n\\def\\boxz@{\\box\\z@}\n\\def\\setbox@ne{\\setbox\\@ne}\n\\def\\wd@ne{\\wd\\@ne}\n\n\\def\\math@atom#1#2{%\n \\binrel@{#1}\\binrel@@{#2}}\n\\def\\binrel@#1{\\setboxz@h{\\thinmuskip0mu\n \\medmuskip\\m@ne mu\\thickmuskip\\@ne mu$#1\\m@th$}%\n \\setbox@ne\\hbox{\\thinmuskip0mu\\medmuskip\\m@ne mu\\thickmuskip\n \\@ne mu${}#1{}\\m@th$}%\n \\setbox\\tw@\\hbox{\\hskip\\wd@ne\\hskip-\\wdz@}}\n\\def\\binrel@@#1{\\ifdim\\wd2<\\z@\\mathbin{#1}\\else\\ifdim\\wd\\tw@>\\z@\n \\mathrel{#1}\\else{#1}\\fi\\fi}\n\n\\def\\m@thit{1}\n\n\\def\\set@skchar#1{\\global\\expandafter\\skewchar\n \\csname\\fontn@me\\endcsname=#1\\relax}\n\n\\def\\NewMathAlphabet#1#2#3{%\n \\def\\tst{#3}%\n \\ifx\\tst\\empty\\else % if a \\skewchar setting is present\n \\expandafter\\gdef\\csname #1@sc\\endcsname{}% \\def\\cmd@sc{..}\n \\fi\n %\n \\expandafter\\def\\csname #1\\endcsname{% \\def\\cmd{\\protect\\@cmd}\n \\protect\\csname @#1\\endcsname}%\n %\n \\expandafter\\def\\csname @#1\\endcsname##1{% \\def\\@cmd{..}\n {%\n \\begingroup\n \\get@font{#1}{#2}{\\s@ze}%\n \\@ifundefined{#1@sc}{}{\\set@skchar{#3}}%\n \\ass@tfont{m@thit}{\\fontn@me}%\n \\get@font{#1}{#2}{\\ss@ze}%\n \\@ifundefined{#1@sc}{}{\\set@skchar{#3}}%\n \\ass@sfont{m@thit}{\\fontn@me}%\n \\get@font{#1}{#2}{\\sss@ze}%\n \\@ifundefined{#1@sc}{}{\\set@skchar{#3}}%\n \\ass@ssfont{m@thit}{\\fontn@me}%\n %\n \\math@atom{##1}{%\n \\mathchoice%\n {\\hbox{$\\m@th\\displaystyle##1$}}%\n {\\hbox{$\\m@th\\textstyle##1$}}%\n {\\hbox{$\\m@th\\scriptstyle##1$}}%\n {\\hbox{$\\m@th\\scriptscriptstyle##1$}}}%\n \\endgroup\n }%\n }%\n}\n\n\n% macro name base font hyphenchar setting e.g -1 (off)\n% \\NewTextAlphabet {textbfit} {mtbxti10} {}\n\n% save a family if \\NewTextAlphabet is not used.\n\\newif\\iffirstta \\firsttatrue\n\n\\def\\set@hchar#1{\\global\\expandafter\\hyphenchar\n \\csname\\fontn@me\\endcsname=#1\\relax}\n\n\\def\\NewTextAlphabet#1#2#3{%\n \\iffirstta\n \\global\\firsttafalse\n \\newfam\\scratchfam\n \\edef\\scrt@fam{\\the\\allocationnumber}%\n \\fi\n \\def\\tst{#3}%\n \\ifx\\tst\\empty\\else % if a \\hyphenchar setting is required\n \\expandafter\\gdef\\csname #1@hc\\endcsname{}% \\def\\cmd@sc{..}\n \\fi\n %\n \\expandafter\\def\\csname #1\\endcsname{% \\def\\cmd{\\protect\\t@cmd}\n \\protect\\csname t@#1\\endcsname}%\n %\n \\long\\expandafter\\def\\csname t@#1\\endcsname##1{% \\def\\t@cmd{..}\n \\ifmmode\n \\typeout{Warning: do not use \\expandafter\\string\\csname #1\\endcsname\n \\space in math mode}\\fi%\n {%\n \\get@font{#1}{#2}{\\s@ze}\\let\\t@xtfnt=\\fontn@me\\relax\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@tfont{scrt@fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\ss@ze}%\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@sfont{scrt@fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\sss@ze}%\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@ssfont{scrt@fam}{\\fontn@me}%\n \\fam\\scratchfam\\csname\\t@xtfnt\\endcsname\n ##1%\n }%\n }%\n %\n \\expandafter\\def\\csname #1shape% \\def\\cmdshape{\\protect\\@cmdshape}\n \\endcsname{\\protect\\csname @#1shape\\endcsname}%\n %\n \\expandafter\\def\\csname @#1shape\\endcsname{% \\def\\@cmdshape\n \\ifmmode\n \\typeout{Warning: do not use \\expandafter\\string\\csname\n #1shape\\endcsname \\space in math mode}\\fi\n %\n \\get@font{#1}{#2}{\\s@ze}\\let\\t@xtfnt=\\fontn@me\\relax\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@tfont{scrt@fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\ss@ze}%\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@sfont{scrt@fam}{\\fontn@me}%\n \\get@font{#1}{#2}{\\sss@ze}%\n \\@ifundefined{#1@hc}{}{\\set@hchar{#3}}%\n \\ass@ssfont{scrt@fam}{\\fontn@me}%\n \\fam\\scratchfam\\csname\\t@xtfnt\\endcsname\n }%\n}\n\n\n% \\bmath{math text}\n\n\\ifprod@font\n \\def\\math@itfnt{mtmib10}\n \\def\\math@syfnt{mtbsy10}\n\\else\n \\def\\math@itfnt{cmmib10}\n \\def\\math@syfnt{cmbsy10}\n\\fi\n\n\\def\\m@thsy{2}\n\n\\def\\bmath{\\protect\\@bmath}\n\\def\\@bmath#1{%\n {%\n \\begingroup\n \\get@font{mthit}{\\math@itfnt}{\\s@ze}\\set@skchar{'177}%\n \\ass@tfont{m@thit}{\\fontn@me}%\n \\get@font{mthit}{\\math@itfnt}{\\ss@ze}\\set@skchar{'177}%\n \\ass@sfont{m@thit}{\\fontn@me}%\n \\get@font{mthit}{\\math@itfnt}{\\sss@ze}\\set@skchar{'177}%\n \\ass@ssfont{m@thit}{\\fontn@me}%\n %\n \\get@font{mthsy}{\\math@syfnt}{\\s@ze}\\set@skchar{'60}%\n \\ass@tfont{m@thsy}{\\fontn@me}%\n \\get@font{mthsy}{\\math@syfnt}{\\ss@ze}\\set@skchar{'60}%\n \\ass@sfont{m@thsy}{\\fontn@me}%\n \\get@font{mthsy}{\\math@syfnt}{\\sss@ze}\\set@skchar{'60}%\n \\ass@ssfont{m@thsy}{\\fontn@me}%\n %\n \\math@atom{#1}{%\n \\mathchoice%\n {\\hbox{$\\m@th\\displaystyle#1$}}%\n {\\hbox{$\\m@th\\textstyle#1$}}%\n {\\hbox{$\\m@th\\scriptstyle#1$}}%\n {\\hbox{$\\m@th\\scriptscriptstyle#1$}}}%\n \\endgroup\n }%\n}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n% Astronomy and Astrophysics symbol macros\n\n\\def\\la{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}}}\n\n\\def\\ga{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}}}\n\n\\def\\getsto{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\n\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr\\gets\\cr\\to\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\\gets\n\\cr\\to\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\\gets\n\\cr\\to\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n\\gets\\cr\\to\\cr}}}}}\n\n\\def\\cor{\\mathrel{\\mathchoice {\\hbox{$\\widehat=$}}{\\hbox{$\\widehat=$}}\n{\\hbox{$\\scriptstyle\\hat=$}}\n{\\hbox{$\\scriptscriptstyle\\hat=$}}}}\n\n\\def\\lid{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\noalign{\\vskip1.2pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr<\\cr\n\\noalign{\\vskip1.2pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr<\\cr\n\\noalign{\\vskip1pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\n\\noalign{\\vskip0.9pt}=\\cr}}}}}\n\n\\def\\gid{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\noalign{\\vskip1.2pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr>\\cr\n\\noalign{\\vskip1.2pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr>\\cr\n\\noalign{\\vskip1pt}=\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\n\\noalign{\\vskip0.9pt}=\\cr}}}}}\n\n\\def\\sol{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr\\sim\\cr<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\\sim\\cr\n<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\\sim\\cr\n<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n\\sim\\cr<\\cr}}}}}\n\n\\def\\sog{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr\\sim\\cr>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\\sim\\cr\n>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n\\sim\\cr>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n\\sim\\cr>\\cr}}}}}\n\n\\def\\lse{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\simeq\\cr}}}}}\n\n\\def\\gse{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\simeq\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\simeq\\cr}}}}}\n\n\\def\\grole{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\noalign{\\vskip-1.5pt}<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\noalign{\\vskip-1.5pt}<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\noalign{\\vskip-1pt}<\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\noalign{\\vskip-0.5pt}<\\cr}}}}}\n\n\\def\\leogr{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\noalign{\\vskip-1.5pt}>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\noalign{\\vskip-1.5pt}>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\noalign{\\vskip-1pt}>\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\noalign{\\vskip-0.5pt}>\\cr}}}}}\n\n\\def\\loa{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\approx\\cr}}}}}\n\n\\def\\goa{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\approx\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\approx\\cr}}}}}\n\n\\def\\sun{\\hbox{$\\odot$}}\n\\def\\degr{\\hbox{$^\\circ$}}\n\\def\\diameter{{\\ifmmode\\mathchoice\n{\\ooalign{\\hfil\\hbox{$\\displaystyle/$}\\hfil\\crcr\n{\\hbox{$\\displaystyle\\mathchar\"20D$}}}}\n{\\ooalign{\\hfil\\hbox{$\\textstyle/$}\\hfil\\crcr\n{\\hbox{$\\textstyle\\mathchar\"20D$}}}}\n{\\ooalign{\\hfil\\hbox{$\\scriptstyle/$}\\hfil\\crcr\n{\\hbox{$\\scriptstyle\\mathchar\"20D$}}}}\n{\\ooalign{\\hfil\\hbox{$\\scriptscriptstyle/$}\\hfil\\crcr\n{\\hbox{$\\scriptscriptstyle\\mathchar\"20D$}}}}\n\\else{\\ooalign{\\hfil/\\hfil\\crcr\\mathhexbox20D}}%\n\\fi}}\n\n\\def\\sq{\\ifmmode\\squareforqed\\else{\\unskip\\nobreak\\hfil\n\\penalty50\\hskip1em\\null\\nobreak\\hfil\\squareforqed\n\\parfillskip=0pt\\finalhyphendemerits=0\\endgraf}\\fi}\n\\def\\squareforqed{\\hbox{\\rlap{$\\sqcap$}$\\sqcup$}}\n\n\\def\\fd{\\hbox{$.\\!\\!^{\\rm d}$}}\n\\def\\fh{\\hbox{$.\\!\\!^{\\rm h}$}}\n\\def\\fm{\\hbox{$.\\!\\!^{\\rm m}$}}\n\\def\\fs{\\hbox{$.\\!\\!^{\\rm s}$}}\n\\def\\fdg{\\hbox{$.\\!\\!^\\circ$}}\n\\def\\farcm{\\hbox{$.\\mkern-4mu^\\prime$}}\n\\def\\farcs{\\hbox{$.\\!\\!^{\\prime\\prime}$}}\n\\def\\fp{\\hbox{$.\\!\\!^{\\scriptscriptstyle\\rm p}$}}\n\\def\\arcmin{\\hbox{$^\\prime$}}\n\\def\\arcsec{\\hbox{$^{\\prime\\prime}$}}\n\n% Simulated Blackboard Bold symbols\n\n\\def\\bbbr{{\\rm I\\!R}}\n\\def\\bbbm{{\\rm I\\!M}}\n\\def\\bbbn{{\\rm I\\!N}}\n\\def\\bbbf{{\\rm I\\!F}}\n\\def\\bbbh{{\\rm I\\!H}}\n\\def\\bbbk{{\\rm I\\!K}}\n\\def\\bbbp{{\\rm I\\!P}}\n\\def\\bbbone{{\\mathchoice {\\rm 1\\mskip-4mu l} {\\rm 1\\mskip-4mu l}\n{\\rm 1\\mskip-4.5mu l} {\\rm 1\\mskip-5mu l}}}\n\\def\\bbbc{{\\mathchoice {\\setbox0=\\hbox{$\\displaystyle\\rm C$}\\hbox{\\hbox\nto0pt{\\kern0.4\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\textstyle\\rm C$}\\hbox{\\hbox\nto0pt{\\kern0.4\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptstyle\\rm C$}\\hbox{\\hbox\nto0pt{\\kern0.4\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptscriptstyle\\rm C$}\\hbox{\\hbox\nto0pt{\\kern0.4\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}}}\n\\def\\bbbq{{\\mathchoice {\\setbox0=\\hbox{$\\displaystyle\\rm\nQ$}\\hbox{\\raise\n0.15\\ht0\\hbox to0pt{\\kern0.4\\wd0\\vrule height0.8\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\textstyle\\rm Q$}\\hbox{\\raise\n0.15\\ht0\\hbox to0pt{\\kern0.4\\wd0\\vrule height0.8\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptstyle\\rm Q$}\\hbox{\\raise\n0.15\\ht0\\hbox to0pt{\\kern0.4\\wd0\\vrule height0.7\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptscriptstyle\\rm Q$}\\hbox{\\raise\n0.15\\ht0\\hbox to0pt{\\kern0.4\\wd0\\vrule height0.7\\ht0\\hss}\\box0}}}}\n\\def\\bbbt{{\\mathchoice {\\setbox0=\\hbox{$\\displaystyle\\rm\nT$}\\hbox{\\hbox to0pt{\\kern0.3\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\textstyle\\rm T$}\\hbox{\\hbox\nto0pt{\\kern0.3\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptstyle\\rm T$}\\hbox{\\hbox\nto0pt{\\kern0.3\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptscriptstyle\\rm T$}\\hbox{\\hbox\nto0pt{\\kern0.3\\wd0\\vrule height0.9\\ht0\\hss}\\box0}}}}\n\\def\\bbbs{{\\mathchoice\n{\\setbox0=\\hbox{$\\displaystyle \\rm S$}\\hbox{\\raise0.5\\ht0\\hbox\nto0pt{\\kern0.35\\wd0\\vrule height0.45\\ht0\\hss}\\hbox\nto0pt{\\kern0.55\\wd0\\vrule height0.5\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\textstyle \\rm S$}\\hbox{\\raise0.5\\ht0\\hbox\nto0pt{\\kern0.35\\wd0\\vrule height0.45\\ht0\\hss}\\hbox\nto0pt{\\kern0.55\\wd0\\vrule height0.5\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptstyle \\rm S$}\\hbox{\\raise0.5\\ht0\\hbox\nto0pt{\\kern0.35\\wd0\\vrule height0.45\\ht0\\hss}\\raise0.05\\ht0\\hbox\nto0pt{\\kern0.5\\wd0\\vrule height0.45\\ht0\\hss}\\box0}}\n{\\setbox0=\\hbox{$\\scriptscriptstyle\\rm S$}\\hbox{\\raise0.5\\ht0\\hbox\nto0pt{\\kern0.4\\wd0\\vrule height0.45\\ht0\\hss}\\raise0.05\\ht0\\hbox\nto0pt{\\kern0.55\\wd0\\vrule height0.45\\ht0\\hss}\\box0}}}}\n\\def\\bbbz{{\\mathchoice {\\hbox{$\\sf\\textstyle Z\\kern-0.4em Z$}}\n{\\hbox{$\\sf\\textstyle Z\\kern-0.4em Z$}}\n{\\hbox{$\\sf\\scriptstyle Z\\kern-0.3em Z$}}\n{\\hbox{$\\sf\\scriptscriptstyle Z\\kern-0.2em Z$}}}}\n\n\n% NUMBER THE DESIGN ELEMENTS\n\n\\def\\Nulle{0} % null element\n\\def\\Afe{1} % author affiliation\n\\def\\Hae{2} % heading A\n\\def\\Hbe{3} % heading B\n\\def\\Hce{4} % heading C\n\\def\\Hde{5} % heading D\n\n\n% TEMPORARY REGISTERS\n\n\\newcount\\LastMac \\LastMac=\\Nulle\n\n\\newskip\\half \\half=5.5pt plus 1.5pt minus 2.25pt\n\\newskip\\one \\one=11pt plus 3pt minus 5.5pt\n\\newskip\\onehalf \\onehalf=16.5pt plus 5.5pt minus 8.25pt\n\\newskip\\two \\two=22pt plus 5.5pt minus 11pt\n\n\\def\\Half{\\addvspace{\\half}}\n\\def\\One{\\addvspace{\\one}}\n\\def\\OneHalf{\\addvspace{\\onehalf}}\n\\def\\Two{\\addvspace{\\two}}\n\n\\def\\Referee{% produce version for refereeing\n \\def\\baselinestretch{2}%\n \\ninepoint\n}\n\n\\def\\Raggedright{% set lines unjustified\n \\rightskip=\\z@ plus \\hsize\\relax\n}\n\n\\def\\Fullout{% set lines justified\n \\rightskip=\\z@\\relax\n}\n\n\\def\\Hang#1#2{% set hanging indentation\n \\hangindent=#1%\n \\hangafter=#2\\relax\n}\n\n\\def\\makeatletter{\\catcode `\\@=11\\relax}\n\\def\\makeatother{\\catcode `\\@=12\\relax}\n\n\n% Pagestyles\n\n\\newif\\ifsp@page\n\\def\\pagestyle#1{\\csname ps@#1\\endcsname}\n\\def\\thispagestyle#1{\\global\\sp@pagetrue\\gdef\\sp@type{#1}}\n\n\\def\\ps@titlepage{%\n \\def\\@oddhead{\\eightpoint\\noindent \\the\\CatchLine\n \\ifprod@font\\else\\qquad Printed\\ \\today\\qquad\n (MN plain \\TeX\\ macros\\ v\\@version)\\fi \\hfil}%\n \\let\\@evenhead=\\@oddhead\n \\def\\@oddfoot{\\eightpoint\\copyright\\ \\@pubyear\\ RAS\\hfil}%\n \\def\\@evenfoot{\\hfil\\eightpoint\\noindent\\copyright\\ \\@pubyear\\ RAS}%\n}\n\n\\def\\ps@headings{%\n \\def\\@oddhead{\\elevenpoint\\it\\noindent\n \\hfill\\the\\RightHeader\\hskip1.5em\\rm\\folio}%\n \\def\\@evenhead{\\elevenpoint\\noindent\n \\folio\\hskip1.5em\\it\\the\\LeftHeader\\hfill}%\n \\def\\@oddfoot{\\eightpoint\\noindent\\copyright\\ \\@pubyear\\ RAS,\n MNRAS {\\bf \\@volume}, \\@pagerange\\hfil}%\n \\def\\@evenfoot{\\hfil\\eightpoint\\copyright\\ \\@pubyear\\ RAS,\n MNRAS {\\bf \\@volume}, \\@pagerange}%\n}\n\n\\def\\ps@plate{%\n \\def\\@oddhead{\\eightpoint\\noindent\\plt@cap\\hfil}%\n \\def\\@evenhead{\\eightpoint\\noindent\\plt@cap\\hfil}%\n \\def\\@oddfoot{\\eightpoint\\noindent\\copyright\\ \\@pubyear\\ RAS,\n MNRAS {\\bf \\@volume}, \\@pagerange\\hfil}%\n \\def\\@evenfoot{\\hfil\\eightpoint\\copyright\\ \\@pubyear\\ RAS,\n MNRAS {\\bf \\@volume}, \\@pagerange}%\n}\n\n\n% DESIGN ELEMENT DEFINITIONS\n\n% Article opening\n\n\\def\\title#1{% article title\n \\bgroup\n \\vbox to 8pt{\\vss}%\n \\seventeenpoint\n \\Raggedright\n \\noindent \\strut{\\bf #1}\\par\n \\egroup\n}\n\n\\def\\author#1{% article author(s)\n \\bgroup\n \\ifnum\\LastMac=\\Afe \\OneHalf\\else \\vskip 21pt\\fi\n \\fourteenpoint\n \\Raggedright\n \\noindent \\strut #1\\par\n \\vskip 3pt%\n \\egroup\n}\n\n\\def\\affiliation#1{% author(s) affiliation\n \\bgroup\n \\vskip -4pt%\n \\eightpoint\n \\Raggedright\n \\noindent \\strut {\\it #1}\\par\n \\egroup\n \\LastMac=\\Afe\\relax\n}\n\n\\def\\acceptedline#1{% acceptance date\n \\bgroup\n \\Two\n \\eightpoint\n \\Raggedright\n \\noindent \\strut #1\\par\n \\egroup\n}\n\n\\long\\def\\abstract#1{%\n \\bgroup\n \\vskip 20pt%\n \\leftskip 11pc\\rightskip\\z@\n \\noindent{\\ninebf ABSTRACT}\\par\n \\tenpoint\n \\Fullout\n \\noindent #1\\par\n \\egroup\n}\n\n\\long\\def\\keywords#1{% keywords\n \\bgroup\n \\Half\n \\leftskip 11pc\\rightskip\\z@\n \\tenpoint\n \\Fullout\n \\noindent\\hbox{\\bf Key words:}\\ #1\\par\n \\egroup\n}\n\n\n% The \\maketitle macro ensures that the two spanning material appears\n% at the top of the first page, and that it has two lines of space\n% underneath it. If you forget this in you input, no output will be produced.\n% The \\BeginOpening (alias \\begintopmatter) macro should be called at the\n% very start of the input file, so that it is in force when the document\n% starts. This ensures that when \\maketitle is called that the group is\n% closed, and the material gets printed.\n\n\\def\\maketitle{%\n \\EndOpening\n \\ifsinglecol \\else \\MakePage\\fi\n}\n\n\n% Page offset\n\n\\def\\pageoffset#1#2{\\hoffset=#1\\relax\\voffset=#2\\relax}\n\n\n% Counter setup\n\n\\def\\@nameuse#1{\\csname #1\\endcsname}\n\\def\\arabic#1{\\@arabic{\\@nameuse{#1}}}\n\\def\\alph#1{\\@alph{\\@nameuse{#1}}}\n\\def\\Alph#1{\\@Alph{\\@nameuse{#1}}}\n\\def\\@arabic#1{\\number #1}\n\\def\\@Alph#1{\\ifcase#1\\or A\\or B\\or C\\or D\\else\\@Ialph{#1}\\fi}\n\\def\\@Ialph#1{\\ifcase#1\\or \\or \\or \\or \\or E\\or F\\or G\\or H\\or I\\or J\\or\n K\\or L\\or M\\or N\\or O\\or P\\or Q\\or R\\or S\\or T\\or U\\or V\\or W\\or X\\or\n Y\\or Z\\else\\errmessage{Counter out of range}\\fi}\n\\def\\@alph#1{\\ifcase#1\\or a\\or b\\or c\\or d\\else\\@ialph{#1}\\fi}\n\\def\\@ialph#1{\\ifcase#1\\or \\or \\or \\or \\or e\\or f\\or g\\or h\\or i\\or j\\or\n k\\or l\\or m\\or n\\or o\\or p\\or q\\or r\\or s\\or t\\or u\\or v\\or w\\or x\\or y\\or\n z\\else\\errmessage{Counter out of range}\\fi}\n\n\n% Equation auto-numbering\n\n\\newcount\\Eqnno\n\\newcount\\SubEqnno\n\n\\def\\theeq{\\arabic{Eqnno}}\n\\def\\thesubeq{\\alph{SubEqnno}}\n\n\\def\\stepeq{\\relax\n \\global\\SubEqnno \\z@\n \\global\\advance\\Eqnno \\@ne\\relax\n {\\rm (\\theeq)}%\n}\n\n\\def\\startsubeq{\\relax\n \\global\\SubEqnno \\z@\n \\global\\advance\\Eqnno \\@ne\\relax\n \\stepsubeq\n}\n\n\\def\\stepsubeq{\\relax\n \\global\\advance\\SubEqnno \\@ne\\relax\n {\\rm (\\theeq\\thesubeq)}%\n}\n\n\n% Headings\n\n\\newcount\\Sec % heading auto number counters\n\\newcount\\SecSec\n\\newcount\\SecSecSec\n\n\\def\\thesection{\\arabic{Sec}}\n\\def\\thesubsection{\\thesection.\\arabic{SecSec}}\n\\def\\thesubsubsection{\\thesubsection.\\arabic{SecSecSec}}\n\n\n\\Sec=\\z@\n\n\\def\\:{\\let\\@sptoken= } \\: % this makes \\@sptoken a space token \n\\def\\:{\\@xifnch} \\expandafter\\def\\: {\\futurelet\\@tempc\\@ifnch}\n\n\\def\\@ifnextchar#1#2#3{%\n \\let\\@tempMACe #1%\n \\def\\@tempMACa{#2}%\n \\def\\@tempMACb{#3}%\n \\futurelet \\@tempMACc\\@ifnch%\n}\n\n\\def\\@ifnch{%\n\\ifx \\@tempMACc \\@sptoken%\n \\let\\@tempMACd\\@xifnch%\n\\else%\n \\ifx \\@tempMACc \\@tempMACe%\n \\let\\@tempMACd\\@tempMACa%\n \\else%\n \\let\\@tempMACd\\@tempMACb%\n \\fi%\n\\fi%\n\\@tempMACd%\n}\n\n\\def\\@ifstar#1#2{\\@ifnextchar *{\\def\\@tempMACa*{#1}\\@tempMACa}{#2}}\n\n\\newskip\\@tempskipb\n\n\\def\\addvspace#1{%\n \\ifvmode\\else \\endgraf\\fi%\n \\ifdim\\lastskip=\\z@%\n \\vskip #1\\relax%\n \\else%\n \\@tempskipb#1\\relax\\@xaddvskip%\n \\fi%\n}\n\n\\def\\@xaddvskip{%\n \\ifdim\\lastskip<\\@tempskipb%\n \\vskip-\\lastskip%\n \\vskip\\@tempskipb\\relax%\n \\else%\n \\ifdim\\@tempskipb<\\z@%\n \\ifdim\\lastskip<\\z@ \\else%\n \\advance\\@tempskipb\\lastskip%\n \\vskip-\\lastskip\\vskip\\@tempskipb%\n \\fi%\n \\fi%\n \\fi%\n}\n\n\\newskip\\@tmpSKIP\n\n\\def\\addpen#1{%\n \\ifvmode\n \\if@nobreak\n \\else\n \\ifdim\\lastskip=\\z@\n \\penalty#1\\relax\n \\else\n \\@tmpSKIP=\\lastskip\n \\vskip -\\lastskip\n \\penalty#1\\vskip\\@tmpSKIP\n \\fi\n \\fi\n \\fi\n}\n\n\\newcount\\@clubpen \\@clubpen=\\clubpenalty\n\\newif\\if@nobreak \\@nobreakfalse\n\n\\def\\@noafterindent{%\n \\global\\@nobreaktrue\n \\everypar{\\if@nobreak\n \\global\\@nobreakfalse\n \\clubpenalty \\@M\n {\\setbox\\z@\\lastbox}%\n \\LastMac=\\Nulle\\relax%\n \\else\n \\clubpenalty \\@clubpen\n \\everypar{}%\n \\fi}%\n}\n\n\\newcount\\gds@cbrk \\gds@cbrk=-300\n\n\\def\\@nohdbrk{\\interlinepenalty \\@M\\relax}\n\n\\let\\@par=\\par\n\\def\\@restorepar{\\def\\par{\\@par}}\n\n\\newif\\if@endpe \\@endpefalse\n \n\\def\\@doendpe{\\@endpetrue \\@nobreakfalse \\LastMac=\\Nulle\\relax%\n \\def\\par{\\@restorepar\\everypar{}\\par\\@endpefalse}%\n \\everypar{\\setbox\\z@\\lastbox\\everypar{}\\@endpefalse}%\n}\n\n\\def\\section{\\@ifstar{\\@ssection}{\\@section}}\n\n\\def\\@section#1{% heading A (\\section{....})\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hae \\addvspace{\\half}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\two}%\n \\fi\n \\bgroup\n \\ninepoint\\bf\n \\Raggedright\n \\global\\advance\\Sec \\@ne\n \\ifappendix\n \\global\\Eqnno=\\z@ \\global\\SubEqnno=\\z@\\relax\n \\def\\ch@ck{#1}%\n \\ifx\\ch@ck\\empty \\def\\c@lon{}\\else\\def\\c@lon{:}\\fi\n \\noindent\\@nohdbrk APPENDIX\\ \\thesection\\c@lon\\hskip 0.5em%\n \\uppercase{#1}\\par\n \\else\n \\noindent\\@nohdbrk\\thesection\\hskip 1pc \\uppercase{#1}\\par\n \\fi\n \\global\\SecSec=\\z@\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hae\\relax\n}\n\n\\def\\@ssection#1{% main section heading (\\section*{....})\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hae \\addvspace{\\half}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\two}%\n \\fi\n \\bgroup\n \\ninepoint\\bf\n \\Raggedright\n% \\ifappendix\n% \\global\\Eqnno=\\z@ \\global\\SubEqnno=\\z@\\relax % mh in apps dont reset\n% \\noindent\\@nohdbrk APPENDIX:\\hskip 0.5em%\n% \\uppercase{#1}\\par\n% \\else\n \\noindent\\@nohdbrk\\uppercase{#1}\\par\n% \\fi\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hae\\relax\n}\n\n\\def\\subsection{\\@ifstar{\\@ssubsection}{\\@subsection}}\n\n\\def\\@subsection#1{% heading B\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hae \\addvspace{1pt plus 1pt minus .5pt}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\onehalf}%\n \\fi\n \\bgroup\n \\ninepoint\\bf\n \\Raggedright\n \\global\\advance\\SecSec \\@ne\n \\noindent\\@nohdbrk\\thesubsection \\hskip 1pc\\relax #1\\par\n \\global\\SecSecSec=\\z@\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hbe\\relax\n}\n\n\\def\\@ssubsection#1{% heading B*\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hae \\addvspace{1pt plus 1pt minus .5pt}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\onehalf}%\n \\fi\n \\bgroup\n \\ninepoint\\bf\n \\Raggedright\n \\noindent\\@nohdbrk #1\\par\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hbe\\relax\n}\n\n\\def\\subsubsection{\\@ifstar{\\@ssubsubsection}{\\@subsubsection}}\n\n\\def\\@subsubsection#1{% heading C\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hbe \\addvspace{1pt plus 1pt minus .5pt}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\onehalf}%\n \\fi\n \\bgroup\n \\ninepoint\\it\n \\Raggedright\n \\global\\advance\\SecSecSec \\@ne\n \\noindent\\@nohdbrk\\thesubsubsection \\hskip 1pc\\relax #1\\par\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hce\\relax\n}\n\n\\def\\@ssubsubsection#1{% heading C*\n \\if@nobreak\n \\everypar{}%\n \\ifnum\\LastMac=\\Hbe \\addvspace{1pt plus 1pt minus .5pt}\\fi\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\onehalf}%\n \\fi\n \\bgroup\n \\ninepoint\\it\n \\Raggedright\n \\noindent\\@nohdbrk #1\\par\n \\egroup\n \\nobreak\n \\vskip\\half\n \\nobreak\n \\@noafterindent\n \\LastMac=\\Hce\\relax\n}\n\n\\def\\paragraph#1{% heading D\n \\if@nobreak\n \\everypar{}%\n \\else\n \\addpen{\\gds@cbrk}%\n \\addvspace{\\one}%\n \\fi%\n \\bgroup%\n \\ninepoint\\it\n \\noindent #1\\ \\nobreak%\n \\egroup\n \\LastMac=\\Hde\\relax\n \\ignorespaces\n}\n\n\n% Appendix\n\n\\newif\\ifappendix\n\n\\def\\appendix{%\n \\global\\appendixtrue\n \\def\\thesection{\\Alph{Sec}}%\n \\def\\thesubsection{\\thesection\\arabic{SecSec}}%\n \\def\\theeq{\\thesection\\arabic{Eqnno}}%\n \\Sec=\\z@ \\SecSec=\\z@ \\SecSecSec=\\z@ \\Eqnno=\\z@ \\SubEqnno=\\z@\\relax\n}\n\n\n% Text\n\n\\let\\tx=\\relax % provided for backward compatibility\n\n\n% Lists\n\n\\def\\beginlist{%\n \\par\\if@nobreak \\else\\addvspace{\\half}\\fi%\n \\bgroup%\n \\ninepoint\n \\let\\item=\\list@item%\n}\n\n\\def\\list@item{%\n \\par\\noindent\\hskip 1em\\relax%\n \\ignorespaces%\n}\n\n\\def\\endlist{\\par\\egroup\\addvspace{\\half}\\@doendpe}\n\n\n% References\n\n\\def\\beginrefs{%\n \\par\n \\bgroup\n \\eightpoint\n \\Fullout\n \\let\\bibitem=\\bib@item\n}\n\n\\def\\bib@item{%\n \\par\\parindent=1.5em\\Hang{1.5em}{1}%\n \\everypar={\\Hang{1.5em}{1}\\ignorespaces}%\n \\noindent\\ignorespaces\n}\n\n\\def\\endrefs{\\par\\egroup\\@doendpe}\n\n\n% Page heads\n\n\\newtoks\\CatchLine\n\n\\def\\@journal{Mon.\\ Not.\\ R.\\ Astron.\\ Soc.\\ } % The journal title string\n\\def\\@pubyear{1994} % Assign a default publication year\n\\def\\@pagerange{000--000} % Assign a default page-range\n\\def\\@volume{000} % Assign a default volume number\n\\def\\@microfiche{} %\n\n\\def\\pubyear#1{\\gdef\\@pubyear{#1}\\@makecatchline}\n\\def\\pagerange#1{\\gdef\\@pagerange{#1}\\@makecatchline}\n\\def\\volume#1{\\gdef\\@volume{#1}\\@makecatchline}\n\\def\\microfiche#1{\\gdef\\@microfiche{and Microfiche\\ #1}\\@makecatchline}\n\n\\def\\@makecatchline{%\n \\global\\CatchLine{%\n {\\rm \\@journal {\\bf \\@volume},\\ \\@pagerange\\ (\\@pubyear)\\ \\@microfiche}}%\n}\n\n\\@makecatchline % Assign a catchline, using the above defaults\n\n\\newtoks\\LeftHeader\n\\def\\shortauthor#1{% left page head\n \\global\\LeftHeader{#1}%\n}\n\n\\newtoks\\RightHeader\n\\def\\shorttitle#1{% right page head\n \\global\\RightHeader{#1}%\n}\n\n\\def\\PageHead{% recto/verso running heads\n \\begingroup\n \\ifsp@page\n \\csname ps@\\sp@type\\endcsname\n \\fi\n \\ifodd\\pageno\n \\let\\the@head=\\@oddhead\n \\else\n \\let\\the@head=\\@evenhead\n \\fi\n \\vbox to \\z@{\\vskip-22.5\\p@%\n \\hbox to \\PageWidth{\\vbox to8.5\\p@{}%\n \\the@head\n }%\n \\vss}%\n \\endgroup\n \\nointerlineskip\n}\n\n\\gdef\\PageFoot{%\n \\nointerlineskip%\n \\begingroup\n \\ifsp@page\n \\csname ps@\\sp@type\\endcsname\n \\global\\sp@pagefalse\n \\fi\n \\vbox to 22pt{\\vfil%\n \\hbox to \\PageWidth{%\n \\eightpoint\\strut\\noindent\n \\ifodd\\pageno\n \\@oddfoot\n \\else\n \\@evenfoot\n \\fi\n }%\n }%\n \\endgroup\n}\n\n\\def\\today{%\n \\number\\day\\space\n \\ifcase\\month\\or January\\or February\\or March\\or April\\or May\\or June\\or\n July\\or August\\or September\\or October\\or November\\or December\\fi\n \\space\\number\\year%\n}\n\n\n\\def\\authorcomment#1{%\n \\gdef\\PageFoot{%\n \\nointerlineskip%\n \\vbox to 20pt{\\vfil%\n \\hbox to \\PageWidth{\\elevenpoint\\noindent \\hfil #1 \\hfil}}%\n }%\n}\n\n\n% Plate pages\n\n\\newif\\ifplate@page\n\\newbox\\plt@box\n\n\\def\\beginplatepage{%\n \\let\\plate=\\plate@head\n \\let\\caption=\\fig@caption\n \\global\\setbox\\plt@box=\\vbox\\bgroup\n \\TEMPDIMEN=\\PageWidth % For \\fig@caption test\n \\hsize=\\PageWidth\\relax\n}\n\n\\def\\endplatepage{\\par\\egroup\\global\\plate@pagetrue}\n\\def\\plate@head#1{\\gdef\\plt@cap{#1}}\n\n% Letters option\n\n\\def\\letters{%\n \\gdef\\folio{\\ifnum\\pageno<\\z@ L\\romannumeral-\\pageno\n \\else L\\number\\pageno \\fi}%\n}\n\n\n% Math setup\n\n% The standard math indentation\n\\newdimen\\mathindent\n\n\\global\\mathindent=\\z@\n\\global\\everydisplay{\\global\\@dspwd=\\displaywidth\\displaysetup}\n\n% New versions of \\displaylines, \\eqalign, \\eqalignno for\n% when non-centered math is in use.\n\n\\def\\@displaylines#1{% (for non-centered math)\n {}$\\displ@y\\hbox{\\vbox{\\halign{$\\@lign\\hfil\\displaystyle##\\hfil$\\crcr\n #1\\crcr}}}${}%\n}\n\n\\def\\@eqalign#1{\\null\\vcenter{\\openup\\jot\\m@th% (for non-centered math)\n \\ialign{\\strut\\hfil$\\displaystyle{##}$&$\\displaystyle{{}##}$\\hfil\n \\crcr#1\\crcr}}%\n}\n\n\\def\\@eqalignno#1{% (for non-centered math)\n \\global\\advance\\@dspwd by -\\mathindent%\n {}$\\displ@y\\hbox{\\vbox{\\halign to\\@dspwd%\n {\\hfil$\\@lign\\displaystyle{##}$\\tabskip\\z@skip\n &$\\@lign\\displaystyle{{}##}$\\hfil\\tabskip\\centering\n &\\llap{$\\@lign##$}\\tabskip\\z@skip\\crcr\n #1\\crcr}}}${}%\n}\n\n% When equations are flushleft ensure, that \\displaylines,\n% \\eqalign, \\eqalignno and \\leqalignno point to the new versions of\n% the macros. Also make \\leqalignno act like \\eqalignno, otherwise the\n% equation text would `crash' into the equation number.\n\n\\global\\let\\displaylines=\\@displaylines\n\\global\\let\\eqalign=\\@eqalign\n\\global\\let\\eqalignno=\\@eqalignno\n\\global\\let\\leqalignno=\\@eqalignno\n\n\\newdimen\\@dspwd \\@dspwd=\\z@\n\\newif\\if@eqno\n\\newif\\if@leqno\n\\newtoks\\@eqn\n\\newtoks\\@eq\n\n\\def\\displaysetup#1$${\\displaytest#1\\eqno\\eqno\\displaytest}\n\n\\def\\displaytest#1\\eqno#2\\eqno#3\\displaytest{%\n \\if!#3!\\ldisplaytest#1\\leqno\\leqno\\ldisplaytest\n \\else\\@eqnotrue\\@leqnofalse\\@eqn={#2}\\@eq={#1}\\fi\n \\generaldisplay$$}\n\n\\def\\ldisplaytest#1\\leqno#2\\leqno#3\\ldisplaytest{%\n\\@eq={#1}%\n \\if!#3!\\@eqnofalse\\else\\@eqnotrue\\@leqnotrue\n \\@eqn={#2}\\fi}\n\n\\def\\generaldisplay{%\n \\if@eqno\n \\if@leqno\n \\hbox to \\displaywidth{\\noindent\n \\rlap{$\\displaystyle\\the\\@eqn$}%\n \\hskip\\mathindent$\\displaystyle\\the\\@eq$\\hfil}%\n \\else\n \\hbox to \\displaywidth{\\noindent\n \\hskip\\mathindent\n $\\displaystyle\\the\\@eq$\\hfil$\\displaystyle\\the\\@eqn$}%\n \\fi\n \\else\n \\hbox to \\displaywidth{\\noindent\n \\hskip\\mathindent$\\displaystyle\\the\\@eq$\\hfil}%\n \\fi\n}\n\n\n% Finishing notice\n\n\\def\\@notice{%\n \\par\\Two%\n \\noindent{\\b@ls{11pt}\\ninerm This paper has been produced using the\n Royal Astronomical Society/Blackwell Science \\TeX\\ macros.\\par}%\n}\n\n% redefine \\bye to output our identification notice :\n\\outer\\def\\bye{\\@notice\\par\\vfill\\supereject\\end}\n\n\n% define a sign on :\n\n\\def\\start@mess{%\n Monthly notices of the RAS journal style (\\@typeface)\\space\n v\\@version,\\space \\@verdate.%\n}\n\n\\everyjob{\\Warn{\\start@mess}}\n\n\n% Two-column macros\n\n%--------------------------------------------------------%\n% INITIALISATION %\n%--------------------------------------------------------%\n\n\\newif\\if@debug \\@debugfalse % when false, only warnings displayed\n\n\\def\\Print#1{\\if@debug\\immediate\\write16{#1}\\else \\fi}\n\\def\\Warn#1{\\immediate\\write16{#1}}\n\\def\\wlog#1{}\n\n\\newcount\\Iteration % temporary loop counter\n\n\\def\\Single{0} \\def\\Double{1} % ItemSPAN's\n\\def\\Figure{0} \\def\\Table{1} % ItemTYPE's\n\n\\def\\InStack{0} % ItemSTATUS\n\\def\\InZoneA{1}\n\\def\\InZoneB{2}\n\\def\\InZoneC{3}\n\n\\newcount\\TEMPCOUNT % temporary count register\n\\newdimen\\TEMPDIMEN % temporary dimen register\n\\newbox\\TEMPBOX % temporary box register\n\\newbox\\VOIDBOX % a box which is permenately void\n\n\\newcount\\LengthOfStack % number of items currently in stack\n\\newcount\\MaxItems % maximum number of items allowed in stack\n\\newcount\\StackPointer\n\\newcount\\Point % used in calculation for generating the\n % physical address of an item in the stack.\n\\newcount\\NextFigure % number of next figure to be output\n\\newcount\\NextTable % number of next table to be output\n\\newcount\\NextItem % Next item to consider by order in stack\n\n\\newcount\\StatusStack % set to point to top of STATUS stack\n\\newcount\\NumStack % set to point to top of NUMBER stack\n\\newcount\\TypeStack % set to point to top of TYPE stack\n\\newcount\\SpanStack % set to point to top of SPAN stack\n\\newcount\\BoxStack % set to point to top of BOX stack\n\n\\newcount\\ItemSTATUS % status of present item\n\\newcount\\ItemNUMBER % number of present item\n\\newcount\\ItemTYPE % type of present item\n\\newcount\\ItemSPAN % span of present item\n\\newbox\\ItemBOX % box of present item\n\\newdimen\\ItemSIZE % size of present item\n % (calculated by GetItemBOX)\n\n\\newdimen\\PageHeight % vertical measure of full page\n\\newdimen\\TextLeading % distance between baselines of body text\n\\newdimen\\Feathering % amount of interline stretch\n\\newcount\\LinesPerPage % height of page in text lines\n\\newdimen\\ColumnWidth % width of 1 column of text\n\\newdimen\\ColumnGap % size of gap between columns\n\\newdimen\\PageWidth % = \\ColumnWidth * 2 + \\ColumnGap\n\\newdimen\\BodgeHeight % Bodge to align figures and tables with text\n\\newcount\\Leading % Set to same as \\TextLeading above\n\n\\newdimen\\ZoneBSize % size of items in ZoneB\n\\newdimen\\TextSize % size of text in ZoneB\n\\newbox\\ZoneABOX % contains Zone A material\n\\newbox\\ZoneBBOX % contains Zone B material\n\\newbox\\ZoneCBOX % contains Zone C material\n\n\\newif\\ifFirstSingleItem\n\\newif\\ifFirstZoneA\n\\newif\\ifMakePageInComplete\n\\newif\\ifMoreFigures \\MoreFiguresfalse % set true in join stack\n\\newif\\ifMoreTables \\MoreTablesfalse % set true in join stack\n\n\\newif\\ifFigInZoneB % used to determine in which zone an item\n\\newif\\ifFigInZoneC % will be placed based on what is in other\n\\newif\\ifTabInZoneB % zones already for a given page.\n\\newif\\ifTabInZoneC\n\n\\newif\\ifZoneAFullPage\n\n\\newbox\\MidBOX % = LeftBOX+gap+RightBOX\n\\newbox\\LeftBOX\n\\newbox\\RightBOX\n\\newbox\\PageBOX % complete made-up page\n\n\\newif\\ifLeftCOL % flags first pass through output routine\n\\LeftCOLtrue\n\n\\newdimen\\ZoneBAdjust\n\n\\newcount\\ItemFits\n\\def\\Yes{1}\n\\def\\No{2}\n\n\\def\\LineAdjust#1{\\global\\ZoneBAdjust=#1\\TextLeading\\relax}\n\n\n% Setup file.\n\n\\MaxItems=15\n\\NextFigure=\\z@ % used for article opening\n\\NextTable=\\@ne\n\n\\BodgeHeight=6pt\n\\TextLeading=11pt % baselineskip of body text\n\\Leading=11\n\\Feathering=\\z@ % amount of interline stretch\n\\LinesPerPage=61 % number of text lines per full page -1\n\\topskip=\\TextLeading\n\\ColumnWidth=20pc % width of text columns\n\\ColumnGap=2pc % gap between columns\n\n\\newskip\\ItemSepamount % space between floats\n\\ItemSepamount=\\TextLeading plus \\TextLeading minus 4pt\n\n\\parskip=\\z@ plus .1pt\n\\parindent=18pt\n\\widowpenalty=\\z@\n\\clubpenalty=10000\n\\tolerance=1500\n\\hbadness=1500\n\\abovedisplayskip=6pt plus 2pt minus 1pt\n\\belowdisplayskip=6pt plus 2pt minus 1pt\n\\abovedisplayshortskip=6pt plus 2pt minus 1pt\n\\belowdisplayshortskip=6pt plus 2pt minus 1pt\n\n\\frenchspacing\n\n\\ninepoint % start main text size\n\n\\PageHeight=682pt\n\\PageWidth=2\\ColumnWidth\n\\advance\\PageWidth by \\ColumnGap\n\n\\pagestyle{headings}\n\n\n%--------------------------------------------------------%\n% STACKS %\n%--------------------------------------------------------%\n\n% THE ITEM STACK\n% The item stack contains contains figures and tables\n% in the order in which they appear in the article source\n% code.\n\n% allocate stack space\n\n\\newcount\\DUMMY \\StatusStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\NumStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\TypeStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\SpanStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newbox\\DUMMY \\BoxStack=\\allocationnumber\n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY\n\n\\def\\wlog{\\immediate\\write\\m@ne}\n\n% \\GetItemSTATUS, \\GetItemNUMBER, \\GetItemTYPE, \\GetItemSPAN,\n% \\GetItemBox \n% are used to get details of a particular item from the item\n% stack. The argument to each of these is the items position\n% in the stack (usually \\StackPointer)...not the items number.\n\n\\def\\GetItemAll#1{%\n \\GetItemSTATUS{#1}\n \\GetItemNUMBER{#1}\n \\GetItemTYPE{#1}\n \\GetItemSPAN{#1}\n \\GetItemBOX{#1}\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemSTATUS#1{%\n \\Point=\\StatusStack\n \\advance\\Point by #1\n \\global\\ItemSTATUS=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemNUMBER#1{%\n \\Point=\\NumStack\n \\advance\\Point by #1\n \\global\\ItemNUMBER=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemTYPE#1{%\n \\Point=\\TypeStack\n \\advance\\Point by #1\n \\global\\ItemTYPE=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemSPAN#1{%\n \\Point\\SpanStack\n \\advance\\Point by #1\n \\global\\ItemSPAN=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemBOX#1{%\n \\Point=\\BoxStack\n \\advance\\Point by #1\n \\global\\setbox\\ItemBOX=\\vbox{\\copy\\Point}\n \\global\\ItemSIZE=\\ht\\ItemBOX\n \\global\\advance\\ItemSIZE by \\dp\\ItemBOX\n \\TEMPCOUNT=\\ItemSIZE\n \\divide\\TEMPCOUNT by \\Leading\n \\divide\\TEMPCOUNT by 65536\n \\advance\\TEMPCOUNT \\@ne\n \\ItemSIZE=\\TEMPCOUNT pt\n \\global\\multiply\\ItemSIZE by \\Leading\n}\n\n% item joins stack\n\n\\def\\JoinStack{%\n \\ifnum\\LengthOfStack=\\MaxItems % stack is full of items\n \\Warn{WARNING: Stack is full...some items will be lost!}\n \\else\n \\Point=\\StatusStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemSTATUS\n \\Point=\\NumStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemNUMBER\n \\Point=\\TypeStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemTYPE\n \\Point\\SpanStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemSPAN\n \\Point=\\BoxStack\n \\advance\\Point by \\LengthOfStack\n \\global\\setbox\\Point=\\vbox{\\copy\\ItemBOX}\n \\global\\advance\\LengthOfStack \\@ne\n \\ifnum\\ItemTYPE=\\Figure % used in \\MakePage\n \\global\\MoreFigurestrue\n \\else\n \\global\\MoreTablestrue\n \\fi\n \\fi\n}\n\n% item leaves stack\n% #1=physical position of the item to be removed\n\n\\def\\LeaveStack#1{%\n {\\Iteration=#1\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\advance\\Iteration \\@ne\n \\GetItemSTATUS{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemSTATUS\n \\GetItemNUMBER{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemNUMBER\n \\GetItemTYPE{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemTYPE\n \\GetItemSPAN{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemSPAN\n \\GetItemBOX{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\setbox\\Point=\\vbox{\\copy\\ItemBOX}\n \\repeat}\n \\global\\advance\\LengthOfStack by \\m@ne\n}\n\n% clean stack\n% This routine scans through the stack and removes anything\n% that does not have STATUS=\\InStack.\n\n\\newif\\ifStackNotClean\n\n\\def\\CleanStack{%\n \\StackNotCleantrue\n {\\Iteration=\\z@\n \\loop\n \\ifStackNotClean\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\advance\\Iteration \\@ne\n \\else\n \\LeaveStack{\\Iteration}\n \\fi\n \\ifnum\\LengthOfStack<\\Iteration\n \\StackNotCleanfalse\n \\fi\n \\repeat}\n}\n\n% Find item.\n% This macro searches from the top to the bottom of the\n% stack for an item of a specified type and number.\n% #1=type, #2=number\n% If the specified item is found, then \\StackPointer is set\n% to point to it, else \\StackPointer=-1.\n% This routine is used to find the next figure or table\n% by number.\n\n\\def\\FindItem#1#2{%\n \\global\\StackPointer=\\m@ne % assume item isn't in stack for now\n {\\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\GetItemTYPE{\\Iteration}\n \\ifnum\\ItemTYPE=#1\n \\GetItemNUMBER{\\Iteration}\n \\ifnum\\ItemNUMBER=#2\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\fi\n \\advance\\Iteration \\@ne\n \\repeat}\n}\n\n% Find next type\n% This macro searches from the top to the bottom of the stack\n% looking for the first item which has STATUS=\\InStack.\n% If it is a figure then a figure is what will be considered\n% next by \\MakePage else table.\n\n\\def\\FindNext{%\n \\global\\StackPointer=\\m@ne % assume stack is empty for now\n {\\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\GetItemTYPE{\\Iteration}\n \\ifnum\\ItemTYPE=\\Figure\n \\ifMoreFigures\n \\global\\NextItem=\\Figure\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\ifnum\\ItemTYPE=\\Table\n \\ifMoreTables\n \\global\\NextItem=\\Table\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\fi\n \\advance\\Iteration \\@ne\n \\repeat}\n}\n\n% Change status\n% Macro to change the status of a specified item in stack.\n% #1=item, #2=new status\n\n\\def\\ChangeStatus#1#2{%\n \\Point=\\StatusStack\n \\advance\\Point by #1\n \\global\\count\\Point=#2\n}\n\n\n%--------------------------------------------------------%\n% MAKEPAGE %\n%--------------------------------------------------------%\n\n% This macro is called at the start of every new page\n% including the first. It scans through the stack picking\n% out items which should be placed on this page. It then\n% leaves space for the items to be placed later. The routine\n% terminates when either there is no room on the page to\n% fit the next figure or table, or there are no more items\n% in the stack.\n\n\\def\\Zone{\\InZoneA}\n\n\\ZoneBAdjust=\\z@\n\n\\def\\MakePage{% allocate space on this page for stack items\n \\global\\ZoneBSize=\\PageHeight\n \\global\\TextSize=\\ZoneBSize\n \\global\\ZoneAFullPagefalse\n \\global\\topskip=\\TextLeading\n \\MakePageInCompletetrue\n \\MoreFigurestrue\n \\MoreTablestrue\n \\FigInZoneBfalse\n \\FigInZoneCfalse\n \\TabInZoneBfalse\n \\TabInZoneCfalse\n \\global\\FirstSingleItemtrue\n \\global\\FirstZoneAtrue\n \\global\\setbox\\ZoneABOX=\\box\\VOIDBOX\n \\global\\setbox\\ZoneBBOX=\\box\\VOIDBOX\n \\global\\setbox\\ZoneCBOX=\\box\\VOIDBOX\n \\loop\n \\ifMakePageInComplete\n \\FindNext\n \\ifnum\\StackPointer=\\m@ne\n \\NextItem=\\m@ne\n \\MoreFiguresfalse\n \\MoreTablesfalse\n \\fi\n \\ifnum\\NextItem=\\Figure\n \\FindItem{\\Figure}{\\NextFigure}\n \\ifnum\\StackPointer=\\m@ne \\global\\MoreFiguresfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Single \\def\\Zone{\\InZoneB}\\relax\n \\ifFigInZoneC \\global\\MoreFiguresfalse\\fi\n \\else\n \\def\\Zone{\\InZoneA}\n \\ifFigInZoneB \\def\\Zone{\\InZoneC}\\fi\n \\fi\n \\fi\n \\ifMoreFigures\\Print{}\\FigureItems\\fi\n \\fi\n\\ifnum\\NextItem=\\Table\n \\FindItem{\\Table}{\\NextTable}\n \\ifnum\\StackPointer=\\m@ne \\global\\MoreTablesfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Single\\relax\n \\ifTabInZoneC \\global\\MoreTablesfalse\\fi\n \\else\n \\def\\Zone{\\InZoneA}\n \\ifTabInZoneB \\def\\Zone{\\InZoneC}\\fi\n \\fi\n \\fi\n \\ifMoreTables\\Print{}\\TableItems\\fi\n \\fi\n \\MakePageInCompletefalse % assume page is complete\n \\ifMoreFigures\\MakePageInCompletetrue\\fi\n \\ifMoreTables\\MakePageInCompletetrue\\fi\n \\repeat\n%\\Print{TextSize=\\the\\TextSize}\n%\\Print{ZoneBSize=\\the\\ZoneBSize}\n \\ifZoneAFullPage\n \\global\\TextSize=\\z@\n \\global\\ZoneBSize=\\z@\n \\global\\vsize=\\z@\\relax\n \\global\\topskip=\\z@\\relax\n \\vbox to \\z@{\\vss}\n \\eject\n \\else\n \\global\\advance\\ZoneBSize by -\\ZoneBAdjust\n \\global\\vsize=\\ZoneBSize\n \\global\\hsize=\\ColumnWidth\n \\global\\ZoneBAdjust=\\z@\n \\ifdim\\TextSize<23pt\n \\Warn{}\n \\Warn{* Making column fall short: TextSize=\\the\\TextSize *}\n \\vskip-\\lastskip\\eject\\fi\n \\fi\n}\n\n\\def\\MakeRightCol{% allocate space for the right column of text\n \\global\\TextSize=\\ZoneBSize\n \\MakePageInCompletetrue\n \\MoreFigurestrue\n \\MoreTablestrue\n \\global\\FirstSingleItemtrue\n \\global\\setbox\\ZoneBBOX=\\box\\VOIDBOX\n \\def\\Zone{\\InZoneB}\n \\loop\n \\ifMakePageInComplete\n \\FindNext\n \\ifnum\\StackPointer=\\m@ne\n \\NextItem=\\m@ne\n \\MoreFiguresfalse\n \\MoreTablesfalse\n \\fi\n \\ifnum\\NextItem=\\Figure\n \\FindItem{\\Figure}{\\NextFigure}\n \\ifnum\\StackPointer=\\m@ne \\MoreFiguresfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Double\\relax\n \\MoreFiguresfalse\\fi\n \\fi\n \\ifMoreFigures\\Print{}\\FigureItems\\fi\n \\fi\n \\ifnum\\NextItem=\\Table\n \\FindItem{\\Table}{\\NextTable}\n \\ifnum\\StackPointer=\\m@ne \\MoreTablesfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Double\\relax\n \\MoreTablesfalse\\fi\n \\fi\n \\ifMoreTables\\Print{}\\TableItems\\fi\n \\fi\n \\MakePageInCompletefalse % assume page is complete\n \\ifMoreFigures\\MakePageInCompletetrue\\fi\n \\ifMoreTables\\MakePageInCompletetrue\\fi\n \\repeat\n \\ifZoneAFullPage\n \\global\\TextSize=\\z@\n \\global\\ZoneBSize=\\z@\n \\global\\vsize=\\z@\\relax\n \\global\\topskip=\\z@\\relax\n \\vbox to \\z@{\\vss}\n \\eject\n \\else\n \\global\\vsize=\\ZoneBSize\n \\global\\hsize=\\ColumnWidth\n \\ifdim\\TextSize<23pt\n \\Warn{}\n \\Warn{* Making column fall short: TextSize=\\the\\TextSize *}\n \\vskip-\\lastskip\\eject\\fi\n\\fi\n}\n\n\\def\\FigureItems{% Stack pointer points to next figure\n \\Print{Considering...}\n \\ShowItem{\\StackPointer}\n \\GetItemBOX{\\StackPointer} % auto calculates ItemSIZE\n \\GetItemSPAN{\\StackPointer}\n \\CheckFitInZone % check to see if item fits\n \\ifnum\\ItemFits=\\Yes\n \\ifnum\\ItemSPAN=\\Single\n \\ChangeStatus{\\StackPointer}{\\InZoneB} % flag to be output\n \\global\\FigInZoneBtrue\n \\ifFirstSingleItem\n \\hbox{}\\vskip-\\BodgeHeight\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\fi\n \\unvbox\\ItemBOX\\ItemSep\n \\global\\FirstSingleItemfalse\n \\global\\advance\\TextSize by -\\ItemSIZE% allocate space\n \\global\\advance\\TextSize by -\\TextLeading\n \\else\n \\ifFirstZoneA\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\global\\FirstZoneAfalse\\fi\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\global\\advance\\ZoneBSize by -\\ItemSIZE\n \\global\\advance\\ZoneBSize by -\\TextLeading\n \\ifFigInZoneB\\relax\n \\else\n \\ifdim\\TextSize<3\\TextLeading\n \\global\\ZoneAFullPagetrue\n \\fi\n \\fi\n \\ChangeStatus{\\StackPointer}{\\Zone}\n \\ifnum\\Zone=\\InZoneC \\global\\FigInZoneCtrue\\fi\n \\fi\n \\Print{TextSize=\\the\\TextSize}\n \\Print{ZoneBSize=\\the\\ZoneBSize}\n \\global\\advance\\NextFigure \\@ne\n \\Print{This figure has been placed.}\n \\else\n \\Print{No space available for this figure...holding over.}\n \\Print{}\n \\global\\MoreFiguresfalse\n \\fi\n}\n\n\\def\\TableItems{% Stack pointer points to next table\n \\Print{Considering...}\n \\ShowItem{\\StackPointer}\n \\GetItemBOX{\\StackPointer} % auto calculates ItemSIZE\n \\GetItemSPAN{\\StackPointer}\n \\CheckFitInZone % check to see of item fits in Zone\n \\ifnum\\ItemFits=\\Yes\n \\ifnum\\ItemSPAN=\\Single\n \\ChangeStatus{\\StackPointer}{\\InZoneB}\n \\global\\TabInZoneBtrue\n \\ifFirstSingleItem\n \\hbox{}\\vskip-\\BodgeHeight\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\fi\n \\unvbox\\ItemBOX\\ItemSep\n \\global\\FirstSingleItemfalse\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\else\n \\ifFirstZoneA\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\global\\FirstZoneAfalse\\fi\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\global\\advance\\ZoneBSize by -\\ItemSIZE\n \\global\\advance\\ZoneBSize by -\\TextLeading\n \\ifFigInZoneB\\relax\n \\else\n \\ifdim\\TextSize<3\\TextLeading\n \\global\\ZoneAFullPagetrue\n \\fi\n \\fi\n \\ChangeStatus{\\StackPointer}{\\Zone}\n \\ifnum\\Zone=\\InZoneC \\global\\TabInZoneCtrue\\fi\n \\fi\n% \\Print{TextSize=\\the\\TextSize}\n% \\Print{ZoneBSize=\\the\\ZoneBSize}\n \\global\\advance\\NextTable \\@ne\n \\Print{This table has been placed.}\n \\else\n \\Print{No space available for this table...holding over.}\n \\Print{}\n \\global\\MoreTablesfalse\n \\fi\n}\n\n% These macros check to see if an item of ItemSIZE will\n% fit in a particular zone. If it will, then ItemFits\n% will be set true else false.\n\n\\def\\CheckFitInZone{%\n{\\advance\\TextSize by -\\ItemSIZE\n \\advance\\TextSize by -\\TextLeading\n \\ifFirstSingleItem\n \\advance\\TextSize by \\TextLeading\n \\fi\n \\ifnum\\Zone=\\InZoneA\\relax\n \\else \\advance\\TextSize by -\\ZoneBAdjust\n \\fi\n \\ifdim\\TextSize<3\\TextLeading \\global\\ItemFits=\\No\n \\else \\global\\ItemFits=\\Yes\\fi}\n}\n\n\\def\\BeginOpening{%\n % start 9pt a.s.a.p. so that \\New.. commands get a chance to init.\n \\ninepoint\n \\thispagestyle{titlepage}%\n \\global\\setbox\\ItemBOX=\\vbox\\bgroup%\n \\hsize=\\PageWidth%\n \\hrule height \\z@\n \\ifsinglecol\\vskip 6pt\\fi % Bodge, to get same pos. as two-column!\n}\n\n\\let\\begintopmatter=\\BeginOpening % alias for \\BeginOpening\n\n\\def\\EndOpening{%\n \\One% 1 line fixed space below opening\n \\egroup\n \\ifsinglecol\n \\box\\ItemBOX%\n \\vskip\\TextLeading plus 2\\TextLeading% var. space: min 1, max 3 lines\n \\@noafterindent\n \\else\n \\ItemNUMBER=\\z@%\n \\ItemTYPE=\\Figure\n \\ItemSPAN=\\Double\n \\ItemSTATUS=\\InStack\n \\JoinStack\n \\fi\n}\n\n\n% Figures\n\n\\newif\\if@here \\@herefalse\n\n\\def\\no@float{\\global\\@heretrue}\n\\let\\nofloat=\\relax % only enabled for one column\n\n\\def\\beginfigure{%\n \\@ifstar{\\global\\@dfloattrue \\@bfigure}{\\global\\@dfloatfalse \\@bfigure}%\n}\n\n\\def\\@bfigure#1{%\n \\par\n \\if@dfloat\n \\ItemSPAN=\\Double\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSPAN=\\Single\n \\TEMPDIMEN=\\ColumnWidth\n \\fi\n \\ifsinglecol\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSTATUS=\\InStack\n \\ItemNUMBER=#1%\n \\ItemTYPE=\\Figure\n \\fi\n \\bgroup\n \\hsize=\\TEMPDIMEN\n \\global\\setbox\\ItemBOX=\\vbox\\bgroup\n \\eightpoint\\nostb@ls{10pt}%\n \\let\\caption=\\fig@caption\n \\ifsinglecol \\let\\nofloat=\\no@float\\fi\n}\n\n\\def\\fig@caption#1{%\n \\vskip 5.5pt plus 6pt%\n \\bgroup % grouping and size change needed for plate pages\n \\eightpoint\\nostb@ls{10pt}%\n \\setbox\\TEMPBOX=\\hbox{#1}%\n \\ifdim\\wd\\TEMPBOX>\\TEMPDIMEN\n \\noindent \\unhbox\\TEMPBOX\\par\n \\else\n \\hbox to \\hsize{\\hfil\\unhbox\\TEMPBOX\\hfil}%\n \\fi\n \\egroup\n}\n\n\\def\\endfigure{%\n \\par\\egroup % end \\vbox\n \\egroup\n \\ifsinglecol\n \\if@here \\midinsert\\global\\@herefalse\\else \\topinsert\\fi\n \\unvbox\\ItemBOX\n \\endinsert\n \\else\n \\JoinStack\n \\Print{Processing source for figure \\the\\ItemNUMBER}%\n \\fi\n}\n\n\n% Tables\n\n\\newbox\\tab@cap@box\n\\def\\tab@caption#1{\\global\\setbox\\tab@cap@box=\\hbox{#1\\par}}\n\n\\newtoks\\tab@txt@toks\n\\long\\def\\tab@txt#1{\\global\\tab@txt@toks={#1}\\global\\table@txttrue}\n\n\\newif\\iftable@txt \\table@txtfalse\n\\newif\\if@dfloat \\@dfloatfalse\n\n\\def\\begintable{%\n \\@ifstar{\\global\\@dfloattrue \\@btable}{\\global\\@dfloatfalse \\@btable}%\n}\n\n\\def\\@btable#1{%\n \\par\n \\if@dfloat\n \\ItemSPAN=\\Double\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSPAN=\\Single\n \\TEMPDIMEN=\\ColumnWidth\n \\fi\n \\ifsinglecol\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSTATUS=\\InStack\n \\ItemNUMBER=#1%\n \\ItemTYPE=\\Table\n \\fi\n \\bgroup\n \\eightpoint\\nostb@ls{10pt}%\n \\global\\setbox\\ItemBOX=\\vbox\\bgroup\n \\let\\caption=\\tab@caption\n \\let\\tabletext=\\tab@txt\n \\ifsinglecol \\let\\nofloat=\\no@float\\fi\n}\n\n\\def\\endtable{%\n \\par\\egroup % end \\vbox\n \\egroup\n \\setbox\\TEMPBOX=\\hbox to \\TEMPDIMEN{%\n \\eightpoint\\nostb@ls{10pt}%\n \\hss\n \\vbox{%\n \\hsize=\\wd\\ItemBOX\n \\ifvoid\\tab@cap@box\n \\else\n \\noindent\\unhbox\\tab@cap@box\n \\vskip 5.5pt plus 6pt%\n \\fi\n \\box\\ItemBOX\n \\iftable@txt\n \\vskip 10pt%\n \\noindent\\the\\tab@txt@toks\n \\global\\table@txtfalse\n \\fi\n }%\n \\hss\n }%\n \\ifsinglecol\n \\if@here \\midinsert\\global\\@herefalse\\else \\topinsert\\fi\n \\box\\TEMPBOX\n \\endinsert\n \\else\n \\global\\setbox\\ItemBOX=\\box\\TEMPBOX\n \\JoinStack\n \\Print{Processing source for table \\the\\ItemNUMBER}%\n \\fi\n}\n\n\n\\def\\UnloadZoneA{%\n\\FirstZoneAtrue\n \\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InZoneA\n \\GetItemBOX{\\Iteration}\n \\ifFirstZoneA \\vbox to \\BodgeHeight{\\vfil}%\n \\FirstZoneAfalse\\fi\n \\unvbox\\ItemBOX\\ItemSep\n \\LeaveStack{\\Iteration}\n \\else\n \\advance\\Iteration \\@ne\n \\fi\n \\repeat\n}\n\n\\def\\UnloadZoneC{%\n\\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InZoneC\n \\GetItemBOX{\\Iteration}\n \\ItemSep\\unvbox\\ItemBOX\n \\LeaveStack{\\Iteration}\n \\else\n \\advance\\Iteration \\@ne\n \\fi\n \\repeat\n}\n\n\n%--------------------------------------------------------%\n% DIAGNOSTICS %\n%--------------------------------------------------------%\n\n\\def\\ShowItem#1{% Show details of on item entry in stack\n {\\GetItemAll{#1}\n \\Print{\\the#1:\n {TYPE=\\ifnum\\ItemTYPE=\\Figure Figure\\else Table\\fi}\n {NUMBER=\\the\\ItemNUMBER}\n {SPAN=\\ifnum\\ItemSPAN=\\Single Single\\else Double\\fi}\n {SIZE=\\the\\ItemSIZE}}}\n}\n\n\\def\\ShowStack{% \n \\Print{}\n \\Print{LengthOfStack = \\the\\LengthOfStack}\n \\ifnum\\LengthOfStack=\\z@ \\Print{Stack is empty}\\fi\n \\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\ShowItem{\\Iteration}\n \\advance\\Iteration \\@ne\n \\repeat\n}\n\n\\def\\B#1#2{%\n\\hbox{\\vrule\\kern-0.4pt\\vbox to #2{%\n\\hrule width #1\\vfill\\hrule}\\kern-0.4pt\\vrule}\n}\n\n\n%-------------------------------------------------------%\n% SINGLE COLUMN OUTPUT ROUTINE %\n%-------------------------------------------------------%\n\n\\newif\\ifsinglecol \\singlecolfalse\n\n\\def\\onecolumn{%\n \\global\\output={\\singlecoloutput}%\n \\global\\hsize=\\PageWidth\n \\global\\vsize=\\PageHeight\n \\global\\ColumnWidth=\\hsize\n \\global\\TextLeading=12pt\n \\global\\Leading=12\n \\global\\singlecoltrue\n \\global\\let\\onecolumn=\\relax% stop them using \\onecolumn again\n \\global\\let\\footnote=\\sing@footnote% enable footnotes\n \\global\\let\\vfootnote=\\sing@vfootnote\n \\ninepoint % reset \\baselineskip after leading change\n \\message{(Single column)}%\n}\n\n\\def\\singlecoloutput{%\n \\shipout\\vbox{\\PageHead\\vbox to \\PageHeight{\\pagebody\\vss}\\PageFoot}%\n \\advancepageno\n%\n \\ifplate@page\n \\shipout\\vbox{%\n \\sp@pagetrue\n \\def\\sp@type{plate}%\n \\global\\plate@pagefalse\n \\PageHead\\vbox to \\PageHeight{\\unvbox\\plt@box\\vfil}\\PageFoot%\n }%\n \\message{[plate]}%\n \\advancepageno\n \\fi\n%\n \\ifnum\\outputpenalty>-\\@MM \\else\\dosupereject\\fi%\n}\n\n\\def\\ItemSep{\\vskip\\ItemSepamount\\relax}\n\n\\def\\ItemSepbreak{\\par\\ifdim\\lastskip<\\ItemSepamount\n \\removelastskip\\penalty-200\\ItemSep\\fi%\n}\n\n% Modify plain's \\endinsert so that the mn's spacing is used\n\n\\let\\@@endinsert=\\endinsert % save plain's original \\endinsert\n\n\\def\\endinsert{\\egroup % finish the \\vbox\n \\if@mid \\dimen@\\ht\\z@ \\advance\\dimen@\\dp\\z@ \\advance\\dimen@12\\p@\n \\advance\\dimen@\\pagetotal \\advance\\dimen@-\\pageshrink\n \\ifdim\\dimen@>\\pagegoal\\@midfalse\\p@gefalse\\fi\\fi\n \\if@mid \\ItemSep\\box\\z@\\ItemSepbreak\n \\else\\insert\\topins{\\penalty100 % floating insertion\n \\splittopskip\\z@skip\n \\splitmaxdepth\\maxdimen \\floatingpenalty\\z@\n \\ifp@ge \\dimen@\\dp\\z@\n \\vbox to\\vsize{\\unvbox\\z@\\kern-\\dimen@}% depth is zero\n \\else \\box\\z@\\nobreak\\ItemSep\\fi}\\fi\\endgroup%\n}\n\n\n% Footnotes (only enabled in single column)\n\n\\def\\gobbleone#1{}\n\\def\\gobbletwo#1#2{}\n\\let\\footnote=\\gobbletwo % Gobble footnote's unless enabled by \\onecolumn\n\\let\\vfootnote=\\gobbleone\n\n\\def\\sing@footnote#1{\\let\\@sf\\empty % parameter #2 (the text) is read later\n \\ifhmode\\edef\\@sf{\\spacefactor\\the\\spacefactor}\\/\\fi\n \\hbox{$^{\\hbox{\\eightpoint #1}}$}\\@sf\\sing@vfootnote{#1}%\n}\n\n\\def\\sing@vfootnote#1{\\insert\\footins\\bgroup\\eightpoint\\b@ls{9pt}%\n \\interlinepenalty\\interfootnotelinepenalty\n \\splittopskip\\ht\\strutbox % top baseline for broken footnotes\n \\splitmaxdepth\\dp\\strutbox \\floatingpenalty\\@MM\n \\leftskip\\z@skip \\rightskip\\z@skip \\spaceskip\\z@skip \\xspaceskip\\z@skip\n \\noindent $^{\\scriptstyle\\hbox{#1}}$\\hskip 4pt%\n \\footstrut\\futurelet\\next\\fo@t%\n}\n\n% Kill footnote rule\n\\def\\footnoterule{\\kern-3\\p@ \\hrule height \\z@ \\kern 3\\p@}\n\n\\skip\\footins=19.5pt plus 12pt minus 1pt\n\\count\\footins=1000\n\\dimen\\footins=\\maxdimen\n\n% for footnotes in double column: use \\note{$\\star$}{footnote}\n\\def\\note#1#2{%\n \\let\\@sf=\\empty \\ifhmode\\edef\\@sf{\\spacefactor\\the\\spacefactor}\\/\\fi\n #1\\insert\\footins\\bgroup\n \\eightpoint\\b@ls{10pt}\\rm\n \\interlinepenalty\\interfootnotelinepenalty\n% \\splittopskip\\ht\\strutbox % top baseline for broken footnotes\n \\splitmaxdepth\\dp\\strutbox \\floatingpenalty\\@MM\n \\leftskip\\z@skip \\rightskip\\z@skip \\spaceskip\\z@skip \\xspaceskip\\z@skip\n \\noindent\\footstrut #1$\\,$#2\\strut\\par\n \\egroup\n \\@sf\\relax}\n\n% Landscape\n\n\\def\\landscape{%\n \\global\\TEMPDIMEN=\\PageWidth\n \\global\\PageWidth=\\PageHeight\n \\global\\PageHeight=\\TEMPDIMEN\n \\global\\let\\landscape=\\relax% stop them using \\landscape again.\n \\onecolumn\n \\message{(landscape)}%\n \\raggedbottom\n}\n\n\n%-------------------------------------------------------%\n% TWO COLUMN OUTPUT ROUTINE %\n%-------------------------------------------------------%\n\n% Very slight redefinition of the \\output routine of mn.tex, to allow footnotes.\n\\output{%\n \\ifLeftCOL\n \\global\\setbox\\LeftBOX=\\vbox to \\ZoneBSize{\\box255\\unvbox\\ZoneBBOX\n \\ifvoid\\footins\\else\n \\vskip\\skip\\footins\\unvbox\\footins\\fi\n }%\n \\global\\LeftCOLfalse\n \\MakeRightCol\n \\else\n \\setbox\\RightBOX=\\vbox to \\ZoneBSize{\\box255\\unvbox\\ZoneBBOX\n \\ifvoid\\footins\\else\n \\vskip\\skip\\footins\\unvbox\\footins\\fi\n }%\n \\setbox\\MidBOX=\\hbox{\\box\\LeftBOX\\hskip\\ColumnGap\\box\\RightBOX}%\n \\setbox\\PageBOX=\\vbox to \\PageHeight{%\n \\UnloadZoneA\\box\\MidBOX\\UnloadZoneC}%\n \\shipout\\vbox{\\PageHead\\vbox to \\PageHeight{\\box\\PageBOX\\vss}\\PageFoot}%\n \\advancepageno\n%\n \\ifplate@page\n \\shipout\\vbox{%\n \\sp@pagetrue\n \\def\\sp@type{plate}%\n \\global\\plate@pagefalse\n \\PageHead\\vbox to \\PageHeight{\\unvbox\\plt@box\\vfil}\\PageFoot%\n }%\n \\message{[plate]}%\n \\advancepageno\n \\fi\n%\n \\global\\LeftCOLtrue\n \\CleanStack\n \\MakePage\n \\fi\n}\n\n\n\n% Startup message\n\n\\Warn{\\start@mess}\n\n\\newif\\ifCUPmtplainloaded % for use in documents\n\\ifprod@font\n \\global\\CUPmtplainloadedtrue\n\\fi\n\n\\def\\mnmacrosloaded{} % so articles can see if a format file has been used.\n\n\\catcode `\\@=12 % @ signs are non-letters\n\n% \\dump\n\n% end of mn.tex\n\n"
},
{
"name": "over.tex",
"string": "%\n% overmerging paper\n%\n% Eelco van Kampen\n%\n% Institute for Astronomy, Edinburgh, 1998-1999\n%\n\n\\ifx\\mnmacrosloaded\\undefined \\input mn\\fi\n\n% author's definitions\n\n\\input psfig\n\\def\\halve{{\\scriptstyle 1 \\over 2}}\n\\def\\Mpc{$h_0^{-1}$Mpc}\n\n\\newif\\ifAMStwofonts\n%\\AMStwofontstrue\n\n\\ifCUPmtplainloaded \\else\n \\NewTextAlphabet{textbfit} {cmbxti10} {}\n \\NewTextAlphabet{textbfss} {cmssbx10} {}\n \\NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode\n \\NewMathAlphabet{mathbfss} {cmssbx10} {} % \" \" \"\n %\n \\ifAMStwofonts\n %\n \\NewSymbolFont{upmath} {eurm10}\n \\NewSymbolFont{AMSa} {msam10}\n \\NewMathSymbol{\\upi} {0}{upmath}{19}\n \\NewMathSymbol{\\umu} {0}{upmath}{16}\n \\NewMathSymbol{\\upartial}{0}{upmath}{40}\n \\NewMathSymbol{\\leqslant}{3}{AMSa}{36}\n \\NewMathSymbol{\\geqslant}{3}{AMSa}{3E}\n \\let\\oldle=\\le \\let\\oldleq=\\leq\n \\let\\oldge=\\ge \\let\\oldgeq=\\geq\n \\let\\leq=\\leqslant \\let\\le=\\leqslant\n \\let\\geq=\\geqslant \\let\\ge=\\geqslant\n \\else\n \\def\\umu{\\mu}\n \\def\\upi{\\pi}\n \\def\\upartial{\\partial}\n \\fi\n\\fi\n\n% Marginal adjustments using \\pageoffset maybe required when printing\n% proofs on a Laserprinter (this is usually not needed).\n% Syntax: \\pageoffset{ +/- hor. offset}{ +/- vert. offset}\n% e.g. \\pageoffset{-3pc}{-4pc}\n\\pageoffset{-2.5pc}{0pc}\n\n\\loadboldmathnames\n\n% \\Referee % uncomment this for referee mode (double spaced)\n\n% \\onecolumn % enable one column mode\n% \\letters % for `letters' articles\n\\pagerange{0--0} % `letters' articles should use \\pagerange{Ln--Ln}\n\\pubyear{2000}\n\\volume{000}\n% \\microfiche{} % for articles with microfiche\n% \\authorcomment{} % author comment for footline\n\n\\begintopmatter % start the two spanning material\n\n\\title{Overmerging in N-body simulations}\n\\author{Eelco van Kampen}\n\\affiliation{Institute for Astronomy, University of Edinburgh, Royal\nObservatory, Blackford Hill, Edinburgh EH9 3HJ,\\ {\\tt [email protected]}}\n\\shortauthor{E.\\ van Kampen}\n\\shorttitle{Overmerging}\n\\acceptedline{Accepted ... Received ...; in original form ...}\n\n\\abstract {The aim of this paper is to clarify the notion and cause of\novermerging in N-body simulations, and to present analytical estimates\nfor its timescale. Overmerging is the disruption of subhaloes\nwithin embedding haloes due to {\\it numerical}\\ problems connected with\nthe discreteness of N-body dynamics. It is shown that the process responsible\nfor overmerging is particle-subhalo two-body heating.\n%Excessive softening worsens the problem.\nVarious solutions to the overmerging problem are discussed.}\n\n\\keywords {galaxies: evolution - dark matter - large-scale structure of Universe}\n\\maketitle % finish the two spanning material\n% \\Referee % uncomment this for referee mode\n\n\\section{Introduction}\n\nIn the study of the formation and evolution of large-scale structure in the\nuniverse, clusters of galaxies, galaxies, and many other gravitational systems,\nhaloes play an important r\\^ole.\nA {\\it halo}\\ is defined as a collapsed and virialized density maximum.\nA halo can contain several smaller haloes, denoted as {\\it subhaloes}.\nWe denote a halo that contains subhaloes as an {\\it embedding halo}.\nThe existence of subhaloes is an important issue in cosmology, especially for\ngalaxies, and groups and clusters of galaxies. For example,\nhierarchical structure formation scenarios for CDM-like spectra predict\nmany more dwarf galaxies (or satellites) than observed (Klypin et al.\\ 1999b,\nMoore et al.\\ 1999).\nAlso, a spiral galaxy cannot retain its disk if there is an high abundance\nof subhaloes within its halo (Moore et al.\\ 1999). Thus, the question\nis whether the initial density fluctuation spetrum is such that not many\ndwarf galaxies form in the first place, or that they are easily destroyed\nwithin our Galaxy, and hard to find outside it. On larger scale, clusters\nof galaxies do contain an abundance of subhaloes, i.e.\\ its member galaxies,\nwhich are often distorted and stripped, but probably not destroyed.\n\nN-body simulations are routinely used to model the formation, evolution,\nand clustering of galaxy and galaxy cluster haloes.\nHowever, the N-body simulation method does have its limitiations, and care\nshould be taken with the interpretation of the simulation results.\nOne such limitation arises from the use of particles to represent\nthe mass distribution whose evolution one tries to simulate.\nIf the physical mass distribution is effectively collisionless,\nas is often the case, the use of particles gives rise to artificial\ncollisional effects within the numerical mass distribution, especially\nthough two-body interaction. Two-body encounters between simulation\nparticles, either close or distant, deflect their orbits significantly,\nwhile they should behave like test particles, and respond only to the\nmean potential. This is especially a problem for subhaloes, which are\neasily destroyed in an N-body simulation with insufficient resolution\n(White et al.\\ 1987; Carlberg 1994; van Kampen 1995).\nWe use the term {\\it overmerging}\\ for the numerical processes that\nartificially merge haloes and subhaloes in an N-body model, usually by\ndisrupting the subhalo. Thus, the term {\\it merging}\\ only denotes\nmerging due to physical processes.\n\n\\beginfigure{1}\n{\\psfig{file=over.eps,width=8.5cm,silent=1}}\n\\caption{{\\bf Figure 1.} Graphical illustration of the main\nnumerical disruption processes that cause overmerging.\nOpen circles represent the 'cold' particles of an isolated\nhalo or a subhalo within an embedded halo, whose 'hot'\nparticles are indicated by filled circles.}\n\\endfigure\n\nHowever, there seems to be some confusion in the literature over the\nnature, cause, and importance of the overmerging problem.\nThis paper attempts to clarify the difference between the three most\nimportant two-body processes operating on subhaloes, and provide\nestimates for their associated timescales.\nThe first process is {\\it two-body evaporation}, which is an\n{\\it internal}\\ process operation within any halo or subhalo.\nIt is due to two-body interactions between the particles within the halo\nor subhalo. The second process is {\\it particle-subhalo two-body heating},\nwhich is the heating of `cold' subhaloes by particles from the `hot'\nembedding halo through two-body interactions.\nThe third process is {\\it particle-subhalo tidal heating}, where the subhalo\nis considered collisionless, and increases its kinetic energy through\ntidal interactions with particles from the embedding halo. All three\nprocess are illustrated in Fig.\\ 1.\n\nBesides the two-body processes, the use of {\\it softened}\\ particles, in order\nto minimize two-body effects, can cause overmerging as well by artificially\nenhancing physical processes like merging and disruption by tidal forces\n(van Kampen 1995; Moore et al.\\ 1996). Groups of softened particles are not\nas compact as real haloes, and their artificially larger sizes make N-body\ngroups more prone to tidal disruption.\n\nCarlberg (1994) proposed particle-subhalo two-body heating as the main\ncause for overmerging. He gave a timescale for this process, but no\nderivation. This was provided by van Kampen (1995).\nIt has been shown before (Carlberg 1994; van Kampen 1995) that the\ntwo-body heating time-scale for small subhaloes orbiting an embedding\nhalo is short enough to result in their complete destruction and dispersion.\nSubsequent authors, including Moore et al.\\ (1996) and Klypin et al.\\ (1999a),\nreferenced Carlberg (1994) as saying that `particle-halo heating'\nis at the root of the problem. Moore et al.\\ (1996) then claim that the\nprocess is not important for the resolution of the simulation performed by\nCarlberg (1994) because the timescale is too long.\nHowever, the process Moore et al.\\ (1996) actually describes and derives a\ntimescale for is a different one,\ndriven by tidal encounters between simulation particles and perfectly\ncollisionless subhaloes, while Carlberg (1994) and van Kampen (1995)\nclearly had a collisonal process in mind, driven by two-body encounters\nbetween individual subhalo particles and particles from the embedding halo.\nThis paper shows that the latter process has a much shorter timescale, and\ntherefore, along with excessive softening, is the main cause for overmerging.\n\n\\section{Two-body effects in N-body simulations}\n\nTwo-body effects become dominant for systems modelled by small numbers of\nparticles. This is usually quantified by the two-body relaxation timescale,\nwhich is defined as the time it takes, on average, for a particle to\nchange its velocity by of order itself. After this time a system is\ndenoted as {\\it relaxed}. The relaxation timescale is defined\nin terms of the {\\it half-mass radius}\\ $r$, the {\\it typical velocity}\\\n$v$ (usually taken to be equal to the velocity dispersion), and the\naverage change $\\Delta v$ per {\\it crossing time}\\ $r/v$:\n$$t_{\\rm relax}\\equiv {v^2 \\over (\\Delta v)^2} {r \\over v}\\ . \\eqno\\stepeq$$\n\\newcount\\timescaledefinition\n\\timescaledefinition=\\Eqnno\nFor an {\\it isolated}\\ virialized system of $N$ point particles, it is easy\nto show that this is of order $0.1 N/\\ln N$ crossing times (eg.\\ Binney \\& \nTremaine 1987). If the time interval one tries to cover for a particular\nproblem is larger than the two-body relaxtion timescale, the problem becomes\nartificially collisional.\n\nAlthough many systems are likely to endure physical mechanisms like violent\nrelaxation and phase mixing during some stage of their evolution, an obvious\nworry is that such physical mechanisms might not actually be important\nin a given situation, so that two-body interactions are very much unwanted\nas they might mimic the effects of physical mechanisms.\nA different problem is that a system might completely evaporate through\ntwo-body interactions.\n\nThe problem can be alleviated somewhat by softening\nthe particles, which reduces the two-body relaxation timescale to\n$0.1 N/\\ln \\Lambda$ crossing times (see van Kampen (1995) and references\ntheirein), where $\\Lambda={\\rm Min}(R/4\\epsilon, N)$, with $R$ the effective\nsize of the system, which we take to be twice the half-mass radius $r$,\nand $\\epsilon$ the softening length of the N-body particles.\nHowever, $\\epsilon$ is necessarily a function of both $N$ and $r$, as softened\nparticles should not overlap too much. Too large a choice for $\\epsilon$ will\nprevent particles from clustering properly and produce haloes which are too\nextended and too cold (that is, the velocity dispersion is too small).\nGiven that $N/2$ particles reside within $r$ by definition, the mean particle\nnumber density within $r$ is $3N/(8\\pi r^3)$. The maximum mean particle density\ndesirable is set by the minimum mean nearest neighbour distance for the\nparticles: $n_{\\rm max}=3/(4\\pi r^3_{\\rm nn})$. Most often used is Plummer\nsoftening, which just means that particles have a Plummer density\nprofile, $\\rho(r)\\sim(r^2+\\epsilon^2)^{5/2}$. The effective force\nresolution, defined as the separation between two particles for which\nthe radial component of the softened force between them is half its\nNewtonian value, is $\\approx 2.6\\epsilon$ for Plummer softening\n(Gelb \\& Bertschinger 1994), so we want $r_{\\rm nn}\\ga 2.6\\epsilon$,\nwhich gives $n_{\\rm max}\\approx 0.014/\\epsilon^3$.\nThus, we find a maximum realistic softening length\n$$\\epsilon \\approx {r\\over 2 N^{1\\over 3}}\\ . \\eqno\\stepeq$$\n\\newcount\\softeningnumber\n\\softeningnumber=\\Eqnno\nFor this $\\epsilon$ the relaxation time becomes $0.3 N/\\ln N$\ncrossing times, i.e.\\ three times larger than for the point particles case.\n\nEven though softening alleviates the problem of two-body effects somewhat,\nsoftened particle groups are more extended and less strongly bound (van Kampen 1995).\nThis makes them more vulnerable to two-body disruption processes, which are more\nefficient for larger subhaloes, as shown below.\nFurthermore, the timescales for {\\it physical}\\ disruption processes are effected.\nSubhalo-subhalo tidal heating has a timescale inversely proportional to the\nsubhalo size (van Kampen 2000), and is therefore slower, although the lower\nbinding energy might compensate for this.\n%Dynamical friction does not or weakly depend on subhalo size. \nTidal stripping and disruption will be artificially enhanced, however, because\nof the larger subhalo size and the weaker binding of the particles inside the\ngroup (van Kampen 1995).\nBecause the enhanced tidal disruption due to softening has the same net\neffect as two-body disruption, which is also enhanced due to the larger\nsubhalo size, the two disruption processes accelerate each other.\n%In order to examine which process is the most important, one can look at\n%simulations of the same matter distribution at different resolutions.\n%If disruption occurs at the same timescale for two different resolutions,\n%it is likely to be tidal, whereas if it is only seen to operate for the\n%lower resolution simulation, it must be two-body disruption.\n%Of the two, two-body disruption seems the dominant process (van Kampen 1995).\nIn the next section we derive two-body disruption timescales without taking\ninto account tidal disruption, and then treat these timescales as upper limits.\n\n\\section{Disruption timescales}\n\n\\subsection{Two-body evaporation}\n\nThis process is internal to haloes and subhaloes\nin other words, it is a self-disruption process. Two-body interactions\nbetween particles within the same (sub)halo change their orbits and\nvelocities, thus every once in a while the velocity will be larger \nthan the escape velocity, and a particle will `leak' out of the (sub)halo.\nThe timescale for this process is about a hundred times the relaxation\ntimescale (e.g.\\ Binney \\& Tremaine 1987),\n$$t_{\\rm dis}\\equiv 30 {N\\over\\ln N} {r \\over v}\n \\ , \\eqno\\stepeq$$\nso for small $N$ this becomes important.\nAs an example, for galaxy haloes, evaporation becomes an issue for $N<10$,\nas the crossing time for most galaxy haloes is larger than 0.2 Gyr,\nindependent of their mass.\n\nMoore et al. (1996) tested whether this process gets enhanced for\nsubhaloes within embedding haloes due to the influence of the mean\ntidal field of the embedding halo. They simulated a\ncollisional group of particles within a {\\it smooth}, and therefore\ncollisionless, isothermal system. They found that the evaporation\nrate was similar to that for an isolated group, and concluded\nthat {\\it \"relaxation effects are not important at driving mass loss\nfrom haloes within current simulations\"}.\nTheir conclusion is incorrect, however, as they did not consider\nthe particle-subhalo two-body heating process, which we discuss next.\n%Their numerical tests should have included a particle distribution\n%for the over-dense region as well, which would have heated the small\n%group into dissolution.\n\n\\subsection{Particle-subhalo two-body heating}\n\nParticles within a subhalo do not just interact amongst themselves\n(driving the evaporation process describe above), but also with\nthe particles of the embedding halo.\nAs the latter are usually hotter than those of the\nsubhalo, velocity changes to the subhalo particles will always\nbe positive. The process very much resembles the kinetic heating\nof a cold system that is introduced into a hot bath:\nan embedding halo `boils' the subhalo into dissolution.\nA derivation for the disruption timescale of this process is\ngiven by van Kampen (1995, his eq.\\ 15, which is erroneous by \na factor of two):\n$$t_{\\rm dis} \\approx {v_{\\rm s}^2 \\over v_{\\rm h}^2}\n {N_{\\rm h} \\over 12\\ln (r_{\\rm h}/2\\epsilon)} \n {r_{\\rm h} \\over v_{\\rm h}} \\ . \\eqno\\stepeq$$\n\\newcount\\disruptiontimescale\n\\disruptiontimescale=\\Eqnno\nHere $N$ denotes the number of particles,\nand the subscripts {\\rm h} and {\\rm s} denote embedding halo and subhalo\nrespectively. A similar expression was given earlier by\nCarlberg (1994, his eq.\\ 13 with his indices c and g swapped,\nno derivation given):\n$$t_{\\rm dis} \\approx {v_{\\rm s}^2 \\over v_{\\rm h}^2}\n {N_{\\rm h} \\over 8\\ln (r_{\\rm h}/\\epsilon)}\n {r_{\\rm h} \\over v_{\\rm h}}\\ . \\eqno\\stepeq$$\nWe can rewrite eq.\\ $(\\the\\disruptiontimescale)$, using eq.\\\n(\\the\\softeningnumber) and the virial theorem for both halo and\nsubhalo, as\n$$t_{\\rm dis} \\approx {N_{\\rm s} \\over 4 \\ln N_{\\rm h}}\n {r_{\\rm h} \\over r_{\\rm s}} {r_{\\rm h} \\over v_{\\rm h}} \n \\approx {N^{2\\over 3}_{\\rm s} \\over 8 \\ln N_{\\rm h}}\n {r^2_{\\rm h} \\over v_{\\rm h}} \\epsilon^{-1}\n \\ . \\eqno\\stepeq$$\n\\newcount\\distimescale\n\\distimescale=\\Eqnno\nThis timescale is shorter than that for two-body evaporation,\nby a factor of (van Kampen 1995)\n$$ 100 {v_{\\rm h}\\over v_{\\rm s}} {r_{\\rm s}^2 \\over r_{\\rm h}^2}\n {\\ln N_{\\rm h}\\over \\ln N_{\\rm s}}\\ , \\eqno\\stepeq$$\nwhere the virial theorem, $v^2\\sim N/r$, is used for both systems.\n\nBecause $r_{\\rm h}$ is at least several times $r_{\\rm s}$,\nthe disruption time (\\the\\distimescale) is at least\n$\\approx N_{\\rm s}/\\ln (N_{\\rm h})$ embedding halo crossing\ntimes, which covers the range $0.05-0.15 N_{\\rm s}$ crossing\ntimes for $N_{\\rm h}\\approx 10^3-10^9$. Thus, it is a much faster\nprocess than two-body evaporation.\n\n\\subsection{Particle-subhalo tidal heating}\n\nA different cause for overmerging was proposed by Moore et al.\\\n(1996): the tidal heating of subhaloes by particles of their embedding\nhaloes. Subhaloes are taken to be {\\it collisionless}, and get\ndisrupted through an increase of their internal kinetic energy\nby tidal distortion from passing N-body particles, which are artificially\nlarge as compared to the true dark matter halo particles.\n\nThe time-scale for this process as given by Moore et al.\\ (1996;\ntheir eq.\\ (3), which is eq.\\ (7-67) of Binney \\& Tremaine 1987 with\nthe assumption that the {\\it r.m.s.}\\ radius is equal to the half-mass\nradius) reads\n$$t_{\\rm dis} \\approx 0.03\n {v_{\\rm h} \\over G n_{\\rm p}}\n {m_{\\rm s}\\over m^2_{\\rm p}}\n {r^2_{\\rm p}\\over r^3_{\\rm s}}\\ , \\eqno\\stepeq$$\n\\newcount\\tdismoore\n\\tdismoore=\\Eqnno\nwhere the subscript p stands for {\\it perturber}. The perturber is an\nN-body particle of the embedding halo with mass $m_{\\rm p}$ and size\n$r_{\\rm p}$, at a distance $q$ from the centre of the embedding halo.\nNote that the impulse approximation implies\n${v^2 / \\Delta v^2} = {E / \\Delta E}$.\nMoore et al.\\ (1996) then assume the embedding halo to be isothermal,\nso that $n_{\\rm p} \\approx v^2_{\\rm h}/2 \\pi G m_{\\rm p} q^2$,\nset the half-mass radius of the subhalo equal to the tidal radius,\n$q v_{\\rm s}/ (3 v_{\\rm h})$, and assume the subhalo to be virialized.\nThis gives\n$$t_{\\rm dis} \\approx 94 \\Bigl({v_{\\rm h}\\over 1000\\ {\\rm km\\ s}^{-1}}\\Bigr)\n \\Bigl({r_{\\rm p}\\over 10\\ {\\rm kpc}} \\Bigr)^2\n \\Bigl({10^9 {\\rm M}_{\\sun} \\over m_{\\rm p}}\\Bigr) {\\rm Gyr}\\ . \\eqno\\stepeq$$\n\\newcount\\mooretime\n\\mooretime=\\Eqnno\n\nRelation (\\the\\tdismoore) was originally derived by Spitzer (1958) for\nthe disruption by giant molecular clouds of open star clusters.\nAn important assumption in its derivation is the tidal approximation,\nwhich is only valid for impact parameters $b>b_{\\rm min}$.\nAguilar \\& White (1985) found that $b_{\\rm min}$ should be at least\nfive times the size of {\\it both} the perturber and the perturbed system.\nBinney \\& Tremaine (1987) use the tidal approximation down to\n$b_{\\rm min}=r_{\\rm cluster}<r_{\\rm cloud}$, and introduce a correction\nfactor $g=3$ to take into account the encounters for which the tidal\napproximation fails.\n\nMoore et al.\\ (1996) take this result and apply it to tidal interactions\nbetween the N-body particles of an embedding halo and its subhaloes theirin.\nThus, they set $r_{\\rm p}$ to the gravitational softening length $\\epsilon$.\nHowever, as the size of the perturbers is now {\\it smaller} than the size\nof the perturbed subhaloes, the tidal approximation, even with the correction\nfactor $g$ included, is only valid for $b>r_{\\rm s}$. Therefore, setting\n$r_{\\rm p}=\\epsilon$ in eq.\\ (\\the\\mooretime) is incorrect; instead, one\nshould set $r_{\\rm p}=r_{\\rm s}$.\nThis means that the timescale becomes $(r_{\\rm s}/\\epsilon)^2$ times longer.\nUsing eq.\\ (\\the\\softeningnumber), the time-scale becomes $4 N^{2/3}_{\\rm s}$\ntimes larger than proposed by Moore et al.\\ (1996).\n\nBut there is another change to be made, as it is in fact the close\nencounters of halo particles that do the most damage to the subhaloes.\nAccording to Binney \\& Tremaine (1987), a good estimate for\nthe disruption timescale can be had from an interpolation between the\napproximations for tidal encounters and for penetrating ($b=0$) encounters. \nFor each tidal encounter (Binney \\& Tremaine 1987, their eq.\\ 7-55),\n$$(\\Delta E)_{\\rm tid} = \n {4 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over 3 v^2_{\\rm h}}\n {1\\over b^4} \\ , \\eqno\\stepeq$$\nwhile for each penetrating encounter (Binney \\& Tremaine 1987, their\neq.\\ 7-57)\n$$(\\Delta E)_{\\rm pen} = {4 \\pi G^2 m^2_{\\rm p}\\over v^2_{\\rm h}}\n \\int_0^{\\infty} {R^3\\over (R^2+\\epsilon^2)^2} \\Sigma_{\\rm s}(R) dR\n \\ . \\eqno\\stepeq$$\nIf the perturbed subhalo is an isothermal sphere, i.e.\\ \n$\\Sigma_{\\rm s}(R)=v^2_{\\rm s}/(6GR)\\approx 0.2m_{\\rm h}/(r_{\\rm h} R)$, we find\n$$(\\Delta E)_{\\rm pen} \\approx\n {2 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over v^2_{\\rm h}}\n {1 \\over \\epsilon r^3_{\\rm s}} . \\eqno\\stepeq$$\nInterpolating contributions from the tidal and penetrating encounters, i.e.\\\n$$\\Delta E = {4 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over 3 v^2_{\\rm h}}\n {1 \\over b^4+{2\\over 3}\\epsilon r^3_{\\rm s}}\\ , \\eqno\\stepeq$$\nfinally allows us to integrate over {\\it all}\\ encounters.\nFollowing the procedure of Binney \\& Tremaine (1987), we simply find\neq.\\ (\\the\\tdismoore) with $r_{\\rm p}$ ($=\\epsilon$) replaced by\n$0.52(\\epsilon r^3_{\\rm s})^{1/2}$. Following Moore et al.\\ (1996) again\nwe get the same functional form as eq.\\ (\\the\\mooretime), but the timescale\nis approximately $2(r_{\\rm s}/\\epsilon)^{3/2}\\approx 5 N^{1/2}_{\\rm s}$\ntimes {\\it longer}\\ than estimated by Moore et al.\\ (1996).\n\nBy definition, $m_{\\rm s}/m_{\\rm p}=N_{\\rm s}$, and we use\neq.\\ (\\the\\softeningnumber) to get\n$$t_{\\rm dis} \\approx 4.5 N^{5\\over 6}_{\\rm s}\n {r_{\\rm h} \\over r_{\\rm s}}\n {r_{\\rm h} \\over v_{\\rm h}}\n \\approx 2.2 N^{1\\over 2}_{\\rm s}\n {r^2_{\\rm h} \\over v_{\\rm h}} \\epsilon^{-1}\n \\ . \\eqno\\stepeq$$\n\\newcount\\tdisNs\n\\tdisNs=\\Eqnno\nAs $r_{\\rm h}$ is at least a few times $r_{\\rm s}$, the disruption\ntime is at least $20 N^{5/6}_{\\rm s}$ embedding halo crossing times.\nIt is also a factor of $18 N^{-1/6}_{\\rm s} \\ln N_{\\rm h}\\approx 100$ times\nlonger than the particle-subhalo two-body disruption timescale.\n\n\\section{Conclusions and discussion}\n\nOvermerging is the numerical disruption of subhaloes within embedding\nhaloes. Of the three main two-body disruption processes, particle-subhalo\ntwo-body heating is clearly identified as the cause for overmerging.\nIts timescale is shown to be much shorter than that for the two other\nprocesses, two-body evaporation and particle-subhalo tidal heating.\nNote that softened particles form into more extended subhaloes than is\nrealistic, so they are more vulnerable to these disruption processes\n(van Kampen 1995), and to possible physical disruption processes as well.\n\nRecently several research groups used simulations with a very high resolution\nin order to resolve the overmerging problem (Klypin et al.\\ 1999a;\nGhinga et al.\\ 1998, 1999; Moore et al.\\ 1999).\nUnfortunately, different group finders and different definitions for disruption\ntimes were used, so a direct comparison of the results is not straightforward.\nStill, the consensus is that increasing the number of particles overcomes,\nat least partially, the overmerging problem. However, the resolution needs to be\nrather high:\n%Klypin et al.\\ (1999a) find that the larger subhaloes survive for resolutions\n%of a few kpc and 10$^8$-10$^9$ $M_\\odot$ respectively.\nfor N-body simulations on a cosmological scale, this requires the use of at\nleast $10^9$ particles, which is not very practical.\nFurthermore, for the smallest groups the overmerging problem simply remains.\n\nAnother option is to include a baryonic component. With the addition\nof dissipative particles, haloes should be more compact and have a higher\ncentral density for the same numbre of particles.\nHowever, as Klypin et al.\\ (1999a) remark, there is a limit to this as some\nfraction of the baryons tend to end up in rotationally supported disks.\nA more practical problem with dissipative particles is the actual simulation\ntechniques needed, which usually is some form of smoothed particle\nhydrodynamics (SPH). The resolution of SPH codes is typically not as high as that\nof N-body codes, so for the purpose of resolving the overmerging problem\nit is not a useful alternative at present.\n\nA third option is to use halo particles, which prevents overmerging by\nconstruction (van Kampen 1995). The idea is that a group of particles that\nhas collapsed into a virialised system is replaced by a single halo particle.\nLocal density percolation, also called adaptive friends-of-friends,\nis adopted for finding the groups.\nThis is designed to identify the embedded haloes that the \ntraditional percolation group finder links up with their parent halo.\nBy applying the algorithm several times during the evolution,\nmerging of already-formed galaxy haloes is taken into account as well.\nOnce a halo particle is formed, more N-body particles will group around\nit at later times. If such a group can virialize, it is replaced by a\nmore massive halo particle. This will usually happen in the field.\nHowever, for halo particles that end up in overdense regions, the\nparticles that swarm around a halo particles will be stripped quite\nrapidly.\n\nOnce the overmerging problem is resolved down to the subhalo mass-scale\none is interested in, the physical processes can be studied. \nThis is becoming feasible for current simulations.\nHowever, whether the physical processes themselves are properly modelled\nusing N-body simulations has yet to be proven. The problem of artificially\nlarge subhaloes due to softening needs to be solved, for example. Another\nproblem might be the modelling of dynamical friction, which requires a very\nsmooth distribution of particles in the embedding halo in order to produce\nthe wake that generates the drag force.\n\n\\section*{ACKNOWLEDGEMENTS}\n\nI am grateful to John Peacock and Ben Moore for useful discussion,\nsuggestions and comments.\n\n\\section*{REFERENCES}\n\n\\beginrefs\n\\bibitem Aquilar L.A., White S.D.M., 1985, ApJ, 295, 374\n%\\bibitem Allan A.J., Richstone D.O., 1988, ApJ, 325, 583\n\\bibitem Binney J., Tremaine S., 1987, Galactic Dynamics, Princeton\n\\bibitem Carlberg R.G., 1994, ApJ, 433, 468\n\\bibitem Gelb J., Bertschinger E., 1994, ApJ, 436, 467\n\\bibitem Ghigna S., Moore B., Governato F., Lake G., Quinn T., Stadel J.,\n\t1998, MNRAS, 300, 146\n\\bibitem Ghigna S., Moore B., Governato F., Lake G., Quinn T., Stadel J.,\n\t1999, astro-ph/9910166\n%\\bibitem Heisler J., White S.D.M., 1990, MNRAS, 243, 199\n\\bibitem Klypin A.A., Gottl\\\"ober S., Kravtsov A.V., Khokhlov A.M., 1999a,\n\tApJ, 516, 530\n\\bibitem Klypin A.A., Kravtsov A.V., Valenzuela O., Prada F., 1999b,\n\tastro-ph/9901240\n%\\bibitem Lin D.N.C., Tremaine S., 1983, ApJ, 264, 364\n%\\bibitem Mateo M., 1998, ARA\\&A, 36, 435\n\\bibitem Moore B., Katz N., Lake G., 1996, ApJ, 457, 455\n\\bibitem Moore B., Governato F., Quinn T., Stadel J., Lake G., 1998,\n\tApJ, 499, L5\n%\\bibitem Moore B., Lake G., Quinn T., Stadel J., 1999, MNRAS, 304, 465\n\\bibitem Moore B., Ghigna S., Governato F., Lake G., Quinn T., Stadel J.,\n\tTozzi P., 1999,\tApJ, 524, L19\n%\\bibitem Saslaw W.C., 1985, Gravitational physics of stellar and galactic\n%\tsystems, Cambridge\n\\bibitem Spitzer L., 1958, ApJ, 127, 17\n%\\bibitem Tormen G., Diaferio A., Syer D., 1998, 299, 728\n%\\bibitem Tremaine S., 1976, ApJ, 203, 72\n\\bibitem van Kampen E., 1995, MNRAS, 273, 295\n%\\bibitem van Kampen E., Katgert P., 1997, MNRAS, 289, 327\n%\\bibitem van Kampen E., Jimenez R., Peacock J.A., 1999, MNRAS, 310, 43\n\\bibitem White S.D.M., Davis M., Efstathiou G., Frenk C.S., 1987,\n\tNat, 330, 451\n\\endrefs\n\n\n%\n% The End\n%\n\n\\end\n\n%A galaxy cluster halo typically has $r_{\\rm c}=1-2\\ {\\rm Mpc}$ and\n%$v_{\\rm c}\\approx 1000-2000$ km s$^{-1}$.\n%With $\\ln \\Lambda=\\ln 4r_{\\rm h}/\\epsilon$ for large $N$ (Farouki and\n%Salpeter 1982) and $\\epsilon=N^{-1/3}r_{\\rm h}/2$ (see Appendix A) we find\n%$$t_{\\rm dis} \\approx 1-3 \\times 10^{-3}\n% \\Bigl( {v_{\\rm s}\\over 100\\ {\\rm km\\ s}^{-1}}\\Bigr)^2 \n% {N_{\\rm h}\\over \\ln 8 N_{\\rm h}} {\\rm Gyr} \\ . \\eqno\\stepeq$$\n%Thus, for a galaxy halo with $v_{\\rm s}=100$ km s$^{-1}$ orbiting within a\n%cluster, the disruption time-scale is only larger than a Hubble time for\n%$N_{\\rm h} > 10^6$.\n\n\n%$$t_{\\rm dis} \\approx 26 \\Bigl({ v_{\\rm h}\\over 1000\\ {\\rm km\\ s}^{-1}}\\Bigr)\n% \\Bigl({\\epsilon^{1\\over 4} r^{3\\over 4}_{\\rm s}\\over 10\\ {\\rm kpc}} \\Bigr)^2\n% \\Bigl({10^9 {\\rm M}_{\\sun} \\over m_{\\rm p}}\\Bigr) {\\rm Gyr}\\ , \\eqno\\stepeq$$\n%\\newcount\\particlehaloheating\n%\\particlehaloheating=\\Eqnno\n%Using eq.\\ (\\the\\softeningnumber), the timescale is\n%$$t_{\\rm dis} \\approx 141 N^{1\\over 2}_{\\rm s}\n% \\Bigl({ v_{\\rm h}\\over 10^3\\ {\\rm km\\ s}^{-1}}\\Bigr)\n% \\Bigl({\\epsilon \\over 10\\ {\\rm kpc}} \\Bigr)^2\n% \\Bigl({10^9 {\\rm M}_{\\sun} \\over m_{\\rm p}}\\Bigr) {\\rm Gyr}\\ , \\eqno\\stepeq$$\n%\\newcount\\particlehalotimescale\n%\\particlehalotimescale=\\Eqnno\n%which is (still) much larger than that given by Moore et al.\\ (1996),\n%i.e.\\ eq.\\ (\\the\\mooretime) with $r_{\\rm p}=\\epsilon$, especially\n%for larger $N_{\\rm s}$.\n%This is still true for larger choices for the softening parameter,\n%for example $\\epsilon=r_{\\rm s}/N^{1/3}_{\\rm s}$.\n%Eq.\\ (\\the\\particlehalotimescale) depends on the {\\it numerical}\\ quantities\n%$\\epsilon$ and $m_{\\rm p}$, which in turn depend on $N_{\\rm s}$. We make this\n%dependence clear by using eq.\\ (\\the\\softeningnumber) again, and applying\n%the virial theorem for the subhalo:\n%$$t_{\\rm dis} \\approx 21 N^{5\\over 6}_{\\rm s}\n% \\Bigl({r^2_{\\rm h} \\over v_{\\rm h}}\\Bigr)\n% \\Bigl({10\\ {\\rm kpc} \\over r_{\\rm s}} \\Bigr)\\ {\\rm Gyr} \n% \\ . \\eqno\\stepeq$$\n%\\newcount\\particlehalotimescaletwo\n%\\particlehalotimescaletwo=\\Eqnno\n\n%This is realistic in a phenomenological sense, but clearly\n%not quantitatively.\n%The technique produces galaxy haloes at the right time and the right\n%place, with a spectrum of masses that compares well to the Press-Schechter\n%formalism at early times, but starts to deviate at later times.\n%This is actually a good result, as it solves some problems for\n%phenomenological galaxy formation models (van Kampen, Jimenez \\& Peacock\n%1999).\n%\n%In concluding, each of these solutions, or a combination of them, will\n%suit a specific situation or system. However, it is clear that overmerging\n%is a real problem and has either to be tackled, or to be taken into account\n%when drawing conclusions from an N-body experiment. \n\n\n%The two-body heating timescale scales as\n%$N_{\\rm s}/r_{\\rm s}$, while the two-body evaporation time-scale scale as\n%$N_{\\rm s} r_{\\rm s}/v_{\\rm s}$ (disregarding logarithmic terms for both).\n%The particle-halo tidal heating processes scales as $N^{5/6}_{\\rm s}/r_{\\rm s}$,\n%so almost the same as the two-body heating process, but with a much larger overall\n%value. It is harder to explicitly derive a timescale for halo-halo tidal\n%heating, as the haloes have a wide range in masses, but its timescale\n%is likely to fall somewhere between those of the particle-halo and two-body\n%processes, with the latter still the shortest (???) .\n"
},
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"string": "% Psfig/TeX \n\\def\\PsfigVersion{1.9}\n% dvips version\n%\n% All psfig/tex software, documentation, and related files\n% in this distribution of psfig/tex are \n% Copyright 1987, 1988, 1991 Trevor J. Darrell\n%\n% Permission is granted for use and non-profit distribution of psfig/tex \n% providing that this notice is clearly maintained. The right to\n% distribute any portion of psfig/tex for profit or as part of any commercial\n% product is specifically reserved for the author(s) of that portion.\n%\n% *** Feel free to make local modifications of psfig as you wish,\n% *** but DO NOT post any changed or modified versions of ``psfig''\n% *** directly to the net. Send them to me and I'll try to incorporate\n% *** them into future versions. If you want to take the psfig code \n% *** and make a new program (subject to the copyright above), distribute it, \n% *** (and maintain it) that's fine, just don't call it psfig.\n%\n% Bugs and improvements to [email protected].\n%\n% Thanks to Greg Hager (GDH) and Ned Batchelder for their contributions\n% to the original version of this project.\n%\n% Modified by J. Daniel Smith on 9 October 1990 to accept the\n% %%BoundingBox: comment with or without a space after the colon. Stole\n% file reading code from Tom Rokicki's EPSF.TEX file (see below).\n%\n% More modifications by J. Daniel Smith on 29 March 1991 to allow the\n% the included PostScript figure to be rotated. The amount of\n% rotation is specified by the \"angle=\" parameter of the \\psfig command.\n%\n% Modified by Robert Russell on June 25, 1991 to allow users to specify\n% .ps filenames which don't yet exist, provided they explicitly provide\n% boundingbox information via the \\psfig command. Note: This will only work\n% if the \"file=\" parameter follows all four \"bb???=\" parameters in the\n% command. This is due to the order in which psfig interprets these params.\n%\n% 3 Jul 1991\tJDS\tcheck if file already read in once\n% 4 Sep 1991\tJDS\tfixed incorrect computation of rotated\n%\t\t\tbounding box\n% 25 Sep 1991\tGVR\texpanded synopsis of \\psfig\n% 14 Oct 1991\tJDS\t\\fbox code from LaTeX so \\psdraft works with TeX\n%\t\t\tchanged \\typeout to \\ps@typeout\n% 17 Oct 1991\tJDS\tadded \\psscalefirst and \\psrotatefirst\n%\n\n% From: [email protected] (George V. Reilly)\n%\n% \\psdraft\tdraws an outline box, but doesn't include the figure\n%\t\tin the DVI file. Useful for previewing.\n%\n% \\psfull\tincludes the figure in the DVI file (default).\n%\n% \\psscalefirst width= or height= specifies the size of the figure\n% \t\tbefore rotation.\n% \\psrotatefirst (default) width= or height= specifies the size of the\n% \t\t figure after rotation. Asymetric figures will\n% \t\t appear to shrink.\n%\n% \\psfigurepath#1\tsets the path to search for the figure\n%\n% \\psfig\n% usage: \\psfig{file=, figure=, height=, width=,\n%\t\t\tbbllx=, bblly=, bburx=, bbury=,\n%\t\t\trheight=, rwidth=, clip=, angle=, silent=}\n%\n%\t\"file\" is the filename. If no path name is specified and the\n%\t\tfile is not found in the current directory,\n%\t\tit will be looked for in directory \\psfigurepath.\n%\t\"figure\" is a synonym for \"file\".\n%\tBy default, the width and height of the figure are taken from\n%\t\tthe BoundingBox of the figure.\n%\tIf \"width\" is specified, the figure is scaled so that it has\n%\t\tthe specified width. Its height changes proportionately.\n%\tIf \"height\" is specified, the figure is scaled so that it has\n%\t\tthe specified height. Its width changes proportionately.\n%\tIf both \"width\" and \"height\" are specified, the figure is scaled\n%\t\tanamorphically.\n%\t\"bbllx\", \"bblly\", \"bburx\", and \"bbury\" control the PostScript\n%\t\tBoundingBox. If these four values are specified\n% *before* the \"file\" option, the PSFIG will not try to\n% open the PostScript file.\n%\t\"rheight\" and \"rwidth\" are the reserved height and width\n%\t\tof the figure, i.e., how big TeX actually thinks\n%\t\tthe figure is. They default to \"width\" and \"height\".\n%\tThe \"clip\" option ensures that no portion of the figure will\n%\t\tappear outside its BoundingBox. \"clip=\" is a switch and\n%\t\ttakes no value, but the `=' must be present.\n%\tThe \"angle\" option specifies the angle of rotation (degrees, ccw).\n%\tThe \"silent\" option makes \\psfig work silently.\n%\n\n% check to see if macros already loaded in (maybe some other file says\n% \"\\input psfig\") ...\n\\ifx\\undefined\\psfig\\else\\endinput\\fi\n\n%\n% from a suggestion by [email protected] to allow\n% loading as a style file. Changed to avoid problems\n% with amstex per suggestion by [email protected]\n\n\\let\\LaTeXAtSign=\\@\n\\let\\@=\\relax\n\\edef\\psfigRestoreAt{\\catcode`\\@=\\number\\catcode`@\\relax}\n%\\edef\\psfigRestoreAt{\\catcode`@=\\number\\catcode`@\\relax}\n\\catcode`\\@=11\\relax\n\\newwrite\\@unused\n\\def\\ps@typeout#1{{\\let\\protect\\string\\immediate\\write\\@unused{#1}}}\n\\ps@typeout{psfig/tex \\PsfigVersion}\n\n%% Here's how you define your figure path. Should be set up with null\n%% default and a user useable definition.\n\n\\def\\figurepath{./}\n\\def\\psfigurepath#1{\\edef\\figurepath{#1}}\n\n%\n% @psdo control structure -- similar to Latex @for.\n% I redefined these with different names so that psfig can\n% be used with TeX as well as LaTeX, and so that it will not \n% be vunerable to future changes in LaTeX's internal\n% control structure,\n%\n\\def\\@nnil{\\@nil}\n\\def\\@empty{}\n\\def\\@psdonoop#1\\@@#2#3{}\n\\def\\@psdo#1:=#2\\do#3{\\edef\\@psdotmp{#2}\\ifx\\@psdotmp\\@empty \\else\n \\expandafter\\@psdoloop#2,\\@nil,\\@nil\\@@#1{#3}\\fi}\n\\def\\@psdoloop#1,#2,#3\\@@#4#5{\\def#4{#1}\\ifx #4\\@nnil \\else\n #5\\def#4{#2}\\ifx #4\\@nnil \\else#5\\@ipsdoloop #3\\@@#4{#5}\\fi\\fi}\n\\def\\@ipsdoloop#1,#2\\@@#3#4{\\def#3{#1}\\ifx #3\\@nnil \n \\let\\@nextwhile=\\@psdonoop \\else\n #4\\relax\\let\\@nextwhile=\\@ipsdoloop\\fi\\@nextwhile#2\\@@#3{#4}}\n\\def\\@tpsdo#1:=#2\\do#3{\\xdef\\@psdotmp{#2}\\ifx\\@psdotmp\\@empty \\else\n \\@tpsdoloop#2\\@nil\\@nil\\@@#1{#3}\\fi}\n\\def\\@tpsdoloop#1#2\\@@#3#4{\\def#3{#1}\\ifx #3\\@nnil \n \\let\\@nextwhile=\\@psdonoop \\else\n #4\\relax\\let\\@nextwhile=\\@tpsdoloop\\fi\\@nextwhile#2\\@@#3{#4}}\n% \n% \\fbox is defined in latex.tex; so if \\fbox is undefined, assume that\n% we are not in LaTeX.\n% Perhaps this could be done better???\n\\ifx\\undefined\\fbox\n% \\fbox code from modified slightly from LaTeX\n\\newdimen\\fboxrule\n\\newdimen\\fboxsep\n\\newdimen\\ps@tempdima\n\\newbox\\ps@tempboxa\n\\fboxsep = 3pt\n\\fboxrule = .4pt\n\\long\\def\\fbox#1{\\leavevmode\\setbox\\ps@tempboxa\\hbox{#1}\\ps@tempdima\\fboxrule\n \\advance\\ps@tempdima \\fboxsep \\advance\\ps@tempdima \\dp\\ps@tempboxa\n \\hbox{\\lower \\ps@tempdima\\hbox\n {\\vbox{\\hrule height \\fboxrule\n \\hbox{\\vrule width \\fboxrule \\hskip\\fboxsep\n \\vbox{\\vskip\\fboxsep \\box\\ps@tempboxa\\vskip\\fboxsep}\\hskip \n \\fboxsep\\vrule width \\fboxrule}\n \\hrule height \\fboxrule}}}}\n\\fi\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% file reading stuff from epsf.tex\n% EPSF.TEX macro file:\n% Written by Tomas Rokicki of Radical Eye Software, 29 Mar 1989.\n% Revised by Don Knuth, 3 Jan 1990.\n% Revised by Tomas Rokicki to accept bounding boxes with no\n% space after the colon, 18 Jul 1990.\n% Portions modified/removed for use in PSFIG package by\n% J. Daniel Smith, 9 October 1990.\n%\n\\newread\\ps@stream\n\\newif\\ifnot@eof % continue looking for the bounding box?\n\\newif\\if@noisy % report what you're making?\n\\newif\\if@atend % %%BoundingBox: has (at end) specification\n\\newif\\if@psfile % does this look like a PostScript file?\n%\n% PostScript files should start with `%!'\n%\n{\\catcode`\\%=12\\global\\gdef\\epsf@start{%!}}\n\\def\\epsf@PS{PS}\n%\n\\def\\epsf@getbb#1{%\n%\n% The first thing we need to do is to open the\n% PostScript file, if possible.\n%\n\\openin\\ps@stream=#1\n\\ifeof\\ps@stream\\ps@typeout{Error, File #1 not found}\\else\n%\n% Okay, we got it. Now we'll scan lines until we find one that doesn't\n% start with %. We're looking for the bounding box comment.\n%\n {\\not@eoftrue \\chardef\\other=12\n \\def\\do##1{\\catcode`##1=\\other}\\dospecials \\catcode`\\ =10\n \\loop\n \\if@psfile\n\t \\read\\ps@stream to \\epsf@fileline\n \\else{\n\t \\obeyspaces\n \\read\\ps@stream to \\epsf@tmp\\global\\let\\epsf@fileline\\epsf@tmp}\n \\fi\n \\ifeof\\ps@stream\\not@eoffalse\\else\n%\n% Check the first line for `%!'. Issue a warning message if its not\n% there, since the file might not be a PostScript file.\n%\n \\if@psfile\\else\n \\expandafter\\epsf@test\\epsf@fileline:. \\\\%\n \\fi\n%\n% We check to see if the first character is a % sign;\n% if so, we look further and stop only if the line begins with\n% `%%BoundingBox:' and the `(atend)' specification was not found.\n% That is, the only way to stop is when the end of file is reached,\n% or a `%%BoundingBox: llx lly urx ury' line is found.\n%\n \\expandafter\\epsf@aux\\epsf@fileline:. \\\\%\n \\fi\n \\ifnot@eof\\repeat\n }\\closein\\ps@stream\\fi}%\n%\n% This tests if the file we are reading looks like a PostScript file.\n%\n\\long\\def\\epsf@test#1#2#3:#4\\\\{\\def\\epsf@testit{#1#2}\n\t\t\t\\ifx\\epsf@testit\\epsf@start\\else\n\\ps@typeout{Warning! File does not start with `\\epsf@start'. It may not be a PostScript file.}\n\t\t\t\\fi\n\t\t\t\\@psfiletrue} % don't test after 1st line\n%\n% We still need to define the tricky \\epsf@aux macro. This requires\n% a couple of magic constants for comparison purposes.\n%\n{\\catcode`\\%=12\\global\\let\\epsf@percent=%\\global\\def\\epsf@bblit{%BoundingBox}}\n%\n%\n% So we're ready to check for `%BoundingBox:' and to grab the\n% values if they are found. We continue searching if `(at end)'\n% was found after the `%BoundingBox:'.\n%\n\\long\\def\\epsf@aux#1#2:#3\\\\{\\ifx#1\\epsf@percent\n \\def\\epsf@testit{#2}\\ifx\\epsf@testit\\epsf@bblit\n\t\\@atendfalse\n \\epsf@atend #3 . \\\\%\n\t\\if@atend\t\n\t \\if@verbose{\n\t\t\\ps@typeout{psfig: found `(atend)'; continuing search}\n\t }\\fi\n \\else\n \\epsf@grab #3 . . . \\\\%\n \\not@eoffalse\n \\global\\no@bbfalse\n \\fi\n \\fi\\fi}%\n%\n% Here we grab the values and stuff them in the appropriate definitions.\n%\n\\def\\epsf@grab #1 #2 #3 #4 #5\\\\{%\n \\global\\def\\epsf@llx{#1}\\ifx\\epsf@llx\\empty\n \\epsf@grab #2 #3 #4 #5 .\\\\\\else\n \\global\\def\\epsf@lly{#2}%\n \\global\\def\\epsf@urx{#3}\\global\\def\\epsf@ury{#4}\\fi}%\n%\n% Determine if the stuff following the %%BoundingBox is `(atend)'\n% J. Daniel Smith. Copied from \\epsf@grab above.\n%\n\\def\\epsf@atendlit{(atend)} \n\\def\\epsf@atend #1 #2 #3\\\\{%\n \\def\\epsf@tmp{#1}\\ifx\\epsf@tmp\\empty\n \\epsf@atend #2 #3 .\\\\\\else\n \\ifx\\epsf@tmp\\epsf@atendlit\\@atendtrue\\fi\\fi}\n\n\n% End of file reading stuff from epsf.tex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% trigonometry stuff from \"trig.tex\"\n\\chardef\\psletter = 11 % won't conflict with \\begin{letter} now...\n\\chardef\\other = 12\n\n\\newif \\ifdebug %%% turn me on to see TeX hard at work ...\n\\newif\\ifc@mpute %%% don't need to compute some values\n\\c@mputetrue % but assume that we do\n\n\\let\\then = \\relax\n\\def\\r@dian{pt }\n\\let\\r@dians = \\r@dian\n\\let\\dimensionless@nit = \\r@dian\n\\let\\dimensionless@nits = \\dimensionless@nit\n\\def\\internal@nit{sp }\n\\let\\internal@nits = \\internal@nit\n\\newif\\ifstillc@nverging\n\\def \\Mess@ge #1{\\ifdebug \\then \\message {#1} \\fi}\n\n{ %%% Things that need abnormal catcodes %%%\n\t\\catcode `\\@ = \\psletter\n\t\\gdef \\nodimen {\\expandafter \\n@dimen \\the \\dimen}\n\t\\gdef \\term #1 #2 #3%\n\t {\\edef \\t@ {\\the #1}%%% freeze parameter 1 (count, by value)\n\t\t\\edef \\t@@ {\\expandafter \\n@dimen \\the #2\\r@dian}%\n\t\t\t\t %%% freeze parameter 2 (dimen, by value)\n\t\t\\t@rm {\\t@} {\\t@@} {#3}%\n\t }\n\t\\gdef \\t@rm #1 #2 #3%\n\t {{%\n\t\t\\count 0 = 0\n\t\t\\dimen 0 = 1 \\dimensionless@nit\n\t\t\\dimen 2 = #2\\relax\n\t\t\\Mess@ge {Calculating term #1 of \\nodimen 2}%\n\t\t\\loop\n\t\t\\ifnum\t\\count 0 < #1\n\t\t\\then\t\\advance \\count 0 by 1\n\t\t\t\\Mess@ge {Iteration \\the \\count 0 \\space}%\n\t\t\t\\Multiply \\dimen 0 by {\\dimen 2}%\n\t\t\t\\Mess@ge {After multiplication, term = \\nodimen 0}%\n\t\t\t\\Divide \\dimen 0 by {\\count 0}%\n\t\t\t\\Mess@ge {After division, term = \\nodimen 0}%\n\t\t\\repeat\n\t\t\\Mess@ge {Final value for term #1 of \n\t\t\t\t\\nodimen 2 \\space is \\nodimen 0}%\n\t\t\\xdef \\Term {#3 = \\nodimen 0 \\r@dians}%\n\t\t\\aftergroup \\Term\n\t }}\n\t\\catcode `\\p = \\other\n\t\\catcode `\\t = \\other\n\t\\gdef \\n@dimen #1pt{#1} %%% throw away the ``pt''\n}\n\n\\def \\Divide #1by #2{\\divide #1 by #2} %%% just a synonym\n\n\\def \\Multiply #1by #2%%% allows division of a dimen by a dimen\n {{%%% should really freeze parameter 2 (dimen, passed by value)\n\t\\count 0 = #1\\relax\n\t\\count 2 = #2\\relax\n\t\\count 4 = 65536\n\t\\Mess@ge {Before scaling, count 0 = \\the \\count 0 \\space and\n\t\t\tcount 2 = \\the \\count 2}%\n\t\\ifnum\t\\count 0 > 32767 %%% do our best to avoid overflow\n\t\\then\t\\divide \\count 0 by 4\n\t\t\\divide \\count 4 by 4\n\t\\else\t\\ifnum\t\\count 0 < -32767\n\t\t\\then\t\\divide \\count 0 by 4\n\t\t\t\\divide \\count 4 by 4\n\t\t\\else\n\t\t\\fi\n\t\\fi\n\t\\ifnum\t\\count 2 > 32767 %%% while retaining reasonable accuracy\n\t\\then\t\\divide \\count 2 by 4\n\t\t\\divide \\count 4 by 4\n\t\\else\t\\ifnum\t\\count 2 < -32767\n\t\t\\then\t\\divide \\count 2 by 4\n\t\t\t\\divide \\count 4 by 4\n\t\t\\else\n\t\t\\fi\n\t\\fi\n\t\\multiply \\count 0 by \\count 2\n\t\\divide \\count 0 by \\count 4\n\t\\xdef \\product {#1 = \\the \\count 0 \\internal@nits}%\n\t\\aftergroup \\product\n }}\n\n\\def\\r@duce{\\ifdim\\dimen0 > 90\\r@dian \\then % sin(x+90) = sin(180-x)\n\t\t\\multiply\\dimen0 by -1\n\t\t\\advance\\dimen0 by 180\\r@dian\n\t\t\\r@duce\n\t \\else \\ifdim\\dimen0 < -90\\r@dian \\then % sin(-x) = sin(360+x)\n\t\t\\advance\\dimen0 by 360\\r@dian\n\t\t\\r@duce\n\t\t\\fi\n\t \\fi}\n\n\\def\\Sine#1%\n {{%\n\t\\dimen 0 = #1 \\r@dian\n\t\\r@duce\n\t\\ifdim\\dimen0 = -90\\r@dian \\then\n\t \\dimen4 = -1\\r@dian\n\t \\c@mputefalse\n\t\\fi\n\t\\ifdim\\dimen0 = 90\\r@dian \\then\n\t \\dimen4 = 1\\r@dian\n\t \\c@mputefalse\n\t\\fi\n\t\\ifdim\\dimen0 = 0\\r@dian \\then\n\t \\dimen4 = 0\\r@dian\n\t \\c@mputefalse\n\t\\fi\n%\n\t\\ifc@mpute \\then\n \t% convert degrees to radians\n\t\t\\divide\\dimen0 by 180\n\t\t\\dimen0=3.141592654\\dimen0\n%\n\t\t\\dimen 2 = 3.1415926535897963\\r@dian %%% a well-known constant\n\t\t\\divide\\dimen 2 by 2 %%% we only deal with -pi/2 : pi/2\n\t\t\\Mess@ge {Sin: calculating Sin of \\nodimen 0}%\n\t\t\\count 0 = 1 %%% see power-series expansion for sine\n\t\t\\dimen 2 = 1 \\r@dian %%% ditto\n\t\t\\dimen 4 = 0 \\r@dian %%% ditto\n\t\t\\loop\n\t\t\t\\ifnum\t\\dimen 2 = 0 %%% then we've done\n\t\t\t\\then\t\\stillc@nvergingfalse \n\t\t\t\\else\t\\stillc@nvergingtrue\n\t\t\t\\fi\n\t\t\t\\ifstillc@nverging %%% then calculate next term\n\t\t\t\\then\t\\term {\\count 0} {\\dimen 0} {\\dimen 2}%\n\t\t\t\t\\advance \\count 0 by 2\n\t\t\t\t\\count 2 = \\count 0\n\t\t\t\t\\divide \\count 2 by 2\n\t\t\t\t\\ifodd\t\\count 2 %%% signs alternate\n\t\t\t\t\\then\t\\advance \\dimen 4 by \\dimen 2\n\t\t\t\t\\else\t\\advance \\dimen 4 by -\\dimen 2\n\t\t\t\t\\fi\n\t\t\\repeat\n\t\\fi\t\t\n\t\t\t\\xdef \\sine {\\nodimen 4}%\n }}\n\n% Now the Cosine can be calculated easily by calling \\Sine\n\\def\\Cosine#1{\\ifx\\sine\\UnDefined\\edef\\Savesine{\\relax}\\else\n\t\t \\edef\\Savesine{\\sine}\\fi\n\t{\\dimen0=#1\\r@dian\\advance\\dimen0 by 90\\r@dian\n\t \\Sine{\\nodimen 0}\n\t \\xdef\\cosine{\\sine}\n\t \\xdef\\sine{\\Savesine}}}\t \n% end of trig stuff\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\def\\psdraft{\n\t\\def\\@psdraft{0}\n\t%\\ps@typeout{draft level now is \\@psdraft \\space . }\n}\n\\def\\psfull{\n\t\\def\\@psdraft{100}\n\t%\\ps@typeout{draft level now is \\@psdraft \\space . }\n}\n\n\\psfull\n\n\\newif\\if@scalefirst\n\\def\\psscalefirst{\\@scalefirsttrue}\n\\def\\psrotatefirst{\\@scalefirstfalse}\n\\psrotatefirst\n\n\\newif\\if@draftbox\n\\def\\psnodraftbox{\n\t\\@draftboxfalse\n}\n\\def\\psdraftbox{\n\t\\@draftboxtrue\n}\n\\@draftboxtrue\n\n\\newif\\if@prologfile\n\\newif\\if@postlogfile\n\\def\\pssilent{\n\t\\@noisyfalse\n}\n\\def\\psnoisy{\n\t\\@noisytrue\n}\n\\psnoisy\n%%% These are for the option list.\n%%% A specification of the form a = b maps to calling \\@p@@sa{b}\n\\newif\\if@bbllx\n\\newif\\if@bblly\n\\newif\\if@bburx\n\\newif\\if@bbury\n\\newif\\if@height\n\\newif\\if@width\n\\newif\\if@rheight\n\\newif\\if@rwidth\n\\newif\\if@angle\n\\newif\\if@clip\n\\newif\\if@verbose\n\\def\\@p@@sclip#1{\\@cliptrue}\n\n\n\\newif\\if@decmpr\n\n%%% GDH 7/26/87 -- changed so that it first looks in the local directory,\n%%% then in a specified global directory for the ps file.\n%%% RPR 6/25/91 -- changed so that it defaults to user-supplied name if\n%%% boundingbox info is specified, assuming graphic will be created by\n%%% print time.\n%%% TJD 10/19/91 -- added bbfile vs. file distinction, and @decmpr flag\n\n\\def\\@p@@sfigure#1{\\def\\@p@sfile{null}\\def\\@p@sbbfile{null}\n\t \\openin1=#1.bb\n\t\t\\ifeof1\\closein1\n\t \t\\openin1=\\figurepath#1.bb\n\t\t\t\\ifeof1\\closein1\n\t\t\t \\openin1=#1\n\t\t\t\t\\ifeof1\\closein1%\n\t\t\t\t \\openin1=\\figurepath#1\n\t\t\t\t\t\\ifeof1\n\t\t\t\t\t \\ps@typeout{Error, File #1 not found}\n\t\t\t\t\t\t\\if@bbllx\\if@bblly\n\t\t\t\t \t\t\\if@bburx\\if@bbury\n\t\t\t \t\t\t\t\\def\\@p@sfile{#1}%\n\t\t\t \t\t\t\t\\def\\@p@sbbfile{#1}%\n\t\t\t\t\t\t\t\\@decmprfalse\n\t\t\t\t \t \t\\fi\\fi\\fi\\fi\n\t\t\t\t\t\\else\\closein1\n\t\t\t\t \t\t\\def\\@p@sfile{\\figurepath#1}%\n\t\t\t\t \t\t\\def\\@p@sbbfile{\\figurepath#1}%\n\t\t\t\t\t\t\\@decmprfalse\n\t \t\t\\fi%\n\t\t\t \t\\else\\closein1%\n\t\t\t\t\t\\def\\@p@sfile{#1}\n\t\t\t\t\t\\def\\@p@sbbfile{#1}\n\t\t\t\t\t\\@decmprfalse\n\t\t\t \t\\fi\n\t\t\t\\else\n\t\t\t\t\\def\\@p@sfile{\\figurepath#1}\n\t\t\t\t\\def\\@p@sbbfile{\\figurepath#1.bb}\n\t\t\t\t\\@decmprtrue\n\t\t\t\\fi\n\t\t\\else\n\t\t\t\\def\\@p@sfile{#1}\n\t\t\t\\def\\@p@sbbfile{#1.bb}\n\t\t\t\\@decmprtrue\n\t\t\\fi}\n\n\\def\\@p@@sfile#1{\\@p@@sfigure{#1}}\n\n\\def\\@p@@sbbllx#1{\n\t\t%\\ps@typeout{bbllx is #1}\n\t\t\\@bbllxtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbbllx{\\number\\dimen100}\n}\n\\def\\@p@@sbblly#1{\n\t\t%\\ps@typeout{bblly is #1}\n\t\t\\@bbllytrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbblly{\\number\\dimen100}\n}\n\\def\\@p@@sbburx#1{\n\t\t%\\ps@typeout{bburx is #1}\n\t\t\\@bburxtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbburx{\\number\\dimen100}\n}\n\\def\\@p@@sbbury#1{\n\t\t%\\ps@typeout{bbury is #1}\n\t\t\\@bburytrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbbury{\\number\\dimen100}\n}\n\\def\\@p@@sheight#1{\n\t\t\\@heighttrue\n\t\t\\dimen100=#1\n \t\t\\edef\\@p@sheight{\\number\\dimen100}\n\t\t%\\ps@typeout{Height is \\@p@sheight}\n}\n\\def\\@p@@swidth#1{\n\t\t%\\ps@typeout{Width is #1}\n\t\t\\@widthtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@swidth{\\number\\dimen100}\n}\n\\def\\@p@@srheight#1{\n\t\t%\\ps@typeout{Reserved height is #1}\n\t\t\\@rheighttrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@srheight{\\number\\dimen100}\n}\n\\def\\@p@@srwidth#1{\n\t\t%\\ps@typeout{Reserved width is #1}\n\t\t\\@rwidthtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@srwidth{\\number\\dimen100}\n}\n\\def\\@p@@sangle#1{\n\t\t%\\ps@typeout{Rotation is #1}\n\t\t\\@angletrue\n%\t\t\\dimen100=#1\n\t\t\\edef\\@p@sangle{#1} %\\number\\dimen100}\n}\n\\def\\@p@@ssilent#1{ \n\t\t\\@verbosefalse\n}\n\\def\\@p@@sprolog#1{\\@prologfiletrue\\def\\@prologfileval{#1}}\n\\def\\@p@@spostlog#1{\\@postlogfiletrue\\def\\@postlogfileval{#1}}\n\\def\\@cs@name#1{\\csname #1\\endcsname}\n\\def\\@setparms#1=#2,{\\@cs@name{@p@@s#1}{#2}}\n%\n% initialize the defaults (size the size of the figure)\n%\n\\def\\ps@init@parms{\n\t\t\\@bbllxfalse \\@bbllyfalse\n\t\t\\@bburxfalse \\@bburyfalse\n\t\t\\@heightfalse \\@widthfalse\n\t\t\\@rheightfalse \\@rwidthfalse\n\t\t\\def\\@p@sbbllx{}\\def\\@p@sbblly{}\n\t\t\\def\\@p@sbburx{}\\def\\@p@sbbury{}\n\t\t\\def\\@p@sheight{}\\def\\@p@swidth{}\n\t\t\\def\\@p@srheight{}\\def\\@p@srwidth{}\n\t\t\\def\\@p@sangle{0}\n\t\t\\def\\@p@sfile{} \\def\\@p@sbbfile{}\n\t\t\\def\\@p@scost{10}\n\t\t\\def\\@sc{}\n\t\t\\@prologfilefalse\n\t\t\\@postlogfilefalse\n\t\t\\@clipfalse\n\t\t\\if@noisy\n\t\t\t\\@verbosetrue\n\t\t\\else\n\t\t\t\\@verbosefalse\n\t\t\\fi\n}\n%\n% Go through the options setting things up.\n%\n\\def\\parse@ps@parms#1{\n\t \t\\@psdo\\@psfiga:=#1\\do\n\t\t {\\expandafter\\@setparms\\@psfiga,}}\n%\n% Compute bb height and width\n%\n\\newif\\ifno@bb\n\\def\\bb@missing{\n\t\\if@verbose{\n\t\t\\ps@typeout{psfig: searching \\@p@sbbfile \\space for bounding box}\n\t}\\fi\n\t\\no@bbtrue\n\t\\epsf@getbb{\\@p@sbbfile}\n \\ifno@bb \\else \\bb@cull\\epsf@llx\\epsf@lly\\epsf@urx\\epsf@ury\\fi\n}\t\n\\def\\bb@cull#1#2#3#4{\n\t\\dimen100=#1 bp\\edef\\@p@sbbllx{\\number\\dimen100}\n\t\\dimen100=#2 bp\\edef\\@p@sbblly{\\number\\dimen100}\n\t\\dimen100=#3 bp\\edef\\@p@sbburx{\\number\\dimen100}\n\t\\dimen100=#4 bp\\edef\\@p@sbbury{\\number\\dimen100}\n\t\\no@bbfalse\n}\n% rotate point (#1,#2) about (0,0).\n% The sine and cosine of the angle are already stored in \\sine and\n% \\cosine. The result is placed in (\\p@intvaluex, \\p@intvaluey).\n\\newdimen\\p@intvaluex\n\\newdimen\\p@intvaluey\n\\def\\rotate@#1#2{{\\dimen0=#1 sp\\dimen1=#2 sp\n% \tcalculate x' = x \\cos\\theta - y \\sin\\theta\n\t\t \\global\\p@intvaluex=\\cosine\\dimen0\n\t\t \\dimen3=\\sine\\dimen1\n\t\t \\global\\advance\\p@intvaluex by -\\dimen3\n% \t\tcalculate y' = x \\sin\\theta + y \\cos\\theta\n\t\t \\global\\p@intvaluey=\\sine\\dimen0\n\t\t \\dimen3=\\cosine\\dimen1\n\t\t \\global\\advance\\p@intvaluey by \\dimen3\n\t\t }}\n\\def\\compute@bb{\n\t\t\\no@bbfalse\n\t\t\\if@bbllx \\else \\no@bbtrue \\fi\n\t\t\\if@bblly \\else \\no@bbtrue \\fi\n\t\t\\if@bburx \\else \\no@bbtrue \\fi\n\t\t\\if@bbury \\else \\no@bbtrue \\fi\n\t\t\\ifno@bb \\bb@missing \\fi\n\t\t\\ifno@bb \\ps@typeout{FATAL ERROR: no bb supplied or found}\n\t\t\t\\no-bb-error\n\t\t\\fi\n\t\t%\n%\\ps@typeout{BB: \\@p@sbbllx, \\@p@sbblly, \\@p@sbburx, \\@p@sbbury} \n%\n% store height/width of original (unrotated) bounding box\n\t\t\\count203=\\@p@sbburx\n\t\t\\count204=\\@p@sbbury\n\t\t\\advance\\count203 by -\\@p@sbbllx\n\t\t\\advance\\count204 by -\\@p@sbblly\n\t\t\\edef\\ps@bbw{\\number\\count203}\n\t\t\\edef\\ps@bbh{\\number\\count204}\n\t\t%\\ps@typeout{ psbbh = \\ps@bbh, psbbw = \\ps@bbw }\n\t\t\\if@angle \n\t\t\t\\Sine{\\@p@sangle}\\Cosine{\\@p@sangle}\n\t \t{\\dimen100=\\maxdimen\\xdef\\r@p@sbbllx{\\number\\dimen100}\n\t\t\t\t\t \\xdef\\r@p@sbblly{\\number\\dimen100}\n\t\t\t \\xdef\\r@p@sbburx{-\\number\\dimen100}\n\t\t\t\t\t \\xdef\\r@p@sbbury{-\\number\\dimen100}}\n%\n% Need to rotate all four points and take the X-Y extremes of the new\n% points as the new bounding box.\n \\def\\minmaxtest{\n\t\t\t \\ifnum\\number\\p@intvaluex<\\r@p@sbbllx\n\t\t\t \\xdef\\r@p@sbbllx{\\number\\p@intvaluex}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluex>\\r@p@sbburx\n\t\t\t \\xdef\\r@p@sbburx{\\number\\p@intvaluex}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluey<\\r@p@sbblly\n\t\t\t \\xdef\\r@p@sbblly{\\number\\p@intvaluey}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluey>\\r@p@sbbury\n\t\t\t \\xdef\\r@p@sbbury{\\number\\p@intvaluey}\\fi\n\t\t\t }\n%\t\t\tlower left\n\t\t\t\\rotate@{\\@p@sbbllx}{\\@p@sbblly}\n\t\t\t\\minmaxtest\n%\t\t\tupper left\n\t\t\t\\rotate@{\\@p@sbbllx}{\\@p@sbbury}\n\t\t\t\\minmaxtest\n%\t\t\tlower right\n\t\t\t\\rotate@{\\@p@sbburx}{\\@p@sbblly}\n\t\t\t\\minmaxtest\n%\t\t\tupper right\n\t\t\t\\rotate@{\\@p@sbburx}{\\@p@sbbury}\n\t\t\t\\minmaxtest\n\t\t\t\\edef\\@p@sbbllx{\\r@p@sbbllx}\\edef\\@p@sbblly{\\r@p@sbblly}\n\t\t\t\\edef\\@p@sbburx{\\r@p@sbburx}\\edef\\@p@sbbury{\\r@p@sbbury}\n%\\ps@typeout{rotated BB: \\r@p@sbbllx, \\r@p@sbblly, \\r@p@sbburx, \\r@p@sbbury}\n\t\t\\fi\n\t\t\\count203=\\@p@sbburx\n\t\t\\count204=\\@p@sbbury\n\t\t\\advance\\count203 by -\\@p@sbbllx\n\t\t\\advance\\count204 by -\\@p@sbblly\n\t\t\\edef\\@bbw{\\number\\count203}\n\t\t\\edef\\@bbh{\\number\\count204}\n\t\t%\\ps@typeout{ bbh = \\@bbh, bbw = \\@bbw }\n}\n%\n% \\in@hundreds performs #1 * (#2 / #3) correct to the hundreds,\n%\tthen leaves the result in @result\n%\n\\def\\in@hundreds#1#2#3{\\count240=#2 \\count241=#3\n\t\t \\count100=\\count240\t% 100 is first digit #2/#3\n\t\t \\divide\\count100 by \\count241\n\t\t \\count101=\\count100\n\t\t \\multiply\\count101 by \\count241\n\t\t \\advance\\count240 by -\\count101\n\t\t \\multiply\\count240 by 10\n\t\t \\count101=\\count240\t%101 is second digit of #2/#3\n\t\t \\divide\\count101 by \\count241\n\t\t \\count102=\\count101\n\t\t \\multiply\\count102 by \\count241\n\t\t \\advance\\count240 by -\\count102\n\t\t \\multiply\\count240 by 10\n\t\t \\count102=\\count240\t% 102 is the third digit\n\t\t \\divide\\count102 by \\count241\n\t\t \\count200=#1\\count205=0\n\t\t \\count201=\\count200\n\t\t\t\\multiply\\count201 by \\count100\n\t\t \t\\advance\\count205 by \\count201\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 10\n\t\t\t\\multiply\\count201 by \\count101\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 100\n\t\t\t\\multiply\\count201 by \\count102\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\edef\\@result{\\number\\count205}\n}\n\\def\\compute@wfromh{\n\t\t% computing : width = height * (bbw / bbh)\n\t\t\\in@hundreds{\\@p@sheight}{\\@bbw}{\\@bbh}\n\t\t%\\ps@typeout{ \\@p@sheight * \\@bbw / \\@bbh, = \\@result }\n\t\t\\edef\\@p@swidth{\\@result}\n\t\t%\\ps@typeout{w from h: width is \\@p@swidth}\n}\n\\def\\compute@hfromw{\n\t\t% computing : height = width * (bbh / bbw)\n\t \\in@hundreds{\\@p@swidth}{\\@bbh}{\\@bbw}\n\t\t%\\ps@typeout{ \\@p@swidth * \\@bbh / \\@bbw = \\@result }\n\t\t\\edef\\@p@sheight{\\@result}\n\t\t%\\ps@typeout{h from w : height is \\@p@sheight}\n}\n\\def\\compute@handw{\n\t\t\\if@height \n\t\t\t\\if@width\n\t\t\t\\else\n\t\t\t\t\\compute@wfromh\n\t\t\t\\fi\n\t\t\\else \n\t\t\t\\if@width\n\t\t\t\t\\compute@hfromw\n\t\t\t\\else\n\t\t\t\t\\edef\\@p@sheight{\\@bbh}\n\t\t\t\t\\edef\\@p@swidth{\\@bbw}\n\t\t\t\\fi\n\t\t\\fi\n}\n\\def\\compute@resv{\n\t\t\\if@rheight \\else \\edef\\@p@srheight{\\@p@sheight} \\fi\n\t\t\\if@rwidth \\else \\edef\\@p@srwidth{\\@p@swidth} \\fi\n\t\t%\\ps@typeout{rheight = \\@p@srheight, rwidth = \\@p@srwidth}\n}\n%\t\t\n% Compute any missing values\n\\def\\compute@sizes{\n\t\\compute@bb\n\t\\if@scalefirst\\if@angle\n% at this point the bounding box has been adjsuted correctly for\n% rotation. PSFIG does all of its scaling using \\@bbh and \\@bbw. If\n% a width= or height= was specified along with \\psscalefirst, then the\n% width=/height= value needs to be adjusted to match the new (rotated)\n% bounding box size (specifed in \\@bbw and \\@bbh).\n% \\ps@bbw width=\n% ------- = ---------- \n% \\@bbw new width=\n% so `new width=' = (width= * \\@bbw) / \\ps@bbw; where \\ps@bbw is the\n% width of the original (unrotated) bounding box.\n\t\\if@width\n\t \\in@hundreds{\\@p@swidth}{\\@bbw}{\\ps@bbw}\n\t \\edef\\@p@swidth{\\@result}\n\t\\fi\n\t\\if@height\n\t \\in@hundreds{\\@p@sheight}{\\@bbh}{\\ps@bbh}\n\t \\edef\\@p@sheight{\\@result}\n\t\\fi\n\t\\fi\\fi\n\t\\compute@handw\n\t\\compute@resv}\n\n%\n% \\psfig\n% usage : \\psfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,\n%\t\t\trheight=, rwidth=, clip=}\n%\n% \"clip=\" is a switch and takes no value, but the `=' must be present.\n\\def\\psfig#1{\\vbox {\n\t% do a zero width hard space so that a single\n\t% \\psfig in a centering enviornment will behave nicely\n\t%{\\setbox0=\\hbox{\\ }\\ \\hskip-\\wd0}\n\t%\n\t\\ps@init@parms\n\t\\parse@ps@parms{#1}\n\t\\compute@sizes\n\t%\n\t\\ifnum\\@p@scost<\\@psdraft{\n\t\t%\n\t\t\\special{ps::[begin] \t\\@p@swidth \\space \\@p@sheight \\space\n\t\t\t\t\\@p@sbbllx \\space \\@p@sbblly \\space\n\t\t\t\t\\@p@sbburx \\space \\@p@sbbury \\space\n\t\t\t\tstartTexFig \\space }\n\t\t\\if@angle\n\t\t\t\\special {ps:: \\@p@sangle \\space rotate \\space} \n\t\t\\fi\n\t\t\\if@clip{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{(clip)}\n\t\t\t}\\fi\n\t\t\t\\special{ps:: doclip \\space }\n\t\t}\\fi\n\t\t\\if@prologfile\n\t\t \\special{ps: plotfile \\@prologfileval \\space } \\fi\n\t\t\\if@decmpr{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{psfig: including \\@[email protected] \\space }\n\t\t\t}\\fi\n\t\t\t\\special{ps: plotfile \"`zcat \\@[email protected]\" \\space }\n\t\t}\\else{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{psfig: including \\@p@sfile \\space }\n\t\t\t}\\fi\n\t\t\t\\special{ps: plotfile \\@p@sfile \\space }\n\t\t}\\fi\n\t\t\\if@postlogfile\n\t\t \\special{ps: plotfile \\@postlogfileval \\space } \\fi\n\t\t\\special{ps::[end] endTexFig \\space }\n\t\t% Create the vbox to reserve the space for the figure.\n\t\t\\vbox to \\@p@srheight sp{\n\t\t% 1/92 TJD Changed from \"true sp\" to \"sp\" for magnification.\n\t\t\t\\hbox to \\@p@srwidth sp{\n\t\t\t\t\\hss\n\t\t\t}\n\t\t\\vss\n\t\t}\n\t}\\else{\n\t\t% draft figure, just reserve the space and print the\n\t\t% path name.\n\t\t\\if@draftbox{\t\t\n\t\t\t% Verbose draft: print file name in box\n\t\t\t\\hbox{\\frame{\\vbox to \\@p@srheight sp{\n\t\t\t\\vss\n\t\t\t\\hbox to \\@p@srwidth sp{ \\hss \\@p@sfile \\hss }\n\t\t\t\\vss\n\t\t\t}}}\n\t\t}\\else{\n\t\t\t% Non-verbose draft\n\t\t\t\\vbox to \\@p@srheight sp{\n\t\t\t\\vss\n\t\t\t\\hbox to \\@p@srwidth sp{\\hss}\n\t\t\t\\vss\n\t\t\t}\n\t\t}\\fi\t\n\n\n\n\t}\\fi\n}}\n\\psfigRestoreAt\n\\let\\@=\\LaTeXAtSign\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002027.extracted_bib",
"string": "\\bibitem=\\bib@item\n}\n\n\\def\\bib@item{%\n \\par\\parindent=1.5em\\Hang{1.5em}{1}%\n \\everypar={\\Hang{1.5em}{1}\\ignorespaces}%\n \\noindent\\ignorespaces\n}\n\n\\def\\endrefs{\\par\\egroup\\@doendpe}\n\n\n% Page heads\n\n\\newtoks\\CatchLine\n\n\\def\\@journal{Mon.\\ Not.\\ R.\\ Astron.\\ Soc.\\ } % The journal title string\n\\def\\@pubyear{1994} % Assign a default publication year\n\\def\\@pagerange{000--000} % Assign a default page-range\n\\def\\@volume{000} % Assign a default volume number\n\\def\\@microfiche{} %\n\n\\def\\pubyear#1{\\gdef\\@pubyear{#1}\\@makecatchline}\n\\def\\pagerange#1{\\gdef\\@pagerange{#1}\\@makecatchline}\n\\def\\volume#1{\\gdef\\@volume{#1}\\@makecatchline}\n\\def\\microfiche#1{\\gdef\\@microfiche{and Microfiche\\ #1}\\@makecatchline}\n\n\\def\\@makecatchline{%\n \\global\\CatchLine{%\n {\\rm \\@journal {\\bf \\@volume},\\ \\@pagerange\\ (\\@pubyear)\\ \\@microfiche}}%\n}\n\n\\@makecatchline % Assign a catchline, using the above defaults\n\n\\newtoks\\LeftHeader\n\\def\\shortauthor#1{% left page head\n \\global\\LeftHeader{#1}%\n}\n\n\\newtoks\\RightHeader\n\\def\\shorttitle#1{% right page head\n \\global\\RightHeader{#1}%\n}\n\n\\def\\PageHead{% recto/verso running heads\n \\begingroup\n \\ifsp@page\n \\csname ps@\\sp@type\\endcsname\n \\fi\n \\ifodd\\pageno\n \\let\\the@head=\\@oddhead\n \\else\n \\let\\the@head=\\@evenhead\n \\fi\n \\vbox to \\z@{\\vskip-22.5\\p@%\n \\hbox to \\PageWidth{\\vbox to8.5\\p@{}%\n \\the@head\n }%\n \\vss}%\n \\endgroup\n \\nointerlineskip\n}\n\n\\gdef\\PageFoot{%\n \\nointerlineskip%\n \\begingroup\n \\ifsp@page\n \\csname ps@\\sp@type\\endcsname\n \\global\\sp@pagefalse\n \\fi\n \\vbox to 22pt{\\vfil%\n \\hbox to \\PageWidth{%\n \\eightpoint\\strut\\noindent\n \\ifodd\\pageno\n \\@oddfoot\n \\else\n \\@evenfoot\n \\fi\n }%\n }%\n \\endgroup\n}\n\n\\def\\today{%\n \\number\\day\\space\n \\ifcase\\month\\or January\\or February\\or March\\or April\\or May\\or June\\or\n July\\or August\\or September\\or October\\or November\\or December\\fi\n \\space\\number\\year%\n}\n\n\n\\def\\authorcomment#1{%\n \\gdef\\PageFoot{%\n \\nointerlineskip%\n \\vbox to 20pt{\\vfil%\n \\hbox to \\PageWidth{\\elevenpoint\\noindent \\hfil #1 \\hfil}}%\n }%\n}\n\n\n% Plate pages\n\n\\newif\\ifplate@page\n\\newbox\\plt@box\n\n\\def\\beginplatepage{%\n \\let\\plate=\\plate@head\n \\let\\caption=\\fig@caption\n \\global\\setbox\\plt@box=\\vbox\\bgroup\n \\TEMPDIMEN=\\PageWidth % For \\fig@caption test\n \\hsize=\\PageWidth\\relax\n}\n\n\\def\\endplatepage{\\par\\egroup\\global\\plate@pagetrue}\n\\def\\plate@head#1{\\gdef\\plt@cap{#1}}\n\n% Letters option\n\n\\def\\letters{%\n \\gdef\\folio{\\ifnum\\pageno<\\z@ L\\romannumeral-\\pageno\n \\else L\\number\\pageno \\fi}%\n}\n\n\n% Math setup\n\n% The standard math indentation\n\\newdimen\\mathindent\n\n\\global\\mathindent=\\z@\n\\global\\everydisplay{\\global\\@dspwd=\\displaywidth\\displaysetup}\n\n% New versions of \\displaylines, \\eqalign, \\eqalignno for\n% when non-centered math is in use.\n\n\\def\\@displaylines#1{% (for non-centered math)\n {}$\\displ@y\\hbox{\\vbox{\\halign{$\\@lign\\hfil\\displaystyle##\\hfil$\\crcr\n #1\\crcr}}}${}%\n}\n\n\\def\\@eqalign#1{\\null\\vcenter{\\openup\\jot\\m@th% (for non-centered math)\n \\ialign{\\strut\\hfil$\\displaystyle{##}$&$\\displaystyle{{}##}$\\hfil\n \\crcr#1\\crcr}}%\n}\n\n\\def\\@eqalignno#1{% (for non-centered math)\n \\global\\advance\\@dspwd by -\\mathindent%\n {}$\\displ@y\\hbox{\\vbox{\\halign to\\@dspwd%\n {\\hfil$\\@lign\\displaystyle{##}$\\tabskip\\z@skip\n &$\\@lign\\displaystyle{{}##}$\\hfil\\tabskip\\centering\n &\\llap{$\\@lign##$}\\tabskip\\z@skip\\crcr\n #1\\crcr}}}${}%\n}\n\n% When equations are flushleft ensure, that \\displaylines,\n% \\eqalign, \\eqalignno and \\leqalignno point to the new versions of\n% the macros. Also make \\leqalignno act like \\eqalignno, otherwise the\n% equation text would `crash' into the equation number.\n\n\\global\\let\\displaylines=\\@displaylines\n\\global\\let\\eqalign=\\@eqalign\n\\global\\let\\eqalignno=\\@eqalignno\n\\global\\let\\leqalignno=\\@eqalignno\n\n\\newdimen\\@dspwd \\@dspwd=\\z@\n\\newif\\if@eqno\n\\newif\\if@leqno\n\\newtoks\\@eqn\n\\newtoks\\@eq\n\n\\def\\displaysetup#1$${\\displaytest#1\\eqno\\eqno\\displaytest}\n\n\\def\\displaytest#1\\eqno#2\\eqno#3\\displaytest{%\n \\if!#3!\\ldisplaytest#1\\leqno\\leqno\\ldisplaytest\n \\else\\@eqnotrue\\@leqnofalse\\@eqn={#2}\\@eq={#1}\\fi\n \\generaldisplay$$}\n\n\\def\\ldisplaytest#1\\leqno#2\\leqno#3\\ldisplaytest{%\n\\@eq={#1}%\n \\if!#3!\\@eqnofalse\\else\\@eqnotrue\\@leqnotrue\n \\@eqn={#2}\\fi}\n\n\\def\\generaldisplay{%\n \\if@eqno\n \\if@leqno\n \\hbox to \\displaywidth{\\noindent\n \\rlap{$\\displaystyle\\the\\@eqn$}%\n \\hskip\\mathindent$\\displaystyle\\the\\@eq$\\hfil}%\n \\else\n \\hbox to \\displaywidth{\\noindent\n \\hskip\\mathindent\n $\\displaystyle\\the\\@eq$\\hfil$\\displaystyle\\the\\@eqn$}%\n \\fi\n \\else\n \\hbox to \\displaywidth{\\noindent\n \\hskip\\mathindent$\\displaystyle\\the\\@eq$\\hfil}%\n \\fi\n}\n\n\n% Finishing notice\n\n\\def\\@notice{%\n \\par\\Two%\n \\noindent{\\b@ls{11pt}\\ninerm This paper has been produced using the\n Royal Astronomical Society/Blackwell Science \\TeX\\ macros.\\par}%\n}\n\n% redefine \\bye to output our identification notice :\n\\outer\\def\\bye{\\@notice\\par\\vfill\\supereject\\end}\n\n\n% define a sign on :\n\n\\def\\start@mess{%\n Monthly notices of the RAS journal style (\\@typeface)\\space\n v\\@version,\\space \\@verdate.%\n}\n\n\\everyjob{\\Warn{\\start@mess}}\n\n\n% Two-column macros\n\n%--------------------------------------------------------%\n% INITIALISATION %\n%--------------------------------------------------------%\n\n\\newif\\if@debug \\@debugfalse % when false, only warnings displayed\n\n\\def\\Print#1{\\if@debug\\immediate\\write16{#1}\\else \\fi}\n\\def\\Warn#1{\\immediate\\write16{#1}}\n\\def\\wlog#1{}\n\n\\newcount\\Iteration % temporary loop counter\n\n\\def\\Single{0} \\def\\Double{1} % ItemSPAN's\n\\def\\Figure{0} \\def\\Table{1} % ItemTYPE's\n\n\\def\\InStack{0} % ItemSTATUS\n\\def\\InZoneA{1}\n\\def\\InZoneB{2}\n\\def\\InZoneC{3}\n\n\\newcount\\TEMPCOUNT % temporary count register\n\\newdimen\\TEMPDIMEN % temporary dimen register\n\\newbox\\TEMPBOX % temporary box register\n\\newbox\\VOIDBOX % a box which is permenately void\n\n\\newcount\\LengthOfStack % number of items currently in stack\n\\newcount\\MaxItems % maximum number of items allowed in stack\n\\newcount\\StackPointer\n\\newcount\\Point % used in calculation for generating the\n % physical address of an item in the stack.\n\\newcount\\NextFigure % number of next figure to be output\n\\newcount\\NextTable % number of next table to be output\n\\newcount\\NextItem % Next item to consider by order in stack\n\n\\newcount\\StatusStack % set to point to top of STATUS stack\n\\newcount\\NumStack % set to point to top of NUMBER stack\n\\newcount\\TypeStack % set to point to top of TYPE stack\n\\newcount\\SpanStack % set to point to top of SPAN stack\n\\newcount\\BoxStack % set to point to top of BOX stack\n\n\\newcount\\ItemSTATUS % status of present item\n\\newcount\\ItemNUMBER % number of present item\n\\newcount\\ItemTYPE % type of present item\n\\newcount\\ItemSPAN % span of present item\n\\newbox\\ItemBOX % box of present item\n\\newdimen\\ItemSIZE % size of present item\n % (calculated by GetItemBOX)\n\n\\newdimen\\PageHeight % vertical measure of full page\n\\newdimen\\TextLeading % distance between baselines of body text\n\\newdimen\\Feathering % amount of interline stretch\n\\newcount\\LinesPerPage % height of page in text lines\n\\newdimen\\ColumnWidth % width of 1 column of text\n\\newdimen\\ColumnGap % size of gap between columns\n\\newdimen\\PageWidth % = \\ColumnWidth * 2 + \\ColumnGap\n\\newdimen\\BodgeHeight % Bodge to align figures and tables with text\n\\newcount\\Leading % Set to same as \\TextLeading above\n\n\\newdimen\\ZoneBSize % size of items in ZoneB\n\\newdimen\\TextSize % size of text in ZoneB\n\\newbox\\ZoneABOX % contains Zone A material\n\\newbox\\ZoneBBOX % contains Zone B material\n\\newbox\\ZoneCBOX % contains Zone C material\n\n\\newif\\ifFirstSingleItem\n\\newif\\ifFirstZoneA\n\\newif\\ifMakePageInComplete\n\\newif\\ifMoreFigures \\MoreFiguresfalse % set true in join stack\n\\newif\\ifMoreTables \\MoreTablesfalse % set true in join stack\n\n\\newif\\ifFigInZoneB % used to determine in which zone an item\n\\newif\\ifFigInZoneC % will be placed based on what is in other\n\\newif\\ifTabInZoneB % zones already for a given page.\n\\newif\\ifTabInZoneC\n\n\\newif\\ifZoneAFullPage\n\n\\newbox\\MidBOX % = LeftBOX+gap+RightBOX\n\\newbox\\LeftBOX\n\\newbox\\RightBOX\n\\newbox\\PageBOX % complete made-up page\n\n\\newif\\ifLeftCOL % flags first pass through output routine\n\\LeftCOLtrue\n\n\\newdimen\\ZoneBAdjust\n\n\\newcount\\ItemFits\n\\def\\Yes{1}\n\\def\\No{2}\n\n\\def\\LineAdjust#1{\\global\\ZoneBAdjust=#1\\TextLeading\\relax}\n\n\n% Setup file.\n\n\\MaxItems=15\n\\NextFigure=\\z@ % used for article opening\n\\NextTable=\\@ne\n\n\\BodgeHeight=6pt\n\\TextLeading=11pt % baselineskip of body text\n\\Leading=11\n\\Feathering=\\z@ % amount of interline stretch\n\\LinesPerPage=61 % number of text lines per full page -1\n\\topskip=\\TextLeading\n\\ColumnWidth=20pc % width of text columns\n\\ColumnGap=2pc % gap between columns\n\n\\newskip\\ItemSepamount % space between floats\n\\ItemSepamount=\\TextLeading plus \\TextLeading minus 4pt\n\n\\parskip=\\z@ plus .1pt\n\\parindent=18pt\n\\widowpenalty=\\z@\n\\clubpenalty=10000\n\\tolerance=1500\n\\hbadness=1500\n\\abovedisplayskip=6pt plus 2pt minus 1pt\n\\belowdisplayskip=6pt plus 2pt minus 1pt\n\\abovedisplayshortskip=6pt plus 2pt minus 1pt\n\\belowdisplayshortskip=6pt plus 2pt minus 1pt\n\n\\frenchspacing\n\n\\ninepoint % start main text size\n\n\\PageHeight=682pt\n\\PageWidth=2\\ColumnWidth\n\\advance\\PageWidth by \\ColumnGap\n\n\\pagestyle{headings}\n\n\n%--------------------------------------------------------%\n% STACKS %\n%--------------------------------------------------------%\n\n% THE ITEM STACK\n% The item stack contains contains figures and tables\n% in the order in which they appear in the article source\n% code.\n\n% allocate stack space\n\n\\newcount\\DUMMY \\StatusStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\NumStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\TypeStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newcount\\DUMMY \\SpanStack=\\allocationnumber\n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY \n\\newcount\\DUMMY \\newcount\\DUMMY \\newcount\\DUMMY\n\n\\newbox\\DUMMY \\BoxStack=\\allocationnumber\n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY \n\\newbox\\DUMMY \\newbox\\DUMMY \\newbox\\DUMMY\n\n\\def\\wlog{\\immediate\\write\\m@ne}\n\n% \\GetItemSTATUS, \\GetItemNUMBER, \\GetItemTYPE, \\GetItemSPAN,\n% \\GetItemBox \n% are used to get details of a particular item from the item\n% stack. The argument to each of these is the items position\n% in the stack (usually \\StackPointer)...not the items number.\n\n\\def\\GetItemAll#1{%\n \\GetItemSTATUS{#1}\n \\GetItemNUMBER{#1}\n \\GetItemTYPE{#1}\n \\GetItemSPAN{#1}\n \\GetItemBOX{#1}\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemSTATUS#1{%\n \\Point=\\StatusStack\n \\advance\\Point by #1\n \\global\\ItemSTATUS=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemNUMBER#1{%\n \\Point=\\NumStack\n \\advance\\Point by #1\n \\global\\ItemNUMBER=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemTYPE#1{%\n \\Point=\\TypeStack\n \\advance\\Point by #1\n \\global\\ItemTYPE=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemSPAN#1{%\n \\Point\\SpanStack\n \\advance\\Point by #1\n \\global\\ItemSPAN=\\count\\Point\n}\n\n% Note: \\LeaveStack uses this routine. Do not destroy \\Point\n\\def\\GetItemBOX#1{%\n \\Point=\\BoxStack\n \\advance\\Point by #1\n \\global\\setbox\\ItemBOX=\\vbox{\\copy\\Point}\n \\global\\ItemSIZE=\\ht\\ItemBOX\n \\global\\advance\\ItemSIZE by \\dp\\ItemBOX\n \\TEMPCOUNT=\\ItemSIZE\n \\divide\\TEMPCOUNT by \\Leading\n \\divide\\TEMPCOUNT by 65536\n \\advance\\TEMPCOUNT \\@ne\n \\ItemSIZE=\\TEMPCOUNT pt\n \\global\\multiply\\ItemSIZE by \\Leading\n}\n\n% item joins stack\n\n\\def\\JoinStack{%\n \\ifnum\\LengthOfStack=\\MaxItems % stack is full of items\n \\Warn{WARNING: Stack is full...some items will be lost!}\n \\else\n \\Point=\\StatusStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemSTATUS\n \\Point=\\NumStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemNUMBER\n \\Point=\\TypeStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemTYPE\n \\Point\\SpanStack\n \\advance\\Point by \\LengthOfStack\n \\global\\count\\Point=\\ItemSPAN\n \\Point=\\BoxStack\n \\advance\\Point by \\LengthOfStack\n \\global\\setbox\\Point=\\vbox{\\copy\\ItemBOX}\n \\global\\advance\\LengthOfStack \\@ne\n \\ifnum\\ItemTYPE=\\Figure % used in \\MakePage\n \\global\\MoreFigurestrue\n \\else\n \\global\\MoreTablestrue\n \\fi\n \\fi\n}\n\n% item leaves stack\n% #1=physical position of the item to be removed\n\n\\def\\LeaveStack#1{%\n {\\Iteration=#1\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\advance\\Iteration \\@ne\n \\GetItemSTATUS{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemSTATUS\n \\GetItemNUMBER{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemNUMBER\n \\GetItemTYPE{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemTYPE\n \\GetItemSPAN{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\count\\Point=\\ItemSPAN\n \\GetItemBOX{\\Iteration}\n \\advance\\Point by \\m@ne\n \\global\\setbox\\Point=\\vbox{\\copy\\ItemBOX}\n \\repeat}\n \\global\\advance\\LengthOfStack by \\m@ne\n}\n\n% clean stack\n% This routine scans through the stack and removes anything\n% that does not have STATUS=\\InStack.\n\n\\newif\\ifStackNotClean\n\n\\def\\CleanStack{%\n \\StackNotCleantrue\n {\\Iteration=\\z@\n \\loop\n \\ifStackNotClean\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\advance\\Iteration \\@ne\n \\else\n \\LeaveStack{\\Iteration}\n \\fi\n \\ifnum\\LengthOfStack<\\Iteration\n \\StackNotCleanfalse\n \\fi\n \\repeat}\n}\n\n% Find item.\n% This macro searches from the top to the bottom of the\n% stack for an item of a specified type and number.\n% #1=type, #2=number\n% If the specified item is found, then \\StackPointer is set\n% to point to it, else \\StackPointer=-1.\n% This routine is used to find the next figure or table\n% by number.\n\n\\def\\FindItem#1#2{%\n \\global\\StackPointer=\\m@ne % assume item isn't in stack for now\n {\\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\GetItemTYPE{\\Iteration}\n \\ifnum\\ItemTYPE=#1\n \\GetItemNUMBER{\\Iteration}\n \\ifnum\\ItemNUMBER=#2\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\fi\n \\advance\\Iteration \\@ne\n \\repeat}\n}\n\n% Find next type\n% This macro searches from the top to the bottom of the stack\n% looking for the first item which has STATUS=\\InStack.\n% If it is a figure then a figure is what will be considered\n% next by \\MakePage else table.\n\n\\def\\FindNext{%\n \\global\\StackPointer=\\m@ne % assume stack is empty for now\n {\\Iteration=\\z@\n \\loop\n \\ifnum\\Iteration<\\LengthOfStack\n \\GetItemSTATUS{\\Iteration}\n \\ifnum\\ItemSTATUS=\\InStack\n \\GetItemTYPE{\\Iteration}\n \\ifnum\\ItemTYPE=\\Figure\n \\ifMoreFigures\n \\global\\NextItem=\\Figure\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\ifnum\\ItemTYPE=\\Table\n \\ifMoreTables\n \\global\\NextItem=\\Table\n \\global\\StackPointer=\\Iteration\n \\Iteration=\\LengthOfStack % terminate loop\n \\fi\n \\fi\n \\fi\n \\advance\\Iteration \\@ne\n \\repeat}\n}\n\n% Change status\n% Macro to change the status of a specified item in stack.\n% #1=item, #2=new status\n\n\\def\\ChangeStatus#1#2{%\n \\Point=\\StatusStack\n \\advance\\Point by #1\n \\global\\count\\Point=#2\n}\n\n\n%--------------------------------------------------------%\n% MAKEPAGE %\n%--------------------------------------------------------%\n\n% This macro is called at the start of every new page\n% including the first. It scans through the stack picking\n% out items which should be placed on this page. It then\n% leaves space for the items to be placed later. The routine\n% terminates when either there is no room on the page to\n% fit the next figure or table, or there are no more items\n% in the stack.\n\n\\def\\Zone{\\InZoneA}\n\n\\ZoneBAdjust=\\z@\n\n\\def\\MakePage{% allocate space on this page for stack items\n \\global\\ZoneBSize=\\PageHeight\n \\global\\TextSize=\\ZoneBSize\n \\global\\ZoneAFullPagefalse\n \\global\\topskip=\\TextLeading\n \\MakePageInCompletetrue\n \\MoreFigurestrue\n \\MoreTablestrue\n \\FigInZoneBfalse\n \\FigInZoneCfalse\n \\TabInZoneBfalse\n \\TabInZoneCfalse\n \\global\\FirstSingleItemtrue\n \\global\\FirstZoneAtrue\n \\global\\setbox\\ZoneABOX=\\box\\VOIDBOX\n \\global\\setbox\\ZoneBBOX=\\box\\VOIDBOX\n \\global\\setbox\\ZoneCBOX=\\box\\VOIDBOX\n \\loop\n \\ifMakePageInComplete\n \\FindNext\n \\ifnum\\StackPointer=\\m@ne\n \\NextItem=\\m@ne\n \\MoreFiguresfalse\n \\MoreTablesfalse\n \\fi\n \\ifnum\\NextItem=\\Figure\n \\FindItem{\\Figure}{\\NextFigure}\n \\ifnum\\StackPointer=\\m@ne \\global\\MoreFiguresfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Single \\def\\Zone{\\InZoneB}\\relax\n \\ifFigInZoneC \\global\\MoreFiguresfalse\\fi\n \\else\n \\def\\Zone{\\InZoneA}\n \\ifFigInZoneB \\def\\Zone{\\InZoneC}\\fi\n \\fi\n \\fi\n \\ifMoreFigures\\Print{}\\FigureItems\\fi\n \\fi\n\\ifnum\\NextItem=\\Table\n \\FindItem{\\Table}{\\NextTable}\n \\ifnum\\StackPointer=\\m@ne \\global\\MoreTablesfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Single\\relax\n \\ifTabInZoneC \\global\\MoreTablesfalse\\fi\n \\else\n \\def\\Zone{\\InZoneA}\n \\ifTabInZoneB \\def\\Zone{\\InZoneC}\\fi\n \\fi\n \\fi\n \\ifMoreTables\\Print{}\\TableItems\\fi\n \\fi\n \\MakePageInCompletefalse % assume page is complete\n \\ifMoreFigures\\MakePageInCompletetrue\\fi\n \\ifMoreTables\\MakePageInCompletetrue\\fi\n \\repeat\n%\\Print{TextSize=\\the\\TextSize}\n%\\Print{ZoneBSize=\\the\\ZoneBSize}\n \\ifZoneAFullPage\n \\global\\TextSize=\\z@\n \\global\\ZoneBSize=\\z@\n \\global\\vsize=\\z@\\relax\n \\global\\topskip=\\z@\\relax\n \\vbox to \\z@{\\vss}\n \\eject\n \\else\n \\global\\advance\\ZoneBSize by -\\ZoneBAdjust\n \\global\\vsize=\\ZoneBSize\n \\global\\hsize=\\ColumnWidth\n \\global\\ZoneBAdjust=\\z@\n \\ifdim\\TextSize<23pt\n \\Warn{}\n \\Warn{* Making column fall short: TextSize=\\the\\TextSize *}\n \\vskip-\\lastskip\\eject\\fi\n \\fi\n}\n\n\\def\\MakeRightCol{% allocate space for the right column of text\n \\global\\TextSize=\\ZoneBSize\n \\MakePageInCompletetrue\n \\MoreFigurestrue\n \\MoreTablestrue\n \\global\\FirstSingleItemtrue\n \\global\\setbox\\ZoneBBOX=\\box\\VOIDBOX\n \\def\\Zone{\\InZoneB}\n \\loop\n \\ifMakePageInComplete\n \\FindNext\n \\ifnum\\StackPointer=\\m@ne\n \\NextItem=\\m@ne\n \\MoreFiguresfalse\n \\MoreTablesfalse\n \\fi\n \\ifnum\\NextItem=\\Figure\n \\FindItem{\\Figure}{\\NextFigure}\n \\ifnum\\StackPointer=\\m@ne \\MoreFiguresfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Double\\relax\n \\MoreFiguresfalse\\fi\n \\fi\n \\ifMoreFigures\\Print{}\\FigureItems\\fi\n \\fi\n \\ifnum\\NextItem=\\Table\n \\FindItem{\\Table}{\\NextTable}\n \\ifnum\\StackPointer=\\m@ne \\MoreTablesfalse\n \\else\n \\GetItemSPAN{\\StackPointer}\n \\ifnum\\ItemSPAN=\\Double\\relax\n \\MoreTablesfalse\\fi\n \\fi\n \\ifMoreTables\\Print{}\\TableItems\\fi\n \\fi\n \\MakePageInCompletefalse % assume page is complete\n \\ifMoreFigures\\MakePageInCompletetrue\\fi\n \\ifMoreTables\\MakePageInCompletetrue\\fi\n \\repeat\n \\ifZoneAFullPage\n \\global\\TextSize=\\z@\n \\global\\ZoneBSize=\\z@\n \\global\\vsize=\\z@\\relax\n \\global\\topskip=\\z@\\relax\n \\vbox to \\z@{\\vss}\n \\eject\n \\else\n \\global\\vsize=\\ZoneBSize\n \\global\\hsize=\\ColumnWidth\n \\ifdim\\TextSize<23pt\n \\Warn{}\n \\Warn{* Making column fall short: TextSize=\\the\\TextSize *}\n \\vskip-\\lastskip\\eject\\fi\n\\fi\n}\n\n\\def\\FigureItems{% Stack pointer points to next figure\n \\Print{Considering...}\n \\ShowItem{\\StackPointer}\n \\GetItemBOX{\\StackPointer} % auto calculates ItemSIZE\n \\GetItemSPAN{\\StackPointer}\n \\CheckFitInZone % check to see if item fits\n \\ifnum\\ItemFits=\\Yes\n \\ifnum\\ItemSPAN=\\Single\n \\ChangeStatus{\\StackPointer}{\\InZoneB} % flag to be output\n \\global\\FigInZoneBtrue\n \\ifFirstSingleItem\n \\hbox{}\\vskip-\\BodgeHeight\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\fi\n \\unvbox\\ItemBOX\\ItemSep\n \\global\\FirstSingleItemfalse\n \\global\\advance\\TextSize by -\\ItemSIZE% allocate space\n \\global\\advance\\TextSize by -\\TextLeading\n \\else\n \\ifFirstZoneA\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\global\\FirstZoneAfalse\\fi\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\global\\advance\\ZoneBSize by -\\ItemSIZE\n \\global\\advance\\ZoneBSize by -\\TextLeading\n \\ifFigInZoneB\\relax\n \\else\n \\ifdim\\TextSize<3\\TextLeading\n \\global\\ZoneAFullPagetrue\n \\fi\n \\fi\n \\ChangeStatus{\\StackPointer}{\\Zone}\n \\ifnum\\Zone=\\InZoneC \\global\\FigInZoneCtrue\\fi\n \\fi\n \\Print{TextSize=\\the\\TextSize}\n \\Print{ZoneBSize=\\the\\ZoneBSize}\n \\global\\advance\\NextFigure \\@ne\n \\Print{This figure has been placed.}\n \\else\n \\Print{No space available for this figure...holding over.}\n \\Print{}\n \\global\\MoreFiguresfalse\n \\fi\n}\n\n\\def\\TableItems{% Stack pointer points to next table\n \\Print{Considering...}\n \\ShowItem{\\StackPointer}\n \\GetItemBOX{\\StackPointer} % auto calculates ItemSIZE\n \\GetItemSPAN{\\StackPointer}\n \\CheckFitInZone % check to see of item fits in Zone\n \\ifnum\\ItemFits=\\Yes\n \\ifnum\\ItemSPAN=\\Single\n \\ChangeStatus{\\StackPointer}{\\InZoneB}\n \\global\\TabInZoneBtrue\n \\ifFirstSingleItem\n \\hbox{}\\vskip-\\BodgeHeight\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\fi\n \\unvbox\\ItemBOX\\ItemSep\n \\global\\FirstSingleItemfalse\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\else\n \\ifFirstZoneA\n \\global\\advance\\ItemSIZE by \\TextLeading\n \\global\\FirstZoneAfalse\\fi\n \\global\\advance\\TextSize by -\\ItemSIZE\n \\global\\advance\\TextSize by -\\TextLeading\n \\global\\advance\\ZoneBSize by -\\ItemSIZE\n \\global\\advance\\ZoneBSize by -\\TextLeading\n \\ifFigInZoneB\\relax\n \\else\n \\ifdim\\TextSize<3\\TextLeading\n \\global\\ZoneAFullPagetrue\n \\fi\n \\fi\n \\ChangeStatus{\\StackPointer}{\\Zone}\n \\ifnum\\Zone=\\InZoneC \\global\\TabInZoneCtrue\\fi\n \\fi\n% \\Print{TextSize=\\the\\TextSize}\n% \\Print{ZoneBSize=\\the\\ZoneBSize}\n \\global\\advance\\NextTable \\@ne\n \\Print{This table has been placed.}\n \\else\n \\Print{No space available for this table...holding over.}\n \\Print{}\n \\global\\MoreTablesfalse\n \\fi\n}\n\n% These macros check to see if an item of ItemSIZE will\n% fit in a particular zone. If it will, then ItemFits\n% will be set true else false.\n\n\\def\\CheckFitInZone{%\n{\\advance\\TextSize by -\\ItemSIZE\n \\advance\\TextSize by -\\TextLeading\n \\ifFirstSingleItem\n \\advance\\TextSize by \\TextLeading\n \\fi\n \\ifnum\\Zone=\\InZoneA\\relax\n \\else \\advance\\TextSize by -\\ZoneBAdjust\n \\fi\n \\ifdim\\TextSize<3\\TextLeading \\global\\ItemFits=\\No\n \\else \\global\\ItemFits=\\Yes\\fi}\n}\n\n\\def\\BeginOpening{%\n % start 9pt a.s.a.p. so that \\New.. commands get a chance to init.\n \\ninepoint\n \\thispagestyle{titlepage}%\n \\global\\setbox\\ItemBOX=\\vbox\\bgroup%\n \\hsize=\\PageWidth%\n \\hrule height \\z@\n \\ifsinglecol\\vskip 6pt\\fi % Bodge, to get same pos. as two-column!\n}\n\n\\let\\begintopmatter=\\BeginOpening % alias for \\BeginOpening\n\n\\def\\EndOpening{%\n \\One% 1 line fixed space below opening\n \\egroup\n \\ifsinglecol\n \\box\\ItemBOX%\n \\vskip\\TextLeading plus 2\\TextLeading% var. space: min 1, max 3 lines\n \\@noafterindent\n \\else\n \\ItemNUMBER=\\z@%\n \\ItemTYPE=\\Figure\n \\ItemSPAN=\\Double\n \\ItemSTATUS=\\InStack\n \\JoinStack\n \\fi\n}\n\n\n% Figures\n\n\\newif\\if@here \\@herefalse\n\n\\def\\no@float{\\global\\@heretrue}\n\\let\\nofloat=\\relax % only enabled for one column\n\n\\def\\beginfigure{%\n \\@ifstar{\\global\\@dfloattrue \\@bfigure}{\\global\\@dfloatfalse \\@bfigure}%\n}\n\n\\def\\@bfigure#1{%\n \\par\n \\if@dfloat\n \\ItemSPAN=\\Double\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSPAN=\\Single\n \\TEMPDIMEN=\\ColumnWidth\n \\fi\n \\ifsinglecol\n \\TEMPDIMEN=\\PageWidth\n \\else\n \\ItemSTATUS=\\InStack\n \\ItemNUMBER=#1%\n \\ItemTYPE=\\Figure\n \\fi\n \\bgroup\n \\hsize=\\TEMPDIMEN\n \\global\\setbox\\ItemBOX=\\vbox\\bgroup\n \\eightpoint\\nostb@ls{10pt}%\n \\let\\caption=\\fig@caption\n \\ifsinglecol \\let\\nofloat=\\no@float\\fi\n}\n\n\\def\\fig@caption#1{%\n \\vskip 5.5pt plus 6pt%\n \\bgroup % grouping and size change needed for plate pages\n \\eightpoint\\nostb@ls{10pt}%\n 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\\ZoneBSize{\\box255\\unvbox\\ZoneBBOX\n \\ifvoid\\footins\\else\n \\vskip\\skip\\footins\\unvbox\\footins\\fi\n }%\n \\setbox\\MidBOX=\\hbox{\\box\\LeftBOX\\hskip\\ColumnGap\\box\\RightBOX}%\n \\setbox\\PageBOX=\\vbox to \\PageHeight{%\n \\UnloadZoneA\\box\\MidBOX\\UnloadZoneC}%\n \\shipout\\vbox{\\PageHead\\vbox to \\PageHeight{\\box\\PageBOX\\vss}\\PageFoot}%\n \\advancepageno\n%\n \\ifplate@page\n \\shipout\\vbox{%\n \\sp@pagetrue\n \\def\\sp@type{plate}%\n \\global\\plate@pagefalse\n \\PageHead\\vbox to \\PageHeight{\\unvbox\\plt@box\\vfil}\\PageFoot%\n }%\n \\message{[plate]}%\n \\advancepageno\n \\fi\n%\n \\global\\LeftCOLtrue\n \\CleanStack\n \\MakePage\n \\fi\n}\n\n\n\n% Startup message\n\n\\Warn{\\start@mess}\n\n\\newif\\ifCUPmtplainloaded % for use in documents\n\\ifprod@font\n \\global\\CUPmtplainloadedtrue\n\\fi\n\n\\def\\mnmacrosloaded{} % so articles can see if a format file has been used.\n\n\\catcode `\\@=12 % @ signs are non-letters\n\n% \\dump\n\n% end of mn.tex\n\n\n%\n% overmerging paper\n%\n% Eelco van Kampen\n%\n% Institute for Astronomy, Edinburgh, 1998-1999\n%\n\n\\ifx\\mnmacrosloaded\\undefined \\input mn\\fi\n\n% author's definitions\n\n\\input psfig\n\\def\\halve{{\\scriptstyle 1 \\over 2}}\n\\def\\Mpc{$h_0^{-1}$Mpc}\n\n\\newif\\ifAMStwofonts\n%\\AMStwofontstrue\n\n\\ifCUPmtplainloaded \\else\n \\NewTextAlphabet{textbfit} {cmbxti10} {}\n \\NewTextAlphabet{textbfss} {cmssbx10} {}\n \\NewMathAlphabet{mathbfit} {cmbxti10} {} % for math mode\n \\NewMathAlphabet{mathbfss} {cmssbx10} {} % \" \" \"\n %\n \\ifAMStwofonts\n %\n \\NewSymbolFont{upmath} {eurm10}\n \\NewSymbolFont{AMSa} {msam10}\n \\NewMathSymbol{\\upi} {0}{upmath}{19}\n \\NewMathSymbol{\\umu} {0}{upmath}{16}\n \\NewMathSymbol{\\upartial}{0}{upmath}{40}\n \\NewMathSymbol{\\leqslant}{3}{AMSa}{36}\n \\NewMathSymbol{\\geqslant}{3}{AMSa}{3E}\n \\let\\oldle=\\le \\let\\oldleq=\\leq\n \\let\\oldge=\\ge \\let\\oldgeq=\\geq\n \\let\\leq=\\leqslant \\let\\le=\\leqslant\n \\let\\geq=\\geqslant \\let\\ge=\\geqslant\n \\else\n \\def\\umu{\\mu}\n \\def\\upi{\\pi}\n \\def\\upartial{\\partial}\n \\fi\n\\fi\n\n% Marginal adjustments using \\pageoffset maybe required when printing\n% proofs on a Laserprinter (this is usually not needed).\n% Syntax: \\pageoffset{ +/- hor. offset}{ +/- vert. offset}\n% e.g. \\pageoffset{-3pc}{-4pc}\n\\pageoffset{-2.5pc}{0pc}\n\n\\loadboldmathnames\n\n% \\Referee % uncomment this for referee mode (double spaced)\n\n% \\onecolumn % enable one column mode\n% \\letters % for `letters' articles\n\\pagerange{0--0} % `letters' articles should use \\pagerange{Ln--Ln}\n\\pubyear{2000}\n\\volume{000}\n% \\microfiche{} % for articles with microfiche\n% \\authorcomment{} % author comment for footline\n\n\\begintopmatter % start the two spanning material\n\n\\title{Overmerging in N-body simulations}\n\\author{Eelco van Kampen}\n\\affiliation{Institute for Astronomy, University of Edinburgh, Royal\nObservatory, Blackford Hill, Edinburgh EH9 3HJ,\\ {\\tt [email protected]}}\n\\shortauthor{E.\\ van Kampen}\n\\shorttitle{Overmerging}\n\\acceptedline{Accepted ... Received ...; in original form ...}\n\n\\abstract {The aim of this paper is to clarify the notion and cause of\novermerging in N-body simulations, and to present analytical estimates\nfor its timescale. Overmerging is the disruption of subhaloes\nwithin embedding haloes due to {\\it numerical}\\ problems connected with\nthe discreteness of N-body dynamics. It is shown that the process responsible\nfor overmerging is particle-subhalo two-body heating.\n%Excessive softening worsens the problem.\nVarious solutions to the overmerging problem are discussed.}\n\n\\keywords {galaxies: evolution - dark matter - large-scale structure of Universe}\n\\maketitle % finish the two spanning material\n% \\Referee % uncomment this for referee mode\n\n\\section{Introduction}\n\nIn the study of the formation and evolution of large-scale structure in the\nuniverse, clusters of galaxies, galaxies, and many other gravitational systems,\nhaloes play an important r\\^ole.\nA {\\it halo}\\ is defined as a collapsed and virialized density maximum.\nA halo can contain several smaller haloes, denoted as {\\it subhaloes}.\nWe denote a halo that contains subhaloes as an {\\it embedding halo}.\nThe existence of subhaloes is an important issue in cosmology, especially for\ngalaxies, and groups and clusters of galaxies. For example,\nhierarchical structure formation scenarios for CDM-like spectra predict\nmany more dwarf galaxies (or satellites) than observed (Klypin et al.\\ 1999b,\nMoore et al.\\ 1999).\nAlso, a spiral galaxy cannot retain its disk if there is an high abundance\nof subhaloes within its halo (Moore et al.\\ 1999). Thus, the question\nis whether the initial density fluctuation spetrum is such that not many\ndwarf galaxies form in the first place, or that they are easily destroyed\nwithin our Galaxy, and hard to find outside it. On larger scale, clusters\nof galaxies do contain an abundance of subhaloes, i.e.\\ its member galaxies,\nwhich are often distorted and stripped, but probably not destroyed.\n\nN-body simulations are routinely used to model the formation, evolution,\nand clustering of galaxy and galaxy cluster haloes.\nHowever, the N-body simulation method does have its limitiations, and care\nshould be taken with the interpretation of the simulation results.\nOne such limitation arises from the use of particles to represent\nthe mass distribution whose evolution one tries to simulate.\nIf the physical mass distribution is effectively collisionless,\nas is often the case, the use of particles gives rise to artificial\ncollisional effects within the numerical mass distribution, especially\nthough two-body interaction. Two-body encounters between simulation\nparticles, either close or distant, deflect their orbits significantly,\nwhile they should behave like test particles, and respond only to the\nmean potential. This is especially a problem for subhaloes, which are\neasily destroyed in an N-body simulation with insufficient resolution\n(White et al.\\ 1987; Carlberg 1994; van Kampen 1995).\nWe use the term {\\it overmerging}\\ for the numerical processes that\nartificially merge haloes and subhaloes in an N-body model, usually by\ndisrupting the subhalo. Thus, the term {\\it merging}\\ only denotes\nmerging due to physical processes.\n\n\\beginfigure{1}\n{\\psfig{file=over.eps,width=8.5cm,silent=1}}\n\\caption{{\\bf Figure 1.} Graphical illustration of the main\nnumerical disruption processes that cause overmerging.\nOpen circles represent the 'cold' particles of an isolated\nhalo or a subhalo within an embedded halo, whose 'hot'\nparticles are indicated by filled circles.}\n\\endfigure\n\nHowever, there seems to be some confusion in the literature over the\nnature, cause, and importance of the overmerging problem.\nThis paper attempts to clarify the difference between the three most\nimportant two-body processes operating on subhaloes, and provide\nestimates for their associated timescales.\nThe first process is {\\it two-body evaporation}, which is an\n{\\it internal}\\ process operation within any halo or subhalo.\nIt is due to two-body interactions between the particles within the halo\nor subhalo. The second process is {\\it particle-subhalo two-body heating},\nwhich is the heating of `cold' subhaloes by particles from the `hot'\nembedding halo through two-body interactions.\nThe third process is {\\it particle-subhalo tidal heating}, where the subhalo\nis considered collisionless, and increases its kinetic energy through\ntidal interactions with particles from the embedding halo. All three\nprocess are illustrated in Fig.\\ 1.\n\nBesides the two-body processes, the use of {\\it softened}\\ particles, in order\nto minimize two-body effects, can cause overmerging as well by artificially\nenhancing physical processes like merging and disruption by tidal forces\n(van Kampen 1995; Moore et al.\\ 1996). Groups of softened particles are not\nas compact as real haloes, and their artificially larger sizes make N-body\ngroups more prone to tidal disruption.\n\nCarlberg (1994) proposed particle-subhalo two-body heating as the main\ncause for overmerging. He gave a timescale for this process, but no\nderivation. This was provided by van Kampen (1995).\nIt has been shown before (Carlberg 1994; van Kampen 1995) that the\ntwo-body heating time-scale for small subhaloes orbiting an embedding\nhalo is short enough to result in their complete destruction and dispersion.\nSubsequent authors, including Moore et al.\\ (1996) and Klypin et al.\\ (1999a),\nreferenced Carlberg (1994) as saying that `particle-halo heating'\nis at the root of the problem. Moore et al.\\ (1996) then claim that the\nprocess is not important for the resolution of the simulation performed by\nCarlberg (1994) because the timescale is too long.\nHowever, the process Moore et al.\\ (1996) actually describes and derives a\ntimescale for is a different one,\ndriven by tidal encounters between simulation particles and perfectly\ncollisionless subhaloes, while Carlberg (1994) and van Kampen (1995)\nclearly had a collisonal process in mind, driven by two-body encounters\nbetween individual subhalo particles and particles from the embedding halo.\nThis paper shows that the latter process has a much shorter timescale, and\ntherefore, along with excessive softening, is the main cause for overmerging.\n\n\\section{Two-body effects in N-body simulations}\n\nTwo-body effects become dominant for systems modelled by small numbers of\nparticles. This is usually quantified by the two-body relaxation timescale,\nwhich is defined as the time it takes, on average, for a particle to\nchange its velocity by of order itself. After this time a system is\ndenoted as {\\it relaxed}. The relaxation timescale is defined\nin terms of the {\\it half-mass radius}\\ $r$, the {\\it typical velocity}\\\n$v$ (usually taken to be equal to the velocity dispersion), and the\naverage change $\\Delta v$ per {\\it crossing time}\\ $r/v$:\n$$t_{\\rm relax}\\equiv {v^2 \\over (\\Delta v)^2} {r \\over v}\\ . \\eqno\\stepeq$$\n\\newcount\\timescaledefinition\n\\timescaledefinition=\\Eqnno\nFor an {\\it isolated}\\ virialized system of $N$ point particles, it is easy\nto show that this is of order $0.1 N/\\ln N$ crossing times (eg.\\ Binney \\& \nTremaine 1987). If the time interval one tries to cover for a particular\nproblem is larger than the two-body relaxtion timescale, the problem becomes\nartificially collisional.\n\nAlthough many systems are likely to endure physical mechanisms like violent\nrelaxation and phase mixing during some stage of their evolution, an obvious\nworry is that such physical mechanisms might not actually be important\nin a given situation, so that two-body interactions are very much unwanted\nas they might mimic the effects of physical mechanisms.\nA different problem is that a system might completely evaporate through\ntwo-body interactions.\n\nThe problem can be alleviated somewhat by softening\nthe particles, which reduces the two-body relaxation timescale to\n$0.1 N/\\ln \\Lambda$ crossing times (see van Kampen (1995) and references\ntheirein), where $\\Lambda={\\rm Min}(R/4\\epsilon, N)$, with $R$ the effective\nsize of the system, which we take to be twice the half-mass radius $r$,\nand $\\epsilon$ the softening length of the N-body particles.\nHowever, $\\epsilon$ is necessarily a function of both $N$ and $r$, as softened\nparticles should not overlap too much. Too large a choice for $\\epsilon$ will\nprevent particles from clustering properly and produce haloes which are too\nextended and too cold (that is, the velocity dispersion is too small).\nGiven that $N/2$ particles reside within $r$ by definition, the mean particle\nnumber density within $r$ is $3N/(8\\pi r^3)$. The maximum mean particle density\ndesirable is set by the minimum mean nearest neighbour distance for the\nparticles: $n_{\\rm max}=3/(4\\pi r^3_{\\rm nn})$. Most often used is Plummer\nsoftening, which just means that particles have a Plummer density\nprofile, $\\rho(r)\\sim(r^2+\\epsilon^2)^{5/2}$. The effective force\nresolution, defined as the separation between two particles for which\nthe radial component of the softened force between them is half its\nNewtonian value, is $\\approx 2.6\\epsilon$ for Plummer softening\n(Gelb \\& Bertschinger 1994), so we want $r_{\\rm nn}\\ga 2.6\\epsilon$,\nwhich gives $n_{\\rm max}\\approx 0.014/\\epsilon^3$.\nThus, we find a maximum realistic softening length\n$$\\epsilon \\approx {r\\over 2 N^{1\\over 3}}\\ . \\eqno\\stepeq$$\n\\newcount\\softeningnumber\n\\softeningnumber=\\Eqnno\nFor this $\\epsilon$ the relaxation time becomes $0.3 N/\\ln N$\ncrossing times, i.e.\\ three times larger than for the point particles case.\n\nEven though softening alleviates the problem of two-body effects somewhat,\nsoftened particle groups are more extended and less strongly bound (van Kampen 1995).\nThis makes them more vulnerable to two-body disruption processes, which are more\nefficient for larger subhaloes, as shown below.\nFurthermore, the timescales for {\\it physical}\\ disruption processes are effected.\nSubhalo-subhalo tidal heating has a timescale inversely proportional to the\nsubhalo size (van Kampen 2000), and is therefore slower, although the lower\nbinding energy might compensate for this.\n%Dynamical friction does not or weakly depend on subhalo size. \nTidal stripping and disruption will be artificially enhanced, however, because\nof the larger subhalo size and the weaker binding of the particles inside the\ngroup (van Kampen 1995).\nBecause the enhanced tidal disruption due to softening has the same net\neffect as two-body disruption, which is also enhanced due to the larger\nsubhalo size, the two disruption processes accelerate each other.\n%In order to examine which process is the most important, one can look at\n%simulations of the same matter distribution at different resolutions.\n%If disruption occurs at the same timescale for two different resolutions,\n%it is likely to be tidal, whereas if it is only seen to operate for the\n%lower resolution simulation, it must be two-body disruption.\n%Of the two, two-body disruption seems the dominant process (van Kampen 1995).\nIn the next section we derive two-body disruption timescales without taking\ninto account tidal disruption, and then treat these timescales as upper limits.\n\n\\section{Disruption timescales}\n\n\\subsection{Two-body evaporation}\n\nThis process is internal to haloes and subhaloes\nin other words, it is a self-disruption process. Two-body interactions\nbetween particles within the same (sub)halo change their orbits and\nvelocities, thus every once in a while the velocity will be larger \nthan the escape velocity, and a particle will `leak' out of the (sub)halo.\nThe timescale for this process is about a hundred times the relaxation\ntimescale (e.g.\\ Binney \\& Tremaine 1987),\n$$t_{\\rm dis}\\equiv 30 {N\\over\\ln N} {r \\over v}\n \\ , \\eqno\\stepeq$$\nso for small $N$ this becomes important.\nAs an example, for galaxy haloes, evaporation becomes an issue for $N<10$,\nas the crossing time for most galaxy haloes is larger than 0.2 Gyr,\nindependent of their mass.\n\nMoore et al. (1996) tested whether this process gets enhanced for\nsubhaloes within embedding haloes due to the influence of the mean\ntidal field of the embedding halo. They simulated a\ncollisional group of particles within a {\\it smooth}, and therefore\ncollisionless, isothermal system. They found that the evaporation\nrate was similar to that for an isolated group, and concluded\nthat {\\it \"relaxation effects are not important at driving mass loss\nfrom haloes within current simulations\"}.\nTheir conclusion is incorrect, however, as they did not consider\nthe particle-subhalo two-body heating process, which we discuss next.\n%Their numerical tests should have included a particle distribution\n%for the over-dense region as well, which would have heated the small\n%group into dissolution.\n\n\\subsection{Particle-subhalo two-body heating}\n\nParticles within a subhalo do not just interact amongst themselves\n(driving the evaporation process describe above), but also with\nthe particles of the embedding halo.\nAs the latter are usually hotter than those of the\nsubhalo, velocity changes to the subhalo particles will always\nbe positive. The process very much resembles the kinetic heating\nof a cold system that is introduced into a hot bath:\nan embedding halo `boils' the subhalo into dissolution.\nA derivation for the disruption timescale of this process is\ngiven by van Kampen (1995, his eq.\\ 15, which is erroneous by \na factor of two):\n$$t_{\\rm dis} \\approx {v_{\\rm s}^2 \\over v_{\\rm h}^2}\n {N_{\\rm h} \\over 12\\ln (r_{\\rm h}/2\\epsilon)} \n {r_{\\rm h} \\over v_{\\rm h}} \\ . \\eqno\\stepeq$$\n\\newcount\\disruptiontimescale\n\\disruptiontimescale=\\Eqnno\nHere $N$ denotes the number of particles,\nand the subscripts {\\rm h} and {\\rm s} denote embedding halo and subhalo\nrespectively. A similar expression was given earlier by\nCarlberg (1994, his eq.\\ 13 with his indices c and g swapped,\nno derivation given):\n$$t_{\\rm dis} \\approx {v_{\\rm s}^2 \\over v_{\\rm h}^2}\n {N_{\\rm h} \\over 8\\ln (r_{\\rm h}/\\epsilon)}\n {r_{\\rm h} \\over v_{\\rm h}}\\ . \\eqno\\stepeq$$\nWe can rewrite eq.\\ $(\\the\\disruptiontimescale)$, using eq.\\\n(\\the\\softeningnumber) and the virial theorem for both halo and\nsubhalo, as\n$$t_{\\rm dis} \\approx {N_{\\rm s} \\over 4 \\ln N_{\\rm h}}\n {r_{\\rm h} \\over r_{\\rm s}} {r_{\\rm h} \\over v_{\\rm h}} \n \\approx {N^{2\\over 3}_{\\rm s} \\over 8 \\ln N_{\\rm h}}\n {r^2_{\\rm h} \\over v_{\\rm h}} \\epsilon^{-1}\n \\ . \\eqno\\stepeq$$\n\\newcount\\distimescale\n\\distimescale=\\Eqnno\nThis timescale is shorter than that for two-body evaporation,\nby a factor of (van Kampen 1995)\n$$ 100 {v_{\\rm h}\\over v_{\\rm s}} {r_{\\rm s}^2 \\over r_{\\rm h}^2}\n {\\ln N_{\\rm h}\\over \\ln N_{\\rm s}}\\ , \\eqno\\stepeq$$\nwhere the virial theorem, $v^2\\sim N/r$, is used for both systems.\n\nBecause $r_{\\rm h}$ is at least several times $r_{\\rm s}$,\nthe disruption time (\\the\\distimescale) is at least\n$\\approx N_{\\rm s}/\\ln (N_{\\rm h})$ embedding halo crossing\ntimes, which covers the range $0.05-0.15 N_{\\rm s}$ crossing\ntimes for $N_{\\rm h}\\approx 10^3-10^9$. Thus, it is a much faster\nprocess than two-body evaporation.\n\n\\subsection{Particle-subhalo tidal heating}\n\nA different cause for overmerging was proposed by Moore et al.\\\n(1996): the tidal heating of subhaloes by particles of their embedding\nhaloes. Subhaloes are taken to be {\\it collisionless}, and get\ndisrupted through an increase of their internal kinetic energy\nby tidal distortion from passing N-body particles, which are artificially\nlarge as compared to the true dark matter halo particles.\n\nThe time-scale for this process as given by Moore et al.\\ (1996;\ntheir eq.\\ (3), which is eq.\\ (7-67) of Binney \\& Tremaine 1987 with\nthe assumption that the {\\it r.m.s.}\\ radius is equal to the half-mass\nradius) reads\n$$t_{\\rm dis} \\approx 0.03\n {v_{\\rm h} \\over G n_{\\rm p}}\n {m_{\\rm s}\\over m^2_{\\rm p}}\n {r^2_{\\rm p}\\over r^3_{\\rm s}}\\ , \\eqno\\stepeq$$\n\\newcount\\tdismoore\n\\tdismoore=\\Eqnno\nwhere the subscript p stands for {\\it perturber}. The perturber is an\nN-body particle of the embedding halo with mass $m_{\\rm p}$ and size\n$r_{\\rm p}$, at a distance $q$ from the centre of the embedding halo.\nNote that the impulse approximation implies\n${v^2 / \\Delta v^2} = {E / \\Delta E}$.\nMoore et al.\\ (1996) then assume the embedding halo to be isothermal,\nso that $n_{\\rm p} \\approx v^2_{\\rm h}/2 \\pi G m_{\\rm p} q^2$,\nset the half-mass radius of the subhalo equal to the tidal radius,\n$q v_{\\rm s}/ (3 v_{\\rm h})$, and assume the subhalo to be virialized.\nThis gives\n$$t_{\\rm dis} \\approx 94 \\Bigl({v_{\\rm h}\\over 1000\\ {\\rm km\\ s}^{-1}}\\Bigr)\n \\Bigl({r_{\\rm p}\\over 10\\ {\\rm kpc}} \\Bigr)^2\n \\Bigl({10^9 {\\rm M}_{\\sun} \\over m_{\\rm p}}\\Bigr) {\\rm Gyr}\\ . \\eqno\\stepeq$$\n\\newcount\\mooretime\n\\mooretime=\\Eqnno\n\nRelation (\\the\\tdismoore) was originally derived by Spitzer (1958) for\nthe disruption by giant molecular clouds of open star clusters.\nAn important assumption in its derivation is the tidal approximation,\nwhich is only valid for impact parameters $b>b_{\\rm min}$.\nAguilar \\& White (1985) found that $b_{\\rm min}$ should be at least\nfive times the size of {\\it both} the perturber and the perturbed system.\nBinney \\& Tremaine (1987) use the tidal approximation down to\n$b_{\\rm min}=r_{\\rm cluster}<r_{\\rm cloud}$, and introduce a correction\nfactor $g=3$ to take into account the encounters for which the tidal\napproximation fails.\n\nMoore et al.\\ (1996) take this result and apply it to tidal interactions\nbetween the N-body particles of an embedding halo and its subhaloes theirin.\nThus, they set $r_{\\rm p}$ to the gravitational softening length $\\epsilon$.\nHowever, as the size of the perturbers is now {\\it smaller} than the size\nof the perturbed subhaloes, the tidal approximation, even with the correction\nfactor $g$ included, is only valid for $b>r_{\\rm s}$. Therefore, setting\n$r_{\\rm p}=\\epsilon$ in eq.\\ (\\the\\mooretime) is incorrect; instead, one\nshould set $r_{\\rm p}=r_{\\rm s}$.\nThis means that the timescale becomes $(r_{\\rm s}/\\epsilon)^2$ times longer.\nUsing eq.\\ (\\the\\softeningnumber), the time-scale becomes $4 N^{2/3}_{\\rm s}$\ntimes larger than proposed by Moore et al.\\ (1996).\n\nBut there is another change to be made, as it is in fact the close\nencounters of halo particles that do the most damage to the subhaloes.\nAccording to Binney \\& Tremaine (1987), a good estimate for\nthe disruption timescale can be had from an interpolation between the\napproximations for tidal encounters and for penetrating ($b=0$) encounters. \nFor each tidal encounter (Binney \\& Tremaine 1987, their eq.\\ 7-55),\n$$(\\Delta E)_{\\rm tid} = \n {4 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over 3 v^2_{\\rm h}}\n {1\\over b^4} \\ , \\eqno\\stepeq$$\nwhile for each penetrating encounter (Binney \\& Tremaine 1987, their\neq.\\ 7-57)\n$$(\\Delta E)_{\\rm pen} = {4 \\pi G^2 m^2_{\\rm p}\\over v^2_{\\rm h}}\n \\int_0^{\\infty} {R^3\\over (R^2+\\epsilon^2)^2} \\Sigma_{\\rm s}(R) dR\n \\ . \\eqno\\stepeq$$\nIf the perturbed subhalo is an isothermal sphere, i.e.\\ \n$\\Sigma_{\\rm s}(R)=v^2_{\\rm s}/(6GR)\\approx 0.2m_{\\rm h}/(r_{\\rm h} R)$, we find\n$$(\\Delta E)_{\\rm pen} \\approx\n {2 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over v^2_{\\rm h}}\n {1 \\over \\epsilon r^3_{\\rm s}} . \\eqno\\stepeq$$\nInterpolating contributions from the tidal and penetrating encounters, i.e.\\\n$$\\Delta E = {4 G^2 m^2_{\\rm p} m_{\\rm s} r^2_{\\rm s}\\over 3 v^2_{\\rm h}}\n {1 \\over b^4+{2\\over 3}\\epsilon r^3_{\\rm s}}\\ , \\eqno\\stepeq$$\nfinally allows us to integrate over {\\it all}\\ encounters.\nFollowing the procedure of Binney \\& Tremaine (1987), we simply find\neq.\\ (\\the\\tdismoore) with $r_{\\rm p}$ ($=\\epsilon$) replaced by\n$0.52(\\epsilon r^3_{\\rm s})^{1/2}$. Following Moore et al.\\ (1996) again\nwe get the same functional form as eq.\\ (\\the\\mooretime), but the timescale\nis approximately $2(r_{\\rm s}/\\epsilon)^{3/2}\\approx 5 N^{1/2}_{\\rm s}$\ntimes {\\it longer}\\ than estimated by Moore et al.\\ (1996).\n\nBy definition, $m_{\\rm s}/m_{\\rm p}=N_{\\rm s}$, and we use\neq.\\ (\\the\\softeningnumber) to get\n$$t_{\\rm dis} \\approx 4.5 N^{5\\over 6}_{\\rm s}\n {r_{\\rm h} \\over r_{\\rm s}}\n {r_{\\rm h} \\over v_{\\rm h}}\n \\approx 2.2 N^{1\\over 2}_{\\rm s}\n {r^2_{\\rm h} \\over v_{\\rm h}} \\epsilon^{-1}\n \\ . \\eqno\\stepeq$$\n\\newcount\\tdisNs\n\\tdisNs=\\Eqnno\nAs $r_{\\rm h}$ is at least a few times $r_{\\rm s}$, the disruption\ntime is at least $20 N^{5/6}_{\\rm s}$ embedding halo crossing times.\nIt is also a factor of $18 N^{-1/6}_{\\rm s} \\ln N_{\\rm h}\\approx 100$ times\nlonger than the particle-subhalo two-body disruption timescale.\n\n\\section{Conclusions and discussion}\n\nOvermerging is the numerical disruption of subhaloes within embedding\nhaloes. Of the three main two-body disruption processes, particle-subhalo\ntwo-body heating is clearly identified as the cause for overmerging.\nIts timescale is shown to be much shorter than that for the two other\nprocesses, two-body evaporation and particle-subhalo tidal heating.\nNote that softened particles form into more extended subhaloes than is\nrealistic, so they are more vulnerable to these disruption processes\n(van Kampen 1995), and to possible physical disruption processes as well.\n\nRecently several research groups used simulations with a very high resolution\nin order to resolve the overmerging problem (Klypin et al.\\ 1999a;\nGhinga et al.\\ 1998, 1999; Moore et al.\\ 1999).\nUnfortunately, different group finders and different definitions for disruption\ntimes were used, so a direct comparison of the results is not straightforward.\nStill, the consensus is that increasing the number of particles overcomes,\nat least partially, the overmerging problem. However, the resolution needs to be\nrather high:\n%Klypin et al.\\ (1999a) find that the larger subhaloes survive for resolutions\n%of a few kpc and 10$^8$-10$^9$ $M_\\odot$ respectively.\nfor N-body simulations on a cosmological scale, this requires the use of at\nleast $10^9$ particles, which is not very practical.\nFurthermore, for the smallest groups the overmerging problem simply remains.\n\nAnother option is to include a baryonic component. With the addition\nof dissipative particles, haloes should be more compact and have a higher\ncentral density for the same numbre of particles.\nHowever, as Klypin et al.\\ (1999a) remark, there is a limit to this as some\nfraction of the baryons tend to end up in rotationally supported disks.\nA more practical problem with dissipative particles is the actual simulation\ntechniques needed, which usually is some form of smoothed particle\nhydrodynamics (SPH). The resolution of SPH codes is typically not as high as that\nof N-body codes, so for the purpose of resolving the overmerging problem\nit is not a useful alternative at present.\n\nA third option is to use halo particles, which prevents overmerging by\nconstruction (van Kampen 1995). The idea is that a group of particles that\nhas collapsed into a virialised system is replaced by a single halo particle.\nLocal density percolation, also called adaptive friends-of-friends,\nis adopted for finding the groups.\nThis is designed to identify the embedded haloes that the \ntraditional percolation group finder links up with their parent halo.\nBy applying the algorithm several times during the evolution,\nmerging of already-formed galaxy haloes is taken into account as well.\nOnce a halo particle is formed, more N-body particles will group around\nit at later times. If such a group can virialize, it is replaced by a\nmore massive halo particle. This will usually happen in the field.\nHowever, for halo particles that end up in overdense regions, the\nparticles that swarm around a halo particles will be stripped quite\nrapidly.\n\nOnce the overmerging problem is resolved down to the subhalo mass-scale\none is interested in, the physical processes can be studied. \nThis is becoming feasible for current simulations.\nHowever, whether the physical processes themselves are properly modelled\nusing N-body simulations has yet to be proven. The problem of artificially\nlarge subhaloes due to softening needs to be solved, for example. Another\nproblem might be the modelling of dynamical friction, which requires a very\nsmooth distribution of particles in the embedding halo in order to produce\nthe wake that generates the drag force.\n\n\\section*{ACKNOWLEDGEMENTS}\n\nI am grateful to John Peacock and Ben Moore for useful discussion,\nsuggestions and comments.\n\n\\section*{REFERENCES}\n\n\\beginrefs\n\n\\bibitem Aquilar L.A., White S.D.M., 1985, ApJ, 295, 374\n%\n\\bibitem Allan A.J., Richstone D.O., 1988, ApJ, 325, 583\n\n\\bibitem Binney J., Tremaine S., 1987, Galactic Dynamics, Princeton\n\n\\bibitem Carlberg R.G., 1994, ApJ, 433, 468\n\n\\bibitem Gelb J., Bertschinger E., 1994, ApJ, 436, 467\n\n\\bibitem Ghigna S., Moore B., Governato F., Lake G., Quinn T., Stadel J.,\n\t1998, MNRAS, 300, 146\n\n\\bibitem Ghigna S., Moore B., Governato F., Lake G., Quinn T., Stadel J.,\n\t1999, astro-ph/9910166\n%\n\\bibitem Heisler J., White S.D.M., 1990, MNRAS, 243, 199\n\n\\bibitem Klypin A.A., Gottl\\\"ober S., Kravtsov A.V., Khokhlov A.M., 1999a,\n\tApJ, 516, 530\n\n\\bibitem Klypin A.A., Kravtsov A.V., Valenzuela O., Prada F., 1999b,\n\tastro-ph/9901240\n%\n\\bibitem Lin D.N.C., Tremaine S., 1983, ApJ, 264, 364\n%\n\\bibitem Mateo M., 1998, ARA\\&A, 36, 435\n\n\\bibitem Moore B., Katz N., Lake G., 1996, ApJ, 457, 455\n\n\\bibitem Moore B., Governato F., Quinn T., Stadel J., Lake G., 1998,\n\tApJ, 499, L5\n%\n\\bibitem Moore B., Lake G., Quinn T., Stadel J., 1999, MNRAS, 304, 465\n\n\\bibitem Moore B., Ghigna S., Governato F., Lake G., Quinn T., Stadel J.,\n\tTozzi P., 1999,\tApJ, 524, L19\n%\n\\bibitem Saslaw W.C., 1985, Gravitational physics of stellar and galactic\n%\tsystems, Cambridge\n\n\\bibitem Spitzer L., 1958, ApJ, 127, 17\n%\n\\bibitem Tormen G., Diaferio A., Syer D., 1998, 299, 728\n%\n\\bibitem Tremaine S., 1976, ApJ, 203, 72\n\n\\bibitem van Kampen E., 1995, MNRAS, 273, 295\n%\n\\bibitem van Kampen E., Katgert P., 1997, MNRAS, 289, 327\n%\n\\bibitem van Kampen E., Jimenez R., Peacock J.A., 1999, MNRAS, 310, 43\n"
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ChaMP and the High Redshift Quasars in X-rays
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"author": "S. Mathur\\altaffilmark{1}"
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"name": "reform.tex",
"string": "% PSAMPLE2.TEX -- PASP Conference Proceedings macro package tutorial paper.\n\n% Lines starting with \"%\" are comments; they will be ignored by LaTeX.\n\n% This is a comprehensive example, meaning thyat we have made use of each\n% of the capabilities of the LaTeX + the PASP macro package that we think\n% you may need to use. If you want to see a \"base-bones\" sample paper,\n% take a look at psample1.tex.\n\n% The first item in a LaTeX file must be a \\documentstyle command to\n% declare the overall style of the paper.\n\n\\documentstyle[11pt,paspconf,epsf,psfig]{article}\n\n\\markboth{Mathur, et al.}{ChaMP at Hi-z}\n\\setcounter{page}{1}\n\n% There is no more markup in the \"preamble\" for paspconf papers. You should\n% not define any \"personal\" LaTeX commands, in the preamble or anyplace else,\n% for that matter. Use only standard LaTeX commands or the additional ones\n% provided as part of the paspconf package.\n%\n% Now start with the real material for the paper, which is indicated with\n% \\begin{document}. Following the \\begin{document} command is the \"front\n% matter\" for the paper, viz., the title, author and address data, the\n% abstract, etc.\n\n\\begin{document}\n\n\\title{ChaMP and the High Redshift Quasars in X-rays}\n\n\\author{S. Mathur\\altaffilmark{1}}\n\\affil{Harvard Smithsonian Center for Astrophysics\n Cambridge, MA 02138}\n\\author{H. Marshall\\altaffilmark{1}}\n\\affil{MIT, Cambridge, MA 02139}\n\\author{N. Evans\\altaffilmark{1}, P. Green\\altaffilmark{1} and B.\nWilkes\\altaffilmark{1} }\n\\affil{Harvard Smithsonian Center for Astrophysics\n Cambridge, MA 02138}\n\n% Notice that some of these authors have alternate affiliations, which\n% are identified by the \\altaffilmark after each name. The actual alternate\n% affiliation information is typeset in footnotes at the bottom of the\n% first page, and the text itself is specified in \\altaffiltext commands.\n% There is a separate \\altaffiltext for each alternate affiliation\n% indicated above.\n\n\\altaffiltext{1}{The Chandra Multiwavelength Project (ChaMP) is an independent\nscientific collaboration for followup studies of serendipitous X-ray\nsources in Chandra X-ray images. The ChaMP Web site is\nhttp://hea-www.harvard.edu/CHAMP.}\n%\\altaffiltext{2}{Society of Fellows, Harvard University}\n%\\altaffiltext{3}{Patron, Alonso's Bar and Grill}\n\n% The abstract is entered in a LaTeX \"environment\", designated with paired\n% \\begin{abstract} -- \\end{abstract} commands. Other environments are\n% identified by the name in the curly braces.\n\n% Poster authors ONLY may omit the abstract in order to gain a little\n% more page space for the text of the poster.\n\n\\begin{abstract}\n{\\it Chandra} X-ray Observatory, (formerly known as AXAF), will\n observe down to the\n flux limit of 2$\\times 10^{-16}$ erg~s$^{-1}$~cm$^{-2}$. In its first\n year of operation {\\it Chandra}'s CCD detectors will observe over 1500\n quasars serendipitously in the soft (0.5--3.5 keV) band.\n Over 200 quasars will be detected in X-rays in the redshift\n range $3<z<4$ and over 400 quasars in $2<z<3$. This will enable us to\n determine the high redshift X-ray luminosity function. This is the\n contribution by unabsorbed sources only. The total numbers would be\n larger by $\\sim 60$\\%.\n\n\\end{abstract}\n\n% Keywords should be included, but they are not printed in the hardcopy.\n\n\\keywords{globular clusters,peanut clusters,bosons,bozos}\n\n% That's it for the front matter. On to the main body of the paper.\n% We'll only put in tutorial remarks at the beginning of each section\n% so you can see entire sections together.\n\n\\section{Introduction}\n\nNASA's {\\it Chandra} X-ray Observatory was\nlaunched on July 23, 1999. The {\\it Chandra} Multiwavelength Project (ChaMP)\nwill combine radio to X-ray observations of serendipitous {\\it\nChandra} sources, with emphasis on optical identification.\nThe ChaMP is superior to previous X-ray surveys because of (1)\nunprecedented X-ray positional accuracy\n ($\\sim 1^{\\prime\\prime}$), (2) X-ray flux limits 20 times deeper than current\n wide area surveys (down to $f(0.5-3.5 keV)\\sim 2\\times 10^{-16}$\nerg~s$^{-1}$~cm$^{-2}$), (3) larger sky coverage ($\\sim$ 8 deg$^2$)\nper year than current deep surveys.\n%For details of ChaMP see: http://hea-www.harvard.edu/CHAMP.\n\n\\section{Prediction of Redshift Distribution of Quasars in ChaMP Fields}\n\n{\\bf The X-ray Luminosity Function} at $z=0$ is described as\n\n$$\\Phi(L_X)=\\Phi^{\\star}_1 L^{-\\gamma1}_{44} ~~~~for ~L<L^{\\star}(0)$$\n\n$$\\Phi(L_X)=\\Phi^{\\star}_2 L^{-\\gamma2}_{44} ~~~~for\n{}~L>L^{\\star}(0)$$\\\\\n\n\\noindent\nwhere L$_{44}$ is the X-ray luminosity in $10^{44}$\nerg~s$^{-1}$. The redshift evolution of the luminosity\nfunction is characterized by\n\n$$ L_{X}(z)= L_{X}(0) (1+z)^k $$\n\nContinuity of the luminosity function at the break luminosity requires\nthat\n\n$$\\Phi^{\\star}_1=\\Phi^{\\star}_2 L^{\\star (\\gamma1-\\gamma2)}_{44} $$\n\nThe total number $N$ of quasars in the sample is obtained by\nintegrating the luminosity function over luminosity and volume, i.e.,\n\n$$ N=\\int\\!\\int \\Phi(L_X, z)\\Omega(L_X, z) dV(z) dL_X $$\n\nHere $\\Omega(L_X, z)$ is the solid angle covered by the survey as a\nfunction of redshift and luminosity. The parameters of the X-ray\nluminosity function determined by Boyle et al. (1993) are as\nfollows: $\\gamma1=1.7 \\pm 0.2$, $\\gamma2=3.4 \\pm 0.1 $, $\\log\nL^{\\star}(0)=43.84$, $\\Phi^{\\star}_1=5.7 \\times 10^{-7} Mpc^{-3}\n(10^{44} erg~ s^{-1})^{\\gamma1-1}$. Following Comastri et al. (1995),\nwe have used k=2.6 and increased the the normalization\n$\\Phi^{\\star}_1$ by 20\\%.\n\n{\\bf The X-ray logN-logS Curve}: Using the above luminosity function\nwe derived the number density of\nquasars as a function of observed flux. The\nluminosity function was\nintegrated over the luminosity range $10^{42}<L_X<10^{48}$ erg s$^{-1}$\nand the redshift range $0<z<4$. H$_0=50$ and q$_0=0$ were assumed\nthroughout. The predicted logN-logS curve is shown in\n figure 1.\n\n\\begin{figure}[h]\n%\\epsscale{0.80}\n\\psfig{figure=smathur-fig1.ps,height=2in,width=5in}\n\\caption{The predicted number counts in the soft band for unabsorbed\nquasars.}\n%\\caption{The total sky coverage of ChaMP fields as a\n%function of flux limit in the soft band.}\n\\end{figure}\n\n\nSince the unabsorbed sources dominate at the faint end in the soft X-ray\nrange, and since they are\nlikely to be observed at high redshift, in the present analysis we\nwill concentrate on unabsorbed sources only. The absorbed sources\nwould contribute an additional $\\sim$ 60\\% (Comastri et al. 1995),\nmaking the total number\nconsistent with the extrapolation of the empirical determination of logN-logS\n(Hasinger\net al. 1993). The flux of unabsorbed\nquasars is given by $f \\propto E^{-\\alpha}$ and in the soft X-ray band,\n$\\alpha$ is typically 1.3.\n\n{\\bf The ChaMP Sky Coverage}: The ChaMP Cycle 1\nconsists of 85 extragalactic fields, |b|$>20^{o}$. From all the Chandra\ncycle 1 fields we have excluded (1) deep fields of PI survey\nobservations, (2) fields with extended sources \\& planetary targets,\n(3) ACIS sub-arrays and continuous clocking modes. See figure 2 for\nChaMP sky coverage as a function of flux limit.\n\n\\begin{figure}[h]\n%\\epsscale{0.80}\n\\psfig{figure=smathur-fig2.ps,height=2in,width=4in,angle=90}\n%\\vspace*{-1.5in}\n\\caption{The total sky coverage of ChaMP fields as a\nfunction of flux limit in the soft band.}\n\\end{figure}\n\n{\\bf Cumulative Number Distribution in ChaMP:} Integrating the\npredicted logN-logS over the ChaMP sky coverage, we\nobtained the cumulative number distribution of quasars in the ChaMP\nfields (figure 3). The total number in soft band is\n expected to be over 1500 for unabsorbed sources and over 2500 total.\n\n\\begin{figure}[h]\n%\\epsscale{0.80}\n\\psfig{figure=smathur-fig3.ps,height=2in,width=5in}\n\\caption{Expected cumulative source counts. Unabsorbed sources only.}\n\\end{figure}\n\n{\\bf Predicted Redshift Distribution:} The histogram (figure 4) shows the\npredicted number distribution of quasars\nin ChaMP fields. Over 200 quasars will be detected in the redshift\nrange $3<z<4$ and over 400 quasars in $2<z<3$.\n\n\\begin{figure}[h]\n%\\epsscale{0.80}\n\\psfig{figure=smathur-fig4.ps,height=2in,width=3in}\n\\caption{Redshift distribution of the unabsorbed sources expected to\nbe detected in ChaMP fields.}\n\\end{figure}\n\n%\\newpage\n\\section{Comparison with Previous X-ray Surveys}\n\n\\begin{table}[h]\n\\begin{tabular}{|lrr|}\n\\hline\\hline\nSurvey & Total number of Sources & Quasars at $z>2$ \\\\\n\\hline\nEMSS & 835 & $<5$ \\\\\n(Gioia et al.)& & \\\\\nROSAT Deep & 661 & 12 \\\\\n(Hasinger et al.)& & \\\\\nROSAT & 89 & $<10$ \\\\\n(Boyle et al.)& & \\\\\nChaMP & $>1500$ & $>600$\\\\\n(soft band, unabsorbed)& & \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{table}\n\nWe will be able to determine the X-ray luminosity function and its\nredshift evolution with unprecedented accuracy.\\\\\n\n\n% Now comes the reference list. Since we typed out the citations ourselves,\n% the reference list is enclosed in a \"references\" environment. Each\n% new reference begins with a \\reference command which sets up the proper\n% indentation. Typography that may be required in the reference list by\n% the editorial staff must be included by the author.\n%\n% Observe the \"standard\" order for bibliographic material: author name(s),\n% publication year, journal name, volume, and page number for articles.\n% Some journal names are available as macros; see the WGAS markup\n% instructions for a listing of which ones have been \"macro-ized\".\n% Note the use of curly braces to delimit the font changes: it is essential\n% that this be done to limit the scope of the font declaration.\n%\n% There is no need to engage in any other typographic manipulation.\n\n\\begin{references}\n\\reference Boyle, B., Griffiths, R., Shanks, T., Stewart, G., \\&\n Georgantopoulus, I. 1993, MNRAS, 260, 49\n\\reference Comstri, A., Setti, G., Zamorani, G., \\& Hasinger, G. 1995,\n A\\&A, 296, 1\n\\reference Gioia et al. 1990, ApJS, 72, 567\n\\reference Hasinger, G. et al. 1993, A\\&A, 275, 1\n\\end{references}\n\n\\vspace{0.2in}\nIt's my pleasure (SM) to thank A. Comastri for useful discussions. This\nwork is supported in parts by NASA grant NAG5-3249 (LTSA).\n\n% That's all, folks.\n%\n% The technique of segregating major semantic components of the document\n% within \"environments\" is a very good one, but you as an author have to\n% come up with a way of making sure each \\begin{whatzit} has a corresponding\n% \\end{whatzit}. If you miss one, LaTeX will probably complain a great\n% deal during the composition of the document. Occasionally, you get away\n% with it right up to the \\end{document}, in which case, you will see\n% \"\\begin{whatzit} ended by \\end{document}\".\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002029
|
High-resolution simulations and visualization of protoplanetary disks
|
[
{
"author": "Pawe{\\l} Cieciel\\c{a}g"
},
{
"author": "Tomasz Plewa"
},
{
"author": "Micha{\\l} R\\'o\\.zyczka"
}
] |
A problem of mass flow in the immediate vicinity of a planet embedded in a protoplanetary disk is studied numerically in two dimensions. Large differences in temporal and spatial scales involved suggest that a specialized discretization method for solution of hydrodynamical equations may offer great savings in computational resources, and can make extensive parameter studies feasible. Preliminary results obtained with help of Adaptive Mesh Refinement technique and high-order explicit Eulerian solver are presented. This combination of numerical techniques appears to be an excellent tool which allows for direct simulations of mass flow in vicinity of the accretor at moderate computational cost. In particular, it is possible to resolve the surface of the planet and to model the process of planet growth with minimal set of assumptions. Some issues related to visualization of the results and future prospects are discussed briefly.
|
[
{
"name": "dppn.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n%\n%\n%\n\\markboth{Cieciel\\c{a}g, Plewa, R\\'o\\.zyczka}\n{High-resolution simulations and visualization of protoplanetary disks}\n\n\\pagestyle{myheadings}\n\n\\begin{document}\n\\title{High-resolution simulations and visualization of protoplanetary\ndisks}\n\\author{Pawe{\\l} Cieciel\\c{a}g, Tomasz Plewa, Micha{\\l} R\\'o\\.zyczka}\n\\affil{Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw,\nPoland}\n%\n%\n%\n\\begin{abstract}\n\nA problem of mass flow in the immediate vicinity of a planet embedded\nin a protoplanetary disk is studied numerically in two dimensions.\nLarge differences in temporal and spatial scales involved suggest that\na specialized discretization method for solution of\nhydrodynamical equations may offer great savings in computational\nresources, and can make extensive parameter studies\nfeasible. Preliminary results obtained with help of Adaptive Mesh\nRefinement technique and high-order explicit Eulerian solver are\npresented. This combination of numerical techniques appears to be an\nexcellent tool which allows for direct simulations of mass flow in\nvicinity of the accretor at moderate computational cost. In\nparticular, it is possible to resolve the surface of the planet\nand to model the process of planet growth with minimal set of\nassumptions. Some issues related to visualization of the results and\nfuture prospects are discussed briefly.\n\n\\end{abstract}\n%\n%\n%\n\\section{The Method}\n%\n%\n%\nExtremely small temporal and spatial scales involved in the problem of\naccretion onto a protoplanet necessitate the use of nonuniform\ndiscretization in the vicinity of the accretor. In our study we used\nadaptive mesh refinement (AMR) method combined with a high-resolution\nGodunov-type advection scheme ({\\sc amra}, Plewa \\& M\\\"uller\n2000). The AMR discretization scheme follows the approach of Berger\nand Colella (1989). The computational domain is covered by a set of\ncompletely nested {\\em patches} occupying {\\em levels}. The levels\ncreate a refinement hierarchy. As one moves toward higher levels, the\nnumerical resolution increases by a prescribed integer factor\n(separate for every direction). The net flow of material between\npatches at different levels is carefully accounted for in order to\npreserve conservation properties of hydrodynamical equations.\nBoundary data for child patches are either obtained by parabolic\ntwo-dimensional conservative interpolation of parental data or set\naccording to prescribed boundary conditions.\n\nHydrodynamical equations are solved with the help of the Direct\nEulerian Piecewise-Parabolic Method (PPMDE) of Colella \\& Woodward\n(1984), as implemented in {\\sc herakles} solver (Plewa \\& M\\\"uller\n2000). Simulations have been done in spherical polar coordinates in a\nframe of reference corotating with the protoplanet. {\\sc herakles}\nguarantees exact conservation of angular momentum which is\nparticularly important in numerical modeling of disk accretion\nproblems. The use of its multifluid option with tracer materials\ndistributed within disk (not presented here) allows to identify the\norigin of the material accreted onto protoplanet. The {\\sc amra} code\nis written purely in FORTRAN 77 and has been successfully used on both\nvector supercomputers and superscalar cache-oriented workstations. Its\nparallelization on shared memory machines exploits microtasking\n(through the use of vendor-specific directives) or the OpenMP\nstandard.\n%\n%\n%\n\\section{Simulation setup}\n%\n%\n%\nThe computational domain extends from 0.25 to 2.5 radii of the planet's\norbit. We employ 7 levels with refinement ratios ranging from (2,4)\nto (4,4). The base level contains the protoplanetary (circumstellar)\ndisk while the 7th level contains the planet and its immediate\nvicinity. The base grid consist of $128\\times128$ cells uniformly\ndistributed in $r$ and $\\theta$. The effective resolution at the 7th\nlevel is $131072\\times524288$ in $r$ and $\\theta$, respectively. The\ntopmost five levels are schematically shown in Figure \\ref{f:levels}.\n%\n%\n%\n\\begin{figure}\n%%%\\plotone{levs-tmp.ps}\n%\\vspace{4in}\n\\plotfiddle{levs.epsf}{4in}{0}{40}{40}{-110}{0}\n\\caption{Breakup of the finest five levels of the refinement hierarchy.}\n\\label{f:levels}\n\\end{figure}\n%\n%\n%\nWhite lines are boundaries of the patches. There are 1, 1, 1, 1, 12, 4\nand 49 patches at levels 1-7, respectively. The structure of the grid\nat level 7 is shown in Figure \\ref{f:zoom-seq}f\n%\n%\n%\n\\begin{figure}\n%\\vspace{7.5in}\n%\\plotone{zoom-seq.epsf}\n\\plotfiddle{zoom-seq-6.epsf}{7.5in}{0}{65}{65}{-170}{0}\n\\caption{Surface density distribution in the final model (frames (a)-(e)) and the\ndistribution of grid cells at level 7 in the vicinity of the\nplanet (frame (f)). There are $\\sim 8$ grid cells in the radius of the planet.}\n\\label{f:zoom-seq}\n\\end{figure}\n%\n%\n%\nwith individual cell boundaries drawn with white lines (the dark blue\ncircle shows size of the planet).\n%\n%\n%\n\\section{Physical model}\n%\n%\n%\nThe simulation is initialized with a Keplerian disk. Originally the\ndisk has a mass of 0.01 M$_{\\sun}$, constant $h/r$ ratio of 0.05 and\nsurface density proportional to $r^{-1/2}$. The temperature is\na fixed function of $r$ throughout the simulation. There is no explicit\nviscosity in the disk. At the outer and inner boundary of the base\ngrid the gas is allowed to flow freely from the computational\ndomain. No inflow is allowed for. The accretion onto the planet is\naccounted for in a very simplified way. At every time step the mean\nvalue of the density within two planetary radii is calculated, and\nwhenever it is higher then a preset value, the excess gas is removed.\nAt $t=0$ a planet of one Jupiter mass in inserted into the disk on a\ncircular orbit. The radius of the orbit and the mass of the planet\nremain constant throughout the simulation. The disk is allowed to\nevolve for 100 planetary orbits. A gap is cleared in it, and a\nsecondary, circumplanetary disk is formed.\n\nThe sequence of surface plots in Figure \\ref{f:zoom-seq} shows the\nfinal structure of both disks (the surface density distribution is\ndisplayed). The red peak in Figure \\ref{f:zoom-seq}a is the\nunresolved image of the very dense circumplanetary disk. We have been able\nfor the first time to see the details of the latter (Figures\n\\ref{f:zoom-seq}(c)-d). The streams of gas flowing across the gap from\nleft and right edge of the frame (light blue) collide with the outer\npart of the circumplanetary disk. The collision regions (green wedges) bear\nstrong resemblance to hot spots in cataclysmic binaries. In every\nregion two strong shock waves are excited, one of them propagating\ninto the stream, and the other into the disk. The shocked gas flows\nfrom the collision region along a loosely wound spiral towards the\nplanet ((Figure \\ref{f:zoom-seq}e). This picture is significantly more\ndetailed than the one recently published by Lubow, Seibert, \\&\nArtymowicz (2000). Streamlines of the flow around the planet are shown\nin Figure \\ref{f:streamlines},\n%\n%\n%\n\\begin{figure}\n%\\vspace{3.5in}\n\\plotfiddle{streamlines.epsf}{3.5in}{0}{45}{45}{-130}{0}\n%%%\\plotone{streamlines.epsf}\n\\caption{Streamlines of the flow near the circumplanetary disk.}\n\\label{f:streamlines}\n\\end{figure}\n%\n%\n%\nand they are in good accordance with those of Lubow et al.\n\nOur simulation is of preliminary nature, and its sole purpose is to\ndemonstrate the capabilities of {\\sc amra}. Currently, we are\nimproving the physics of the model. One of the problems we are going\nto attack is the calculation of the accurate value of the\ngravitational torque from the disk onto the planet in the phase\npreceding gap formation.\n%\n%\n%\n\\section{Visualization}\n%\n%\n%\nTo visualize the complicated {\\sc amra} output, we have chosen the\nAVS/Express environment for visual programming. It allows the user to\nquickly built simple applications employing standard library\nmodules. Advanced users can develop their own, highly specialized\nmodules and applications. Our {\\sc amra}-visualization application\n({\\sc visa}) is partly based on modules written by Favre, Walder, \\&\nFollini (1999), which have been substantially modified, and partly on\nour own modules. A screenshot of {\\sc visa} is shown in Figure\n\\ref{f:visa}.\n%\n%\n%\n\\begin{figure}\n%%%\\plotone{VISA.epsf}\n%\\vspace{3.5in}\n\\plotfiddle{VISA.epsf}{3.5in}{0}{45}{45}{-160}{0}\n\\caption{A screenshot of the {\\sc visa} application.}\n\\label{f:visa}\n\\end{figure}\n%\n%\n%\nThe panel and the viewer are contained in the two topmost windows,\nwhile the bottom window contains the AVS/Express programming\nplatform. Currently we are able to read the AMR data, extract\ncomponents, perform mathematical operations on data sets and\ncoordinates, extract any subset of levels or patches, and apply to\nthem various visualization technique (e.g.\\ 2-D plot, surface plot,\nisolines, slice). Streamlines can also be calculated. The application\nis still under development, and new options are being added.\n%\n%\n%\n\\acknowledgements{This research is supported by the Polish Committee\nfor Scientific Research through the grant 2.P03D.004.13.}\n%\n%\n%\n\\begin{references}\n%\n%\n%\n\\reference \nBerger, M. J., \\& Colella, P. 1989, J. Comput. Phys., 82, 64\n\\reference\nColella, P., \\& Woodward, P.R. 1984, J. Comput. Phys., 59, 264\n\\reference\nPlewa, T., \\& M\\\"uller, E. 2000, Comp. Phys. Commun.\\ (in preparation)\n\\reference\nLubow, S.H, Seibert, M., \\& Artymowicz, P. 2000, \\apj\\ (astro-ph/9910404)\n\\reference \nFavre, J. M., Walder, R., \\& Follini, D. 1998, in Proceedings, 40th Cray\nUser Group Conference, Stuttgart, Germany (June 1998) \n%\n%\n%\n\\end{references}\n%\n%\n%\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002030
|
COSMIC DEFECTS AND COSMOLOGY
|
[
{
"author": "JO\\~AO MAGUEIJO"
}
] |
We provide a pedagogical overview of defect models of structure formation. We first introduce the concept of topological defect, and describe how to classify them. We then show how defects might be produced in phase transitions in the Early Universe and approach non-pathological scaling solutions. A very heuristic account of structure formation with defects is then provided, following which we introduce the tool box required for high precision calculations of CMB and LSS power spectra in these theories. The decomposition into scalar vector and tensor modes is reviewed, and then we introduce the concept of unequal-time correlator. We use isotropy and causality to constrain the form of these correlators. We finally show how these correlators may be decomposed into eigenmodes, thereby reducing a defect problem to a series of ``inflation'' problems. We conclude with a short description of results in these theories and how they fare against observations. We finally describe yet another application of topological defects in cosmology: baryogenesis.
|
[
{
"name": "defects1.tex",
"string": "\\documentstyle[editedvolume,numreferences,epsf]{crckapb} \n\\input psfig\n\\newcommand{\\stt}{\\small\\tt}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\n\\def\\al{\\alpha} \n\n\\def\\ga{\\gamma}\n\\def\\de{\\delta}\n\\def\\ep{\\epsilon}\n\\def\\ze{\\zeta}\n\\def\\et{\\eta}\n\\def\\th{\\theta}\n\\def\\io{\\iota}\n\\def\\ka{\\kappa}\n\\def\\la{\\lambda}\n\\def\\rh{\\rho}\n\\def\\si{\\sigma}\n\\def\\ta{\\tau}\n\\def\\up{\\upsilon}\n\\def\\ph{\\phi}\n\\def\\ch{\\chi}\n\\def\\ps{\\psi}\n\\def\\om{\\omega}\n\\def\\Ga{\\Gamma}\n\\def\\Th{\\Theta}\n\\def\\La{\\Lambda}\n\\def\\Si{\\Sigma}\n\\def\\Up{\\Upsilon}\n\\def\\Ph{\\Phi}\n\\def\\Ch{\\Chi}\n\\def\\Ps{\\Psi}\n\\def\\Om{\\Omega}\n\\def\\na{\\nabla}\n\\def\\ap{\\approx}\n\\def\\vp{\\varphi}\n\\def\\pa{\\partial}\n\n\\def\\vev#1{\\left\\langle#1\\right\\rangle}\n\n\\def\\bk{\\mathbf{k}}\n\\def\\bXd{\\dot{\\bX}}\n\\def\\bXp{\\mathaccent 19 {\\bX}}\n\\def\\Xd{\\dot X}\n\\def\\Xp{\\mathaccent 19 X}\n\\def\\dprime{\\mathaccent\"707D}\n\n\n\\newcommand{\\bX}{{\\mathbf{X}}}\n\\newcommand{\\ben}{\\begin{equation}}\n\\newcommand{\\een}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\n\n\\begin{opening}\n\\title{COSMIC DEFECTS AND COSMOLOGY}\n \n% Joao Magueijo and Robert Brandengerger\n\\author{JO\\~AO MAGUEIJO}\n\\institute{Theoretical Physics, The Blackett Laboratory, Imperial College\\\\\n Prince Consort Road, London SW7 2BZ, UK}\n\n\\author{ROBERT H. BRANDENBERGER}\n\\institute{Physics Department, Brown University\\\\\n Providence, RI, 02912, USA}\n\n\\end{opening}\n\n\\runningtitle{Cosmic Defects}\n\n\\begin{document}\n\n\\begin{abstract}\nWe provide a pedagogical overview of defect models of structure\nformation. We first introduce the concept of topological defect,\nand describe how to classify them. We then show how defects might\nbe produced in phase transitions in the Early Universe and approach\nnon-pathological scaling solutions. A very heuristic account of structure\nformation with defects is then provided, following which we introduce\nthe tool box required for high precision calculations of CMB and LSS\npower spectra in these theories. The decomposition into scalar\nvector and tensor modes is reviewed, and then we introduce\nthe concept of unequal-time correlator. We use isotropy and causality\nto constrain the form of these correlators. We finally show how these\ncorrelators may be decomposed into eigenmodes, thereby reducing a defect\nproblem to a series of ``inflation'' problems. We conclude with a short\ndescription of results in these theories and how they fare against\nobservations. We finally describe yet another application of topological\ndefects in cosmology: baryogenesis. \n\\end{abstract}\n\n\\section{Introduction}\n\nPhase transitions are ubiquitous in nature. Typically, as the temperature of a system drops below the critical temperature, the system makes a transition from a state with greater symmetry to one with less symmetry. In general, the state with less symmetry is not unique, but can lie anywhere in a so-called {\\it vacuum manifold}. Depending on the topology of this vacuum manifold, defects will form during the phase transition. If the topology of the vacuum manifold admits defects, then these defects will inevitably arise during the phase transition unless the dynamics is completely adiabatic.\n\nIn the early Universe the temperature was decreasing very rapidly. On length scales larger than the Hubble radius, causality prevents the system from maintaining adiabaticity through interactions, and therefore on these scales defects will arise in any cosmological phase transition in which they are topologically allowed. The Universe has undergone several phase transitions. We are quite confident about those which occurred at lower temperatures: the confinement transition at a temperature $T \\sim 10^2 {\\rm GeV}$ and the electroweak symmetry breaking transition at $T \\sim 10^3 {\\rm GeV}$. Unified field theories of fundamental interactions predict the existence of other transitions at higher temperatures, e.g. a phase transition at $T \\sim 10^{16} {\\rm GeV}$ in Grand Unified Models, the supersymmetry breaking phase transition in supersymmetric models, and various compactification transitions in string (and M-) theory.\n\nSince topological defects carry energy density, they will curve space-time and can thus act as the seeds for gravitational accretion (see e.g. Refs. \\cite{TK80,Vil85,ShellVil,HK95,RB94} for comprehensive reviews). Since inside of topological defects the symmetry characteristic of the high temperature phase is unbroken, topological defects can interact in various interesting ways with the surrounding matter and can have an effect on cosmological issues such as baryogenesis (see e.g. \\cite{BDH,BD,BDPT}), magnetic field generation (see e.g. \\cite{DD,BZ99}), and ultra-high-energy cosmic ray production \\cite{MB,PB,Sigl,BV}.\n\nIn these lectures, we first review the classification of topological defects and explain why in models with the appropriate topology, defects will inevitably form during the symmetry breaking phase transition. In Section 3 we discuss some initial applications of topological defects to cosmology. We review the domain wall and monopole problems and explain why the cosmic string model yields a promising mechanism for structure formation.\n\nIn the following sections we provide a more technical description\nof how high accuracy calculations of structure formation in defect\ntheories are performed. We first \ndescribe the details of the scalar, vector and tensor decomposition\n(Section \\ref{svt}). This is an invaluable tool in linear perturbation\ntheory. Then in Section \\ref{corrs} we introduce the concept of UETC\nand show their general form, assuming isotropy and scaling, but not\nenergy conservation. In Section~\\ref{caus} we show how\ncausality limits further the form of the correlators, in the\nlarge wavelength limit. These results will be important when checking\nupon the numerics. Then in Section~\\ref{result}\nwe present the UETCs measured for cosmic strings, and highlight \nsome of their features. Their remarkable novelty is the\ndominance of the energy density over any other components of the\nstress energy tensor. This property sets strings apart, resulting in\na dominance of scalar modes over vector and tensor modes. \nWe present some conclusions on string scenarios of structure formation,\nand also hybrid scenarios combining strings and inflation.\n\nIn the final section we illustrate one application of topological defects to cosmology which involves microscopic physics rather than gravitational accretion: we discuss the basics of defect-mediated baryogenesis.\n\n\\section{Defect Classification and Formation}\n\nAccording to our current particle physics theories, matter at high energies and\ntemperatures must be described in terms of fields. Gauge symmetries have\nproved to be extremely useful in describing the standard model of particle\nphysics, according to which at high energies the laws of nature are invariant\nunder some non-abelian group of internal symmetry transformations $G = {\\rm SU} (3)_c \\times {\\rm SU} (2)_L \\times U(1)_Y$, where the first factor is the symmetry group of the strong interactions, and the second and third factors form the gauge group of the Glashow-Weinberg-Salam theory of electroweak interactions which is spontaneously broken to the $U(1)$ of electromagnetism at a scale of $T \\sim 10^3 {\\rm GeV}$.\n \nSpontaneous symmetry breaking is induced by an order parameter $\\varphi$ taking\non a nontrivial expectation value $< \\varphi >$ below a certain temperature\n$T_c$. In some particle physics models, $\\varphi$ is a fundamental scalar\nfield in a nontrivial representation of the gauge group $G$. However, $\\varphi$ could also be a fermion condensate, as in the BCS theory of superconductivity.\n\nThe transition taking place at $T = T_c$ is a phase transition and $T_c$ is\ncalled the critical temperature. From condensed matter physics it is well\nknown that in many cases topological defects form during phase transitions,\nparticularly if the transition rate is fast on a scale compared to the system\nsize. When cooling a metal, defects in the crystal configuration will be\nfrozen in; during a temperature quench of $^4$He, thin vortex tubes of the\nnormal phase are trapped in the superfluid; and analogously in a temperature\nquench of a superconductor, flux lines are trapped in a surrounding sea of the\nsuperconducting Meissner phase. \n\nIn cosmology, the rate at which the phase transition proceeds is given by the\nexpansion rate of the Universe. Hence, topological defects will inevitably be\nproduced in a cosmological phase transition \\cite{Kibble}, provided the underlying particle physics model allows such defects.\n\nTopological defects can be point-like (monopoles), string-like (cosmic\nstrings) \\cite{ZelVil} or planar (domain walls), depending on the particle physics model. Also of importance are textures \\cite{Davis,Turok}, point\ndefects in space-time.\nTopological defects represent regions in space with trapped energy density.\nThese regions of surplus energy can act as seeds for structure formation. \n \nConsider a single component real scalar field with a typical symmetry breaking\npotential\n\\be \\label{pot}\nV (\\varphi) = {1\\over 4} \\lambda (\\varphi^2 - \\eta^2)^2 \n\\ee\nUnless $\\lambda \\ll 1$ there\nwill be no inflation. The phase transition will take place on a short time\nscale $\\tau < H^{-1}$, and will lead to correlation regions of radius $\\xi <\nt$ inside of which $\\varphi$ is approximately constant, but outside of which\n$\\varphi$ ranges randomly over the vacuum manifold ${\\cal M}$, the set of\nvalues\nof $\\varphi$ which minimizes $V(\\varphi)$ -- in our example $\\varphi\n= \\pm \\eta$. The correlation regions are separated by domain walls, regions in\nspace where $\\varphi$ leaves the vacuum manifold ${\\cal M}$ and where,\ntherefore, potential energy is localized. Via the usual gravitational\nforce, this energy density can act as a seed for structure.\n\nAs mentioned above, topological defects are familiar from solid state and condensed matter systems. \nThe analogies between defects in particle physics and condensed matter\nphysics are quite deep. Defects form for the same reason: the vacuum\nmanifold is topologically nontrivial. The arguments which say that in\na theory which admits defects, such defects will inevitably form, are\napplicable both in cosmology and in condensed matter physics.\nDifferent, however, is the defect dynamics. The motion of defects in\ncondensed matter systems is friction-dominated, whereas the defects in\ncosmology obey relativistic equations, second order in time\nderivatives, since they come from a relativistic field theory.\n\nTurning to a classification of\ntopological defects, we consider theories with an $n$-component order\nparameter $\\varphi$ and with a potential energy function (free energy\ndensity) of the form (\\ref{pot}) with\n\\be\n\\varphi^2 = \\sum\\limits^n_{i = 1} \\, \\varphi^2_i \\, . \n\\ee\n\nThere are various types of local and global topological defects\n(regions of trapped energy density) depending on the number $n$ of components\nof $\\varphi$. The more rigorous mathematical definition refers to the homotopy\nof ${\\cal M}$. The words ``local\" and ``global\" refer to whether the symmetry\nwhich is broken is a gauge or global symmetry. In the case of local\nsymmetries, the topological defects have a well defined core outside of which\n$\\varphi$ contains no energy density in spite of nonvanishing gradients\n$\\nabla \\varphi$: the gauge fields $A_\\mu$ can absorb the gradients,\n{\\it i.e.,} $D_\\mu \\varphi = 0$ when $\\partial_\\mu \\varphi \\neq 0$,\nwhere the covariant derivative $D_\\mu$ is defined by\n\\be\nD_\\mu = \\partial_\\mu + ie \\, A_\\mu \\, , \n\\ee\n$e$ being the gauge coupling constant.\nGlobal topological defects, however, have long range density fields and\nforces.\n \nTable 1 contains a list of topological defects with their topological\ncharacteristic. A ``v\" marks acceptable theories, a ``x\" theories which are\nin conflict with observations (for $\\eta \\sim 10^{16}$ GeV).\n \n\\begin{table}[htb]\n\\begin{center}\n\\caption{Classification of cosmologically allowed (v) and forbidden (x) defects.}\n\\begin{tabular}{llll}\n\\hline\nDefect name & n & Local defect & Global defect\\\\\n\\hline\nDomain wall & 1 & x & x\\\\\nCosmic string & 2 & v & v\\\\\nMonopole & 3 & x & v\\\\\nTexture & 4 & - & v\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nWe now describe examples of domain walls, cosmic strings, monopoles and\ntextures, focussing on configurations with maximal symmetry.\n\n \n{\\it Domain walls} arise in theories with a single real order\nparameter and free energy density given by (\\ref{pot}). The vacuum manifold\nof this model consists of two points\n\\be\n{\\cal M} = \\{ \\pm \\eta \\} \n\\ee\nand hence has nontrivial zeroth homotopy group:\n\\be\n\\Pi_0 ({\\cal M}) \\neq 1 \\, \\ . \n\\ee\n \nTo construct a domain wall configuration with planar symmetry (without\nloss of generality the $y-z$ plane can be taken to be the plane of\nsymmetry), assume that\n\\begin{eqnarray}\n\\varphi (x) \\simeq \\eta \\>\\>\\> & x \\gg \\eta^{-1} \\\\\n\\varphi (x) \\simeq - \\eta \\>\\>\\> & x \\ll - \\eta^{-1} \n\\end{eqnarray}\nBy continuity of $\\varphi$, there must be an intermediate value of $x$\nwith $\\varphi (x) = 0$. \nThe set of points with $\\varphi = 0$ constitute the center of the\ndomain wall. Physically, the wall is a thin sheet of trapped energy\ndensity. The width $w$ of the sheet is given by the balance of potential\nenergy and tension energy. Assuming that the spatial gradients are\nspread out over the thickness $w$ we obtain\n\\be\nw V (0) = w \\lambda \\eta^4 \\sim {1\\over w} \\, \\eta^2 \n\\ee\nand thus\n\\be \\label{width}\nw \\sim \\lambda^{-1/2} \\eta^{-1} \\, . \n\\ee\n \nA theory with a complex order parameter $(n = 2)$ admits\n{\\it cosmic strings}. In this case the vacuum manifold of the\nmodel is\n\\be\n{\\cal M} = S^1 \\, , \n\\ee\nwhich has nonvanishing first homotopy group:\n\\be\n\\Pi_1 ({\\cal M}) = Z \\neq 1 \\, . \n\\ee\nA cosmic string is a line of trapped energy density which arises\nwhenever the field $\\varphi (x)$ circles ${\\cal M}$ along a closed path\nin space ({\\it e.g.}, along a circle). In this case, continuity of\n$\\varphi$ implies that there must be a point with $\\varphi = 0$ on any\ndisk whose boundary is the closed path. The points on different sheets\nconnect up to form a line over-density of field energy, a cosmic string. \n\nTo construct a field configuration with a string along the $z$ axis \\cite{NO},\ntake $\\varphi (x)$ to cover ${\\cal M}$ along a circle with radius $r$\nabout the point $(x,y) = (0,0)$:\n\\be \\label{string}\n\\varphi (r, \\vartheta ) \\simeq \\eta e^{i \\vartheta} \\, , \\, r \\gg\n\\eta^{-1} \\, . \n\\ee\nThis configuration has winding number 1, {\\it i.e.}, it covers ${\\cal\nM}$ exactly once. Maintaining cylindrical symmetry, we can extend\n(\\ref{string}) to arbitrary $r$\n\\be\n\\varphi (r, \\, \\vartheta) = f (r) e^{i \\vartheta} \\, , \n\\ee\nwhere $f (0) = 0$ and $f (r)$ tends to $\\eta$ for large $r$. The\nwidth $w$ can again be found by balancing potential and tension\nenergy. The result is identical to the result (\\ref{width}) for domain walls.\n\nFor local cosmic strings, {\\it i.e.}, strings arising due to the\nspontaneous breaking of a gauge symmetry, the energy density decays\nexponentially for $r \\gg \\eta^{-1}$. In this case, the energy $\\mu$\nper unit length of a string is finite and depends only on the symmetry\nbreaking scale $\\eta$\n\\be\n\\mu \\sim \\eta^2 \n\\ee\n(independent of the coupling $\\lambda$). The value of $\\mu$ is the\nonly free parameter in a cosmic string model.\n\nIf the order parameter of the model has three components $(n = 3)$,\nthen {\\it monopoles} result as topological defects. The vacuum\nmanifold is\n\\be\n{\\cal M} = S^2 \n\\ee\nand has topology given by\n\\be\n\\Pi_2 ({\\cal M}) \\neq 1 \\, . \n\\ee\nGiven a sphere $S$ in space, it is possible that $\\varphi$ takes on\nvalues in ${\\cal M}$ everywhere on $S$, and that it covers ${\\cal M}$\nonce. By continuity, there must be a point in space in the interior\nof $S$ with $\\varphi = 0$. This is the center of a point-like defect,\nthe monopole.\n\nTo construct a spherically symmetric monopole with the origin as its\ncenter, consider a field configuration $\\varphi$ which defines a map\nfrom physical space to field space such that all spheres $S_r$ in\nspace of radius $r \\gg \\eta^{-1}$ about the origin are mapped onto\n${\\cal M}$:\n\\begin{eqnarray}\n\\varphi: \\> & S_r \\longrightarrow {\\cal M} \\\\\n& (r, \\vartheta,\\varphi) \\longrightarrow (\\vartheta,\n\\varphi) \\, . \n\\end{eqnarray}\nThis configuration defines a winding number one magnetic monopole.\n\nDomain walls, cosmic strings and monopoles are examples of\n{\\it topological} defects. A topological defect has a\nwell-defined\ncore, a region in space with $\\varphi \\notin {\\cal M}$ and hence $V\n(\\varphi) > 0$. There is an associated winding number which is\nquantized, {\\it i.e.}, it can take on only integer values. Since the\nwinding number can only change continuously, it must be conserved, and\nhence topological defects are stable. Furthermore, topological\ndefects exist for theories with global and local symmetries.\n\nNow, let us consider a theory with a four-component order parameter\n({\\it i.e.,} $n = 4$), and a potential given by (\\ref{pot}). In this case,\nthe vacuum manifold is\n\\be\n{\\cal M} = S^3 \n\\ee\nand the associated topology is given by\n\\be\n\\Pi_3 ({\\cal M}) \\neq 1 \\, . \n\\ee\nThe corresponding defects are called {\\it textures} \\cite{Davis,Turok}. \n\nTextures, however, are quite different than the previously discussed topological defects.\nThe texture construction will render this manifest. To construct a\nradially symmetric texture, we give a field configuration $\\varphi (x)$ which\nmaps physical space onto ${\\cal M}$. The origin 0 in space (an arbitrary point\nwhich will be the center of the texture) is mapped onto the north pole $N$ of\n${\\cal M}$. Spheres in space of radius $r$ surrounding 0 are mapped onto spheres in ${\\cal M}$ surrounding $N$, with distance from $N$ increasing as $r$ increases. In\nparticular, some sphere with radius $r_c (t)$ is mapped onto the equator\nsphere of ${\\cal M}$. The distance $r_c (t)$ can be defined as the radius of\nthe texture. Inside this sphere, $\\varphi (x)$ covers half the vacuum\nmanifold.\nFinally, the sphere at infinity is mapped onto the south pole of ${\\cal M}$.\nThe configuration $\\varphi ({\\it x})$ can be parameterized\nby \\cite{Turok}\n\\be\n\\varphi (x,y,z) = \\left(\\cos \\chi (r), \\> \\sin \\chi (r) {x\\over r}, \\>\n\\sin \\chi (r) {y\\over r}, \\> \\sin \\chi (r) {z\\over r} \\right) \n\\ee\nin terms of a function $\\chi (r)$ with $\\chi (0) = 0$ and $\\chi (\\infty) =\n\\pi$. Note that at all points in space, $\\varphi ({\\it x})$ lies in\n${\\cal M}$. There is no defect core. All the energy is in spatial gradient (and possibly kinetic) terms.\n \nIn a cosmological context, there is infinite energy available in an infinite\nspace. Hence, it is not necessary that $\\chi (r) \\rightarrow \\pi$ as $r\n\\rightarrow \\infty$. We can have\n\\be\n\\chi (r) \\rightarrow \\chi_{\\rm max} < \\pi \\>\\> {\\rm as} \\>\\> r \\rightarrow\n\\infty \\, . \n\\ee\nIn this case, only a fraction\n\\be\nn_W = {{\\chi_{\\rm max}} \\over {\\pi}} - {{\\sin (2 \\chi_{\\rm max})} \\over{2 \\pi}}\n\\ee\nof the vacuum manifold is covered: the winding number $n_W$ is not quantized.\nThis is a reflection of the fact that whereas topologically nontrivial maps\nfrom $S^3$ to $S^3$ exist, all maps from $R^3$ to $S^3$ can be deformed to\nthe trivial map.\n \nTextures in $R^3$ are unstable. For the configuration described above, the\ninstability means that $r_c (t) \\rightarrow 0$ as $t$ increases: the texture\ncollapses. When $r_c (t)$ is microscopical, there will be sufficient energy\ninside the core to cause $\\varphi (0)$ to leave ${\\cal M}$, pass through 0 and\nequilibrate at $\\chi (0) = \\pi$: the texture unwinds.\n \nA further difference compared to topological defects: textures are relevant\nonly for theories with global symmetry. Since all the energy is in spatial\ngradients, for a local theory the gauge fields can re-orient themselves such as\nto cancel the energy:\n\\be\nD_\\mu \\varphi = 0 \\, . \n\\ee \n\nTherefore, it is reasonable to regard textures as an example of a new class of\ndefects, {\\it semi-topological defects}. In contrast to topological\ndefects, there is no core, and $\\varphi ({\\it x}) \\in {\\cal M}$ for all\n${\\it x}$. In particular, there is no potential energy. In addition,\nthe winding number is not quantized, and hence the defects are unstable. Finally, they exist as long-lived coherent configurations only in theories with a global internal symmetry.\n \nThe Kibble mechanism \\cite{Kibble} ensures that in theories which admit\ntopological or semi-topological defects, such defects will be produced\nduring a phase transition in the very early Universe.\nAt high temperatures $T \\gg T_c$, the symmetry is unbroken. The ground state of the finite temperature effective potential \\cite{KL,DJ} (see e.g. \\cite{RB85} for an introductory review) is the symmetric configuration $\\varphi = 0$. \nOnce the Universe cools below the temperature $T_c$, the symmetry is broken, and $\\varphi(x)$ rolls into the zero temperature vacuum manifold ${\\cal M}$. However, by causality there can be no correlation between the specific points in ${\\cal M}$ which are taken on on scales larger than the correlation length $\\xi (t)$. In a relativistic theory the causality bound on $\\xi$ is\n\\be\n\\xi (t) < t \\, , \n\\ee\nwhere $t$ is the causal horizon. This leads to the formation of defects with a mean separation of $\\xi (t)$.\n\nThe correlation length $\\xi (t)$ can be determined by equating the free energy gained by symmetry breaking (a volume effect) with the gradient energy lost (a surface effect). As expected, $\\xi (T)$ diverges at $T_c$. Very close to $T_c$, the thermal energy $T$ is larger than the volume energy gain $E_{corr}$ in a\ncorrelation volume. Hence, these domains are unstable to thermal fluctuations.\nAs $T$ decreases, the thermal energy decreases more rapidly than $E_{corr}$.\nBelow the Ginsburg temperature $T_G$, there\nis insufficient thermal energy to excite a correlation volume into the\nstate $\\varphi = 0$. Domains of size\n\\be \\label{GBL}\n\\xi (t_G) \\sim \\lambda^{-1} \\eta^{-1} \n\\ee\nfreeze out \\cite{Kibble,Kibble2}. The boundaries between these domains become\ntopological defects. An improved version of this argument has been given by Zurek \\cite{Zurek}. \n\nWe conclude that in a theory in which a symmetry breaking phase\ntransition satisfies the topological criteria for the existence of a\ngiven type of defect, a network of such defects will form during the\nphase transition and will freeze out at the Ginsburg temperature. The\ncorrelation length is initially given by (\\ref{GBL}), if the field\n$\\varphi$ is in thermal equilibrium before the transition.\nIndependent of this last assumption, the causality bound implies that\n$\\xi (t_G) < t_G$.\n\nFor times $t > t_G$ the evolution of the network of defects may be\ncomplicated (as for cosmic strings) or trivial (as for textures). In\nany case (see the caveats of Refs. \\cite{caveat1,caveat2}), the causality bound\npersists at late times and states that even at late times, the mean\nseparation and length scale of defects is bounded by $\\xi (t) \\leq t$.\n\nApplied to cosmic strings, the Kibble mechanism implies that at the\ntime of the phase transition, a network of cosmic strings with typical\nstep length $\\xi (t_G)$ will form. According to numerical\nsimulations \\cite{VV1}, about 80\\% of the initial energy is in infinite\nstrings (strings with curvature radius larger than the Hubble radius) and 20\\% in closed loops.\n\nThe evolution of the cosmic string network for $t > t_G$ is\ncomplicated. The key processes are loop production\nby intersections of infinite strings and loop shrinking\nby gravitational radiation. These two processes combine to create a\nmechanism by which the infinite string network loses energy (and\nlength as measured in comoving coordinates). The dynamics of a string in an expanding Universe changes as the curvature radius increases. If the curvature radius is smaller than the Hubble radius $H^{-1}(t)$, the dynamics is dominated by the acceleration term and the string will oscillate at relativistic speeds. However, if the curvature radius exceeds the Hubble radius, the strings are frozen in by the Hubble damping term in the string equation of motion. Therefore, if the string correlation length is smaller than the Hubble radius, string intersections will be frequent, the network will loose a lot of energy to loops and $\\xi(t)$ will increase faster than $t$. However, if at any time $\\xi(t)$ exceeds the Hubble radius, the strings will be effectively frozen in comoving coordinates and hence in a standard radiation or matter dominated cosmology the Hubble radius will catch up to $\\xi(t)$. According to this argument \\cite{Vil85}, at sufficiently late times the correlation leng!\nth of the string network will always be proportional to its causality limit\n\\be \\label{scaling}\n\\xi (t) \\sim t \\, . \n\\ee\nHence, the energy density $\\rho_\\infty (t)$ in long strings is a fixed\nfraction of the background energy density $\\rho_c (t)$\n\\be\n\\rho_\\infty (t) \\sim \\mu \\xi (t)^{-2} \\sim \\mu t^{-2} \n\\ee\nor\n\\be\n{\\rho_\\infty (t)\\over{\\rho_c (t)}} \\sim G \\mu \\, . \n\\ee\n\nWe conclude that the cosmic string network approaches a ``scaling\nsolution\" in which the statistical properties of the\nnetwork are time independent if all distances are scaled to the\nHubble radius.\n\nApplied to textures (see e.g. \\cite{Turok2} for a review), the Kibble mechanism implies that on all\nscales $r \\geq t_G$, field configurations with winding number $n_W\n\\geq n_{cr}$ are frozen in with a probability $p (n_{cr})$ per volume\n$r^3$. The critical winding number $n_{cr}$ is defined as the winding\nnumber above which field configurations collapse and below which they\nexpand. Only collapsing configurations form clumps of energy which\ncan accrete matter. For spherically symmetric textures, \nthe critical winding $n_{cr}$ is slightly larger than 0.5 \\cite{ncr}. \n\nFor $t > t_G$, any configuration on scale $\\sim t$ with winding number\n$n_W \\ge n_{cr}$ begins to collapse (if the scale of the texture is larger than $t$, the Hubble damping\nterm dominates over the spatial gradient forces, and the field\nconfiguration is frozen in comoving coordinates). After unwinding,\n$\\varphi ({\\it x})$ is homogeneous inside the horizon.\n\nThe texture model thus also leads to a scaling solution: at all times\n$t > t_G$ there is the same probability that a texture configuration\nof scale $t$ will enter the horizon, become dynamical and collapse\non a typical time scale $t$.\n\n\\section{Defects and Structure Formation: An Overview}\n\nTopological defects are regions in space with trapped energy density.\nBy Newtonian gravity, these defects can act as seeds about which the\nmatter in the Universe clusters, and hence they play a very important\nrole in cosmology.\n\nAs indicated in Table 1, theories with domain walls or with local\nmonopoles are ruled out, and those with only local textures do not give\nrise to a structure formation model. As mentioned earlier, theories with\ndomain walls are\nruled out since a single wall stretching across the present Universe\nwould overclose it. Local monopoles are also problematic since they\ndo not interact and come to dominate the energy density of the\nUniverse. Local textures do not exist as coherent structures with\nnonvanishing gradient energy since the gauge fields can always\ncompensate scalar field gradients.\n\\par\nLet us demonstrate explicitly why stable domain walls are a\ncosmological disaster \\cite{Zel74}. If domain walls form during a phase transition\nin the early Universe, it follows by causality (see however the caveats\nof Refs. \\cite{caveat1,caveat2}) that even today there will be at least one wall\nper Hubble volume. Assuming one wall per Hubble volume, the energy\ndensity $\\rho_{DW}$ of matter in domain walls is\n\\be\n\\rho_{DW} (t) \\sim \\eta^3 t^{-1} \\, , \n\\ee\nwhereas the critical density $\\rho_c$ is\n\\be\n\\rho_c = H^2 \\, {3\\over{8 \\pi G}} \\sim m^2_{p\\ell} \\, t^{-2} \\, .\n \\ee\nHence, for $\\eta \\sim 10^{16}$ GeV the ratio evaluated at the present time $t_0$ is\n\\be\n{\\rho_{DW}\\over \\rho_c} \\, (t_0) \\sim \\, \\left({\\eta\\over{m_{p\\ell}}}\n\\right)^2 \\, (\\eta t_0) \\sim 10^{52} \\, . \n\\ee\n\nThe above argument depends in an essential way on the dimension of the\ndefect. One cosmic string per Hubble volume leads to an energy\ndensity $\\rho_{cs}$ in string\n\\be\n\\rho_{cs} \\sim \\eta^2 \\, t^{-2} \\, . \n\\ee\nAs we have seen above, the cosmic string network approaches a scaling distribution (\\ref{scaling}). Hence, cosmic strings do not lead to\ncosmological problems. On the contrary, since for GUT models with\n$\\eta \\sim 10^{16}$ GeV\n\\be\n{\\rho_{cs}\\over \\rho_c} \\sim \\, \\left({\\eta\\over m_{p \\ell}} \\right)^2\n\\sim 10^{-6} \\, , \n\\ee\ncosmic strings in such theories could provide the seed perturbations\nresponsible for structure formation.\n\nTheories with local monopoles are ruled out on cosmological\ngrounds \\cite{Zel78} (see again the caveats of Refs. \\cite{caveat1,caveat2}) for\nrather different reasons. Since there are no long range forces\nbetween local monopoles, their number density in comoving coordinates\ndoes not decrease. Since their contribution to the energy density\nscales as $a^{-3} (t)$, they will come to dominate the mass of the\nUniverse, provided $\\eta$ is sufficiently large.\n\nTheories with global monopoles \\cite{BV89,RB90} are not ruled out, since\nthere are long range forces between monopoles which lead to a\n``scaling solution\" with a fixed number of monopoles per Hubble\nvolume.\n\nLet us now briefly discuss some of the basic mechanisms of the cosmic string scenario of structure formation. The implementation of the mechanisms in concrete models will be covered in the following sections.\n\nThe starting point of the structure formation scenario in the cosmic\nstring theory is the scaling solution for the cosmic string network,\naccording to which at all times $t$ (in particular at $t_{eq}$, the\ntime when perturbations can start to grow) there will be a few long\nstrings crossing each Hubble volume, plus a distribution of loops of\nradius $R \\ll t$. \n\nThe cosmic string model admits three mechanisms for structure\nformation: loops, filaments, and wakes. Cosmic string loops have the same\ntime averaged field as a point source with mass \\cite{Turok84}\n\\be\nM (R) = \\beta R \\mu \\, , \n\\ee\n$R$ being the loop radius and $\\beta \\sim 2 \\pi$. Hence, loops will be seeds\nfor spherical accretion of dust and radiation.\n\nFor loops with $R \\leq t_{eq}$, growth of perturbations in a model\ndominated by cold dark matter starts at $t_{eq}$. Hence, the mass at\nthe present time will be\n\\be\nM (R, \\, t_0) = z (t_{eq}) \\beta \\, R \\mu \\, . \n\\ee\n\nIn the original cosmic string model \\cite{ZelVil,TB86} it was assumed\nthat loops dominate over wakes. In this case, the theory could be\nnormalized ({\\it i.e.}, $\\mu$ could be determined) by demanding that loops\nwith the mean separation of clusters $d_{cl}$ accrete the correct mass, {\\it i.e.}, that\n\\be\nM (R (d_{cl}), t_0) = 10^{14} M_{\\odot} \\, . \n\\ee\nThis condition yields \\cite{TB86}\n\\be\n\\mu \\simeq 10^{32} {\\rm GeV}^2 \n\\ee\nThus, if cosmic strings are to be relevant for structure formation,\nthey must arise due to a symmetry breaking at an energy scale $\\eta\n\\simeq 10^{16}$GeV. This scale happens to be the scale of unification (GUT)\nof weak, strong and electromagnetic interactions. It is tantalizing\nto speculate that cosmology is telling us that there indeed was new\nphysics at the GUT scale.\n\n\\begin{figure}[kish2fig1.eps]\n\\begin{center}\n\\leavevmode\n\\epsfysize=5cm \\epsfxsize=12cm \\epsfbox{kish2fig1.eps}\n\\end{center}\n\\caption{Sketch of the mechanism by which a long\nstraight cosmic string $S$ moving with velocity $v$ in transverse\ndirection through a plasma induces a velocity perturbation $\\Delta v (dv)$\ntowards the wake. Shown on the left is the deficit angle $a$, in the\ncenter is a sketch of the string moving in the plasma, and on the\nright is the sketch of how the plasma moves towards the wake with velocity $dv$ in the frame in which the string is at rest.}\n\\label{fig0}\n\\end{figure}\n\nThe second mechanism involves long strings moving with relativistic\nspeed in their normal plane which give rise to\nvelocity perturbations in their wake \\cite{SV84}. The mechanism is illustrated in Fig. 1: space normal to the string is a cone with deficit angle \\cite{V81}\n\\be \\label{deficit}\n\\alpha = 8 \\pi G \\mu \\, . \n\\ee\nIf the string is moving with normal velocity $v$ through a bath of dark\nmatter, a velocity perturbation\n\\be\n\\delta v = 4 \\pi G \\mu v \\gamma \n\\ee\n[with $\\gamma = (1 - v^2)^{-1/2}$] towards the plane behind the string\nresults. At times after $t_{eq}$, this induces planar over-densities,\nthe most\nprominent ({\\it i.e.}, thickest at the present time) and numerous of which were\ncreated at $t_{eq}$, the time of equal matter and\nradiation \\cite{TV86,SVBST,BPS}. The\ncorresponding planar dimensions are (in comoving coordinates)\n\\be\nt_{eq} z (t_{eq}) \\times t_{eq} z (t_{eq}) v \\sim (40 \\times 40 v) \\,\n{\\rm Mpc}^2\n\\, . \n\\ee\n\nThe thickness $d$ of these wakes can be calculated using the\nZel'dovich approximation \\cite{BPS}. The result is\n\\be\nd \\simeq G \\mu v \\gamma (v) z (t_{eq})^2 \\, t_{eq} \\simeq 4 v \\, {\\rm\nMpc} \\, . \n\\ee\n \nWakes arise if there is little small scale structure on the string.\nIn this case, the string tension equals the mass density, the string\nmoves at relativistic speeds, and there is no local gravitational\nattraction towards the string.\n\nIn contrast, if there is small scale structure on strings,\nthen the string tension $T$ is smaller \\cite{BC90} than the mass per unit\nlength $\\mu$ and the metric of a string in $z$ direction becomes \\cite{VV91}\n\\be \\label{metric2}\nds^2 = (1 + h_{00}) (dt^2 - dz^2 - dr^2 - (1 - 8G \\mu) r^2 dy^2 )\n\\ee\nwith\n\\be\nh_{00} = 4G (\\mu - T) \\ln \\, {r\\over r_0} \\, , \n\\ee\n$r_0$ being the string width. Since $h_{00}$ does not vanish, there\nis a gravitational force towards the string which gives rise to\ncylindrical accretion, thus producing filaments.\n\nAs is evident from the last term in the metric (\\ref{metric2}), space\nperpendicular to the string remains conical, with deficit angle given\nby (\\ref{deficit}). However, since the string is no longer relativistic, the\ntransverse velocities $v$ of the string network are expected to be\nsmaller, and hence the induced wakes will be shorter and thinner.\n\nWhich of the mechanisms -- filaments or wakes -- dominates is\ndetermined by the competition between the velocity induced by $h_{00}$\nand the velocity perturbation of the wake. The total velocity\nis \\cite{VV91}\n\\be\nu = - {2 \\pi G (\\mu - T)\\over{v \\gamma (v)}} - 4 \\pi G \\mu v \\gamma\n(v) \\, , \n\\ee\nthe first term giving filaments, the second producing wakes. Hence,\nfor small $v$ the former will dominate, for large $v$ the latter.\n\nBy the same argument as for wakes, the most numerous and prominent\nfilaments will have the distinguished scale\n\\be\nt_{eq} z (t_{eq}) \\times d_f \\times d_f \n\\ee\nwhere $d_f$ can be calculated using the Zel'dovich approximation \\cite{AB95}.\n\nThe cosmic string model predicts a scale-invariant spectrum of density\nperturbations, exactly like inflationary Universe models but for a\nrather different reason. Consider the {\\it r.m.s.} mass fluctuations\non a length scale $2 \\pi k^{-1}$ at the time $t_H (k)$ when this scale\nenters the Hubble radius $H^{-1}(t)$. From the cosmic string scaling solution it follows that a fixed ({\\it i.e.}, $t_H (k)$ independent) number\n$\\tilde v$ of strings of length of the order $t_H (k)$ contribute to\nthe mass excess $\\delta M (k, \\, t_H (k))$. Thus\n\\be\n{\\delta M\\over M} \\, (k, \\, t_H (k)) \\sim \\, {\\tilde v \\mu t_H\n(k)\\over{G^{-1} t^{-2}_H (k) t^3_H (k)}} \\sim \\tilde v \\, G \\mu \\, .\n\\ee\nNote that the above argument predicting a scale invariant spectrum\nwill hold for all topological defect models which have a scaling\nsolution, in particular also for global monopoles and textures.\n\nThe amplitude of the {\\it r.m.s.} mass fluctuations (equivalently: of\nthe power spectrum) can be used to normalize $G \\mu$. Since today on\ngalaxy cluster scales\n\\be\n{\\delta M\\over M} (k, \\, t_0) \\sim 1 \\, , \n\\ee\nthe growth rate of fluctuations linear in $a(t)$ yields\n\\be\n{\\delta M\\over M} \\, (k, \\, t_{eq}) \\sim 10^{-4} \\, , \n\\ee\nand therefore, using $\\tilde v \\sim 10$,\n\\be\nG \\mu \\sim 10^{-5} \\, . \n\\ee\n\nIn contrast to the situation in inflationary Universe\nmodels, hot dark matter (HDM) is not from the outset ruled out as a dark matter candidate. As non-adiabatic seeds, cosmic string loops survive free streaming and can\ngenerate nonlinear structures on galactic scales, as discussed in\ndetail in Refs. \\cite{BKST,BKT}. Accretion of hot dark matter by a string wake\nwas studied in Ref. \\cite{BPS}. In this case, nonlinear perturbations\ndevelop only late. At some time $t_{nl}$, all scales up to a distance\n$q_{\\rm max}$ from the wake center go nonlinear. Here\n\\be\nq_{\\rm max} \\sim G \\mu v \\gamma (v) z (t_{eq})^2 t_{eq} \\sim 4 v \\,\n{\\rm Mpc} \\, , \n\\ee\nis the comoving thickness of the wake at $t_{nl}$. Demanding\nthat $t_{nl}$ corresponds to a redshift greater than 1 leads to the\nconstraint\n\\be\nG \\mu > 5 \\cdot 10^{-7} \\, . \n\\ee\nNote that in a cosmic string and hot dark matter model, wakes form nonlinear structures only very recently. Accretion onto loops \\cite{MB96} and onto\nfilaments \\cite{ZLB} provide two mechanisms which may lead to high redshift objects such as quasars and high redshift galaxies. \n \n\n\n\n\\section{Introduction to high precision calculations with defects}\n\nThe last decade has\nwitnessed unprecedented progress in mapping the\ncosmic microwave background (CMB) \ntemperature anisotropy\nand the large scale structure (LSS) of the Universe. \nThe prospect of fast improving data has\nforced theorists to \nnew standards of precision in computing observable quantities.\nThe new standards have been met in theories based\non cosmic inflation\\cite{hsselj,hw}. \nTopological defect scenarios \\cite{ShellVil,HK95}\nhave been more challenging. However, \nrecently there have been a number of computational breakthroughs in defect\ntheories, partly related to improvements in computer technology.\nMost strikingly, the method described in \\cite{pst} showed how\none could glean from defect simulations all the information required\nto compute accurately CMB and LSS power spectra.\nIn this method the simulations are used uniquely for evaluating\nthe two point functions (known as unequal time\ncorrelators, or UETCs) of the defects' stress-energy tensor. \nUETCs are all that is required for computing CMB and LSS power spectra. \nFurthermore, they are constrained by requirements of self-similarity \n(or scaling) and\ncausality, which enable us to radically extend the dynamical \nrange of simulations, a fact \ncentral to the success of the method.\n\n\nThis method was applied to theories based on global\nsymmetries. In recent work \\cite{chm,chm1} we have shown how the same\nmethod could be applied to local cosmic strings (see also \\cite{steb,abr}). \nIn the next few Sections we shall describe in detail the simulation\nand measurement of UETCs which led to the work in \\cite{chm,chm1};\nas well as present the analytical tools used in this enterprise. \nThe formalism we had to use is unfortunately more complicated than\n\\cite{pst}. Local strings have an extra complication over global defects, which stems \nfrom the fact that we are unable to simulate the underlying field theory. \nInstead, we approximate the true dynamics with line-like relativistic strings. \nThis is thought to be reasonable for the large scale properties of the \nstress-energy tensor, but we do not have a good understanding of how \nthe string network loses energy in order to maintain scaling. \n\nThis leads\nto two problems. Firstly one is forced\nto make assumptions about which cosmological fluids pick up this deficit. \nIt is often assumed that all the strings' energy and momentum is radiated \ninto gravitational waves, approximated by a relativistic fluid. \nThis is by no means certain, and it may well be that the energy and momentum\nis transferred to particles \\cite{VinAntHin98}, \nand hence to the baryon, photon and CDM \ncomponents. \n\nSecondly, it is not enough to find\ncorrelators for a reduced number of stress energy tensor\ncomponents (two scalar, two vector, two tensor), and then \nfind the others by means of energy conservation. If energy \nconservation can be used then one needs to compute 3 scalar,\n1 vector, and 1 tensor UETCs. If one is not allowed\nto make use of energy conservation, one has to compute 10\nscalar, 3 vector, and 1 tensor UETC. \n\nIn the following sections we first give a qualitative description\nof the technical novelties introduced in defect scenarios. We describe\ndefects as active incoherent perturbations. We then describe \na set of tools with which we can perform high accuracy calculations\nof structure power spectra in these scenarios. \n\n\\section{Defects as active, incoherent perturbations}\n\nWe first focus on the basic assumptions of\ninflationary and defect theories and isolate the most striking\ncontrasting properties. \nWe define the concepts of active and passive perturbations,\nand of coherent and incoherent perturbations. In terms of \nthese concepts inflationary perturbations are \npassive coherent perturbations.\nDefect perturbations are active perturbations more or less\nincoherent depending on the defect \\cite{inc}.\n\n\\subsection{Active and passive perturbations, and their different\nperceptions of causality and scaling}\n\nThe way in which inflationary and defect perturbations come about\nis radically different. Inflationary fluctuations \nwere produced at a remote epoch, and were \ndriven far outside the Hubble radius by inflation. The\nevolution of these fluctuations is linear (until \ngravitational collapse becomes non-linear at late times), and we call\nthese fluctuations ``passive''. Also, because\nall scales observed today have been in causal contact since the onset\nof inflation, causality does not strongly constrain the fluctuations\nwhich result. In contrast, defect fluctuations are continuously seeded by\ndefect evolution, which is a non-linear process.\nWe therefore say these are ``active'' perturbations. Also, the\nconstraints imposed by causality on defect formation and evolution \nare much greater than those placed on inflationary perturbations.\n\n\\subsubsection{Active and passive scaling}\n\nThe notion of scale invariance has different implications\nin these two types of theory. For instance, a scale invariant gauge-invariant\npotential $\\Phi$ with dimensions $L^{3/2}$ has a power spectrum \n$$P(\\Phi)=\\langle |\\Phi_{\\bf k}|^2\\rangle\\propto k^{-3}$$ \nin passive theories (the Harrison-Zel'dovich spectrum). \nThis results from the fact that\nthe only variable available is $k$, and so the only spectrum one\ncan write down which has the right dimensions and does not have a \nscale is the Harrison-Zel'dovich spectrum. \nThe situation is different\nfor active theories, since time is now a variable.\nThe most general counterpart to the Harrison-Zel'dovich spectrum is \n\\begin{equation}\\label{scale}\nP(\\Phi) = \\eta^3F_{\\Phi}(k\\eta)\n\\end{equation}\nwhere $F_{\\Phi}$\nis, to begin with, an arbitrary function of $x=k\\eta$. All other\nvariables may be written as a product of a power of $\\eta$, ensuring\nthe right dimensions, and an arbitrary function of $x$. \nInspecting all equations it can be checked that it is possible to do\nthis consistently for all variables. All equations respect scaling\nin the active sense.\n\n\\subsubsection{Causality constraints on active perturbations}\\label{causal}\n\nMoreover, active perturbations are constrained by causality, in the form of \nintegral constraints \\cite{trasch12,james}. These consist of \nenergy and momentum conservation laws for fluctuations\nin an expanding Universe. The integral constraints can be used to \nfind the low $k$ behaviour of the power spectrum of the perturbations, \nassuming their causal generation and evolution\n\\cite{traschk4}. Typically, it is found that the causal creation\nand evolution of defects requires that their energy $\\rho^s$ and scalar\nvelocity $v^s$\nbe white noise at low $k$, but that the total energy power spectrum \nof the fluctuations is required to go like $k^4$. To reconcile these two facts\none is forced to consider the compensation. \nThis is an under-density in the matter-radiation energy density\nwith a white noise low $k$ tail, correlated with the defect network\nso as to cancel the defects' white-noise tail. When one combines the\ndefects energy with the compensation density, one finds that the \ngravitational potentials they generate also have to be\nwhite noise at large scales \\cite{inc}. Typically the scaling function\n$ F_{\\Phi}(k\\eta)$ will start as a constant and decay as a power law\nfor $x=k\\eta>x_c$. The value $x_c$ is a sort of coherence wavenumber\nof the defect. The larger it is the smaller the defect is. For instance\n$x_c\\approx 12$ for cosmic strings (thin, tiny objects), whereas\n$x_c\\approx 5.5$ for textures (round, fat, big things). Sophisticated\nwork on causality \\cite{james} has shed light on how small $x_c$\nmay be before violating causality. The limiting lower bound $x_c\n\\approx 2.7$ has been suggested.\n\nAlthough we will not here have a chance to dwell on technicalities,\nit should be stated that the rather general discussion presented above\nis enough to determine the general form of the potentials for active \nperturbations. This has been here encoded in the single parameter $x_c$.\nWe shall see that $x_c$ will determine the Doppler peak position\nfor active perturbations. Doppler peaks are driven by the gravitational\npotential, so it should not be surprising that the defect length scale\npropagates into its potential, and from that into the position of the \nDoppler peaks.\n\n\\subsection{Coherent and incoherent perturbations}\n\nActive perturbations may also differ from\ninflation in the way ``chance'' comes into the theory. \nRandomness occurs in inflation only when the initial \nconditions are set up. Time evolution is linear and\ndeterministic, and may be found by\nevolving all variables from an\ninitial value equal to the square root of \ntheir initial variances. By squaring the\nresult one obtains the variances of the variables at any time.\nFormally, this results from unequal time correlators of the form\n\\begin{equation}\\label{2cori}\n{\\langle\\Phi({\\bf k},\\eta)\\Phi({\\bf k'},\\eta ')\\rangle}=\n\\delta({\\bf k}-{\\bf k'})\\sigma({\\Phi}(k,\\eta))\\sigma\n({\\Phi}(k,\\eta')),\n\\end{equation}\n%with $\\sigma(\\cdot)={\\sqrt{P(\\cdot)}}$.\nwhere $\\sigma$ denotes the square root of the power spectrum $P$.\n% and where $\\Phi$ can also be any other variable.\nIn defect models however, randomness may intervene in the time\nevolution as well as the initial conditions. \nAlthough deterministic in principle, \nthe defect network evolves as a result of a \ncomplicated non-linear process.\nIf there is strong non-linearity, a given mode will be ``driven'' \nby interactions with the other modes in a way which will force\nall different-time correlators to zero on a time scale\ncharacterized by the ``coherence time'' $\\theta_c(k,\\eta)$.\nPhysically this means that one has to perform a new ``random'' draw \nafter each coherence time in order to\nconstruct a defect history \\cite{inc}. \nThe counterpart to (\\ref{2cori}) for incoherent perturbations is\n\\begin{equation}\\label{pr0}\n{\\langle\\Phi({\\bf k},\\eta)\\Phi({\\bf k'},\\eta ')\\rangle}=\n\\delta({\\bf k}-{\\bf k'}) P({\\Phi}(k,\\eta),\\eta'-\\eta)\\; .\n\\end{equation}\nFor $|\\eta'-\\eta| \\equiv |\\Delta\\eta|> \\theta_c(k,\\eta)$\nwe have $P({\\Phi}(k,\\eta),\\Delta\\eta)=0$. For $\\Delta\\eta=0$,\nwe recover the power spectrum $P({\\Phi}(k,\\eta),0)=P({\\Phi}(k,\\eta))$.\n\nWe shall label as coherent and incoherent\n(\\ref{2cori}) and (\\ref{pr0}) respectively. \nThis feature does not affect the position of the Doppler peaks,\nbut it does affect the structure of secondary oscillations.\nAn incoherent potential will drive the CMB oscillator incoherently,\nand therefore it may happen that the secondary oscillations get\nwashed out as a result of incoherence.\n\n\n\\section{Tool 1: Scalar, vector, and tensor decomposition}\\label{svt}\nHaving identified the main qualitative novelties in defecy calculations,\nwe now proceed to present the set of tools required for performing\nhigh accuracy calculations in these scenarios. We start with the decomposition\ninto scalar, vector, and tensor components. \nLet $\\Theta_{\\mu\\nu}({\\bf x})$ be the defect stress-energy tensor. \nWe may Fourier analyze it \n\\begin{equation}\n\\Theta_{\\mu\\nu}({\\bf x})={\\int d^3k}\\Theta_{\\mu\\nu}({\\bf k})\ne^{i{\\bf k}\\cdot {\\bf x}}\n\\end{equation}\nand decompose its Fourier components as:\n\\begin{eqnarray}\n\\Theta_{00}&=&\\rho^d\\\\\n\\Theta_{0i}&=&i{\\hat k_i}v^d+\\omega^d_i\\\\\n\\Theta_{ij}&=&p^d\\delta_{ij}+\n{\\left({\\hat k_i}{\\hat k_j}-{1\\over 3}\\delta_{ij}\\right)}\n\\Pi^S+\\nonumber\\\\\n&&i{\\left({\\hat k_i}\\Pi_j^V+{\\hat k_j}\\Pi_i^V\\right)}\n+\\Pi_{ij}^T\n\\end{eqnarray}\nwith ${\\hat k^i}\\omega^d_i=0$, ${\\hat k^i}\\Pi^V_i=0$,\n${\\hat k^i}\\Pi_{ij}^T=0$, and $\\Pi^{Ti}_{i}=0$.\nThe variables $\\{\\rho^d, v^d, p^d, \\Pi^S\\}$\nare the scalars, $\\{ \\omega^d_i, \\Pi^V_i\\}$ the vectors,\nand $\\Pi^T_{ij}$ the tensors. The decomposition\ncan be inverted by means of\n\\begin{eqnarray}\nv^d&=&-i{\\hat k^i}\\Theta_{0i}\\\\\n\\omega^d_i&=&(\\delta_i^j-{\\hat k^i}{\\hat k_j})\\Theta_{0j}\n\\end{eqnarray}\nand\n\\begin{eqnarray}\np^s&=&{1\\over 3}\\Theta^i_i\\\\\n\\Pi^S&=&{3\\over 2}({\\hat k^i}{\\hat k^j}-{1\\over 3}\n\\delta^{ij})\\Theta_{ij}\\\\\n\\Pi^V_i&=&-i{\\left({\\hat k^j}\\delta^l_i-{\\hat k_i}{\\hat k^j}\n{\\hat k^l}\\right)}\\Theta_{lj}\\\\\n\\Pi^T_{ij}&=&( \\delta^l_i\\delta^m_j-{1\\over 2}\\delta_{ij}\\delta^{lm}\n+{1\\over 2} {\\hat k_i}{\\hat k_j}{\\hat k^l}{\\hat k^m}\n+{1\\over 2} ({\\hat k^l}{\\hat k^m}\\delta_{ij}+\\nonumber\\\\\n&&{\\hat k_i}{\\hat k_j}\\delta^{lm})- ({\\hat k_i}{\\hat k^l}\n\\delta^m_j+{\\hat k_j}{\\hat k^l}\\delta^m_i) )\\Theta_{lm}\n\\end{eqnarray}\nalthough simpler recursive formulae may be written.\n\nThis decomposition and choice of harmonics is slightly different from \nthe one used in Hu and White \\cite{hw}, and Kodama and Sasaki \\cite{KS}. The reason for this\nis that in \\cite{hw} and \\cite{KS} one assumes that all variables represent \nsquare roots of power spectra. Isotropy can then be assumed.\nThis procedure will indeed lead to the right ensemble average \n$P(k)$ and $C_\\ell$ if the source is coherent (or a decomposition\ninto coherent eigenmodes has been performed.) However it is not\nvalid for each realization of an incoherent source.\n\n\n\\section{Tool 2: Unequal-time correlators}\\label{corrs}\n\nThe unequal time correlators are defined as \n\\begin{equation} \n{\\langle \\Theta_{\\mu\\nu}({\\bf k},\\eta)\\Theta^\\star_{\\alpha\\beta} \n({\\bf k},\\eta ')\\rangle}\\equiv{\\cal C}_{\\mu\\nu,\\alpha\\beta}(k,\\eta,\\eta ') \n\\end{equation} \nwhere $\\Theta_{\\mu\\nu}$ is the stress energy tensor, \n${\\bf k}$ is the wave-vector, and $\\eta$ and $\\eta '$ \nare any two (conformal) times. The \nUETCs determine all other 2 point functions, most notably \nCMB and LSS power spectra $C_\\ell$ and $P(k)$. \n\nAll correlators between modes at $({\\bf k},\\eta)$ and\n$({\\bf k}',\\eta')$ will be proportional to $\\delta({\\bf k}-{\\bf k}')$\ndue to translational invariance. We shall drop this factor in all formulae.\nThe correlators can also be functions of $k$ alone,\ndue to isotropy. Since conjugation corresponds to ${\\bf k}\\rightarrow -{\\bf k}$, isotropy implies that the correlators must be real. Because of incoherence \nthe correlators will be generic functions of $\\eta$ and $\\eta'$. \n\nFurthermore, the form of the S+V+T decomposition fixes\nfurther the form of the correlators. One can always write down the most\ngeneral form of a correlator, and then contract the result with\n${\\hat k_i}$ or $\\delta_{ij}$, wherever appropriate, \nto obtain further conditions. For instance for\nany scalar $S$ and vector $V_i$ we could write\n\\begin{equation}\n{\\langle S V_i\\rangle}=\\alpha(k){\\hat k_i}\n\\end{equation}\nBy contracting with ${\\hat k_i}$ we would then conclude that\n$\\alpha(k)=0$. Proceeding in this way we can show that cross\ncorrelators involving components of different type (S, V, or T)\nmust be zero. Furthermore for any two vectors $V_i$, $W_i$,\none has\n\\begin{equation}\n{\\langle V_i W^*_j\\rangle}=\nf^{VW}(k,\\eta,\\eta')(\\delta_{ij}- {\\hat k_i}{\\hat k_j})\n\\end{equation}\nand so instead of 6 functions we have only one. In order to agree\nwith conventions used in the literature we shall instead define this single\nfunction by means of \n\\begin{equation}\nf^{VW}(k,\\eta,\\eta')=\\sum_{i}{\\langle V_i W^*_i\\rangle}\n\\end{equation}\n\n\nFor correlators involving two tensor quantities one can use similar\narguments to prove the general form \n\\begin{eqnarray}\n{\\langle \\Pi^T_{ij} \\Pi^{T\\star}_{kl}\\rangle}&=&\nf^{\\Pi^T\\Pi^T}(k,\\eta,\\eta')\n( \\delta_{ij}\\delta_{kl} -(\\delta_{ik}\\delta_{jl}+\\delta_{il}\\delta_{jk})\\nonumber\\\\\n&&-(\\delta_{ij}{\\hat k_k}{\\hat k_l}\n+\\delta_{kl}{\\hat k_i}{\\hat k_j}) \n+(\\delta_{ik}{\\hat k_j}{\\hat k_l}\n+\\delta_{il}{\\hat k_j}{\\hat k_k}+\\nonumber\\\\\n&&\\delta_{jk}{\\hat k_i}{\\hat k_l}+\n\\delta_{jl}{\\hat k_i}{\\hat k_k})-{\\hat k_i}{\\hat k_j}\n{\\hat k_k}{\\hat k_l})\n\\end{eqnarray}\nand again we have a single function rather than 21. Again in order to\ncomply with conventions in the literature we shall define this single function\nby means of \n\\begin{equation}\nf^{\\Pi^T\\Pi^T}(k,\\eta,\\eta')=\\sum_{ij}{\\langle \\Pi^T_{ij} \\Pi^{T\\star}_{ij}\n\\rangle}\n\\end{equation}\n\n\nHence there should be 10 scalar correlator functions\n\\begin{equation}\n\\begin{array} {cccc} \nf^{\\rho^d\\rho^d}& f^{\\rho^d v^d}& f^{\\rho^d p^d}& f^{\\rho^d \\Pi^S}\\\\\n\\cdots&f^{v^d v^d}&f^{v^dp^d} &f^{v^d \\Pi^S}\\\\ \n\\cdots&\\cdots &f^{p^d p^d}&f^{p^d \\Pi^S}\\\\\n\\cdots&\\cdots &\\cdots &f^{\\Pi^S\\Pi^S}\\\\\n\\end{array}\n\\end{equation}\n3 vector correlators:\n\\begin{equation}\n\\begin{array} {cc}\nf^{\\omega^d\\omega^d}&f^{\\omega^d\\Pi^V}\\\\\n\\cdots& f^{\\Pi^V\\Pi^V}\n\\end{array}\n\\end{equation}\nand a single tensor correlator function $f^{\\Pi^T\\Pi^T}$.\n\n\nIn general these functions are functions of $(k,\\eta,\\eta')$,\nand this is indeed the case during the matter radiation transition.\nHowever well into the matter and radiation epochs there is scaling,\nand these functions may be written as:\n\\begin{equation}\nf^{XY}(k,\\eta,\\eta')={F^{XY}(x,x')\\over \\sqrt{\\eta\\eta '}}\n\\end{equation}\nwhere $XY$ represents any pair of superscripts considered above,\nand $x=k\\eta$ and $x'=k\\eta'$. The above scaling form results\nfrom the dimensional analysis argument: $[\\Theta_{\\mu\\nu}(x)]=1/L^2$, \n$[\\Theta_{\\mu\\nu}(k)]=L$, $[\\delta({\\bf k})]=L^3$, $[f^{XY}]=1/L$.\nWe have used units where $G=c=1$.\n\n\n\\section{Causality constraints}\\label{caus}\n\nFrom analyticity conditions \\cite{tps} we can use isotropy and symmetry\n\\cite{tps,uzan} to derive general expansions in $\\bf k$ around\n$k_i=0$. This is usually very helpful to check numerical results. \nWe find:\n\n\\bea\n\\vev{\\Theta_{00}(k,\\eta)\\Theta_{00}(k,\\eta')}&=&X\\nonumber\\\\\n\\vev{\\Theta_{00}(k,\\eta)\\Theta_{0i}(k,\\eta')}&=&ik_iY\\nonumber\\\\\n\\vev{\\Theta_{00}(k,\\eta)\\Theta_{ij}(k,\\eta')}&=&V\\delta_{ij}+Wk_ik_j\\nonumber\\\\\n\\vev{\\Theta_{0i}(k,\\eta)\\Theta_{0j}(k,\\eta')}&=&T\\delta_{ij}+Uk_ik_j\\nonumber\\\\\n\\vev{\\Theta_{0i}(k,\\eta)\\Theta_{jk}(k,\\eta')}&=&i [ Qk_i\\delta_{jk} +\nR(k_j\\delta{ik}+k_k\\delta_{ij})\\nonumber\\\\\n&&+Sk_ik_jk_k ]\\nonumber\\\\\n\\vev{\\Theta_{ij}(k,\\eta)\\Theta_{kl}(k,\\eta')}&=&A\\delta_{ij}\\delta_{kl}\n+ B(\\delta_{ik}\\delta_{jl}+\\delta{il}\\delta{jk})\\nonumber\\\\\n&&+C(k_ik_j\\delta{kl}+k_kk_l\\delta{ij})\\nonumber\\\\\n&&+D(k_ik_k\\delta{jl}+k_ik_l\\delta{jk}\n+k_jk_l\\delta{ik}\\nonumber\\\\\n&&+k_jk_k\\delta{il}) + Ek_ik_jk_kk_l\n\\eea\nwhere A, B etc. are functions independent of $k$.\nBy applying the scalar, vector and tensor decomposition we can then find\nthe specific form of the correlators in our formalism to obtain relations\nbetween the correlators\n\\bea\nf^{\\rho\\rho}&=&X\\nonumber\\\\\nf^{\\rho p}&=&V+{1\\over 3}k^2W\\nonumber\\\\\nf^{\\rho v}&=&kY\\nonumber\\\\\nf^{\\rho\\Pi^S}&=&{3\\over 2}W(k^2-{1\\over 3})\\nonumber\\\\\nf^{pp}&=&A+{2\\over3}B+{2\\over 3}k^2(C+{2\\over 3}D)+{1\\over 9}k^4E\\nonumber\\\\\nf^{pv}&=&k(Q+{2\\over 3}R) +{1\\over 3}Sk^2\\nonumber\\\\\nf^{p\\Pi^S}&=&(C-{4\\over3}D)k^2+{1\\over 3}Ek^4\\nonumber\\\\\nf^{vv}&=&-(T+k^2U)\\nonumber\\\\\nf^{v\\Pi^S}&=&k(2R-Sk^2)\\nonumber\\\\\nf^{\\Pi^S\\Pi^S}&=&3B+4Dk^2+Ek^4\\nonumber\\\\\nf^{\\omega\\omega}&=&2T\\nonumber\\\\\nf^{\\omega\\Pi^S}&=&2Rk\\nonumber\\\\ \nf^{\\Pi^V\\Pi^V}&=&2B\\nonumber\\\\ \nf^{\\Pi^T\\Pi^T}&=&4B\n\\eea\nWe can now derive ${\\bf{k}}\\rightarrow 0$ constraints on the correlators.\nThese may \nhelp to complete the functions $F^{XY}$ near the origin, where they may\nnot be accessible from simulations due to low sampling of\npoints on the lattice. Specifically, we get ratios between the scalar,\nvector and tensor anisotropic stresses and between the momentum and\nvorticity,\n\\bea\\label{stress}\nf^{\\Pi^S\\Pi^S}:f^{\\Pi^V\\Pi^V}:f^{\\Pi^T\\Pi^T}\n&=&3:2:4\\nonumber\\\\\nf^{vv}:f{\\omega\\omega}&=&1:2\n\\eea\nto zeroth order and,\n\\bea\nf^{v\\Pi^S}&\\approx&f^{\\omega_i\\Pi^V_i}\n\\eea\nto first order.\n\n\\section{Tool 3: Simulation determination of the correlators}\\label{sim}\nHaving developped the necessary analytical tools we now describe\nhow to apply them to simulations. We consider the work in \\cite{chm}.\nThe simulation starts with a network of strings obtained using the algorithm\ndeveloped in \\cite{VV1} which simulates the symmetry breaking of the \nunderlying field by selecting random phases for the field at each point in\nthe lattice. Strings are identified on points in the lattice where the phase\nof the field has a non-zero winding number. The strings are described by\ntheir position $\\bX(\\sigma,\\eta)$ where $\\sigma$ is a parameter running\nalong the string and $\\eta$ is conformal time. By imposing the following\ngauge conditions \n\\begin{equation}\n\\bXd.\\bXp=0 \\qquad \\bXd^2+\\bXp^2=1\n\\end{equation}\nwhere dots and primes denote derivatives with respect to $\\eta$ and $\\sigma$, respectively,\nthe equation of motion takes on the simple form of the wave equation \n\\begin{equation}\n\\dprime \\bX^2 +\\ddot{\\bX}^2 = 0\n\\end{equation}\n and can be discretised on the lattice so that all the possible velocities\ntake integer values only\\cite{fst,mairi}. This greatly increases the\naccuracy and speed of \nstring network codes based on this algorithm. \nThe network is then evolved using the discretised equations of motion and\nintercommuting relations. To simulate the extraction of energy from the\nsystem due to the decay of the string loops into gravitational radiation\nand/or particles, loops of a minimum size are excised from the\nsimulation at each time step. This also ensures that the network scales with\nrespect to the conformal time $\\eta$ which enables us to extend the\ndynamical range of the resulting correlation functions beyond the limited\nrange covered in the simulation. Fig.~\\ref{fig1} shows how the correlation\nlength defined by \n$\\xi={\\sqrt{\\mu/\\rho_l}}$\nscales as a function of conformal time. Here, $\\rho_l$ is the density of 'long' strings.\n\n\\begin{figure}[plot.ps]\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{plot.ps}\n%\\centerline{\\psfig{file=plot.ps,width=8 cm,angle=0}}\n\\end{center}\n\\caption{Scaling of the correlation length $\\xi$ for various loop\ncut off sizes.}\n\\label{fig1}\n\\end{figure}\n\t\nWe performed simulations\nwith box sizes ranging from $128^3$ to $600^3$, with a cut-off on the loop\nsize of two links. Realisation averages were carried out with $256^3$ boxes\nonce it was determined that the general form of the correlators scaled very\naccurately with box size. To evaluate the UETCs from the simulations we\nselected times in the range $0.1 N<t<N/4$, where $N$ is the box size,\nwhen we were sure that\nthe string network was scaling, and when boundary effects are \nstill excluded by causality. At each of the time steps the vectors $\\bXd$ and\n$\\bXp$\nfrom each point along the strings in the network were stored. From\nthis we obtained the time evolution of the network's stress-energy\ntensor$\\Theta_{\\mu\\nu}$ at each point on the lattice using \n\\begin{equation}\n\\Theta_{\\mu\\nu}({\\bf x})={\\mu\\int d\\si\n(\\Xd^{\\mu}\\Xd^{\\nu}-\\Xp^{\\mu}\\Xp^{\\nu})\\delta^3({\\bf x}-\\bX(\\si,\\eta))} \n\\end{equation}\n\nThe Fast Fourier Transforms of all 10 independent components of the string \nstress-energy were then decomposed into irreducible scalar, vector and\ntensor modes using eqns in Section (\\ref{svt}). \nThis resulted in all the SVT components being\ncomputed directly from the simulation without making assumptions on energy\nconservation and on the details of energy dissipation from the string\nnetwork. The drawback of obtaining all the components directly in such a\nmanner is that the process becomes computationally intensive for even\nmodestly sized simulations, e.g. $256^3$, as, in effect, one has to deal with\n$\\approx 10$ times the number of variables at each point on the lattice. \n\nBy cross-correlating the decomposed stress-energy components from a central\ntime with those from all the stored time steps the 14 independent UETCs\n$f^{XY}(k,\\eta,\\eta')$ were computed. \n\n\nIn Figs.\\ref{first}-\\ref{last} we display the forms of the various functions \n$f^{XY}(k,25,\\eta)$ where $k$, $\\eta$ and $\\eta'$ are in lattice units.\nThis is enough to infer the scaling functions $F^{XY}(x,x')$.\nOne can see that these correlators fall off very quickly away from the\ndiagonal, a phenomenon known as incoherence \\cite{inc} as we explained\nabove. Incoherence\ndetermines whether or not we have enough dynamical range to compute\nthe UETCs: if we see the fall off completly clearly we have enough\ndynamical range!\n\n\\begin{figure}[pow.ps]\n%\\centerline{\\epsfig{file=pow.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{pow.ps}\n\\end{center}\n\\caption{The function ${\\langle |\\rho^{d}|^2\\rangle}(k,25,\\eta)$.}\n\\label{first}\n\\end{figure}\n\n\\begin{figure}[U-U.ps]\n%\\centerline{\\psfig{file=U-U.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{U-U.ps}\n\\end{center}\n\\caption{The function ${\\langle |v^d|^2 \\rangle}(k,25,\\eta)$.}\n\\label{fig2}\n\\end{figure}\n\n\\begin{figure}[p-p.ps]\n%\\centerline{\\psfig{file=p-p.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{p-p.ps}\n\\end{center}\n\\caption{The function ${\\langle |p^d|^2\\rangle}(k,25,\\eta)$.}\n\\label{fig3}\n\\end{figure}\n\n\\begin{figure}[sca.ps]\n%\\centerline{\\psfig{file=sca.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{sca.ps}\n\\end{center}\n\\caption{The function ${\\langle |\\Pi^S|^2\\rangle}(k,25,\\eta)$.}\n\\label{fig4}\n\\end{figure}\n\n\\begin{figure}[V.ps]\n%\\centerline{\\psfig{file=V.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{V.ps}\n\\end{center}\n\\caption{The function $\\sum_i{\\langle |\\omega^d_i|^2 \\rangle}(k,25,\\eta)$.}\n\\label{fig5}\n\\end{figure}\n\n\\begin{figure}[vec.ps]\n%\\centerline{\\psfig{file=vec.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{vec.ps}\n\\end{center}\n\\caption{The function $\\sum_i{\\langle |\\Pi^V_i|^2\\rangle}(k,25,\\eta)$.}\n\\label{fig6}\n\\end{figure}\n\n\\begin{figure}[ten.ps]\n%\\centerline{\\psfig{file=ten.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{ten.ps}\n\\end{center}\n\\caption{The function $\\sum_{ij}{\\langle |\\Pi^T_{ij}|^2\\rangle}(k,25,\\eta)$.}\n\\label{fig7}\n\\end{figure}\n\n\\begin{figure}[rho-U.ps]\n%\\centerline{\\psfig{file=rho-U.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{rho-U.ps}\n\\end{center}\n\\caption{The function ${\\langle \\rho^d v^{d\\star}\\rangle}(k,25,\\eta)$.}\n\\label{fig8}\n\\end{figure}\n\n\\begin{figure}[rho-p.ps]\n%\\centerline{\\psfig{file=rho-p.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{rho-p.ps}\n\\end{center}\n\\caption{The function ${\\langle \\rho^d p^{d\\star} \\rangle}(k,25,\\eta)$.}\n\\label{fig9}\n\\end{figure}\n\n\\begin{figure}[rho-sca.ps]\n%\\centerline{\\psfig{file=rho-sca.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{rho-sca.ps}\n\\end{center}\n\\caption{The function ${\\langle \\rho^d \\Pi^{S\\star}\\rangle}(k,25,\\eta)$.}\n\\label{fig10}\n\\end{figure}\n\n\\begin{figure}[p-U.ps]\n%\\centerline{\\psfig{file=p-U.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{p-U.ps}\n\\end{center}\n\\caption{The function ${\\langle p^d v^{d\\star}\\rangle}(k,25,\\eta)$.}\n\\label{fig11}\n\\end{figure}\n\n\\begin{figure}[p-sca.ps]\n%\\centerline{\\psfig{file=p-sca.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{p-sca.ps}\n\\end{center}\n\\caption{The function ${\\langle p^d \\Pi^{S\\star}\\rangle}(k,25,\\eta)$.}\n\\label{fig12}\n\\end{figure}\n\n\\begin{figure}[U-sca.ps]\n%\\centerline{\\psfig{file=U-sca.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{U-sca.ps}\n\\end{center}\n\\caption{The function ${\\langle v^d\\Pi^{S\\star}\\rangle}(k,25,\\eta)$.}\n\\label{fig13}\n\\end{figure}\n\n\\begin{figure}[v-V.ps]\n%\\centerline{\\psfig{file=v-V.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{v-V.ps}\n\\end{center}\n\\caption{The function $\\sum_i{\\langle \\omega^d_i \\Pi^{V\\star}_i\\rangle}(k,25,\\eta)$.}\n\\label{last}\n\\end{figure}\n\n\\begin{figure}[rat.ps]\n%\\centerline{\\psfig{file=rat.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{rat.ps}\n\\end{center}\n\\caption{This plot shows the scaling autocorrelation of the energy\ndensity, the scalar vector and tensor anisotropic stresses.\nWe see that the energy density dominates all the other components.}\n\\label{fig15}\n\\end{figure}\n\n\\begin{figure}[vel.ps]\n%\\centerline{\\psfig{file=vel.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{vel.ps}\n\\end{center}\n\\caption{Same but for the energy density, the pressure, the\nvelocity and the vorticity}\n\\label{fig16}\n\\end{figure}\n\nA striking feature \nof our results is the dominance of \n$\\Theta_{00}$ over all other components (see Figs.~\\ref{fig15}\nand \\ref{fig16}).\n The string anisotropic \nstresses are in the predicted \\cite{tps} ratios \n$|\\Theta^S|^2:|\\Theta^V|^2:|\\Theta^T|^2$ of $3:2:4$, \nas $k\\tau\\rightarrow 0$. \nHowever $|\\Theta_{00}|^2\\gg | \\Theta^S|^2$, and so scalars dominate \nover vectors and tensors. Also the energy density power spectrum \nrises from a white noise tail at $k\\tau\\approx 0$ into a peak \nat $k\\tau\\approx 20$, after which it falls off. Sub-horizon \nmodes are therefore of great importance. \nThese features consistently appeared for all \nbox sizes, and are independent of the cutoff size imposed \non the loops. \n\n\n\n\\section{Tool 4: Decomposition into eigenmodes}\\label{eig}\nThe UETCs $c_{\\mu\\nu,\\alpha\\beta}(k\\tau,k\\tau ')$ may be diagonalised \n\\cite{pst} and written as \n\\begin{equation}\\label{eig1} \nc_{\\mu\\nu,\\alpha\\beta}(k\\tau,k\\tau ')={\\sum_i}\\lambda^{(i)} \nv^{(i)}_{\\mu\\nu}(k\\tau)v^{(i)}_{\\alpha\\beta}(k\\tau') \n\\end{equation} \nwhere $\\lambda^{(i)}$ are eigenvalues. In general, defects are \nincoherent sources for perturbations \\cite{inc}, which means that \nthis matrix does not \nfactorize into the product of two vectors \n$v_{\\mu\\nu}(k\\tau)v_{\\alpha\\beta}(k\\tau')$. Standard codes solving for \nCMB and LSS power spectra assume coherence. However \nwe see that an incoherent source may be represented as an \nincoherent sum of coherent sources. We may therefore \nfeed each eigenmode into standard codes \\cite{cmbfast} to find the \n$C^{(i)}_\\ell$ and $P^{(i)}(k)$ associated with each mode. \nThe series $\\sum \\lambda^{(i)} \nC_\\ell^{(i)}$ and $\\sum \\lambda^{(i)}P^{(i)}(k)$ provide \nconvergent approximations to the power spectra.\n\n\n\\begin{figure}[eigenpow.ps]\n%\\centerline{\\psfig{file=eigenpow.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{eigenpow.ps}\n\\end{center}\n\\caption{Decomposition into eigenmodes of the energy density.}\n\\label{fig17}\n\\end{figure}\n \n\nIn Fig.~\\ref{fig17} we show the eigenmodes corresponding to the energy\ndensity $\\Theta_{00}$. We see that the leading eigenmode carries\nthe mark of the peak in the energy power spectrum at $x \\approx 20$.\nThe other eigenmodes become very small very quickly and change sign\nwith higher and higher frequency. If we compute the $C_\\ell$ power\nspectrum for each of these modes, and sum the series, we find\nquick convergence shortly after 20 modes have been included\n(see Fig.~\\ref{fig18}).\n\n\\begin{figure}[cl.ps]\n%\\centerline{\\psfig{file=cl.ps,width=8 cm,angle=0}}\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{cl.ps}\n\\end{center}\n\\caption{The $C_\\ell$ spectrum and inferred from 20 eigenmodes.}\n\\label{fig18}\n\\end{figure}\n \n\n\\section{Some results}\\label{result}\n\nThe methods described above supplied a variety of interesting results\nfor cosmic strings. They show that local strings, unlike global defects\nhave a Doppler peak. The main uncertainty seems to be in the details\nof how strings loose energy (see e.g. \\cite{vinc,vhs}). String decay products are clearly the most uncertain aspect \nof cosmic string theory. By measuring the full 14 UETCs associated \nwith long strings, we assume nothing \nabout decay products when extracting information from simulations \nThe simulations will then also place constraints \nupon the decay products. \n\nIn Fig.~\\ref{res1} we plot $\\surd[\\ell(\\ell+1)C_\\ell/2\\pi]$, \nsetting the Hubble constant to \n$H_0=50$ Km sec$^{-1}$ Mpc$^{-1}$, the baryon fraction to \n$\\Omega_b=0.05$, and assuming a flat geometry, no cosmological \nconstant, 3 massless neutrinos, standard recombination, \nand cold dark matter. \nWe also superimpose current experimental points. \nThe most interesting feature is \nthe presence of a reasonably high Doppler peak at $\\ell=400-600$, \nfollowing a pronouncedly tilted large angle plateau\n(cf. \\cite{per}). \nThis feature sets local strings apart from global defects. \nIt puts them in a better shape to face the current data. \n \nThe CMB power spectrum is relatively insensitive to \nthe equation of state of the extra fluid. \nWe have plotted results for $w^X=1/3, 0.1, 0.01$. \nDumping some energy into CDM has negligible effect. \nSmall dumps into \nbaryon and radiation fluids, on the contrary, \nboost the Doppler peak very strongly. We plotted the effect \nof dumping 5\\% of the energy into the radiation fluid. \n \n\\begin{figure}[res1.ps] \n%\\centerline{\\psfig{file=res1.ps,width=8 cm,angle=0}} \n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{res1.ps}\n\\end{center}\n\\caption{The CMB power spectra predicted by cosmic strings decaying \ninto loop and radiation fluids with $w^X=1/3, 0.1, 0.01, 0$. \nWe have plotted $(\\ell(\\ell+1)C_\\ell/2\\pi)^{1/2}$ in $\\mu K$, \nand superposed several experimental points. The higher curve \ncorresponding to $w^X=1/3$ shows what happens if 5\\% of the \nenergy goes into the radiation \nfluid.} \n\\label{res1} \n\\end{figure} \n\n\n\\begin{figure}[res2.ps] \n%\\centerline{\\psfig{file=res2.ps,width=8 cm,angle=0}} \n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{res2.ps}\n\\end{center}\n\\caption{The power spectrum in CDM fluctuations for \ncosmic strings, with $w^X=0.01,0.1,1/3$. We plotted \nalso the standard CDM scenario prediction and points inferred \nby Peacock and Dodds from galaxy surveys. The top 2 $w^X=1/3$ curves \ncorrespond to a 5\\% transfer into CDM, and a 20\\% transfer into \nbaryons (top).} \n\\label{res2} \n\\end{figure} \n\n\nThe LSS power spectra on the other hand is strongly dependent \non $w^X$. \nIn Fig.~\\ref{res2} we plotted the CDM power spectrum $P(k)$ \ntogether with experimental points as in \\cite{pdodds}. \nThe normalization has been fixed by COBE data points. \nWe see that the peak of the spectrum is always at smaller scales \nthan standard CDM predictions, or observations. \nHowever the overall normalization of the spectrum increases \nconsiderably as $w^X$ decreases. \n \nThe CDM rms fluctuation in 8 $h^{-1}$Mpc spheres is $\\sigma_8=0.4, \n0.6, 1.8$ for $w^X=1/3,0.1,0.01$. Hence relativistic decay products \nmatch well the observed $\\sigma_8\\approx 0.5$. On the other hand \nin 100 $h^{-1}$Mpc spheres one requires bias $b_{100}= \n\\sigma_{100}^{data}/\\sigma_{100}=4.9, 3.7, 1.6$ \nto match observations. \n \nEnergy dumps into radiation have no effect on the CDM power spectrum. \nHowever if there is energy transfer into CDM or baryons, even \nwith $w^X=1/3$, the CDM power spectrum is highly enhanced. \nThis is due to the addition of small scale entropy fluctuations \nto the usual fluctuations gravitationally induced by the stings. \nWe plot the result of a 5\\% transfer into CDM and a 20\\% \ntransfer into baryons (with $w^X=1/3$) \nfor which $b_{100}=2.0, 1.5$. \n \nHence in our calculations local strings have a bias problem \nat 100 $h^{-1}$Mpc, although its magnitude is not \nas great as found in \\cite{abr}. It depends sensitively on \nthe decay products, being reduced if the strings have a channel \ninto non-relativistic particles, \nor if there is some energy transfer into the baryon and CDM fluid. \nThe main problem with strings in an $\\Omega=1$, $\\Omega_b=0.05$, \n$\\Omega_\\Lambda = 0$ CDM Universe \nis that the \nshape of $P(k)$ never seems to match observations. This may not \nbe the case with other cosmological parameters \\cite{abr2,avelino}. \n \n\\section{Strings and inflation}\n\nOne way of improving upon the previous situation is to consider \nmixed scenarios: strings and inflation. \nRecent developments in inflation model building, based on supersymmetry,\nhave produced compelling models in which strings are \nproduced at the end of inflation.\nIn such models the cosmological perturbations are \nseeded both by the defects and by the quantum fluctuations.\n\nA major drawback of inflationary theories \nis that they are far-removed from particle physics\nmodels. Attempts to improve on this state of affairs have been made\nrecently, resorting to supersymmetry \n\\cite{Cas+89,DTermInfl,rachel,LytRio98,Cop+94,Tka+98,sug}.\nIn these models one identifies\nflat directions in the potentials, which are enforced by a (super)symmetry. \nSuch flat directions produce ``slow-roll inflation''. \nIn order to stop inflation one must tilt the potential, allowing \nfor the fields to roll down. \nIn so-called D-term supersymmetric inflationary scenarios, \ninflation stops with a symmetry-breaking phase transition, \nat which a U(1) symmetry is spontaneously broken, leading to the \nformation of cosmic strings. This is only the most \nnatural of a whole class of models of so-called hybrid inflation.\nHence a network of cosmic strings is formed at the end of inflation.\n\nIn Figs. (\\ref{res3}) and (\\ref{res4})\n we present power spectra in CMB and CDM produced \nby a sCDM scenario, by cosmic strings, and by strings plus inflation. \nWe have assumed the traditional choice of parameters, setting the Hubble \nparameter\n$H_0=50$ km sec$^{-1}$ Mpc$^{-1}$, the baryon fraction to\n$\\Omega_b=0.05$, and assumed a flat geometry, no cosmological\nconstant, 3 massless neutrinos, standard recombination,\nand cold dark matter. The inflationary perturbations have a \nHarrison-Zel'dovich or scale invariant spectrum, and the amount of\ngravitational radiation (tensor modes)\nproduced during inflation is assumed to be negligible.\n\n\\begin{figure}[res3.ps]\n%\\centering\n%\\leavevmode\\leavevmode \\epsfysize=8cm \\epsfbox{res3.ps}\\\\ \n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{res3.ps}\n\\end{center}\n\\caption{\\label{res3}The CMB power spectra predicted by cosmic strings, sCDM, \nand by inflation and strings with\n$ R_{\\rm{SI}}=0.25,0.5,0.75.$ \nThe large angle\nspectrum is always slightly tilted. The Doppler peak becomes a thick\nDoppler bump at $\\ell=200-600$, modulated by mild undulations.} \n\\end{figure} \n\n\\begin{figure}[res4.ps]\n%\\centering\n\\begin{center}\n\\leavevmode \\epsfysize=8cm \\epsfbox{res4.ps}\n\\end{center} \n\\caption{\\label{res4} The power spectra in CDM fluctuations \npredicted by cosmic strings, sCDM, \nand by inflation and strings with $R_{\\rm{SI}}=0.25,0.5,0.75.$\nWe have also superposed the power spectrum as inferred from surveys\nby Peacock and Dodds.} \n\\end{figure} \n\nWe now summarise the results.\n\\begin{itemize}\n\\item \nThe CMB power spectrum shape in these models\nis highly exotic. The inflationary \ncontribution is close to being Harrison-Zel'dovich. Hence it produces\na flat small $\\ell$ CMB spectrum. The admixture of strings, \nhowever, imparts a tilt.\nDepending on $R_{\\mathrm{SI}}$ (the ratio of large angle anisotropy\ndue to strings and inflation)\none may tune the CMB plateau tilt between 1\nand about 1.4, without invoking primordial tilt and inflation\nproduced gravity waves.\n\n\\item\nThe proverbial inflationary Doppler peaks are transfigured in these\nscenarios into a thick Doppler bump, covering the region \n$\\ell=200-600$. The height of the peak is similar for sCDM and strings,\nwith standard cosmological parameters. \nThe Doppler bump is modulated by small undulations, \nwhich cannot truly be called secondary peaks. \nBy tuning $R_{\\mathrm{SI}}$ one may achieve any degree\nof secondary oscillation softening. This provides a major\nloophole in the argument linking inflation with secondary\noscillations in the CMB power spectrum \\cite{andbar,inc}. \nIf these oscillations were not\nobserved, inflation could still survive, in the form of the models\ndiscussed above.\n\n\\item\nIn these scenarios the LSS of \nthe Universe is almost all produced by inflationary fluctuations. \nHowever COBE scale CMB anisotropies are due to both strings and \ninflation. Therefore COBE normalized CDM fluctuations are \nreduced by a factor $(1+R_{\\mathrm{SI}})$ in strings plus inflation scenarios. \nThis is equivalent to multiplying \nthe sCDM bias by ${\\sqrt{1+R_{\\mathrm{SI}}}}$ on all scales, except\nthe smallest, where the string contribution may be\nnon negligible. Given that \nsCDM scenarios produce too much structure on small scales\n(too many clusters) \nthis is a desirable feature. \n\\end{itemize}\n\n\nOverall ``Strings plus inflation'' are interesting first of all as an inflationary\nmodel. Its ``flat potential'' is not the result of a finely tuned coupling\nconstant, but the result of a symmetry. Hence in some sense\nthese models achieve inflation without fine tuning. The only free parameters\nare the number of inflationary e-foldings, and the scale of symmetry\nbreaking. These parameters also fix the absolute (and therefore relative)\nnormalizations of string and inflationary fluctuations.\n\nThe combination of these two scenarios smoothes \nthe hard edges of either separate component, leaving \na much better fit to LSS and CMB power spectra. We illustrated this\npoint in this review, but left\nout a couple of issues currently under investigation\nwhich we now summarise.\n\nThe CDM power spectrum in these scenarios has a break at very small\nscales, when string produced CDM fluctuations become dominant over\ninflationary ones. This aspect was particularly emphasized in\n\\cite{stinf2}, and there is some observational evidence in favour\nof such a break. An immediate implication of this result is that\nit is easier to form structure at high redshifts \\cite{steidel,lalfa}. \nIn \\cite{bmw} it is shown that even with Hot Dark Matter, these\nscenarios produce enough damped\nLyman-$\\alpha$ systems, to account for the recent high-redshift\nobservations.\n\nAnother issue currently under investigation is the timing of structure\nformation \\cite{steidel}. Active models drive fluctuations\nat all times, and therefore produce a time-dependence\nin $P(k)$ different from passive models. The effect is subtle,\nbut works so as to slow down structure formation. Hence for\nthe same normalization nowadays there is more structure at high\nredshifts in string scenarios \\cite{AB95,MB96,ZLB}. \n\n\n\\section{Defects and Baryogenesis}\n\nBaryogenesis forms another overlap area between defects in particle physics and cosmology. The goal is to explain the observed asymmetry between matter and antimatter in the Universe. In particular, the objective is to be able to deduce the observed value of the net baryon to entropy ratio at the present time\n\\begin{equation}\n{{\\Delta n_B} \\over s}(t_0) \\, \\sim \\, 10^{-10} \n\\end{equation}\nstarting from initial conditions in the very early Universe when this ratio vanishes. Here, $\\Delta n_B$ is the net baryon number density and $s$ the entropy density.\n\nAs pointed out by Sakharov \\cite{Sakharov}, three basic criteria must be satisfied in order to have a chance at explaining the data:\n\\begin{enumerate}\n\\item{} The theory describing the microphysics must contain baryon number violating processes.\n\\item{} These processes must be C and CP violating.\n\\item{} The baryon number violating processes must occur out of thermal equilibrium.\n\\end{enumerate}\n\nAs was discovered in the 1970's \\cite{GUTBG}, all three criteria can be satisfied in GUT theories. In these models, baryon number violating processes are mediated by superheavy Higgs and gauge particles. The baryon number violation is visible in the Lagrangian, and occurs in perturbation theory (and is therefore in principle easy to calculate). In addition to standard model CP violation, there are typically many new sources of CP violation in the GUT sector. The third Sakharov condition can also be realized: After the GUT symmetry-breaking phase transition, the superheavy particles may fall out of thermal equilibrium. The out-of-equilibrium decay of these particles can thus generate a nonvanishing baryon to entropy ratio. \n\nThe magnitude of the predicted $n_B / s$ depends on the asymmetry $\\varepsilon$ per decay, on the coupling constant $\\lambda$ of the $n_B$ violating processes, and on the ratio $n_X / s$ of the number density $n_X$ of superheavy Higgs and gauge particles to the number density of photons, evaluated at the time $t_d$ when the baryon number violating processes fall out of thermal equilibrium, and assuming\nthat this time occurs after the phase transition. The quantity $\\varepsilon$ is proportional to the CP-violation parameter in the model. In a GUT theory, this CP violation parameter can be large (order 1), whereas in the standard electroweak theory it is given by the CP violating phases in the CKM mass matrix and is very small. As shown in \\cite{GUTBG} it is easily possible to construct models which give the right $n_B / s$ ratio after the GUT phase transition (for recent reviews of baryogenesis see \\cite{Dolgov} and \\cite{RubShap}).\n \nThe ratio $n_B / s$, however, does not only depend on $\\varepsilon$, but also on $n_X / s (t_d)$. If the temperature $T_d$ at the time $t_d$ is greater than the mass $m_X$ of the superheavy particles, then it follows from the thermal history in standard cosmology that $n_X \\sim s$. However, if $T_d < m_X$, then the number density of $X$ particles is diluted exponentially in the time interval between when $T = m_X$ and when $T = T_d$. Thus, the predicted baryon to entropy ratio is also exponentially suppressed:\n\\begin{equation} \\label{expdecay}\n{n_B \\over s} \\, \\sim \\, {1 \\over {g^*}} \\lambda^2 \\varepsilon e^{- m_X / T_d} \\, ,\n\\end{equation}\nwhere $g^*$ is the number of spin degrees of freedom in thermal equilibrium at the time of the phase transition.\nIn this case, the standard GUT baryogenesis mechanism is ineffective.\n\nHowever, topological defects may come to the rescue \\cite{BDH}. As was discussed at the beginning of these lecture notes, topological defects will inevitably be produced in the symmetry breaking GUT transition provided they are topologically allowed in that symmetry breaking scheme. The topological defects provide an alternative mechanism of GUT baryogenesis in the following way:\nInside of topological defects, the GUT symmetry is restored. In fact, the defects can be viewed as solitonic configurations of $X$ particles. The continuous decay of defects at times after $t_d$ provides an alternative way to generate a nonvanishing baryon to entropy ratio. The defects constitute out of equilibrium configurations, and hence their decay can produce a nonvanishing $n_B / s$ in the same way as the decay of free $X$ quanta. \n\nThe way to estimate the $n_B / s$ ratio is as follows: The defect\nscaling solution gives the energy density in defects at all times. Taking the time derivative of this density, and taking into account the expansion of the Universe, we obtain the loss of energy attributed to defect decay. By energetics, we can estimate the number of decays of individual quanta which the defect decay corresponds to. We can then use the usual perturbative results to compute the resulting net baryon number.\n\nProvided that $m_X < T_d$, then at the time when the baryon number violating processes fall out of equilibrium (when we start generating a nonvanishing $n_B$) the energy density in free $X$ quanta is much larger than the defect density, and hence the defect-driven baryogenesis mechanism is subdominant. However, if $m_X > T_d$, then as indicated in (\\ref{expdecay}), the energy density in free quanta decays exponentially. In contrast, the density in defects only\ndecreases as a power of time, and hence can soon dominate baryogenesis.\n\nOne of the most important ingredients in the calculation is the time dependence of $\\xi(t)$, the separation between defects. Immediately after the phase transition at time $t_f$ (when the defect network is formed), the separation is $\\xi(t_f) \\sim \\lambda^{-1} \\eta^{-1}$. In the time period immediately following, the time period of relevance for baryogenesis, $\\xi(t)$ approaches the Hubble radius according to the equation \\cite{Kibble2} \n\\begin{equation} \\label{defsep}\n\\xi(t) \\, \\simeq \\, \\xi(t_f) ({t \\over {t_f}})^{5/4} \\, .\n\\end{equation}\nUsing this result to calculate the defect density, we obtain after some algebra\n\\begin{equation} \\label{barres}\n{{n_B} \\over s}|_{\\rm defect} \\, \\sim \\, \\lambda^2 {{T_d} \\over \\eta} {{n_B} \\over s}|_0 \\, ,\n\\end{equation}\nwhere $n_B / s|_0$ is the unsuppressed value of $n_B / s$ which can be obtained using the standard GUT baryogenesis mechanism. We see from (\\ref{barres}) that even for low values of $T_d$, the magnitude of $n_B / s$ which is obtained via the defect mechanism is only suppressed by a power of $T_d$. However, the maximum strength of the defect channel is smaller than the maximum strength of the usual mechanism by a geometrical suppression factor $\\lambda^2$ which expresses the fact that even at the time of defect formation, the defect network only occupies a small fraction of the volume of space.\n\nIt has been known for some time that there are baryon number violating processes even in the standard electroweak theory. These processes are, however, non-perturbative. They are connected with the t'Hooft anomaly \\cite{tHooft}, which in turn is due to the fact that the gauge theory vacuum is degenerate, and that the different degenerate vacuum states have different quantum numbers (Chern-Simons numbers). In theories with fermions, this implies different baryon number. Configurations such as sphalerons \\cite{sphal} which interpolate between two such vacuum states thus correspond to baryon number violating processes.\n\nAs pointed out in \\cite{KRS85}, the anomalous baryon number violating processes are in thermal equilibrium above the electroweak symmetry breaking scale. Therefore, any net baryon to entropy ratio generated at a higher scale will be erased, unless this ratio is protected by an additional quantum number such as a nonvanishing $B - L$ which is conserved by electroweak processes.\n\nHowever, as first suggested in \\cite{Shap} and discussed in detail in many recent papers (see \\cite{EWBGrev} for reviews of the literature), it is possible to regenerate a nonvanishing $n_B / s$ below the electroweak symmetry breaking scale. Since there are $n_B$ violating processes and both C and CP violation in the standard model, Sakharov's conditions are satisfied provided that one can realize an out-of-equilibrium state after the phase transition. Standard model CP violation is extremely weak. Thus, it appears necessary to add some sector with extra CP violation to the standard model in order to obtain an appreciable $n_B / s$ ratio. A simple possibility which has been invoked often is to add a second Higgs doublet to the theory, with CP violating relative phases. \n\nThe standard way to obtain out-of-equilibrium baryon number violating processes immediately after the electroweak phase transition is \\cite{EWBGrev} to assume that the transition is strongly first order and proceeds by the nucleation of bubbles (note that these are two assumptions).\n\nBubbles are out-of-equilibrium configurations. Outside of the bubble (in the false vacuum), the baryon number violating processes are unsuppressed, inside they are exponentially suppressed. In the bubble wall, the Higgs fields have a nontrivial profile, and hence (in models with additional CP violation in the Higgs sector) there is enhanced CP violation in the bubble wall. In order to obtain net baryon production, one may either use fermion scattering off bubble walls \\cite{CKN1} (because of the CP violation in the scattering, this generates a lepton asymmetry outside the bubble which converts via sphalerons to a baryon asymmetry) or sphaleron processes in the bubble wall itself \\cite{TZ,CKN2}. It has been shown that, using optimistic parameters (in particular a large CP violating phase $\\Delta \\theta_{CP}$ in the Higgs sector) it is possible to generate the observed $n_B / s$ ratio. The resulting baryon to entropy ratio is of the order\n\\begin{equation} \\label{ewres}\n{{n_B} \\over s} \\, \\sim \\, \\alpha_W^2 (g^*)^{-1} \\bigl( {{m_t} \\over T} \\bigr)^2 \\Delta \\theta_{CP} \\, ,\n\\end{equation}\nwhere $\\alpha_W$ refers to the electroweak interaction strength, $g^*$ is the number of spin degrees of freedom in thermal equilibrium at the time of the phase transition, and $m_t$ is the top quark mass. The dependence on the top quark mass enters because net baryogenesis only appears at the one-loop level.\n\nHowever, analytical and numerical studies show that, for the large Higgs masses which are indicated by the current experimental bounds, the electroweak phase transition will unlikely be sufficiently strongly first order to proceed by bubble nucleation. In addition, there are some concerns as to whether it will proceed by bubble nucleation at all (see e.g. \\cite{Gleiser}).\n\nOnce again, topological defects come to the rescue. In models which admit defects, such defects will inevitably be produced in a phase transition independent of its order. Moving topological defects can play the same\nrole in baryogenesis as nucleating bubbles. In the defect core, the electroweak symmetry is unbroken and hence sphaleron processes are unsuppressed \\cite{Perkins}, provided that the core is sufficiently thick to contain the sphalerons (in recent work \\cite{Cline} it has been shown that this is a rather severe constraint on workable string-mediated electroweak baryogenesis mechanisms). In the defect walls there is enhanced CP violation for the same reason as in bubble walls. Hence, at a given point in space, a nonvanishing baryon number will be produced when a topological defect passes by.\n\nDefect-mediated electroweak baryogenesis has been worked out in detail in \\cite{BDPT} (see \\cite{BD} for previous work) in the case of cosmic strings. The scenario is as follows: at a particular point $x$ in space, antibaryons are produced when the front side of the defect passes by. While $x$ is in the defect core, partial equilibration of $n_B$ takes place via sphaleron processes. As the back side of the defect passes by, the same number of baryons are produced as the number of antibaryons when the front side of the defect passes by. Thus, at the end a positive number of baryons are left behind. Obviously, the advantage of the defect-mediated baryongenesis scenario is that it does not depend on the order and on the detailed dynamics of the electroweak phase transition.\n\nAs in the case of defect-mediated GUT baryogenesis, the strength of defect-mediated electroweak baryogenesis is suppressed by the ratio ${\\rm SF}$ of the volume which is passed by defects divided by the total volume, i.e.\n\\begin{equation}\n{{n_B} \\over s} \\, \\sim \\, {\\rm SF} {{n_B} \\over s}|_0 \\, ,\n\\end{equation}\nwhere $(n_B / s)|_0$ is the result of (\\ref{ewres}) obtained in the bubble nucleation mechanism. \n\nA big caveat for defect-mediated electroweak baryogenesis is that the standard electroweak theory does not admit topological defects. However, in a theory with additional physics just above the electroweak scale it is possible to obtain defects (see e.g. \\cite{TDB95} for some specific models). The closer the scale $\\eta$ of the new physics is to the electroweak scale $\\eta_{EW}$, the larger the volume in defects and the more efficient defect-mediated electroweak baryogenesis (however, as pointed out in \\cite{Cline}, this effect is counteracted by the fact that the defect velocity at $T = \\eta_{EW}$ decreases as $\\eta$ decreases). Using the result of (\\ref{defsep}) for the separation of defects, we obtain (for non-superconducting strings)\n\\begin{equation}\n{\\rm SF} \\, \\sim \\, \\lambda \\bigl( {{\\eta_{EW}} \\over \\eta} \\bigr)^{3/2} v_D\\, .\n\\end{equation} \nwhere $v_D$ is the mean defect velocity. Typically \\cite{Cline}, the resulting value of $SF$ is too small for string-mediated electroweak baryogenesis to be efficient.\n \nDefect-mediated baryogenesis is much more efficient if the defects are domain walls (since by purely geometrical arguments the factor $SF$ will be much larger). However, as seen in earlier sections of this review, theories with topologically stable domain walls are ruled out because the wall network would overclose the Universe. What one would like is a theory in which a network of walls forms at some time before the electroweak phase transition, remains present until after the transition and then decays. As has recently been\nrealized \\cite{NB99}, this goal may be achieved in theories with embedded defects.\n\nEmbedded defects (see \\cite{AV99} for a recent review) in a theory with vacuum manifold ${\\cal M}$ are exact solutions of the field equations which correspond to topological defects with respect to a submanifold ${\\cal M}'$ of ${\\cal M}$\nof strictly lower dimension. Embedded defects are unstable in the absence of field fluctuations. However \\cite{NB99} if plasma effects provide effective masses to some of the components of the order parameter of the theory such that the space of ground states in the plasma reduces to ${\\cal M}'$, then the embedded defects can be stabilized in the plasma. Embedded strings which can be stabilized in the electric plasma before recombination exist in the standard electroweak theory. It is interesting to investigate if extension of the minimal electroweak theory admit embedded walls. 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{
"name": "astro-ph0002030.extracted_bib",
"string": "\\begin{thebibliography}{10} \n\n\\bibitem{TK80} T.W.G. Kibble, {\\it Phys. Rep.} {\\bf 67}, 183 (1980).\n\\bibitem{Vil85} A. Vilenkin, {\\it Phys. Rep.} {\\bf 121}, 263 (1985).\n\\bibitem{ShellVil} A. Vilenkin and E.P.S. Shellard, `Strings and Other Topological Defects' (Cambridge Univ. Press, Cambridge, 1994).\n\\bibitem{HK95} M. Hindmarsh and T.W.B. Kibble, {\\it Rep. Prog. Phys.} {\\bf 58}, 477 (1995).\n\\bibitem{RB94} R. Brandenberger, {\\it Int. J. Mod. Phys.} {\\bf A9}, 2117 (1994).\n\\bibitem{BDH} R. Brandenberger, A.-C. Davis and M. Hindmarsh, {\\it Phys. Lett.} {\\bf B263}, 239 (1991).\n\\bibitem{BD} R. Brandenberger, A.-C. Davis and M. Trodden, {\\it Phys. Lett.} {\\bf B332}, 305 (1994);\\\\\nR. Brandenberger and A.-C. Davis, {\\it Phys. Lett.} {\\bf B308}, 79 (1993).\n\\bibitem{BDPT} R. Brandenberger, A.-C. Davis and M. Trodden, {\\it Phys. Lett.} {\\bf B332}, 305 (1994);\\\\\nR. Brandenberger, A.-C. Davis, T. Prokopec and M. Trodden, {\\it Phys. 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}
] |
astro-ph0002031
|
The Role of H$_{2}$ Molecules in Cosmological Structure Formation
|
[
{
"author": "T. Abel$^1$"
},
{
"author": "\\ns Z. Haiman$^2$\\footnote{Hubble Fellow}"
}
] |
We review the relevance of ${H_2}$ molecules for structure formation in cosmology. Molecules are important at high--redshifts, when the first collapsed structures appear with typical temperatures of a few hundred Kelvin. In these chemically pristine clouds, radiative cooling is dominated by ${H_2}$ molecules. As a result, ${H_2}$ ``astro--chemistry'' is likely to determine the epoch when the first astrophysical objects appear. We summarize results of recent three--dimensional simulations. A discussion of the effects of feedback, and implications for the reionization of the universe is also given.
|
[
{
"name": "h2rev.tex",
"string": "\\documentstyle[english,psfig]{cupconf}\n\n% use these four lines when finally presenting your CRC. (See Appendix B\n% of the guide.)\n%\\magnification 1200 % always use 1200 when presenting your chapter\n%\\oddsidemargin -0.5pc % appropriate for A4, you may need to vary value\n%\\evensidemargin -0.5pc % appropriate for A4, you may need to vary value\n%\\topmargin -5pc % appropriate for A4, you may need to vary value\n\n\\ifoldfss\n\\else\n \\ifnfssone\n \\newmathalphabet{\\mathit}\n \\addtoversion{normal}{\\mathit}{cmr}{m}{it}\n \\addtoversion{bold}{\\mathit}{cmr}{bx}{it}\n \\newmathalphabet{\\mathcal}\n \\addtoversion{normal}{\\mathcal}{cmsy}{m}{n}\n \\else\n \\ifnfsstwo\n \\fi\n \\fi\n\\fi\n\n%%%%% USER-DEFINED MACROS HERE %%%%%\n% Keep your own macro definitions separate from the examples below.\n%\n\\def\\ga{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;}\n\\def\\la{\\;\\rlap{\\lower 2.5pt\n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;}\n\\newcommand\\msun{\\rm M_\\odot}\n\n% Some useful examples of macro definitions follow.\n%%%%%\n\n%%%%% For units of measure %%%%%\n%\n\\def\\dynpercm{\\nobreak\\mbox{$\\;$dynes\\,cm$^{-1}$}}\n\\def\\cmpermin{\\nobreak\\mbox{$\\;$cm\\,min$^{-1}$}}\n%\n%%%%%\n\n\n%%%%% For authors without AMSTeX %%%%%\n% \n% Uncomment the definitions as far as: %%% STOP HERE without AMSTeX %%% \n%\n\\def\\upi{\\pi} % to be replaced with upright Greek character\n\\def\\umu{\\mu} % to be replaced with upright Greek character\n\\def\\BbbE{\\mbox{\\sf E}} % to be replaced with blackboard bold \n\\def\\blackbox{\\rule{4pt}{4pt}} % to be replaced with \\blacksquare\n%\n%%%%% STOP HERE without AMSTeX %%%%%\n\n\\def\\hexnumber#1{\\ifcase#1 0\\or1\\or2\\or3\\or4\\or5\\or6\\or7\\or8\\or9\\or\n A\\or B\\or C\\or D\\or E\\or F\\fi }\n\n%%%%% For sans serif characters %%%%%\n%\n\\def\\ssC{\\mbox{\\sf C}} % for sans serif C\n\\def\\sfsP{\\mbox{\\sfs P}} % for sans serif sloping P\n\\def\\slsQ{\\mbox{\\sls Q}} % for sans serif bold-sloping Q\n%\n\\makeatletter\n\\ifx\\CUP@mtlplain@loaded\\undefined\n \\font\\sfs = cmssi10 % sans-serif slanted\n \\font\\sfb = cmssi10 % sans-serif bold maths\n \\font\\sls = cmssi10 % sans-serif bold maths, slanted\n \\font\\bit = cmmib10 % bold math italic\n\\else\n % CUP times font substitutions for above (not to be used by authors)\n \\font\\sfs = mtssi10 % sans-serif italic\n \\font\\sfb = mtssbx10 % sans-serif bold maths\n \\font\\sls = mtssbi10 % sans-serif bold maths, slanted\n \\font\\bit = mtmib10 % bold math italic\n\\fi\n\\makeatother\n%\n%%%%%\n\n%%%%% The minus sign is in different positions for the two fonts %%%%%\n%\n\\makeatletter\n\\ifx\\CUP@mtlplain@loaded\\undefined\n \\newcommand{\\pvi}{\\int_0^{\\infty}\\mskip -33mu -\\quad} % 33mu for cm\n\\else\n \\newcommand{\\pvi}{\\int_0^{\\infty}\\mskip -30mu -\\quad} % 30mu for mt\n\\fi\n\\makeatother\n%\n%%%%%\n\n\n\\def\\cm{\\rm cm}\n\\def\\K{\\rm K}\n\\def\\HH{H$_2$}\n\\def\\tento#1{\\times 10^{#1}}\n%-----title and author----------------------\n\n\\title[H$_{\\it 2}$ Molecules and Structure Formation]{The Role of H$_{\\bf 2}$ Molecules\n in Cosmological Structure Formation}\n\n\\author[T. Abel \\& Z. Haiman]\n{T. Abel$^1$ \\and \\ns Z. Haiman$^2$\\footnote{Hubble Fellow}}\n\n\\affiliation{$^1$Harvard Smithsonian Center for Astrophysics,\n60 Garden Street, Cambridge, MA 02138, USA\\\\[\\affilskip]\n$^2$Princeton University Observatory, Princeton, NJ 08544, USA}\n\n\\setcounter{page}{1}\n\n% -----------------------------\n\n\\begin{document}\n\\ifnfssone\n\\else\n \\ifnfsstwo\n \\else\n \\ifoldfss\n \\let\\mathcal\\cal\n \\let\\mathrm\\rm\n \\let\\mathsf\\sf\n \\fi\n \\fi\n\\fi\n\n\\maketitle\n\n\\begin{abstract}\n\nWe review the relevance of ${\\rm H_2}$ molecules for structure formation in\ncosmology. Molecules are important at high--redshifts, when the first\ncollapsed structures appear with typical temperatures of a few hundred Kelvin.\nIn these chemically pristine clouds, radiative cooling is dominated by ${\\rm\nH_2}$ molecules. As a result, ${\\rm H_2}$ ``astro--chemistry'' is likely to\ndetermine the epoch when the first astrophysical objects appear. We summarize\nresults of recent three--dimensional simulations. A discussion of the effects\nof feedback, and implications for the reionization of the universe is also\ngiven.\n\n\\end{abstract}\n\n\\firstsection % if your document starts with a section,\n % remove some space above using this command.\n\\section{Introduction}\n\nIn current ``best--fit'' cosmological models, cold dark matter (CDM) dominates\nthe dynamics of structure formation, and processes the initial density\nfluctuation power spectrum $P(K)\\propto k^n$ with $n=1$ to predict $n=1$ on\nlarge scales and $n\\approx-3$ on small scales (Peebles 1982). The\nr.m.s. density fluctuation $\\sigma_M$ then varies inversely with the\nmass--scale ($\\sigma_M\\propto M^{-2/3}$ for $M\\gg 10^{12}\\msun$, while the\ndependence is only logarithmic for $M\\ll 10^{12}\\msun$). The more overdense a\nregion, the earlier it collapses, implying that the present structure was built\nfrom the bottom up, with smaller objects appearing first, and subsequently\nmerging and/or clustering together to assemble the larger objects (Peebles\n1980). The predicted formation epochs of ``objects'' (i.e. collapsed dark\nmatter halos) with various masses in the so--called standard CDM cosmology\n(Bardeen et al. 1986) are shown in Figure~\\ref{fig:zcollintro}. Galaxies,\nwhich have masses around $10^{11-12}\\msun$, are expected to have formed when\nthe universe had approximately 10\\% of its present age (redshift $z\\sim3$),\njust around the limit of the deepest present--day observations (i.e. the Hubble\nDeep Field, HDF, Williams et al. 1996; or Ly$\\alpha$ emission line detections,\nWeymann et al. 1998). Clusters of galaxies with masses around\n$10^{14-15}\\msun$ are predicted to have formed as recently as 80\\% of the\ncurrent age, with the more massive clusters still assembling at the present\ntime.\n\n\\begin{figure} \n% \\vspace{6.5cm}\n% use \\vspace to leave a blank space to glue a figure\n% comment \\vspace and uncomment next line, il you insert a .ps file\n\\centerline{\\psfig{figure=zcoll.ps,width=10cm,angle=0}}\n \\caption{\\label{fig:zcollintro} The formation epoch of objects with various\n masses in a standard CDM model ($\\Omega=n=\\sigma_{8h^{-1}}=1$), shown as a\n fraction of the current age of the universe. The upper labels indicate\n redshifts. The first objects form at redshift $z\\sim 20$, at a ``lookback''\n fraction of $\\sim$99\\%.}\n\\end{figure} \n%\n\nObjects with the masses of globular clusters, $10^{5-6}\\msun$, are predicted to\nhave condensed as early as $\\sim$1\\% of the current age, or $z\\sim 20$. It is\nnatural to identify these condensations as the sites where the first\n``astrophysical'' objects (stars, or quasars) might be born. Although the CDM\nmodel in Figure~\\ref{fig:zcollintro} predicts still smaller condensations at\neven earlier times, the cosmological Jeans mass in the smooth gas after\nrecombination is $\\sim 10^{4}\\msun$ (Peebles 1965), implying that gas pressure\ninhibits the collapse of gas below this scale (see Haiman, Thoul \\& Loeb 1996\non collapse on somewhat smaller scales due to gas/DM shell--crossing, hereafter\nHTL96).\n\nWhat happens in a newly collapsed halo? Formally, in the absence of\nnon--gravitational forces, a perfectly spherical top--hat perturbation simply\ncollapses to a point (Peebles 1980). According to more accurate treatments\ndescribing self--similar solutions of spherical, but inhomogeneous secondary\ninfall for a mixture of cold dark matter and baryons (Gunn \\& Gott 1972,\nFillmore \\& Goldreich 1984, Bertschinger 1985), the evolution is as follows.\nIn the initial stages, while the bulk of the cloud is still turning around or\nexpanding, the central, densest region of the cloud collapses and forms a dense\nvirialized clump. The dark matter component virializes through violent\nrelaxation (Lynden--Bell 1967), while the kinetic energy of the gas is\nconverted into thermal energy through a hydrodynamic shock that raises the gas\ntemperature to its virial value. As subsequent gas shells fall towards the\ncenter, they encounter an outward--propagating shock, and are brought to a\nsudden a halt. Continuous accretion onto the center then establishes a\nstationary, virialized object with a $\\rho\\propto r^{-2.25}$ density profile.\n\nEarly discussions of the formation of galaxies and clusters have argued that\nthe subsequent behavior of the gas in such a virialized object is determined by\nits ability to cool radiatively on a dynamical time (Rees \\& Ostriker 1977;\nDekel \\& Silk 1986). The same ideas apply on the smaller scales expected for\nthe first collapsed clouds (Silk 1977; Kashlinsky \\& Rees 1983). Objects that\nare unable to cool and radiate away their thermal energy maintain their\npressure support and identity, until they become part of a larger object via\naccretion or mergers. On the other hand, objects that can radiate efficiently\nwill cool and continue collapsing.\n\nThe cooling time is determined by the virial temperature, $T_{\\rm vir} \\sim\n10^4{\\rm K}$ $(M/10^8{\\rm M_\\odot})^{2/3}$ $[(1+z)/11]$. For the largest\nhalos, above $T_{\\rm vir}\\ga10^6$K, the most important cooling mechanism is\nBremsstrahlung; for galaxy--sized halos ($10^4$K$\\la T_{\\rm vir}\\la10^6$K),\ncooling is possible via collisional excitation of neutral H and He. As first\npointed out by Saslaw \\& Zipoy (1967) and Peebles and Dicke (1968), the virial\ntemperatures of the first clouds are below $10^4$K. In the primordial gas, the\nonly molecule that could have a sufficient abundance is ${\\rm H_2}$, allowing\ncooling between $10^2$K$\\la T\\la10^4$K (see Dalgarno \\& Lepp 1987 for a review\nof astrochemistry in the early universe, and Stancil, Lepp and Dalgarno 1996 on\nthe possible importance of other molecules, such as HD and LiH). Below\n$T\\la10^2$K, the collapsed clouds are unable to cool, and remain\npressure--supported for longer than a Hubble time.\n\nAlthough ${\\rm H_2}$ molecules are unimportant in the formation of structures\non galactic scales, they likely play a key role in the formation of the first,\nsmaller structures. In particular, the abundance of ${\\rm H_2}$ controls the\nminimum sizes and formation times of the very first systems (HTL96, Tegmark et\nal. 1997).\n\nThe main issues regarding ${\\rm H_2}$ molecules in structure formation,\naddressed in this review, are:\n\n\\begin{itemize}\n\n\\item What is the ${\\rm H_2}$ abundance in the first collapsed objects?\n\n\\item What is the parameter space (in mass, redshift and metallicity) when\n${\\rm H_2}$ cooling dominates over all other cooling mechanisms?\n\n\\item What is the parameter space when the ${\\rm H_2}$ cooling time\nis shorter than the dynamical time, so that ${\\rm H_2}$ can effect\nthe dynamics of a system?\n\n\\item What feedback mechanisms effect the ${\\rm H_2}$ abundance once\nthe first stars or quasars light up?\n\n\n\\end{itemize}\n\n\n\\section{${\\bf H_2}$ Chemistry and Cooling}\n\nBecause the cosmological background density of baryons $\\sim (\\Omega_B\nh^2/0.01) (1+z)^3\\, 10^{-7} \\cm^{-3}$ is very small, chemical reactions in the\nsmooth background gas occur on long timescales. As a consequence, for dynamical\nsituations of structure formation chemical equilibrium is rarely an appropriate\nassumption. The dominant \\HH\\ formation process in the gas phase,\n\\begin{eqnarray}\\label{equ:H2paths}\n\\rm\nH \\ \\ \\ \\ + \\ \\ e^- \\ & \\rightarrow & \\ \\ {\\rm H^-} \\ \\ + \\ \\ h\\nu, \\\\\n\\rm H^- \\ \\ + \\ \\ H \\ \\ & \\rightarrow & \\ \\ \\rm H_2 \\ \\ \\ + \\ \\ e^-,\n\\end{eqnarray}\nrelies on the abundance of free electrons to act as catalysts. At temperatures\nlow enough to inhibit collisional dissociations by collisions with neutral\nhydrogen such electrons can only exist due to non-equilibrium\neffects. Electrons are also produced by photoionization of neutral hydrogen\nfrom an external UV radiation field. It is required to solve the time\ndependent chemical reaction network including the dominant chemical reactions.\nA very fast numerical method to solve this set of stiff ordinary differential\nequations has been developed by Anninos et al. (1997). The number of possible\nchemical reactions involving \\HH\\ is large, even in the simple case of metal\nfree primordial gas. The tedious work of selecting the dominant reactions and\ntheir reaction rates has been done by many authors, some recent examples being\nHTL96, Abel et al. (1997) and Galli \\& Palla (1998, see also Galli and Palla in\nthis volume).\n\nCooling (defined here as the radiative loss of internal energy of the gas) is\neither due to reaction enthalpy released by a photon, or due to the radiative\ndecay of collisionally excited atomic or molecular levels. For typical\ndensities and proto-galactic scales it is accurate to assume the gas to be\noptically thin and only consider excitations from atomic and molecular ground\nstates. The latter fact is due to the low densities resulting in collisional\nexcitation time scales much longer than the corresponding radiative decay times\n(sometimes referred to as the coronal limit). For \\HH\\ molecules this\nassumption breaks down for neutral hydrogen number densities in excess of $\\sim\n10^{2-3}\\cm^{-3}$. In comparison, for hydrogen atoms the coronal limit is\nreached only at electron densities of $\\sim 10^{17}\\cm^{-3}$ (Abel et al. 1997,\nand references therein). The calculations of the appropriate cooling function\nfor molecular hydrogen seem to be converging. See Flower (2000, this volume)\nfor a discussion and further references.\n\n\\section{${\\bf H_2}$ and the First Structures}\n\nStudies that incorporate ${\\rm H_2}$ chemistry into cosmological models and\naddress issues such as non--equilibrium chemistry, dynamics, or radiative\ntransfer, have appeared only in the past few years. However, pioneering works\non the effect of ${\\rm H_2}$ molecules during the formation of ultra--high\nredshift structures go back to the 1960's. Saslaw \\& Zipoy (1967) first\nmentioned the importance of ${\\rm H_2}$ in cosmology. Peebles \\& Dicke (1968)\nspeculated that globular clusters formed via ${\\rm H_2}$ cooling constitute the\nfirst building blocks of subsequent larger structures. Several papers soon\nconstructed complete gas--phase reaction networks, and identified the two\npossible ways of gas--phase formation of ${\\rm H_2}$ via the ${\\rm H_2^+}$ or\n${\\rm H^-}$ channels. These were applied to derive the ${\\rm H_2}$ abundance\nin the smooth gas in the post--recombination universe (Lepp \\& Shull 1984;\nShapiro, Giroux \\& Babul 1994), and under densities and temperatures expected\nin collapsing high--redshift objects (Hirasawa 1969; Matsuda et al 1969;\nRuzmaikina 1973). Palla et al. (1983) combined the molecular chemistry with\nsimplified dynamics, assuming a uniform sphere in free--fall, finding that\nthree--body reactions significantly increase the ${\\rm H_2}$ abundance at the\nlater (dense) stages of the collapse. The significance of non--equilibrium\n\\HH\\ chemistry was realized by Shapiro \\& Kang (1987), who studied \\HH\\\nformation in a shock--heated gas, and found that the high electron fraction in\nthe post--shock region leads to a significantly enhanced \\HH\\ abundance. Based\non a self--consistent treatment of radiative transfer of the diffuse radiation\nfield (Kang and Shapiro 1992), this \\HH\\ enhancement, regulated by\nphotodissociation inside proto--galaxies, was suggested to lead to the\nformation of globular clusters (Kang et al. 1990).\n\n\nThe basic picture that emerged from this papers is as follows. The ${\\rm H_2}$\nfraction after recombination in the smooth 'intergalactic' gas is small\n($x_{\\rm H2}=n_{\\rm H2}/n_{\\rm H}\\sim 10^{-6}$). At high redshifts ($z\\ga\n100$), ${\\rm H_2}$ formation is inhibited even in overdense regions because the\nrequired intermediaries ${\\rm H_2^+}$ and H$^-$ are dissociated by cosmic\nmicrowave background (CMB) photons. However, at lower redshifts, when the CMB\nenergy density drops, a sufficiently large ${\\rm H_2}$ abundance builds up\ninside collapsed clouds ($x_{\\rm H2}\\sim 10^{-3}$) at redshifts $z\\la 100$ to\ncause cooling on a timescales shorter than the dynamical time. This last\nconclusion was found to hold when the rotation of a collapsing sphere was also\nincluded (Hutchins 1976). Using a different approach, Silk (1983) explicitly\ndemonstrated that a thermal instability exists for a collapsing gas--cloud\nforming ${\\rm H_2}$ molecules, leading to fragmentation. In summary, these\nearly papers identified the most important reactions for ${\\rm H_2}$ chemistry,\nand established the key role of ${\\rm H_2}$ molecules in cooling the first,\nrelatively metal--free clouds, and thus in the formation of population III\nstars.\n\nThe minimum mass of an object that can collapse and cool as a function of\nredshift has been studied by Tegmark et al. (1997) assuming constant density\nobjects, and by HTL96 (see also Bodenheimer and Villere 1986), using\nspherically symmetric one--dimensional Lagrangian hydrodynamical models (see\nalso Bodenheimer and Villere 1986). Sufficient \\HH\\ formation and cooling\nrequires the gas to reach temperatures in excess of a few hundred Kelvin; or\nmasses of few $\\times 10^5~{\\rm M_\\odot}[(1+z)/11]^{-3/2}$. Initially linear\ndensity perturbations are followed as they turn around and grow in mass. When\nthe DM dynamics are included, the center of the collapsing object contracts\nadiabatically into the growing DM potential well. As the object grows in mass,\na weak accretion shock is formed. One might imagine a case where the adiabatic\ncentral core forms molecules early and allows rapid collapse before the\naccretion shock is formed; however this is not seen in the simulations. These\ntemperatures are much larger than the temperature of the intergalactic medium\n($T_{IGM}\\sim 0.014 (1+z)^2$) at the redshifts of interest. In other words, CDM\nmodels predicts the existence of numerous virialized objects with temperatures\n$\\la 500\\,\\K$ that cannot cool. The object that contained the first star in the\nuniverse grows by the infall of both intergalactic DM and of gas, heated in an\naccretion shock. The residual fraction of free electrons catalyze the formation\nof \\HH\\ molecules in its central region.\n\n\\section{Three-dimensional Numerical Simulations}\n\nCosmological hydrodynamical simulations of hierarchical models of structure\nformation have proven very successful in explaining cosmic structure on\nsub-galactic scales (Cen et al. 1994, Zhang et al. 1995, Hernquist et al. 1996,\nDav\\'e et al. 1999), galactic scales (e.g. Kauffmann et al. 1999, Katz et\nal. 1999) and galaxy clusters (e.g. Frenk et al. 1999, Bryan and Norman 1998).\nWith a realistic primordial chemistry model (e.g. Abel et al. 1997) and\nefficient numerical methods (e.g. Anninos et al. 1997) it is possible to also\nsimulate the formation of the first cosmological objects. The first\ntwo--dimensional simulations of structure formation studied the collapse and\nfragmentation of cosmological sheets (Anninos and Norman~1996). In these\nsimulations, the collapsing gas is heated in the accretion shock, and\nsubsequently found to cool isobarically. The non--equilibrium abundance of\nelectrons behind the strong accretion shock with $T\\gg 10^4\\K$ reaches its\nmaximum value, and fast \\HH\\ formation up to an abundance of a few $10^{-3}$\n(number fraction) is observed, in agreement with the study of \\HH\\ formation in\nshock--heated gas by Shapiro \\& Kang (1987). A similar calculation has been\ncarried out by Abel et al. (1998b) for the study of the two dimensional\ncollapse of long cosmic string induced sheets. In this cosmic string scenario,\nthe dominant mass component was assumed to be hot dark matter (HDM,\ne.g. massive neutrinos). One then envisions long, fast moving cosmic strings\nto induce velocity perturbations, causing sheets to collapse, cool and fragment\n(Rees 1986). The feedback from the newly formed stars might have then induced\nfurther structure formation as in Ikeuchi and Ostriker (1986). It turns out,\nhowever, that \\HH\\ formation is inefficient at high redshift where the CMBR\ndissociates the intermediaries H$^-$ and H$_2^+$. Furthermore, the shocks\ncaused by the string--induced velocity perturbations are too weak to enhance\n\\HH\\ formation. Consequently Abel et al. (1998b) concluded that the cosmic\nstring plus HDM model cannot develop luminous objects before the HDM component\nbecomes gravitationally unstable.\n\nNumerical calculations of more ``mainstream'' structure formation scenarios\nhave been presented by Abel (1995), Gnedin and Ostriker (1997, GO97 hereafter),\nAbel et al. (1998a, AANZ98), and Abel, Bryan, and Norman (2000, ABN00). The\nsimulations presented in GO97 focused on simulating the thermal history of the\nintergalactic medium and included star formation and feedback mechanisms. Their\nsimulations were designed to accurately compute the number of the first objects\nable to cool and collapse and hence had to sacrifice numerical resolution\nwithin the collapsed objects. Results such as the typical fragment masses,\ntypical temperatures, etc. are also found in multi--dimensional simulations\nthat start from more idealized initial conditions (e.g. Bromm, Coppi, and\nLarson 1999)\n\nIn general cosmological hydrodynamical simulations treat the dynamics\nof the assumed collisionless cold dark matter using N--body\ntechniques. This is typically coupled to a hydrodynamic grid code,\nsolving the fluid equations for a gas of primordial composition. The\nsimulations are initialized at a high redshift ($\\ga 100$) where\ndensity and velocity perturbations are small and in the linear\nregime. The simulation volume typically needs to be chosen rather\nsmall ($\\la 1\\,$ comoving Mpc) to make sure that the simulation is at\nleast capable of resolving the baryonic Jeans Mass prior to\nreionization,\n\\begin{eqnarray}\n \\label{eq:MJ_IGM}\n M_{J,IGM} \\approx 1.0\\tento{4}M_\\odot\\ \\left(\\frac{1+z}{10}\\right)^{3/2} \n \\left(\\frac{\\Omega_B h^2}{0.02}\\right)^{-1/2}. \n\\end{eqnarray}\nThe use of periodic boundary conditions for such small box sizes is only\naccurate at relatively high redshifts where they do model a representative\npiece of the model universe. Even in the lowest resolution simulations it\nbecomes clear that an intricate network of sheets, and dense knots at the\nintersection of filaments is found. To the eye this structure is very similar\nto the simulation results on much larger scales.\n\nSufficient \\HH\\ molecules, enabling the gas to cool, form only in the dense\nspherical knots at the intersection of filaments (AANZ98). These knots consist\nof virializing dark matter halos that accrete gas mostly from the nearby\nfilaments but also from the neighboring voids. An accretion shock transforms\nthe kinetic energy of the incoming gas into internal thermal energy. This shock\ntends to be spherical towards the directions of the voids but is often\ndisturbed and more complex in morphology at the interface to the filaments. For\nthe first objects that show any molecular hydrogen cooling the accretion shock\nis too weak to raise the ionization level of the gas over its residual\nprimordial fraction of ${n_{H^+}}/{n_H} \\approx 2.4 \\times 10^{-4}~\n\\Omega_0^{1/2} {0.05}/(h\\Omega_B)$ Peebles (1993). However, the associated\nraise in temperature of the post-shock gas allows molecule formation to proceed\nat time scales smaller than the Hubble time.\n\nFor the very first (i.e. least massive) objects with virial temperatures $\\la\n1000\\,$K molecule formation is relatively slow, and the cooling time remains\nlonger than the free fall time. As the objects merge and accrete, the higher\nvirial temperature allows the chemistry and cooling to operate on faster than\ndynamical time scales. This further merging induces a rather complex velocity\nand density field in the gas, as well as the dark matter. Typical cosmological\nhydrodynamic methods can not follow the further evolution of the fragmentation\nof the gas clouds due to lack of numerical resolution and it was not possible\nto asses the nature of the first luminous objects by direct simulation. This\ndrawback was recently overcome by the simulations presented in Abel, Bryan and\nNorman (2000, ABN00) by exploiting adaptive mesh refinement techniques (Berger\nand Collela, 1989, Bryan \\& Norman 1997, 1999). This numerical scheme allows to\nfollow the gas dynamics to smaller and smaller scales by introducing new finer\ngrids as they are needed. Since this is done at a scale much below the local\nJeans length one is confident to capture the essential scale of the\nfragmentation due to gravitational instability.\n\nThese simulations clearly show how a region at the center of the virialized\nhalo, containing approximately $200\\,M_\\odot$ in baryons, collapses rapidly.\nThis ``core'' is formed via the classical Bonnor--Ebert instability of\nisothermal spheres. It contracts faster than the dynamical time scales in its\nparent halo. Hence these simulations indicate that the first luminous object(s)\n(perhaps a massive star) will form before most of the gas in the halo can\nfragment (ABN00). This core might still fragment further when it turns fully\nmolecular via the three body formation process (Palla et al. 1983, Silk\n1983)\\footnote{Abel, Bryan, and Norman (unpublished) have carried out a\nsimulation which includes the three--body \\HH\\ formation covering a dynamic\nrange of $3\\tento{7}$. A preliminary analysis suggests that the core does not\nfragment further when it turns full molecular. This suggests that most likely a\nmassive star will form in the collapsing core.}. If the core forms stars at\n100\\% efficiency an the ratio of produced UV photons per solar mass is the same\nas in present day star clusters than about $6\\times 10^{63}$ UV photons would\nbe liberated during the average life time of massive star ($\\sim 5\\times\n10^{7}\\,$yrs). This is a few million times more than the $\\sim 10^{57}$\nhydrogen molecules within the virial radius, further suppressing \\HH\\ cooling\nand fragmentation. Hence, the first star(s) may halt star formation until the\nmassive star(s) die(s). Only a small fraction of primordial gas might be able\nto condense into PopIII stars of pristine primordial composition.\n\n\\section{Feedback Issues}\n\nThe first stars formed via ${\\rm H_2}$ cooling are expected to produce UV\nradiation, and explode as supernovae (if they are more massive than $\\sim 8{\\rm\nM_\\odot}$), producing significant prompt feedback on the ${\\rm H_2}$ abundance\nin their own parent cloud. In addition, any soft UV radiation produced below\n13.6eV and/or X--rays above $\\ga 1$keV from the first sources can propagate\nacross the smooth H background gas, possibly influencing the chemistry of\ndistant regions. Soft UV radiation is expected either from either a star or an\naccreting black hole, with a black hole possibly contributing X--rays, as well.\n(Although recent studies find that metal--free stars have unusually hard\nspectra, these do not extend to $\\ga 1$keV. See, e.g. Tumlinson \\& Shull 1999).\nThe most important (and uncertain) quantity for assessing a stellar feedback is\nthe IMF of the first stars. Several authors have argued that the IMF might be\n(see, e.g. Larson 1999 and references therein) biased towards massive\nstars. The lack of zero--metallicity stars, the so--called G--dwarf problem is\nresolved if the first generation of stars were short--lived; while the\nrelatively inefficient cooling of metal--free gas could impose a minimum mass.\nA similar conclusion was reached by a recent 3D simulation (Bromm, Coppi, and\nLarson 1999).\n\nThe key question is whether the ${\\rm H_2}$ abundance in a collapsed region is\neffected shortly after the first few sources turn on (either in the same\ncollapsed region, or elsewhere in the universe), i.e. before the ${\\rm H_2}$\nabundance becomes irrelevant either because objects with $T_{\\rm vir}\\la 10^4$K\nare already collapsing, or because metal enrichment has reached sufficiently\nhigh levels that ${\\rm H_2}$--cooling no longer dominates ($\\sim 1\\%$ solar,\nB\\\"ohringer \\& Hensler 1989). Ferrara (1998) considered the internal feedback\nfrom supernova explosions, and found that the non--equilibrium chemistry in the\nshocked gas can increase the ${\\rm H_2}$ abundance. However, Omukai \\& Nishi\n(1999) argued that a single OB star can photodissociate the ${\\rm H_2}$\nmolecules inside the whole $M\\sim10^6{\\rm M_\\odot}$ cloud. Even if molecules\nre-form after SN explosions, they found a net negative feedback.\n\nExternal feedback from an early soft UV background were considered by Haiman,\nRees \\& Loeb (1997). It was found that ${\\rm H_2}$ molecules are fragile, and\neasily photo--dissociated even inside large collapsed clumps via the two--body\nSolomon process (cf. Field et al. 1966)\\footnote{Note that these objects might\nalso explain the large number of Lyman Limit Systems observed in high redshift\nquasar spectra (Abel \\& Mo 1998).} -- even when the background flux is several\norders of magnitude smaller than the level $\\sim 10^{-21}~{\\rm erg\\, cm^{-2}\\,\ns^{-1}\\, Hz^{-1}\\, sr^{-1}}$ inferred from the proximity effect at $z\\sim 3$\n(Bajtlik et al. 1988), and needed for cosmological reionization at $z>5$.\nThese results were confirmed by a more detailed, self--consistent calculation\nof the build-up of the background and its effect on the contributing sources\n(Haiman, Abel \\& Rees 1999). The implication is a pause in the cosmic\nstar--formation history: the buildup of the UVB and the epoch of reionization\nare delayed until larger halos ($T_{\\rm vir}\\ga 10^4$K) collapse. (This is\nsomewhat similar to the pause caused later on at the 'H-reionization' epoch,\nwhen the Jeans mass is abruptly raised from $\\sim 10^{4}~{\\rm M_\\odot}$ to\n$\\sim 10^{8-9}~{\\rm M_\\odot}$.) An early background extending to the X--ray\nregime would change this conclusion, because it catalyzes the formation of\n${\\rm H_2}$ molecules in dense regions (Haiman, Rees \\& Loeb 1996, Haiman, Abel\n\\& Rees 2000). If quasars with hard spectra ($\\nu F_\\nu \\approx$ const)\ncontributed significantly to the early cosmic background radiation then the\nfeedback might even be positive, and reionization can be caused early on by the\nsmall halos.\n\n\n\n\\section{Conclusions} \n \nIn popular CDM models, the first stars or quasars likely appeared inside\ncondensed clumps with virial temperatures $T{\\rm vir}\\la 10^4$K at redshifts\n$z\\sim 20$. Because of the low virial temperatures, ${\\rm H_2}$ cooling (or\nlack thereof) played a dominant role in the gas dynamics inside these\ncondensations. State--of--the art numerical simulations identify the sites for\nthe first star--formation with the intersection of dense filaments (Abel et\nal. 1998, 2000). Although not directly visible in ${\\rm H_2}$ emission, these\nstar--formation sites could be detected out to $z\\sim 15$ with the Next\nGeneration Space Telescope, provided they have a star formation efficiency of\n$\\ga$ one percent (Haiman \\& Loeb 1998), or they form quasar black holes with\nan efficiency of $\\sim 10^{-3}$ and shine at the Eddington luminosity (Haiman\n\\& Loeb 1998). In the latter case, early mini--quasars from ${\\rm H_2}$\ncooling would reionize intergalactic hydrogen by $z\\sim 10$. The average\nstar--formation efficiency in collapsed halos before $z\\sim 3$ can be estimated\nby matching the average metal enrichment of the Ly $\\alpha$ forest. If the\nlatter is $\\sim 10^{-3}$ solar, this implies that $\\sim$2\\% of the gas mass in\ncollapsed regions are processed through stars (assuming a ratio in the number\nof high--mass to intermediate--mass stars as in a Scalo IMF, see Haiman \\& Loeb\n1997). This value is not far from the efficiency of $\\sim$1\\% suggested by 3D\nsimulations that resolve sub--parsec scales (ABN00); however it is unlikely\nthat the early IMF was similar to the one observed in the local universe\n(e.g. Larson 1999). Arguably, further progress towards answering this question\nwill have to come from a combination of more accurate simulations of\nstar--formation in a metal--free plasma; including realistic radiative\ntransfer.\n\n\\begin{acknowledgments}\n\nWe thank M. Rees for helpful comments. This work was supported by NASA through\na Hubble Fellowship. TA acknowledges partial support by NSF grant AST-9803137\nand NASA grant NAG5-3923.\n\n\\end{acknowledgments}\n\n\\begin{thebibliography}{} \n\n\\bibitem[Abel 1995]{Abel95} {\\sc Abel, T.} 1995, {\\it Thesis}, University of\nRegensburg, Germany \n\n\\bibitem[Abel et al. (1997)]{Abel97} {\\sc Abel, T., Anninos, P.,\nZhang, Y., Norman, M. L.} 1997, {\\it NewA} {\\bf 2}, 181\n\n\\bibitem[Abel et al. (1998a)]{Abel98a} {\\sc Abel, T., Anninos, P.,\nNorman, M. L., Zhang, Y.} 1998a, {\\it ApJ} {\\bf 508}, 518 (AANZ98)\n\n\\bibitem[Abel et al. (1998b)]{Abel98b} {\\sc Abel, T., Stebbins, A.,\nAnninos, P., Norman, M.L.} 1998, {\\it ApJ} {\\bf 508}, 530\n\n\\bibitem[Abel and Mo (1998)]{Abel99c} {\\sc Abel, T., Mo, H. J.} 1998,\n{\\it ApJ} {\\bf 494}, L151\n\n\\bibitem[Abel, Norman, and Madau (1999)]{Abel99} {\\sc Abel, T.,\nNorman, M. L., Madau, P.} 1999, {\\it ApJ} {\\bf 523}, 66\n\n\\bibitem[Abel, Bryan, and Norman (2000)]{Abel2000} {\\sc Abel, T.,\nBryan, G. L., Norman, M. L.} 2000, {\\it ApJ} in press (ABN00)\n\n\\bibitem[Anninos and Norman (1996)]{Anninos96} {\\sc Anninos, P.,\nNorman, M.L.} 1996, {\\it ApJ} {\\bf 460}, 556\n\n\\bibitem[Anninos et al. (1997)]{Anninos97} {\\sc Anninos, P., Zhang, Y.,\nAbel, T., Norman, M. L.} 1997, {\\it NewA} {\\bf 2}, 209\n\n\\bibitem[Bajtlik, Duncan \\& Ostriker (1988)]{Bajt1988} {\\sc Bajtlik, S., Duncan, R. C., \\& Ostriker, J. P.} 1988 {\\it ApJ} {\\bf 327}, 570\n\n\\bibitem[Bardeen et al. (1986)]{Bard1986} {\\sc Bardeen, J. M., Bond, J. R., Kaiser, N., \\& Szalay, A. S.} 1986 {\\it ApJ} {\\bf 304}, 15 \n\n\\bibitem[Bertschinger (1985)]{Bert1985} {\\sc Bertschinger, E.} 1985 {\\it ApJS} {\\bf 58}, 39\n\n\\bibitem[B\\\"ohringer & Hensler (1989)]{Bohr1989} {\\sc B\\\"ohringer, H., \\& Hensler, G.} 1989 {\\it A\\&A} {\\bf 215}, 147\n\n\\bibitem[Bodenheimer and Villere (1986)]{Bod1986} {\\sc Bodenheimer,\nP. and Villere, K. R.} 1986 {\\it Final Technical Report, UC Santa Cruz}\n\n\\bibitem[Bromm et al. (1999)]{Brom1999} {\\sc Bromm, V., Coppi, P. S., \\& Larson, R. B.} 1999 {\\it ApJL} {\\bf 527}, 5\n\n\\bibitem[Bryan and Norman (1997)]{Bryan97} {\\sc Bryan, G. L., Norman,\n M. L.} 1997, in {\\it\n Computational Astrophysics}, eds. D.A. Clarke and M. Fall, ASP\n Conference \\#123\n\n\\bibitem[Bryan and Norman (1998)]{Bryan98} {\\sc Bryan, G. L., Norman,\nM. L.} 1998, {\\it ApJ} {\\bf 495}, 80\n\n\\bibitem[Bryan and Norman (1998)]{Bryan99} {\\sc Bryan, G. L., Norman,\nM. L.} 1999, in {\\it Workshop on\n Structured Adaptive Mesh Refinement Grid Methods}, IMA Volumes\n in Mathematics No. 117, ed. N. Chrisochoides, p. 165\n\n\\bibitem[Cen et al. (1994)]{Cen94} {\\sc Cen, R., Miralda-Escud\\'e, J.,\nOstriker, J. P., \\& Rauch, M.} 1994, {\\it ApJ} {\\bf 437}, L9 \n\n\\bibitem[Dalgarno and Lepp (1987)]{Dalg87} {\\sc Dalgarno, A., \\& Lepp, S.} 1987, in {\\it Astrochemistry}, eds. Vardya, M.S. \\& Tarafdar, S.P. (Dordrecht:Reidel), 109\n\n\\bibitem[Dav\\'e et al. (1999)]{Dave99} {\\sc Dav\\'e, R., Hernquist,\nL., Katz, N., Weinberg, D. H.} 1999, {\\it ApJ} {\\bf 511}, 521\n\n\\bibitem[Dekel \\& Silk (1986)]{Deke1986} {\\sc Dekel, A., \\& Silk, J.} 1986 {\\it ApJ} {\\bf 303}, 39\n\n\\bibitem[Field, Somerville \\& Dressler, K. (1966)]{Fiel1966} {\\sc Field, G. B.,Somerville, W. B., \\& Dressler, K.} 1966 {\\it ARA\\&A} {\\bf 4}, 207\n\n\\bibitem[Fillmore \\& Goldreich (1984)]{Fill1984} {\\sc Fillmore, J. A., \\& Goldreich, P.} 1984 {\\it ApJ} {\\bf 281}, 1\n\n\\bibitem[Frenk et al. (1999)]{Frenk99} {\\sc Frenk, C. S., White,\nS. D. M., Bode, P. et al. } 1999, {\\it ApJ} {\\bf 525}, 554\n\n\\bibitem[Gnedin \\& Ostriker (1997)]{Gnedin1996} {\\sc Gnedin, N. Y., \\& Ostriker, J. P.} 1997 {\\it ApJ} {\\bf 486}, 581\n\n\\bibitem[Gunn \\& Gott (1972)]{Gunn1972} {\\sc Gunn, J. E., \\& Gott, J. R. III.} 1972 {\\it ApJ} {\\bf 176}, 1\n\n\\bibitem[Haiman, Abel \\& Rees (2000)]{Haim2000} {\\sc Haiman, Z., Abel, T., \\& Rees, M. J.} 2000 {\\it ApJ}, in press, astro-ph/9903336 \n\n\\bibitem[Haiman \\& Loeb (1997)]{Haim1997} {\\sc Haiman, Z., \\& Loeb, A.} 1997 {\\it ApJ} {\\bf 483}, 21\n\n\\bibitem[Haiman \\& Loeb (1998)]{Haim1998} {\\sc Haiman, Z., \\& Loeb, A.} 1998 {\\it ApJ} {\\bf 503}, 505\n\n\\bibitem[Haiman, Rees \\& Loeb (1996)]{Haim1996} {\\sc Haiman, Z., Rees, M. J., \\& Loeb, A.} 1996 {\\it ApJ} {\\bf 467}, 522\n\n\\bibitem[Haiman, Rees \\& Loeb (1997)]{Haim1997b} {\\sc Haiman, Z., Rees, M. J., \\& Loeb, A.} 1997 {\\it ApJ} {\\bf 476}, 458\n\n\\bibitem[Haiman, Thoul\\& Loeb (1996)]{Haim1996b} {\\sc Haiman, Z.,\n Thoul, A., \\& Loeb, A.} 1996 {\\it ApJ} {\\bf 464}, 523 (HTL96)\n\n\\bibitem[Hernquist et al. (1996)]{Hern96} {\\sc Hernquist, L., Katz, N.,\nWeinberg, D. H., \\& Miralda-Escud\\'e, J.} 1996, {\\it ApJ}, {\\bf 457}, L51\n\n\\bibitem[Hirasawa (1969)]{Hira1969} {\\sc Hirasawa, T.} 1969 {\\it Prog. Theor. Phys.} {\\bf v. 42}, no. 3, p. 523\n\n\\bibitem[Hutchins (1976)]{Hutc1976} {\\sc Hutchins, J. B.} 1976 {\\it ApJ} {\\bf 205}, 103\n\n\\bibitem[Ikeuchi and Ostriker (1986)]{Ikeu86} {\\sc Ikeuchi, S.,\nOstriker, J. P. } 986, {\\it ApJ} {\\bf 301}, 522\n\n\\bibitem[Kashlinsky \\& Rees (1983)]{Kash1983} {\\sc Kashlinsky, A., \\& Rees, M. J.} 1983 {\\it MNRAS} {\\bf 205}, 955 \n\n\\bibitem[Kang \\& Shapiro (1992)]{Kang1992} {\\sc Kang, H., \\& Shapiro, P. R.} 1992 {\\it ApJ} {\\bf 386}, 432\n\n\\bibitem[Kang et al. (1990)]{Kang1990} {\\sc Kang, H., Shapiro, P. R., Fall, S. M., \\& Rees, M. J.} 1990 {\\it ApJ} {\\bf 363}, 488\n\n\\bibitem[Kauffmann et al. (1999)]{Kauff99} {\\sc Kauffmann, G.,\nColberg, J. M., Diaferio, A., White, S. D. M.} 1999 {\\it MNRAS} {\\bf\n303}, 188 \n\n\\bibitem[Katz et al. (1999)]{Katz99} {\\sc Katz, N., Hernquist, L.,\n Weinberg, D. H.} 1999, {\\it ApJ} {\\bf 523}, 463\n\n\\bibitem[Kolb \\& Turner (1990)]{Kolb1990} {\\sc Kolb, E. W., \\& Turner, M.S.} 1990 {\\it The Early Universe}, Addison-Wesley, Redwood City, CA\n\n\\bibitem[Larson (1999)]{Larson1999} {\\sc Larson, R. B.} 1999 in {\\it Star Formation From the Small to the Large Scale}, eds. F. Favata, A.A. Kaas, \\& A. Wilson, (ESA Special Publications Series, Noordwijk, Holland)\n\n\\bibitem[Lepp \\& Shull (1983)]{Lepp1983} {\\sc Lepp, S., \\& Shull, J. M.} 1983 {\\it ApJ} {\\bf 270}, 578 \n\n\\bibitem[Lepp \\& Shull (1984)]{Lepp1984} {\\sc Lepp, S., \\& Shull, J. M.} 1984 {\\it ApJ} {\\bf 280}, 465 \n\n\\bibitem[Lynden--Bell (1967)]{Lynd1967} {\\sc Lynden--Bell, D.} 1967 {\\it MNRAS} {\\bf 136}, 101\n\n\\bibitem[Matsuda, Sato \\& Takeda (1969)]{Mats1969} {\\sc Matsuda, T., Sato, H., \\& Takeda, H.} 1969 {\\it Prog. Theor. Phys.} {\\bf v. 42}, no. 2, p. 219\n\n\\bibitem[Omukai \\& Nishi (1999)]{Omuk1999} {\\sc Omukai, K., \\& Nishi, R.} 1999\n{\\it ApJ} {\\bf 518}, 64\n\n\\bibitem[Palla, Salpeter \\& Stahler (1983)]{Pall1983} {\\sc Palla, F., Salpeter, E. E., \\& Stahler, S.W.} 1983 {\\it ApJ} {\\bf 271}, 632\n\n\\bibitem[Peebles (1965)]{Peeb1965} {\\sc Peebles, P. J. E.} 1965 {\\it ApJ}, {\\bf 142}, 1317\n\n\\bibitem[Peebles (1980)]{Peeb1980} {\\sc Peebles, P. J. E.} 1980 {\\it\nLarge-Scale Structure of the Universe} {\\bf Princeton Univ. Press, NJ}\n\n\\bibitem[Peebles (1993)]{Peeb1993} {\\sc Peebles, P. J. E.} 1993 \n {\\it Principles of Physical Cosmology} {\\bf Princeton Univ. Press} \n\n\\bibitem[Peebles (1982)]{Peeb1982} {\\sc Peebles, P. J. E.} 1982, \n {\\it ApJ} {\\bf 263}, L1\n\n\\bibitem[Peebles \\& Dicke (1968)]{Peeb1968} {\\sc Peebles, P.J.E., \\&\nDicke, R.H.} 1968 {\\it ApJ} {\\bf 154}, 891 \n\n\\bibitem[Rees \\& Ostriker (1977)]{Rees1977} {\\sc Rees, M. J., \\& Ostriker, J. P.} 1977 {\\it MNRAS} {\\bf 179}, 541\n\n\\bibitem[Rees (1986)]{Rees86} {\\sc Rees, M. J.} 1986, {\\it MNRAS} {\\bf 222}, 27 \n\\bibitem[Ruzmaikina (1973)]{Ruzm1973} {\\sc Ruzmaikina, T. V.} 1973 {\\it Sov. Astron.} {\\bf v. 16}, no. 6, p. 991\n\n\\bibitem[Saslaw \\& Zipoy (1967)]{Sasl1967} {\\sc Saslaw, W. C., \\& Zipoy, D.} 1967 {\\it Nature} {\\bf 216}, 976\n\n\\bibitem[Shapiro, Giroux \\& Babul (1994)]{Shap1994} {\\sc Shapiro, P. R., Giroux, M. L., \\& Babul, A.} 1994 {\\it ApJ} {\\bf 427}, 25\n\n\\bibitem[Shapiro \\& Kang (1987)]{Shap1987} {\\sc Shapiro, P. R., \\& Kang, H.} 1987 {\\it ApJ} {\\bf 318}, 32\n\n\\bibitem[Silk (1983)]{Silk1983} {\\sc Silk, J.} 1983 {\\it MNRAS} {\\bf 205}, 705\n\n\\bibitem[Stancil, Lepp and Dalgarno (1996)]{Stancil96} {\\sc Stancil, P.C.,\nLepp, S., Dalgarno, A.} 1996, {\\it ApJ} {\\bf 458}, 401\n\n\\bibitem[Tegmark et al. (1997)]{Tegm1997} {\\sc Tegmark, M., Silk, J.,\nRees, M. J., Blanchard, A., Abel, T., \\& Palla, F.} 1997 {\\it ApJ}\n{\\bf 474}, 1 \n\n\\bibitem[Tumlinson \\& Shull (1999)]{Tuml1999} {\\sc Tumlinson, J., \\& Shull, J. M.} 1999 {\\it ApJL}, in press, astro-ph/9911339\n\n\\bibitem[Weymann et al. (1998)]{Weym1998} {\\sc Weymann, R. J., et al.} 1998, {\\it ApJ} {\\bf 505}, 95\n\n\\bibitem[Williams et al. (1996)]{Will1996} {\\sc Williams, R. E., et al.} 1996, {\\it AJ} {\\bf 112}, 1335\n\n\\bibitem[Zhang et al. (1995)]{Zhang95} {\\sc Zhang, Y., Anninos, P., \\&\nNorman, M. L.} 1995, {\\it ApJ}, {\\bf 453}, L57\n\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002031.extracted_bib",
"string": "\\begin{thebibliography}{} \n\n\\bibitem[Abel 1995]{Abel95} {\\sc Abel, T.} 1995, {\\it Thesis}, University of\nRegensburg, Germany \n\n\\bibitem[Abel et al. (1997)]{Abel97} {\\sc Abel, T., Anninos, P.,\nZhang, Y., Norman, M. L.} 1997, {\\it NewA} {\\bf 2}, 181\n\n\\bibitem[Abel et al. (1998a)]{Abel98a} {\\sc Abel, T., Anninos, P.,\nNorman, M. L., Zhang, Y.} 1998a, {\\it ApJ} {\\bf 508}, 518 (AANZ98)\n\n\\bibitem[Abel et al. (1998b)]{Abel98b} {\\sc Abel, T., Stebbins, A.,\nAnninos, P., Norman, M.L.} 1998, {\\it ApJ} {\\bf 508}, 530\n\n\\bibitem[Abel and Mo (1998)]{Abel99c} {\\sc Abel, T., Mo, H. J.} 1998,\n{\\it ApJ} {\\bf 494}, L151\n\n\\bibitem[Abel, Norman, and Madau (1999)]{Abel99} {\\sc Abel, T.,\nNorman, M. L., Madau, P.} 1999, {\\it ApJ} {\\bf 523}, 66\n\n\\bibitem[Abel, Bryan, and Norman (2000)]{Abel2000} {\\sc Abel, T.,\nBryan, G. L., Norman, M. L.} 2000, {\\it ApJ} in press (ABN00)\n\n\\bibitem[Anninos and Norman (1996)]{Anninos96} {\\sc Anninos, P.,\nNorman, M.L.} 1996, {\\it ApJ} {\\bf 460}, 556\n\n\\bibitem[Anninos et al. (1997)]{Anninos97} {\\sc Anninos, P., Zhang, Y.,\nAbel, T., Norman, M. L.} 1997, {\\it NewA} {\\bf 2}, 209\n\n\\bibitem[Bajtlik, Duncan \\& Ostriker (1988)]{Bajt1988} {\\sc Bajtlik, S., Duncan, R. C., \\& Ostriker, J. P.} 1988 {\\it ApJ} {\\bf 327}, 570\n\n\\bibitem[Bardeen et al. (1986)]{Bard1986} {\\sc Bardeen, J. M., Bond, J. R., Kaiser, N., \\& Szalay, A. S.} 1986 {\\it ApJ} {\\bf 304}, 15 \n\n\\bibitem[Bertschinger (1985)]{Bert1985} {\\sc Bertschinger, E.} 1985 {\\it ApJS} {\\bf 58}, 39\n\n\\bibitem[B\\\"ohringer & Hensler (1989)]{Bohr1989} {\\sc B\\\"ohringer, H., \\& Hensler, G.} 1989 {\\it A\\&A} {\\bf 215}, 147\n\n\\bibitem[Bodenheimer and Villere (1986)]{Bod1986} {\\sc Bodenheimer,\nP. and Villere, K. R.} 1986 {\\it Final Technical Report, UC Santa Cruz}\n\n\\bibitem[Bromm et al. (1999)]{Brom1999} {\\sc Bromm, V., Coppi, P. S., \\& Larson, R. B.} 1999 {\\it ApJL} {\\bf 527}, 5\n\n\\bibitem[Bryan and Norman (1997)]{Bryan97} {\\sc Bryan, G. L., Norman,\n M. L.} 1997, in {\\it\n Computational Astrophysics}, eds. D.A. Clarke and M. Fall, ASP\n Conference \\#123\n\n\\bibitem[Bryan and Norman (1998)]{Bryan98} {\\sc Bryan, G. L., Norman,\nM. L.} 1998, {\\it ApJ} {\\bf 495}, 80\n\n\\bibitem[Bryan and Norman (1998)]{Bryan99} {\\sc Bryan, G. L., Norman,\nM. L.} 1999, in {\\it Workshop on\n Structured Adaptive Mesh Refinement Grid Methods}, IMA Volumes\n in Mathematics No. 117, ed. N. Chrisochoides, p. 165\n\n\\bibitem[Cen et al. (1994)]{Cen94} {\\sc Cen, R., Miralda-Escud\\'e, J.,\nOstriker, J. P., \\& Rauch, M.} 1994, {\\it ApJ} {\\bf 437}, L9 \n\n\\bibitem[Dalgarno and Lepp (1987)]{Dalg87} {\\sc Dalgarno, A., \\& Lepp, S.} 1987, in {\\it Astrochemistry}, eds. Vardya, M.S. \\& Tarafdar, S.P. (Dordrecht:Reidel), 109\n\n\\bibitem[Dav\\'e et al. (1999)]{Dave99} {\\sc Dav\\'e, R., Hernquist,\nL., Katz, N., Weinberg, D. H.} 1999, {\\it ApJ} {\\bf 511}, 521\n\n\\bibitem[Dekel \\& Silk (1986)]{Deke1986} {\\sc Dekel, A., \\& Silk, J.} 1986 {\\it ApJ} {\\bf 303}, 39\n\n\\bibitem[Field, Somerville \\& Dressler, K. (1966)]{Fiel1966} {\\sc Field, G. B.,Somerville, W. B., \\& Dressler, K.} 1966 {\\it ARA\\&A} {\\bf 4}, 207\n\n\\bibitem[Fillmore \\& Goldreich (1984)]{Fill1984} {\\sc Fillmore, J. A., \\& Goldreich, P.} 1984 {\\it ApJ} {\\bf 281}, 1\n\n\\bibitem[Frenk et al. (1999)]{Frenk99} {\\sc Frenk, C. S., White,\nS. D. M., Bode, P. et al. } 1999, {\\it ApJ} {\\bf 525}, 554\n\n\\bibitem[Gnedin \\& Ostriker (1997)]{Gnedin1996} {\\sc Gnedin, N. Y., \\& Ostriker, J. P.} 1997 {\\it ApJ} {\\bf 486}, 581\n\n\\bibitem[Gunn \\& Gott (1972)]{Gunn1972} {\\sc Gunn, J. E., \\& Gott, J. R. III.} 1972 {\\it ApJ} {\\bf 176}, 1\n\n\\bibitem[Haiman, Abel \\& Rees (2000)]{Haim2000} {\\sc Haiman, Z., Abel, T., \\& Rees, M. J.} 2000 {\\it ApJ}, in press, astro-ph/9903336 \n\n\\bibitem[Haiman \\& Loeb (1997)]{Haim1997} {\\sc Haiman, Z., \\& Loeb, A.} 1997 {\\it ApJ} {\\bf 483}, 21\n\n\\bibitem[Haiman \\& Loeb (1998)]{Haim1998} {\\sc Haiman, Z., \\& Loeb, A.} 1998 {\\it ApJ} {\\bf 503}, 505\n\n\\bibitem[Haiman, Rees \\& Loeb (1996)]{Haim1996} {\\sc Haiman, Z., Rees, M. J., \\& Loeb, A.} 1996 {\\it ApJ} {\\bf 467}, 522\n\n\\bibitem[Haiman, Rees \\& Loeb (1997)]{Haim1997b} {\\sc Haiman, Z., Rees, M. J., \\& Loeb, A.} 1997 {\\it ApJ} {\\bf 476}, 458\n\n\\bibitem[Haiman, Thoul\\& Loeb (1996)]{Haim1996b} {\\sc Haiman, Z.,\n Thoul, A., \\& Loeb, A.} 1996 {\\it ApJ} {\\bf 464}, 523 (HTL96)\n\n\\bibitem[Hernquist et al. (1996)]{Hern96} {\\sc Hernquist, L., Katz, N.,\nWeinberg, D. H., \\& Miralda-Escud\\'e, J.} 1996, {\\it ApJ}, {\\bf 457}, L51\n\n\\bibitem[Hirasawa (1969)]{Hira1969} {\\sc Hirasawa, T.} 1969 {\\it Prog. Theor. Phys.} {\\bf v. 42}, no. 3, p. 523\n\n\\bibitem[Hutchins (1976)]{Hutc1976} {\\sc Hutchins, J. B.} 1976 {\\it ApJ} {\\bf 205}, 103\n\n\\bibitem[Ikeuchi and Ostriker (1986)]{Ikeu86} {\\sc Ikeuchi, S.,\nOstriker, J. P. } 986, {\\it ApJ} {\\bf 301}, 522\n\n\\bibitem[Kashlinsky \\& Rees (1983)]{Kash1983} {\\sc Kashlinsky, A., \\& Rees, M. J.} 1983 {\\it MNRAS} {\\bf 205}, 955 \n\n\\bibitem[Kang \\& Shapiro (1992)]{Kang1992} {\\sc Kang, H., \\& Shapiro, P. R.} 1992 {\\it ApJ} {\\bf 386}, 432\n\n\\bibitem[Kang et al. (1990)]{Kang1990} {\\sc Kang, H., Shapiro, P. R., Fall, S. M., \\& Rees, M. J.} 1990 {\\it ApJ} {\\bf 363}, 488\n\n\\bibitem[Kauffmann et al. (1999)]{Kauff99} {\\sc Kauffmann, G.,\nColberg, J. M., Diaferio, A., White, S. D. M.} 1999 {\\it MNRAS} {\\bf\n303}, 188 \n\n\\bibitem[Katz et al. (1999)]{Katz99} {\\sc Katz, N., Hernquist, L.,\n Weinberg, D. H.} 1999, {\\it ApJ} {\\bf 523}, 463\n\n\\bibitem[Kolb \\& Turner (1990)]{Kolb1990} {\\sc Kolb, E. W., \\& Turner, M.S.} 1990 {\\it The Early Universe}, Addison-Wesley, Redwood City, CA\n\n\\bibitem[Larson (1999)]{Larson1999} {\\sc Larson, R. B.} 1999 in {\\it Star Formation From the Small to the Large Scale}, eds. F. Favata, A.A. Kaas, \\& A. Wilson, (ESA Special Publications Series, Noordwijk, Holland)\n\n\\bibitem[Lepp \\& Shull (1983)]{Lepp1983} {\\sc Lepp, S., \\& Shull, J. M.} 1983 {\\it ApJ} {\\bf 270}, 578 \n\n\\bibitem[Lepp \\& Shull (1984)]{Lepp1984} {\\sc Lepp, S., \\& Shull, J. M.} 1984 {\\it ApJ} {\\bf 280}, 465 \n\n\\bibitem[Lynden--Bell (1967)]{Lynd1967} {\\sc Lynden--Bell, D.} 1967 {\\it MNRAS} {\\bf 136}, 101\n\n\\bibitem[Matsuda, Sato \\& Takeda (1969)]{Mats1969} {\\sc Matsuda, T., Sato, H., \\& Takeda, H.} 1969 {\\it Prog. Theor. Phys.} {\\bf v. 42}, no. 2, p. 219\n\n\\bibitem[Omukai \\& Nishi (1999)]{Omuk1999} {\\sc Omukai, K., \\& Nishi, R.} 1999\n{\\it ApJ} {\\bf 518}, 64\n\n\\bibitem[Palla, Salpeter \\& Stahler (1983)]{Pall1983} {\\sc Palla, F., Salpeter, E. E., \\& Stahler, S.W.} 1983 {\\it ApJ} {\\bf 271}, 632\n\n\\bibitem[Peebles (1965)]{Peeb1965} {\\sc Peebles, P. J. E.} 1965 {\\it ApJ}, {\\bf 142}, 1317\n\n\\bibitem[Peebles (1980)]{Peeb1980} {\\sc Peebles, P. J. E.} 1980 {\\it\nLarge-Scale Structure of the Universe} {\\bf Princeton Univ. Press, NJ}\n\n\\bibitem[Peebles (1993)]{Peeb1993} {\\sc Peebles, P. J. E.} 1993 \n {\\it Principles of Physical Cosmology} {\\bf Princeton Univ. Press} \n\n\\bibitem[Peebles (1982)]{Peeb1982} {\\sc Peebles, P. J. E.} 1982, \n {\\it ApJ} {\\bf 263}, L1\n\n\\bibitem[Peebles \\& Dicke (1968)]{Peeb1968} {\\sc Peebles, P.J.E., \\&\nDicke, R.H.} 1968 {\\it ApJ} {\\bf 154}, 891 \n\n\\bibitem[Rees \\& Ostriker (1977)]{Rees1977} {\\sc Rees, M. J., \\& Ostriker, J. P.} 1977 {\\it MNRAS} {\\bf 179}, 541\n\n\\bibitem[Rees (1986)]{Rees86} {\\sc Rees, M. J.} 1986, {\\it MNRAS} {\\bf 222}, 27 \n\\bibitem[Ruzmaikina (1973)]{Ruzm1973} {\\sc Ruzmaikina, T. V.} 1973 {\\it Sov. Astron.} {\\bf v. 16}, no. 6, p. 991\n\n\\bibitem[Saslaw \\& Zipoy (1967)]{Sasl1967} {\\sc Saslaw, W. C., \\& Zipoy, D.} 1967 {\\it Nature} {\\bf 216}, 976\n\n\\bibitem[Shapiro, Giroux \\& Babul (1994)]{Shap1994} {\\sc Shapiro, P. R., Giroux, M. L., \\& Babul, A.} 1994 {\\it ApJ} {\\bf 427}, 25\n\n\\bibitem[Shapiro \\& Kang (1987)]{Shap1987} {\\sc Shapiro, P. R., \\& Kang, H.} 1987 {\\it ApJ} {\\bf 318}, 32\n\n\\bibitem[Silk (1983)]{Silk1983} {\\sc Silk, J.} 1983 {\\it MNRAS} {\\bf 205}, 705\n\n\\bibitem[Stancil, Lepp and Dalgarno (1996)]{Stancil96} {\\sc Stancil, P.C.,\nLepp, S., Dalgarno, A.} 1996, {\\it ApJ} {\\bf 458}, 401\n\n\\bibitem[Tegmark et al. (1997)]{Tegm1997} {\\sc Tegmark, M., Silk, J.,\nRees, M. J., Blanchard, A., Abel, T., \\& Palla, F.} 1997 {\\it ApJ}\n{\\bf 474}, 1 \n\n\\bibitem[Tumlinson \\& Shull (1999)]{Tuml1999} {\\sc Tumlinson, J., \\& Shull, J. M.} 1999 {\\it ApJL}, in press, astro-ph/9911339\n\n\\bibitem[Weymann et al. (1998)]{Weym1998} {\\sc Weymann, R. J., et al.} 1998, {\\it ApJ} {\\bf 505}, 95\n\n\\bibitem[Williams et al. (1996)]{Will1996} {\\sc Williams, R. E., et al.} 1996, {\\it AJ} {\\bf 112}, 1335\n\n\\bibitem[Zhang et al. (1995)]{Zhang95} {\\sc Zhang, Y., Anninos, P., \\&\nNorman, M. L.} 1995, {\\it ApJ}, {\\bf 453}, L57\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002032
|
The Fading of Supernova Remnant Cassiopeia A from 38 MHz to 16.5 GHz from 1949 to 1999 with New Observations at 1405 MHz\altaffilmark{1}
|
[
{
"author": "Daniel E. Reichart\\altaffilmark{2} and Andrew W. Stephens\\altaffilmark{3}"
}
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We report 1405 MHz measurements of the flux density of the $\approx 320$ year old supernova remnant Cassiopeia A, relative to the flux density of Cygnus A, made between 1995 and 1999. When compared to measurements made between 1957 and 1976, we find that the rate at which Cassiopeia A has been fading at this and nearby frequencies has changed from $\approx 0.9$ \% yr$^{-1}$ in the 1960s to $\approx 0.6 - 0.7$ \% yr$^{-1}$ now. Furthermore, we have collected from the literature measurements of this fading rate at lower (38 -- 300 MHz) and higher (7.8 -- 16.5 GHz) frequencies. We show that the fading rate has dropped by a factor of $\approx 3$ over the past 50 years at the lower frequencies, while remaining relatively constant at the higher frequencies, which is in agreement with the findings of others. Our findings at 1405 MHz, in conjunction with a measurement of the fading rate at the nearby frequency of 927 MHz by Vinyajkin (1997), show an intermediate behavior at intermediate frequencies. We also find that Cassiopeia A, as of $\approx$ 1990, was fading at about the same rate, $\approx 0.6 - 0.7$ \% yr$^{-1}$, at all of these frequencies. Future measurements are required to determine whether the fading rate will continue to decrease at the lower frequencies, or whether Cassiopeia A will now fade at a relatively constant rate at all of these frequencies.
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{
"name": "casb.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aaspptwo]{article}\n\n%\\tighten\n%\\eqsecnum\n\n\\def\\la{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\ga{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\\def\\lesssim{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\etal{et al.\\,\\,}\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{}{15 January 1989}\n%\\articleid{}{}\n\n\\slugcomment{Accepted to {\\it The Astrophysical Journal}}\n\n\\begin{document}\n\n\\title{The Fading of Supernova Remnant Cassiopeia A from 38 MHz to 16.5 GHz from 1949 to 1999 with New Observations at 1405 MHz\\altaffilmark{1}}\n\n\\author{Daniel E. Reichart\\altaffilmark{2} and Andrew W. Stephens\\altaffilmark{3}}\n\n\\altaffiltext{1}{The data presented herein were obtained by participants of Educational Research in Radio Astronomy (ERIRA) 1992 -- 1999, an outreach program that has received support from the National Radio Astronomy Observatory, the Ohio State University, the Pennsylvania State University, and the University of Pittsburgh at Bradford.}\n\\altaffiltext{2}{Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637; [email protected]}\n\\altaffiltext{3}{Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210} \n\n\\begin{abstract}\nWe report 1405 MHz measurements of the flux density of the $\\approx 320$ year old supernova remnant Cassiopeia A, relative to the flux density of Cygnus A, made between 1995 and 1999. When compared to measurements made between 1957 and 1976, we find that the rate at which Cassiopeia A has been fading at this and nearby frequencies has changed from $\\approx 0.9$ \\% yr$^{-1}$ in the 1960s to $\\approx 0.6 - 0.7$ \\% yr$^{-1}$ now. Furthermore, we have collected from the literature measurements of this fading rate at lower (38 -- 300 MHz) and higher (7.8 -- 16.5 GHz) frequencies. We show that the fading rate has dropped by a factor of $\\approx 3$ over the past 50 years at the lower frequencies, while remaining relatively constant at the higher frequencies, which is in agreement with the findings of others. Our findings at 1405 MHz, in conjunction with a measurement of the fading rate at the nearby frequency of 927 MHz by Vinyajkin (1997), show an intermediate behavior at intermediate frequencies. We also find that Cassiopeia A, as of $\\approx$ 1990, was fading at about the same rate, $\\approx 0.6 - 0.7$ \\% yr$^{-1}$, at all of these frequencies. Future measurements are required to determine whether the fading rate will continue to decrease at the lower frequencies, or whether Cassiopeia A will now fade at a relatively constant rate at all of these frequencies.\n\\end{abstract}\n\n\\keywords{ISM: individual (Cassiopeia A) --- supernova remnants}\n\n\\section{Introduction: A History of Measurements of Cassiopeia A's Fading Rate}\n\nCassiopeia A is thought to have exploded around $1681 \\pm 15$, based on radial velocity and proper motion measurements of 15 of the supernova remnant's high-velocity [N II]-emitting knots, also called fast-moving flocculi or FMFs (Fesen, Becker, \\& Goodrich 1988). Indeed, Flamsteed (1725) observed a 6th magnitude star within 13$\\arcmin$ of Cassiopeia A's location in 1680 (Ashworth 1980) that later became a subject of debate when the star could not be found in the sky (Herschel 1798; Baily 1835). Cassiopeia A was re-discovered in 1943 at 160 MHz by Reber (1944), although a re-analysis of a day-long strip chart recording published by Jansky (1935) suggests that he unknowingly detected it as early as 1932 at 20.5 MHz (Sullivan 1978). Accurate measurements of Cassiopeia A's flux density - both absolute measurements and measurements relative to the flux density of the extragalactic radio source Cygnus A - began in 1949 at 81.5 MHz (Ryle \\& Elsmore 1951).\n\n\\subsection{The Fading Rate of Cassiopeia A around 1965}\n\nH\\\"ogbom \\& Shakeshaft (1961), with Ryle \\& Elsmore's (1951) 1949 measurement and two measurements of their own made in 1956 and 1960 also at 81.5 MHz, first showed that Cassiopeia A was fading; they measured a fading rate of $1.06 \\pm 0.14$ \\% yr$^{-1}$, which was later refined to $1.29 \\pm 0.08$ \\% yr$^{-1}$ with the addition of four measurements made between 1966 and 1969 also at 81.5 MHz (Scott, Shakeshaft, \\& Smith 1969). \nUsing data spanning 1957 -- 1972, Baars \\& Hartsuijker (1972) measured significantly lower fading rates at 1420 and 3000 MHz, $0.89 \\pm 0.12$ and $0.92 \\pm 0.15$ \\% yr$^{-1}$, respectively; they first suggested that Cassiopeia A was fading at different rates at different frequencies. By 1977, accurate fading rates had been determined at six different frequencies, spanning 81.5 to 9400 MHz. Baars et al. (1977; see also Dent, Aller, \\& Olsen 1974) collected these measurements, which we re-list in Table 1 and plot in Figure 1, and determined the following empirical equation that describes the frequency dependence of Cassiopeia A's fading rate for the $\\approx$ 1965 epoch:\n\\begin{equation}\n-\\frac{100}{F_{\\nu}}\\frac{dF_{\\nu}}{dt} = 0.97(\\pm0.04)-0.30(\\pm0.04)\\log{\\nu_{GHz}}.\n\\end{equation}\nUsing this equation and absolute measurements of Cassiopeia A's flux density made around 1965 over a frequency range that spans 22 MHz to 31 GHz, Baars et al. (1977) also determined an empirical equation that describes the absolute spectrum of Cassiopeia A for the 1965 epoch to an accuracy of $\\approx 2$\\%. Empirical equations that describe the absolute spectra of Cygnus A and Taurus A, and a semi-absolute spectrum for Virgo A, were also determined.\n\n\\subsection{The Decreasing Fading Rate of Cassiopeia A at Low Radio Frequencies (38 -- 300 MHz)}\n\nEquation (1) was first challenged by Erickson \\& Perley (1975) who's\n1974 measurement of the flux density of Cassiopeia A at 38 MHz was\nbrighter than the prediction of Baars et al. (1977) at the 3.5 $\\sigma$\nlevel. Subsequent measurements at 38 MHz by Read (1977a,b), Walczowski\n\\& Smith (1985), Rees (1990), and Vinyajkin (1997) confirmed that the\nfading rate had decreased from $1.9 \\pm 0.5$ \\% yr$^{-1}$ (determined\nusing only the 1955 -- 1966 measurements; Read 1977a) to $0.66 \\pm\n0.17$ \\% yr$^{-1}$ (determined using all of the measurements through\n1995; Vinyajkin 1997).\\footnote{Rees (1990) suggested that the\nmeasurements at 38 MHz, as of 1987, could be treated as being\nconsistent with a constant fading rate of $\\sim 0.8$ \\% yr$^{-1}$,\nparticularly if one ignored the 1949 -- 1969 measurements of Ryle \\&\nElsmore (1951), H\\\"ogbom \\& Shakeshaft (1961), and Scott, Shakeshaft,\n\\& Smith (1969), which imply a significantly higher fading rate, $1.29\n\\pm 0.08$ \\% yr$^{-1}$, at the nearby frequency of 81.5 MHz. However,\nRees (1990) did not rule out the possibility of a changing fading rate\nat 38 MHz, and indeed, the later measurement of this fading rate by\nVinyajkin (1997) suggests that it has changed at the $\\approx 2.3$\n$\\sigma$ confidence level.}\n\nSimilar and more accurate results have been found at 81.5 MHz. As stated above Scott, Shakeshaft, \\& Smith (1969) found a 1949 -- 1969 fading rate of $1.29 \\pm 0.08$ \\% yr$^{-1}$ at this frequency. Hook, Duffett-Smith, \\& Shakeshaft (1992) found a significantly lower fading rate of $0.92 \\pm 0.16$ \\% yr$^{-1}$ when they included their 1989 measurement, and a fading rate of $\\approx 0.63$ \\% yr$^{-1}$ when they considered only the measurements made after 1965. Agafonov (1996) found similar, although slightly higher values: $1.25 \\pm 0.06$ \\% yr$^{-1}$ (1949 -- 1985) and $\\sim 0.8$ \\% yr$^{-1}$ (1973 -- 1985). \n\nConsistent measurements have also been made at 102 MHz (Agafonov 1996), 151 -- 152 MHz (Read 1977a; Agafonov 1996; Vinyajkin 1997), and 290 -- 300 MHz (Baars \\& Hartsuijker 1972; Vinyajkin 1997). We plot the low frequency (38 -- 300 MHz) measurements of Cassiopeia A's fading rate, as well as the intervals of time over which these measurements were made, in Figure 2, and we list this information in Table 2. Clearly, as is suggested by Hook, Duffett-Smith, \\& Shakeshaft (1992), and advocated by Agafonov (1996), the rate at which Cassiopeia A is fading at low frequencies has decreased over the past 50 years.\\footnote{Hook, Duffett-Smith, \\& Shakeshaft (1992) suggested that instrumental uncertainties and/or flaring of Cassiopeia A's radio emission might systematically affect measurements of Cassiopeia A's fading rate at these low frequencies. However, they made arguments to the contrary, and Agafonov (1996) provided evidence to the contrary. Consequently, we do not further pursue these scenarios in this paper; instead, we refer the interested reader to these papers.} We find the fading rate to be decreasing by $\\approx 2$ \\% yr$^{-1}$ per century at these frequencies. \n\n\\subsection{The Constant Fading Rate of Cassiopeia A at High Radio Frequencies (7.8 -- 16.5 GHz)}\n\nHowever, different conclusions have been reached at significantly higher frequencies. O'Sullivan \\& Green (1999) compare four measurements of Cassiopeia A's relative brightness to Cygnus A that they made in 1994 and 1995 at 13.5, 15.5, and 16.5 GHz to the predictions of Baars et al. (1977). The measurements of O'Sullivan \\& Green (1999) are perfectly consistent with the $\\approx 0.6$ \\% yr$^{-1}$ predictions of Equation (1),\\footnote{Technically, Equation (1) is an extrapolation at frequencies greater than 9.4 GHz; however, this is not a large extrapolation.} suggesting that the rate at which Cassiopeia A fades has not changed significantly over the course of the last half century at these high frequencies. We plot the high frequency (7.8 -- 16.5 GHz) measurements of Cassiopeia A's fading rate in Figure 3, and we list this information in Table 3. \n\nThese apparently contradictory behaviors at low and high radio\nfrequencies suggests that the rate at which Cassiopeia A fades is\nchanging in a frequency-dependent way: the fading rate is decreasing\nat the low frequencies (38 -- 300 MHz) and is relatively constant at\nthe high frequencies (7.8 -- 16.5 GHz). In this paper, we investigate\nand confirm this trend at the intermediate frequency of 1405 MHz with\nmeasurements of the relative flux density of Cassiopeia A to Cygnus A\nthat we made between 1995 and 1999 with the 40-foot telescope at the\nNational Radio Astronomy Observatory in Green Bank, WV. We analyze\nthese measurements in \\S 2; we draw conclusions in \\S 3.\n\n\\section{Green Bank 40-foot Telescope Measurements of the Relative Flux Density of Cassiopeia A to Cygnus A at 1405 MHZ from 1995 to 1999}\n\nIn August of 1995, 1996, 1997, and 1999, we took drift scans of\nCassiopeia A and Cygnus A using the 40-foot telescope at the National\nRadio Astronomy Observatory in Green Bank, WV. In 1995, we used a 70\nMHz band centered about 1405 MHz; in 1996 -- 1999, we used a 110 MHz\nband, also centered about 1405 MHz. The drift scans were $\\approx 4$\ndegrees in length, which is $\\approx 4$ times the resolution element of\nthe telescope. We describe these observations and their analysis in\ngreater detail below. In total, we measured the relative flux density\nof Cassiopeia A to Cygnus A, $F_{1405}^{Cas\\,A}/F_{1405}^{Cyg\\,A}$,\nfive times over a span of five years. We list these measurements in\nTable 4. If one models the flux density of Cassiopeia A as a constant\nover this interval of time, we find that\n$F_{1405}^{Cas\\,A}/F_{1405}^{Cyg\\,A} = 1.266 \\pm 0.023$ for a mean\nepoch of 1997.4. This implies a statistical measurement error of\n$\\approx 1.8$ \\%, which is an upper limit since Cassiopeia A is in\nreality fading over this time interval. Since we used only one of two\northogonal linears, we add in quadrature to this statistical error,\nsystematic errors of $\\la 0.2$ \\% and $\\la 0.5$ \\%, corresponding to\nthe polarizations of Cassiopeia A and Cygnus A, respectively. This\nimplies a total measurement error of $\\la 1.9$ \\%. Conservatively\nadopting a total measurement error of 1.9 \\%, a value of\n$F_{1405}^{Cyg\\,A} = 1581$ Jy from the absolute spectrum calibration of\nCygnus A from Baars et al. (1977), and a 2 \\% uncertainty in this\ncalibration, we find that $F_{1405}^{Cas\\,A} = 2002 \\pm 55$ Jy for this\nmean epoch.\n\nPrior to the transit of each source, we manually adjusted the\ndeclination of the telescope, ensuring, with the aid of a strip chart\nrecorder, that the pointing of the telescope contributed no more than\n$\\approx 0.5$ \\% of error to the flux density measurement. During\ntransit and for the remainder of the observation, we left the telescope\nat this, its final declination. Afterward, we excised the data from\nthe first half of the observation that we had taken at declinations\nother than the final declination. This allowed the background to be\nreliably modeled and subtracted. Across the $\\approx 4$ degree lengths\nof the observations, the background appears to be linear, both in the\ncase of the Cassiopeia A observations and in the case of the Cygnus A\nobservations. Consequently, we modeled the background as linear and\nsubtracted it, simultaneously removing any H I component to the\nemission. We estimate that background subtraction contributes $\\approx\n1$ \\% of error to each flux density measurement. Finally, before and\nafter the $\\approx 30$ minute durations of the Cassiopeia A\nobservations and the $\\approx 20$ minute durations of the Cygnus A\nobservations, we took two-minute-long calibration readings. Each pair\nof readings agreed to better than $\\approx 1$ \\%; none-the-less, we\nlinearly interpolated between the readings, making this a negligible\nsource of error. Consequently and in total, we estimate that the\nmeasured flux density ratios, $F_{1405}^{Cas\\,A}/F_{1405}^{Cyg\\,A}$,\nshould be in error by no more than $\\approx 1.6$ \\%; this is consistent\nwith the statistical measurement error of $\\la 1.8$ \\% that we\ndetermine above. Conservatively adopting total measurement errors of\n1.9 \\%, a 1965 value of $F_{1405}^{Cas\\,A}/F_{1405}^{Cyg\\,A} = 1.542$\nfrom the absolute spectrum calibrations of Cassiopeia A and Cygnus A\nfrom Baars et al. (1977), and 2 \\% uncertainties in each of these\ncalibrations, we find a 1965 -- 1999 fading rate of $0.62 \\pm 0.12$ \\%\nyr$^{-1}$ ($\\chi^2 = 0.36$ for $\\nu = 4$ degrees of freedom) at 1405\nMHz. We plot the 1405 MHz light curve in Figure 4.\n\n\\section{Conclusions: A Decreasing Fading Rate of Cassiopeia A at Intermediate Radio Frequencies (927 -- 3060 MHz)}\n\nWe plot the intermediate frequency (927 -- 3060 MHz) measurements of Cassiopeia A's fading rate in Figure 5, and we list this information in Table 5. When compared to measurements of the fading rate between 1957 and 1976, our measurement at 1405 MHz, in conjunction with a recent measurement at the nearby frequency of 927 MHz by Vinyajkin (1997), show that the fading rate is decreasing at a rate that is intermediate to the rates measured at the lower (38 -- 300 MHz) and the higher (7.8 -- 16.5 GHz) frequencies. We find the fading rate to be decreasing by $\\approx 1$ \\% yr$^{-1}$ per century at these intermediate frequencies. \n \nFurthermore, we find that around 1990, Cassiopeia A was fading at about the same rate, $\\approx 0.6 - 0.7$ \\% yr$^{-1}$, at all of these frequencies. The next decade of observations should reveal whether the fading rate will continue to decrease at the lower frequencies, or whether Cassiopeia A will now fade at a relatively constant rate at all of these frequencies. \n\n\\acknowledgements\n\nThis research is supported in part by NASA grant NAG5-2868 and NASA contract NASW-4690. We are grateful to Rick Fisher and Don Lamb, whose comments greatly improved this paper. \nWe are extremely grateful to Sue Ann Heatherly for her dedication to educational and outreach activities at Green Bank, and for making the 40-foot telescope and the facilities at Green Bank available to ERIRA since 1992. We are also very grateful to Carl Chestnut for the technical assistance he has given us over the years. We also want to thank Dan Fellows, Randy Bish, and Alan Fuller for their past contributions to ERIRA, and Walter Glogowski and Jeremy Garris for their continued dedication to the program. Last, but not least, we want to thank the over 100 students and educators who have participated in ERIRA over the past eight years, many of whom helped to collect the data presented in this paper.\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\n\\bibitem[Agafonov 1996]{a96}\nAgafonov, M. I. 1996, A\\&A, 306, 578\n\n\\bibitem[Ashworth 1980]{a80}\nAshworth, W. B. 1980, J. Hist. Astr., 11, 1\n\n\\bibitem[Baily 1835]{b35}\nBaily, F. 1835, An account of the Revd. John Flamsteed...to which is added, his British Catalog of Stars, Corrected and Enlarged (London)\n\n\\bibitem[Baars \\& Hartsuijker 1972]{bh72}\nBaars, J. W. M., \\& Hartsuijker, A. P. 1972, A\\&A, 17, 172\n\n\\bibitem[Baars et al. 1977]{bea77}\nBaars, J. W. M., Genzel, R., Pauliny-Toth, I. I. K., \\& Witzel, A. 1977, A\\&A, 61, 99\n\n\\bibitem[Dent, Aller, \\& Olsen 1974]{dao74}\nDent, W. A., Aller, H. D., \\& Olsen, E. T. 1974, ApJ, 188, L11\n\n\\bibitem[Erickson, \\& Perley 1975]{ep75}\nErickson, W. C., \\& Perley, R. A. 1975, ApJ, 200, L83\n\n\\bibitem[Fesen, Becker, \\& Goodrich 1988]{fbg88}\nFesen, R. A., Becker, R. H., \\& Goodrich, R. 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L. 1977b, MNRAS, 181, P63\n\n\\bibitem[Reber 1944]{r44}\nReber, G. 1944, ApJ, 100, 279\n\n\\bibitem[Rees 1990]{r90}\nRees, N. 1990, MNRAS, 243, 637\n\n\\bibitem[Ryle \\& Elsmore 1949]{re49}\nRyle, M., \\& Elsmore, B. 1949, Nature, 168, 555\n\n\\bibitem[Scott, Shakeshaft, \\& Smith]{sss69}\nScott, P. F., Shakeshaft, J. R., \\& Smith, M. A. 1969, Nature, 223, 1140\n\n\\bibitem[Stankevich et al. 1973]{sea73}\nStankevich, K. S., Ivanov, V. P., Pelyushenko, S. A., Torkhov, V. A., \\& Ibannikova, A. N. 1973, Radiofizika, 16, 786\n\n\\bibitem[Stankevich, Ivanov, \\& Torkov]{sik73}\nStankevich, K. S., Ivanov, V. P., \\& Torkhov, V. A. 1973, Soviet. Astron., 17, 410\n\n\\bibitem[Sullivan 1978]{s78}\nSullivan, W. T. 1978, Sky \\& Telescope, 56, 101\n\n\\bibitem[Vinyajkin 1997]{v97}\nVinyajkin, E. N. 1997, Astroph. \\& Space Sci., 252, 249\n\n\\bibitem[Walczowski \\& Smith 1985]{ws85}\nWalczowski, L. T., \\& Smith, K. L. 1985, MNRAS, 212, 27\n\n\\end{thebibliography}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n%\\footnotesize\n\\tablecolumns{5}\n\\tablewidth{0pc}\n\\tablecaption{Fading Rates of Cassiopeia A around 1965}\n\\tablehead{\\colhead{Frequency\\tablenotemark{a}} & \\colhead{Measurement Epochs} & \\colhead{Central Epoch} & \\colhead{Fading Rate\\tablenotemark{b}} & \\colhead{Reference\\tablenotemark{c}}}\n\\startdata\n81.5 & 1949 -- 1969 & 1959 & $1.29 \\pm 0.08$ & 1 \\nl\n950 & 1964 -- 1972 & 1968 & $0.85 \\pm 0.05$ & 2 \\nl\n1420 & 1957 -- 1971 & 1964 & $0.89 \\pm 0.12$ & 3 \\nl\n1420 & 1957 -- 1976 & 1966 & $0.86 \\pm 0.02$ & 4 \\nl\n3000 & 1961 -- 1972 & 1966 & $0.92 \\pm 0.15$ & 3 \\nl\n3060 & 1961 -- 1971 & 1966 & $1.04 \\pm 0.21$ & 5 \\nl\n7800 & 1963 -- 1974 & 1968 & $0.70 \\pm 0.10$ & 6 \\nl\n9400 & 1961 -- 1971 & 1966 & $0.63 \\pm 0.12$ & 5 \\nl\n\\enddata\n\\tablenotetext{a}{MHz.}\n\\tablenotetext{b}{\\% yr$^{-1}$.}\n\\tablenotetext{c}{1. Scott, Shakeshaft, \\& Smith 1969; 2. Stankevich, Ivanov, \\& Torkhov 1973; 3. Baars \\& Hartsuijker 1972; 4. Read 1977a; 5. Stankevich et al. 1973; 6. Dent, Aller, \\& Olsen 1974.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n%\\footnotesize\n\\tablecolumns{5}\n\\tablewidth{0pc}\n\\tablecaption{Fading Rates of Cassiopeia A at Low Radio Frequencies (38 -- 300 MHz)}\n\\tablehead{\\colhead{Frequency\\tablenotemark{a}} & \\colhead{Measurement Epochs} & \\colhead{Central Epoch} & \\colhead{Fading Rate\\tablenotemark{b}} & \\colhead{Reference\\tablenotemark{c}}}\n\\startdata\n38 & 1955 -- 1966 & 1960 & $1.9 \\pm 0.5$ & 1 \\nl\n38 & 1955 -- 1995 & 1975 & $0.66 \\pm 0.17$ & 2 \\nl\n81.5 & 1949 -- 1960 & 1954 & $1.06 \\pm 0.14$ & 3 \\nl\n81.5 & 1949 -- 1969 & 1959 & $1.29 \\pm 0.08$ & 4 \\nl\n81.5 & 1949 -- 1985 & 1967 & $1.25 \\pm 0.06$ & 5 \\nl\n81.5 & 1949 -- 1989 & 1969 & $0.92 \\pm 0.16$ & 6 \\nl\n81.5 & 1966 -- 1989 & 1978 & $\\approx 0.63\\tablenotemark{d}$ & 6 \\nl\n102 & 1977 -- 1993 & 1985 & $0.80 \\pm 0.12$ & 5 \\nl\n151 & 1966 -- 1976 & 1971 & $1.2 \\pm 0.4$ & 1 \\nl\n152 & 1966 -- 1985 & 1975 & $1.06 \\pm 0.15$ & 5 \\nl\n151.5 & 1966 -- 1994 & 1980 & $0.86 \\pm 0.09$ & 2 \\nl\n151.5 & 1980 -- 1994 & 1988 & $1.11 \\pm 0.22$ & 2 \\nl\n300 & 1961 -- 1971 & 1966 & $0.91 \\pm 0.15$ & 7 \\nl\n290 & 1978 -- 1996 & 1988 & $0.66 \\pm 0.07$ & 2 \\nl\n\\enddata\n\\tablenotetext{a}{MHz.}\n\\tablenotetext{b}{\\% yr$^{-1}$.}\n\\tablenotetext{c}{1. Read 1977a; 2. Vinyajkin 1997; 3. H\\\"ogbom \\& Shakeshaft 1961; 4. Scott, Shakeshaft, \\& Smith 1969; 5. Agafonov 1996; 6. Hook, Duffett-Smith, \\& Shakeshaft 1992; 7. Baars \\& Hartsuijker 1972.}\n\\tablenotetext{d}{We calculate an error of $\\pm 0.17$ from information provided in their paper and in Scott, Shakeshaft, \\& Smith 1969.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n%\\footnotesize\n\\tablecolumns{5}\n\\tablewidth{0pc}\n\\tablecaption{Fading Rates of Cassiopeia A at High Radio Frequencies (7.8 -- 16.5 GHz)}\n\\tablehead{\\colhead{Frequency\\tablenotemark{a}} & \\colhead{Measurement Epochs} & \\colhead{Central Epoch} & \\colhead{Fading Rate\\tablenotemark{b}} & \\colhead{Reference\\tablenotemark{c}}}\n\\startdata\n7.8 & 1963 -- 1974 & 1968 & $0.70 \\pm 0.10$ & 1 \\nl\n9.4 & 1961 -- 1971 & 1966 & $0.63 \\pm 0.12$ & 2 \\nl\n13.5 & 1965 -- 1994 & 1980 & $\\approx 0.63\\tablenotemark{d}$ & 3 \\nl\n15.5 & 1965 -- 1994 & 1980 & $\\approx 0.61\\tablenotemark{d}$ & 3 \\nl\n16.5 & 1965 -- 1995 & 1980 & $\\approx 0.60\\tablenotemark{d}$ & 3 \\nl\n\\enddata\n\\tablenotetext{a}{GHz.}\n\\tablenotetext{b}{\\% yr$^{-1}$.}\n\\tablenotetext{c}{1. Dent, Aller, \\& Olsen 1974; 2. Stankevich et al. 1973; 3. O'Sullivan \\& Green 1999.}\n\\tablenotetext{d}{We estimate errors of $\\pm 0.14$ from information provided in their paper.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccc}\n%\\footnotesize\n\\tablecolumns{3}\n\\tablewidth{0pc}\n\\tablecaption{Green Bank 40-foot Telescope Measurements of the Relative Flux Density of Cassiopeia A to Cygnus A at 1405 MHZ from 1995 to 1999}\n\\tablehead{\\colhead{Epoch} & \\colhead{$F_{1405}^{Cas\\,A}/F_{1405}^{Cyg\\,A}$\\tablenotemark{a}} & \\colhead{$F_{1405}^{Cas\\,A}$\\tablenotemark{b}}}\n\\startdata\n1995.6 & 1.294 & $2046 \\pm 56$ \\nl\n1996.6 & 1.267 & $2003 \\pm 55$ \\nl\n1997.6 & 1.273 & $2013 \\pm 56$ \\nl\n1997.6 & 1.265 & $2000 \\pm 55$ \\nl\n1999.6 & 1.231 & $1946 \\pm 54$ \\nl\n\\enddata\n\\tablenotetext{a}{$\\pm 1.9$ \\% (see \\S 2).}\n\\tablenotetext{b}{Jy; for $F_{1405}^{Cyg\\,A} = 1581 \\pm 32$ Jy (see \\S 2).}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n%\\footnotesize\n\\tablecolumns{5}\n\\tablewidth{0pc}\n\\tablecaption{Fading Rates of Cassiopeia A at Intermediate Radio Frequencies (927 -- 3060 MHz)}\n\\tablehead{\\colhead{Frequency\\tablenotemark{a}} & \\colhead{Measurement Epochs} & \\colhead{Central Epoch} & \\colhead{Fading Rate\\tablenotemark{b}} & \\colhead{Reference\\tablenotemark{c}}}\n\\startdata\n950 & 1964 -- 1972 & 1968 & $0.85 \\pm 0.05$ & 1 \\nl\n927 & 1977 -- 1996 & 1986 & $0.73 \\pm 0.05$ & 2 \\nl\n1420 & 1957 -- 1971 & 1964 & $0.89 \\pm 0.12$ & 3 \\nl\n1420 & 1957 -- 1976 & 1966 & $0.86 \\pm 0.02$ & 4 \\nl\n1405 & 1965 -- 1999 & 1982 & $0.62 \\pm 0.12$ & 5 \\nl\n3000 & 1961 -- 1972 & 1966 & $0.92 \\pm 0.15$ & 3 \\nl\n3060 & 1961 -- 1971 & 1966 & $1.04 \\pm 0.21$ & 6 \\nl\n\\enddata\n\\tablenotetext{a}{MHz.}\n\\tablenotetext{b}{\\% yr$^{-1}$.}\n\\tablenotetext{c}{1. Stankevich, Ivanov, \\& Torkhov 1973; 2. Vinyajkin 1997; 3. Baars \\& Hartsuijker 1972; 4. Read 1977a; 5. this paper; 6. Stankevich et al. 1973.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\figcaption[cas1.ps]{Fading rates of Cassiopeia A as a function of frequency for the $\\approx 1965$ epoch, from Baars et al. (1977; see Table 1). Equation (1), also from Baars et al. (1977), is plotted as the solid line.\\label{cas1.ps}}\n\n\\figcaption[cas2.ps]{Fading rates of Cassiopeia A as a function of epoch for the low radio frequencies (38 -- 300 MHz; see Table 2). The dotted lines indicate over what interval of time measurements were taken to determine each fading rate. Triangles denote 38 MHz measurements, squares denote 81.5 MHz measurements, pentagons denote 102 MHz measurements, hexagons denote 151 -- 152 MHz measurements, and circles denote 290 -- 300 MHz measurements. The solid line corresponds to a fading rate that is decreasing at a rate of $\\approx 2$ \\% yr$^{-1}$ per century.\\label{cas2.ps}}\n\n\\figcaption[cas3.ps]{Fading rates of Cassiopeia A as a function of epoch for the high radio frequencies (7.8 -- 16.5 GHz; see Table 3). The dotted lines are as defined in Figure 2. Triangles denote 7.8 GHz measurements, squares denote 9.4 GHz measurements, pentagons denote 13.5 GHz measurements, hexagons denote 15.5 GHz measurements, and circles denote 16.5 GHz measurements. The solid line corresponds to a constant fading rate.\\label{cas3.ps}}\n\n\\figcaption[cas4.ps]{Light curve of measurements of the relative flux density of Cassiopeia A to Cygnus A at 1405 MHz. Circles denote our measurements (see Table 4); the square denotes the 1965 value from Baars et al. (1977). The solid line corresponds to a fading rate of 0.62 \\% yr$^{-1}$.\\label{cas4.ps}}\n\n\\figcaption[cas5.ps]{Fading rates of Cassiopeia A as a function of epoch for the intermediate radio frequencies (927 -- 3060 MHz; see Table 5). The dotted lines are as defined in Figure 2. Triangles denote 927 -- 950 MHz measurements, squares denote 1405 -- 1420 MHz measurements, and circles denote 3000 -- 3060 MHz measurements. The solid line corresponds to a fading rate that is decreasing at a rate of $\\approx 1$ \\% yr$^{-1}$ per century. The dashed lines are the same as the solid lines in Figures 2 and 3.\\label{cas5.ps}}\n\n\\clearpage\n\n\\setcounter{figure}{0}\n\n\\begin{figure}[tb]\n\\plotone{cas1.ps}\n\\end{figure}\n\n\\begin{figure}[tb]\n\\plotone{cas2.ps}\n\\end{figure}\n\n\\begin{figure}[tb]\n\\plotone{cas3.ps}\n\\end{figure}\n\n\\begin{figure}[tb]\n\\plotone{cas4.ps}\n\\end{figure}\n\n\\begin{figure}[tb]\n\\plotone{cas5.ps}\n\\end{figure}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002032.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Agafonov 1996]{a96}\nAgafonov, M. I. 1996, A\\&A, 306, 578\n\n\\bibitem[Ashworth 1980]{a80}\nAshworth, W. B. 1980, J. Hist. Astr., 11, 1\n\n\\bibitem[Baily 1835]{b35}\nBaily, F. 1835, An account of the Revd. John Flamsteed...to which is added, his British Catalog of Stars, Corrected and Enlarged (London)\n\n\\bibitem[Baars \\& Hartsuijker 1972]{bh72}\nBaars, J. W. M., \\& Hartsuijker, A. P. 1972, A\\&A, 17, 172\n\n\\bibitem[Baars et al. 1977]{bea77}\nBaars, J. W. M., Genzel, R., Pauliny-Toth, I. I. K., \\& Witzel, A. 1977, A\\&A, 61, 99\n\n\\bibitem[Dent, Aller, \\& Olsen 1974]{dao74}\nDent, W. A., Aller, H. D., \\& Olsen, E. T. 1974, ApJ, 188, L11\n\n\\bibitem[Erickson, \\& Perley 1975]{ep75}\nErickson, W. C., \\& Perley, R. A. 1975, ApJ, 200, L83\n\n\\bibitem[Fesen, Becker, \\& Goodrich 1988]{fbg88}\nFesen, R. A., Becker, R. H., \\& Goodrich, R. W. 1988, ApJ, 329, L89\n\n\\bibitem[Flamsteed 1725]{f25}\nFlamsteed, J. 1725, Historia coelestis Britannica (London)\n\n\\bibitem[Herschel 1798]{h98}\nHerschel, C. 1798, Catalog of stars, taken from Flamsteed's observations...and not inserted in the British Catalog. With an index [and] a collection of errata (London)\n\n\\bibitem[H\\\"ogbom \\& Shakeshaft 1961]{hs61}\nH\\\"ogbom, J. A., \\& Shakeshaft, J. R., Nature, 189, 561\n\n\\bibitem[Hook, Duffett-Smith, \\& Shakeshaft 1992]{hds92}\nHook, I. M., Duffett-Smith, P. J., \\& Shakeshaft, J. R. 1992, A\\&A, 255, 285\n\n\\bibitem[Jansky 1935]{j35}\nJansky, K. G. 1935, Proc. I. R. E., 23, 1158\n\n\\bibitem[O'Sullivan \\& Green 1999]{og99}\nO'Sullivan, C., \\& Green, D. A. 1999, MNRAS, 303, 575\n\n\\bibitem[Read 1977a]{r77a}\nRead, P. L. 1977a, MNRAS, 178, 259\n\n\\bibitem[Read 1977b]{r77b}\nRead, P. L. 1977b, MNRAS, 181, P63\n\n\\bibitem[Reber 1944]{r44}\nReber, G. 1944, ApJ, 100, 279\n\n\\bibitem[Rees 1990]{r90}\nRees, N. 1990, MNRAS, 243, 637\n\n\\bibitem[Ryle \\& Elsmore 1949]{re49}\nRyle, M., \\& Elsmore, B. 1949, Nature, 168, 555\n\n\\bibitem[Scott, Shakeshaft, \\& Smith]{sss69}\nScott, P. F., Shakeshaft, J. R., \\& Smith, M. A. 1969, Nature, 223, 1140\n\n\\bibitem[Stankevich et al. 1973]{sea73}\nStankevich, K. S., Ivanov, V. P., Pelyushenko, S. A., Torkhov, V. A., \\& Ibannikova, A. N. 1973, Radiofizika, 16, 786\n\n\\bibitem[Stankevich, Ivanov, \\& Torkov]{sik73}\nStankevich, K. S., Ivanov, V. P., \\& Torkhov, V. A. 1973, Soviet. Astron., 17, 410\n\n\\bibitem[Sullivan 1978]{s78}\nSullivan, W. T. 1978, Sky \\& Telescope, 56, 101\n\n\\bibitem[Vinyajkin 1997]{v97}\nVinyajkin, E. N. 1997, Astroph. \\& Space Sci., 252, 249\n\n\\bibitem[Walczowski \\& Smith 1985]{ws85}\nWalczowski, L. T., \\& Smith, K. L. 1985, MNRAS, 212, 27\n\n\\end{thebibliography}"
}
] |
astro-ph0002033
|
Multiwavelength Observations of the Second Largest Known FR II Radio Galaxy, NVSS 2146+82
|
[
{
"author": "Christopher Palma\\altaffilmark{1}"
},
{
"author": "Franz E. Bauer\\altaffilmark{2}"
}
] |
We present multi-frequency VLA, multicolor CCD imaging, optical spectroscopy, and {ROSAT} HRI observations of the giant FR II radio galaxy NVSS 2146+82. This galaxy, which was discovered by the NRAO VLA Sky Survey (NVSS), has an angular extent of nearly 20\arcmin\ from lobe to lobe. The radio structure is normal for an FR~II source except for its large size and regions in the lobes with unusually flat radio spectra. Our spectroscopy indicates that the optical counterpart of the radio core is at a redshift of $z=0.145$, so the linear size of the radio structure is $\sim$4$h_{50}^{-1}$ Mpc, $H_{0} = 50h_{50}$. This object is therefore the second largest FR II known (3C 236 is $\sim$6$h_{50}^{-1}$ Mpc). Optical imaging of the field surrounding the host galaxy reveals an excess number of candidate galaxy cluster members above the number typically found in the field surrounding a giant radio galaxy. WIYN HYDRA spectra of a sample of the candidate cluster members reveal that six share the same redshift as NVSS 2146+82, indicating the presence of at least a ``rich group'' containing the FR II host galaxy. {ROSAT} HRI observations of NVSS 2146+82 place upper limits on the X-ray flux of $1.33\times10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ for any hot IGM and $3.52\times10^{-14}$ ergs cm$^{-2}$ s$^{-1}$ for an X-ray AGN, thereby limiting any X-ray emission at the distance of the radio galaxy to that typical of a poor group or weak AGN. Several other giant radio galaxies have been found in regions with overdensities of nearby galaxies, and a separate study has shown that groups containing FR~IIs are underluminous in X-rays compared to groups without radio sources. We speculate that the presence of the host galaxy in an optically rich group of galaxies that is underluminous in X-rays may be related to the giant radio galaxy phenomenon.
|
[
{
"name": "Palmaep.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n\\begin{document}\n\n\\title{\\bf Multiwavelength Observations of the Second Largest Known\nFR II Radio Galaxy, NVSS 2146+82}\n\\author{Christopher Palma\\altaffilmark{1}, Franz E. Bauer\\altaffilmark{2}}\n\\affil{Department of Astronomy, University of Virginia}\n\\authoraddr{P. O. Box 3818, Charlottesville, VA 22903-0818}\n\\altaffiltext{1}{NOAO WIYN Queue Investigator}\n\\altaffiltext{2}{National Radio Astronomy Observatory Jansky\nPre-Doctoral Fellow} \n\n\\author{William D. Cotton, Alan H. Bridle}\n\\affil{National Radio Astronomy Observatory\\altaffilmark{3}}\n\\authoraddr{520 Edgemont Road, Charlottesville, VA 22903-2475}\n\\altaffiltext{3}{The National Radio Astronomy Observatory is a facility\nof the National Science Foundation operated under cooperative agreement\nby Associated Universities, Inc.}\n\n\\author{Steven R. Majewski\\altaffilmark{4}, \\& Craig L. Sarazin}\n\\authoraddr{P. O. Box 3818, Charlottesville, VA 22903-0818}\n\\affil{Department of Astronomy, University of Virginia}\n\\altaffiltext{4}{David and Lucile Packard Foundation Fellow; Cottrell\nScholar of the Research Corporation; National Science Foundation\nCAREER Fellow; Visiting Associate, The Observatories of the Carnegie\nInstitution of Washington} \n\n\n\\begin{abstract} \n\nWe present multi-frequency VLA, multicolor CCD imaging, optical\nspectroscopy, and {\\it ROSAT} HRI observations of the giant FR II radio\ngalaxy NVSS 2146+82. This galaxy, which was discovered by the NRAO VLA\nSky Survey (NVSS), has an angular extent of nearly 20\\arcmin\\ from lobe\nto lobe. The radio structure is normal for an FR~II source except for\nits large size and regions in the lobes with unusually flat radio\nspectra. Our spectroscopy indicates that the optical counterpart of\nthe radio core is at a redshift of $z=0.145$, so the linear size of the\nradio structure is $\\sim$4$h_{50}^{-1}$ Mpc, $H_{0} = 50h_{50}$.\nThis object is therefore the second largest FR II known (3C 236 is\n$\\sim$6$h_{50}^{-1}$ Mpc). Optical imaging of the field surrounding\nthe host galaxy reveals an excess number of candidate galaxy cluster\nmembers above the number typically found in the field surrounding a\ngiant radio galaxy. WIYN HYDRA spectra of a sample of the candidate\ncluster members reveal that six share the same redshift as NVSS\n2146+82, indicating the presence of at least a ``rich group''\ncontaining the FR II host galaxy. {\\it ROSAT} HRI observations of NVSS\n2146+82 place upper limits on the X-ray flux of\n$1.33\\times10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ for any hot IGM and\n$3.52\\times10^{-14}$ ergs cm$^{-2}$ s$^{-1}$ for an X-ray\nAGN, thereby limiting any X-ray emission at the distance of the radio\ngalaxy to that typical of a poor group or weak AGN. Several other\ngiant radio galaxies have been found in regions with overdensities of\nnearby galaxies, and a separate study has shown that groups containing\nFR~IIs are underluminous in X-rays compared to groups without radio\nsources. We speculate that the presence of the host galaxy in an\noptically rich group of galaxies that is underluminous in X-rays may be\nrelated to the giant radio galaxy phenomenon.\n\n\\end{abstract}\n\n\\keywords{galaxies: distances and redshifts --- galaxies: individual: (NVSS 2146+82) ---\ngalaxies: photometry --- radio continuum: galaxies --- \nX-rays: galaxies}\n\n\\section{\\bf Introduction}\n\nThe ``giant'' radio galaxies (GRGs), which we define as double radio sources\nwhose overall projected linear extents exceed 2$h_{50}^{-1}$ Mpc, are \ninteresting as extreme examples of radio source development and evolution.\nMembers of this class, which comprise only a few percent of all\npowerful extragalactic radio sources, have been documented for almost\n25 years (e.g., \\cite{wil74}). They have been used to constrain the\nspectral aging and evolution of radio sources and as tests for the\nevolution of conditions in intergalactic environments on Mpc scales\n(\\cite{str80}; \\cite{sub93}; \\cite{cot96}). Their 1.4 GHz radio powers\nare generally in the regime $10^{24.5}< P_{1.4}<10^{26}$ $h_{50}^{-2}$ W Hz$^{-1}$,\njust above the transition between Fanaroff-Riley Types I (plumed) and\nII (lobed) radio structures (\\cite{fan74}). It is unclear whether the\ngiant sources are examples of unusually long-lived (and directionally\nstable) nuclear activity in radio-loud systems, or of the development\nof sources in unusually low-density environments.\n\nBecause of their large angular sizes, nearby giant radio galaxies can\nin principle be studied in great detail, but their\nlargest-scale structures may be over-resolved and undersampled by\ninterferometers. They have traditionally been discovered through sky\nsurveys with compact interferometers or single dishes at relatively\nlow frequencies, where angular resolution is modest but large fields\nof view and diffuse steep-spectrum structures can be imaged more\neasily. The source NVSS 2146+82 was noted as a candidate giant radio\ngalaxy when it appeared in the first 4$^\\circ$\\ by 4$^\\circ$\\ field\nsurveyed by the NRAO VLA Sky Survey (NVSS: \\cite{Condon98}), a\nnorthern-hemisphere survey at 1.4 GHz using the VLA D configuration at\n45\\arcsec\\ (FWHM) resolution.\n\nFigure \\ref{fig:NVSScontours} shows contours of the NVSS image at\n45\\arcsec\\ resolution. There are two symmetric, extended lobes (D and\nE) on either side of an unresolved component C, plus an unusually\nlarge number of other radio sources within 10\\arcmin\\ of C. Two of\nthese (A and B) are also symmetrically located around C.\n\nComparison with the Digital Sky Survey (DSS) showed that source C\ncoincides with an $\\sim$18$^{\\rm th}$ mag elliptical galaxy to within\nthe uncertainties in the NVSS and DSS positions. If the elliptical\ngalaxy is the host of an unusually large radio source (C+D+E), then\nthe apparent magnitude suggests that the whole structure may be\nsimilar in linear scale to 3C\\,236. The DSS also shows a nearby image\nthat might be another galactic nucleus, and a faint extended feature\nsuggesting a possible ``tail'' or interaction.\n\nWe have undertaken several observational studies of the radio and\noptical objects in the field to determine their nature and to clarify\nthe relationships between the optical and radio sources. These studies\ninclude:\n\n\\begin{enumerate}\n\\item High resolution radio imaging at 4.9 and 8.4 GHz to locate any \ncompact flat-spectrum radio components in the field, and thus to \nidentify any AGN that could be responsible for some or all of the \nother radio emission,\n\\item A search for fainter diffuse radio emission between the D and E\ncomponents that might link them together or to other sources in the\nfield and thus clarify their physical relationship,\n\\item Higher-resolution radio imaging of the other radio sources in the\nfield to explore whether they might be physically related to the\ndiffuse components, or to each other by gravitational lensing,\n\\item Optical spectroscopy of both optical ``nuclei'' and other galaxies in\nthe field,\n\\item UBVRI optical photometry of the field, and\n\\item X-ray imaging using {\\it ROSAT} HRI observations to search for\nany hot X-ray emitting gas which might be associated with an overdensity of\ngalaxies or non-thermal X-ray emission from an AGN.\n\\end{enumerate}\n\nThroughout this paper, we assume a Hubble constant $H_{0} = 50h_{50}$ km\ns$^{-1}$ Mpc$^{-1}$ .\nAt a redshift of $z = 0.145$, the angular diameter\ndistance to the radio galaxy is 708.4$h_{50}^{-1}$ Mpc, the luminosity distance is\n928.7$h_{50}^{-1}$ Mpc, and $1\\arcmin$ corresponds to 206$h_{50}^{-1}$ kpc.\n\n\n\\section{\\bf Radio Observations}\nTable \\ref{VLAObsLog} gives a journal of our VLA observations. The\nobservations in the A configuration were designed to locate any \ncompact radio components in the field. Those in the B, C, and D\nconfigurations were intended to image the largest scale emission in\nenough detail to reveal any relationships and connections between the\nextended components, as well as to determine their spectral and\nFaraday rotation/depolarization properties. The BnC configuration\ndata were designed as a sensitive search for connections, such as\njets, between the central radio source and the extended features.\n\nThe flux density calibration was based on 3C\\,48 and 3C\\,286. The\non-axis instrumental polarization corrections were determined from\nobservations of the unresolved synthesis phase calibrator 2005+778,\nand the absolute polarization position angle scale from observations\nof 3C\\,286. Multiple observations of 3C\\,286 and other polarized\nsources were used to detect problems with ionospheric Faraday\nrotation, but none was noted in any of the sessions. \nThe data were calibrated using the source 2005+778 as an intermediate\nphase reference, then self-calibrated using AIPS software developed by\nW. D. Cotton for the NVSS survey.\n\nDue to the large size of this source, 1.4 and 1.6 GHz observations\nused three pointings; one on the central source C, and one near the\ncenter of each putative lobe. The B, C, and D VLA configuration\nobservations were made at 1.365 and 1.636 GHz to measure rotation\nmeasure and spectral index. The data from these frequencies were\ncalibrated and imaged separately. Data taken in the BnC configuration\nwere in two adjacent 50 MHz bands centered on 1.4 GHz. Since the\nsource extent is comparable to that of the antenna pattern and the\nbandwidth used was relatively large, the deconvolution (CLEAN) and\nself calibration applied corrections for the frequency dependence of\nthe antenna pattern. Data from each of the three pointings were\nimaged independently and combined into a single image by interpolating\nthe images onto a common grid, averaging weightings by the square of the\nantenna power pattern, and correcting for the effects of the antenna\npattern. The 0.3 GHz observations were of limited use owing to\ninterference.\n\n\\subsection{Radio Results}\nThe most sensitive image of NVSS 2146+82 is derived from our BnC\nconfiguration data at 1.4 GHz which has a resolution of 13\\arcsec\\\n(FWHM). Figure \\ref{fig:NVSSLhi} shows logarithmic contours of the\ntotal intensity in the region around the source in this image; the rms\nnoise is 20 $\\mu$Jy per CLEAN beam area. A gray scale representation\nof the same image showing the filamentary structure of the lobes is\ngiven in Figure \\ref{fig:BnCgray}. Figure \\ref{fig:NVSSjets} shows\nthe inner region of this image contoured to lower levels using an\ninitially linear contour interval.\n\n\\subsection {Association of Features}\nThe structures of the extended features D and E shown in Figures\n\\ref{fig:NVSSLhi} and \\ref{fig:BnCgray} are entirely consistent with\ntheir being associated with each other as the two lobes of a large\nFR\\,II double source of overall angular size 19\\farcm5. Both features\nare brightest in the regions furthest from C, contain bright (but\nresolved) substructure near their outer edges resembling the hot spots\nof FR\\,II sources, and have their steepest brightness gradients on\ntheir outer edges. The overall length of the two lobes is the same to\nwithin 5\\%. Although features A and B in Figure \\ref{fig:NVSScontours}\nappear symmetric around feature C, the higher resolution VLA images \n(Figures \\ref{fig:NVSSLhi} and \\ref{fig:BnCgray}) reveal\nthem to be background sources, unrelated to NVSS 2146+82.\n\nThe northern feature (D) contains a region of enhanced emission (hot\nspot) at its northern extremity with about 65 mJy in an area 30\\arcsec\\\nby 18\\arcsec\\, and an L-shaped extension to the West. The southern\nfeature (E) has 75 mJy in a region of enhanced emission 50\\arcsec\\ by\n30\\arcsec\\ (a ``warm spot'') recessed by 10\\% of the distance from the core \nand sharp brightness gradients around its southern and\nwestern boundaries. Both regions of enhanced emission show evidence of finer, but\nresolved, structure in our data taken in the B configuration (see\ncontour plots in Figure \\ref{fig:hotspots}). Figure \\ref{fig:BnCgray}\nclearly shows that the internal brightness distributions of both lobes\nare non-uniform, and suggest the presence of filamentary structures,\nagain a common characteristic of FR\\,II radio lobes at this relative\nresolution.\n\nMost importantly, Figures \\ref{fig:NVSSLhi}, \\ref{fig:BnCgray}, and\n\\ref{fig:NVSSjets} also show that these lobes are linked to the\ncentral compact feature C by elongated features that are plausibly\nthe brightest segments of a weak jet-counterjet system. \nThese features are labeled in Figure \\ref{fig:NVSSjets}.\n\nWe interpret the following features as belonging to the jet in the\nsouth lobe.\n\n{\\bf J1}. This feature is clearly part of a jet that points towards\nthe south lobe but not directly at the peak of feature E.\n\n{\\bf J2}. \nThis feature (1\\farcm5 from C) and feature K (1\\farcm4 to the\nnorth of C) are roughly symmetric in distance from C and in intensity\nbut are not quite collinear with C.\nOn both sides of the source the jet becomes harder to trace further\ninto the lobe.\nJ2 appears to be south of the C--J1 direction, suggesting a southward\nbend, however.\n\n{\\bf J3}. This feature is plausibly a knot in the continuation of the\njet into the south lobe.\nThe lobe brightens beyond J3 and contains a diffuse ridge that is a\nplausible continuation of the (possibly decollimated) jet in the\ndirection of the ``warm spot'' E.\nThe north lobe also brightens at about the same distance from C\nalthough there is no feature corresponding to J3 in the north.\n\nTable \\ref{table:fluxes} gives flux density estimates for the main\nfeatures of the source. \nWe estimate that the jet and counterjet together comprise about 1\\% of\nthe total flux density of the extended lobes, a typical jet\n``prominence\" for radio galaxies slightly above the FR\\,I--II\ntransition. \n\nThe higher-resolution radio images provide no evidence that sources A,\nB, or F in Figure 1 are physically related to each other, or to C, D\nand E. Although none can be optically identified, we consider it\nlikely that these are three (or more) unrelated background sources.\nThe symmetrical alignment of A and B around C is apparently\ncoincidental, and there is no evidence for any radio ``bridge'' between\nthese sources and component C.\n\n\n\\subsection{Polarimetry}\nThe polarization structure derived from the sensitive BnC configuration observations\nis shown in Figure \\ref{fig:polarization}. The 1.4 and 1.6 GHz data\nare sufficiently separated in frequency to enable us to measure\nFaraday rotation but still maintain comparable surface brightness\nsensitivity. The derived rotation measure images of the two lobes are\nshown in Figure \\ref{fig:RM}. The rotation measure distribution over\nthe north lobe is featureless but several filamentary rotation measure\nstructures can be seen over the southern lobe. The average rotation\nmeasure is about the same in the two lobes, -9 rad\\ m$^{-2}$ in the\nnorth and -8 rad\\ m$^{-2}$ in the south. The Faraday rotation measure\nin the south lobe has a somewhat larger root mean square variation, 8\nrad\\ m$^{-2}$ compared to 5 rad\\ m$^{-2}$ in the north.\n\n\\subsection{Spectral Index Distribution}\n\nFigure \\ref{fig:WENSS} shows the 0.35 to 1.4 GHz spectral index\ndistribution inferred from comparing the WENSS (\\cite{WENSS}) image\nwith our BnC configuration image convolved to the same resolution. The northern and\nsouthern warm spots have spectral indices\\footnote{Spectral index,\n$\\alpha$, as used here is given by $S = S_0\\nu^{\\alpha}$.}\n$\\alpha^{1.4}_{0.35}$ of -0.6 and -0.55, not unusual for the hot spots\nof FR~II sources in this frequency regime. The background sources also\nexhibit spectral indices that are quite typical of extragalactic\nsources (A, -0.68; B, -1.0; F, -0.7). Near the centers of the north\nand south lobes of NVSS 2146+82, however, this comparison shows regions\nof unusually ``flat'' spectral index ($\\alpha^{1.4}_{0.35}\\ \\approx\\\n-0.3\\ \\pm 0.02$ in the north lobe, $\\alpha^{1.4}_{0.35}\\ \\approx\\\n-0.4\\ \\pm 0.03$ in the south lobe).\n\nThe spectral index variations across the lobes can also be studied from\nour 1.36 and 1.63 GHz data. Due to the low surface brightness the data\nwere tapered to 55$\\arcsec$ resolution before imaging for this\ncomparison. To eliminate any complication from the mosaicing\ntechnique, only data derived from the pointing on a given lobe were\nused to determine the spectral index variations for that lobe. Thus,\nthe data from two pointings were imaged independently at 1.36 and 1.63\nGHz, corrected for the antenna power pattern, and spectral index images\nwere derived independently for the two lobes. These results are shown\nin Figure \\ref{fig:SI}. The close spacing of the frequencies makes\ndetermining the spectral index more difficult; but this is compensated\nto some extent by the nearly identical imaging properties at the two\nfrequencies, which reduce systematic errors. These data sets are fully\nindependent of those used for the spectral index image in Figure\n\\ref{fig:WENSS}, but also reveal symmetric regions of unusually flat \nspectral index, $\\alpha^{1.6}_{1.4}\\ \\approx$ -0.3$ \\pm 0.08$, in both\nlobes.\n\nWe conclude that four independent data sets show evidence for regions\nwith $\\alpha^{1.4}_{0.35}\\ \\approx$ -0.3 in regions of relatively high\nsignal to noise ratio. These regions are not artifacts of\n``lumpiness'' in the zero levels of the images.\n\n\\subsection {Source Alignment}\nNVSS 2146+82 is not aligned along a single axis. The two warm regions\n(E and D) and the core (C) are not collinear. The jet in the south\nappears to have several bends; one near the end of J1 (see Figure\n\\ref{fig:NVSSjets}) where it bends toward J2, a change in position\nangle from -150$^\\circ$ to -170$^\\circ$. Beyond J3, the ridge line of\nthe lobe is fairly well defined and is again at position angle\n-150$^\\circ$, consistent with a second bend (apparently $\\approx$\n20$^\\circ$) in the neighborhood of J3. The jet is not so prominent in\nthe north but feature K, which may be the brightest part of a\ncounterjet, is elongated along position angle of -169$^\\circ$.\n\nThe general ``C'' shape of the source suggests that the overall\nmisalignment is due to environmental effects that have bent the jets,\nrather than to a changing initial jet direction which is likely to\nproduce overall ``S'' symmetry.\n\nWe consider it beyond doubt that C, D and E comprise a single large FR\\,II\nradio source with weak radio jets, whose parent object is the galaxy\nidentified with C.\n\n\\section{\\bf Optical Observations of NVSS 2146+82 and its Environs} \n\nOptical photometric and spectroscopic observations were obtained to\nidentify the host galaxy of the radio emission and to measure its\nredshift. We began the search for the optical counterpart to the radio\nsource using the Digitized Sky Survey (\\cite{dss}; hereafter\nDSS). The radio core is aligned with an elliptical galaxy on the DSS\nimage to within the astrometric accuracy of\nthe radio and optical positions from the NVSS and DSS. There is also a\nsecond, equally bright object a few arcseconds east of the galaxy at\nthe radio core position. Finally, in the DSS image, there appears to\nbe S--shaped diffuse emission that passes through both bright\n``nuclei''.\nTherefore, our initial assumption was that\nthe host galaxy of NVSS 2146+82 was possibly a disturbed, double\nnucleus galaxy. In the following sections, we summarize the optical\nimaging of the field surrounding the candidate host galaxy and the\nspectroscopic observations of this host galaxy and its candidate\ngalactic companions.\n\n\n\\subsection{Photometric Observations} \n\nU, B, V, R, and I CCD observations were obtained at the 1.52-m\ntelescope at Palomar Observatory on the nights of 7-9 January 1997. In\naddition, U, B, V, and I CCD observations were made at Kitt Peak\nNational Observatory on 4 April 1997. The Palomar 1.52-m observations\nwere made with a 2048 $\\times$ 2048 CCD with a pixel scale of 0\\farcs37\nper pixel, resulting in a 12\\farcm63 field of view. Though\nphotometric, the seeing was poor ($2-5\\arcsec\\:$ on 7 January,\n$1.5-2.5\\arcsec\\:$ on 8,9 January) during the Palomar run, so higher\nresolution ($1.2-1.4\\arcsec\\:$ seeing) images were obtained with the KPNO\n4-m telescope in April. The KPNO observations were made with the prime\nfocus T2KB CCD with a pixel scale of $0\\farcs47$ per pixel, resulting\nin a 16$^{'}$ field of view. Because the KPNO data were not taken in\nphotometric conditions, the Palomar data remained useful for\ncalibration. Data from both observing runs were reduced using the \nstandard IRAF CCDRED reduction tasks.\n\nAfter the initial reduction, aperture photometry was performed on the\nhost galaxy of NVSS 2146+82 using the IRAF package APPHOT.\nUnfortunately, due to the poor seeing on the first night of the Palomar\nrun and the proximity of the foreground star (see \\S 3.3) to the AGN\nhost, it was impossible to photometer NVSS 2146+82 without significant\nflux contamination from the foreground star. Therefore, we used the\nDAOPHOT II package (\\cite{stetson87}) to PSF fit and subtract stars from\nthe Palomar NVSS 2146+82 images.\n\nAfter the foreground star was subtracted, photometry of the galaxy\nwas performed identically to the photometry of several \\cite{landolt}\nstandard stars. Approximately 20 stars were selected from each frame\ncontaining the AGN host galaxy. A circular aperture 2.5 times the\naverage FWHM of these stars was used to measure the flux of the host\ngalaxy. This aperture was chosen to be consistent with the standard\nstar photometry and because it completely enclosed the host without\nincluding contaminating flux from other nearby objects.\n\nOnce instrumental magnitudes for the galaxy were determined, they were\ntransformed to the standard system using transformation equations\nincorporating an airmass and color term that were \ndetermined for the Landolt standard stars. The results of our\nU,B,V,R,\\& I photometry of the host galaxy are listed in Table\n\\ref{table:magnitudes}.\n\n\\subsection{Spectroscopic Observations}\n\nOptical spectra of NVSS 2146+82 were obtained at Kitt Peak National\nObservatory on 9 December 1996. The spectroscopic observations were\nmade with the RC Spectrograph on the KPNO Mayall 4-meter telescope.\nThe detector in use was the T2KB CCD in a 700 $\\times$ 2048 pixel\nformat. All exposures were made with a $1\\arcsec$ slit width and a 527\nlines/mm grating. The spectral resolution, measured using unresolved\nnight sky lines, is $\\sim$3.4 \\AA. The data were reduced using the\nstandard IRAF reduction tasks. The extracted spectra were wavelength\ncalibrated using a solution determined from the spectrum of a HeNeAr\ncomparison source. Finally, spectrophotometric calibration was applied\nusing a flux scale extrapolated from several standard star spectra.\n\nSpectra of candidate galactic companions to NVSS 2146+82 (see \\S 3.5\nbelow) were obtained with the HYDRA multi-fiber positioner and the\nBench Spectrograph as part of the WIYN\\footnote[6]{The WIYN Observatory\nis a joint facility of the University of Wisconsin-Madison, Indiana\nUniversity, Yale University, and the National Optical Astronomy\nObservatories.} Queue Experiment over the period of 14-22 September\n1998. The T2KC CCD was used as the spectrograph detector in its\nspatially binned 1024 $\\times$ 2048 pixel mode. All exposures were\nmade with the red fibers, the Simmons camera, and a 400 lines/mm\ngrating. The spectral resolution in this configuration is $\\sim$4.5\n\\AA.\n\nWe calculated an astrometric solution for the KPNO 4-m frame of the\nNVSS 2146+82 field using positions for stars in the frame taken from\nthe USNO A1.0 catalog (\\cite{monet96}). Using this solution, we\nderived positions with the accuracy required by the HYDRA positioner\nfor our target galaxies. Due to fiber placement restrictions and the\ndensity of our target galaxies on the sky, we were only able to place\n46 fibers on targets. The remaining 50 fibers were randomly placed on\nblank sky, and they were used during the reduction process for night\nsky subtraction.\n\nThe nine 30 minute program exposures were reduced using the IRAF\nDOHYDRA script. The weather conditions during the last two nights were\npoor, and the spectra from these nights were not usable.\nTherefore the final spectra were obtained by co-adding only the data\nfrom nights one and two, a total of two hours of integration.\n\n\\subsection{Redshifts and Line Luminosities}\n\nIn Figure \\ref{fig:oldfig2}, we present a contour plot of the V band\nsurface brightness from the central $40\\arcsec \\times 40\\arcsec$ region\nof the KPNO 4-m image after smoothing with a 3 pixel by 3 pixel boxcar\nkernel. Although we find that the elliptical galaxy at the radio core\nposition ($\\alpha = 21^{\\rm h}45^{\\rm m}30^{\\rm s}$, $\\delta =\n+81\\arcdeg54\\arcmin55\\arcsec$ J2000.0) has a narrow line AGN emission\nspectrum with a redshift of $z=0.145$, we find that the object\njust to the east, which was assumed to be potentially a second nucleus,\nhas a zero-redshift stellar spectrum, indicating it is a foreground\nstar. Figure \\ref{fig:oldfig3} shows two plots of the wavelength and\nflux calibrated spectrum of the host galaxy of NVSS 2146+82.\n\nAn unusual feature of the spectrum (Figure \\ref{fig:oldfig3}) of the\nAGN is that all of the emission lines appear to be double peaked. The\nsecond panel in Figure \\ref{fig:oldfig3} shows an expanded view of the\n$[{\\rm O III}]$ doublet clearly showing the double peaked profile of\nthe emission lines. Each emission line was easily fit with a blend of\ntwo gaussians, indicating that AGN line emission is coming from two\nsources with a velocity separation of $\\sim$450 km s$^{-1}$.\n\nSince the AGN emission line spectrum gives two different velocities, we\nhave decided to take the velocity of the stellar component of the\ngalaxy as the systemic velocity of the galaxy. The stellar absorption\nline redshift, calculated by cross-correlating the host galaxy spectrum\nwith the spectrum of the star immediately to the east, is\n0.1450$\\pm$0.0002.\n\nTable \\ref{table:linedata} lists the properties of the observed\nemission features in the spectrum of NVSS 2146+82. The redshifts of\nthe AGN emission line components were calculated by identifying\nfeatures and taking the average redshift of all of the identified\nfeatures. In this way, the two AGN emission line components have been\nmeasured to be at velocities of 40070$\\pm$50 km s$^{-1}$ and 40520$\\pm$50\nkm s$^{-1}$, which corresponds to redshifts of 0.1440$\\pm$0.0002 and\n0.1456$\\pm$0.0002 respectively. This indicates that the gas which is\ngiving rise to the bluer component of the AGN emission line spectrum\nis moving relative to the stars in the AGN host galaxy at $-280$ km s$^{-1}$\nand the gas emitting the redder lines is moving at 170 km s$^{-1}$ with\nrespect to the stars.\n\nEach emission feature identified in Table \\ref{table:linedata} was fit\nwith a blend of two gaussian components (except for the two\nweak lines $[$\\ion{Ne}{3}$]$ $\\lambda3967$ and $[$\\ion{O}{3}$]$\n$\\lambda4363$, where a single gaussian was used) to determine the line\nflux. The fluxes listed in Table \\ref{table:linedata} were measured\nafter the spectrum of NVSS 2146+82 was flux calibrated using the\naverage of four measurements of the calibrator Feige 34. The flux of\nthe calibrator varied significantly among our four separate exposures,\nand we therefore estimate our spectrophotometry is only accurate to\nabout 20\\%. In addition to calibration error, there is an additional\nerror in the profile fitting, and therefore the errors listed for the\nfluxes include both calibration and measurement error.\n\nWe derived an extinction of $A_{V} = 0.9\\pm0.9$ (the large error is due\nmostly to the calibration error in the fluxes) using the standard\nBalmer line ratios for Case B recombination (\\cite{osterbrock}) and the\nextinction law of \\cite{cardelli}. The Galactic extinction at\nthe position of NVSS 2146+82 is given as $A_{V} = 0.5$ on the\nreddening maps of \\cite{schlegel}. This value is consistent\nwith our Balmer line derived value, but possibly indicates that there\nmay be some dust in the host galaxy itself. We decided to correct the\nmeasured line fluxes for reddening using the mean value we derived of\n$A_{V} = 0.9$. The errors listed in Table \\ref{table:linedata} for\nthe fluxes do not include the error in the extinction determination.\n\n\\subsection{Optical Properties of the Host Galaxy}\n\n\\cite{sandage72} found that the\noptical luminosity function of radio galaxy hosts was similar to that\nof first ranked cluster members, and he noted that their optical\nmorphology was similar to bright E galaxies. Although it was\ntherefore generally believed that the hosts of all radio galaxies were\ngE types, subsequent large surveys of radio galaxies showed a good deal of\nevidence for peculiar morphologies (e.g., \\cite{heckman86}). We\nfind that the host galaxy of NVSS 2146+82 is likely typical, i.e. it\nis a gE galaxy, but with evidence of some peculiar morphological\nfeatures.\n\nThe broadband colors of NVSS 2146+82 are typical of bright FR II host\ngalaxies. The absolute magnitude we derive for the host is $M_{V} =\n-22.9$ at $z=0.145$ if we adopt a K correction of 0.46 magnitudes in\nthe V passband (\\cite{kinney96}). This magnitude is consistent\nwith the host being a gE galaxy, and also is very similar to the mean V\nmagnitude for 50 low redshift FR IIs of -22.6 (\\cite{zirbel96}).\n\nSimilar to other FR II host galaxies, we find the optical morphology\nof the host elliptical of NVSS 2146+82 to be disturbed. In Figure\n\\ref{fig:oldfig2}, the four distinct objects besides the host galaxy\nand foreground star have been identified as having non-stellar\nmorphologies with the Faint Object Classification and Analysis System\n(FOCAS, \\cite{valdes82}). If these four galaxies share the same redshift\nas the gE host of NVSS 2146+82, they all lie 50--100 kpc away from its\nnucleus, a distance that implies that they may be dynamically\ninteracting with it. Figure \\ref{fig:oldfig2} also shows what appears\nto be a bridge of diffuse optical light that almost connects NVSS\n2146+82 to the galaxy to the southwest. This bridge may indicate that\nthis smaller galaxy has recently passed close enough to NVSS 2146+82\nto interact with it gravitationally. There is also a fifth object $5\\arcsec\\:$\nto the southeast of the center of NVSS 2146+82, which could\nbe in the process of merging with the gE galaxy. However, due to the\nfaintness of this object and its proximity to the nucleus of 2146+82,\nwe are unable to classify this object definitively as a galaxy with\nthe FOCAS software. Although we cannot conclude based on this image\nthat NVSS 2146+82 is undergoing a merger, its outer\nisophotes do show evidence that it has been disturbed.\n\nCorrelations between the radio power and optical emission line\nluminosities in radio galaxies have been established in several studies\n(e.g., \\cite{raw91}; \\cite{zirbel95}; \\cite{tad98}). These\nradio/optical correlations are assumed to arise primarily due to the\nfact that both the radio jet and the ionization source originate in the\ncentral engine. The radio core power at 5 GHz ($\\log P [W/Hz] =\n23.85$) and the H$\\alpha+[$\\ion{N}{2}$]$ luminosity ($\\log L [W] =\n35.2$) for NVSS 2146+82 lie well within the dispersion in the\ncorrelation in these quantities found for low redshift FR IIs\n(\\cite{zirbel95}). This apparently indicates that the physical\nconditions that cause this radio/optical correlation to arise may be\nsimilar in this GRG and in ``normal'' FR IIs.\n\nThe shape of the emission line profiles in NVSS 2146+82 are not unique; \nemission line profiles and narrow band imaging of Seyfert galaxies and\nradio galaxies have shown evidence for interaction between the radio\nsynchrotron emitting plasma and the optically emitting ionized gas (see\ne.g., \\cite{dmw89}). Although the majority of objects that show\nkinematic evidence for interactions between the radio jets and ionized\ngas clouds tend to have more compact radio structures, the double\npeaked line profiles seen in NVSS 2146+82 appear similar to those seen\nin radio galaxies with jet/cloud interactions. A recent model \n(\\cite{tda92}) for interactions between the nuclear radio emission and\nNLR gas in Seyferts produces $[$\\ion{O}{3}$]$ profiles for objects near\nthe plane of the sky that are very similar to the double peaked profiles\nseen in NVSS 2146+82. The model of Taylor et al.\\ (1992) produces double\npeaks in the line profiles of objects oriented close to the plane of the sky \nbecause the emission lines are postulated to arise from gas that is \nbeing accelerated as a bowshock expands into the ionized medium surrounding the nucleus.\nThey model the bowshock as a series of annuli, and each annulus contributes\nmost of its luminosity at the two extreme radial velocities found along the\nline of sight. Although the specifics of the model of Taylor et al.\\ (1992),\nsuch as the discrete plasmon emission from the radio nucleus, may not necessarily\napply in the case of NVSS 2146+82, it suggests that the narrow line profiles\nobserved for this FR II (which is assumed to be very near the plane of the sky)\ncan be produced plausibly in a model where the ionized\ngas is in a cylindrical geometry around the radio jet. \n\nDouble peaked {\\em broad} lines have been observed in radio galaxies (e.g.,\nPictor A [\\cite{he94}]), however the model that is typically invoked to explain\nthe broad line profiles requires the radio galaxy to be oriented close to the\nline of sight. Since NVSS 2146+82 does not show a broad line component\nand is unlikely to be oriented close to the line of sight, the accretion disk\nmodel relied on to fit double peaked broad lines in AGN is probably unrelated\nto the emission line profiles observed in NVSS 2146+82.\n\nAlthough a jet/cloud interaction appears to be the most reasonable\nexplanation for the double peaked narrow emission lines observed in the\nspectrum of NVSS 2146+82, it is also plausible that a gravitational\ninteraction between the FR II host galaxy and its nearest companions\nmay be the source of the $\\sim$450 km/sec separation between the blue\nand red emission line peaks. Higher spatial resolution long slit\nspectroscopy is necessary to determine which cause is more likely.\n\n\n\\subsection{Environment}\n\nDeep CCD imaging of the region surrounding the host galaxy of NVSS\n2146+82 has revealed a large number of nearby galaxies. These galaxies\nare near the limiting magnitude of the POSS/DSS images, so NVSS 2146+82\nappears to lie in a sparsely populated region of the sky in the DSS.\nHowever, photometry from the deeper Palomar 1.52-m images gives $-22\n\\lesssim M_{V} \\lesssim -19.5$ for these nearby galaxies if they also\nlie at $z = 0.145$, indicating a possible association with NVSS\n2146+82. In Figure \\ref{fig:oldfig4}, we present a region of the KPNO\n4-m image of NVSS 2146+82 that is 0.5 Mpc on a side and that has all\nidentified galaxies with $m_{v} \\lesssim 21.3$ (corresponding to $M_{V}\n\\lesssim -19$ at $z=0.145$) circled. These images do not go deep\nenough to allow accurate identification and photometry of all galaxies\nto $M_{V} = -19$, so this sample is not complete. However, even though the\nsample shown in Figure \\ref{fig:oldfig4} is probably only complete to\n$M_{V} \\sim -20.5$, we have identified 34 candidate galaxies\nsurrounding NVSS 2146+82.\n\nAlthough there are no previous identifications of the cluster around\nNVSS 2146+82 (at $b=21\\fdg5$, it is too close to the Galactic Plane to\nhave been included in the Abell [1958] catalog), there is a Zwicky\ncluster to the north, with NVSS 2146+82 lying only $\\sim\\!5\\arcmin$\nsouth of the southern border of the Zwicky cluster. The Zwicky cluster\n2147.0+8155 (B1950.0 coordinates) is a compact group with 56 members\nclassified as ``extremely distant'' or $z > 0.22$ (\\cite{zwicky}).\nWhile this gives a redshift for the Zwicky cluster larger than that of\nNVSS 2146+82, it is close enough to $z = 0.145$ ($< 400$ Mpc more\ndistant) that we may be seeing NVSS 2146+82 in projection against a\nbackground rich cluster.\n\nIn September of 1998 WIYN/HYDRA spectra were obtained of 46 candidate\ngalactic companions of NVSS 2146+82 to determine their redshifts. The\nsample of 46 was selected in the following way: (1) We selected all\nobjects morphologically classified as galaxies in the KPNO 4-m frame by\nFOCAS with aperture magnitudes $<21$, resulting in an initial sample of\n205 galaxies. (2) We divided this group into two subdivisions: the\nfirst being all galaxies within 0.5 Mpc of 2146+82 in projected radius,\nand the second being all those outside of the 0.5 Mpc radius. \nHowever, due to exposure time limitations, the available sample taken\nfrom the 34 galaxies identified in Figure \\ref{fig:oldfig4} within\n0.5 Mpc of the host was reduced to the 17 brightest galaxies. Fiber\nplacement restrictions allowed us to observe only 11 of these 17\ngalaxies. Objects\nfrom the sample outside of the 0.5 Mpc radius from NVSS 2146+82 were\nassigned to 35 of the remaining fibers, leaving about 45 fibers on blank\nsky to allow accurate sky subtraction. Unfortunately, as mentioned in\n\\S 3.2 above, the weather conditions during some of the queue observing\nwere poor, and this limited the success of the program. There was enough\nsignal-to-noise to identify features in the spectra of only 24 of the\n46 objects successfully. We found that 7 of the 24 objects with good\nspectra were actually misidentified stars.\n\nNonetheless, from the remaining 17 spectra of galaxies in the field\nsurrounding NVSS 2146+82, we were successful in identifying what we\nbelieve to be a true cluster that contains the radio source host\ngalaxy. Figure \\ref{fig:oldfig5} presents an image with the 17\ngalaxies with measured redshifts marked. The\npositions, redshifts, and magnitudes for these objects are listed in\nTable \\ref{table:redshifts}. A quality factor is assigned for each\nredshift using the 0 (unreliable) to 6 (highly reliable) scale of \n\\cite{munn97}. The quality is determined using: $q =\n{\\rm min}[6,{\\rm min}(1,N_{def}),+2N_{def}+N_{prob}]$, where $N_{def}$ is the\nnumber of spectral features that are accurately identified (less than\n5\\% chance of being incorrect) and $N_{prob}$ is the number of\nspectral features that are probably correct (about a 50\\% chance of\nbeing correct). If $q > 3$ is adopted as the requirement for a reliable\nredshift, 5 of the 17 galaxies have unreliable redshifts. The\nhistogram plotted in Figure \\ref{fig:oldfig6} is a redshift\ndistribution for the 17 galaxies, and it shows that 50\\% (6) of the\nreliable redshifts fall in the range of $z = 0.135 - 0.148$, with 5 of\nthose having redshifts of $z = 0.144 - 0.148$.\n\nExtrapolating the redshift distribution for the sample of galaxies\nidentified around NVSS 2146+82 from the redshift distribution of the 17\nreliable galaxy spectra suggests that the 2146+82 cluster may be Abell\nrichness class 0 or 1. Of course, the statistics are very uncertain.\nOf the 11 galaxies within a projected distance of 0.5 Mpc of NVSS\n2146+82 that were in the WIYN/HYDRA sample, redshifts were measured for\nthree of them. Two of these have $z=0.144-0.145$, while the third has\n$z=0.135$. We identified features in 21 of the remaining 35 spectra\nthat were measured for objects outside of the projected 0.5 Mpc\nradius. We found that 7 were misclassified stars, and 3 of the 14\ngalaxies with reliable redshifts had $0.144 < z < 0.148$. Abell's\n(1958) richness criterion was based on the number of cluster galaxies\nwithin the range $m_{3}$ to $m_{3} + 2$ ($m_{3}$ is the magnitude of\nthe third brightest cluster member). For the NVSS 2146+82 cluster,\n$m_{3}$ should be $< 18.3$, since the third brightest galaxy of the 7\n(which includes NVSS 2146+82) we have found at $z = 0.145$ has $m =\n18.3$. Of the 205 galaxies originally found in the KPNO 4-m field\ncontaining NVSS 2146+82, 123 of these fall within the $m_{3}$ to $m_{3}\n+ 2$ range used for estimating the Abell richness. If we apply the\npercentages above to this sample of 123 galaxies, then $37 \\pm 13$\nmight be at the same redshift as NVSS 2146+82. To this point, we have\nbeen considering the cluster richness inside of 0.5 Mpc, for comparison\nwith the $N_{0.5}^{-19}$ richnesses of Allington-Smith et al.\\ (1993)\nand Zirbel (1997), and also within an area $\\sim$3.8 Mpc on a side,\nwhich is the size of the KPNO 4-m field at $z=0.145$. However, we must\nnote that the original richness criterion for Abell class 1 clusters\nwas that 50 or more galaxies were contained in a radius of 3 Mpc for\n$H_{0} = 50$ km sec$^{-1}$ Mpc$^{-1}$ (\\cite{abell}). A circle of\nradius 3$h_{50}^{-1}$ Mpc at $z=0.145$ subtends 507 square arcminutes\non the sky, nearly twice the amount of area covered in our image. If\nthe calculated optical richness from the 4-m image galaxy sample is\ntaken as a lower limit to the number of galaxies within an Abell\nradius, the richness class of the group surrounding NVSS 2146+82\nappears to be at least Abell class 0.\n\n\\section{X--ray Observations and Constraints} % \\label{sec:xray_obs}\n\nRichness class 0 clusters of galaxies typically have luminosities\nwith L$_{x} \\approx 10^{43-45}$ ergs s$^{-1}$ (\\cite{Ebeling98}),\nwhile X-ray AGN range from L$_{x} \\approx 10^{40-44}$ ergs s$^{-1}$\n(\\cite{Green92}), so a cluster or bright AGN will easily be seen with a\nmedium length exposure with {\\it ROSAT}. NVSS 2146+82 was observed\nwith the {\\it ROSAT} High Resolution Imager (HRI) between 1998\nFebruary 24 and 1998 March 13 for a duration of 30.3 ksec to search\nfor any hot gas that might be associated with the apparent overdensity of\ngalaxies or for an X-ray luminous AGN. \n\nThe data were analyzed with the IRAF Post-Reduction Off-line Software\n(PROS). The HRI data were filtered for periods of high background and\ncorrected for non-X-ray background, vignetting, and exposure using the\ncomputer programs developed by Snowden (\\cite{Plucinsky93};\n\\cite{Snowden98}). After filtering, the live exposure was 29.8 ksec.\nThe resulting X-ray image was convolved with a gaussian beam with\n$\\sigma = 2\\arcsec$ to recover diffuse X-ray emission. The contours of\nthe image are shown superposed on the DSS image in Figure\n\\ref{fig:xray}.\n\nA few sources were visible near the edge of the field, but there seem\nto be no significant sources of X-ray emission associated with any\noptical or radio sources within the $20\\arcmin$ extent of NVSS 2146+82 (Figure\n\\ref{fig:xray}). We derived upper limits on both the AGN or cluster\nemission by extracting the X-ray counts from the corrected X-ray image\nusing circular regions centered on the host galaxy of $20\\arcsec$ and\n$2\\farcm25$, respectively. The region sizes were chosen simply because\n$20\\arcsec$ represents the size of a typical HRI point source and\n$2\\farcm25$ is roughly 1-2 times the typical size of a cluster\ncore at the distance of the radio galaxy. The X-ray background was\ndetermined by extracting the X-ray counts from an annulus of\n$2.25-5\\arcmin$ centered on the nucleus of the radio host and removing\n3 point sources using $20\\arcsec$ circular regions. We used PIMMS\n(\\cite{Mukai93}) to convert the HRI count rate into an unabsorbed flux\nin the 0.1-2.0 keV band, assuming an emission model and a Galactic\nphotoelectric absorption column of $1.058\\times10^{21}$ cm$^{2}$\n(\\cite{stark}). For the AGN, we assumed a power law with a photon\nindex, $\\Gamma$, of 2.0 and derived an upper limit at the $90\\%$\nconfidence level of $3.52\\times10^{-14}$ ergs cm$^{-2}$ s$^{-1}$, or\n$3.63\\times10^{42}\\ h_{50}^{-2}$ ergs s$^{-1}$ at the distance of the radio\ngalaxy. Similarly for the cluster, we assumed a Raymond-Smith thermal\nemission spectrum characterized by $kT=1$ keV which yielded an upper\nlimit of $1.33\\times10^{-13}$ ergs cm$^{-2}$ s$^{-1}$, or \n$1.37\\times10^{43}\\ h_{50}^{-2}$ ergs s$^{-1}$.\n\nUnfortunately, our limit on the X-ray emission from the radio galaxy is\nnot very stringent. \\cite{fabbiano84} studied the X-ray properties of\nseveral 3CR radio galaxies with the {\\it Einstein} Observatory. They\nfound that the FR II's radio and X-ray luminosities are strongly\ncorrelated. Thus with a radio flux of 6.8 mJy at 5 GHz, NVSS 2146+82\nshould have a nuclear X-ray flux of a few times $10^{42}$ ergs s$^{-1}$. This\nflux is comparable to our upper limit. Taking into account the\nintrinsic scatter in the radio/X-ray correlation, our non-detection of\nthe AGN is quite reasonable.\n\nOur upper limit on the X-ray emission from hot cluster gas provides a\nmuch stronger constraint. Most Abell richness class 0 clusters have\nX-ray luminosities of $\\approx10^{43-45}$ erg/s (\\cite{Ebeling98}).\nTherefore any cluster of galaxies associated with the radio galaxy\nmust be either intrinsically weak in X-rays or must be \npoorer than our optical estimate. \\cite{wan96} studied the X-ray emission\nof low-redshift FR II galaxies and found that poor clusters that contain FR II\nsources are underluminous in X-rays compared to similar clusters that do not\ncontain FR IIs. The median X-ray luminosity for low-$z$ clusters with FR IIs\nwas found to be $1.3\\times10^{42} h_{50}^{-2}$ ergs s$^{-1}$ while it is \n$1.33\\times10^{43} h_{50}^{-2}$ ergs s$^{-1}$ for a sample of low-$z$ clusters\nwithout FR IIs (Wan \\& Daly 1996). Assuming that the group surrounding\nNVSS 2146+82 is similar to that of other clusters found around low-$z$ FR IIs\nand is underluminous in X-rays, the optical richness estimate is probably\ncorrect.\n\n\\section{Discussion}\n\n\\subsection{Physical Properties of the Radio Source}\n\n\\subsubsection{Size and Luminosity}\n\nOur observations of NVSS 2146+82 clearly show that it is an unusually\nlarge FR II radio galaxy. Its angular distance from the north lobe to\nthe south lobe gives an unusually large extent of $\\theta=19\\farcm5$.\nFor our assumed cosmology and our measured redshift of $z=0.145$, the\nlinear extent of the radio structure is 4$h_{50}^{-1}$ Mpc, placing it\nin the Giant Radio Galaxy (GRG) class, which we define as sources\nlarger than 2$h_{50}^{-1}$ Mpc. NVSS 2146+82 is therefore the second\nlargest FR II known, surpassed only by 3C236 which is\n$\\sim$6$h_{50}^{-1}$ Mpc in extent. FR II galaxies of this size are\nextremely rare; a literature search by \\cite{nilsson} of 540 FR IIs\ncontains only 27 objects with sizes greater than 1$h_{50}^{-1}$ Mpc.\nOf this sample of 27 large FR IIs, only 5 are larger than\n2$h_{50}^{-1}$ Mpc. For comparison, the other known giant radio\nsources are shown in Table \\ref{table:giants}. The log radio luminosity\nof NVSS 2146+82 at 1.4 GHz is 25.69, in the middle of the range for\ngiant radio sources.\n\nIt remains unclear if there are fundamental differences between GRGs\nand ``normal'' radio galaxies. The relative paucity of known GRGs may\nbe in part due to observational selection effects in past radio\nsurveys. An alternative reason for the rarity of giant radio galaxies\nmay be that the physical conditions necessary for the creation of a GRG\nare uncommon in the universe. Although the similarity between NVSS\n2146+82 and other FR IIs suggests that it is a typical FR II radio galaxy\nat the extreme end of the size distribution, a study of a complete\nsample of radio galaxies that includes GRGs will have to be made to\ndetermine if GRGs are part of a continuous distribution in size of\nnormal radio galaxies or if there are fundamental differences between\nGRGs and smaller FR IIs.\n\n\\subsubsection {Equipartition calculations}\n\nIf the usual equipartition assumptions are made, then it is possible to\nestimate the magnetic field strength and pressure in the lobes.\nAssuming that the observed spectral index is maintained from 10 MHz to\n100 GHz, that there are equal energies in the radiating electrons and\nother particles, and that the filling factor is unity, the derived\nmagnetic field is B$_{min}\\ \\approx\\ 5\\times 10^{-6}\\ h_{50}^{2/7}$ Gauss\nand p$_{min}\\ \\approx\\ 3.5\\times 10^{3}\\ h_{50}^{4/7}$ cm$^{-3}$K for the\nhot spots. At the midpoint of the lobes these values are\nB$_{min}\\ \\approx\\ 8\\times 10^{-7}\\ h_{50}^{2/7}$ Gauss and\np$_{min}\\ \\approx\\ 2.3 \\times 10^{2}\\ h_{50}^{4/7}$ cm$^{-3}$K. At this\nredshift, the 3~K microwave background has an equivalent magnetic field\nof 4.2$\\times 10^{-6}$ Gauss so the energy loss in the lobes should be\ndominated by inverse Compton scattering of this background, and the\ntime for the electrons radiating at 1400 MHz to lose half of their\nenergy will be $\\approx\\ 10^{8}\\ h_{50}^{-3/7}$ years.\n\n\\subsubsection {Magnetic Field and Faraday Rotation}\nThe mean Faraday rotation of $\\approx$ $-9$ rad\\ m$^{-2}$ shown in\nFigure \\ref{fig:RM} is consistent with the results of\n\\cite{Simon-Normandin} for other extragalactic sources seen through \nthis region of the Galaxy ($l=116.^\\circ7, b=21.^\\circ5$). It is\ntherefore likely that the rotation measure screen seen in Figure \n\\ref{fig:RM} is primarily the foreground screen of our Galaxy. \nThe low apparent rotation measure and the smoothness of the\npolarization structure shown in Figure \\ref{fig:polarization} suggests\nthat the magnetic field in this source is well ordered. The field\nconfiguration is entirely typical of older extended FR II sources, with\nthe E vectors lying approximately perpendicular to the ridge line of\nthe radio emission in most features.\n\nWe note that the greater variance and evidence for organized\nstructure in the Faraday rotation of the southern lobe is the\nopposite of what would be expected if the jet sidedness were due to\nDoppler favoritism and the Faraday rotating medium were local to\nthe source. We think it more likely that the Faraday rotation\nstructure arises along the line of sight in our Galaxy.\n\n\\subsubsection {Spectral Index Variations}\nThe spectral index variations shown in Figure \\ref{fig:SI} indicate\nthat there are regions $2\\farcm4$ back towards C from the brightest\nregion in each lobe that have unusually flat spectra\n($\\alpha^{1.4}_{0.35}\\ \\approx$ -0.3), flatter even than the hot spots.\nThe only extended synchrotron sources known with spectra this flat are\na few Galactic supernova remnants (\\cite{Berkhuijsen}).\n\nThe spectral index structure in NVSS 2146+82 is unlike the systematic\nsteepening of the spectrum away from the hot spots that is usually\ninterpreted as an effect of spectral aging in extended lobes. In such\ninterpretations, electrons are presumed to be injected into a high\nfield region in or around the hot spots, and their energy spectrum\nsteepens with distance as they diffuse into lower field regions of the\nextended lobes. Clearly no such interpretation can be made here.\n\nThese flatter spectrum regions occur in the transition zone from the\nfeatureless parts of the lobes (closer to the core) to the parts near\nthe regions of enhanced emission that contain significant filamentary\nstructure. The anomalous regions are near the midline of the lobes;\nthe southern region is centered on the path of the jet and the northern\nregion is at one end of a prominent filament (the path of the jet is\nuncertain). The relative symmetry of the flatter spectrum regions of\nthe lobes suggests that they might be produced by an intrinsic property\nof the source, such as a variable spectral index in the injection\nspectrum of the relativistic electrons from the jet, rather than local\nenvironmental effects.\n\nIf the magnetic field has values near those\nestimated by the equipartition calculations given above, then the\nenergy loss of the radiating electrons is dominated by inverse Compton\nscattering against the Cosmic Microwave Background. In the low\ndensity, low magnetic fields in these lobes, the aging effects will be\nslow and the history of a variable electron spectrum could be\nmaintained along the length of the lobe.\n\n\\subsubsection{Size Scales of Symmetry in the Radio Source}\n\nThere are three size scales on which symmetries appear or change in the\nradio structure: The first is $1\\farcm5 = 300 h_{50}^{-1}$ kpc. The\njets appear to become symmetric on this scale but are asymmetric on\nsmaller scales. If the J2 and K components (Figure 4) are symmetric\nfeatures in the jet and counterjet, any Doppler boosting from\nrelativistic motion must have disappeared by this point in the jet.\nThe second scale is $3\\farcm2 = 640 h_{50}^{-1}$ kpc. On this scale,\nthere is a dramatic brightening of both lobes. The third scale is\n$6\\farcm5 = 1300 h_{50}^{-1}$ kpc. At this distance, the lobes become\neven brighter and strong filamentary structure appears. This is the\ndistance at which regions of spectral anomaly appear in the extended\nemission.\n\nThe largest scale symmetries thus suggest a symmetric overall\nenvironment, apart from the slight non-collinearity (C-symmetry) of the\nstructure. The small scale brightness asymmetries of the jet and\ncounterjet might be attributed to Doppler boosting and dimming by\nrelativistic motion which effectively disappears by $\\sim 300\nh_{50}^{-1}$ kpc, i.e. on a scale more typical of a ``non-giant'' FR\nII source. We reiterate however that the small asymmetry in rotation\nmeasure dispersion (variance) between the lobes is opposite in sign to\nthat expected on this interpretation. This asymmetry seems more likely\nto reflect an intrinsic asymmetry (or gradient) in the foreground\nmagnetoionic medium.\n\n\\subsection{The Optical Environment}\n\nOne possibility for the origin of GRGs is that they are\notherwise normal FR II sources that reside in extremely low\ndensity gaseous environments. \nThe environments in which radio galaxies reside have been studied in\ndepth (e.g. \\cite{longair79}; \\cite{heckman86}; \\cite{prestage88};\n\\cite{hill91}; \\cite{aezo}; \\cite{zirbel97})\nbecause the gas density and pressure in the host galaxy's ISM,\nany intracluster medium, and the IGM are at least partly responsible\nfor determining the resulting radio morphology. \n\nAn intriguing result of recent studies (\\cite{hill91};\n\\cite{aezo}, \\cite{zirbel97}) is that FR II galaxies are\nfound in a range of cluster richnesses at moderate redshifts, but they\nare only found in poor to very poor groups at low redshift. The\n``richness'' of the cluster associated with a radio galaxy can be\nestimated in a statistical sense in the absence of redshift data on\nnearby galaxies. Allington-Smith et al. (1993) define the richness\nparameter $N_{0.5}^{-19}$ as the number of galaxies within a projected\nradius of 500 kpc and with $M_{V} \\leq -19.0$ assuming the same redshift\nas the AGN. The number counts are corrected for contamination by\nforeground and background galaxies by subtracting number counts from a\nfield offset from the radio galaxy. Zirbel (1997) gives a conversion\nof $N_{0.5}^{-19}$ to Abell class as $N_{Abell} = 2.7\n(N_{0.5}^{-19})^{0.9}$. With this conversion, the thresholds for\nAbell Classes 0 and 1 are $N_{0.5}^{-19} = 15$ and 26 respectively.\nUsing this richness estimation technique, Zirbel (1997) found that of\na sample of 29 low redshift ($z < 0.2$) FR IIs: (1) 41\\% of the sample\nof low $z$ FR IIs reside in very poor groups ($N_{0.5}^{-19}< 3.5$),\nand (2) more importantly, no low redshift FR II was found in a rich\ngroup with $N_{0.5}^{-19} > 20$. Based on the results given in \\S 3.5,\nNVSS 2146+82 appears to reside in a group with an anomalously high\ngalaxy richness compared to other low redshift FR IIs. Although\nthe galaxy counts from the field surrounding NVSS 2146+82 were not\ncalculated identically to those of Zirbel (1997), the value of\n$N_{0.5}^{-19}$ is likely $> 25 - 30$ for NVSS 2146+82.\n\nThe upper limit on the cluster X-ray emission is consistent with the\nNVSS 2146+82 group being at the low end of the X-ray luminosity \ndistribution for poor clusters. \\cite{wan96} found that \nin a comparison of low redshift clusters with and without FR II\nsources, clusters that contained FR IIs were underluminous in X-rays\ncompared to clusters without FR IIs. Although the cluster surrounding\nNVSS 2146+82 may be Abell Class 0, its lack of associated X-ray gas\nsuggests that the pressure in the surrounding medium is low enough\nfor a giant radio source to form with little disruption of the FR II jet.\n\nCuriously, several other GRGs listed in Table \\ref{table:giants} also\nappear to lie in regions with overdensities of nearby galaxies. The\nGRG 0503-286 appears to lie in a group of 30 or so galaxies\n(\\cite{sar86}). These companions are concentrated to the northeast of\nthe host galaxy of 0503-286, and may have caused the asymmetric\nappearance of the northern lobe of the radio structure. Overdensities\nof nearby galaxies are also reported for 1358+305 (\\cite{par96}) and 8C\n0821+695 (\\cite{lacy93}); however, in both cases there is no\nspectroscopic confirmation of the redshifts of the candidate cluster\ngalaxies. In a recent study of the optical and X-ray environments of\nradio galaxies, \\cite{miller99} find that for a sample of FR I\nsources, all have extended X-ray emission and overdensities of optical\ngalaxies. However of their sample of seven FR II sources, none have\noverdensities of optical galaxies or extended X-ray emission except for\nthe GRG DA240, which has no extended X-ray emission\nbut does have a marginally significant excess of optical companions.\nPerhaps for at least some of the GRG population, the presence of the host\ngalaxy in an optically rich group with little associated X-ray gas is\nrelated to the formation or evolution of the radio source?\n\n\n\\section{Summary and Conclusions}\n\nWe have presented multi-wavelength observations of the\nunusually large FR II radio galaxy NVSS 2146+82. The overall size of the radio\nsource is $4h_{50}^{-1}$ Mpc, making it the second largest known\nFR~II source. We have found the host galaxy to be similar in both\nluminosity and morphology to a sample of other low redshift FR II\ngalaxies. Emission line profiles seen in the spectrum of the host\ngalaxy are double peaked, which may indicate that the ionized gas may\nbe being accelerated by the bipolar radio jet.\n\nWe have also found evidence for an anomalously rich group of \ngalaxies at the same redshift as NVSS 2146+82 that has little\nassociated X-ray emitting gas. Though unusual in having a rich\nenvironment, this source is similar to other low redshift FR IIs in clusters;\nthe NVSS 2146+82 group is underluminous in X-rays compared to clusters\nof similar richness that contain no FR II. The large radio size, lack\nof significant Faraday rotation and non detection of X-rays all suggest\nthat in spite of the richness of the cluster in which this galaxy\nresides, it has a low gas density.\n\nThere is some morphological evidence that the host galaxy of NVSS 2146+82\nmay be undergoing tidal interaction with one or more of its nearest\ncompanions. Also, an interaction may be responsible for the double-peaked\nemission line profiles, however the spatial resolution of the spectrum\nof the nucleus is not high enough to distinguish between a merger \norigin or radio jet/cloud interaction origin for the peculiar profiles.\n\nApart from the radio spectral index anomaly, the radio properties of \nthis source are like a normal FR II\nsource scaled up by a factor of ten, preserving the standard overall\nmorphology and polarization structure. In the outer regions of the\nsource the magnetic field is likely to be so weak that inverse\nCompton losses to the Cosmic Microwave Background dominate synchrotron\nlosses.\n\n\\acknowledgements\n\nWe are grateful to Mark Whittle for many helpful conversations. We are\ngrateful to Matt Bershady, Randy Phelps, and Mike Siegel for either sharing\nobserving time or taking observations in support of this research.\nCP acknowledges the support of a Grant-in-aid of Research from Sigma\nXi, the Scientific Research Society. This research has made use of the\nNASA/IPAC Extragalactic Database (NED) which is operated by the Jet\nPropulsion Laboratory, California Institute of Technology, under\ncontract with the National Aeronautics and Space Administration. We\nacknowledge the use of NASA's {\\it SkyView} facility\n(http://skyview.gsfc.nasa.gov) located at NASA Goddard Space Flight\nCenter.\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\n\\bibitem[Abell 1958]{abell} Abell, G. O. 1958, \\apjs, 3, 211 \n\n\\bibitem[Allington-Smith et al.\\ 1993]{aezo} Allington-Smith, J. R.,\nEllis, R. S., Zirbel, E. L., \\& Oemler, A., 1993, \\apj, 404, 521 \n\n\\bibitem[Berkhuijsen 1986]{Berkhuijsen}\nBerkhuijsen, E. 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G. 1980, \\aap, 85, 36\n\n\\bibitem[Subrahmanyan \\& Saripalli 1993]{sub93}\nSubrahmanyan, R. \\& Saripalli, L. 1993, \\mnras, 260, 908\n\n\\bibitem[Tadhunter et al.\\ 1998]{tad98} Tadhunter, C. N., Morganti, R., Robinson, A.,\nDickson, R., Villar-Martin, M., \\& Fosbury, R. A. E. 1998, \\mnras, 298, 1035\n\n\\bibitem[Taylor, Dyson, \\& Axon 1992]{tda92} Taylor, D., Dyson, J. E., \\& Axon,\nD. J. 1992, \\mnras, 255, 351\n\n\\bibitem[Valdes 1982]{valdes82} Valdes, F. 1982, FOCAS User's Manual, (Tucson: NOAO)\n\n\\bibitem[Wan \\& Daly (1996)]{wan96} Wan, L., \\& Daly, R. A. 1996, \\apj, 467, 145\n\n\\bibitem[Whittle 1989]{dmw89} Whittle, M. 1989, in Extranuclear Activity in Galaxies,\ned. E. Meurs \\& R. Fosbury (Munich: ESO), 199\n\n\\bibitem[Willis, Strom, \\& Wilson 1974]{wil74}\nWillis, A. G., Strom, R. G., \\& Wilson, A. S. 1974, {\\it Nature}, 250, 625\n\n\\bibitem[Zirbel 1996]{zirbel96} Zirbel, E. L. 1996, \\apj, 473, 713\n\n\\bibitem[Zirbel 1997]{zirbel97} Zirbel, E. L. 1997, \\apj, 476, 489\n\n\\bibitem[Zirbel \\& Baum 1995]{zirbel95} Zirbel, E. L., \\& Baum, S. A. 1995, \\apj,\n448, 521\n\n\\bibitem[Zwicky et al.\\ 1961]{zwicky} Zwicky, F., Herzog, E., Wild, P.,\nKarpowicz, M., \\& Kowal, C. 1961-68, Catalogue of Galaxies and Clusters\nof Galaxies, (Pasadena: CIT)\n\n\\end{thebibliography}\n\n\\clearpage\n\\pagestyle{empty}\n\n\\begin{figure}\n \\plotfiddle{Palma.fig1.eps}{6truein}{0}{70}{70}{-220}{-50}\n\t\\caption{Contour plot of the NVSS 1.4 GHz \n\ttotal intensity data for the field. Contours are\n\tshown at -1, 1, 2,4, 8, 16, and 32 mJy per CLEAN beam\n\tarea.}\n \\label{fig:NVSScontours}\n \\end{figure}\n \n \n\\begin{figure}\n \\plotfiddle{Palma.fig2alt.eps}{6truein}{0}{70}{70}{-220}{-50}\n\t\\caption{Contour plot of the new 1.4 GHz \n\ttotal intensity data for the field at 13\\arcsec\\ (FWHM)\n\tresolution. Contours are\n\tshown at -1, 1, 2,4, 8, 16, 32 and 64 times 100 $\\mu$Jy per CLEAN beam\n\tarea.}\n \\label{fig:NVSSLhi}\n \\end{figure}\n \n \n\\begin{figure}\n \\plotfiddle{Palma.fig3.eps}{6truein}{0}{70}{70}{-220}{-50}\n\t\\caption{Gray scale image at 13\\arcsec\\ (FWHM) resolution using\n a nonlinear transfer function to emphasize the lower\n brightness levels.\n The jet and strong filaments in the lobes can be seen.\n\t}\n \\label{fig:BnCgray}\n \\end{figure}\n \n \n \\begin{figure}\n \\plotfiddle{Palma.fig4.eps}{6truein}{0}{70}{70}{-220}{-50}\n \t\\caption{Contour plot of the new 1.4 GHz \n\ttotal intensity data for the field at 13\\arcsec\\ (FWHM)\n\tresolution. \n Contours are shown at \n -1, 1, 2, 3, 4, 5, 6, 7, 8, 10, and 12 times 50 $\\mu$Jy per CLEAN beam\n \tarea.\n The core and various features in the jet are marked.}\n\t \\label{fig:NVSSjets}\n \\end{figure}\n \n\\begin{figure}\n\\plottwo{Palma.fig5left.eps}{Palma.fig5right.eps}\n\\caption{Contour plot of the 1.5 GHz total intensity data from the B configuration \nover the north D (left) and south E (right) hot spots\nof the source at 5\\farcs75 by 3\\farcs7\n(FWHM) resolution. \nContours are shown at a linear interval of 0.25 mJy per CLEAN beam area}\n\\label{fig:hotspots}\n\\end{figure}\n\n\n\\begin{figure}\n\\plottwo{Palma.fig6left.eps}{Palma.fig6right.eps}\n\\caption{Distribution of degree of 1.4 GHz linear polarization $p$ and {\\bf E}-vector\nposition angle $\\chi$ over the north D (left) and south E (right) \nlobes of the source at 13\\arcsec\\\n(FWHM) resolution, superposed on selected contours of total intensity.\nA vector of length 15\\arcsec\\ corresponds to $p$=0.5.}\n\\label{fig:polarization}\n\\end{figure}\n\n\n \\begin{figure}\n\\plottwo{Palma.fig7left.eps}{Palma.fig7right.eps}\n \\caption{Gray scale representation of the rotation measure at 20\\arcsec\\\n resolution with superimposed contours of the 1.6 GHz total\n intensity at the same resolution.\n The bar at the top gives the grayscale values and the resolution\n is shown in the lower--left corner.\n The north lobe is shown in the left and the south lobe on the right.\n } \n \\label{fig:RM}\n \\end{figure}\n \n \\begin{figure}\n\\plotfiddle{Palma.fig8alt.eps}{6truein}{0}{70}{70}{-220}{-50}\n \t\\caption{Gray scale representation of the spectral index\n distribution derived from VLA measurements at 1.4 GHz and the\n 0.35 GHz WENSS image with superimposed contours from the VLA image.\n\tThe resolution is 54\\arcsec\\ (FWHM), illustrated in the\n lower--left and the bar at the top gives the gray scale values.\n \t}\n \\label{fig:WENSS}\n \\end{figure}\n \n \\begin{figure}\n\\plottwo{Palma.fig9left.eps}{Palma.fig9right.eps}\n \\caption{Gray scale representation of the spectral index at\n 55$\\arcsec\\ $ resolution derived from the 1.36 and 1.63 GHz data\n with superimposed contours of the 1.63 GHz total intensity at the\n same resolution. \n The bar at the top gives the gray scale values and the resolution\n is shown in the lower--left corner.\n The north lobe is shown in the left and the south lobe on the right.\n } \n \\label{fig:SI}\n \\end{figure}\n \n\\begin{figure}\n\\plotone{Palma.fig10.eps}\n\\caption{A contour plot of the V band surface brightness of\nthe region immediately surrounding the host galaxy of NVSS 2146+82.\nThe object just east of the host galaxy (at center) is a foreground\nstar. The remaining four discrete objects all have non-stellar PSFs,\nindicating that they are very likely galaxies. The object to the\nnorthwest of NVSS 2146+82 is a galaxy and has a spectroscopic redshift\nfrom our WIYN program of $z = 0.144$. }\n\\label{fig:oldfig2} \n\\end{figure}\n\n\n\\begin{figure}\n\\plottwo{Palma.fig11topalt.eps}{Palma.fig11bottomalt.eps}\n\\caption{Spectrum of the host galaxy of NVSS 2146+82. The\nleft panel shows the full spectrum, with several of the stronger\nemission features identified in Table \\ref{table:linedata} are marked.\nMost of the \nemission lines have a double-peaked profile, as illustrated in the\nright panel with the $[$\\ion{O}{3}$]$ $\\lambda\\lambda 4959$, 5007 pair.}\n\\label{fig:oldfig3} \n\\end{figure}\n\n\n\\begin{figure}\n\\plotone{Palma.fig12alt.eps}\n\\caption{A view of the field surrounding NVSS 2146+82 from\nthe central region of our KPNO 4 meter image (north is up, east to the\nleft). This field is 0.5 Mpc on a side at the redshift of NVSS\n2146+82, and it contains 34 objects down to $m_{v} = 21.3$ ($M_{V} \\geq\n-19$ at $z = 0.145$) that are morphologically identified as galaxies.\nFor reference, the host galaxy of NVSS 2146+82 is marked with hash\nmarks, and the three galaxies in this region that we measured\nspectroscopic redshifts for are marked with their ID numbers from\nTable \\ref{table:redshifts}}\n\\label{fig:oldfig4} \n\\end{figure}\n\n\n\\begin{figure}\n\\plotone{Palma.fig13alt.eps}\n\\caption{The full field that we observed with the KPNO 4\nmeter surrounding NVSS 2146+82. In this image, the 17 galaxies with\nspectroscopic redshifts are circled and identified with their ID number\nfrom Table \\ref{table:redshifts}. Those objects with reliable\nredshifts in the range \n$0.135 < z < 0.149$ are marked with arrows. NVSS 2146+82 is the galaxy\njust outside of the southeast edge of the circle surrounding galaxy 5.}\n\\label{fig:oldfig5} \n\\end{figure}\n\n\n\\begin{figure}\n\\plotone{Palma.fig14.eps}\n\\caption{A histogram of the redshifts of the 17 galaxies\nthat we obtained spectra for with the WIYN. The empty histogram is the\ndistribution of redshifts that have $q > 3$, and the hatched histogram\nis the distribution of the lower quality redshifts. The arrow shows\nthe redshift for NVSS 2146+82, $z=0.145$. The peak in this diagram is\ncentered around $z=0.1425$, showing that 6 -- 8 galaxies in our sample\nof 17 share the same redshift as NVSS 2146+82.}\n\\label{fig:oldfig6} \n\\end{figure}\n\n\n\\begin{figure}\n\\plotone{Palma.fig15alt2.eps}\n\\caption{A contour plot of the {\\it ROSAT} HRI X-ray image\nin the 0.5--2.0 keV band. The X-ray image has been corrected for\nnon-X-ray background, vignetting, and exposure and convolved with a 2\narcsec sigma gaussian beam. The contours are superposed on an optical image\nfrom the Digitized Sky Survey (Lasker et al.\\ 1990). The base contour\nlevel is 1.1 counts$/$pixel. The contours plotted are multiples ($1$,\n$2^{1/2}$, $2^{1}$, $2^{3/2}$, ...) of the base contour level. The\narrows indicate the position of the host galaxy.}\n\\label{fig:xray}\n\\end{figure}\n\n\\clearpage\n\n\\pagestyle{empty}\n\n\\begin{table}\n\\caption[VLA Observing Log]{VLA Observing Log}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\n\\tableline\n\\tableline\nVLA & Observing & Center Frequencies & Bandwidth & Number & Integration \\\\\nConfiguration & Date & (MHz) & (MHz) & of Fields & (min) \\\\\n\\tableline\nA & 1995 Jul 08 & 8415, 8465 & 50 & 6 & 5 \\\\\nA & 1995 Jul 08 & 4835, 4885 & 50 & 6 & 6 \\\\\nB & 1995 Dec 23 & 1365, 1636 & 12.5& 3 & 13 \\\\\nC & 1996 Feb 15 & 1365, 1636 & 25 & 3 & 22 \\\\\nD & 1996 Sep 02 & 1365, 1636 & 25 & 3 & 18 \\\\\nB & 1995 Dec 23 & 327.5, 333 & 3.1 & 1 & 69 \\\\\nC & 1996 Feb 15 & 327.5, 333 & 3.1 & 1 & 30 \\\\\nD & 1996 Sep 02 & 327.5, 333 & 3.1 & 1 & 7.5 \\\\\nBnC & 1997 Jun 17 & 1365, 1435 & 50 & 3 & 185 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\label{VLAObsLog}\n\\end{table}\n\n\\clearpage\n\n\\begin{table}\n\\label{Flux Densities}\n\\caption[Flux Densities]{Flux Densities}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\n\\tableline\n\\tableline\n & 0.35 GHz\\tablenotemark{a} & 1.4 GHz & 4.9 GHz & 8.4 GHz & $\\alpha^{1.4}_{0.35}$ \\\\\n\\tableline\nTotal & 0.99 $\\pm$ 0.02 Jy & 0.53 $\\pm$ 0.1 Jy & &\n& -0.45 $\\pm$ 0.06 \\\\\nN lobe & 0.43 $\\pm$ 0.01 Jy & 0.24 $\\pm$ 0.05 Jy & &\n& -0.42 $\\pm$ 0.07 \\\\\nS lobe & 0.52 $\\pm$ 0.01 Jy & 0.27 $\\pm$ 0.05 Jy & &\n& -0.47 $\\pm$ 0.06 \\\\\nC & 23 $\\pm$ 2 mJy & 13.6 $\\pm$ 0.5 mJy & 6.8 $\\pm$ 0.2 mJy\n& 3.4 $\\pm$ 0.2 mJy & -0.38 $\\pm$ 0.03 \\\\\nJ1 & & 1.3 $\\pm$ 0.2 mJy & & & \\\\\nJ2 & & 0.3 $\\pm$ 0.2 mJy & & & \\\\\nJ3 & & 0.8 $\\pm$ 0.2 mJy & & & \\\\\nK & & 0.7 $\\pm$ 0.2 mJy & & & \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\tablenotetext{a}{ 0.35 GHz measurements are from the WENSS image.}\n\\label{table:fluxes}\n\\end{table}\n\n\\clearpage\n\n\\begin{table}\n\\caption[Mean Aperture Magnitudes for NVSS 2146+82 Host Galaxy]\n{Mean Aperture Magnitudes for NVSS 2146+82 Host Galaxy}\n\\begin{center}\n\\begin{tabular}{c c c c}\n\\tableline\n\\tableline\nNight & Filter & Magnitude & Error \\\\\n\\tableline\n2 & U & 19.57 & 0.45 \\\\\n1 & B & 18.83 & 0.09 \\\\\n1 & V & 17.53 & 0.04 \\\\\n2 & R & 17.19 & 0.07 \\\\\n2 & I & 16.47 & 0.07 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\label{table:magnitudes} \n\\end{table}\n\n\\clearpage\n\n\n\\begin{table}\n\\caption[Emission Line Data for NVSS 2146+82]{Emission Line Data for NVSS 2146+82}\n\\begin{center}\n\\begin{tabular}{l c c c c c c}\n\\tableline\n\\tableline\nSpecies & $\\lambda_{\\rm red}$ & $z_{\\rm red}$ & $\\lambda_{\\rm blue}$ & $z_{\\rm bl\nue}$ & \nFlux\\tablenotemark{a} & Luminosity\\tablenotemark{a} \\\\\n & \\AA & & \\AA & & $10^{-15}$ erg/sec/cm$^{2}$ & $10^{41}$ erg/sec $h_{50}^{-2}$ \\\\\n\\hline\n$[$\\ion{O}{2}$]$ $\\lambda3727$ & 4262.5 & 0.1436 & 4269.6 & 0.1455 & \n\\phn7.4$\\pm$0.5 & \\phn7.6$\\pm$0.5 \\\\\n$[$\\ion{Ne}{3}$]$ $\\lambda3869$ & 4425.3 & 0.1439 & 4432.6 & 0.1458 & \n\\phn2.8$\\pm$0.3 & \\phn2.9$\\pm$0.3 \\\\\n$[$\\ion{Ne}{3}$]$ $\\lambda3967$\\tablenotemark{b} & & & 4545.1 & 0.1456 & \n\\phn0.9$\\pm$0.1 & \\phn0.9$\\pm$0.1\\\\\nH$\\delta$ & 4693.7 & 0.1443 & 4698.2 & 0.1454 & \n\\phn0.3$\\pm$0.1 & \\phn0.3$\\pm$0.1 \\\\\nH$\\gamma$ & 4963.9 & 0.1436 & 4971.9 & 0.1455 & \n\\phn1.4$\\pm$0.2 & \\phn1.4$\\pm$0.2 \\\\\n$[$\\ion{O}{3}$]$ $\\lambda4363$\\tablenotemark{b} & & & 4998.8 & 0.1457 & \n\\phn0.8$\\pm$0.1 & \\phn0.8$\\pm$0.1 \\\\\n\\ion{He}{2} $\\lambda4686$ & 5360.8 & 0.1440 & 5367.5 & 0.1454 & \n\\phn0.8$\\pm$0.2 & \\phn0.8$\\pm$0.2 \\\\\nH$\\beta$ & 5560.5 & 0.1438 & 5569.2 & 0.1456 & \n\\phn3.0$\\pm$0.4 & \\phn3.1$\\pm$0.4 \\\\\n$[$\\ion{O}{3}$]$ $\\lambda4959$ & 5672.4 & 0.1439 & 5681.6 & 0.1457 & \n12.3$\\pm$1.1 & 12.7$\\pm$1.1 \\\\\n$[$\\ion{O}{3}$]$ $\\lambda5007$ & 5727.2 & 0.1439 & 5736.4 & 0.1457 & \n35.7$\\pm$3.2 & 36.9$\\pm$3.3 \\\\\n$[$\\ion{O}{1}$]$ $\\lambda6300$ & 7206.2 & 0.1438 & 7217.4 & 0.1456 & \n\\phn1.6$\\pm$0.4 & \\phn1.7$\\pm$0.4 \\\\\n$[$\\ion{N}{2}$]$ $\\lambda6548$ & 7493.7 & 0.1444 & 7505.4 & 0.1462 & \n\\phn1.7$\\pm$0.3 & \\phn1.8$\\pm$0.3 \\\\\nH$\\alpha$ & 7508.9 & 0.1442 & 7520.3 & 0.1459 & \n\\phn8.9$\\pm$1.0 & \\phn9.2$\\pm$1.0 \\\\\n$[$\\ion{N}{2}$]$ $\\lambda6584$ & 7530.6 & 0.1438 & 7542.8 & 0.1457 & \n\\phn5.1$\\pm$0.6 & \\phn5.3$\\pm$0.6 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\n\\tablenotetext{a}{These values have been dereddened using a value\nof $A_{V} = 0.9$. Errors include only\ncalibration and measurement error, error in reddening is not included.}\n\\tablenotetext{b}{These lines were not resolved into a blue and red component; the\n values \nlisted in the table were determined by fitting the profile with a single gaussian.\n}\n\n\\label{table:linedata} \n\\end{table}\n\n\\clearpage\n\n\\begin{table}\n\\caption[Redshifts of Candidate Cluster Members in the Field of NVSS 2146+82]\n{Redshifts of Candidate Cluster Members in the Field of NVSS 2146+82}\n\\begin{center}\n\\begin{tabular}{c c c c c c}\n\\tableline\n\\tableline\nGalaxy ID & $\\alpha_{2000.0}$ & $\\delta_{2000.0}$ & z & q & $m_{v}$ \\\\\n\\tableline\n 1 & 21:42:18.5 & 81:55:34 & 0.242 & 5 & 20.0 \\\\\n 2 & 21:42:56.3 & 81:48:29 & 0.378 & 3 & 20.2 \\\\\n 3 & 21:42:58.5 & 81:57:40 & 0.350 & 5 & 19.4 \\\\\n 4 & 21:44:47.8 & 81:56:15 & 0.145 & 6 & 18.8 \\\\\n 5 & 21:45:24.5 & 81:55:05 & 0.144 & 6 & 19.3 \\\\\n 6 & 21:45:27.7 & 81:57:54 & 0.267 & 6 & 19.4 \\\\\n 7 & 21:45:54.8 & 81:53:23 & 0.135 & 6 & 18.4 \\\\\n 8 & 21:46:08.8 & 81:48:08 & 0.123 & 6 & 20.1 \\\\\n 9 & 21:46:24.3 & 81:57:43 & 0.243 & 6 & 18.4 \\\\\n10 & 21:46:48.6 & 82:01:46 & 0.183 & 2 & 19.8 \\\\\n11 & 21:47:05.7 & 81:52:35 & 0.144 & 6 & 18.3 \\\\\n12 & 21:47:07.2 & 81:55:36 & 0.145 & 6 & 18.4 \\\\\n13 & 21:47:20.4 & 81:51:40 & 0.149 & 1 & 19.7 \\\\\n14 & 21:47:24.7 & 81:50:40 & 0.173 & 6 & 20.0 \\\\\n15 & 21:47:53.7 & 81:53:43 & 0.208 & 2 & 19.4 \\\\\n16 & 21:48:19.9 & 82:01:03 & 0.143 & 1 & 17.7 \\\\\n17 & 21:48:44.3 & 81:56:59 & 0.148 & 6 & 18.9 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\label{table:redshifts} \n\\end{table}\n\n\\clearpage\n\n\\begin{table}\n\\caption[Giant Radio Galaxies]{Giant Radio Galaxies}\n\\begin{center}\n\\begin{tabular}{c c c c c c}\n\\tableline\n\\tableline\nIAU Name & Other Name & z & LAS & log$P_{1.4}$ & LLS \\\\\n & & & (arcsec) & ($h_{50}^{-2}$ W Hz$^{-1}$) & ($h_{50}^{-1}$ Mpc)\\\\\n\\tableline\n 1003+351 & 3C\\,236 & 0.0989 & 2478 & 26.37 & 6.04\\\\\n{\\bf 2146+82} & {\\bf NVSS 2146+82} & {\\bf 0.1450} & {\\bf 1175} & {\\bf 25.69} & {\\bf 3.91 }\\\\\n 0821+695 & 8C 0821+695 & 0.5380 & 402 & 26.30 & 2.94 \\\\\n 1637+826 & NGC\\,6251 & 0.0230 & 4500 & 24.73 & 2.89 \\\\\n 0319-454 & & 0.0633 & 1644 & 25.83 & 2.72 \\\\\n 1549+202 & 3C\\,326 & 0.0885 & 1206 & 26.08 & 2.67 \\\\\n 1358+305 & B2 1358+305 & 0.2060 & 612 & 25.93 & 2.64 \\\\\n 1029+570 & HB\\,13 & 0.0450 & 2100 & 24.57 & 2.54 \\\\\n 0503-286 & & 0.0380 & 2400 & 25.23 & 2.48 \\\\\n 1452-517 & MRC 1452-517 & 0.08 & 1218 & 25.66 & 2.48 \\\\\n 0114-476 & PKS 0114-476 & 0.1460 & 702 & 26.51 & 2.36 \\\\\n 1127-130 & PKS 1127-130 & 0.6337 & 297 & 27.53 & 2.30 \\\\\n 0707-359 & PKS 0707-359 & 0.2182 & 492 & 26.71 & 2.21 \\\\\n 1910-800 & & 0.3460 & 366 & 26.65 & 2.18 \\\\\n 0745+560 & DA\\,240 & 0.0350 & 2164 & 25.39 & 2.07 \\\\\n 0313+683 & WENSS 0313+683 & 0.0902 & 894 & 25.64 & 2.01 \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\label{table:giants}\n\n\\end{table}\n\n\n\n\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002033.extracted_bib",
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R. \n1996, \\apj, 467, 38 \n\n\\bibitem[Lacy et al.\\ 1993]{lacy93} Lacy, M., Rawlings, S., Saunders, R.,\n\\& Warner, P. J. 1993, \\mnras, 264, 721\n\n\\bibitem[Landolt (1992)]{landolt} Landolt, A. U., 1992, \\aj, 104, 340\n\n\n\\bibitem[Lasker et al.\\ 1990]{dss} Lasker, B. M., Sturch, C. R., McLean, B. J., \nRussell, J. L., Jenkner, H., \\& Shara, M. M., 1990, \\aj, 99, 2019\n\n\\bibitem[Longair \\& Seldner 1979]{longair79} Longair, M. S. \\& \nSeldner, M. 1979, \\mnras, 189, 433 \n\n\\bibitem[Miller et al.\\ (1999)]{miller99} Miller, N. A., Owen, F. N., Burns, J. O., \nLedlow, M. J., \\& Voges, W. 1999, preprint (astro-ph/9908244)\n\n\\bibitem[Monet et al.\\ 1996]{monet96} Monet, D., Bird, A., Canzian, B., Harris, H., \nReid, N., Rhodes, A., Sell, S., Ables, H., Dahn, C., Guetter, H., Henden,\nA., Leggett, S., Levison, H., Luginbuhl, C., Martini, J., Monet, A., Pier, J., \nRiepe, B., Stone, R., Vrba, F., Walker, R.\n1996, USNO-SA1.0, (Washington D.C.: U.S. Naval Observatory)\n\n\\bibitem[Mukai 1993]{Mukai93} Mukai, K. 1993, Legacy 3, 21-31\n\n\\bibitem[Munn et al.\\ (1997)]{munn97} Munn, J. A., Koo, D. C., Kron, R. G., Majewski,\nS. R., Bershady, M. A., \\& Smetanka, J. J., 1997, \\apjs, 109, 45\n\n\\bibitem[Nilsson et al.\\ (1993)]{nilsson}Nilsson, K., Valtonen, M. J., Kotilainen, J., \n\\& Jaakkola, T., 1993, \\apj, 413, 453\n\n\\bibitem[Osterbrock 1989]{osterbrock} Osterbrock, D. E., 1989, Astrophysics of Gaseous\nNebulae and Active Galactic Nuclei, (Mill Valley: University Science Books)\n\n\\bibitem[Parma et al.\\ 1996]{par96}\nParma, P., de Ruiter, H., Mack, K.-H., van Breugel, W., Dey, A., Fanti, R.,\n\\& Klein, U., 1996, \\aap, 311, 49\n\n\\bibitem[Plucinsky et al.\\ 1993]{Plucinsky93} Plucinsky, P. P., Snowden, S. L., \nBriel, U. G., Hasinger, G., \\& Pfeffermann, E. 1993, \\apj, 418, 519\n\n\\bibitem[Prestage \\& Peacock 1988]{prestage88} Prestage, R. M. \\& \nPeacock, J. A. 1988, \\mnras, 230, 131\n\n\\bibitem[Rawlings \\& Saunders 1991]{raw91} Rawlings, S., \\& Saunders, R., 1991,\nNature, 349, 138\n\n\\bibitem[Rengelink et al.\\ 1997]{WENSS}\nRengelink, R. B., Tang, Y., de Bruyn, A. G., Miley, G. K., Bremer, M.\nN., R\\\"ottgering, H. J. A., Bremer, M. A. R. 1997, \\aaps, 124,259\n\n\\bibitem[Sandage (1972)]{sandage72} Sandage, A. R. 1972, \\apj, 178, 25\n\n\\bibitem[Saripalli et al.\\ 1986]{sar86} Saripalli, L., Gopal-Krishna, Reich, W., \n\\& K\\\"{u}hr, H. 1986, \\aap, 170, 20\n\n\\bibitem[Schlegel et al.\\ (1998)]{schlegel} Schlegel, \nD. J., Finkbeiner, D. P. \\& Davis, M. 1998, \\apj, 500, 525 \n\n\\bibitem[Simard-Normandin, Kronberg, \\& Button (1981)]{Simon-Normandin}\nSimard-Normandin, M., Kronberg, P. P., \\& Button, S. 1981, \\apjs, 45, 97\n\n\\bibitem[Snowden 1998]{Snowden98} \nSnowden, S. L. 1998, \\apjs, 117, 233\n\n\\bibitem[Stark et al.\\ 1992]{stark} Stark, A. A., Gammie, C. F., \nWilson, R. W., Bally, J., Linke, R. A., Heiles, C., \\& Hurwitz, M. 1992, \\apjs, 79, 77\n\n\\bibitem[Stetson 1987]{stetson87} Stetson, P. B. 1987, \\pasp, 99, 191\n\n\\bibitem[Strom \\& Willis 1980]{str80}\nStrom, R. G. \\& Willis, A. G. 1980, \\aap, 85, 36\n\n\\bibitem[Subrahmanyan \\& Saripalli 1993]{sub93}\nSubrahmanyan, R. \\& Saripalli, L. 1993, \\mnras, 260, 908\n\n\\bibitem[Tadhunter et al.\\ 1998]{tad98} Tadhunter, C. N., Morganti, R., Robinson, A.,\nDickson, R., Villar-Martin, M., \\& Fosbury, R. A. E. 1998, \\mnras, 298, 1035\n\n\\bibitem[Taylor, Dyson, \\& Axon 1992]{tda92} Taylor, D., Dyson, J. E., \\& Axon,\nD. J. 1992, \\mnras, 255, 351\n\n\\bibitem[Valdes 1982]{valdes82} Valdes, F. 1982, FOCAS User's Manual, (Tucson: NOAO)\n\n\\bibitem[Wan \\& Daly (1996)]{wan96} Wan, L., \\& Daly, R. A. 1996, \\apj, 467, 145\n\n\\bibitem[Whittle 1989]{dmw89} Whittle, M. 1989, in Extranuclear Activity in Galaxies,\ned. E. Meurs \\& R. Fosbury (Munich: ESO), 199\n\n\\bibitem[Willis, Strom, \\& Wilson 1974]{wil74}\nWillis, A. G., Strom, R. G., \\& Wilson, A. S. 1974, {\\it Nature}, 250, 625\n\n\\bibitem[Zirbel 1996]{zirbel96} Zirbel, E. L. 1996, \\apj, 473, 713\n\n\\bibitem[Zirbel 1997]{zirbel97} Zirbel, E. L. 1997, \\apj, 476, 489\n\n\\bibitem[Zirbel \\& Baum 1995]{zirbel95} Zirbel, E. L., \\& Baum, S. A. 1995, \\apj,\n448, 521\n\n\\bibitem[Zwicky et al.\\ 1961]{zwicky} Zwicky, F., Herzog, E., Wild, P.,\nKarpowicz, M., \\& Kowal, C. 1961-68, Catalogue of Galaxies and Clusters\nof Galaxies, (Pasadena: CIT)\n\n\\end{thebibliography}"
}
] |
astro-ph0002034
|
The Detectability of Gamma-Ray Bursts and Their Afterglows at Very High Redshifts
|
[
{
"author": "Donald Q. Lamb and Daniel E. Reichart"
}
] |
There is increasingly strong evidence that gamma-ray bursts (GRBs) are associated with star-forming galaxies, and occur near or in the star-forming regions of these galaxies. These associations provide indirect evidence that at least the long GRBs detected by BeppoSAX are a result of the collapse of massive stars. The recent evidence that the light curves and the spectra of the afterglows of GRB 970228 and GRB 980326 appear to contain a supernova component, in addition to a relativistic shock wave component, provide more direct clues that this is the case. Here we establish that GRBs and their afterglows are both detectable out to very high redshifts ($z \gtrsim 5$). %Consequently, if many GRBs are indeed produced by the collapse of %massive stars, GRBs and their afterglows provide a powerful probe of %the very high redshift universe.
|
[
{
"name": "grb_highz.tex",
"string": "\\documentstyle[psfig]{aipproc}\n\n\\def\\la{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\ga{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\n\\begin{document}\n\\title{The Detectability of Gamma-Ray Bursts and Their \nAfterglows at Very High Redshifts}\n\n\\author{Donald Q. Lamb and Daniel E. Reichart} \n\\address{Department of Astronomy \\& Astrophysics, University of Chicago,\n\\\\ 5640 South Ellis Avenue, Chicago, IL 60637}\n\n\\maketitle\n\n\\begin{abstract}\nThere is increasingly strong evidence that gamma-ray bursts (GRBs) are\nassociated with star-forming galaxies, and occur near or in the\nstar-forming regions of these galaxies. These associations provide\nindirect evidence that at least the long GRBs detected by BeppoSAX are\na result of the collapse of massive stars. The recent evidence that\nthe light curves and the spectra of the afterglows of GRB 970228 and\nGRB 980326 appear to contain a supernova component, in addition to a\nrelativistic shock wave component, provide more direct clues that this\nis the case. Here we establish that GRBs and their afterglows are both\ndetectable out to very high redshifts ($z \\gtrsim 5$).\n%Consequently, if many GRBs are indeed produced by the collapse of\n%massive stars, GRBs and their afterglows provide a powerful probe of\n%the very high redshift universe. \n\\end{abstract}\n\n\\section*{Introduction} \n\nWe first show that the GRBs with well-established redshifts could have been\ndetected out to very high redshifts (VHRs). Then, we show that their\nsoft X-ray, optical, and infrared afterglows could also have been\ndetected out to these redshifts.\n\n\\section*{Detectability of GRBs} \n\nWe first show that GRBs are detectable out to very high redshifts. The\npeak photon number luminosity is \\begin{equation} L_P =\n\\int_{\\nu_l}^{\\nu_u}\\frac{dL_P}{d\\nu}d\\nu \\; , \\end{equation} where\n$\\nu_l < \\nu < \\nu_u$ is the band of observation. Typically, for\nBATSE, $\\nu_l = 50$ keV and $\\nu_u = 300$ keV. The corresponding peak\nphoton number flux $P$ is \\begin{equation} P =\n\\int_{\\nu_l}^{\\nu_u}\\frac{dP}{d\\nu}d\\nu \\; . \\end{equation} Assuming\nthat GRBs have a photon number spectrum of the form $dL_P/d\\nu \\propto\n\\nu^{-\\alpha}$ and that $L_P$ is independent of z, the observed peak\nphoton number flux $P$ for a burst occurring at a redshift $z$ is given\nby \\begin{equation} P = \\frac{L_P}{4\\pi D^2(z)(1+z)^{\\alpha}} \\; ,\n\\end{equation} where $D(z)$ is the comoving distance to the GRB. \nTaking $\\alpha = 1$, which is typical of GRBs [1], Equation (3) coincidentally reduces to the form that one gets\nwhen $P$ and $L_P$ are\nbolometric quantities.\n\nUsing these expressions, we have calculated the limiting redshifts\ndetectable by BATSE and HETE-2, and by {\\it Swift}, for the seven GRBs\nwith well-established redshifts and published peak photon number\nfluxes. In doing so, we have used the peak photon number fluxes given\nin Table 1 of [2], taken a detection threshold of 0.2 ph s$^{-1}$ for BATSE\n[3] and HETE-2 [4] and 0.04 ph s$^{-1}$ for\n{\\it Swift} [5], and set $H_0 = 65$ km s$^{-1}$ Mpc$^{-1}$,\n$\\Omega_m = 0.3$, and $\\Omega_{\\Lambda} = 0.7$ (other cosmologies give\nsimilar results).\n\n\\begin{figure}\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\psfig{file=vhrfig1.ps,width=2.75truein,clip=}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\caption{Cumulative distributions of the limiting redshifts at which\nthe seven GRBs with well-determined redshifts and published peak photon\nnumber fluxes would be detectable by BATSE and HETE-2, and by {\\it\nSwift}.}\n\\end{minipage}\n\\end{figure}\n\nFigure 1 displays the results. This figure shows that BATSE and\nHETE-2 would be able to detect four of these GRBs (GRBs 970228,\n970508, 980613, and 980703) out to redshifts $2 \\lesssim z \\lesssim 4$,\nand three (GRBs 971214, 990123, and 990510) out to redshifts of $20\n\\lesssim z \\lesssim 30$. {\\it Swift} would be able to detect the former\nfour out to redshifts of $5 \\lesssim z \\lesssim 15$, and the latter\nthree out to redshifts in excess of $z \\approx 70$, although it is\nunlikely that GRBs occur at such extreme redshifts (see \\S 3 below). \nConsequently, if GRBs occur at VHRs, BATSE has probably already\ndetected them, and future missions should detect them as well.\n\n\n\\section*{Detectability of GRB Afterglows} \n\nThe soft X-ray, optical and infrared afterglows of GRBs are also\ndetectable out to VHRs. The effects of distance and redshift tend to\nreduce the spectral flux in GRB afterglows in a given frequency band,\nbut time dilation tends to increase it at a fixed time of observation\nafter the GRB, since afterglow intensities tend to decrease with time. \nThese effects combine to produce little or no decrease in the spectral\nenergy flux $F_{\\nu}$ of GRB afterglows in a given frequency band and\nat a fixed time of observation after the GRB with increasing redshift:\n\\begin{equation}\nF_{\\nu}(\\nu,t) = \\frac{L_{\\nu}(\\nu,t)}{4\\pi D^2(z) (1+z)^{1-a+b}},\n\\end{equation}\nwhere $L_\\nu \\propto \\nu^at^b$ is the intrinsic spectral luminosity of\nthe GRB afterglow, which we assume applies even at early times, and\n$D(z)$ is again the comoving distance to the burst. Many afterglows\nfade like $b \\approx -4/3$, which implies that $F_{\\nu}(\\nu,t) \\propto\nD(z)^{-2} (1+z)^{-5/9}$ in the simplest afterglow model where $a =\n2b/3$ [6]. In addition,\n$D(z)$ increases very slowly with redshift at redshifts greater than a\nfew. Consequently, there is little or no decrease in the spectral flux\nof GRB afterglows with increasing redshift beyond $z \\approx 3$. \n\nFor example, [7] find in the case of GRB 980519 that\n$a = -1.05\\pm0.10$ and $b = -2.05\\pm0.04$ so that $1-a+b = 0.00 \\pm\n0.11$, which implies no decrease in the spectral flux with increasing\nredshift, except for the effect of $D(z)$. In the simplest afterglow\nmodel where $a = 2b/3$, if the afterglow declines more rapidly than $b\n\\approx 1.7$, the spectral flux actually {\\it increases} as one moves\nthe burst to higher redshifts! \n\nAs another example, we calculate the best-fit spectral flux\ndistribution of the early afterglow of GRB 970228 from [8], as observed one day after the burst, transformed to various\nredshifts. The transformation involves (1) dimming the\nafterglow,\\footnote{Again, we have set $\\Omega_m = 0.3$ and\n$\\Omega_{\\Lambda} = 0.7$; other cosmologies yield similar results.} (2)\nredshifting its spectrum, (3) time dilating its light curve, and (4)\nextinguishing the spectrum using a model of the Ly$\\alpha$ forest. \nFor the model of the Ly$\\alpha$ forest, we have adopted the best-fit\nflux deficit distribution to Sample 4 of [9] from [10]. At redshifts in excess of $z = 4.4$, this model is an\nextrapolation, but it is consistent with the results of theoretical\ncalculations of the redshift evolution of Ly$\\alpha$ absorbers [11]. Finally, we have convolved\nthe transformed spectra with a top hat smearing function of width\n$\\Delta \\nu = 0.2\\nu$. This models these spectra as they would be\nsampled photometrically, as opposed to spectroscopically; i.e., this\ntransforms the model spectra into model spectral flux distributions.\n\nFigure 2 shows the resulting K-band light curves. For a fixed\nband and time of observation, steps (1) and (2) above dim the afterglow\nand step (3) brightens it, as discussed above. Figure 2 shows that in\nthe case of the early afterglow of GRB 970228, as in the case of GRB\n980519, at redshifts greater than a few the three effects nearly cancel\none another out. Thus the afterglow of a GRB occurring at a redshift\nslightly in excess of $z = 10$ would be detectable at K $\\approx 16.2$\nmag one hour after the burst, and at K $\\approx 21.6$ mag one day after\nthe burst, if its afterglow were similar to that of GRB 970228 (a\nrelatively faint afterglow). \n\nFigure 3 shows the resulting spectral flux distribution. The spectral\nflux distribution of the afterglow is cut off by the Ly$\\alpha$ forest\nat progressively lower frequencies as one moves out in redshift. Thus \nhigh redshift ($1 \\lesssim z \\lesssim 5$) afterglows are characterized\nby an optical ``dropout'' [12], and very high redshift ($z\n\\gtrsim 5$) afterglows by an infrared ``dropout.''\n\n%We also show in Figure 3 the effect of a moderate ($A_V = 1/3$), fixed\n%amount of extinction at the redshift of the GRB. However, the amount\n%of extinction is likely to be very small at large redshifts because of\n%the rapid decrease in metallicity beyond $z = 3$.\n\nIn conclusion, if GRBs occur at very high redshifts, both they and\ntheir afterglows would be detectable.\n\n\\begin{figure}\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\psfig{file=vhrfig2.ps,width=2.75truein,clip=}\n\\caption{The best-fit light curve of the early\nafterglow of GRB 970228 from Reichart (1999), transformed to various\nredshifts.}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\psfig{file=vhrfig3.ps,width=2.75truein,clip=}\n\\caption{The best-fit spectral flux distribution of the\nearly afterglow of GRB 970228 from Reichart (1999), as observed one\nday after the burst, after transforming it to various redshifts, and\nextinguishing it with a model of the Ly$\\alpha$ forest.}\n\\end{minipage}\n\\end{figure}\n\n\\begin{references}\n\\bibitem{mpp00}\nMazzoli, R. S., Pendleton, G. N., \\& Paciesas, W. S. 1996, ApJ, 471, 636\n\\bibitem{lr00}\nLamb, D. Q., \\& Reichart, D. E., 2000, ApJ, in press (astro-ph/9909002)\n\\bibitem{mea93}\nMeegan, C. A., et al. 1993, Second BATSE Catalog\n\\bibitem{r98}\nRicker, G. 1998, BAAS, 30, Abstract 33.14\n\\bibitem{g99}\nGehrels, N. 1999, BAAS, 31, 993\n\\bibitem{wrm97}\nWijers, R. A. M. J., Rees, M. J., \\& M\\'esz\\'aros, P. 1997, MNRAS, 288, L51\n\\bibitem{hea99}\nHalpern, J. P. 1999, ApJ, 517, L105\n\\bibitem{r99}\nReichart, D. E., 1999, ApJ, 521, L111 \n\\bibitem{zl93}\nZuo, L., \\& Lu, L. 1993, ApJ, 418, 601\n\\bibitem{r00}\nReichart, D. E., 2000, ApJ, submitted (astro-ph/9912368)\n\\bibitem{vss99}\nValageas, P., Schaeffer, R., \\& Silk, J. 1999, A\\&A, 345, 691\n\\bibitem{fea99}\nFruchter, A. S. 1999, ApJ, 512, L1\n\\end{references}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002034.extracted_bib",
"string": "\\bibitem{mpp00}\nMazzoli, R. S., Pendleton, G. N., \\& Paciesas, W. S. 1996, ApJ, 471, 636\n\n\\bibitem{lr00}\nLamb, D. Q., \\& Reichart, D. E., 2000, ApJ, in press (astro-ph/9909002)\n\n\\bibitem{mea93}\nMeegan, C. A., et al. 1993, Second BATSE Catalog\n\n\\bibitem{r98}\nRicker, G. 1998, BAAS, 30, Abstract 33.14\n\n\\bibitem{g99}\nGehrels, N. 1999, BAAS, 31, 993\n\n\\bibitem{wrm97}\nWijers, R. A. M. J., Rees, M. J., \\& M\\'esz\\'aros, P. 1997, MNRAS, 288, L51\n\n\\bibitem{hea99}\nHalpern, J. P. 1999, ApJ, 517, L105\n\n\\bibitem{r99}\nReichart, D. E., 1999, ApJ, 521, L111 \n\n\\bibitem{zl93}\nZuo, L., \\& Lu, L. 1993, ApJ, 418, 601\n\n\\bibitem{r00}\nReichart, D. E., 2000, ApJ, submitted (astro-ph/9912368)\n\n\\bibitem{vss99}\nValageas, P., Schaeffer, R., \\& Silk, J. 1999, A\\&A, 345, 691\n\n\\bibitem{fea99}\nFruchter, A. S. 1999, ApJ, 512, L1\n"
}
] |
astro-ph0002035
|
Gamma-Ray Bursts as a Probe of the Very High Redshift Universe
|
[
{
"author": "Donald Q. Lamb and Daniel E. Reichart"
}
] |
We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift ($z \gtrsim 5$) universe.
|
[
{
"name": "T-32.tex",
"string": "\\documentstyle[psfig]{aipproc}\n\n\\def\\la{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\ga{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\n\\begin{document}\n\\title{Gamma-Ray Bursts as a Probe of the Very High Redshift Universe}\n\n\\author{Donald Q. Lamb and Daniel E. Reichart} \n\\address{Department of Astronomy \\& Astrophysics, University of Chicago,\n\\\\ 5640 South Ellis Avenue, Chicago, IL 60637}\n\n\\maketitle\n\n\\begin{abstract} \nWe show that, if many GRBs are indeed produced by the collapse of\nmassive stars, GRBs and their afterglows provide a powerful probe of\nthe very high redshift ($z \\gtrsim 5$) universe. \n\\end{abstract}\n\n\\section*{Introduction} \n\nThere is increasingly strong evidence that gamma-ray bursts (GRBs) are\nassociated with star-forming galaxies [1,2,3,4] and occur near or in\nthe star-forming regions of these galaxies [5,3,4,6,2]. These\nassociations provide indirect evidence that at least the long GRBs\ndetected by BeppoSAX are a result of the collapse of massive stars. \nThe discovery of what appear to be supernova components in the\nafterglows of GRBs 970228 [7,8] and 980326 [9] provides direct evidence\nthat at least some GRBs are related to the deaths of massive stars, as\npredicted by the widely-discussed collapsar model of GRBs\n[10,11,12,13,14,15]. If GRBs are indeed related to the collapse of\nmassive stars, one expects the GRB rate to be approximately\nproportional to the star-formation rate (SFR).\n\n\\section*{GRBs as a Probe of Star Formation}\n\nObservational estimates [16,17,18,19] indicate that\nthe SFR in the universe was about 15 times larger at a redshift $z\n\\approx 1$ than it is today. The data at higher redshifts from the\nHubble Deep Field (HDF) in the north suggests a peak in the SFR at $z\n\\approx 1-2$ [19], but the actual\nsituation is highly uncertain. However, theoretical calculations show\nthat the birth rate of Pop III stars produces a peak in the\nSFR in the universe at redshifts $16 \\lesssim z\n\\lesssim 20$, while the birth rate of Pop II stars produces a much\nlarger and broader peak at redshifts $2 \\lesssim z \\lesssim 10$\n[20,21,22]. Therefore one expects GRBs to occur out to at least $z \\approx\n10$ and possibly $z \\approx 15-20$, redshifts that are far larger than\nthose expected for the most distant quasars. Consequently GRBs may be\na powerful probe of the star-formation history of the universe, and\nparticularly of the SFR at VHRs. \n\n\\begin{figure}\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\psfig{file=T-32-fig01.eps,width=2.75truein,clip=}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\caption{The cosmic SFR $R_{SF}$ as a function of\nredshift $z$. The solid curve at $z < 5$ is the SFR\nderived by [23]; the solid curve at $z \\ge 5$ is the \nSFR calculated by [21] (the dip in\nthis curve at $z \\approx 6$ is an artifact of their numerical\nsimulation). The dotted curve is the SFR derived by\n[19].}\n\\end{minipage}\n\\end{figure}\n\nIn Figure 1, we have plotted the SFR versus redshift from a\nphenomenological fit [23] to the SFR\nderived from submillimeter, infrared, and UV data at redshifts $z < 5$,\nand from a numerical simulation by [21] at redshifts $z \\geq 5$. The simulations done by\n[21] indicate that the SFR increases with\nincreasing redshift until $z \\approx 10$, at which point it levels\noff. The smaller peak in the SFR at $z \\approx 18$ corresponds to the\nformation of Population III stars, brought on by cooling by molecular\nhydrogen. Since GRBs are detectable at these VHRs and their redshifts\nmay be measurable from the absorption-line systems and the Ly$\\alpha$\nbreak in the afterglows [24], if the GRB rate is\nproportional to the SFR, then GRBs could provide unique\ninformation about the star-formation history of the VHR universe.\n\nMore easily but less informatively, one can examine the GRB peak photon\nflux distribution $N_{GRB}(P)$. To illustrate this, we have calculated\nthe expected GRB peak flux distribution assuming (1) that the GRB rate\nis proportional to the SFR\\footnote{This may\nunderestimate the GRB rate at VHRs since it is generally thought that\nthe initial mass function will be tilted toward a greater fraction of\nmassive stars at VHRs because of less efficient cooling due to the\nlower metallicity of the universe at these early times.}, (2) that the\nSFR is that given in Figure 1, and (3) that the peak\nphoton luminosity distribution $f(L_P)$ of the bursts is independent of\n$z$. There is a mis-match of about a factor of three between the $z <\n5$ and $z \\geq 5$ regimes. However, estimates of the star formation\nrate are uncertain by at least this amount in both regimes. We have\ntherefore chosen to match the two regimes smoothly to one another, in\norder to avoid creating a discontinuity in the GRB peak flux\ndistribution that would be entirely an artifact of this mis-match.\n\n%We calculate the observed GRB peak photon flux distribution\n%$N_{GRB}(P)$ as follows. Assuming that GRBs are standard candles of\n%peak photon luminosity $L_P$, the peak photon flux distribution is\n%\\begin{equation}\n%N_{GRB}(P|L_P) = \\Delta T_{obs} \n%\\frac{R_{SF}(z)}{1+z}\\frac{dV(z)}{dz}\\left|\\frac{dz(P|L_P)}{dP}\\right|\n%\\; ,\n%\\end{equation}\n%where $\\Delta T_{obs}$ is the length of time of observation, %$R_{SF}(z)$ is the local co-moving SFR at $z$, \n%\\begin{equation}\n%\\frac{dV(z)}{dz} = 4\\pi %\\frac{d_L^2(z)}{1+z}\\left|\\frac{dt(z)}{dz}\\right|\n%\\end{equation}\n%is the differential comoving volume, $d_L(z)$ is the luminosity %distance,\n%and \n%\\begin{equation}\n%\\frac{dz(P|L_P)}{dP} = \\left[\\frac{dP(z|L_P)}{dz}\\right]^{-1} \\; .\n%\\end{equation}\n%For $\\Omega_m + \\Omega_{\\Lambda} = 1$,\n%\\begin{equation}\n%\\frac{dV(z)}{dz} = 4\\pi D^2(z)\\frac{dD(z)}{dz} \\; ,\n%\\end{equation}\n%where $D(z)$ is the comoving distance. For $dL_P/d\\nu \\propto\n%\\nu^{-\\alpha}$,\n%\\begin{equation}\n%P(z|L_P) = \\frac{L_P}{4\\pi D^2(z)(1+z)^{\\alpha}} \\; .\n%\\end{equation}\n%Taking $\\alpha = 1$, which is typical of GRBs [25], \n%\\begin{equation}\n%P(z|L_P) = \\frac{L_P}{4\\pi D^2(z)(1+z)} \\; .\n%\\end{equation}\n%Then \n%\\begin{equation}\n%\\left|\\frac{dP(z|L_P)}{dz}\\right| = %\\frac{L_P}{4\\pi}\\left[\\frac{2}{D^3(z)(1+z)}\\frac{dD(z)}{dz} + %\\frac{1}{D^2(z)(1+z)^2}\\right].\n%\\end{equation} \n%For a luminosity function $f(L_P)$ and for $dL_P/d\\nu \\propto \n%\\nu^{-\\alpha}$, $N_{GRB}(P)$ is given by the following convolution %integration:\n%\\begin{equation}\n%N_{GRB}(P) = \\int_0^{\\infty}N_{GRB}(P|L_P)\n%f[L_P-4\\pi D^2(z)(1+z)^{\\alpha}P]dL_P \\; .\n%\\end{equation}\n\nFor a peak luminosity function $f(L_P)$ and for $dL_P/d\\nu \\propto \n\\nu^{-\\alpha}$, the observed GRB peak flux distribution $N_{GRB}(P)$ is given by the following convolution integration:\n\\begin{equation}\nN_{GRB}(P) = \\Delta T_{obs} \\int_0^{\\infty}R_{GRB}(P|L_P)f[L_P-4\\pi D^2(z)(1+z)^{\\alpha}P]dL_P \\; ,\n\\end{equation}\nwhere $\\Delta T_{obs}$ is the length of time of observation, $D(z)$ is comoving distance,\n\\begin{equation}\nR_{GRB}(P|L_P) \\propto \n\\frac{R_{SF}(z)}{1+z}\\frac{dV(z)}{dz}\\left|\\frac{dz(P|L_P)}{dP}\\right|\n\\; ,\n\\end{equation}\n$R_{SF}(z)$ is the local co-moving SFR at $z$, and $dV(z)/dz$ is differential comoving volume [24].\n\n\\begin{figure}[t]\n\\psfig{file=T-32-fig02.eps,width=5.75truein,clip=} \n\\caption{Top panel: The number $N_*$ of stars expected as a function\nof redshift $z$ (i.e., the SFR from Figure 1, weighted\nby the differential comoving volume, and time-dilated) assuming that\n$\\Omega_M = 0.3$ and $\\Omega_\\Lambda = 0.7$. Bottom panel: The\ncumulative distribution of the number $N_*$ of stars expected as a\nfunction of redshift $z$. Note that $\\approx 40\\%$ of all stars have\nredshifts $z > 5$. The solid and dashed curves in both panels have the\nsame meanings as in Figure 1.}\n\\end{figure}\n\nThe left panel of Figure 2 shows the number $N_*(z)$ of stars expected\nas a function of redshift $z$ (i.e., the SFR, weighted\nby the co-moving volume, and time-dilated) for an assumed cosmology\n$\\Omega_M = 0.3$ and $\\Omega_\\Lambda = 0.7$ (other cosmologies give\nsimilar results). The solid curve corresponds to the star-formation\nrate in Figure 1. The dashed curve corresponds to the star-formation\nrate derived by [19]. This figure shows that $N_*(z)$\npeaks sharply at $z \\approx 2$ and then drops off fairly rapidly at\nhigher $z$, with a tail that extends out to $z \\approx 12$. The rapid\nrise in $N_*(z)$ out to $z \\approx 2$ is due to the rapidly increasing\nvolume of space. The rapid decline beyond $z \\approx 2$ is due almost\ncompletely to the ``edge'' in the spatial distribution produced by the\ncosmology. In essence, the sharp peak in $N_*(z)$ at $z \\approx 2$\nreflects the fact that the SFR we have taken is fairly\nbroad in $z$, and consequently, the behavior of $N_*(z)$ is dominated\nby the behavior of the co-moving volume $dV(z)/dz$; i.e., the shape of\n$N_*(z)$ is due almost entirely to cosmology. The right panel in\nFigure 2 shows the cumulative distribution $N_*(>z)$ of the number of\nstars expected as a function of redshift $z$. The solid and dashed\ncurves have the same meaning as in the upper panel. This figure shows\nthat $\\approx 40\\%$ of all stars have redshifts $z > 5$.\n\n\\begin{figure}\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\psfig{file=T-32-fig03.eps,width=2.75truein,clip=}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{2.75truein}\n\\mbox{}\\\\\n\\caption{Top panel: The differential peak photon flux distribution of\nGRBs, assuming that (1) the GRB rate is proportional to the\nSFR, (2) the SFR is that shown in\nFigure 1; and (3) the bursts are standard candles with a peak photon\nluminosity $L_P = 10^{58}$ ph cm$^{-2}$ s$^{-1}$ (solid curve), or have\na logarithmically flat peak photon luminosity function that spans a\nfactor of 10, 100, or 1000 (dashed curves). Approximate detection\nthresholds are plotted for BATSE and HETE-2, and for {\\it Swift}\n(dotted lines). Middle panel: The cumulative peak photon flux\ndistribution of GRBs for the same luminosity functions. Lower panel: \nThe fraction of GRBs with peak photon flux $P$ that have redshifts of\n$z \\ga 5$ for the same luminosity functions. In all three panels, the \ndotted hashes mark the peak photon fluxes of the bursts with known peak\nphoton luminoisities and redshifts .}\n\\end{minipage}\n\\end{figure}\n\nThe upper panel of Figures 3 shows the predicted peak photon flux\ndistribution $N_{GRB}(P)$. The solid curve assumes that all bursts\nhave a peak (isotropic) photon luminosity $L_P = 10^{58}$ ph s$^{-1}$. \nHowever, there is now overwhelming evidence that GRBs are not\n``standard candles.'' Consequently, we also show in Figure 3, as an\nillustrative example, the convolution of this same SFR\nand a logarithmically flat photon luminosity function $f(L_P)$\ncentered on $L_P = 10^{58}$ ph s$^{-1}$, and having widths $\\Delta L_P\n/ L_P = 10$, 100 and 1000.\\footnote{The seven bursts with\nwell-determined redshifts and published peak (isotropic) photon\nluminosities have a mean peak photon luminosity and sample variance\n$\\log L_P = 58.1 \\pm 0.7$.} The actual luminosity function of GRBs\ncould well be even wider [25]. \n\nThe middle panel of Figure 3 shows the predicted cumulative peak photon\nflux distribution $N_{GRB}(> P)$ for the same luminosity function. For\nthe SFR that we have assumed, we find that, if GRBs are\nassumed to be ``standard candles,'' the predicted peak photon flux\ndistribution falls steeply throughout the BATSE and HETE-2 regime, and\ntherefore fails to match the observed distribution, in agreement with\nearlier work. In fact, we find that a photon luminosity function\nspanning at least a factor of 100 is required in order to obtain\nsemi-quantitative agreement with the principle features of the observed\ndistribution; i.e., a roll-over at a peak photon flux of $P \\approx 6$\nph cm$^{-2}$ s$^{-1}$ and a slope above this of about -3/2. This\nimplies that there are large numbers of GRBs with peak photon number\nfluxes below the detection threshold of BATSE and HETE-2, and even of\n{\\it Swift}. \n\nThe lower panel of Figure 3 shows the predicted fraction of bursts with\npeak photon number flux $P$ that have redshifts of $z > 5$, for the\nsame luminosity functions. This panel shows that a significant fraction\nof the bursts near the {\\it Swift} detection threshold will have\nredshifts of $z > 5$.\n\n\n\\section*{Conclusions}\n\nWe have shown that, if many GRBs are indeed produced by the collapse of\nmassive stars, one expects GRBs to occur out to at least $z \\approx 10$\nand possibly $z \\approx 15-20$, redshifts that are far larger than\nthose expected for the most distant quasars. GRBs therefore give us\ninformation about the star-formation history of the universe, including\nthe earliest generations of stars. The absorption-line systems and the\nLy$\\alpha$ forest visible in the spectra of GRB afterglows can be used\nto trace the evolution of metallicity in the universe, and to probe the\nlarge-scale structure of the universe at very high redshifts. Finally,\nmeasurement of the Ly$\\alpha$ break in the spectra of GRB afterglows\ncan be used to constrain, or possibly measure, the epoch at which\nre-ionization of the universe occurred, using the Gunn-Peterson test. \nThus GRBs and their afterglows may be a powerful probe of the very high\nredshift ($z \\gtrsim 5$) universe.\n\n\\begin{references}\n\\bibitem{cl99}\nCastander, F. J., \\& Lamb, D. Q. 1999, ApJ, 523, 593 \n\\bibitem{fea99a}\nFruchter, A. S., et al. 1999, ApJ, 516, 683 \n\\bibitem{kea98}\nKulkarni, S. R., et al. 1998, Nature, 395, 663\n\\bibitem{f99}\nFruchter, A. S. 1999, ApJ, 516, 683\n\\bibitem{sea97a}\nSahu, K. C., et al. 1997, Nature, 387, 476\n\\bibitem{kea99}\nKulkarni, S. R., et al. 1999, Nature, 398, 389\n\\bibitem{r99}\nReichart, D. E., 1999, ApJ, 521, L111 \n\\bibitem{gea99}\nGalama, T. J., et al. 2000, ApJ, submitted (astro-ph/9907264) \n\\bibitem{bea99}\nBloom, J. S., et al. 1999, Nature, 401, 453 \n\\bibitem{w93}\nWoosley, S. E. 1993, ApJ, 405, 273 \n\\bibitem{w96}\nWoosley, S. E. 1996, in Gamma-Ray Bursts, eds. C. A. Meegan, R. D. Preece, \\& T. M. Koshut (New York: AIP), 520\n\\bibitem{p98}\nPaczy\\'nski, B. 1998, ApJ, 494, L45\n\\bibitem{mw99}\nMacFadyen, A. I., \\& Woosley, S. E. 1999, ApJ, 524, 262\n\\bibitem{wea99}\nWheeler, J. C., et al. 1999, ApJ, submitted (astro-ph/9909293)\n\\bibitem{mw99}\nMacFadyen, A. I., Woosley, S. E., \\& Heger A. 1999, ApJ, submitted (astro-ph/9910034)\n\\bibitem{gea95}\nGallego, J. 1995, ApJ, 455, L1\n\\bibitem{lea96}\nLilly, S.~J., et al. 1996, ApJ, 460, L1\n\\bibitem{cea97}\nConnolly, A.~J. 1997, ApJ, 486, L11\n\\bibitem{mpd98}\nMadau, P., Pozzetti, L., \\& Dickinson, M. 1998, ApJ, 498, 106\n\\bibitem{og96}\nOstriker, J. P., \\& Gnedin, N. Y. 1996, ApJ, 472, L63\n\\bibitem{go97}\nGnedin, N. Y., \\& Ostriker, J. P. 1997, ApJ, 486, 581\n\\bibitem{vs99}\nValageas, P., \\& Silk, J. 1999, A\\&A, 347, 1\n\\bibitem{r99}\nRowan-Robinson, M. 1999, Astroph. \\& Space Sci., in press (astro-ph/9906308)\n\\bibitem{lr2000}\nLamb, D. Q., \\& Reichart, D. E. 2000, ApJ, in press (astro-ph/9912368)\n%\\bibitem{mpp00}\n%Mazzoli, R. S., Pendleton, G. N., \\& Paciesas, W. S. 1996, ApJ, 471, 636\n\\bibitem{lw98}\nLoredo, T.~J., \\& Wasserman, I.~M. 1998, ApJ, 502, 108\n\n\n\\end{references}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002035.extracted_bib",
"string": "\\bibitem{cl99}\nCastander, F. J., \\& Lamb, D. Q. 1999, ApJ, 523, 593 \n\n\\bibitem{fea99a}\nFruchter, A. S., et al. 1999, ApJ, 516, 683 \n\n\\bibitem{kea98}\nKulkarni, S. R., et al. 1998, Nature, 395, 663\n\n\\bibitem{f99}\nFruchter, A. S. 1999, ApJ, 516, 683\n\n\\bibitem{sea97a}\nSahu, K. C., et al. 1997, Nature, 387, 476\n\n\\bibitem{kea99}\nKulkarni, S. R., et al. 1999, Nature, 398, 389\n\n\\bibitem{r99}\nReichart, D. E., 1999, ApJ, 521, L111 \n\n\\bibitem{gea99}\nGalama, T. J., et al. 2000, ApJ, submitted (astro-ph/9907264) \n\n\\bibitem{bea99}\nBloom, J. S., et al. 1999, Nature, 401, 453 \n\n\\bibitem{w93}\nWoosley, S. E. 1993, ApJ, 405, 273 \n\n\\bibitem{w96}\nWoosley, S. E. 1996, in Gamma-Ray Bursts, eds. C. A. Meegan, R. D. Preece, \\& T. M. Koshut (New York: AIP), 520\n\n\\bibitem{p98}\nPaczy\\'nski, B. 1998, ApJ, 494, L45\n\n\\bibitem{mw99}\nMacFadyen, A. I., \\& Woosley, S. E. 1999, ApJ, 524, 262\n\n\\bibitem{wea99}\nWheeler, J. C., et al. 1999, ApJ, submitted (astro-ph/9909293)\n\n\\bibitem{mw99}\nMacFadyen, A. I., Woosley, S. E., \\& Heger A. 1999, ApJ, submitted (astro-ph/9910034)\n\n\\bibitem{gea95}\nGallego, J. 1995, ApJ, 455, L1\n\n\\bibitem{lea96}\nLilly, S.~J., et al. 1996, ApJ, 460, L1\n\n\\bibitem{cea97}\nConnolly, A.~J. 1997, ApJ, 486, L11\n\n\\bibitem{mpd98}\nMadau, P., Pozzetti, L., \\& Dickinson, M. 1998, ApJ, 498, 106\n\n\\bibitem{og96}\nOstriker, J. P., \\& Gnedin, N. Y. 1996, ApJ, 472, L63\n\n\\bibitem{go97}\nGnedin, N. Y., \\& Ostriker, J. P. 1997, ApJ, 486, 581\n\n\\bibitem{vs99}\nValageas, P., \\& Silk, J. 1999, A\\&A, 347, 1\n\n\\bibitem{r99}\nRowan-Robinson, M. 1999, Astroph. \\& Space Sci., in press (astro-ph/9906308)\n\n\\bibitem{lr2000}\nLamb, D. Q., \\& Reichart, D. E. 2000, ApJ, in press (astro-ph/9912368)\n%\n\\bibitem{mpp00}\n%Mazzoli, R. S., Pendleton, G. N., \\& Paciesas, W. S. 1996, ApJ, 471, 636\n\n\\bibitem{lw98}\nLoredo, T.~J., \\& Wasserman, I.~M. 1998, ApJ, 502, 108\n\n\n"
}
] |
astro-ph0002036
|
The Merger Rate to Redshift One from Kinematic Pairs: \\ Caltech Faint Galaxy Redshift Survey XI
|
[
{
"author": "R.~G.~Carlberg\\altaffilmark{1,2}"
},
{
"author": "Judith~G.~Cohen\\altaffilmark{3}"
},
{
"author": "D.~R.~Patton\\altaffilmark{1,2}"
},
{
"author": "Roger~Blandford\\altaffilmark{4}"
},
{
"author": "David~W.~Hogg\\altaffilmark{5,6}"
},
{
"author": "H.~K.~C.~Yee\\altaffilmark{1,2}"
},
{
"author": "S.~L.~Morris\\altaffilmark{1,7}"
},
{
"author": "H.~Lin\\altaffilmark{1,6,8}"
},
{
"author": "Lennox L. Cowie\\altaffilmark{9,10}"
},
{
"author": "Esther Hu\\altaffilmark{9,10}"
},
{
"author": "and Antoinette Songaila\\altaffilmark{9,10}"
}
] |
The rate of mass accumulation due to galaxy merging depends on the mass, density, and velocity distribution of galaxies in the near neighborhood of a host galaxy. The fractional luminosity in kinematic pairs combines all of these effects in a single estimator which is relatively insensitive to population evolution. Here we use a k-corrected and evolution compensated volume-limited sample having an R-band absolute magnitude of $M_R^{k,e} \le -19.8+5\log{h}$ mag drawing about 300 redshifts from CFGRS and 3000 from CNOC2 to measure the rate and redshift evolution of merging. The combined sample has an approximately constant co-moving number and luminosity density from redshift 0.1 to 1.1 ($\Omega_M=0.2, \Omega_\Lambda=0.8$); hence, any merger evolution will be dominated by correlation and velocity evolution, not density evolution. We identify kinematic pairs with projected separations less than either 50 or 100 \hkpc\ and rest-frame velocity differences of less than 1000\kms. The fractional luminosity in pairs is modeled as $f_L(\Delta v,r_p,M_r^{ke})(1+z)^{m_L}$ where $[f_L,m_L]$ are $[0.14\pm0.07,0\pm1.4]$ and $[0.37\pm0.7,0.1\pm0.5]$ for $r_p\le 50$ and 100\hkpc, respectively ($\Omega_M=0.2, \Omega_\Lambda=0.8$). The value of $m_L$ is about 0.6 larger if $\Lambda=0$. To convert these redshift space statistics to a merger rate we use the data to derive a conversion factor to physical space pair density, a merger probability and a mean in-spiral time. The resulting mass accretion rate per galaxy ($M_1,M_2\ge 0.2 M_\ast$) is $0.02\pm0.01(1+z)^{0.1\pm0.5} M_\ast~{Gyr}^{-1}$. Present day high-luminosity galaxies therefore have accreted approximately $0.15M_\ast$ of their mass over the approximately 7 Gyr to redshift one. Since merging is likely only weakly dependent on host mass, the fractional effect, $\delta M/M \simeq 0.15M_\ast/M$, is dramatic for lower mass galaxies but is, on the average, effectively perturbative for galaxies above $M_\ast$.
|
[
{
"name": "merger.tex",
"string": "\\def\\km{{\\rm\\,km}}\n\\def\\cms{{\\rm\\,cm\\,s^{-1}}}\n\\def\\kms{\\ifmmode{\\,\\hbox{km}\\,s^{-1}}\\else {\\rm\\,km\\,s$^{-1}$}\\fi}\n\\def\\kpc{{\\rm\\,kpc}}\n\\def\\mpc{{\\rm\\,Mpc}}\n\\def\\msun{{\\rm\\,M_\\odot}}\n\\def\\lsun{{\\rm\\,L_\\odot}}\n\\def\\rsun{{\\rm\\,R_\\odot}}\n\\def\\pc{{\\rm\\,pc}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\yr{{\\rm\\,yr}}\n\\def\\gyr{{\\rm\\,Gyr}}\n\\def\\au{{\\rm\\,AU}}\n\\def\\AU{{\\rm\\,AU}}\n\\def\\gm{{\\rm\\,g}}\n\\def\\kmsm{{\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}}\n\\def\\kmps{{\\rm\\,km\\,s^{-1}}}\n\\def\\hmpc{\\ifmmode{h^{-1}\\,\\hbox{Mpc}}\\else{$h^{-1}$\\thinspace Mpc}\\fi}\n\\def\\hkpc{\\ifmmode{\\,h^{-1}\\,{\\rm kpc}}\\else {$h^{-1}$\\,kpc}\\fi}\n\\def\\eg{{\\it e.g.}~}\n\\def\\etal{{\\it et~al.}~}\n\\def\\et{{\\it et~al.}~}\n\\def\\cf{{\\it cf.}~}\n\\def\\ie{{\\it i.e.}~}\n\n%\\documentclass[preprint]{aastex}\n\\documentclass{aastex}\n%\\usepackage{emulateapj}\n\n%\\slugcomment{DRAFT: \\today}\n\n\\begin{document}\n\n\\title{The Merger Rate to Redshift One from Kinematic Pairs: \\\\\nCaltech Faint Galaxy Redshift Survey XI}\n\n\\author{R.~G.~Carlberg\\altaffilmark{1,2},\nJudith~G.~Cohen\\altaffilmark{3},\nD.~R.~Patton\\altaffilmark{1,2},\nRoger~Blandford\\altaffilmark{4},\nDavid~W.~Hogg\\altaffilmark{5,6},\nH.~K.~C.~Yee\\altaffilmark{1,2},\nS.~L.~Morris\\altaffilmark{1,7},\nH.~Lin\\altaffilmark{1,6,8},\nLennox L. Cowie\\altaffilmark{9,10}, \nEsther Hu\\altaffilmark{9,10},\nand\nAntoinette Songaila\\altaffilmark{9,10}\n}\n\n\\altaffiltext{1}{Visiting Astronomer, Canada--France--Hawaii Telescope, \n which is operated by the National Research Council of Canada,\n le Centre National de Recherche Scientifique, and the University \n\tof Hawaii.}\n\\altaffiltext{2}{Department of Astronomy, University of Toronto, \n Toronto ON, M5S~3H8 Canada}\n\\altaffiltext{3}{Department of Astronomy, Caltech 105-24, \n\tPasadena, CA 91125}\n\\altaffiltext{4}{Theoretical Astrophysics, Caltech 130-33,\n\tPasadena, CA 91125}\n\\altaffiltext{5}{Institute for Advanced Study, Olden Lane,\n\tPrinceton, NJ 08540}\n\\altaffiltext{6}{Hubble Fellow}\n\\altaffiltext{7}{Dominion Astrophysical Observatory, \n Herzberg Institute of Astrophysics, , \n National Research Council of Canada,\n 5071 West Saanich Road,\n Victoria, BC, V8X~4M6, Canada}\n\\altaffiltext{8}{Steward Observatory, University of Arizona,\n Tucson, AZ, 85721}\n\\altaffiltext{9}{Visiting Astronomer, W. M. Keck Observatory, jointly\n\toperated by the California Institute of Technology and the\n\tUniversity of California.}\n\\altaffiltext{10}{Institute for Astronomy, University of Hawaii,\n\t2680 Woodlawn Drive, Honolulu, HI 97822}\n\n\n\\begin{abstract} \nThe rate of mass accumulation due to galaxy merging depends on the\nmass, density, and velocity distribution of galaxies in the near\nneighborhood of a host galaxy. The fractional luminosity in kinematic\npairs combines all of these effects in a single estimator which is\nrelatively insensitive to population evolution. Here we use a\nk-corrected and evolution compensated volume-limited sample having an\nR-band absolute magnitude of $M_R^{k,e} \\le -19.8+5\\log{h}$ mag\ndrawing about 300 redshifts from CFGRS and 3000 from CNOC2 to measure\nthe rate and redshift evolution of merging. The combined sample has\nan approximately constant co-moving number and luminosity density from\nredshift 0.1 to 1.1 ($\\Omega_M=0.2, \\Omega_\\Lambda=0.8$); hence, any\nmerger evolution will be dominated by correlation and velocity\nevolution, not density evolution. We identify kinematic pairs with\nprojected separations less than either 50 or 100 \\hkpc\\ and rest-frame\nvelocity differences of less than 1000\\kms. The fractional luminosity\nin pairs is modeled as $f_L(\\Delta v,r_p,M_r^{ke})(1+z)^{m_L}$ where\n$[f_L,m_L]$ are $[0.14\\pm0.07,0\\pm1.4]$ and $[0.37\\pm0.7,0.1\\pm0.5]$\nfor $r_p\\le 50$ and 100\\hkpc, respectively ($\\Omega_M=0.2,\n\\Omega_\\Lambda=0.8$). The value of $m_L$ is about 0.6 larger if\n$\\Lambda=0$. To convert these redshift space statistics to a merger\nrate we use the data to derive a conversion factor to physical space\npair density, a merger probability and a mean in-spiral time. The\nresulting mass accretion rate per galaxy ($M_1,M_2\\ge 0.2 M_\\ast$) is\n$0.02\\pm0.01(1+z)^{0.1\\pm0.5} M_\\ast~{\\rm Gyr}^{-1}$. Present day\nhigh-luminosity galaxies therefore have accreted approximately\n$0.15M_\\ast$ of their mass over the approximately 7 Gyr to redshift\none. Since merging is likely only weakly dependent on host mass, the\nfractional effect, $\\delta M/M \\simeq 0.15M_\\ast/M$, is dramatic for\nlower mass galaxies but is, on the average, effectively perturbative\nfor galaxies above $M_\\ast$.\n\\end{abstract}\n\n\\keywords{cosmology: large scale structure, galaxies: evolution}\n\n\\section{Introduction}\n\nMerging is a fundamental mode of stellar mass addition to galaxies.\nMoreover, merging brings in new gas and creates gravitational\ndisturbances that enhance star formation or fuel a nuclear black hole.\nThe general process of substructure infall may be the rate fixing\nprocess for the buildup of a galaxy's stars and consequently may\nlargely regulate its luminosity history. Gravitational forces on\nrelatively large scales dominate merger dynamics which allows direct\nobservation of the mechanism, although with the considerable\ncomplication that dark matter dominates the mass. N-body simulations\n\\citep{tt,bh} give the detailed orbital evolution, morphological\ndisturbances and eventual outcomes of the encounters of pairs of\ngalaxies.\n\nThe purpose of this paper is to estimate the rate of mass gain per\ngalaxy due to mergers over the redshift zero to one interval. Our\nprimary statistic is the fractional luminosity in close kinematic\npairs, which is readily related to n-body simulations and sidesteps\nmorphological interpretation. This approach provides a clear sample\ndefinition which is closely connected to the large scale dynamics of\nmerging. In common with all merger estimates it requires an estimate\nof the fraction of the pairs that will merge and a mean time to\nmerger.\n\nThe number of kinematic pairs is proportional to the volume integral\nat small scales of the product of two-point correlation function,\n$\\xi$, and the luminosity function (LF). The high luminosity\ngalaxies appear to be evolving purely in luminosity\n\\citep{cfrs_lf,huan_lf}, which can be easily compensated. \nThe measured evolution of $\\xi$ suggests that the density of physical\npairs should not vary much with redshift, $(1+z)^{0\\pm1}$\n\\citep{cfrsxi,kkeck,cnoc_xi}. This inference is in notable contrast with the\npair counts or morphological typing approaches to merger estimation\n\\citep{zk,cpi,ye_pairs,patton_cnoc1,cfrs_mg}, which suggest that\nmerging rate by number varies as $(1+z)^{3\\pm1}$. HST\nphotometric pairs, with no redshift information leads to \na dependence of $(1+z)^{1.2\\pm0.4}$ \\citep{mdss}.\n\nIn the next section we combine the Caltech Faint Galaxy Redshift\nSurvey (CFGRS) and the Canadian Network for Observational Cosmology\nfield galaxy survey (CNOC2) from which we construct evolution\ncompensated, volume-limited, subsamples. In Section 3 we measure the\nfractional luminosity in 50 and 100\\hkpc\\ companions as a function of\nredshift. The CNOC2 sample is used in Section 4 to relate this wide\npair sample to a close pair sample which is more securely converted\ninto a mass merger rate. Section 5 discusses our conclusions. We\nuse $H_0= 100h\\kmsm$, $\\Omega_M=0.2$ in open and flat cosmologies.\n\n\\section{The CFGRS and CNOC2 Volume-Limited Samples}\n\nThe CFGRS sample of the HDF plus flanking fields is discussed in\ndetail elsewhere \\citep{cfgrs_phot,cfgrs_z}. We use the high coverage\nsubsample lying within a 240 arcsecond radius circle, with a center\nlocated at 12$^h$ 36$^m$ 50$^s$ and 62$^\\circ$ 12$^\\prime$\n55$^{\\prime\\prime}$ (J2000). The computed magnitude selection\nfunction, $s(m_R)$, (in Cousins R) is accurately approximated as a\nconstant 90\\% spectroscopic completeness for $m_R<22.8$ mag with a\nlinear decline to 19\\% at $m_R<23.4$ mag, our sample limit. The\nmagnitude weight is $1/s(m_R)$. The CFGRS k-corrections and evolution\ncompensation are here approximated as $k(z)= K z$ mag from the tables\nof Poggianti (1997). For galaxies that Cohen et al. (2000) classify as\n``E'' (emission), $K=1.0$, ``A'' types have $K=2.0$ and all types have\n$K=1.7$\n\nThe CNOC2 selection weights and k-corrections are discussed in Yee et\nal. (2000). . The evolution of the luminosity function is\napproximated as a uniform $M_\\ast(z) = M_\\ast-Qz$, with $Q\\simeq 1$,\n\\citep{huan_lf} which we use over the entire CNOC2-CFGRS redshift range.\n\nThe kinematic pair fraction is directly proportional to the mean\ndensity of the sample and is therefore sensitively dependent on\ncorrecting to a complete and uniform sample \\citep{patton_ssrs2}. The\nmost straightforward approach is to impose a strict volume limit. For\nour primary sample we will limit the CFGRS and the CNOC2 samples at\n$M_R^{k,e} = -19.8+5\\log{h}$ mag, which yields volume-limited samples\nof about 300 CFGRS galaxies between redshift 0.3 to 1.1 and 3000 CNOC2\ngalaxies between 0.1 to 0.5. The volume density of the sample is\napproximately constant at $1.2\\times10^{-2} h^3$ Mpc$^{-3}$ over the\nentire redshift range for $\\Omega_\\Lambda=0.8$ but rises roughly as\n$(1+z)^{0.8}$ for $\\Omega_\\Lambda=0$. Both the CFGRS and the CNOC2\nsurveys are multiply masked, which minimizes the effects of slit\ncrowding, however there is still a measurable pair selection function.\nThe CNOC2 catalogue has about a 20\\% deficiency of close angular\npairs. We model the measured angular pair selection weight as,\n$w(\\theta) =[1+a_s {\\rm tanh}(\\theta/\\theta_s)]^{-1},$ where\n$[a_s,\\theta_s]$ is $[0.5,5^{\\prime\\prime}]$ for the CFGRS sample and\n$[-0.3,10^{\\prime\\prime}]$ for the CNOC2 sample with typical pair\ncorrections being 10\\%.\n\n\\section{The Pair Fractional Luminosity Fraction}\n\nThe preferred choice of pair statistic depends on the application\n\\citep{patton_ssrs2}. Here we are primarily interested in the impact\nof merging on galaxy mass increase, for which the k-corrected,\nevolution compensated R luminosity is a stand-in. The rate of merging\nper galaxy depends on the density of galaxies in the near\nneighborhood and their velocity distribution. As a practical redshift\nspace estimator, we compute the fractional luminosity in close kinematic pairs,\n\\begin{equation}\nf_L(z|\\Delta v^{\\rm max},r_p^{\\rm max}, M_R^{k,e}) = {{\\sum_j \n\t\\sum_{i\\ne j,<\\Delta v^{\\rm max},<r_P^{\\rm max}} \n\tw_j w_i w(\\theta_{ij})\n\tL_i }\\over\n\t{\\sum_j w_j L_j}},\n\\label{eq:fl}\n\\end{equation}\nwhere the weights, $w_i$, allow for the magnitude selection function.\nNote that the $ij$ and $ji$ pairs are both counted. The ratio has the\nbenefit of being fairly stable for different luminosity limits,\nself-normalizing for luminosity evolution, identical to a mass ratio\nfor a fixed $M/L$ population. For an unperturbed pair luminosity\nfunction it is mathematically identical to the $N_c$ of Patton \\et\\\n(2000a) although constructed out of somewhat different quantities. The\ntwo parameters, $\\Delta v^{\\rm max}$ and $r_p^{\\rm max}$, are chosen\non the basis of merger dynamics and the characteristics of the\nsample. The rate of mass increase per galaxy is calculated from this\nstatistical estimator using a knowledge of merger dynamics and the\nmeasured correlations and kinematics of galaxy pairs in the sample.\n\nThe mean fractional pair luminosity, based on 18 CFGRS pairs and 91\nCNOC2 pairs, with $\\Delta v\\le 1000\n\\kms$ and $5\\le r_p \\le 50\\hkpc$ pairs is displayed in Figure~1. \nThese kinematic separation parameters are larger than is suitable for\nreliably identifying ``soon-to-merge'' pairs. However, they provide a\nstatistically robust connection to those pairs and take into account\nthe lower velocity precision and sample size of the CFGRS relative to\nCNOC2. The errors are computed from the pair counts,\n$n_p^{-1/2}$. The measurements of $f_L(z)$ in Figure~1 are fit to\n$f_L(\\Delta v,r_p,M_r^{ke})(1+z)^{m_L}$, finding $[f_L,m_L]$ of\n$[0.14\\pm0.07,0\\pm1.4]$ for $r_p \\le 50\\hkpc$ pairs and\n$[0.37\\pm0.7,0.1\\pm0.5]$ for $ r_p\\le 100\\hkpc$, both for\n$\\Omega_M=0.2, \\Omega_\\Lambda=0.8$. The increase with $r_p$ of $f_L$\nis consistent with a $\\gamma=1.8$ two-point correlation function. If\n$\\Omega_M=0.3, \\Omega_\\Lambda=0.7$, then $m_L$ at 100\\hkpc\\ rises by\nabout 0.05 whereas if $\\Omega_M=0.2,\n\\Omega_\\Lambda=0.0$, then $m_L=0.50$. The increase\nis largely as a result of the rise in the implied co-moving sample\ndensity over this redshift range. \n\nThe merger probability of a kinematic pair depends sensitively on the\npairwise velocity dispersion, $\\sigma_{12}$, of galaxies. The model\npairwise velocity distribution is computed as the convolution of the\ncorrelation function with the distribution of random velocities. The\ninfall velocities are negligible at these small separations and we\nwill assume that the peculiar velocities are drawn from a Gaussian\ndistribution. The measured fraction of the CNOC2 pair sample with\nvelocities smaller than some $\\Delta v$, normalized to the value at\n1000\\kms, is displayed in Figure~2. The 50\\hkpc\\ wide pairs limited at\n$-19.5$ mag are plotted as open squares, the 20\\hkpc\\ pairs limited at\n$-18.5$ and $-19.5$ mag are plotted as octagons and diamonds,\nrespectively. The upper curve assumes that $\\sigma_{12}$ is 200 \\kms\\\nand the lower one 300\n\\kms, which approximately span the data.\n\n\\section{Merger Rate Estimation}\n\nThe merger rate is best estimated from very close kinematic pairs,\n20\\hkpc\\ or less, about half of which are physically close and have\nsignificant morphological disturbance \\cite{patton_ssrs2}. However the\nfraction of galaxies in such close pairs is about one percent, giving\npoor statistics. Since the number of pairs increases smoothly as\n$r^{3-\\gamma}$, where $\\gamma$ is the slope of the small scale\ncorrelation function, we can use pairs at somewhat larger separations\nas statistically representative of the close pairs, however we prefer\nto stay within the radius of virialized material around a galaxy over\nour redshift range, which is no larger than about 100\\hkpc. The mass\naccretion rate from major mergers is therefore estimated as,\n\\begin{equation}\n{\\cal R}_M = {1\\over 2} f_L(\\Delta v, r_p,z) C_{zs}(\\Delta v,\\gamma) \n\tF(v<v_{mg})\n\t\\langle M \\rangle T_{mg}^{-1}(z,r_p),\n\\label{eq:mgf}\n\\end{equation}\nwhere the factor of one half allows for the double counting of pairs,\n$C_{zs}(\\Delta v,\\gamma)$ converts from redshift space to real space pairs, F\ngives the fraction of the pairs that will merge in the next $T_{mg}$\n(the ``last orbit'' in-spiral time from $r_p$) and $\\langle M\n\\rangle$ is the mean incoming mass as estimated assuming a constant\nM/L. For the relatively massive galaxies considered here the\ndynamical friction is so strong that it is more violent relaxation\nwith little timescale dependence on the masses. The measured ratio of\nthe numbers of 50 and 100\\hkpc\\ pairs to 20\\hkpc\\ pairs in the CNOC2\nsample is $3.8\\pm1.0$ and $9.4\\pm3.0$, respectively, in accord with\nthe expectation of a growth as $r_p^{3-\\gamma}$ with the inner cutoff\nof 5\\hkpc.\n\nNot all kinematic pairs are close in physical space. The relation\nbetween the kinematic pairs closer than $r_p$ and $\\Delta v$ and pairs\nwith a 3D physical distance $r_p$ is readily evaluated by integrating\nthe velocity convolved correlation function over velocity and\nprojected radius and ratioing to the 3D integral of the correlation\nfunction. We find that $C_{zs}=0.54$ for $\\Delta v=1000\\kms $ and\n$\\gamma=1.8$ There is support for this value on the basis of\nmorphological classification, as tested in Patton et al. (1999), where\nabout half of the kinematic pairs exhibited strong tidal features.\n\nThe fraction of physically close pairs that are at sufficiently low\nvelocity to merge is a key part of the rate calculation. It is clear\nthat many galaxies will have close encounters which do not lead to\nimmediate mergers, although mergers could of course occur on\nsubsequent orbital passages. The key quantity that we need is the\nratio of the critical velocity to merge, $v_{mg}$, to $\\sigma_{12}$.\nThe timescale for close pairs to merge is much shorter than the time\nover which morphological disturbances are clearly evident, by nearly\nan order of magnitude\n\\citep{bh,mh,dmh}. This is one of our reasons for preferring kinematic\npairs as a merger estimator. The simulation results indicate that the\ntime to merge is, on the average, roughly that of a ``half-circle''\norbit, which at $r_p$ of 20\\hkpc\\ at a velocity of 200 \\kms\\ is close\nto 0.3 Gyr. A straight-line orbit with instantaneous merging would\nmerge in about 0.1 Gyr, although that is not likely to be\nrepresentative.\n\nTo compute the merger probability, $F(<v_{mg})$, we need to know the\nmaximal velocity to merge, $v_{mg}$, at a physical separation of\n20\\hkpc\\ for a typical $M_\\ast$ galaxy. A not very useful lower bound\nis fixed by the Keplerian escape velocity at 20\\hkpc, $v_c\\sqrt{2}\n\\kms$, where the circular velocity is approximately 200\n\\kms. An upper bound to $v_{mg}$ is the velocity that an object would have if it is captured into a galaxy's extended dark halo at the virialization \nradius and orbits to 20\\hkpc\\ with no dynamical friction. The\nvirialization radius is approximately at the radius where the mean\ninterior overdensity is $200\\rho_c$, implying $r_{200} = v_c/(10H_0)$,\nor, about 200\\hkpc\\ for our typical galaxy. The largest possible\napogalactic velocity at $r_{200}$ is $v_c$, which leads to an\nundissipated velocity at 20\\hkpc\\ of $2.37v_c$. Using $\\sigma_{12}=\n200(300)\\kms$ at 20\\hkpc, we find that the fraction of all physical\npairs that merge in one $T_{mg}$ is about 0.40(0.16). Therefore, we\nwill normalize to a merger probability of 0.3, noting the 50\\% or so\nuncertainty.\n\nThe absolute magnitude limit of $-19.8+5\\log{h}$ mag corresponds to\n$L\\ge 0.5L_\\ast$ which contains about 58\\% of the luminosity for the\nmean CNOC2 LF, $M_\\ast=-20.4$ and $\\alpha=-1.2$. To make our merger\nrate inclusive of major mergers we normalize to $L\\ge 0.2L_\\ast$,\nwhich includes 85\\% of the luminosity. Within the current statistical\naccuracy, the paired and field galaxies have identical LFs. On the\nbasis of n-body experiments \\citep{bh} galaxies with masses greater\nthan about $0.2M_\\ast$ will merge in approximately one orbital time.\n\nOn the basis of these considerations we find that the rate of mass\naccumulation of galaxies with luminosities of $0.2M_\\ast$ and above\nis,\n\\begin{equation}\n{\\cal R}_M = (0.02\\pm0.01)M_\\ast (1+z)^{0.1\\pm0.5} \n\t{F(v_{mg}/\\sigma_{12})\\over 0.3} {0.3 {\\rm Gyr}\\over T_{mg} }\n\t{\\rm Gyr}^{-1},\n\\label{eq:mgr}\n\\end{equation}\nwhere we have adopted the 100\\hkpc\\ $m_L$ value for a flat, low\ndensity cosmology and explicitly assumed that the velocity and \ntimescale factors do not vary over this redshift range, as expected at\nthese small scales in a low $\\Omega$ universe\n\\citep{ccc}. There is direct evidence that once evolution compensated\nthat the luminous galaxies retain have no evolution in their circular\nvelocities \\citep{vogt,gabriella}.\n\n\\section{Discussion and Conclusions}\n\nOur main observational result is that for galaxies with $M_R^{k,e}\\le\n-19.8+5\\log{h}$ mag, the fraction of galaxy luminosity in 50\\hkpc\\\nwide kinematic pairs is about 14\\%, with no noticeable redshift\ndependence over the redshift zero to one range. This implies an\nintegrated mass accretion rate of about 2\\% of $L_\\ast$ per Gyr per\ngalaxy for merging galaxies having $L\\ge 0.2L_\\ast$. Our rate is\nuncertain at about the factor of two level due to uncertainty in the\ndynamical details of merging for our sample definitions. This merger\nrate implies a 15\\% mass increase in an $M_\\ast$ galaxy since\nredshift one. If the correlations of lower luminosity galaxies are\nonly somewhat weaker than these \\citep{roysoc} then the same\n$0.15M_\\ast$ merged-in mass causes a 50\\% mass increase in a\n0.3$M_\\ast$ galaxy.\n\nThere are several issues that require further investigation. First, the\nrate of merging of similarly selected kinematic pairs should be\nstudied in appropriately matched n-body experiments to better\ndetermine the orbital timescales. Second, the absence of a redshift\ndependence of $\\sigma_{12}$ and $v_{mg}$ needs to\nbe observationally checked. Third, the connection between close\nkinematic pairs and morphologically disturbed galaxies, which does\nconform to the kinematic pair predictions at low redshift\n\\citep{patton_ssrs2}, needs to be better understood at high redshift.\n\n\\acknowledgments\n\nThis research was supported by NSERC and NRC of Canada. HL and DWH\nacknowledge support provided by NASA through Hubble Fellowship grants\nHF-01110.01-98A and HF-01093.01-97A, respectively, \nawarded by the Space Telescope Science Institute, which is operated by\nthe Association of Universities for Research in Astronomy, Inc., for\nNASA under contract NAS 5-26555.\n\n\\begin{thebibliography}{}\n\\bibitem[Barnes \\& Hernquist 1992]{bh} Barnes, J. E. \\& \n\tHernquist, L. 1992, \\araa, 30, 705 \n\\bibitem[Carlberg Pritchet \\& Infante 1994]{cpi}\n Carlberg, R. G., Pritchet, C. J., \\& Infante, L. 1994, \\apj, 435, 540\n\\bibitem[Carlberg et al.~1997]{kkeck}\n Carlberg, R. G., Cowie, L., L., Songaila, A., \\& Hu, E. M. 1997, \\apj,\n 483, 538\n\\bibitem[Carlberg et al.~1998]{roysoc}\n Carlberg, R. G., Yee, H. K. C., Morris, S. L., Lin, H.,\n Sawicki, M., Wirth, G., Patton, D., \n Shepherd, C. W., Ellingson, E., Schade, D.,\n Pritchet, C. J., \\& Hartwick, F. D. A. 1998, \n Phil. Trans. Roy. Soc. Lond. A. 357, 167\n\\bibitem[Carlberg et al. 1999]{cnoc_xi} Carlberg, R. G., Yee, H. K. C., \n\tMorris, S. L., Lin, H., Hall, P. B., Patton, D., \n\tSawicki, M. \\& Shepherd, C. W. 1999, \\apj, submitted\n\\bibitem[Cohen et al. 2000]{cfgrs_z}\n\tCohen, J. G., Hogg, D. W., Blandford, R.,\n\tCowie, L. L., Hu, E., Songaila, A.,\n\tShopbell, P. \\& Richberg, K. 1999, \\apj, accepted (astro-ph/9912048)\n\\bibitem[Colin Carlberg \\& Couchman 1997]{ccc}\n Colin, P., Carlberg, R. G., \\& Couchman, H. M. P. 1997, \\apj, 390, 1\n\\bibitem[Dubinski Mihos \\& Hernquist 1999]{dmh}\n\tDubinski, J., Mihos, J. C. \\& Hernquist, L. 1999, \\apj, submitted\n\t(astro-ph/9902217)\n\\bibitem[Hogg et al 1999]{cfgrs_phot} \n\tHogg, D. W., Pahre, M. A., Adelberger, K. L.,\n\tBlandford, R., Cohen, J. G., Gautier, T. N., Jarrett, T.,\n\tNeugebauer, G., \\& Steidel, C. C. 1999, \\aj, submitted.\n\\bibitem[LeF\\`evre et al.~1996]{cfrsxi}\n LeF\\`evre, O, Hudon, D., Lilly, S. J. Crampton, D., Hammer, F. \n \\& Tresse, L.1996, \\apj, 461, 534\n\\bibitem[LeF\\`evre et al.~1999]{cfrs_mg}\n\tLeF\\`evre, O, Abraham, R., Lilly, S. J., Ellis, R. S.,\n\tBrinchmann, J., Schade, D., Tresse, L.,\n\tColless, M., Crampton, Glazebrook, K., Hammer, F., \\&\n\tBroadhurst, T. 1999, \\mnras, in press\n\\bibitem[Lilly et al.~1995]{cfrs_lf} Lilly, S. J., Tresse, L., \n Hammer, F., Crampton, D., \\& Le Fevre, O. 1995, \\apj, 455, 108 \n\\bibitem[Lin et al.~1999]{huan_lf}\n\tLin, H., Yee., H. K. C., Carlberg, R. G., Morris, S. L.,\n Sawicki, M., Patton, D., Wirth, G. \\& Shepherd, C. W. 1999,\n \\apj, 518, 533\n\\bibitem[Mallen-Ornelas Lilly Crampton \\& Schade 1999]{gabriella} \n\tMallen-Ornelas, G. , Lilly, S. J., Crampton, D. \\& Schade, D. 1999, \n\t\\apjl, 518, L83 \n\\bibitem[Mihos \\& Hernquist 1996]{mh} Mihos, J. C. \\& \n\tHernquist, L. 1996, \\apj, 464, 641 \n\\bibitem[Neuschaefer et al. 1997]{mdss} Neuschaefer, L. W., \n\tIm, M., Ratnatunga, K. U., Griffiths, R. E. \\& Casertano, S. 1997, \n\t\\apj, 480, 59 \n\\bibitem[Patton et al. 1997]{patton_cnoc1} Patton, D. R., Pritchet, \n\tC. J., Yee, H. K. C., Ellingson, E. \\& Carlberg, R. G. 1997, \n\t\\apj, 475, 29 \n\\bibitem[Patton et al. 2000a]{patton_ssrs2} Patton, D. R., Marzke, R. O.,\n Carlberg, R. G., Pritchet, C. J., da Costa, L. N, \\&\n\tPellegrini, P. S. 2000, \\apj,\n\tin press\n\\bibitem[Patton et al. 2000b]{patton_cnoc2} Patton, D. R., \n Carlberg, R. G., Marzke, R. O., \n Yee, H. K. C., Lin, H., Morris, S. L., Sawicki, M., \n Wirth, G. D., Shepherd, C. W., Ellingson, E.,\n Schade, D., \\& Pritchet, C. J., 2000, \\apj, in prepartion\n\\bibitem[Poggianti 1997]{poggianti} Poggianti, B. M. 1997, \\aaps, 122, 399 \n\\bibitem[Toomre \\& Toomre 1972]{tt} Toomre, A. \\& Toomre, \n J. 1972, \\apj, 178, 623 \n\\bibitem[Vogt et al. 1997]{vogt} Vogt, N. P., et al. 1997, \n\t\\apjl, 479, L121 \n\\bibitem[Yee \\& Ellingson 1995]{ye_pairs}\n\tYee, H. K. C. \\& Ellingson, E. 1995, \\apj, 445, 37 \n\\bibitem[Yee et al. 2000]{yee2}\n Yee, H. K. C., et al. 2000, to be submitted to \\apjs\n\\bibitem[Zepf \\& Koo 1989]{zk}\n\tZepf, S. E. \\& Koo, D. C. 1989, \\apj, 337, 34 \n\\end{thebibliography}\n\n\\newpage\n~\n\\figcaption[fig1.eps]{The fraction of the sample luminosity in pairs\nwith $\\Delta v \\le 1000\n\\kms$ and $5\\le r_p\\le 50\\hkpc$ as a function of redshift. The octagons\nare from the CNOC2 sample and the triangles from CFGRS.\n\\label{fig:flz}}\n\n\\figcaption[fig2.eps]{The velocity distribution function for\nCNOC2 galaxy pairs. The filled points are for 20\\hkpc\\ pairs limited\nat $M_R^{k,e}$ of $-19.5$ mag (diamonds) and $-18.5$ mag (octagons) and\nthe open squares are for 50\\hkpc\\ pairs limited at $-19.5$ mag. The\nlines are the distributions expected for an $r^{-1.8}$ correlation\nfunction convolved with Gaussian velocity distribution functions of\n200 and 300 \\kms, the upper and lower lines respectively.\n\\label{fig:pv}}\n\n\\newpage\n\\includegraphics[width=0.9\\hsize]{fig1.eps} \n\n\\newpage\n\\includegraphics[width=0.9\\hsize]{fig2.eps}\n\n\\end{document}\n\n\n"
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{
"name": "astro-ph0002036.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Barnes \\& Hernquist 1992]{bh} Barnes, J. E. \\& \n\tHernquist, L. 1992, \\araa, 30, 705 \n\\bibitem[Carlberg Pritchet \\& Infante 1994]{cpi}\n Carlberg, R. G., Pritchet, C. J., \\& Infante, L. 1994, \\apj, 435, 540\n\\bibitem[Carlberg et al.~1997]{kkeck}\n Carlberg, R. G., Cowie, L., L., Songaila, A., \\& Hu, E. M. 1997, \\apj,\n 483, 538\n\\bibitem[Carlberg et al.~1998]{roysoc}\n Carlberg, R. G., Yee, H. K. C., Morris, S. L., Lin, H.,\n Sawicki, M., Wirth, G., Patton, D., \n Shepherd, C. W., Ellingson, E., Schade, D.,\n Pritchet, C. J., \\& Hartwick, F. D. A. 1998, \n Phil. Trans. Roy. Soc. Lond. A. 357, 167\n\\bibitem[Carlberg et al. 1999]{cnoc_xi} Carlberg, R. G., Yee, H. K. C., \n\tMorris, S. L., Lin, H., Hall, P. B., Patton, D., \n\tSawicki, M. \\& Shepherd, C. W. 1999, \\apj, submitted\n\\bibitem[Cohen et al. 2000]{cfgrs_z}\n\tCohen, J. G., Hogg, D. W., Blandford, R.,\n\tCowie, L. L., Hu, E., Songaila, A.,\n\tShopbell, P. \\& Richberg, K. 1999, \\apj, accepted (astro-ph/9912048)\n\\bibitem[Colin Carlberg \\& Couchman 1997]{ccc}\n Colin, P., Carlberg, R. G., \\& Couchman, H. M. P. 1997, \\apj, 390, 1\n\\bibitem[Dubinski Mihos \\& Hernquist 1999]{dmh}\n\tDubinski, J., Mihos, J. C. \\& Hernquist, L. 1999, \\apj, submitted\n\t(astro-ph/9902217)\n\\bibitem[Hogg et al 1999]{cfgrs_phot} \n\tHogg, D. W., Pahre, M. A., Adelberger, K. L.,\n\tBlandford, R., Cohen, J. G., Gautier, T. N., Jarrett, T.,\n\tNeugebauer, G., \\& Steidel, C. C. 1999, \\aj, submitted.\n\\bibitem[LeF\\`evre et al.~1996]{cfrsxi}\n LeF\\`evre, O, Hudon, D., Lilly, S. J. Crampton, D., Hammer, F. \n \\& Tresse, L.1996, \\apj, 461, 534\n\\bibitem[LeF\\`evre et al.~1999]{cfrs_mg}\n\tLeF\\`evre, O, Abraham, R., Lilly, S. J., Ellis, R. S.,\n\tBrinchmann, J., Schade, D., Tresse, L.,\n\tColless, M., Crampton, Glazebrook, K., Hammer, F., \\&\n\tBroadhurst, T. 1999, \\mnras, in press\n\\bibitem[Lilly et al.~1995]{cfrs_lf} Lilly, S. J., Tresse, L., \n Hammer, F., Crampton, D., \\& Le Fevre, O. 1995, \\apj, 455, 108 \n\\bibitem[Lin et al.~1999]{huan_lf}\n\tLin, H., Yee., H. K. C., Carlberg, R. G., Morris, S. L.,\n Sawicki, M., Patton, D., Wirth, G. \\& Shepherd, C. W. 1999,\n \\apj, 518, 533\n\\bibitem[Mallen-Ornelas Lilly Crampton \\& Schade 1999]{gabriella} \n\tMallen-Ornelas, G. , Lilly, S. J., Crampton, D. \\& Schade, D. 1999, \n\t\\apjl, 518, L83 \n\\bibitem[Mihos \\& Hernquist 1996]{mh} Mihos, J. C. \\& \n\tHernquist, L. 1996, \\apj, 464, 641 \n\\bibitem[Neuschaefer et al. 1997]{mdss} Neuschaefer, L. W., \n\tIm, M., Ratnatunga, K. U., Griffiths, R. E. \\& Casertano, S. 1997, \n\t\\apj, 480, 59 \n\\bibitem[Patton et al. 1997]{patton_cnoc1} Patton, D. R., Pritchet, \n\tC. J., Yee, H. K. C., Ellingson, E. \\& Carlberg, R. G. 1997, \n\t\\apj, 475, 29 \n\\bibitem[Patton et al. 2000a]{patton_ssrs2} Patton, D. R., Marzke, R. O.,\n Carlberg, R. G., Pritchet, C. J., da Costa, L. N, \\&\n\tPellegrini, P. S. 2000, \\apj,\n\tin press\n\\bibitem[Patton et al. 2000b]{patton_cnoc2} Patton, D. R., \n Carlberg, R. G., Marzke, R. O., \n Yee, H. K. C., Lin, H., Morris, S. L., Sawicki, M., \n Wirth, G. D., Shepherd, C. W., Ellingson, E.,\n Schade, D., \\& Pritchet, C. J., 2000, \\apj, in prepartion\n\\bibitem[Poggianti 1997]{poggianti} Poggianti, B. M. 1997, \\aaps, 122, 399 \n\\bibitem[Toomre \\& Toomre 1972]{tt} Toomre, A. \\& Toomre, \n J. 1972, \\apj, 178, 623 \n\\bibitem[Vogt et al. 1997]{vogt} Vogt, N. P., et al. 1997, \n\t\\apjl, 479, L121 \n\\bibitem[Yee \\& Ellingson 1995]{ye_pairs}\n\tYee, H. K. C. \\& Ellingson, E. 1995, \\apj, 445, 37 \n\\bibitem[Yee et al. 2000]{yee2}\n Yee, H. K. C., et al. 2000, to be submitted to \\apjs\n\\bibitem[Zepf \\& Koo 1989]{zk}\n\tZepf, S. E. \\& Koo, D. C. 1989, \\apj, 337, 34 \n\\end{thebibliography}"
}
] |
astro-ph0002037
|
Gravitational Clustering from $\chi^2$ Initial Conditions
|
[
{
"author": "Rom\\'{a}n Scoccimarro"
}
] |
We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from large-scale structure galaxy surveys. Non-Gaussian initial conditions provide additional non-linear couplings otherwise forbidden by symmetry that cause non-linear gravitational corrections to become important at larger scales than in the Gaussian case. In fact, the lack of hierarchical scaling in the initial conditions is partially restored by gravitational evolution at scales $k> 0.1$ h/Mpc. However, the bispectrum shows much larger amplitude and residual scale dependence not present in evolution from Gaussian initial conditions that can be used to test this model against observations. We include the effects of biasing and redshift distortions essential to compare this model with galaxy redshift surveys. We also discuss the effects of primordial non-Gaussianity on the redshift-space power spectrum and show that it changes the shape of the quadrupole to monopole ratio through non-linear corrections to infall velocities.
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[
{
"name": "chisq.tex",
"string": "\\documentstyle[aaspp4,tighten,flushrt]{article}\n%\\documentstyle[11pt,aasms4,tighten]{article}\n\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\\newcommand{\\beqa}{\\begin{eqnarray}}\n\\newcommand{\\eeqa}{\\end{eqnarray}}\n\n\\def\\eq#1{equation~(\\ref{#1})}\n%\\def\\lexp{\\mathop{{}{\\langle}{}}}\n%\\def\\rexp{\\mathop{{}{\\rangle}{}}}\n\\newcommand{\\lexp}{\\mathop{\\langle}}\n\\newcommand{\\rexp}{\\mathop{\\rangle}}\n\\newcommand{\\rexpc}{\\mathop{\\rangle_c}}\n\\def\\dD{\\delta_{\\rm D}} % Dirac delta-function\n\\def\\dt{\\tilde \\delta}\n\\def\\Ft{\\tilde F}\n\\def\\d{\\delta}\n\n\\font\\BFd=cmmib10\n\\font\\BFt=cmmib10\n\\font\\BFs=cmmib10 scaled 700\n\\font\\BFss=cmmib10 scaled 500\n\n\\def\\bbox#1{%\n\\relax\\ifmmode\n\\mathchoice\n{{\\hbox{\\BFd #1}}}\n{{\\hbox{\\BFt #1}}}\n{{\\hbox{\\BFs #1}}}\n{{\\hbox{\\BFss #1}}}\n\\else \\mbox{#1} \\fi }\n\n\\def\\d{\\delta}\n\\def\\te{\\theta}\n\\def\\ds{\\delta_s}\n\\def\\dt{\\tilde \\delta}\n\\def\\dD{[\\delta_{\\rm D}]}\n\\def\\del{\\nabla}\n\\def\\knl{k_{n\\ell}}\n\\def\\pleg{{\\mathsf P}}\n\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrel{\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfill##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n\n\\def\\k{{\\bbox{k}}}\n\\def\\x{{\\bbox{x}}}\n\\def\\r{{\\bbox{r}}}\n\\def\\s{{\\bbox{s}}}\n\\def\\z{{\\bbox{z}}}\n\\def\\shot{{\\rm shot}}\n\\def\\q{{\\bbox{q}}}\n\\def\\uz{{\\hbox{$u_z$}}}\n\\def\\u{{\\bbox{u}}}\n\\def\\v{{\\bbox{v}}}\n\n\n\\begin{document}\n\n\\title{Gravitational Clustering from $\\chi^2$ Initial Conditions}\n\n\n\\vskip 1pc\n\n\\author{Rom\\'{a}n Scoccimarro}\n\n\\vskip 2pc\n\n\\affil{Institute for Advanced Study, School of Natural Sciences,\nOlden Lane, Princeton, NJ 08540}\n\n\n\\begin{abstract}\n\nWe consider gravitational clustering from primoridal non-Gaussian\nfluctuations provided by a $\\chi^2$ model, as motivated by some models\nof inflation. The emphasis is in signatures that can be used to\nconstrain this type of models from large-scale structure galaxy\nsurveys. Non-Gaussian initial conditions provide additional non-linear\ncouplings otherwise forbidden by symmetry that cause non-linear\ngravitational corrections to become important at larger scales than in\nthe Gaussian case. In fact, the lack of hierarchical scaling in the\ninitial conditions is partially restored by gravitational evolution at\nscales $k> 0.1$ h/Mpc. However, the bispectrum shows much larger\namplitude and residual scale dependence not present in evolution from\nGaussian initial conditions that can be used to test this model\nagainst observations. We include the effects of biasing and redshift\ndistortions essential to compare this model with galaxy redshift\nsurveys. We also discuss the effects of primordial non-Gaussianity on\nthe redshift-space power spectrum and show that it changes the shape\nof the quadrupole to monopole ratio through non-linear corrections to\ninfall velocities.\n\n\n\n\\end{abstract}\n\n\n\\subjectheadings{large-scale structure of universe}\n\n\n\\clearpage \n\n\\section{Introduction}\n\n\nThe current paradigm for the formation of large-scale structures in\nthe universe is that small primordial fluctuations, with a roughly\nscale-invariant spectrum, are amplified by non-linear gravitational\ninstability to form the galaxies, clusters and superclsuters that we\nsee today in galaxy surveys. A common assumption is that the\nstatistics of these primordial fluctuations is Gaussian, which is\nconsistent with current observations. However, at this point we\ncannot rule out the possibility that primordial fluctuations were in\nfact non-Gaussian to some extent. Fortunately, rapid progress in\nmicrowave background anisotropy experiments and large galaxy redshift\nsurveys in the next few years will provide high quality data that can\nbe used to test the nature of primordial fluctuations.\n\n\nThe consideration of non-Gaussian initial conditions is a difficult\nissue because there is an infinite class of non-Gaussian models. In a\nGaussian field $\\phi$, $n-$point connected correlation functions,\n$\\xi_n = \\lexp \\phi_{1} \\ldots \\phi_{n} \\rexp_{c}$ of order $n \\geq 3$\nvanish; however, in a non-Gaussian field higher-order correlations can\nvirtually behave arbitrarily subject to the constraint of\nrealizability, that is, that the multivariate probability\ndistributions be positive definite. In general, however, we can\ndivide non-Gaussian models into {\\em weakly} and {\\em strongly}\nnon-Gaussian, depending on the magnitude of normalized cumulants\n$s_{p} \\equiv \\lexp \\d^p \\rexpc / \\lexp \\d^2 \\rexp^{p/2}$ of the\nsmoothed density contrast $\\d$ compared to unity. A minimal way of\nachieving strongly non-Gaussian models is by {\\em dimensional\nscaling}, where the hierarchy of $n$-point correlation functions obeys\n$\\xi_n \\propto \\xi_2^{n/2}$. In this case, normalized cumulants are\nnumbers not necessarily smaller than unity. This is opossed to {\\em\nweakly non-Gaussian models} where normalized cumulants are forced to\nbe small quantities, e.g. {\\em hierarchical scaling} models, where\n$\\xi_n \\propto \\xi_2^{n-1}$ with $\\xi_2 \\ll 1$.\n\nIn this paper we consider $\\chi^2$ initial conditions, which belong to\nthe class of dimensional scaling models. As a strongly non-Gaussian\nmodel, it has the potential to be more easily constrained or detected\nby large-scale structure observations than primordial weakly\nnon-Gaussian models. Furthermore, there is a number of inflationary\nmodels in the literature that motivate $\\chi^2$ initial conditions\n(e.g. Kofman et al. 1989; Antoniadis et al. 1997, Linde \\& Muhanov\n1997; Peebles 1997). In addition, this model has been recently argued\nto fit a significant set of observational constraints (Peebles 1999a,\n1999b). It is also possible that this particular model may be a good\nrepresentation of the general behavior of dimensional scaling models,\nand thus provide general insight about their advantages and\ndisadvantages. Furthermore, models in which primordial fluctuations\nare generated by topological defects also generally obey dimensional\nscaling (e.g. Turok \\& Spergel 1991).\n\n\nPrevious work on clustering from non-Gaussian initial conditions was\ndone using numerical simulations (e.g. Moscardini et al. 1991;\nWeinberg and Cole 1992; Coles et al. 1993; White 1999), and\nperturbation theory (Fry \\& Scherrer 1994; Jaffe 1994; Chodorowski \\&\nBouchet 1996; Gazta\\~naga \\& Fosalba 1998). In this work, we\nconcentrate on aspects of $\\chi^2$ initial conditions that can be\ntested with current and future observations in galaxy redshift\nsurveys. In particular, we concentrate on the study of the\nredshift-space power spectrum and bispectrum; applications of these\nresults to observations will be considered elsewhere (Scoccimarro et\nal. 2000). \n\n\nDifferent aspects of the effects of primordial non-Gaussianity on the\npower spectrum have been considered in the literature (e.g. Feldman,\nKaiser \\& Peacock 1994; Stirling \\& Peacock 1996; Sutherland et\nal. 1999). The skewness of the smoothed density field in texture\nmodels was studied by Gazta\\~naga \\& M\\\"ah\\\"onen (1996), whereas the\nimpact of hierarchical scaling models of primordial non-Gaussianity on\nthe bispectrum was considered by Verde et al. (1999). Our approach is\ncomplementary to recent studies of the impact of primordial\nnon-Gaussian models in other aspects of large-scale structure\n(e.g. Robinson, Gawiser \\& Silk 1999; Koyama, Soda \\& Taruya 1999;\nWillick 1999; Pierpaoli, Garc\\'{\\i}a-Bellido \\& Borgani 1999).\n\n\nThis paper is organized as follows. In Section~2 we review\nperturbation theory results regarding the evolution of the bispectrum\nfrom general initial conditions. Section~3 presents results for the\nparticular case of $\\chi^2$ initial conditions. In Section~4 we\ndiscuss the effects of galaxy biasing and Section~5 those of redshift\ndistortions. Finally, we present our conclusions in Section~6.\n\n\n\n\n\n\\section{Gravitational Clustering from Non-Gaussian Initial Conditions}\n\nWe are interested in the effects of non-Gaussianity on clustering\nstatistics at large scales. A convenient approach is to use non-linear\nperturbation theory (PT), where the density field in Fourier space\nat time $t$ reads (Fry 1984)\n\n\\beq\n\\d(\\k,t) = \\d^{(1)}(\\k,t) + \\d^{(2)}(\\k,t) + \\ldots \n= D_{1} \\d_I(\\k) + D_{1}^2 \\int \\d_D(\\k-\\k_{12}) \\\nF_2(\\k_1,\\k_2) \\d_I(\\k_1) \\d_I(\\k_2)+ \\ldots,\n\\label{den2}\n\\eeq\n\n\\noindent where $\\d_I(\\k)$ is the initial density contrast,\n$k_{i\\ldots j} \\equiv \\k_i + \\ldots + \\k_j$, and we assumed that to a\nvery good approximation, in second-order PT fluctuations grow\naccording to $D_{2}(t) \\propto D_{1}^2(t)$, with $D_{1}(t)$ the linear\ngrowth factor. The kernel $F_2(\\k_1,\\k_2) \\equiv 5/7 + 1/2 \\cos\\theta\n(k_1/k_2+k_2/k_1) + 2/7 \\cos^2 \\theta$ with $\\cos\\theta \\equiv \\k_1\n\\cdot \\k_2 /(k_1 k_2)$, describes to leading order the non-local\nevolution of the density field due to the long-range nature of\ngravitational interactions.\n\nThe non-Gaussianity of initial conditions is encoded in the\nstatistical properties of the random field $\\d_I(\\k)$, in particular,\nits lowest order connected moments are\n\n\\beqa\n\\lexp \\d_I(\\k) \\rexp &=& 0 ,\\\\\n\\lexp \\d_I(\\k_1) \\d_I(\\k_2) \\rexp &=& \\d_D(\\k_{12})\\ P^I(\\k_1), \\\\\n\\lexp \\d_I(\\k_1) \\d_I(\\k_2) \\d_I(\\k_3) \\rexp &=& \\d_D(\\k_{123})\\ B^I(\\k_1,\\k_2,\\k_3), \\\\\n\\lexp \\d_I(\\k_1) \\d_I(\\k_2) \\d_I(\\k_3) \\d_I(\\k_4) \\rexpc &=& \\d_D(\\k_{1234})\\ T^I(\\k_1,\\k_2,\\k_3,\\k_4),\n\\eeqa\n\n\\noindent where $P^I$, $B^I$ and $T^I$ denote the power spectrum,\nbispectrum, and trispectrum of the initial density field. In linear\nPT, these just scale with the linear growth factor, but at the scales\nof current galaxy surveys, non-linear corrections can be\nsignificant. From Eq.~(\\ref{den2}) we derive non-linear corrections to\nthe power spectrum and bispectrum \n\\begin{eqnarray}\nP(k) &=& P^I(k) + 2 \\int d^3 q\\ F_2(\\k+\\q,-\\q)\\ B^I(\\k,\\q),\n\\label{pknl} \\\\\nB_{123} &=& B_{123}^I + B_{123}^G + B_{123}^T,\n\\label{Bispnl}\n\\end{eqnarray}\n\n\\noindent where $B_{123}^I$ denotes the contribution of the initial\nbispectrum scaled to the present time using linear PT,\n$B_{123}^I(t)\\propto [D_{1}(t)]^{3}$, $B_{123}^G$ represents the usual\ngravitationally induced bispectrum from Gaussian initial conditions\n(Fry 1984)\n\n\\begin{equation}\nB_{123}^G = 2 F_2(\\k_1,\\k_2)\\ P^I(k_1) P^I(k_2) + {\\rm cyc.},\n\\label{BG} \n\\end{equation}\n\n\\noindent and the last term in Eq.~(\\ref{Bispnl}) \n\n\\begin{equation}\nB_{123}^T = \\int d^3q\\\nF_2(\\k_{12}-\\q,\\q)\\ T^I(\\k_1,\\k_2,\\k_{12}-\\q,\\q) + {\\rm cyc.},\n\\label{BT} \n\\end{equation}\n\n\\noindent represents the contribution coming from the initial\ntrispectrum linearly evolved to the present. Note that only the first\nterm in Eq.~(\\ref{Bispnl}) scales as $[D_{1}(t)]^{3}$, the last two\nterms have the same scaling with time, $[D_{1}(t)]^{4}$, and therefore\neventually dominate at late times.\n\n\n\\section{Evolution from $\\chi^2$ Initial Conditions}\n\nWe now evaluate the results of the previous section for the particular\ncase of $\\chi^2$ initial conditions. In this case, the density field\nafter inflation is proportional to the square of a Gaussian scalar\nfield $\\phi(\\x)$, $\\rho(\\x) \\propto \\phi(\\x)^2$. Thus, the density\nconstrast $\\d(\\x) = \\phi(\\x)^2 /\\sigma^2_\\phi -1$, where\n$\\sigma^2_\\phi \\equiv \\lexp \\phi^2 \\rexp $. If the auxiliary Gaussian\nfield has two-point correlation function $\\xi_\\phi \\equiv \\lexp \\phi_1\n\\phi_2 \\rexp$, then the density 2-, 3-, and 4-point correlation\nfunctions are respectively (Peebles 1999b)\n\n\\beqa\n\\xi^I_{12} &=& 2 \\frac{\\xi_\\phi^2(r_{12})}{\\sigma_\\phi^4},\n\\label{xiI}\\\\\n\\zeta_{123}^I &=& 2^{3/2} \\sqrt{ \\xi_{12}^I \\xi_{23}^I \\xi_{31}^I},\n\\label{zetaI}\\\\\n\\eta_{1234}^I &=& 4 \\left[ \\sqrt{ \\xi_{12}^I \\xi_{23}^I \\xi_{34}^I\n\\xi_{41}^I } + \\sqrt{ \\xi_{12}^I \\xi_{24}^I \\xi_{43}^I\n\\xi_{31}^I } + \\sqrt{ \\xi_{13}^I \\xi_{32}^I \\xi_{24}^I\n\\xi_{41}^I } \\right],\n\\label{etaI}\n\\eeqa\n\n\\noindent and the initial density power spectrum, bispectrum, and\ntrispectrum are given by\n\n\\beqa\nP^I &=& 2 \\int d^3 q\\ P_{\\phi}(q) P_{\\phi}(|\\k-\\q|),\n\\label{powerI}\\\\ \nB^I_{123} &=& 8 \\int d^3 q\\ P_{\\phi}(q)P_{\\phi}(|\\k_1-\\q|)\nP_{\\phi}(|\\k_2+\\q|), \n\\label{bispI}\\\\\nT^I_{1234} &=& 16 \\int d^3 q\\ P_{\\phi}(q)P_{\\phi}(|\\k_1-\\q|)\nP_{\\phi}(|\\k_{14}-\\q|) P_{\\phi}(|\\k_{3}+\\q|) + \n16 \\int d^3 q\\ P_{\\phi}(q)P_{\\phi}(|\\k_1+\\q|)\n\\nonumber \\\\\n& & \\times P_{\\phi}(|\\k_{23}-\\q|) P_{\\phi}(|\\k_{2}-\\q|) \n+ 16 \\int d^3 q\\ P_{\\phi}(q)P_{\\phi}(|\\k_1+\\q|)\nP_{\\phi}(|\\k_{24}-\\q|) P_{\\phi}(|\\k_{2}-\\q|) , \n\\label{trispI}\n\\eeqa\n\n\n\n\\noindent where $\\sigma^2_\\phi P_{\\phi}(k)$ denotes the power spectrum\nof the $\\phi$ field. For scale-free spectra, $P_{\\phi}(k) = A\nk^{n_\\phi}$, \n\n\\beq\nP^I(k) = 2 \\pi^{3/2} \\frac{ \\Gamma^2\n\\left(\\frac{n_\\phi+3}{2}\\right) \\Gamma\n\\left(-n_\\phi-\\frac{3}{2}\\right)}{\\Gamma^2 (-n_\\phi/2)\n\\Gamma(3-n_\\phi)} \\ A^2 k^{2n_\\phi+3},\n\\label{PI}\n\\eeq \n\n\n\n\\noindent similarly the bispectrum can be expressed in terms of\nhypergeometric functions, using the results in Scoccimarro (1997).\nSimple analytic results can be obtained for the particular case\n$n_{\\phi}=-2$, which gives a density spectral index $n=-1$, reasonably\nclose to the observed one at the non-linear scale. Using\nEq.~(\\ref{pknl}) we get \n\n\\begin{equation}\nP(k) = \\frac{2 \\pi^3 A^2}{k} + \\frac{96 \\pi^4 A^3}{7},\\ \\ \\ \\ \\ \\ \\ \\\n\\ \\ B^I_{123} = \\frac{8 \\pi^3 A^3}{k_1 k_2 k_3}.\n\\label{powbispI} \n\\end{equation}\n\n\\noindent However, the initial trispectrum does not seem to have a\nsimple closed form. Defining the non-linear scale from the linear\npower spectrum, $\\Delta^I(k_{nl}) \\equiv 4\\pi k_{nl}^3 P^I(k_{nl})\n\\equiv 1$, we have\n\n\\begin{equation}\n\\Delta(k) = \\left( \\frac{k}{k_{nl}} \\right)^2\\ \\left( 1 +\n\\frac{24}{7\\sqrt{2} \\pi} \\frac{k}{k_{nl}} \\right) \\approx \\left(\n\\frac{k}{k_{nl}} \\right)^2\\ \\left( 1 + 0.77 \\frac{k}{k_{nl}} \\right),\n\\label{delnl} \n\\end{equation}\n\nRather than working with the bispectrum itself, it is convenient to\nconsider the reduced bispectrum $Q_{123}$ defined by\n\n\\beq\nQ_{123} = \\frac{B_{123}}{\\Sigma_{123}}\n\\equiv \\frac{B_{123}}{P_1 P_2 +P_2 P_3 +P_3 P_1},\n\\label{Q123}\n\\eeq\n\n\\noindent which for Gaussian initial conditions has the important\nproperties that it is independent of time, and to a very good\napproximation independent of the matter density parameter $\\Omega$. In\naddition, for scale-free initial conditions is independent of overall\nscale, for CDM-type models the scale-dependence is only weak through\nthe scale variation of the spectral index. From these results, the\nreduced bispectrum for $\\chi^2$ initial conditions, including\nnon-linear gravitational corrections is\n\n\\begin{eqnarray}\nQ_{123} &=& \\frac{4\\sqrt{2}}{\\pi}\\ \\frac{k_{nl}}{k_1+ k_2+ k_3}-\n\\frac{192}{7\\pi^2} \\frac{k_1 k_2+k_2 k_3+k_3 k_1}{(k_1+ k_2+ k_3)^2}\n+ Q_{123}^G + Q_{123}^T, \n\\label{QI} \n\\end{eqnarray}\n\n\\noindent where $Q_{123}^G$ denotes the reduced bispectrum obtained\nfrom Gaussian initial conditions, and $Q_{123}^T$ denotes the\ncontribution from Eq.~(\\ref{BT}) which is difficult to calculate\nanalytically (however, we shall give a full numerical evaluation of\nthe bispectrum below). In particular, for equilateral configurations\n\n\\beq\nQ_{eq}=\\frac{4\\sqrt{2}}{3 \\pi}\\ \\frac{k_{nl}}{k} - \\frac{64}{7 \\pi^2}\n+ \\frac{4}{7} + Q^T_{eq} \\approx 0.6 \\frac{k_{nl}}{k} -0.35 + Q^T_{eq},\n\\label{Qeq}\n\\eeq\n\n\\noindent where we used that $Q^G_{eq}=4/7$ (Fry 1984). Since the last\nterm is a number independent of scale, Eq.~(\\ref{Qeq}) illustrates the\nsignature of this type of non-Gaussian initial conditions: $Q_{eq}$\nshows a strong scale dependence at large scales as $k/k_{nl}\n\\rightarrow 0$. This is not just a property of $\\chi^2$ initial\nconditions, but rather of dimensional scaling models ($\\xi_n \\propto\n\\xi_2^{n/2}$). \n\nA simple generalization of $\\chi^2$ initial conditions is to consider\n$N$ independent fields, each of them $\\chi^2$ distributed with the\nsame power spectrum $P_{\\phi}(k)$. As $N$ increases, the Gaussian\nlimit is achieved as a result of the central limit theorem. This might\nbe a useful way of parametrizing constraints on non-Gaussianity from\nlarge-scale structure observations. For a fixed linear density power\nspectrum $P^I(k)$, the primordial bispectrum and trispectrum obey $B^I\n\\propto 1/\\sqrt{N}$ and $T^I \\propto 1/N$,\nrespectively. Equation~(\\ref{QI}) then reduces to\n\n\\begin{eqnarray}\nQ_{123} &=& \\frac{1}{\\sqrt{N}} \\frac{4\\sqrt{2}}{\\pi}\\\n\\frac{k_{nl}}{k_1+ k_2+ k_3}- \\frac{1}{N} \\frac{192}{7\\pi^2} \\frac{k_1\nk_2+k_2 k_3+k_3 k_1}{(k_1+ k_2+ k_3)^2} + Q_{123}^G + \\frac{1}{N}\nQ_{123}^T.\n\\label{QIN} \n\\end{eqnarray}\n\n\\noindent Thus, the approach rate to the Gaussian initial conditions\nresult is $1/\\sqrt{N}$ at large $N$. The same scaling holds for the\nskewness parameter, similarly, the kurtosis relaxes towards the\nGaussian initial conditions value as $S_4 \\propto 1/N$. Note, however,\nthat the scaling at small $N$ is stronger; in fact, such a behavior is\nseen in the N-body simulation results by White (1999) on the skewness\nand kurtosis as a function of $N$ (see his Fig.~7).\n\n\nFrom Eq.~(\\ref{delnl}) we see that non-linear corrections to linear PT\ncan be significant even at wavenumbers smaller than the non-linear\nscale. In order to check for significant contributions from third and\nhigher-order in the perturbation expansion [Eq.(\\ref{den2})], we\nresort to numerical realizations of second-order Lagrangian PT (2LPT),\nwhich by being formulated in Lagrangian space incorporate the\nremaining terms in Eq.(\\ref{den2}), although only approximately beyond\n$F_2$ (but the error is small, see e.g. Scoccimarro (1998) for a\nquantitative comparison of one-point cumulants). In this case, the\nperturbation expansion is done about particle trayectories $\\x(t)$,\n\n\\beq \n\\x(t) = \\q + \\Psi(\\q,t) = \\q + \\Psi^{(1)}(\\q,t) + \\Psi^{(2)}(\\q,t)\n+\\ldots,\n\\label{lag}\n\\eeq\n\n\\noindent so that $\\q$ represents the initial (Lagrangian) position of\na particle whose current (Eulerian) position is $\\x(t)$ and\n$\\Psi(\\q,t)$ denotes the displacement vector assumed to be a small\nquantity. In 2LPT, Eq.~(\\ref{lag}) is truncated at second order. The\nsolutions for the displacement field are obtained from the equations\nof motion and read\n\n\\beqa\n\\x(\\q) &=& \\q -D_1\\ \\del_q \\phi^{(1)} + D_2\\ \\del_q \\phi^{(2)},\n\\label{dis2} \\\\\n\\del_q^2 \\phi^{(1)}(\\q) &=& \\d(\\q), \n\\label{phi1} \\\\\n\\del_q^2 \\phi^{(2)}(\\q) &=& \\sum_{i>j} [\\phi_{,ii}^{(1)}(\\q)\\\n\\phi_{,jj}^{(1)}(\\q) - (\\phi_{,ij}^{(1)}(\\q))^2],\n\\label{phi2}\n\\eeqa\n\n\\noindent where to a very good approximation, $D_2 \\approx -3D_1^2/7$\n(Bouchet et al. 1995). For a detailed exposition of 2LPT see\ne.g. Buchert et al. (1994) and Bouchet et al. (1995), who also\ncompared to N-body simulations. Similarly, in a companion paper\n(Scoccimarro 2000), we explore the validity of 2LPT for the evolution\nof the bispectrum in redshift-space from Gaussian initial conditions,\nby comparing to N-body simulations. In this paper, we use 2LPT for\n$\\chi^2$ initial conditions and adopt the criterion of validity found\nfor the Gaussian case, namely, we only include waves up to a maximum\nwavenumber $k_c \\approx 0.5$ h/Mpc, so that the percentage of\nshell-crossing is below $10\\%$. Given that 2LPT is computationally\ninexpensive, we can generate many realizations which is essential to\nbeat down cosmic variance.\n\nFigures~\\ref{figiso} and \\ref{figisoeq} show the results of 100 2LPT\nrealizations. We have chosen the auxiliary Gaussian field $\\phi$ with\na spectral index $n_{\\phi}=-2.4$, leading to $n=-1.8$ as proposed in\nPeebles (1999a). The amplitude of the power spectrum has been chosen\nto give $k_{nl} \\equiv 0.33$ h/Mpc. First, we checked that the initial\nconditions were generated correctly by comparing the power spectrum\nand the bispectrum with theoretical expectations. The dashed lines in\nFig.~\\ref{figiso} show the predictions of the first term in\nEq.~(\\ref{QI}) for the reduced bispectrum at $k_1=0.068$ h/Mpc, $k_2=2\nk_1$, as a function of angle $\\theta$ between $\\k_1$ and $\\k_2$. This\ncorresponds to $n=-1$, however, it approximately matches the numerical\nresults (triangles, $n=-1.8$). The latter show less dependence on\nangle, as expected because the scale dependence in the $n=-1.8$ case\n($Q^I \\propto k^{-0.6}$) is weaker than for $n=-1$ ($Q^I\\propto\nk^{-1}$). In Fig.~\\ref{figisoeq} we show equilateral configurations as\na function of scale for $\\chi^2$ initial conditions (triangles) and\n$Q^I_{eq}(k) = 0.8 (k/k_{nl})^{-0.6}$ (dashed lines), where the\nproportionality constant was chosen to fit the numerical result, this\nis slightly larger than the prediction in the first term of\nEq.~(\\ref{Qeq}) for $n=-1$, and closer to the real-space result\n$Q_{eq}(r) = 0.94 (r/r_{nl})^{0.6}$.\n\nThe behavior of the $\\chi^2$ bispectrum is notoriously different from\nthat generated by gravity from Gaussian initial conditions for\nidentical power spectrum (dot-dashed lines in\nFigs.~\\ref{figiso}-\\ref{figisoeq}) (Frieman \\& Gazta\\~naga 1999). The\nstructures generated by squaring a Gaussian field roughly correspond\nto the underlying Gaussian high-peaks which are mostly spherical, thus\nthe reduced bispectrum is approximately flat. In fact, the increase of\n$Q^I$ as $\\theta \\rightarrow \\pi$ seen in Fig.\\ref{figisoeq} is\nbasically due to the scale dependence of $Q^I$, i.e. as $\\theta\n\\rightarrow \\pi$, the side $k_3$ decreases and thus $Q^I$ increases.\n\n\nAs shown in Eqs.~(\\ref{QI}-\\ref{Qeq}), non-linear corrections to the\nbispectrum are significant at the scales of interest, so linear\nextrapolation of the initial bispectrum is insufficient to make\ncomparison with current observations. The square symbols in\nFigs.~\\ref{figiso} and \\ref{figisoeq} show the reduced bispectrum\nafter non-linear corrections are included. As a result, the familiar\ndependence of $Q_{123}$ on the triangle shape due to the dynamics of\nlarge-scale structures is recovered (Fig.~\\ref{figiso}), and the scale\ndependence shown by $Q^I$ is now reduced (Fig.~\\ref{Qeq}). However,\nthe differences between the Gaussian and $\\chi^2$ case are very\nobvious: the $\\chi^2$ evolved bispectrum has an amplitude about 2-4\ntimes larger than that of an initially Gaussian field with the same\npower spectrum. Furthermore, the $\\chi^2$ case shows residual scale\ndependence that reflects the dimensional scaling of the initial\nconditions. The analogous results for the skewness were obtained using\nnumerical simulations (White 1999) and non-linear PT in the spherical\ncollapse approximation (Gazta\\~naga \\& Fosalba 1998). These\nsignatures can be used to test this model against obervations;\nhowever, before we can do so we have to test the robustness of these\nconclusions against the effects of galaxy biasing and redshift\ndistortions.\n\n\n\n\n\n\\section{Galaxy Biasing}\n\n\nWe now consider the effects of local biasing when initial conditions\nare non-Gaussian. If we restrict ourselves to scales larger than those\nrelevant to galaxy formation, the galaxy density field can be thought\nof as a local transformation of the density field smoothed over large\nenough scales so that $\\d \\ll 1$, and thus expanded as (Fry \\&\nGazta\\~naga 1993)\n\n\\beq\n\\d_g = b_1 \\d + \\frac{b_2}{2} \\d^2 + \\ldots,\n\\label{locbias}\n\\eeq\n\n\\noindent which implies the following mapping for the power spectrum\nand bispectrum\n\n\\beqa\nP_g(k) &=& b_1^2 P(k) + b_1 b_2 \\int d^3 q\\ B^I(\\k,\\q),\n\\label{powerg} \\\\\nB_g(k_1,k_2,k_3) &=& b_1^3 B_{123} + b_1^2 b_2 \\Sigma_{123}^{I} + \n\\frac{3}{2} b_1^2 b_2 \\int d^3q\\ T_{123}^I(\\q),\n\\label{Bispg}\n\\eeqa \n\n\\noindent where $T_{123}^I(\\q)$ denotes the trispectrum\n$T^I(\\k_1,\\k_2,\\q)$ symmetrized over $\\{k_1,k_2,k_3\\}$, and\n$\\Sigma_{123}^{I}$ is defined in Eq.~(\\ref{Q123}). The reduced\nbispectrum then reads\n\n\\beq\nQ_g= \\frac{1}{b_1} Q_{123} + \\frac{b_2^{\\rm eff}}{b_1^2},\n\\label{QgNG}\n\\eeq\nwhere the effective non-linear bias parameter is given by \n\n\\beq b_2^{\\rm eff} = b_2\\ \\left[ 1 + \\frac{3}{2 \\Sigma_{123}^{I}} \\int\nd^3q\\ T_{123}^I(\\q) -\n\\frac{Q_{123}^{I}}{\\Sigma_{123}^{I}} \\left( P_1^I \\int d^3 q\\\nB^I(\\k_2,\\q) + {\\rm cyc.} \\right)\n\\right] \\label{b2eff} \\eeq\n\n\\noindent The analogous result to Eq.~(\\ref{QgNG}) for the \ncase of the skewness was derived by Fry \\& Scherrer (1994). So far\nthe derivation does not assume any particular non-Gaussian model. In\norder to compute the effective non-linear bias parameter, we need to\nmake assumptions about the initial bispectrum and trispectrum. The\nparticular form of the convolution integrals in Eq.~(\\ref{b2eff})\nrequire knowledge of the three- and four-point functions where two\npoints coincide. Using Eqs.(\\ref{zetaI}-\\ref{etaI}) we obtain\n\n\\beq\n\\int d^3 q\\ B^I(\\k_1,\\q) = 2^{3/2} \\sqrt{\\xi^I(0)}\\ P^I(k_1),\n\\eeq\n\n\\beq\n\\int d^3q\\ T_{123}^I(\\q) = 2^{3/2} \\sqrt{\\xi^I(0)}\\ \nB_{123}^I + \\frac{4}{3} \\Sigma_{123}^I,\n\\eeq\nso that\n\n\\beq \nb_2^{\\rm eff} = b_2\\ \\left[ 3 - \\sqrt{2 \\xi^I(0)}\\ Q_{123}^I \\right]\n\\label{b2effchi}\n\\eeq\n\n\\noindent In this expression, the meaning of $\\xi^I(0)$ is the\nfollowing. As we said above, the local bias model in\nEq.~(\\ref{locbias}) holds for {\\em smoothed} fields, so $\\xi^I(0)$ is\nthe rms density fluctuation at the smoothing scale. The\nsmoothing filter is the Fourier transform, so in this case we should\nreplace $\\xi^I(0) \\approx \\Delta^I(k)$ for the average scale $k\n\\approx (k_1+k_2+k_3)/3$ under consideration. Using Eq.~(\\ref{delnl})\nand Eq.~(\\ref{QI}) we find\n\n\\beq\nb_2^{\\rm eff} \\approx (3-\\frac{8}{\\sqrt{3}\\pi})\\ b_2 \\approx 1.53\\ b_2\n\\label{b2effchi2}\n\\eeq\n\n\\noindent Thus, for $\\chi^2$ initial conditions, the usual Gaussian\ninitial conditions biasing formula is recovered (with no additional\nscale or configuration dependence) provided a proper redefinition of\nthe non-linear bias parameter is made. Note that for other spectral\nindices than $n=-1$, the resulting $b_2^{\\rm eff}$ remains independent\nof scale. In principle, there could be some residual dependence on\ntriangle configuration; however, for $n=-1.8$ the 2LPT results\ndescribed above give negligible residual configuration dependence as\nwell.\n\n\n\\section{Redshift Distortions}\n\nIn redshift space, the radial coordinate $\\s$ of a galaxy is given by\nits observed radial velocity, a combination of its Hubble flow plus\n``distortions'' due to peculiar velocities. The mapping from\nreal-space position ${\\bf \\x}$ to redshift space is given by: \n\n\\beq\n\\s=\\x - f \\ \\uz(\\x) {\\hat z},\n\\label{zmap} \n\\eeq \n\n\\noindent where $f= d\\ln D_1 / d\\ln a \\approx \\Omega^{0.6}$, and\n$\\u(\\x) \\equiv - \\v(\\x)/({\\cal H} f)$, where $\\v(\\x)$ is the peculiar\nvelocity field, and ${\\cal H}(\\tau) \\equiv (1/a)(da/d\\tau)= Ha$ is the\nconformal Hubble parameter (with FRW scale factor $a(\\tau)$ and\nconformal time $\\tau$). In Eq.~(\\ref{zmap}), we have assumed the\n``plane-parallel'' approximation, so that the line-of-sight is taken\nas a fixed direction, denoted by ${\\hat z}$. Using this mapping, the\nFourier transform of the density field contrast in redshift space\nreads (Scoccimarro et al. 1999)\n\n\\beq\n\\ds(\\k) = \\int \\frac{d^3x}{(2\\pi)^3} {\\rm e}^{-i \\k\\cdot\\x}\n{\\rm e}^{i f k_z \\uz(\\x)} \\Big[ \\d(\\x) + f \\nabla_z \\uz(\\x) \\Big].\n\\label{d_s}\n\\eeq\n\n\\noindent This equation describes the fully non-linear density field\nin redshift space in the plane-parallel approximation. In linear\nperturbation theory, the exponential factor becomes unity, and we\nrecover the well known formula (Kaiser 1987)\n\n\\beq \n\\ds(\\k)=\\d(\\k)\\ (1+f\\mu^2)\n\\label{delta_sl}, \n\\eeq\n\n\\noindent where $\\mu \\equiv k_z/k$. Redshift distortions are trivial\nto include for $Q^I_{123}$, since only linear PT is involved. Assuming\nlinear biasing, Eq.~(\\ref{delta_sl}) gives the monopole of the reduced\nbispectrum\n\n\n\\beq\nQ^I_{s\\ 123} = \\frac{\\overline{ (1+\\beta \\mu_1^2)(1+\\beta\n\\mu_2^2)(1+\\beta \\mu_3^2)}}{(1+2 \\beta/3+\\beta^2/5)^2} \\times\n\\frac{Q^I_{123}}{b_1} \\equiv A_s \\frac{Q^I_{123}}{b_1}, \n\\label{Qs123}\n\\eeq\n\n\\noindent where $\\beta \\equiv f/b_1$, $\\mu_i k_i \\equiv \\k_i \\cdot\n\\hat{z}$ and the bar denotes angular average over triangle\norientations. Note that this results holds irrespective of the type of\nnon-Gaussian initial conditions. After some algebra, we obtain $A_s =\nC_s/(1+2 \\beta/3+\\beta^2/5)^2$ with\n\n\\beq\nC_s = 1+ \\beta + \\frac{2}{5}\\beta^2 +\\frac{2}{35}\\beta^3 +\n\\frac{\\beta^2 (7+3\\beta)}{210} \\left[\n\\frac{k_1^6+k_2^6+k_3^6-k_1^4k_2^2-k_1^2k_2^4-k_1^4k_3^2-k_2^4k_3^2-\nk_1^2k_3^4-k_2^2k_3^4}{k_1^2 k_2^2 k_3^2} \\right]\n\\label{As}\n\\eeq\n\nIn Fig.~\\ref{figAs} we show the correction factor for redshift\ndistortions $A_s$. Unlike the Gaussian initial conditions case, where\nthe redshift-space correction is only about $10\\%$ (Hivon et\nal. 1995), for non-Gaussian models it can be significantly more,\ndepending on the value of $\\beta$. The reason is simply due to the\nscaling of the primordial bispectrum being dimensional rather than\nhierarchical (as that generated by gravity from Gaussian initial\nconditions). That is, from Eq.~(\\ref{Qs123}) one expects that\napproximately $A_s \\approx 1/\\sqrt{1+2/3 \\beta + \\beta^2 /5}$, which\ndescribes very well the mean value of $A_s$ shown in\nFig.~\\ref{figAs}. \n\nAs seen from Eq.~(\\ref{d_s}), the density field in redshift-space is\nexponentially sensitive to the velocity field. Thus, expanding this\neffect by linear PT is only valid at very large scales. In order to\nincorporate the non-linear effects of the redshift-space mapping, we\nran 2LPT realizations in redshift space, which take into account this\nmapping exactly. We assume a cosmological model with $\\Omega=0.3$ and\n$\\Omega_\\Lambda=0.7$, for which $\\beta \\approx\n0.51$. Figures~\\ref{figisoz} and~\\ref{figisoeqz} show the results\ncorresponding to the same triangles as in Figs.~\\ref{figiso}\nand~\\ref{figisoeq}, respectively. The amplitudes in redshift space\nare changed, but the overall behavior is the same: the $\\chi^{2}$\nmodel shows larger bispectrum amplitude and scale dependence than the\nGaussian initial conditions case. Note that 2LPT calculations in the\nlatter case also automatically include non-linear effects besides\nthose due to redshift-space distortions (``loop corrections''), which\nwere not present in the predictions shown as dot-dashed lines in\nFigs.~\\ref{figiso} and~\\ref{figisoeq}; this explains the mild scale\ndependence of the equilateral bispectrum in Fig.~\\ref{figisoeqz} {\\em\nopossite} to that of the $\\chi^{2}$ model. In summary, we conclude\nthat the results of Section~3 are robust against the effects of\nredshift distortions.\n\n\nAnother signature of primordial non-Gaussianity is provided by the\nredshift-space power spectrum. As we discussed above, when initial\nconditions are non-Gaussian, new couplings become available and\nnon-linear corrections become important at larger scales than in the\nGaussian initial conditions case. In redshift-space, this manifests\nitself in a particular way, as we now discuss. Consider the\nredshift-space power spectrum, from Eq.~(\\ref{d_s}) we can write a\nsimple expression for the power spectrum in redshift space\n(Scoccimarro et al. 1999)\n\n\\beq \nP_s(k,\\mu) = \\int \\frac{d^3 r}{(2 \\pi)^3} {\\rm e}^{-i \\k \\cdot \\r}\n\\Big\\langle {\\rm e}^{i f k \\mu [ \\uz(\\x)-\\uz(\\x') ]} \\Big[ \\d(\\x) + f\n\\nabla_z \\uz(\\x) \\Big] \\Big[ \\d(\\x') + f \\nabla_z' \\uz(\\x') \\Big]\n\\Big\\rangle\n\\label{Ps},\n\\eeq\n\n\\noindent where $\\r \\equiv \\x-\\x'$. This is a fully non-linear\nexpression, no approximation has been made except for the\nplane-parallel approximation. The factors in square brackets denote\nthe amplification of the power spectrum in redshift space due to\ninfall, and they constitute the only contribution in linear PT, giving\nKaiser's (1987) result \n\\beq\nP_s(k,\\mu) = (1+ f \\mu^2)^2 P(k)\n\\label{pkaiser}.\n\\eeq\n\\noindent The anisotropy of the power spectrum in redshift space can\nbe characterized by expanding it in multipole moments with respect to\n$\\mu$, the cosine of the angle between a given wave vector $\\k$ and\nthe line of sight $\\hat{z}$. This gives a monopole $P_0(k)=\n(1+2/3f+f^2/5) P(k)$, and quadrupole $P_2(k)= (4/3f+4/7f^2)P(k)$. The\nquadrupole to monopole ratio $P_2/P_0$ is thus sensitive to the matter\ndensity parameter $\\Omega$, in fact, assuming linear bias $P_2/P_0$ is\njust a function of $\\beta = f/b_1$ (Kaiser 1987; Hamilton 1992).\n \nOn the other hand, at smaller scales the pairwise velocity along the\nline of sight in the exponential factor in Eq.~(\\ref{Ps}) starts to\nplay a role. This eventually leads to a decrease in monopole and\nquadrupole power with respect to the linear contribution; in\nparticular, the quadrupole changes sign and becomes negative. Note\nthat this effect is distinct from that of velocity dispersion\nassociated with clusters which takes place at smaller scales than\nconsidered here, and leads to a strong negative quadrupole. In fact,\nat the scales we work the decrease in the quadrupole to monopole ratio\ncan be understood from perturbative dynamics, as has been noted before\n(Taylor \\& Hamilton 1996; Fisher \\& Nusser 1996; Hui, Kofman \\&\nShandarin 1999; Scoccimarro et al. 1999).\n\n\nFrom Eq.~(\\ref{Ps}), one expects that the scale of quadrupole zero\ncrossing is very sensitive to the magnitude of infall velocities. In\nredshift-space, infall into large-scale structures can become large\nenough that ``near'' and ``far'' sides of large-scale structures in\nreal space reverse sides in redshift-space (Hui et al. 1999). At this\npoint statistical isotropy is recovered and thus the quadrupole\nvanishes. The magnitude of infall at a given scale $k$ is essentially\ngiven by the power spectrum $P_\\theta(k)$ of the velocity divergence,\n($\\theta(\\x) \\equiv \\nabla \\cdot \\u$), which evolves according to\n(compare with Eq.\\ref{pknl})\n\n\n\\begin{equation}\nP_\\theta(k) = P^I(k) + 2 \\int d^3 q\\ G_2(\\k+\\q,-\\q) \\ B^I(\\k,\\q),\n\\label{pknlt} \n\\end{equation}\n\n\\noindent where the kernel $G_2(\\k_1,\\k_2) \\equiv 3/7 + 1/2 \\cos\\theta\n(k_1/k_2+k_2/k_1) + 4/7 \\cos^2 \\theta$ describes the second-order\nevolution of the velocity field, similar to $F_2$ in Eq.~(\\ref{den2})\nfor the density field. Thus, the velocity divergence power spectrum is\nsensitive to the primordial bispectrum. For the $\\chi^2$ model with\n$n=-1$ model as in Section~3 gives (compare with Eq.\\ref{delnl})\n\n\n\\begin{equation}\n\\Delta_\\theta(k) = \\left( \\frac{k}{k_{nl}} \\right)^2\\ \\left( 1 -\n\\frac{8}{7\\sqrt{2} \\pi} \\frac{k}{k_{nl}} \\right) \\approx \\left(\n\\frac{k}{k_{nl}} \\right)^2\\ \\left( 1 - 0.26 \\frac{k}{k_{nl}} \\right).\n\\label{delnlt} \n\\end{equation}\n\n\\noindent Thus, for $\\chi^2$ initial conditions we expect large-scale\ninfall velocities to be smaller than for Gaussian initial\nconditions. The effect of primordial non-Gaussianity on the pairwise\nvelocity distribution has been explored by Catelan \\& Scherrer (1995).\n\n\nFigures \\ref{figPk} and \\ref{figRP} show results of 100 2LPT\nrealizations of Gaussian and $\\chi^2$ initial conditions with spectral\nindex $n=-1.4$, $k_{nl} = 0.33$ h/Mpc, $\\Omega=0.3$ and\n$\\Omega_\\Lambda=0.7$. The dashed lines show the predictions of linear\nPT, Eq.~(\\ref{pkaiser}). Clearly, non-linear effects are important\neven at scales as large as $k = 0.06$ h/Mpc. Comparing the Gaussian\n(squares) and the $\\chi^2$ model (triangles), we see that the $\\chi^2$\nmodel shows a smaller amplification and the zero crossing of the\nquadrupole happens at smaller scales, consistent with infall\nvelocities being smaller as described above. In fact, the quadrupole\nhas not yet reached its large-scale limit at $k=0.06$h/Mpc. We have\nchecked that this result is not an artifact by verifying that lowering\nthe power spectrum normalization brings the quadrupole to agreement\nwith linear PT. Therefore, the shape of the quadrupole to monopole\nratio is sensitive to primordial non-Gaussianity, in this case\nbecoming flatter than the corresponding Gaussian model with the same\npower spectrum. At small scales sensitive to virial motions inside\nclusters, however, we expect a different behavior. Models with\nprimordial positive skewness such as the $\\chi^2$ model tend to have\nmore prominent ``fingers of god'' (Weinberg \\& Cole 1992).\n\n\n\n\\section{Conclusions}\n\n\nWe have explored the predictions of $\\chi^2$ initial conditions for\nclustering statistics, in particular the power spectrum and\nbispectrum. We found that extrapolation of the initial conditions\nusing linear perturbation theory is not accurate enough at the scales\nbest probed by current and future galaxy redshift surveys ($k \\ga\n0.05$ h/Mpc). This is not surprising, non-Gaussian initial conditions\nprovide additional non-linear couplings otherwise forbidden by\nsymmetry, thus non-linear gravitational corrections can become\nimportant at larger scales than in the Gaussian case.\n\n\nWe showed that when non-linear corrections are included, the\nbispectrum shows a similar configuration dependence as in the Gaussian\ncase; however its amplitude is much larger than the latter and has a\nresidual scale dependence not present in evolution from Gaussian\ninitial conditions. We included the effects of galaxy biasing and\nshowed that the galaxy bispectrum obeys the same relation to the dark\nmatter bispectrum as in the Gaussian case with a proper redefinition\nof the non-linear bias parameter. Thus, a large linear bias decreases\nthe dependence of the bispectrum on triangle configuration, and a\nnon-linear bias contributes a constant independent of configuration\njust as in the Gaussian case. The effects of redshift distortions were\nshown to change the overall amplitude of Gaussian and non-Gaussian\nbispectra, but clear difference between them remains. Thus, we\nconclude that the bispectrum is a very useful statistic to probe the\nGaussianity of initial conditions, at least for models where the\nscaling is dimensional as in the $\\chi^2$ case. Application of these\nresults to current galaxy surveys will be reported elsewhere\n(Scoccimarro et al. 2000).\n\n\nWe also discussed the effects of non-Gaussianity on the power spectrum\nin redshift space. The shape of the quadrupole to monopole ratio is\nvery sensitive to the large-scale pairwise velocity which depends on\nthe primordial bispectrum through non-linear corrections. For the\n$\\chi^2$ model, this leads to a smaller infall velocity and thus a\nsupression of overall power and smaller quadrupole zero crossing scale\ncompared to the case of Gaussian initial conditions. This provides an\nadditional signature of primordial non-Gaussianity that can be\nexplored with the future generation of galaxy redshift surveys.\n\n\n\n\\acknowledgments\n\nI thank Francis Bernardeau, Josh Frieman, Enrique Gazta\\~naga, Lam\nHui, Lev Kofman, and Jim Peebles for useful discussions.\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{AMM97} Antoniadis I., Mazur P. O., Mottola E. 1997, \\prl,\n79, 14\n\n\\bibitem{BCHJ95} Bouchet F.R., Colombi S., Hivon E., Juszkiewicz\nR. 1995, \\aap, 296, 575\n\n\\bibitem{BMW94} Buchert T., Melott A. L., Wei$\\beta$ A. G. 1994, \\aap,\n288, 349\n\n\\bibitem{CaSc95} Catelan, P., \\& Scherrer, R. J. 1995, \\apj, 445, 1\n\n\\bibitem{ChoBo96} Chodorowski, M.J., \\& Bouchet, F.R. 1996, \\mnras,\n279, 557\n\n\\bibitem{CMLMM93} Coles, P., Moscardini, L., Lucchin, F., Matarrese,\nS., \\& Messina, A. 1993, \\mnras, 264, 749\n\n\\bibitem{FKP94} Feldman H.A., Kaiser N., Peacock J. 1994, \\apj, 426,\n23\n\n\\bibitem{FiNu96} Fisher, K., \\& Nusser, A., 1996, \\mnras, 279, L1\n\n\\bibitem{FrGa99} Frieman, J.A., \\& Gazta\\~naga, E. 1999, \\apj, 521,\nL83 \n\n\\bibitem{Fry84} Fry, J.N. 1984, \\apj, 279, 499\n\n\\bibitem{FG93} Fry, J.~N., \\& Gazta\\~naga, E. 1993, ApJ, 413, 447\n\n\\bibitem{FrSc94} Fry, J.N., \\& Scherrer, R.J. 1994, \\apj, 429, 36\n\n\\bibitem{GaMa96} Gazta\\~naga, E., \\& M\\\"ah\\\"onen, P. 1996, \\apj, 462,\nL1\n\n\\bibitem{GaFo98} Gazta\\~naga, E., \\& Fosalba, P. 1998, \\mnras, 301,\n524 \n\n\\bibitem{Hamilton92} Hamilton, A. J. S. 1992, \\apj, 385, L5\n\n\\bibitem{HBCJ95} Hivon, E., Bouchet, F. R., Colombi, S., \\&\nJuszkiewicz, R. 1995, \\aap, 298, 643\n\n\\bibitem{HKS99} Hui, L., Kofman, L., \\& Shandarin, S. F. 1999,\nastro-ph/9901104\n\n\\bibitem{Jaffe94} Jaffe, A. 1994, \\prd, 49, 3893\n\n\\bibitem{K87} Kaiser, N. 1987, \\mnras, 277, 1\n\n\\bibitem{KBHP89} Kofman, L., Blumenthal, G. R., Hodges, H., \\&\nPrimack, J. R. 1989, in ``Large-Scale Structures and Peculiar Motions\nin the Universe'', eds. Latham, D. W., \\& da Costa, L. A. N., 339\n\n\\bibitem{KST99} Koyama, K., Soda, J., \\& Taruya, A. 1999,\nastro-ph/9903027 \n\n\\bibitem{LiMu97} Linde, A.D., \\& Muhanov, V. 1997, \\prd, 56, 535\n\n\\bibitem{MMLM91} Moscardini, L., Matarrese,\nS., Lucchin, F., \\& Messina, A. 1991, \\mnras, 248, 424\n\n\n\\bibitem{Peebles97} Peebles, P.J.E., 1997, \\apj, 483, L1\n\n\\bibitem{Peebles99a} Peebles, P.J.E., 1999a, \\apj, 510, 523\n\n\\bibitem{Peebles99b} Peebles, P.J.E., 1999b, \\apj, 510, 531\n\n\\bibitem{PGBB99} Pierpaoli, E., Garc\\'{\\i}a-Bellido, J., \\& Borgani,\nS. 1999, hep-ph/9909420\n\n\\bibitem{RGS99} Robinson, J., Gawiser, E., \\& Silk, J. 1999,\nastro-ph/9906156 \n\n\\bibitem{Scoccimarro97} Scoccimarro, R. 1997, \\apj, 487, 1\n\n\\bibitem{Scoccimarro98} Scoccimarro, R. 1998, \\mnras, 299, 1097\n\n\\bibitem{SCF99}\nScoccimarro, R., Couchman H. M. P., \\& Frieman J. A. 1999, \n\\apj, 517, 531\n\n\\bibitem{Scoccimarro00} Scoccimarro, R. 2000, in preparation \n\n\\bibitem{SFFF00} Scoccimarro, R., Feldman, H., Fry, J. N., Frieman,\nJ. A. 2000, in preparation \n\n\\bibitem{StPe96} Stirling, A. J., Peacock, J. A. 1996, \\mnras, 283,\nL99 \n\n\\bibitem{PSCZ99}Sutherland, W., Tadros, H., Efstathiou, G., Frenk,\nC. S., Keeble, O., Maddox, S., McMahon, R. G., Oliver, S.,\nRowan-Robinson, M., Saunders, W. \\& White, S. D. M. 1999, \\mnras, 308,\n289\n\n\\bibitem{TaHa96} Taylor, A.~N., \\& Hamilton, A.~J.~S., 1996, \\mnras,\n282, 767\n\n\\bibitem{TuSp91} Turok, N., \\& Spergel, D. N. 1991, \\prl, 66, 3093\n\n\\bibitem{VWHK99} Verde, L., Wang, L., Heavens, A.F., \\& Kamionkowski,\nM. 1999, astro-ph/9906301 \n\n\\bibitem{WeCo92} Weinberg, D., Cole, S. 1992, \\mnras, 259, 652\n\n\\bibitem{White99} White, M. 1999, \\mnras, 310, 511\n\n\\bibitem{Willick99} Willick, J. A. 1999, astro-ph/9904367\n\n\\end{thebibliography}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{bisp_isoc_r2.eps}}\n\\caption{The reduced bispectrum $Q$ for triangles with sides\n$k_1=0.068$ h/Mpc and $k_2=2 k_1$ as a function of the angle $\\theta$\nbetween $\\k_1$ and $\\k_2$. Triangles denote linear extrapolation from\n$\\chi^2$ initial conditions, whereas square symbols show the result\nof non-linear evolution. Dot-dashed lines show the predictions of\nnon-linear PT from Gaussian initial conditions with the same initial\npower spectrum as the $\\chi^2$ model.}\n\\label{figiso}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{bisp_isoc_eq.eps}}\n\\caption{The reduced bispectrum for equilateral triangles as a\nfunction of scale $k$. Line styles as in Fig.~\\protect\\ref{figiso}. }\n\\label{figisoeq}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{As_isoc.eps}}\n\\caption{The correction factor for redshift distortions to the\nprimordial bispectrum, $A_s$, as a function of angle $\\theta$ between\n$\\k_1$ and $\\k_2$ for triangles with sides $k_1/k_2=2$, for different\nvalues of $\\beta \\approx \\Omega^{0.6}/b_1$.}\n\\label{figAs}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{bispz_isoc_r2.eps}}\n\\caption{Same as Fig.~\\protect\\ref{figiso} but in redshift space.}\n\\label{figisoz}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{bispz_isoc_eq.eps}}\n\\caption{Same as Fig.~\\protect\\ref{figisoeq} but in redshift space.}\n\\label{figisoeqz}\n\\end{figure}\n\n\\clearpage\n\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{pk_isoc.eps}}\n\\caption{The power spectrum monopole (top set of curves) and\nquadrupole (bottom) as a function of scale for scale-free initial\nspectra $n=-1.4$ for Gaussian (squares) and $\\chi^2$ initial\nconditions (triangles). The dashed lines show the predictions of\nlinear PT.}\n\\label{figPk}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}[t!]\n\\centering\n\\centerline{\\epsfxsize=18truecm\\epsfysize=18truecm\\epsfbox{RP_isoc.eps}}\n\\caption{The power spectrum quadrupole to monopole ratio\n$\\Delta_2/\\Delta_0$ as a function of scale for scale-free initial\nspectra $n=-1.4$ for Gaussian (squares) and $\\chi^2$ initial\nconditions (triangles). The horizonal line denotes the large-scale\nlimit expected in linear perturbation theory.}\n\\label{figRP}\n\\end{figure}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002037.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{AMM97} Antoniadis I., Mazur P. O., Mottola E. 1997, \\prl,\n79, 14\n\n\\bibitem{BCHJ95} Bouchet F.R., Colombi S., Hivon E., Juszkiewicz\nR. 1995, \\aap, 296, 575\n\n\\bibitem{BMW94} Buchert T., Melott A. L., Wei$\\beta$ A. G. 1994, \\aap,\n288, 349\n\n\\bibitem{CaSc95} Catelan, P., \\& Scherrer, R. J. 1995, \\apj, 445, 1\n\n\\bibitem{ChoBo96} Chodorowski, M.J., \\& Bouchet, F.R. 1996, \\mnras,\n279, 557\n\n\\bibitem{CMLMM93} Coles, P., Moscardini, L., Lucchin, F., Matarrese,\nS., \\& Messina, A. 1993, \\mnras, 264, 749\n\n\\bibitem{FKP94} Feldman H.A., Kaiser N., Peacock J. 1994, \\apj, 426,\n23\n\n\\bibitem{FiNu96} Fisher, K., \\& Nusser, A., 1996, \\mnras, 279, L1\n\n\\bibitem{FrGa99} Frieman, J.A., \\& Gazta\\~naga, E. 1999, \\apj, 521,\nL83 \n\n\\bibitem{Fry84} Fry, J.N. 1984, \\apj, 279, 499\n\n\\bibitem{FG93} Fry, J.~N., \\& Gazta\\~naga, E. 1993, ApJ, 413, 447\n\n\\bibitem{FrSc94} Fry, J.N., \\& Scherrer, R.J. 1994, \\apj, 429, 36\n\n\\bibitem{GaMa96} Gazta\\~naga, E., \\& M\\\"ah\\\"onen, P. 1996, \\apj, 462,\nL1\n\n\\bibitem{GaFo98} Gazta\\~naga, E., \\& Fosalba, P. 1998, \\mnras, 301,\n524 \n\n\\bibitem{Hamilton92} Hamilton, A. J. S. 1992, \\apj, 385, L5\n\n\\bibitem{HBCJ95} Hivon, E., Bouchet, F. R., Colombi, S., \\&\nJuszkiewicz, R. 1995, \\aap, 298, 643\n\n\\bibitem{HKS99} Hui, L., Kofman, L., \\& Shandarin, S. F. 1999,\nastro-ph/9901104\n\n\\bibitem{Jaffe94} Jaffe, A. 1994, \\prd, 49, 3893\n\n\\bibitem{K87} Kaiser, N. 1987, \\mnras, 277, 1\n\n\\bibitem{KBHP89} Kofman, L., Blumenthal, G. R., Hodges, H., \\&\nPrimack, J. R. 1989, in ``Large-Scale Structures and Peculiar Motions\nin the Universe'', eds. Latham, D. W., \\& da Costa, L. A. N., 339\n\n\\bibitem{KST99} Koyama, K., Soda, J., \\& Taruya, A. 1999,\nastro-ph/9903027 \n\n\\bibitem{LiMu97} Linde, A.D., \\& Muhanov, V. 1997, \\prd, 56, 535\n\n\\bibitem{MMLM91} Moscardini, L., Matarrese,\nS., Lucchin, F., \\& Messina, A. 1991, \\mnras, 248, 424\n\n\n\\bibitem{Peebles97} Peebles, P.J.E., 1997, \\apj, 483, L1\n\n\\bibitem{Peebles99a} Peebles, P.J.E., 1999a, \\apj, 510, 523\n\n\\bibitem{Peebles99b} Peebles, P.J.E., 1999b, \\apj, 510, 531\n\n\\bibitem{PGBB99} Pierpaoli, E., Garc\\'{\\i}a-Bellido, J., \\& Borgani,\nS. 1999, hep-ph/9909420\n\n\\bibitem{RGS99} Robinson, J., Gawiser, E., \\& Silk, J. 1999,\nastro-ph/9906156 \n\n\\bibitem{Scoccimarro97} Scoccimarro, R. 1997, \\apj, 487, 1\n\n\\bibitem{Scoccimarro98} Scoccimarro, R. 1998, \\mnras, 299, 1097\n\n\\bibitem{SCF99}\nScoccimarro, R., Couchman H. M. P., \\& Frieman J. A. 1999, \n\\apj, 517, 531\n\n\\bibitem{Scoccimarro00} Scoccimarro, R. 2000, in preparation \n\n\\bibitem{SFFF00} Scoccimarro, R., Feldman, H., Fry, J. N., Frieman,\nJ. A. 2000, in preparation \n\n\\bibitem{StPe96} Stirling, A. J., Peacock, J. A. 1996, \\mnras, 283,\nL99 \n\n\\bibitem{PSCZ99}Sutherland, W., Tadros, H., Efstathiou, G., Frenk,\nC. S., Keeble, O., Maddox, S., McMahon, R. G., Oliver, S.,\nRowan-Robinson, M., Saunders, W. \\& White, S. D. M. 1999, \\mnras, 308,\n289\n\n\\bibitem{TaHa96} Taylor, A.~N., \\& Hamilton, A.~J.~S., 1996, \\mnras,\n282, 767\n\n\\bibitem{TuSp91} Turok, N., \\& Spergel, D. N. 1991, \\prl, 66, 3093\n\n\\bibitem{VWHK99} Verde, L., Wang, L., Heavens, A.F., \\& Kamionkowski,\nM. 1999, astro-ph/9906301 \n\n\\bibitem{WeCo92} Weinberg, D., Cole, S. 1992, \\mnras, 259, 652\n\n\\bibitem{White99} White, M. 1999, \\mnras, 310, 511\n\n\\bibitem{Willick99} Willick, J. A. 1999, astro-ph/9904367\n\n\\end{thebibliography}"
}
] |
astro-ph0002038
|
A Search for Resonant Structures in the Zodiacal Cloud with COBE DIRBE: The Mars Wake and Jupiter's Trojan Clouds
|
[
{
"author": "Marc J. Kuchner"
}
] |
We searched the COBE DIRBE Sky and Zodi Atlas for a wake of dust trailing Mars and for Trojan dust near Jupiter's L5 Lagrange point. We compare the DIRBE images to a model Mars wake based on the empirical model of the Earth's wake as seen by the DIRBE and place a 3-$\sigma$ upper limit on the fractional overdensity of particles in the Mars wake of 18\% of the fractional overdensity trailing the Earth. We place a 3-$\sigma$ upper limit on the effective emitting area of large (10-100 micron diameter) particles trapped at Jupiter's L5 Lagrange point of $6 \times 10^{17}$ cm${}^2$, assuming that these large dust grains are distributed in space like the Trojan asteroids. We would have detected the Mars wake if the surface area of dust in the wake scaled simply as the mass of the planet times the Poynting-Robertson time scale.
|
[
{
"name": "paper.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n\\lefthead{Kuchner, Reach and Brown}\n\\righthead{Resonant Structures in the Zodiacal Cloud with DIRBE}\n\\begin{document}\n\n\\title{A Search for Resonant Structures in the Zodiacal Cloud with COBE DIRBE: The Mars Wake and Jupiter's Trojan Clouds}\n\\author{Marc J. Kuchner}\n\\affil{Palomar Observatory, California Institute of Technology, Pasadena, CA 91125}\n\\authoremail{[email protected]}\n\\author{William T. Reach}\n\\affil{Infrared Processing and Analysis Center, Caltech, Pasadena, CA 91125}\n\\author{Michael E. Brown\\altaffilmark{1}}\n\\affil{Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125}\n\\altaffiltext{1}{Alfred P. Sloan Research Fellow}\n\\author{Running head: Resonant Structures in the Zodiacal Cloud with DIRBE} \n\n\n\\begin{abstract}\nWe searched the COBE DIRBE Sky and Zodi Atlas for a wake of dust\ntrailing Mars and for Trojan dust near Jupiter's L5 Lagrange point. \nWe compare the DIRBE images to a model Mars wake\nbased on the empirical model of the Earth's wake as seen by the DIRBE\nand place a 3-$\\sigma$ upper limit on the fractional overdensity of particles\nin the Mars wake of 18\\% of the fractional overdensity trailing the Earth. We place a 3-$\\sigma$ upper limit on the effective emitting area\nof large (10-100 micron diameter) particles trapped at Jupiter's L5 Lagrange\npoint of $6 \\times 10^{17}$ cm${}^2$, assuming that these large dust grains are distributed in space like the Trojan asteroids. We would have detected\nthe Mars wake if the surface area of dust in the wake scaled simply as\nthe mass of the planet times the Poynting-Robertson time scale. \n\\end{abstract}\n\n\\keywords{asteroids -- extrasolar planets -- interplanetary dust -- Jupiter -- Mars -- resonances}\n\n\\section {Introduction}\nA planet interacting with a circumstellar dust cloud can produce a variety\nof dynamical structures in the dust. Planets can clear central holes and\ncreate large-scale asymmetries, such as arcs and warps\n\\markcite{roqu94}(Roques et al. 1994). Planets can also detain dust in\nmean motion resonances, forming structures such as the circumsolar ring\nand wake of dust trailing the Earth in its orbit \\markcite{jack89}(Jackson\nand Zook 1989; \\markcite{derm94}Dermott et al. 1994) and clouds of dust at\nthe planet's Lagrange points \\markcite{liou95}(Liou and Zook 1995). \n\nUnderstanding the structures of circumstellar debris disks is vital\nto the search for extra-solar analogs of our solar system. Concentrations\nin circumstellar dust clouds may confuse planet-finding interferometers\nlike the Keck Interferometer or the proposed Terrestrial Planet Finder \\markcite{beic99}(Beichman 1999). Smooth exo-zodiacal clouds can be\nidentified by their symmetry and subtracted from the signal of a Bracewell\ninterferometer \\markcite{macp79}(MacPhie and Bracewell 1979), but cloud\nasymmetries can be difficult to distinguish from planets \\markcite{beic98}(Beichman 1998). On the other hand, planet-induced\nasymmetries can serve to reveal the presence of a planet that is\notherwise undetectable \\markcite{wyat99}(Wyatt et al. 1999).\n\nIf we understand the inhomogeneities in our own zodiacal dust cloud, we\nwill be better prepared to interpret observations of other planetary\nsystems. The Diffuse Infrared Background Experiment (DIRBE) aboard the\nCosmic Background Explorer (COBE) satellite has provided detailed,\nrevealing images of the zodiacal cloud \\markcite{spie95}(eg. Spiesman et\nal. 1995, \\markcite{reac97}Reach et al. 1997). It surveyed the entire\nsky from near-Earth orbit in 10 broad infrared bands simultaneously with\na $0.7^{\\circ}$ by $0.7^{\\circ}$ field of view over a period of 41 weeks\n\\markcite{bogg92}(Boggess et al. 1992), and imaged the Earth's ring and wake\n\\markcite{reac95}(Reach et al. 1995). We investigated the COBE DIRBE\ndata set as a source of information about structure in the solar zodiacal\ncloud associated with planets other than Earth. \n\n\\section{The Data Set}\n\nWe worked with a version of the DIRBE data set which contains the sky\nbrightness with a model for the background zodiacal emission subtracted:\nthe zodi-subtracted weekly data set from the DIRBE Sky and Zodi Atlas\n(DSZA). The DIRBE team created the DZSA by fitting an 88-parameter model\nof the zodiacal dust emission to the observed sky brightness \\markcite{kels98}(Kelsall et al. 1998). The model includes a smooth\nwidened-fan component, three pairs of dust bands near the ecliptic plane,\nand the Earth's ring and trailing wake, but no structures associated with\nMars, Jupiter, or any other planets. The zodi-subtracted weekly data\nset contains 41 files for each DIRBE band, spanning a period from\n10~December 1989 to 21~September 1990, covering 10 bands, centered\nat 1.25, 2.2, 3.5, 4.9, 12, 25, 60, 100, 140, and 240 microns.\n\nGalactic emission dominates the zodi-subtracted maps in the mid and\nfar-infrared near the galactic plane. Near the ecliptic plane, the\nzodi-subtracted maps are dominated by residuals from the subtraction of\nthe dust bands that are associated with prominent asteroid families\n\\markcite{reac97}\\markcite{kels98} (Reach et al. 1997; Kelsall et al.\n1998). The presence of these bands makes searching for smooth, faint\nheliocentric rings of dust near the ecliptic plane impossible. However,\nwe could hope to distinguish a blob of dust following a planet across\nthe sky from other cloud components and from the galactic background by\nthe apparent motion of the blob during the COBE mission.\n\nThe COBE satellite orbited the Earth near the day/night terminator and\nrepeatedly mapped a swath of the sky extending about 30 degrees before\nand behind the terminator (see the COBE DIRBE Explanatory Supplement\n\\markcite{cobe}(1997) for details). Each weekly map contains a robust\naverage of all the week's data and covers a region a little larger than\nthe daily viewing swath. This weekly averaging tends to\nexclude transient events that would contaminate our final maps, but\nshould not otherwise significantly affect a search for large features\nthat move only a few degrees per week. Figure 1 is a schematic view of\nthe solar system during week 34 of the mission (9--16 July 1990) showing\nthe positions of Earth, Mars and Jupiter, and the DIRBE viewing swath\nfor that week. \n\nBecause DIRBE never imaged the sky within $60^{\\circ}$ of the sun, the\norbits of Mercury and Venus, for instance, do not appear in the data.\nMars appeared in the DIRBE viewing swath for 25 weeks of the mission, and\nmoved $111^{\\circ}$ in ecliptic longitude during those weeks. Jupiter\nmoved only $40^{\\circ}$ in ecliptic longitude during the entire mission,\nbut this is sufficient to allow some crude background subtraction. More\ndistant planets moved less. Based on these constraints, we decided to\nsearch the weekly maps for dust features following the orbital paths\nof Mars and Jupiter. Figure 2 shows the intersection of the DIRBE viewing\nswath with the ecliptic plane throughout the 41 weeks of the mission,\nand the ecliptic longitudes of Mars, Jupiter and the Sun during those\nweeks. \n\n\\section{The Mars Wake}\n\nA ring of zodiacal dust particles detained in near-Earth resonances\nfollows the Earth around the sun \\markcite{jack89}(Jackson and Zook 1989; \\markcite{derm94}Dermott et al. 1994). This ring consists mainly of\ndust in mean-motion resonances where the particles orbit the sun $j$\ntimes every $j+1$ Earth years (j is a whole number). Smaller trapped\nparticles experience greater Poynting-Robertson acceleration, so the\nequilibrium locations of their orbital pericenters shift closer to\nthe Earth on the trailing side, where the component of Earth's gravity\nthat opposes Poynting-Robertson drag is stronger. The result, averaged\nover many particles, appears as a density enhancement in the ring\nbehind the Earth---a trailing dust wake. The Earth's wake was detected by\nby IRAS \\markcite{derm88}\\markcite{reac91}(Dermott et al. 1988,\nReach 1991), and later, by DIRBE as an asymmetry in the near-Earth dust\nbrightness of $\\sim 1.1$ MJy ster${}^{-1}$ at 12 microns and $\\sim 1.7$\nMJy ster${}^{-1}$ at 25 microns \\markcite{reac95} (Reach et al. 1995).\nWe searched the DIRBE data set for a similar wake of dust trailing Mars.\n\nBlackbody dust at the heliocentric distance of Mars has a typical\ntemperature of $\\sim 220$ K; it emits most strongly in the 12 and 25\nmicron DIRBE bands. We restricted our exploration to data from these\ntwo bands. We began by assembling a composite map of the emission\nfrom beyond the solar system, mostly due to stars and dust in the\nGalactic plane, by averaging together all the zodi-subtracted weekly\nmaps in their native COBE quadrilateralized spherical cube coordinates,\na coordinate system that is stationary on the celestial sphere. We\nsubtracted this composite map from each of the zodi-subtracted weekly\nmaps, effectively removing most of the galactic emission and any other\nstationary emission except within a few degrees of the galactic plane,\nwhere the emission is so high that detector and pointing instabilities\nmake our linear subtraction method ineffective. \n\nThe remaining maps, with outlying data removed, had surface brightness\nresiduals in the range of -1.7 to +1.0 MJy ster${}^{-1}$ at 12 microns,\nand -1.6 to 2.1 MJy ster${}^{-1}$ at 25 microns. For comparison, the\ntypical total zodiacal background near Mars during the mission is\n$\\sim 35$ MJy ster${}^{-1}$ at 12 microns and $\\sim 66$ MJy ster${}^{-1}$\nat 25 microns. The most prominent remaining features were the stripes\nparallel to the ecliptic plane within a few degrees of the ecliptic\nplane that are associated with the asteroidal dust bands. The\nnext most prominent remaining features were wide bands extending\n$\\pm 30$ degrees from the ecliptic that appeared to follow the sun.\nThe $12 - 25$ micron color temperature of the wide bands was\n$\\sim 280$ K; they are probably residuals resulting from imperfect\nsubtraction of the Earth's ring and wake. We assembled a crude map of\nthe residual near-Earth flux by averaging together the galaxy-subtracted\nmaps in geocentric ecliptic coordinates referenced to the position of\nthe Sun. Subtracting this from the weekly maps cancelled most of\nthe signal in the wide bands. Mars moved $87^{\\circ}$ with respect\nto the Sun during the mission, allowing us to subtract this composite\nmap without subtracting a significant flux from a wake moving with Mars.\nFigure 3a shows our map of the galactic background; Figure 3b shows the\nnear-Earth residuals.\n\nNext we chose subframes of each weekly map centered on the ecliptic\ncoordinates of Mars in the middle of the week, and inspected them\nvisually. No structure in the data appeared to move with Mars from\nweek to week.\n\nIn order to understand the data better, we constructed a simple model\nof the Mars wake from the empirical model of the Earth's trailing wake\nfit to the DIRBE data by \\markcite{kels98}Kelsall et al. (1998). The model\nhas the following form:\n\\begin{equation}\nn = n_0 \\exp{\\left [ -{{(r-r_{0})^2} \\over { 2 \\sigma_r^2}}-{{|z|} \\over {\\sigma_z}} - {{(\\theta - \\theta_0)^2} \\over {2 \\sigma_{\\theta}^2}}\\right ]}\n\\end{equation}\nwhere $n$ is the local average of particle number density times particle\ncross section, and $r$,$z$, and $\\theta$ are cylindrical coordinates in\nthe plane of the orbit of Mars centered on the sun. Mars is located at\n$r=r_{0}$, $z=0$, $\\theta = 0$. The parameters of the model, $\\theta_0$,\n$\\sigma_r$, $\\sigma_z$, $\\sigma_{\\theta}$, and $n_0$, are the same as\nthe corresponding parameters for the Earth's wake:\n$\\theta_0 = -10^{\\circ}$, $\\sigma_r =0.10$ AU, $\\sigma_z=0.091$ AU, $\\sigma_{\\theta} = 12.1^{\\circ}$. The shaded area trailing Mars in\nFigure 1 shows how this model would appear viewed from above the\necliptic plane. The \\markcite{kels98}Kelsall et al. (1998) Earth wake\nhas $n_0 = 1.9 \\times 10^{-8} \\ {\\rm AU}^{-1}$, but we chose\n$n_0 = 1.08 \\times 10^{-8} \\ {\\rm AU}^{-1}$ so that the density of\nthe model would be proportional to the local background dust density at\nthe orbit of Mars. The model represents what the Earth wake would\nlook like if it were trailing Mars instead of Earth.\n\nWe evaluated the model's surface brightness by computing the line-of-sight integral\n\\begin{equation}\nI_{\\lambda} = E_{\\lambda} \\int n (r,z,\\theta) B_{\\lambda}(T) ds\n\\end{equation}\nwhere $B_{\\lambda}(T)$ is the Planck function and $E_{\\lambda}$ is an\nemissivity modification factor prescribed by the COBE model to account\nfor the deviation of the Earth wake's spectrum from a blackbody;\n$E_{12 \\mu {\\rm m}} = 1.06$, $E_{25 \\mu {\\rm m}} = 1.00$. The\ntemperature of the dust varies with heliocentric distance, $R$, as\n$T = 286 \\ {\\rm K}\\ R^{-0.467}$, following the DIRBE model. This\nexpression is similar to what you would expect for grey-body dust\n($T = 278 \\ {\\rm K}\\ R^{-0.5}$). \n\nIn Figure 4, we compare a synthesized image of the model wake with a background-subtracted image of the infrared sky around Mars. The image\nshows the flux in the 25 micron band averaged over weeks 26--34\n(14 May 1990 to 15 July 1990) in ecliptic coordinates referenced to\nthe position of Mars. The subset of the weekly 25-micron data used in\nthis image is indicated by the horizontal stripes labeled ``M'' in\nFigure 2. Mars moved 40 degrees in ecliptic longitude\nover this period. The DIRBE team blanked the data within a square about\n$2.5^{\\circ}$ on a side centered on Mars, and within a $1.5^{\\circ}$\nradius circle centered on Jupiter. A software mask in Figure 4\ncovers the region around Mars affected by this processing. \nThis whole region, up to $40^{\\circ}$ behind Mars, shows no sign of\na brightness enhancement that we would associate with a wake\nof dust trailing Mars.\n \nMaps from the later weeks suffer from an oversubtraction due to\nimperfections in the \\markcite{kels98}Kelsall et al. (1998) zodi\nmodel, visible as the dark region to the lower right. \nWeeks earlier in the mission suffer from a similar undersubtraction.\nThese artifacts, our primary source of noise, appear to arise\nfrom dust bands at latitudes of $\\sim \\pm10^{\\circ}$, where bands\nassociated with the Eos asteroids are prominent in the raw DIRBE\ndata \\markcite{reac97}(Reach et al. 1997). \nAs the dust from the asteroid belt spirals towards the sun, perturbations\nfrom planets deform the bands. The Kelsall et al. model includes a\nsimple model of this dust band which could not take these perturbations\ninto account. We chose the span of weeks used to create Figure 4\nto minimize these artifacts, which are easily discernible by their\nextent in latitude and longitude.\n\nTo better compare the model with the data, we focused on a narrow\nstrip with a height of $3^{\\circ}$ in ecliptic latitude, extending from\n$8^{\\circ}$ ahead of Mars to $39^{\\circ}$ behind Mars in ecliptic\nlongitude. This strip contains most of the flux in the model wake. We\naveraged together maps from weeks 26--34 prepared as described above\nto produce an image of this strip. In Figure 5, we plot a cut through\nthis strip, and we compare it with the model, processed in the same\nmanner as the data. The data are dominated by residuals from the\necliptic bands and the Earth's ring, smeared out in the ecliptic plane\nby the orbital motion of Mars. The standard deviation of the data is\n0.54 MJy ster${}^{-1}$; although the distribution of the residuals\nis not Gaussian, based on this comparison we can place a rough\n3-$\\sigma$ upper limit on the central peak of the Mars wake of 18\\% of\nthe flux expected from our simple model.\n\nThe empirical model of the Earth's wake we have used for comparison to\nthe Mars dust environment is not an ideal model for the Mars wake. It\nmay not even be a good representation of the Earth's wake. Since COBE\nviewed the Earth wake from near the Earth only, the observations constrain\nthe product $n_0 \\sigma_{\\theta}$ for the Earth wake, but do not provide\ngood constraints on either of these parameters alone. Kelsall et al. \\markcite{kels98}(1998) quote a formal error of 28\\% on the\ndetermination of $\\sigma_{\\theta}$. Calculations for 12 micron particles\nsuggest that $\\sigma_{\\theta}$ for the Earth wake might be 40\\% lower\nthan the Kelsall et al. \\markcite{kels98}(1988) number; this figure is\nbased on Figure 5 in Dermott et al. \\markcite{derm94}(1994). Since we\nare sensitive to the wake's surface brightness peak as seen from the\nEarth, not Mars, using a more compact wake model affects our upper\nlimits. Holding $n_0 \\sigma_{\\theta}$ constant and decreasing\n$\\sigma_{\\theta}$ by 40\\% translates into a decrease of our upper limit\nto 11\\% of one Earth wake.\n\nMars has 11\\% of the mass of the Earth, so we expect it to trap less\ndust than the Earth, but not simply 11\\% as much dust. In fact,\nthere is no simple scaling law that describes how the density of a \ndust ring relates to the size of the planet that traps it. The density\nof the Mars ring is proportional to the capture probability\ntimes the trapping time for each resonance summed over all relevant\nresonances and the distribution of particle sizes. In the adiabatic\ntheory for resonant capture due to Poynting-Robertson drag, the capture probabilities depend on the mass of the planet compared to the\nmass of the star and on the eccentricity of the particle near\nresonance and \\markcite{beau94}(Beauge and Ferraz-Mello 1994). So one\ncomplicating factor is that the orbits of the dust particles are\nslightly more eccentric when they pass Mars than when they pass the\nEarth; a particle released on the orbit of a typical asteroid, at\n2.7 AU with an eccentricity of 0.14, will have an eccentricity of 0.07\nas it passes Mars, and an eccentricity of 0.04 when it passes the Earth\n\\markcite{wyat50}(Wyatt \\& Whipple 1950). The higher eccentricity\nmakes them harder to trap.\n\nThe trapping time scale is proportional to the time it takes for the\nresonant interaction to significantly affect the eccentricity and\nlibration amplitude of the particle. When the planet has a circular\norbit, these time scales are on the order of the local\nPoynting-Robertson decay time \\markcite{liou97}(Liou and Zook 1997),\nwhich scales as $r_0^2/\\beta$, where $\\beta$ is the ratio\nof the Sun's radiation-pressure force on a particle to the Sun's\ngravitational force on the particle. Compared to the P-R drag at the\nheliocentric distance of the Earth, the Poynting-Robertson drag force\nat the orbit of Mars is less for a given particle by a factor of\n$1.52^2 = 2.31$. The small mass of Mars and the higher eccentricities\nof the orbits of the incoming particles work against the formation of\na dense ring, but the greater heliocentric distance of Mars compared\nto the Earth works in favor of the formation of the ring.\n\nSo far our discussion has assumed that the trapping is adiabatic---\nthat the orbital elements of the particles change on time scales much\nlonger than the orbital period. This approximation may not be as good\nfor trapping by Mars as it is for trapping by the Earth. Mars has\na greater orbital eccentricity ($e=0.093$) than the Earth ($e=0.017$).\nThis increases the widths of the zones of resonance overlap, and makes\na larger fraction of dust orbits chaotic \\markcite{murr97}(Murray and\nHolman 1997). \n\nPredicting the density of the Mars wake is another step more complex\nthan predicting the density of the Mars ring.\nCompared to the Earth wake, the Mars wake may form closer to the planet\nand have a smaller $\\sigma_{\\theta}$. Since Mars is less massive than\nthe Earth, a given particle would need to have a closer interaction\nwith Mars than with the Earth to receive an impulse from the planet's\ngravity that would balance the Poynting-Robertson drag on the particle\n(Weidenschilling and Jackson \\markcite{weid93}1993). For this reason,\nwe expect the trapped particles which form the Mars wake to prefer\nresonant orbits with higher $j$ and lower $\\phi$ than similar particles\ntrapped by the Earth, where $\\phi$ is the angle between the perihelion\nof the orbit of a particle and the longitude of conjunction of the\nparticle and the planet. Our upper limit shows that the Mars wake is\nless dense than the Earth wake by more than the simple factor of the\nmass ratio times the square of the ratio of the semimajor axes\n$= 0.11 \\times 2.31 = 0.25$. However, a thorough numerical simulation\nwhich includes the effects we mentioned and others such as resonant\ninteractions with Jupiter may be the only good way to relate our upper\nlimit to the dynamical properties of the dust near Mars. \n\n\\section{Trojan Dust}\n\nWhile the Earth and Mars can collect abundant low eccentricity particles\nfrom all different orbital phases spiraling in from the asteroid belt,\nJupiter orbits in a distinctly different dust environment. Outside the\nasteroid belt, the dust background probably consists mainly of small\nparticles with high orbital eccentricities: submicron particles released\nby asteroids or comets that are kicked by radiation pressure into more\neccentric orbits than their parent bodies (\\markcite{berg73}Berg and\nGr\\\"un 1973; \\markcite{mann95}Mann and Gr\\\"un 1995). There is also a\nstream of submicron particles from the interstellar medium\n\\markcite{grun94}\\markcite{grog96}(Gr\\\"un et al. 1994, Grogan et al. 1996)\nand there are probably a few particles near Jupiter that originated in\nthe Kuiper belt \\markcite{liou96}(Liou et al. 1996). Jupiter\nprobably traps many of the small particles in 1:1 mean motion resonances\n(Liou and Zook 1995\\markcite{liou95}). However these small trapped\nparticles should occupy both ``tadpole'' and ``horseshoe''\norbits, without a strong preference for either, and the locations of\ntheir Lagrange points vary with $\\beta$ \\markcite{murr94}(Murray 1994).\nThey probably form large, diffuse ring-like clouds which are difficult\nfor us to detect.\n\nBut there is another potential source of dust that could form concentrated\nclouds we could hope to detect against the asteroid bands in the DIRBE\ndata: the Trojan asteroids. This population of asteroids orbits the Sun\nat $\\sim 5.2$ AU in 1:1 resonances with Jupiter, librating about Jupiter's\nL4 and L5 Lagrange points, roughly $60^{\\circ}$ before and behind the planet. \nThey number about as many as the main-belt asteroids.\n\nMarzari et al. \\markcite{marz97}(1997) have simulated the collisional\nevolution of the Trojan asteroids, and concluded that collisions in\nthe L4 swarm produce on the order of 2000 fragments in the 1--40 km\ndiameter range every million years. If we simplisticly assume a\nequilibrium size distribution for the produced particles,\n$dn \\propto a^{-3.5} da$, where a is the particle radius (Dohnanyi 1969),\nwe find that there are roughly $10^{23}$ particles in the 10--100 micron diameter size range produced every million years. These large particles\nare likely to stay in roughly the same orbits as their parent bodies,\ntrapped by Jupiter in ``tadpole'' orbits---orbits that librate\naround a single Lagrange point. They could conceivably form detectable\nclouds at L4 and L5. \n\nLiou and Zook (1995) calculated that 2-micron diameter particles will\nstay trapped in 1:1 resonances for $\\sim5000$ years. A 20-micron diameter particle at Jupiter's orbit experiences $1/10$ of the Poynting-Robertson acceleration of 2 micron\nparticles, and will typically stay trapped for 10 times as long\n\\markcite{schu80}(Schuerman 1980). Assuming a trapping time of\n$5000$ years $\\times$ the dust grain diameter/2 microns, and emissivity appropriate for amorphous icy grains\n\\markcite{back93}(eg. Backman and Paresce 1993), the 10--100\nmicron diameter particles in the Trojan cloud will emit a total flux, as viewed\nfrom the Earth, of $\\sim 3 \\times 10^{-4}$ MJy at 60 microns, a few orders\nof magnitude below our detection limit.\n\nHowever, this is a drastic extrapolation and probably a poor guess at\nthe actual cloud brightness; the size-frequency distribution of the\nTrojan asteroids is not well known and dust cloud is probably not near\ncollisional equilibrium. Moreover, the total amount of trapped dust\nis subject to severe transients, such as the events that produced the\ndust bands associated with main belt asteroid families\n\\markcite{syke86}(Sykes and Greenberg 1986). For example, a 20-km\ndiameter Trojan asteroid ground entirely into 10-micron diameter\ndust corresponds to a transient cloud which, as viewed from the Earth,\nwould produce a 60 micron flux of $\\sim 6$ MJy. A similarly enhanced\ncloud might be visible a few percent of the time.\n\nUnfortunately, Jupiter's Lagrange points do not move far with respect to the\ngalactic background during the COBE mission; L4 moves 10 degrees and L5\nmoves 50 degrees, as shown in Figure 2. Only L5, the trailing Lagrange\npoint, moves far enough during the mission to make subtracting the\ngalactic background feasible. There are about half as many L5 Trojans\nknown as L4 Trojans, but this is probably because the L5 region has\nbeen searched less intensely than the L4 region, not because the L4\nand L5 populations are significantly different\n\\markcite{shoe89}(Shoemaker et al. 1989).\n\nTo make a background-subtracted image of the L5 region, we chose two\nsubsets from the zodi-subtracted data set. The first, subset A, is\nfrom the beginning of the mission (weeks 5-10) when L5 was in the\nviewing swath and approximately stationary on the sky. The second,\nsubset B, is the same region of sky, but contains data from half a\nyear later in the mission (weeks 33--38), when L5 has moved 45 degrees\naway, out of the viewing swath. The average distance from Earth to\nL5 is approximately the same during each time period. These data\nsets are depicted in Figure 2. We focused on data in the 60 micron\nband, the band which contains the emission peak for dust at the local\nblackbody temperature at 5.2 AU. To minimize the residuals from\nthe zodiacal dust model, we used only data from solar elongations\nbetween 65 and 115 degrees, (or between 245 and 295 degrees).\nFigure 6 shows an image constructed from data set A and an image\nconstructed from data set B, and the difference, A$-$B, which is\ndominated by residuals from dust bands associated with asteroid bands\nand shows no obvious evidence of enhanced emission at L5. \n\nWe made a simple model for a Trojan cloud of large dust particles by\nassuming that they occupy the same dynamical space as the Trojan\nasteroids themselves, following Sykes \\markcite{syke90}(1990). Sykes\nmodeled the asteroidal dust bands by showing how particles constrained\nto orbits with a given inclination, eccentricity, and semimajor axis\nform a cloud when the remaining three orbital elements are randomized.\nHe then convolved the shapes of these clouds with the distributions of\norbital elements of the asteroids. In our case, however, the\ndistribution of orbital elements is much broader and more important in\ndetermining the shape of the final distribution of particles. Since\nthere are only about 70 Trojan asteroids whose orbits are well studied,\nthe distributions of Trojan asteroid orbital parameters have severe\nstatistical uncertainties. Therefore we settle for a simple Gaussian\nmodel for the Trojan cloud, using the orbital parameters as a guide to\nthe parameters of the Gaussian. In the following calculations, we will\nneglect the inclination of Jupiter's orbit relative to the the Earth's\norbit ($1.305^{\\circ}$).\n \nA typical Trojan asteroid librates around its Lagrange point with a\nperiod of 148 days. The mean longitude of the asteroid with respect to\nJupiter, $\\phi$, oscillates within limits $\\phi_{min}$ and $\\phi_{max}$,\nwhich can be calculated, according to Yoder et al.\n\\markcite{yode83}(1983), from \n\\begin{equation}\n\\sin{ \\phi_{min} \\over 2} = {\\sin{( \\alpha / 3)} \\over B} \\qquad \\sin{ \\phi_{max} \\over 2} = {\\sin{( \\alpha / 3 + 120^{\\circ})} \\over B}\n\\end{equation}\nwhere $B= \\eta_0 ({{3 \\mu} / {2E}})^{1/2}$, $\\sin{\\alpha}=B$, $\\mu = {\\rm M}_{\\rm Jupiter}/{\\rm M}_{\\odot} = 0.000955$ and $\\eta_0$ = mean motion of Jupiter = 0.01341 rad yr${}^{-1}$. \nThese limits are set by $E$, which is a constant of the motion in the\nabsence of Poynting Robertson drag:\n\\begin{equation}\nE=-{1 \\over 6} \\Bigl({{d \\phi} \\over {d t}}\\Bigr)^2 - {{\\mu \\eta_0^2} \\over {2 x}} (1+ 4x^3)\n\\end{equation}\nwhere $ x = |\\sin{(\\phi/2)}|$. The libration amplitude, $D$, is $\\phi_{max} -\\phi_{min}$. We find that the energy constant is approximately\n\\begin{equation}\nE \\approx - {{3} \\over {2}} \\mu \\eta_0^2 \\bigl(1 - 0.0133 D + 0.2266 D^2 - 0.0392 D^3\\bigr)\n\\end{equation}\nfor $D \\leq 1.3$.\n\nThe fraction of time a particle spends at a given phase, or equivalently,\nthe distribution in phase of an ensemble of particles is given by\n\\begin{equation}\nP_\\phi \\propto {{1} \\over {d \\phi / d t}}.\n\\end{equation}\nWe can evaluate this as a function of $D$ with the aid of equations (4)\nand (5). For the distribution of dust libration amplitudes, $P_D$, we\nused a simple analytic function that approximates the distribution of\nlibration amplitudes for Trojan asteroids shown in Figure~5 of\nShoemaker et al. \\markcite{shoe89}(1989). When we average $P_{\\phi}$\nover $P_D$, we find that the L5 dust cloud is distributed in orbital\nphase roughly as a Gaussian centered at $\\theta_0=59.5^{\\circ}$ behind\nJupiter with a dispersion $\\sigma_{\\theta}=10^{\\circ}$. \n\nThe distribution of the dust in heliocentric latitude can be approximated\nin a similar way. If particle in an orbit of given inclination, $i$,\nwith small eccentricity, spends a fraction of its time, $f$, at latitude,\n$\\beta$, an ensemble of particles with small eccentricities and evenly\ndistributed ascending nodes will have a distribution, at a fixed orbital\nphase, of\n\\begin{equation}\nP_{\\beta} \\propto f \\propto (\\cos^2{\\beta} - \\cos^2{i})^{-1/2}.\n\\end{equation}\nWe takes the inclination distribution of the particles, $P_i$, to be\na simple analytic function that approximates the data for ``independently\ndiscovered Trojans'' shown in Figure 3 of Shoemaker et al. \\markcite{shoe89}(1989).\nWhen we average $P_{\\beta}$ over $P_i$, we find the distribution in\nlatitude is roughly a Gaussian with dispersion $\\sigma_{\\beta}=10^{\\circ}$,\nand the distribution in height above the ecliptic has a dispersion\n$\\sigma_z=0.94$ AU.\n\nThe radial distribution of Trojans is more complicated to model, since\nboth librations and epicycles include radial excursions. The average L5\nTrojan eccentricity is 0.063; a particle with this eccentricity orbits at\na range of heliocentric distances, $\\Delta r \\approx $ 0.66 AU. In the\ncourse of its librations, a particle with a typical Trojan libration\namplitude, $D=29^{\\circ}$, oscillates in semi-major axis over a range\nof $\\Delta a \\approx $0.14 AU. We are not sensitive to the radial\nstructure of the Trojan clouds, so we simply model the radial\ndistribution as a Gaussian with a full width at half maximum of 0.66 AU,\nor a dispersion $\\sigma_r=0.24$ AU.\n\nOur final model has the form:\n\\begin{equation}\nn = n_0 \\exp{\\left [ -{{(r-r_{0})^2} \\over { 2 \\sigma_r^2}}-{{z^2} \\over { 2 \\sigma_z^2}} - {{(\\theta - \\theta_0)^2} \\over {2 \\sigma_{\\theta}^2}}\\right ]}\n\\end{equation}\nwhere $r$, $z$, and $\\theta$ are cylindrical coordinates in the plane of the orbit of Jupiter, and the parameters are: $r_0=5.203$ AU, $\\sigma_r=0.24$ AU, $\\sigma_z=0.94$ AU, $\\theta_0=-59.5^{\\circ}$, and $\\sigma_{\\theta}=9.7^{\\circ}$.\nWe calculated the surface brightness in the same way as we calculated the surface brightness of the model Mars wake, using an emissivity $E_{60 \\mu {\\rm m}} = 1$ because we are not considering small grains. The shaded region\nat L5 in Figure 1 represents this model as viewed from above the ecliptic plane.\n \nIn Figure 6, we compare the difference image A$-$B to a synthesized image\nof our model cloud. For this image, $n_0$ is\n$3.4 \\times 10^{-8} {\\rm AU}^{-1}$, corresponding to an effective\nemitting surface area at 60 microns of\n$3.3 \\times 10^{18}$ cm${}^2$, or one 3-km diameter\nasteroid ground entirely into 10-micron diameter dust. Figure 7 compares the\ndifference image A$-$B and the model image in a different way; it shows\nthe region within $\\pm 10^{\\circ}$ of the ecliptic plane averaged in\necliptic latitude. The 1-$\\sigma$ noise in the data in Figure 7 is\n0.09 MJy ster${}^{-1}$. Based on this, we can place a rough 3-$\\sigma$\nupper limit on the effective surface area of the large dust grains at L5 of\n$\\sim 6 \\times 10^{17} {\\rm cm}^2$. \n\n\\section{Conclusions}\n\nThe zodiacal cloud near the ecliptic plane is a complex tapestry of\ndynamical phenomena. We could not detect the Mars wake or Jupiter's\nTrojan clouds among the asteroidal dust bands in the DIRBE maps, despite \nthe efforts of the DIRBE team to subtract these bands from the maps. \nWe would have detected the Mars wake if it had 18\\% of the overdensity\nof the Earth wake, based on our empirical model for the Earth\nwake. This upper limit illustrates the complexity of relating resonant\nstructures in circumstellar dust disks to the properties of perturbing\nplanets. For instance, we would have detected the Mars wake if the\nsurface area of the dust in the wake scaled simply with the mass of the\nplanet times the Poynting-Robertson time scale. \n\nThe Trojan clouds, by our crude estimation, would have been a few orders\nof magnitude too faint to detect if the dust concentration in these clouds\nwere at its mean levels. However, a transient cloud created by a\nrecent collision of Trojan asteroids might have been detectable. We\nmeasured that the total 60-micron flux from large\n(10--100 micron diameter) dust particles trapped at Jupiter's\nL5 Lagrange point is less than $\\sim30$ kJy.\n\n\\acknowledgments\n\nWe thank Antonin Bouchez, Eric Gaidos, Peter Goldreich, Renu Malhotra and\nIngrid Mann for helpful discussions, and our referees for their\nthoughtful comments.\n\n\\begin{references}\n\n\\reference{beau94}Beaug\\'e, C., and S. Ferraz-Mello 1994. Capture in Exterior Mean-Motion Resonances Due to Poynting-Robertson Drag. Icarus 110, 239-260\n\n\\reference{beic98}Beichman, C. A. 1998. Sensitivity of the Terrestrial Planet Finder. In Exozodiacal Dust Workshop Conference Proceedings (D. E. Backman, L. J. Caroff, S. A. Sandford, and D. H. Wooden, Eds.), pp. 149-172 (NASA/CP-1998-10155)\n\n\\reference{beic99}Beichman, C. A., Woolf, N. J., \\& Lindensmith, C. A. (eds)\n1999, JPL Publication 99-3, The Terrestrial Planet Finder (Pasadena: JPL)\n\n\\reference{berg73}Berg, O. E., and E. Gr\\\"un 1973. Evidence of Hyperbolic Cosmic Dust Particles. In Space Research XIII, p. 1047 Akademie-Verlag, Berlin.\n\n\\reference{bogg92}Boggess, N. W., Msther, J. C., Weiss, R., Bennett, C. L.,\nCheng, E. S., Dwek, E., Gulkis, S., Hauser, M. G., Janssen, M. A.,\nKelsall, T., Meyer, S. S., Moseley, S. H., Murdock, T. L., Shafer, R. A.,\nSilverberg, R. F., Smoot, G. F., Wilkinson, D. T., Wright, E. L.\n1992, ApJ, 379, 420\n%``The COBE mission - Its design and performance two years after launch''\n\n\\reference{cobe}COBE Diffuse Infrared Background Experiment (DIRBE) Explanatory Supplement, ed. M.G. Hauser, T. Kelsall, D. Lesiawitz, and J. Weiland, COBE Ref. Pub. No. 97-A (Greenbelt, MD: NASA/GSFC), available in electronic form from the NSSDC\n\n\\reference{derm94}Dermott, S.F., S. Jayaraman, Y. L. Xu, B.\\AA.S. Gustafson, and J. C. Liou 1994. A Circumsolar Ring of Asteroidal Dust in Resonant Lock With The Earth. Nature 369, 719--723\n\n\\reference{derm88}Dermott, S.F., P. D. Nicholson, Y. Kim, B. Wolven, and E. F. Tedesco 1988. The Impact of IRAS on Asteroidal Science. In Comets to Cosmology (A. Lawrence, Ed.), pp. 3--18. Springer-Verlag, Berlin\n\n\\reference{grog96}Grogan, K., S. F. Dermott, and B. \\AA. S. Gustafson 1996. Astrophys. J. 472, 812--817\n\n\\reference{grun94}Gr\\\"un, E., B. \\AA. S. Gustafson, I. Mann, M. Baguhl, G. E. Morfill, P. Staubach, A. Taylor, and H. A. Zook 1994. Astron. Astrophys. 286, 915-924\n\n\\reference{jack89}Jackson, A. A., and H. A. Zook 1989. A Solar System Dust Ring with the Earth as its Shepherd. Nature 337, 629--31\n\n\\reference{kels98}Kelsall, T., J. L. Weiland, B. A. Franz, W. T. Reach, R. G. Arendt, E. Dwek, H. T. Freudenreich, M. G. Hauser, S. H. Moseley, N. P. Odegard,\n R. F. Silverberg, R. F. and E. L. Wright 1998. The COBE Diffuse Infrared Background Experiment Search for the Cosmic Infrared Background. II. Model of\nthe Interplanetary Dust Cloud. Astrophys. J. 508, 44--73\n\n\\reference{liou95}Liou, J.C., and H. A. Zook 1995. An Asteroidal Dust Ring of Micron Sized Particles Trapped in the 1:1 Mean Motion Resonance with Jupiter.\nIcarus 113, 403--414\n\n\\reference{liou97}Liou, J. C., and H. A. Zook 1997. Evolution of Interplanetary Dust Particles in Mean Motion Resonances. Icarus, 128, 354--367\n\n\\reference{liou96}Liou, J.C., H. A. Zook, and S. F. Dermott 1996. Kuiper Belt Dust Grains as a Source of Interplanetary Dust Particles. Icarus 124, 429--440\n\n\\reference{mann95}Mann, I., and E. Gr\\\"un 1995. Dust Particles Beyond The Asteroid Belt--a Study Based on Recent Results of the Ulysses Dust Experiment. \nPlanet. Space Sci. 43, 827--832\n\n\\reference{marz97}Marzari, F., P. Farinella, D. R. Davis, H. Scholl, and A. Campo Bagatin 1997. Collisional Evolution of Trojan Asteroids. Icarus\n125, 39--49\n\n\\reference{macp79}MacPhie, R. H. and R. N. Bracewell 1979. An Orbiting Infrared Interferometer to Search for Non-Solar Planets. Proc. SPIE 172, 271--278\n\n\\reference{murr94}Murray, C. Dynamical Effects of Drag in the Circular Restricted Three-Body Problem. Icarus. 112, 465--484\n\n\\reference{murr97}Murray, N., and M. Holman 1997. Diffusive Chaos in the Outer Asteroid Belt. Astron. J. 114, 1246--1259\n\n\\reference{reac91}Reach, W.T. 1991. Zodiacal Emission. II. Dust Near Ecliptic Astrophys. J. 369, 529--543\n\n\\reference{reac95}Reach, W.T., B. A. Franz, J. L. Weiland, M. G. Hauser, T. N. Kelsall, E. L. Wright, G. Rawley, S. W. Stemwedel, and W. J. Spiesman 1995. Observational Confirmation of a Circumsolar Dust Ring by the COBE Satellite. Nature 374, 521--523\n\n\\reference{reac97}Reach, W.T., B. A. Franz, and J. L. Weiland 1997. The Three Dimensional Structure of the Zodiacal Dust Bands. Icarus 127, 461--484\n\n\\reference{roqu94}Roques, F., H. Scholl, B. Sicardy, and B. A. Smith 1994. Is There a Planet around Beta Pictoris? Perturbations of a Planet on a\nCircumstellar Dust Dist: 1 The Numerical Model. Icarus 108, 37--58\n\n\\reference{schu80}Schuerman, D. W. 1980. The Restricted Three-Body Problem Including Radiation Pressure. Astrophys. J. 238, 337--342\n\n\\reference{shoe89}Shoemaker, E. M., C. S. Shoemaker, and R. F. Wolfe 1989.\nTrojan Asteroids: Populations, Dynamical Structure and Origin of the\nL4 and L5 Swarms. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S.\nMatthews, Eds.), pp. 487--523. Univ. of Arizona Press, Tucson.\n\n\\reference{spie95}Spiesman, W. J., M. G. Hauser, T. Kelsall, C. M. Lisse, S. H.\nMoseley, W. T. Reach, R. F. Silverberg, S. W. Stemwedel, and J. L. Wieland 1995.\nNear- and Far-Infrared Observations in Interplanetary Dust Bands From the COBE Diffuse Infrared Background Experiment. Astrophys. J. 442, 662--667\n\n\\reference{syke90}Sykes, M. V. 1990. Zodiacal Dust Bands: Their Relation to Asteroid Families. Icarus 84, 267--289\n\n\\reference{syke86}Sykes, M. V. and R. Greenberg 1986. The Formation\nand Origin of the IRAS Zodiacal Dust Bands as a Consequence of Single\nCollisions between Asteroids. Icarus 65, 51--69\n\n\\reference{weid93}Weidenschilling, S. J., and A. A. Jackson 1993. Orbital Resonances and Poynting-Robertson Drag. Icarus 104, 244--254\n\n\\reference{wyat99}Wyatt, M. C., S. F. Dermott, C. M. Telesco, R. S. Fisher, K. Grogan, E. K. Holmes, and R. K. Pi\\~na 1999. How Observations of Circumstellar Disk Asymmetries Can Reveal Hidden Planets: Pericenter Glow and its Application to the HR 4796 Disk. In preparation.\n\n\\reference{wyat50}Wyatt, S. P. and F. L. Whipple 1950. The\nPoynting-Robertson Effect On Meteor Orbits. Astrophys. J. 111, 134-141\n\n\\reference{yode83}Yoder, C.F., G. Colombo, S. P. Synnott, and K. A. Yoder 1983. Theory of Motion of Saturn's Coorbiting Satellites. Icarus 53, 431--443\n\\end{references}\n\n\n\\newpage\n\n\\figcaption{The solar system during week 34. The shaded regions following Mars represents our model for the Mars wake; the shaded region centered on L5 represents our model for the Trojan cloud. The hatched area represents the DIRBE viewing swath for that week. \\label{fig1}} \n\n\\figcaption{The ecliptic longitudes of the Sun, Mars, Jupiter, and Jupiter's L4 and L5 Lagrange points during 40 weeks of the COBE mission when DIRBE was recording. The shaded diagonal stripes show the intersection of the DIRBE viewing swath with the ecliptic plane. The vertical dashed lines show where the galactic plane crosses the ecliptic. The horizontal bars show the data sets used to construct Figures 4,5,and 6. \\label{fig2}} \n\n\\figcaption{Two 25-micron backgrounds that we subtracted from the Mars images. a) The galactic background, constructed by averaging all the weekly maps in their native quadrilateralized spherical cube coordinates. b) Residuals from the Earth's wake, constructed by averaging all the weekly galaxy-subtracted maps in a geocentric ecliptic coordinate system with the sun at the origin.\\label{fig3}}\n\n\\figcaption{An image of the sky near Mars at 25 microns, compared to a model based on the COBE DIRBE empirical model for the wake trailing Earth. The image is averaged over weeks 26--34 (data set M). The region within $1.5^{\\circ}$ of Mars has been covered by a software mask.\\label{fig4}}\n\n\\figcaption{A cut through the image of the 25-micron sky near Mars shown in Figure 4, compared to the same model. \\label{fig5}}\n\n\\figcaption{Raw DSZA images in the ecliptic plane at 60 microns. L5 is at the center of image A, but it has moved 45 degrees to the right of center in image B. The difference, A$-$B cancels most of the galactic emission, but is dominated by residuals from dust bands associated with the asteroid belt and does not reveal any Trojan dust. The model shows what we would expect the difference A$-$B to look like, given some simple assumptions about the Trojan clouds.\\label{fig6}}\n\n\\figcaption{The difference A$-$B compared to the model for the L5 cloud. This plot shows a region of the 60-micron maps from Figure 6 within $\\pm 10^{\\circ}$ of the ecliptic plane that has been averaged in latitude. Based on this comparison, we place a 3-$\\sigma$ upper limit on the surface area of the L5 cloud of $6 \\times 10^{17} {\\rm cm}^2$.\\label{fig7}}\n\n\\end{document}\n\n\n"
}
] |
[] |
astro-ph0002039
|
Keck Speckle Imaging of the White Dwarf G29-38: No Brown Dwarf Companion Detected
|
[
{
"author": "Marc J. Kuchner"
},
{
"author": "Christopher D. Koresko"
},
{
"author": "and Michael E. Brown\\altaffilmark{1}"
}
] |
The white dwarf Giclas 29-38 has attracted much attention due to its large infrared excess and the suggestion that excess might be due to a companion brown dwarf. We observed this object using speckle interferometry at the Keck telescope, obtaining diffraction-limited resolution (55 milliarcseconds) at K band, and found it unresolved. Assuming the entire K band excess is due to a single point-like companion, we place an upper limit on the binary separation of $30$ milliarcseconds, or $0.42$ AU at the star's distance of 14.1 pc. This result, combined with astroseismological data and other images of G29-38, supports the hypothesis that the source of the near-infrared excess is not a cool companion but a dust cloud.
|
[
{
"name": "paper.tex",
"string": "% Incorporating comments from Ben Zuckerman\n\\documentstyle[12pt,aaspp4]{article}\n\\begin{document}\n\n\\title{Keck Speckle Imaging of the White Dwarf G29-38: No Brown Dwarf Companion Detected}\n\\author{Marc J. Kuchner, Christopher D. Koresko, and Michael E. Brown\\altaffilmark{1}}\n\\affil{Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125}\n\\altaffiltext{1}{Alfred P. Sloan Research Fellow}\n\\authoremail{[email protected]}\n\n\\begin{abstract}\nThe white dwarf Giclas 29-38 has attracted much attention\ndue to its large infrared excess and the suggestion that excess\nmight be due to a companion brown dwarf. We observed this\nobject using speckle interferometry at the Keck telescope, obtaining diffraction-limited resolution (55 milliarcseconds)\nat K band, and found it unresolved. Assuming the entire K band excess is\ndue to a single point-like companion, we place an upper limit on the binary separation of $30$ milliarcseconds, or $0.42$ AU at the star's distance of 14.1 pc. This result, combined with astroseismological data and other images of G29-38, supports the hypothesis that the source of the near-infrared excess is not a cool companion but a dust cloud.\n\n\\end{abstract}\n\n\\keywords{binaries: general --- circumstellar matter --- stars: individual (G29-38) --- stars: low mass, brown dwarfs --- white dwarfs}\n\n\\section {Introduction}\n\n\\markcite{zuck87} Zuckerman and Becklin (1987) discovered that the\nwhite dwarf Giclas 29-38 has\na large infrared excess and proposed that\nthe excess could be due to a brown dwarf companion. This suggestion\ninspired discussion of brown dwarfs as white dwarf companions\n\\markcite{stri90} (Stringfellow, Black \\& Bodenheimer 1990),\noscillating brown dwarfs \\markcite{marl90} (Marley, Lunine \\&\nHubbard 1990), and other possible cool companions\nthat could explain the excess \\markcite{gree88} (Greenstein 1988).\nLater photometry by \\markcite{toku90}Tokunaga\net al. (1990) and \\markcite{tele90}Telesco, Joy \\& Sisk (1990)\nsuggested that the 10 micron excess greatly exceeds that\nexpected from a brown dwarf companion, leading to the interpretation that the mid-infrared excess originates from a cloud of circumstellar dust.\nHowever, new data from ISOCAM \\markcite{char98}(Chary, Zuckerman \\& \nBecklin 1998) show that the 7 and 15 micron excesses are in agreement \nwith a 1000 K blackbody fit to the excess at other wavelengths. \nThe source of the infrared excess of G29-38 remains uncertain.\n\nDirect searches for a companion have produced mixed results. Tokunaga et al. \\markcite{toku88}(1988) imaged G29-38 at H and K bands and limited the\nextent of the source to a diameter of 400 milliarcseconds (mas) or 5.64 AU. Tokunaga et al. \\markcite{toku88}(1988) and Tokunaga et al.\n\\markcite{toku90}(1990) took near-infrared spectra of the object and\nfound no evidence for\nabsorption features due to a brown dwarf. Haas and Leinert\n\\markcite{haas90}(1990) took slit scans of G29-38 in 1988, and\nfound a North-South extension at K-band that was well fit by a binary\nmodel with a flux ratio of 1:1 and a separation of $230 \\pm 40$ mas ($3.24 \\pm 0.56$ AU). However, when Haas and Lienert repeated their\nobservations the following year under better\nseeing conditions, the object appeared unextended. Shelton, Becklin\nand Zuckerman \\markcite{shel98}(1998) took slit scans of G29-38 in\nthe J and K bands at the Lick 3-meter telescope in October of 1989 to look\nfor the centroid shift that would arise if, as the photometry suggests,\nthe hypothetical cool companion is brighter in K and the white dwarf\nis brighter in J. They did not see this effect. They place an upper limit of\n$40$ mas (0.56 AU) on the North-South binary separation, and\nan upper limit of $120$ mas (1.69 AU) on the East-West separation.\n\nAttempts to find the radial velocity signature of a companion to G29-38\nhave also proven frustrating. \\markcite{barn92}Barnbaum \\& Zuckerman (1992)\ncombined their own spectroscopy with radial velocity data by \\markcite{grah90}Graham et al. (1990),\nGraham, Reid, \\& Rich (1991, personal communication reported in Graham\net al. 1990), Liebert \\& Saffer (1989,\npersonal communication reported in Graham et al. 1990) and \\markcite{lieb89}\nLiebert, Saffer, \\& Pilachowski (1989), and\nreported a probable radial velocity variation with a period of\n11.2 months and an amplitude of $10 \\ {\\rm km} \\ {\\rm s}^{-1}$. Kleinman et al.\n\\markcite{klei94}(1994), however, argued\nbased on extensive astroseismological observations that the radial velocity variation due to a binary companion must be less than $\\pm 0.65 \\ {\\rm km} \\ {\\rm s}^{-1}$ assuming a $\\sim$1 year period. \n\nHoping to find another clue to the mystery of the infrared excess,\nwe imaged G29-38 at K band on the 10-m W. M. Keck\ntelescope using speckle interferometry to search for a resolved companion\nat the diffraction limit. \n\n\\section {Observations}\n\nWe imaged G29-38 at K band with NIRC (the Near-Infrared Camera; \\markcite{matt94}Matthews \\& Soifer 1994) on the W. M. Keck telescope\non December 15, 1997. The seeing was extraordinary; we used 0.5 second integrations and saw about 5 speckles and a diffraction-limited core. \nWe took 12 sets of 100 frames of G29-38. Among observations of\nG29-38 we interspersed observations of two nearby, presumably unresolved\ncalibrator stars, S23291+0515 and S23292+0521, which we observed in the\nsame manner as G29-38, for a total of 6 sets of calibrator frames. We\nused a version of the speckle reduction software described in Koresko et al. \\markcite{kore91}(1991) adapted for use with NIRC. We chose\na $128 \\times 128$ pixel subframe centered on the object, and constructed\n$128 \\times 128$ pixel sky frames from the corners of the\n$256 \\times 256$ pixel NIRC images. From each set of object and sky frames\nwe computed a power spectrum, and a bi-spectrum, and\nre-constructed Fourier phases and amplitudes. We divided the Fourier components\nfrom each target set by the Fourier components from a few different calibrator\nsets to correct for the telescope-aperture transfer function, and in\nthis way assembled 18 calibrated images and 18 calibrated power spectra.\n\nFigure 1 shows the mean of the images, compared to a simulated image of a\npoint source---the Fourier transform of the Gaussian$\\times$Hanning apodizing function used to synthesize the speckle images. The plate scale is 20.57 mas per pixel. Figure 2 shows the azimuthal average of the arithmetic\nmean of the calibrated power spectra, where we normalized each power\nspectrum by dividing it by the geometric mean of the first 15 data points after\nthe zero-frequency component.\nThe error bars represent the 1-$\\sigma$ variations among the 18 power spectra. The $\\lambda/D$ diffraction limit of Keck at K-band is 55 mas. The noise increases at high frequencies because the power in the images decreases\nnear the diffraction limit. The low frequency spike probably occurs because of\nseeing noise, the change in seeing between observations of G29-38 and observations of the calibrators. Because the final image closely resembles a point source and the power spectrum is consistent with a constant,\nthe power spectrum of a $\\delta$-function, we conclude that we did not resolve G29-38. \n\n\n\\section {Discussion}\n\nThe K-band flux of G29-38 is $5.46 \\pm 0.15$ mJy; 2.05 mJy of this is in excess of Greenstein's \\markcite{gree88}(1988) white dwarf model\n\\markcite{toku90}(Tokunaga, Becklin \\& Zuckerman 1990).\nWe computed the power spectrum of a binary system consisting of\na Greenstein white dwarf and a point-like companion which supplies\nall the excess flux. The only free parameter for this binary model is the angular separation of the components. We fit the model to the observed power spectrum, and derive a best fit binary separation of 20 mas. The maximum deviation of the power spectrum from a straight line, however, is consistent with typical deviations due to time variations of the atmosphere-telescope point-spread function. In figure 2, we compare the 20 mas model with the observed power spectrum and a model with the same flux ratio but a 30 mas separation. The latter model is marginally inconsistent with our observations, so we report 30 mas as an upper limit to the binary separation.\n\nAt G29-38's distance of 14.1 pc \\markcite{toku90}(Tokunaga et al. 1990), 30 mas corresponds to a transverse separation\nof 0.42 AU. Assuming that G29-38 is 0.61 $M_{\\odot}$\n\\markcite{berg95}(Bergeron et al. 1995), an 0.06 $M_{\\odot}$\nbrown dwarf orbiting the star at 0.42 AU would have a period of about\n0.33 years and would create a reflex motion in G29-38 that\nwould have been detectable to Kleinman et al. \\markcite{klei94}(1994)\nif the orbit were inclined more than 10 degrees from face-on. The statistical likelyhood of an inclination $\\le 10$ degrees is 1.5\\%. Closer orbits\nwould be easier to detect from reflex motion.\n\nPerhaps a brown dwarf orbits G29-38 with a long period that would be hard to identify in reflex motion and the brown dwarf happened to pass in front of the star or behind it when we observed it on December 15, 1997. For instance, Kleinman et al. \\markcite{klei94}(1994) saw a long-term trend in their radial velocity data which could be interpreted as a companion with an $\\sim 8$ year period causing radial velocity variations on the order of 0.8 km/s. Such a companion would have a semimajor axis of $\\sim 3.4$ AU. If the orbit had a semi-major axis $a$, and were edge-on, the fraction of the time the brown dwarf would spend in the region where we couldn't resolve it is $\\sim {2 \\over \\pi} \\sin^{-1}{0.42 AU \\over a}$; for $a=3.4$ AU, there is a $<8$\\% chance that the brown dwarf would have been hidden from us. Since Shelton et al. \\markcite{shel98}(1998) also missed the hypothetical edge-on brown dwarf in 1989 as it passed close to the star, we find this scenario unlikely.\n\nA companion in an eccentric orbit is easier to detect from reflex motion than a companion in a circular orbit with the same semi-major axis. Therefore such a companion would have to be farther away from the star on average for Kleinman et al. \\markcite{klei94}(1994) to have missed it, making it even more unlikely that it would have been hidden from us, Haas \\& Lienert \\markcite{1990}(1990), and Shelton et al. \\markcite{shel98}(1998). A companion in an eccentric, face-on orbit would spend relatively little time close to the star, and probably would not have been missed by both us and Shelton et al. \\markcite{shel98}(1998). \n\nThe infrared excess may represent thermal radiation from a cloud of dust rather than a cool companion \\markcite{zuck87}(Zuckerman\n\\& Becklin 1987). We can place no constraints on the concentration or geometry of such a cloud. Dust radiating thermally at 1--15 microns heated by radiation from the white dwarf alone would be far too close to the star ($ < 10^{-3}$ AU) for us to resolve. \n\n\\section {Conclusions}\n\nWe conclude that the infrared excess of G29-38 is not due to a single\norbiting companion. If there were a single companion producing the excess, it would have to orbit almost face-on and closer than 0.4 AU; or it could orbit roughly edge on, with a period of several years, in such a way that it happened to appear at a minimum angular separation from the star in December, 1997 when we observed it and in the fall of 1989 when Haas \\&\nLienert \\markcite{haas90}(1990) and Shelton et al. \\markcite{shel98}(1998) observed it. Either case is highly improbable. This result supports the hypothesis that source of the near-infrared excess is not\na cool companion but a dust cloud \\markcite{zuck87}(Zuckerman\n\\& Becklin 1987; \\markcite{wick87}Wickramasinghe et al. 1987; \\markcite{grah90} Graham et al. 1990; \\markcite{koes97} Koester et al. 1997).\n\n\\acknowledgments\n\nWe thank Eugene Chiang, Chris\nClemens, Peter Goldreich, and Ben Zuckerman for inspiration and\nhelpful discussions. The observations reported here were obtained at\nthe W. M. Keck Observatory, which is operated by the California\nAssociation for Research in Astronomy, a scientific partnership among\nCalifornia Institute of Technology, the University of California, and\nthe National Aeronautics and Space Administration. It was made possible\nby the generous financial support of the W. M. Keck Foundation.\n\n\\begin{references}\n\n\\reference{barn92}Barnbaum, C., \\& Zuckerman, B. 1992, ApJ, 396, L31\n%``THE RADIAL-VELOCITY OF THE WHITE-DWARF GICLAS 29-38''\n\n\\reference{berg95}Bergeron, P., Wesemael, F., Lamontagne, R., Fontaine, G., Saffer, R.A., \\& Allard, N.F. 1995, 449, 258\n%``Optical and Ultraviolet Analyses of ZZ Ceti Stars and Study of the \n%Atmospheric Convective Efficiency in DA White Dwarfs''\n\n\\reference{char98}Chary, R., Zuckerman, B., \\& Becklin, E. E., 1998, in preparation\n\n\\reference{grah90}Graham, J. R., McCarthy, J. K., Reid, I. N., \\& Rich,\nR. M. 1990, ApJ, 357, L21 \n% ``Does G 29-38 have a massive companion ?''\n\n\\reference{gree88}Greenstein, J. L. 1988, AJ, 95, 1494 \n%``The companion of the white dwarf G 29-38 as a brown dwarf''\n \n\\reference{haas90}Haas, M., \\& Leinert, C. 1990, A\\&A, 230, 87\n%binary separation is 0.23 arcsec plus/minus 0.04 arcsec\n%``SEARCH FOR THE SUSPECTED BROWN DWARF COMPANION TO\n%GICLAS-29-38 USING IR-SLIT-SCANS''\n\n\\reference{klei94}Kleinman, S. J. et al. 1994, ApJ, 436, 875 \n% ``Observational limits on companions to G29-38'' \n% KLEINMAN S.J., NATHER R.E., WINGET D.E., CLEMENS J.C., BRADLEY\n% P.A., KANAAN A., PROVENCAL J.L., CLAVIER C.F., WATSON T.K.,\n% YANAGIDA K., DIXSON J.S., WOOD M.A., SULLIVAN D.J., MEISTAS E.,\n% LEIBOWITZ E.M., MOSKALIK P., ZOLA S., PAJDOSZ G., KRZESINSKI J.,\n% SOLHEIM J.-E., BRUVOLD A., O'DONOGHUE D., KATZ M., VAUCLAIR G.,\n% DOLEZ N., CHEVRETON M., BARSTOW M.A., KEPLER S.O., GIOVANNINI\n% O., HANSEN C.J., KAWALER S.D\n\n\\reference{koes97}Koester, D., Provencal, J., \\& Shipman, H. L. 1997, A\\&A, 230, L57\n\n\\reference{kore91}Koresko, C. D., Beckwith, S. V., Ghez, A. M., Matthews, K., \\& Neugebauer, G. 1991, AJ, 102, 2073\n%``An Infrared Companion to Z Canis Majoris''\n\n\\reference{lieb89}Liebert, J., Saffer, R. A., \\& Pilachowski, C.A. 1989, AJ, 97, 182\n% radial velocity data \n \n\\reference{marl90}Marley, M. S., Lunine J. I., \\& Hubbard, W. B. 1990, ApJ 348, L37 \n% ``The periodicities in the infrared excess of G 29-38 : an\n% oscillating brown dwarf ?'' \n\n\\reference{matt96}Matthews, K., Ghez, A. M., Weinberger, A. J., \\& Neugebauer, G. 1996, PASP, 615\n%``The First Diffraction-Limited Images from the W. M. Keck Telescope''\n\n\\reference{matt94}Matthews, K. \\& Soifer, B.T. 1994, Infrared Astronomy with Arrays: the Next Generation, I. McLean ed. (Dordrecht: Kluwer Academic Publishers), p.239 \n \n\\reference{shel98}Shelton, C., Becklin, E. E., \\& Zuckerman, B. 1998, personal communication\n% Infrared Slit Scans in J and K\n% binary separation is\n% <0.04 arcsec North/South <0.12 arcsec East West\n% plus 0.04 arc sec statistical errors\n\n\\reference{stri90}Stringfellow, G., Black, D. C., \\& Bodenheimer, P. 1990, ApJ, 349, L59\n%``Brown Dwarfs as Close Companions to White Dwarfs''\n\n\\reference{tele90}Telesco, C. M., Joy, M., \\& Sisk, C. 1990, ApJ, 358, L17 \n%``Observations of G 29-28 at 10 microns. ''\n\n\n\\reference{toku90}Tokunaga, A. T., Becklin, E. E., \\& Zuckerman, B. 1990, ApJ, 358, L21 \n% ``The infrared spectrum of G 29-38 '' \n\n\\reference{toku88}Tokunaga, A. T., Hodapp, K.-W., Becklin, E. E., Cruikshank, D. P., Rigler, M., Toomey, D., Brown, R. H., \\& Zuckerman, B. 1988, ApJ, L71\n%``Infrared Spectroscopy, Imaging, and 10 Micron Photometry of Giclas 29-38''\n\n\\reference{wick87}Wickramasinghe, N. C., Hoyle, F., \\& Al-Mufti, S. 1987, Ap. Space Sci., 143, 193 \n\n\\reference{zuck87}Zuckerman, B. \\& Becklin, E. E. 1987, Nature, 330, 138 \n%``Excess infrared radiation from a white dwarf-an orbiting brown dwarf ? ''\n\n\\end{references}\n\n\\newpage\n\n\\figcaption{Reconstructed K-band speckle image of G29-38 compared to a synthesized image of a point source. Both are normalized so their intensities range from 0 to 1, and have contour levels of 0.1, 0.3, 0.5, 0.7, and 0.9.\nG29-38 is unresolved. \\label{fig1}}\n\n\\figcaption{Azimuthally averaged spatial power spectrum of G29-38 compared to simulated azimuthally-averaged power spectra of a binary with a flux ratio equal to the G29-38's K-band excess. The error bars represent 1-$\\sigma$ variations among the 18 object-calibrator pairs. If G29-38 were a binary with this K-band flux ratio and the separation were larger than 30 mas, we would\nhave detected the companion. \\label{fig2}}\n\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002040
|
An 11.6 Micron Keck Search For Exo-Zodiacal Dust
|
[
{
"author": "Marc J. Kuchner"
},
{
"author": "Michael E. Brown and Chris D. Koresko"
}
] |
We have begun an observational program to search nearby stars for dust disks that are analogous to the disk of zodiacal dust that fills the interior of our solar system. We imaged six nearby main-sequence stars with the Keck telescope at 11.6 microns, correcting for atmosphere-induced wavefront aberrations and deconvolving the point spread function via classical speckle analysis. We compare our data to a simple model of the zodiacal dust in our own system based on COBE/DIRBE observations (Kelsall et al. 1998) and place upper limits on the density of exo-zodiacal dust in these systems.
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"name": "paper.tex",
"string": "\n\\documentstyle[12pt,aaspp4]{article}\n\\begin{document}\n\n\\title{An 11.6 Micron Keck Search For Exo-Zodiacal Dust}\n\\author{Marc J. Kuchner, Michael E. Brown and Chris D. Koresko}\n\\affil{California Institute of Technology, Pasadena, CA 91125}\n\\authoremail{[email protected], [email protected], [email protected]}\n\n\\begin{abstract}\n\n\nWe have begun an observational program to search nearby stars for dust disks\nthat are analogous to the disk of\nzodiacal dust that fills the interior of our solar system.\nWe imaged six nearby\nmain-sequence stars with the Keck telescope at 11.6 microns,\ncorrecting for atmosphere-induced wavefront aberrations and\ndeconvolving the point spread function via classical speckle\nanalysis. We compare our data to a simple model of the zodiacal\ndust in our own system based on COBE/DIRBE observations (Kelsall et\nal. 1998) and place upper limits on the density of exo-zodiacal\ndust in these systems.\n\n\\end{abstract}\n\n\\keywords{circumstellar matter --- infrared radiation --- interplanetary medium --- planetary systems --- techniques: image processing}\n\n\\section {INTRODUCTION}\n\nOur sun is surrounded by a disk of warm ($>$150 K) ``zodiacal'' dust\nthat radiates most of its thermal energy at 10--30 microns.\nThis zodiacal dust is produced largely in the inner part of the solar\nsystem by collisions in the asteroid belt\n\\markcite{derm92}(Dermott et al. 1992) and cometary outgassing \\markcite{liouz96}(Liou and Zook 1996). \nZodiacal dust is interesting as a general feature of planetary systems,\nand as an indicator of the presence of larger bodies which supply it;\ndust orbiting a few AU from a star is quickly removed as it loses angular\nmomentum to Poynting-Robertson drag (Robertson 1937). Understanding\nthe extra-solar analogs of zodiacal dust may also be crucial in the\nsearch for extra-solar planets \\markcite{beich96}\n(Beichman et al. 1996) since exo-zodiacal dust in a planetary system\ncould easily outshine the planets and make them much harder to detect.\n\nThe best current upper limits for the existence of\nexo-zodiacal dust disks come from IRAS measurements of 12 and 25 micron\nexcesses above\nphotospheric emission. Seen from a nearby star, solar system\nzodiacal dust would create only a $10^{-4}$ excess over the sun's\nphotospheric emission at 20 microns. IRAS measurements, however, have\ntypical measurement errors of 5 percent\\markcite{mosh92} (Moshir et al. 1992) and display systematic offsets of a similar magnitude when they are compared to other photometry \\markcite{cohe96} (Cohen et al. 1996). If there were a solar-type zodiacal disk with 1000 times the density of the disk\naround the sun around Tau Ceti, the nearest G star, the excess infrared\nemisison would barely exceed the formal 68\\% confidence intervals of the IRAS\nphotometry. Moreover, all photometric detection schemes of this sort are limited by how accurately the star's mid-infrared photospheric emission is known. For farther, fainter stars than Tau Ceti, inferring the presence of dust from the IRAS data becomes still harder.\n\nThe detection of faint exo-zodiacal-dust emission is more feasible if one\ncan resolve the dust emitting region. The high resolution and dynamic range needed for these observations will generally require large interferometers like the Keck Interferometer, the Large Binocular Telescope, and the Very Large Telescope Interferometer. But it is already possible to resolve the zodiacal dust mid-infrared emitting regions of the nearest stars. A 10-meter telescope operating at 12 microns has a diffraction-limited resolution of 0.25 arc seconds, corresponding, for example, to a transverse distance of 2 AU at 8 parsecs.\n\nWe have begun a search for zodiacal dust around the nearest stars using the\nmid-infrared imaging capabilities of the Long Wavelength Spectrometer (LWS) \\markcite{jone93}(Jones \\& Peutter 1993) on the W. M. Keck telescope.\nThe large aperture of the telescope\nallows us to make spatially resolved images of the\nzodiacal dust 11.6 micron emitting region around the stars so that we\ncan look for dust emission\nabove the wings of the point-spread function (PSF) rather than\nas a tiny photometric excess against the photosphere. We present here\nthe results of two nights of observations, and compare them with a simple model of exo-zodiacal thermal emission to place upper limits on the amount of dust present in the systems we observed.\n\n\\section {OBSERVATIONS}\n\nWe observed six nearby stars with LWS on the W. M. Keck telescope on\nAugust 3rd and 4th, 1996 using standard mid-infrared imaging\ntechniques. The target stars were the nearest A--K main-sequence stars\nobservable from Mauna Kea on those dates. With the object\non-axis, we took a series of frames lasting 0.8 ms each, chopping the\nsecondary mirror between the object and blank sky 8 arcseconds to the\nnorth at a frequency of 10 Hz. Then we nodded the primary\nmirror for the next series of frames so that the sky was on-axis and\nthe object off-axis. We repeated this process for 3 nods over a period of 5\nminutes, for an on-source integration time of 1.1 minutes, and a\ntypical noise of 2 mJy in one 0.11 by 0.11 arcsecond pixel \ndue to the thermal background. The seeing was poor both nights, up to 2 arc seconds in the visible. To measure the atmosphere-telescope\ntransfer function, we made similar observations of seven distant,\nluminous calibrator stars near our targets on the sky, alternating between target and calibrator every 5--10 minutes.\n\nWe increased our frame-rate for the second night of observations so that we could compensate for the seeing using speckle analysis. Figure 1 shows a cut through a single 84 ms exposure of Altair on August 4, compared to an Airy\nfunction representing the diffraction-limited PSF of a filled 10-meter\naperture at 11.6 microns. The cores of the images are diffraction-limited, but the wings are sensitive to the instantaneous seeing, making speckle analysis necessary. Table 1 provides a summary of our observations.\n\nWe flat-fielded the images by comparing the response of each pixel to\nthe response of a reference pixel near the center of the detector.\nFirst we plotted the data number (DN) recorded by a given pixel\nagainst the DN in the reference pixel for all the frames in each run.\nSince the response of each pixel is approximately linear over the \ndynamic range of our observations and most of\nthe signal is sky background, which varies with\ntime but is uniform across the chip, the plotted points for each\npixel describe a straight line; if all the pixels had\nthe same response, the slope of each line would equal 1. We divided\neach pixel's DN by the actual slope of its response curve relative to\nthe reference pixel, effectively matching all pixels to the reference pixel.\nWe then interpolated over bad pixels, frame by frame.\n\nTo compensate for the differences in the thermal background between the\ntwo nod positions, we averaged together all the on-axis sky frames to\nmeasure the on-axis thermal background and subtracted this average\nfrom all of the on-axis frames---both object and sky. We used the\nsame procedure to correct the off-axis frames.\n\nNext, we chose subframes of 32 by 32 pixels on each image, centered\non the star (or for sky frames, the location of the star in an\nadjacent object frame), and processed these according to classical\nspeckle analysis \\markcite{labe70}(Labeyrie 1970). We Fourier\ntransformed them, and summed the power spectra, yielding a sky\npower spectrum and an object power spectrum for each series. Then\nwe azimuthally averaged the power spectra in the u-v plane---that\nis, we averaged over all the frequency vectors of a given magnitude,\n$\\sqrt{u^2+v^2}$. This azimuthal averaging corrects for the rotation\nof the focal plane of the alt-az-mounted Keck telescope with respect\nto the sky. We then subtracted from every object power\nspectrum the corresponding sky power spectrum and divided each\ncorrected target power spectrum by the corrected power spectrum of a\ncalibrator star observed in the same manner as the target star\nimmediately before or after the target star. Figure 2 shows an\nazimuthally-averaged power spectrum of Altair and the corresponding\nsky power spectrum, compared with a power spectrum of calibrator\nGamma Aquila and its corresponding sky power. \n\nWe then averaged all the calibrated power spectra for a given target. \nIf the object and calibrator are both unresolved, the average calibrated\npower spectrum should be the power spectrum of the delta function: a\nconstant. We found that the pixels along the u and v axes of the power\nspectra were often contaminated by noise artifacts from the detector\namplifiers, so we masked them out. \n\nFigures 3 and 4 show the calibrated azimuthally-averaged power spectra\nfor our target stars. To compare different power spectra from\nthe same target, we normalized each\nazimuthally-averaged power spectrum so that the geometric mean\nof the first 10 data points in each spectrum equals 1. \n%A geometric mean is appropriate because it inverts\n%if you invert the ratios.\nFor Altair and 61 Cygni A and B we had more than three pairs of\ntarget and calibrator observations, i.e. calibrated power \nspectra, so we show the average of all the spectra and \nerror bars representing the 68\\% confidence interval for each datum,\nestimated from the variation among the individual power spectra. The\nerror is primarily due to differences in the\natmosphere-telescope transfer function between object and calibrator. \nNone of the calibrated power spectra deviate from a straight line by more\nthan a typical error; all the targets are unresolved to the\naccuracy of a our measurements.\n\n\\section{DISCUSSION}\n\nTo interpret our observations we compared them to models of the\nIR emission from the solar zodiacal cloud.\nWe constructed a model for exo-zodiacal emission based on the smooth\ncomponent of the Kelsall et al.\n\\markcite{kels98}(1998) model of the solar system zodiacal cloud as\nseen by COBE/DIRBE, with emissivity $\\epsilon \\propto r^{-0.34}$ and a\ntemperature $T = 286 \\ {\\rm K} \\ r^{-0.467}L^{0.234}$,\nwhere $r$ is the distance from the star in AU, and $L$ is the\nluminosity of the star in terms of $L_\\odot$. \nFor a dust cloud consisting entirely of a single kind of dust\nparticle of a given size and albedo, the $L$ exponent in the\nexpression for the temperature is simply $-1/2$ times the $r$ exponent\n\\markcite{back93}(Backman \\& Paresce 1993).\n\nThe physics of the innermost\npart of the solar zodiacal dust is complicated\n(see \\markcite{mann93} Mann \\& MacQueen 1993), but our results are not\nsensitive to the details,\nbecause the hottest dust is too close to the star for us to resolve. \nWe assume that the dust sublimates at a temperature\nof 1500 K, and allow this assumption to define the inner radius of the\ndisk. We set the outer radius of the\nmodel to 3 AU, the heliocentric distance of the\ninner edge of our own main asteroid belt. \nOur conclusions are not sensitive to this assumption;\ndecreasing the outer radius to 2 AU or increasing it to\ninfinity makes a negligible difference in the visibility of the\nmodel, even for A stars.\n\nThe assumed surface density profile, however, does make a difference.\nA collisionless cloud of dust in approximately circular orbits spiraling into a\nstar due to Poynting-Robertson drag that is steadily replenished at its outer\nedge attains an equilibrium surface density\nthat is independent of radius \\markcite{wyat50}\\markcite{brig62}\n(Wyatt and Whipple 1950, Briggs 1962). Models that fit data\nfrom the Helios space probes \\markcite{lein81}(Leinert et al\n1981), the fit by Kelsall et al. \\markcite{kels98}(1998) to the\nCOBE/DIRBE measurements and Good's \\markcite{good97}(1997) revised\nfit to the IRAS data all have surface densities\nthat go roughly as $r^{-0.4}$. This distribution appears to\ncontinue all the way in to the solar corona \\markcite{macq95}(MacQueen\n\\& Greely 1995). We find that in general, if we assume an\n$r^{-\\alpha}$ surface density profile, our upper limit for the\n1 AU density of a given disk scales roughly as $10^{\\alpha/2}$; disks\nwith more dust towards the outer edge of the 11.6 micron emitting region\nare easier to resolve.\n\nLikewise, the assumed temperature profile strongly affects our upper\nlimits. Unfortunately, we know little about the temperature profile of the\nsolar zodiacal cloud. COBE/DIRBE and IRAS only probed the dust\nthermal emission near 1 AU, and Helios measured the solar system cloud in\nscattered light, which does not indicate the dust temperature.\nWe found that a dust cloud model with the IRAS temperature profile\n($T = 266 \\ {\\rm K} \\ r^{-0.359}L^{0.180}$) was much easier to resolve\nthan the model based on DIRBE measurements that we present here,\nespecially for G and K stars.\n\nTo compare the models with the observations, we synthesized high\nresolution images of the model disks\nat an inclination of 30 degrees. We calculated the\nIR flux of the stars from the blackbody function, and obtained the parallaxes\nof the stars from the Hipparcos Catalog \\markcite{esa97}(ESA 1997). We\ninferred stellar radii and effective temperatures for each\nstar from the literature and checked them by comparing the blackbody\nfluxes to spectral energy distributions based on photometry from\nthe SIMBAD database \\markcite{simbad} (Egret et al. 1991). For\nAltair and Vega, we use the interferometrically measured angular diameters\n\\markcite{hanb74}(1974) (they are 2.98 +/-0.14 mas and 3.24 mas).\nStellar fluxes typically disagree with fitted blackbody curves by $\\sim10\\%$ in the mid-infrared \\markcite{enge90}(Engelke 1990), but our method does not require precise photometry, and the blackbody numbers\nsuffice for determining conservative upper limits.\nWe computed the power spectra of the images, and normalized them just like\nthe observed power spectra. In figures 3 and 4, the azimuthally-averaged\npower spectra for our target stars are compared to the extrapolated\nCOBE/DIRBE model at a range of model surface densities. Disks \nwith masses as high as $10^3$ times the mass of the solar disk will suffer\ncollisional depletion in their inner regions, so they are unlikely to have\nthe same structure as the solar disk. By neglecting this effect we are\nbeing conservative in our mass limits. The density of the densest model\ndisk consistent with the data in each case is listed in table 1.\n\nAltair\n\nOur best upper limit is for Altair (spectral type A7, distance 5.1 pc);\nwith 11 pairs of object and calibrator observations\nwe were able to rule out a solar-type disk a few\ntimes $10^3$ as dense as our zodiacal cloud. Such a disk would have been\nmarginally detectable by IRAS as a photometric excess. \n\nVega\n\nIRAS detected no infrared excess in Vega's spectral energy distribution\nat 12 microns, with an uncertainty of 0.8 Jy. This may be\ndue to a central void in the disk interior to about 26\nAU \\markcite{back93} (Backman \\& Paresce 1993). \\markcite{auma84}Aumann et al\n(1984) suggested that Vega (A0, 7.8 pc) could have a hot grain component (500 K)\nwith up to $10^{-3}$ of the grain area of the observed component and not\nviolate this limit. The apparent upward trend in the visibility data may\nbe a symptom of resolved flux in the calibrator stars. We have only 3 object/calibrator pairs for Vega, not enough to test this hypothesis.\nOur upper limit is a solar-type disk with approximately $3 \\times 10^3$\ntimes the density of the solar disk. This disk would have a $\\geq$500 K\nemitting area of $10^{24} \\ {\\rm cm}^2$, about $10^{-3}$ of the grain area\nof the observed component. \n\n61 Cygni A and B\n\nThough 61 Cygni is close to the galactic plane and\nsurrounded by cool cirrus emission, \\markcite{back86}Backman, Gillett and Low (1986)\nidentified an IRAS point source with this binary system and deduced a\nfar-infrared excess not unlike Vega's. The color temperature of the excess suggests the presence of dust at distances $> 15$ AU from either star.\nHowever these stars are dim (spectral types\nK5 and K7) and the region of the disk hot enough to emit strongly\nat 11.6 microns is close to the star and difficult to resolve; we\ncould not detect a solar-type dust disk around either of these\nobjects at any density, assuming the COBE/DIRBE model, or unless it\nhad $10^{5}$ times the density of the solar disk, assuming the IRAS model. \n\n70 Oph B\n\n70 Oph is a binary (types K0 and K4) with a separation of 24 pixels (2.6 arcsec). We were able to assemble a power spectrum for B from 9 object/calibrator pairs, but the image of A fell on a part of the LWS chip that suffered from many bad pixels and was unusable. The image of A may also have been distorted by off-axis effects. 70 Oph B, like 61 Cygni A and B, is dim, making any dust around it cool and hard to detect at 11.6 microns.\n\n$\\tau$ Ceti\n\nIRAS could have barely detected a disk with $\\sim 1000$ times the emitting area of the solar disk around Tau Ceti (G8, 3.6 pc),\nthe nearest G star. We have only three object/calibrator pairs for\nthis object, not enough data to improve on this limit. \n\n\\acknowledgments\n\n We are grateful to Dana Backman, Alycia Weinberger, Keith Matthews and Eric Gaidos for helpful discussions, and to Keith Matthews and Shri Kulkarni for assistance with the observations. This research has made use of the Simbad database, operated at CDS, Strasbourg, France. The observations\nreported here were obtained at the W. M. Keck Observatory, which\nis operated by the California Association for\nResearch in Astronomy, a scientific partnership among California Institute of Technology, the University of California, and the National Aeronautics\nand Space Administration. It was made possible by the generous financial support of the W. M. Keck Foundation.\n\n\\begin{references}\n\n\\reference{auma84}Aumann, H. H. 1984, ApJ, 278, L23\n%The Vega Paper\n\n\\reference{back93}Backman, D. E., \\& Paresce, F. 1993, ``Main Sequence Stars with Circumstellar\nSolid Material: The Vega Phenomenon'', {\\it Protostars and Planets III} (eds Levy E. H. \\& Lunine, J. I.)\n\n\\reference{back86}Backman, D. E., Gillette, F. C. \\& Low, F. J. 1986, Adv. Space Res., 6, 43\n\n\\reference{beich96}Beichman, C. 1996, A Road Map for the Exploration of Neighboring Planetary Systems (ExNPS), JPL Publication 96-22, ed. C. A. Beichman\n\n\\reference{brig62}Briggs, R. E. 1962, AJ, 67, 710\n%``Steady State Space Distribution of Meteoric Particles under the\n%Operation Of the Poynting Robertson Effect''\n\n\\reference{cohe96}Cohen, M., Witteborn, F. C., Carbon, D. F., Davies, J. K., Wooden, D. H., Bergman, J. D. 1996, AJ, 112, 2274\n%``Spectral Irradience Calibration inte the Infrared VII\n%New Composite Spectra, Comparison with Model Atmospheres,\n%And Far-Infrared Extrapolations''\n\n\\reference{derm92}Dermott, S.F., Gomes, R.S., Dorda, D.D., Gustafson,\nB. \\AA., Jayaraman, S., Xu, Y.L., \\& Nicholson, P.D. 1992, in\nFerraz-Mello S. ed., Chaos, Resonance and Collective Dynamical\nPhenomena in the Solar System. Kluwer, Dordrect, p.333\n%\"Dynamics Of the Zodiacal Cloud\"\n\n\\reference{simbad}Egret, D., Wenger, M., Dubois, P. (1991), in {\\em\nDatabases \\& On--line Data in Astronomy}, Albrecht \\&\nEgret (Eds.), Kluwer Acad. Publ., pp. 79--88.\n\n\\reference{enge90}Engelke, C. W. 1990, LWIR Stellar Calibration: Infrared Spectral Curves for 30 Standard Stars. Lincoln Lab. Project Rept. SDP-327.\n\n\\reference{esa97}ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200 \n\n\\reference{good97}Good, J. 1997, private communication\n\n\\reference{hanb74}Hanbury Brown, R., Davis, J., \\& Allen, L. R. 1974, MNRAS, 167, 121\n% Angular Diameters of Stars\n\n\\reference{jone93}Jones, B. \\& Peutter, R. 1993, Proc. SPIE, 1946, 610\n%\"The Keck Long-Wavelength Spectrometer\"\n\n\\reference{kels98}Kelsall, T., et al. 1998, ApJ, in press\n\n\\reference{labe70}Labeyrie, A. 1970, A\\&A, 6, 85\n% \"Attainment of Diffraction Limited Resolution in Large\n% Telescopes by Fourier Analyzing Speckle Patterns in Star Images\"\n\n\\reference{lein81}Leinert, C., Richter, I., Pitz, E., \\& Planck, B. 1981, A\\&A, 103, 177\n%\"The Zodiacal Light from 1.0 to 0.3 AU. as observed by the\n%Helios Space Probes\"\n\n\\reference{liouz96}Liou, J.C., \\& Zook, H.A. 1996, Icarus, 123, 491\n% Comets as a source of low eccentricity and low inclination\n% interplanetary dust particles.\n\n\\reference{macq95}MacQueen, R. M., \\& Greeley, B. W. 1995, ApJ, 440, 361\n% \"Solar Coronal Dust Scattering In The Infrared\"\n\n\\reference{mann93}Mann, I., \\& MacQueen, R. M. 1993, A\\&A, 275, 293\n%\"The Solar F Corona at 2.12 microns: Calculations of Near-Solar\n%Dust in Comparison to 1991 Eclipse Observations\n\n\\reference{mosh92}Moshir, M., et al. 1992, Explanatory Supplement to the\nIRAS Faint Source Survey, Version 2, JPL D-10015 8/92 (Pasadena: JPL)\n\n\\reference{wyat50}Wyatt, S. P., \\& Whipple, F. L. 1950, ApJ, 111, 134\n% \"The Poynting-Robertson Effect On Meteor Orbits\"\n\n\\end{references}\n\n\n\\newpage\n\n\\begin{deluxetable}{ccccccc}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\scriptsize\n\\tablecaption{\\label{tbl-1}}\n\\tablecaption{Observations}\n\\tablehead{\n & & & \\colhead{Exposure Time}& \\colhead{Object} & \\colhead{} & \\colhead{Log Disk Density} \\nl\n\\colhead{Date} & \\colhead{Target} & \\colhead{Calibrator} & \\colhead{Per Frame (ms)} & \\colhead{Frames} & \\colhead{Pairs} &\n\\colhead{Solar Disk = 0\\tablenotemark{a}} \n} \n\\startdata\nAugust 3 & Vega& R Lyr& 800 & 90& 2 & $\\le 4.0$\\nl\n & &$\\kappa$ Lyr&800 &90& 1 &\\nl\n & 61 Cyg A & $\\zeta$ Cyg & 800 & 90 & 4 & \\dots \\nl\n & 61 Cyg B & $\\zeta$ Cyg & 800 & 90 & 5 & \\dots \\nl\n &$\\tau$ Cet & $\\nu$ Cet & 800 & 90 &2 & \\dots \\nl\n\\medskip & & & 210 & 348& 1 &\\nl\nAugust 4 & 70 Oph B& $\\beta$ Oph &84 &864 & 5 &\\dots \\nl\n & & 74 Oph & 84 & 864 & 4 & \\nl\n & Altair & $\\gamma$ Aql& 84 & 864 & 6 &$\\le 3.2$\\nl\n & & $\\beta$ Aql &84 &864 & 5 &\\nl\n\\enddata\n\n\\tablenotetext{a}{based on the COBE/DIRBE model of the solar zodiacal cloud (Kelsall et al. 1998)}\n\n\\end{deluxetable}\n\n\n\\newpage\n\n\\figcaption{ A cut through a single 4 ms image of Altair, compared to a similar cut through an image of a calibrator star, Gamma Aquila, and an Airy function representing the PSF of an ideal, filled, 10-meter aperture at 11.6 microns. The cores of the images are diffraction-limited, but the wings are sensitive to the instantaneous seeing, making speckle analysis necessary. \\label{fig1}}\n\n\\figcaption{ An azimuthally-averaged power spectrum of Altair and the corresponding sky power spectrum, compared with a power spectrum of calibrator\nGamma Aquila and its corresponding sky power. The power in the star images approaches the sky power near the diffraction limit at 4 cycles per arcsecond. \\label{fig2}}\n\n\\figcaption{ Azimuthally-integrated power spectrum of Altair compared to simulated power spectra of model disks with various densities (1 = the solar disk). An unresolved point-source would appear as a straight line at a normalized power of 1.0. The densest model disk consistent with the observations has a density of roughly $10^3$ times that of the solar disk\\label{fig3}}\n\n\\figcaption{ Azimuthally-integrated power spectra of other target stars compared to simulated power spectra of model disks with various densities. \\label{fig4}}\n\n\n\n\n\\end{document}\n"
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astro-ph0002041
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Cosmic Ray Rejection by Linear Filtering of Single Images\footnote{ Accepted for publication in the May 2000 issue of the {Publications of the Astronomical Society of the Pacific.} }
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"author": "James E. Rhoads"
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We present a convolution-based algorithm for finding cosmic rays in single well-sampled astronomical images. The spatial filter used is the point spread function (approximated by a Gaussian) minus a scaled delta function, and cosmic rays are identified by thresholding the filtered image. This filter searches for features with significant power at spatial frequencies too high for legitimate objects. Noise properties of the filtered image are readily calculated, which allows us to compute the probability of rejecting a pixel not contaminated by a cosmic ray (the false alarm probability). We demonstrate that the false alarm probability for a pixel containing object flux will never exceed the corresponding probability for a blank sky pixel, provided we choose the convolution kernel appropriately. This allows confident rejection of cosmic rays superposed on real objects. Identification of multiple-pixel cosmic ray hits can be enhanced by running the algorithm iteratively, replacing flagged pixels with the background level at each iteration.
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"name": "crrej_eprint.tex",
"string": "% Manuscript of a PASP paper outlining our cosmic ray rejection formalism.\n% writeup started 24 July 1999\n% last modification before submission July 29\n% First revisions based on referee's report Nov 10-11\n% Further revisions Dec 6- based on results of Artificial Data simulations\n% Further revisions Jan 4 and Jan 21-23 based on referee's second report\n\\documentstyle[11pt,aaspp4]{article}\n\n\\def\\sky{B_I}\n\\def\\filtsky{B_J}\n\\def\\skysig{\\sigma_I}\n\\def\\skysigl{\\sigma_{I,\\ell}}\n\\def\\filtsig{\\sigma_{J}}\n\\def\\fsigpk{\\sigma_{J}(\\hbox{peak})}\n% \\def\\psfsig{\\hat{\\sigma}_A}\n% \\def\\psf2{\\hat{\\sigma}_A^2}\n\\def\\psfsig{\\xi}\n\\def\\psf2{\\xi^2}\n\\def\\psffunc{A}\n\\def\\filterfunc{F}\n\\def\\star{S_0}\n\\def\\siq{S_I(q)}\n\\def\\sjq{S_J(q)}\n\\def\\crampi{C_I}\n\\def\\crampj{C_J}\n\\def\\gain{g}\n\\def\\cutoff{k}\n\\def\\rad2{( \\Delta x^2 + \\Delta y^2)}\n\\def\\r2q{( [\\Delta x - q]^2 + \\Delta y^2)}\n\\def\\thresh{t}\n\\def\\p0{p_{sky}}\n\\def\\ps{p_{obj}}\n\\def\\betalim{\\beta_{\\hbox{lim}}}\n\\def\\negthresh{k_{\\hbox{neg}}}\n\\def\\posthresh{k_{\\hbox{cr}}}\n\\def\\G3LHS{{\\cal L}}\n\n\\begin{document}\n\\title{Cosmic Ray Rejection by Linear Filtering of Single Images\\footnote{\nAccepted for publication in the May 2000 issue of the {\\it Publications of \nthe Astronomical Society of the Pacific.}\n}}\n\n\\author{James E. Rhoads}\n\\affil{Kitt Peak National Observatory, 950 North Cherry Avenue,\nTucson, AZ 85719\\altaffilmark{2}; [email protected]}\n\\altaffiltext{2}{Current address: Space Telescope Science Institute,\n3700 San Martin Drive, Baltimore, MD 21218; [email protected]}\n\n\n\\begin{abstract}\nWe present a convolution-based algorithm for finding cosmic rays in\nsingle well-sampled astronomical images. The spatial filter used is\nthe point spread function (approximated by a Gaussian) minus a scaled\ndelta function, and cosmic rays are identified by thresholding the\nfiltered image. This filter searches for features with significant\npower at spatial frequencies too high for legitimate objects.\nNoise properties of the filtered\nimage are readily calculated, which allows us to compute the probability\nof rejecting a pixel not contaminated by a cosmic ray (the false alarm\nprobability). We demonstrate that the false alarm probability for a\npixel containing object flux will never exceed the corresponding\nprobability for a blank sky pixel, provided we choose the convolution\nkernel appropriately. This allows confident rejection of cosmic rays\nsuperposed on real objects. Identification of multiple-pixel cosmic\nray hits can be enhanced by running the algorithm iteratively,\nreplacing flagged pixels with the background level at each iteration.\n\\end{abstract}\n\n\\keywords{techniques: image processing}\n\n\\section{Introduction}\\label{intro}\nImages from most current-day astronomical instruments have tractable\nnoise properties. An exemplary case is optical images from CCD\ndetectors, whose uncertainties are generally dominated by the Poisson\nstatistics of the detected photons, with (usually smaller)\ncontributions from detector read noise, dark current, and other\ncomparatively minor nuisances. Most of these noise sources are well\napproximated by Gaussian distributions, and their sum is therefore\nalso well approximated by a Gaussian.\n\nCosmic rays impinging on a detector can yield large signals over\nsingle pixels or small groups of pixels, thereby introducing a\ndistinctly non-Gaussian tail to the noise distribution. The most\ncommon approach to removing cosmic rays from astronomical images is to\ntake multiple exposures and combine them with some sort of outlier\nrejection. Real astronomical objects should (usually) be present on\nmultiple frames, while cosmic ray hits will not generally repeat.\nSuch methods have been presented in the literature by (e.g.) Shaw \\&\nHorne (1992) and Windhorst, Franklin, \\& Neuschaefer (1994), and are\nwidely implemented in astronomical image processing packages.\n\nHowever, there are times when multiple images are not available, or\nwhen the sources of interest may be moving or varying on timescales\nshort compared to the interval between exposures. In these cases, a\ncosmic ray rejection method capable of operating on single exposures\nis necessary. Cosmic ray rejection in single frames can also be\nuseful even when multiple exposures are to be stacked, since stacking\noften requires spatial interpolation of the input images, and any\ncosmic rays not previously identified can be spread over many pixels\nby spatially extended interpolation kernels. Additionally, if a stack\nof images has widely different point spread function (PSF) widths,\nrejection algorithms used while stacking tend either to be overly\nlenient, potentially admitting cosmic rays; or overly strict,\ndiscarding valid data from images with very good or very bad seeing.\nExamples of both these behaviors are offered by sigma clipping\nalgorithms, where the contribution of a particular exposure to a stack\nis discarded if it differs from the mean (or median) intensity at that\nlocation by more than $k \\sigma$, where $k$ is a constant (generally\nwith $2 \\la k \\la 5$) and $\\sigma$ measures the intensity uncertainty\nat that location. If $\\sigma$ is measured directly from the list of\nexposure intensities at a fixed sky position, a lenient rejection results,\nwhile if $\\sigma$ is taken from the known Poisson statistics of electrons in\nsingle exposures, a strict rejection results.\n\nTo identify cosmic rays in single exposures, rejection algorithms rely\non the sharpness of cosmic rays relative to true astronomical objects.\nThat is, any legitimate object in our astronomical image is blurred by\nthe PSF, but there is no such requirement on cosmic ray hits.\nProvided the image is well-sampled (in practice, $\\ga 2$ pixels across\nthe PSF full width at half maximum), cosmic ray hits can be identified\nas those features with spatial variations too rapid for consistency\nwith the PSF. Murtagh (1992) and Salzberg et al (1995) have explored\ntrainable classifier approaches to single-image cosmic ray rejection.\nTheir methods have the advantage of applicability to substantially\nundersampled data (from the WF/PC-I instrument on the Hubble Space\nTelescope). On the other hand, these methods ultimately rely on a\ntraining set, which may be subjectively defined.\n\nThe present paper explores a method suggested by Fischer and Kochanski\n(1994), who remark that the optimal filter for detecting\n[single-pixel] cosmic ray hits is the point spread function minus a\ndelta function. This can be regarded as a difference between the\nmatched filter for detecting point sources (i.e. the PSF) and that for\ndetecting single pixels (i.e. a delta function). There is one free\nparameter in such a filter, which is the amplitude ratio of the two\nfunctions. We develop this filtering method in detail by considering\nthe cosmic ray rejection rates and false alarm rates. Much of our\nanalysis is devoted to choosing the delta function amplitude\nappropriately. With a careful choice of this parameter, it is\npossible to ensure that the false alarm rate nowhere exceeds its value\nin blank sky regions.\n\nIn section~\\ref{math}, we derive the noise properties of our\nfiltered image, and explain how to tune the filter to avoid excessive\nrejection of valid data. In section~\\ref{iraf}, we\ndiscuss practical issues that arise when implementing our algorithm.\nSection~\\ref{simulations} presents simulations used to verify the\nalgorithm's performance.\nFinally, in section~\\ref{theend} we summarize our work,\ndescribe our usual application for our algorithm, and comment on a\ndesirable future direction for cosmic ray rejection algorithms.\n\n\\section{Mathematical formalism}\\label{math}\nSuppose we have an image $I$ with the following properties: First, it\nhas some background level $\\sky$ and noise $\\skysig$, and the sky\nnoise is uncorrelated between any pair of pixels. Second, it is\nlinear in the input signal with a gain $\\gain$ photons per count, so\nthat a pixel containing object flux $S$ counts will have a noise\ncontribution of $\\sqrt{S/g}$ counts from Poisson noise in the object\nsignal. Third, it has a point spread function that can be well\napproximated by a Gaussian of characteristic width $\\psfsig$ (i.e.,\nthe stellar profiles have a functional form $\\propto \\exp[-\\rad2 / (2\n\\psf2)]$), and is well sampled (i.e., $\\psfsig \\ga 1$ pixel). This\nthird property is an analytical convenience that is reasonably near\ntruth for seeing-limited optical images from ground-based telescopes.\nOther PSF models would complicate the mathematical analysis that\nfollows, but would not greatly change either its flavor or its\nquantitative results.\n\nNow consider convolving this image with a spatial filter $\\filterfunc$ \nconsisting of a unit-normalized point spread function $\\psffunc =\n\\exp[ -\\rad2 / (2 \\psf2) ] / (2 \\pi \\psf2)$ minus a scaled delta function:\n$\\filterfunc = \\psffunc - \\alpha \\delta(\\Delta x) \\delta(\\Delta y)$.\nCall the convolved image $J$, so that $J=I * \\filterfunc = I * \\psffunc\n- \\alpha I$. (Here and throughout the paper, ``$*$'' is the\nconvolution operator.)\n\nIf we regard the convolution kernel as a matched filter, it is clear that\na broader kernel (likely using a functional form besides the Gaussian)\nwould be more effective at separating cosmic rays from faint galaxies\nor other extended sources. However, almost all astronomical images\ncontain some legitimate pointlike sources, which should not be\nrejected. Using a template more extended than a point source would\nrisk rejecting stars, and such templates are therefore not explored\nfurther.\n\n\\subsection{Noise properties of the filtered image}\nWe calculate the noise in the convolved image in two steps, first\ndetermining the noise in $I * \\psffunc$ and then modifying the result\nto account for the second term in filter $\\filterfunc$.\nTreating the noise in each pixel as an independent random variable with\nvariance $\\skysig^2$, the variance in the convolved image is simply a\nweighted sum $\\filtsig^2 = \\sum_\\ell w_\\ell^2 \\skysigl^2$, where\nthe sum runs over pixels and $w_\\ell$ is simply $\\filterfunc$ evaluated\nat the location $(\\Delta x_\\ell, \\Delta y_\\ell)$ of pixel $\\ell$.\nNow, in regions of blank sky, $\\skysigl \\equiv \\skysig$ is constant,\nso $\\sigma_{I * \\filterfunc} = \\skysig^2 \\sum_\\ell w_\\ell^2$.\n\nWe can calculate the noise level in $I * \\psffunc$ by defining weights\n$v_\\ell$ as $\\psffunc$ evaluated at $(\\Delta x_\\ell, \\Delta y_\\ell)$,\nand noting that \n\\begin{equation}\n{\\sigma_{I * \\psffunc}^2 \\over \\skysig^2} =\n\\sum_\\ell v_\\ell^2 \\approx \\int_0^\\infty { 2 \\pi r dr \\over (2 \\pi\n\\psf2)^2 } \\left[ \\exp\\left(-r^2 \\over 2 \\psf2 \\right) \\right]^2\n= { 1 \\over 4 \\pi \\psf2 } ~~,\n\\label{ssigAI}\n\\end{equation}\nso that $\\sigma_{I * \\psffunc}^2 = \\skysig^2 / ( 4 \\pi \\psf2)$.\nThe continuous approximation to the discrete sum made here should be\nreasonably accurate for well-sampled data.\n\nModifying this for the central pixel, which has weight $w = 1/(2 \\pi \\psf2)\n- \\alpha$ rather than $v = 1/(2 \\pi \\psf2)$ as used above, we find\n\\begin{equation}\n{\\filtsig^2 \\over \\skysig^2} = \\sum_\\ell w_\\ell^2 \\approx \n { 1 \\over 4 \\pi \\psf2 } - \\left( 1 \\over 2 \\pi \\psf2 \\right)^2 + \n \\left({ 1 \\over 2 \\pi \\psf2 } - \\alpha \\right)^2 \n= { 1 \\over 4 \\pi \\psf2 } - { \\alpha \\over \\pi \\psf2 } + \\alpha^2 ~~.\n\\label{ssigJ}\n\\end{equation}\n\nThat accomplished, we can determine the significance level that a cosmic\nray with amplitude $n \\skysig$ will have in image $J$. A single pixel\ncosmic ray with $\\crampi$ counts will result in a pixel with\nexpectation value $\\crampj = \\left[ 1/(2 \\pi \\psf2) - \\alpha \\right] \\crampi$\nbelow the sky level of $J$ (which is $\\filtsky = (1-\\alpha) \\sky$).\nIf $ \\crampi = n \\skysig$, then the final significance level is \n\\begin{equation}\n{ -\\crampj \\over \\filtsig} =\n{\\crampi \\over \\skysig} \\times { 1/(2 \\pi \\psf2) - \\alpha \\over\n\\left( 1/(4 \\pi \\psf2) - \\alpha / (\\pi \\psf2) + \\alpha^2 \\right)^{1/2} }\n = {\\crampi \\over \\skysig} \\times \\left[1 + { \\pi \\psf2 - 1 \\over (2\n\\pi \\psf2 \\alpha - 1)^2 } \\right]^{-1/2} ~~.\n\\end{equation}\nIn general, this is a lower significance level than in the original\nimage. In the limit of very well sampled data ($\\psfsig\n\\rightarrow \\infty$) this reduces to a significance level of \n$\\crampi / \\skysig$, recovering the input as one might expect.\nThe gradual approach to this limit simply reflects the dependence of\ncosmic ray identification on the sampling of an image.\nFigure~\\ref{crsig_a} shows contours of ${ -\\crampj \\skysig}\n\\big/ {(\\crampi \\filtsig)}$.\n\n\\begin{figure}\n\\plotone{fg1.eps}\n\\caption{ Contours show the factor ${ -\\crampj\n\\skysig} \\big/ {(\\crampi \\filtsig)}$ by which a single-pixel\ncosmic ray's significance is reduced in the convolved image $J$, as a\nfunction of the seeing and the scale factor $\\alpha$ for the delta\nfunction in the convolution kernel.\nContour levels are $0.98, 0.95, 0.90, 0.85, 0.80, 0.75, 0.667, 0.50,\n0.25,$ and $0$, beginning with the top right corner and continuing to\nthe boundary of the hatched region. The crosshatching indicates the\nregion of the parameter space where $\\alpha < 1/(2 \\pi \\psf2)$, where\nthe method will necessarily fail.}\n\\label{crsig_a}\n\\end{figure}\n\nWhen we reject cosmic rays, we need to be careful not to reject the\ncores of legitimate point sources. In order to avoid doing so, we\ncalculate the noise level at a location near a point source, making\nthe same continuous approximation to discrete sums used in deriving\nequation~\\ref{ssigAI}. The complication arising in this procedure is\nthat the presence of a source changes the noise properties of the\nimage. A pixel containing object flux $I_\\ell$ has noise level given\nby $\\skysigl^2 = \\skysig^2 + I_\\ell / \\gain$.\n\nWe consider below the noise at a location $q$ pixels from the location\nof a star with peak counts $\\star$, and define function $\\siq = \\star\n\\exp\\left[-q^2 / (2 \\psf2) \\right]$. In the convolved image, this\npixel has expected flux\n\\begin{equation}\n\\sjq = \\star \\left( {1 \\over 2} \\exp\\left[ -q^2 \\over 4\\psf2 \\right] -\n\\alpha \\exp\\left[-q^2 \\over 2\\psf2 \\right] \\right) ~~.\n\\label{sjq}\n\\end{equation}\nSince variances add linearly, modifying our earlier analysis for the\nadditional noise term is relatively straightforward. For image $I *\n\\psffunc$, we find\n\\begin{eqnarray}\n\\lefteqn{ \\sigma_{A * I}^2(q) = \\sum_\\ell v_\\ell^2 \\skysigl^2 } \\\\\n& = & \\sum_{\\Delta x} \\sum_{\\Delta y}\n \\left( { 1 \\over 2 \\pi \\psf2 } \\exp\\left[-\\rad2 \\over 2 \\psf2 \\right]\n\\right)^2\n\\left( \\skysig^2 + {\\star \\over \\gain} \\exp\\left[-\\r2q \\over 2 \\psf2\n\\right] \\right)\n\\end{eqnarray}\nwhere we have assumed (without loss of generality) that the offset to\nthe star is along the $x$-axis. Defining $\\Delta x' = \\Delta x -\nq/3$, and substituting our result from equation~\\ref{ssigAI}, this becomes\n\\begin{eqnarray}\n\\sigma_{A * I}^2(q) & = & \n { \\skysig^2 \\over 4 \\pi \\psf2 } + { \\star \\over (2 \\pi \\psf2)^2 \\gain }\n \\exp\\left[ -q^2 \\over 3 \\psf2 \\right]\n \\sum_{\\Delta x} \\sum_{\\Delta y} \\exp\\left[-3 (\\Delta x'^2 + \\Delta y^2)\n \\over 2 \\psf2 \\right] \\\\\n& \\approx & { \\skysig^2 \\over 4 \\pi \\psf2 } + {\\star \\over (2\\pi \\psf2)^2\n \\gain} \\exp\\left[ -q^2 \\over 3 \\psf2 \\right]\n \\int_0^\\infty 2 \\pi r \\exp\\left[-3 r^2 \\over 2 \\psf2 \\right] dr \\\\\n & = & { \\skysig^2 \\over 4 \\pi \\psf2 } + \\exp\\left[ -q^2 \\over 3 \\psf2 \\right]\n{ \\star /\\gain \\over 6 \\pi \\psf2 }\n~~.\n\\end{eqnarray}\n\nAgain modifying the result to account for the delta function in the\nconvolution kernel, we obtain for the noise at distance $q$ from the\npoint source\n\\begin{eqnarray}\n\\lefteqn{ \\filtsig^2(q) = \\sigma_{A*I}^2 +\n\\left( \\skysig^2 + \\siq/\\gain \\right) \\left( \\left[{1 \\over 2 \\pi\n\\psf2} - \\alpha \\right]^{2} \n - \\left[ 1 \\over 2 \\pi \\psf2 \\right]^{2} \\right) } \\\\\n & = & \\skysig^2 \\left(\n { 1 \\over 4 \\pi \\psf2 } - { \\alpha \\over \\pi \\psf2 } + \\alpha^2 \\right)\n+ {\\star \\over \\gain} \\exp\\left[-q^2 \\over 2 \\psf2 \\right] \\left(\n { \\exp\\left[+q^2/(6 \\psf2)\\right] \\over 6 \\pi \\psf2 } -\n { \\alpha \\over \\pi \\psf2 } + \\alpha^2 \\right) ~~.\n\\label{noise2}\n\\end{eqnarray}\nIn the limit $q \\rightarrow \\infty$, this expression reproduces our\nblank sky result (equation~\\ref{ssigJ}), while at the peak of the\nstar, it simplifies somewhat as the exponential terms go to unity.\n\nThese results can easily be generalized to a superposition of point\nsources; the second terms on the right hand sides of\nequations~\\ref{sjq} and~\\ref{noise2} would simply be replaced by a sum\nof such terms, each with its own value of the intensity parameter\n$\\star$ and distance parameter $q$.\n% The generalization to extended sources would be more challenging,\n% except insofar as extended sources can be modeled as sums of point\n% sources (as is done in the CLEAN algorithm). \n\n\\subsection{Keeping the valid peaks}\nTo identify cosmic rays in our image, we plan to threshold the\nconvolved image $J$, flagging all pixels with excessively negative\nvalues in $J$. There are two probabilities of interest here, namely\nthe probability that we will correctly flag a cosmic ray with\nintensity $\\crampi$ (the detection rate), and the probability that we\nwill incorrectly flag a pixel without cosmic ray flux (the false alarm\nrate). We have chosen to concentrate our efforts on controlling the\nfalse alarm rate, and to accept the resulting detection rate.\nFrom a hypothesis testing perspective (e.g., Kendall \\& Stuart~1967,\nchapter~22), this approach corresponds to making the null hypothesis\nthat a given pixel is uncontaminated by cosmic ray flux. The false\nalarm rate is then the probability of a type~I error. Missed cosmic\nray events are type~II errors, and their probability can be calculated\nas a function of cosmic ray intensity. The tradeoffs between these\ntwo errors for a variety of cosmic ray rejection algorithms are\nreviewed by Murtagh \\& Adorf (1991).\n\nWe can never set the probability of rejecting valid pixels to be\nprecisely zero so long as we have noise in our image and we reject any\npixels at all. Instead we note that there is some finite probability\n$\\p0$ of rejecting an arbitrary sky pixel, and demand that the\nprobability $\\ps$ of rejecting a pixel containing positive object flux\nnot exceed $\\p0$.\n\nConsider a threshold level in image $J$, $\\thresh = -k \\filtsig$.\nThe expected count level in $J$ is given by equation~\\ref{sjq},\nand the noise level there is given by equation \\ref{noise2}.\nWe demand that\n\\begin{equation}\n\\sjq - k \\filtsig(q) \\ge -k \\filtsig(\\infty) \\label{goal}\n\\end{equation}\nin order to ensure that $\\ps \\le \\p0$.\nBy using our previous expressions for $\\sjq$ and $\\filtsig(q)$, we\nconvert this into a constraint on $\\alpha$. An immediate (though\nweak) constraint is that $0 \\le \\alpha < 1/2$, since $\\filtsig(0) >\n\\filtsig(\\infty)$, and the expected count rate must be positive to \ncompensate for the increased noise at the star's location.\n\nIn the remainder of section~\\ref{math}, we derive conditions\nguaranteeing that inequality~\\ref{goal} will hold for all values of\n$\\star$ and $q$. Readers who are not interested in the mathematical\ndetails may wish to skim section~\\ref{alphsec}, which explains how to\nchoose the parameter $\\alpha$, and then move on to section~\\ref{iraf},\nwhere we discuss implementation of the cosmic ray rejection algorithm.\n\nBy construction, condition~\\ref{goal} is fulfilled as an equality for\n$\\star = 0$ and for any value of $q$.\nTo ensure that \\ref{goal} holds for all $\\star>0$, \nit is sufficient to show that \n\\begin{equation}\n{d \\over d\\star}\\left[ \\sjq - k \\filtsig(q) \\right] \\ge 0 \\label{goal2}\n\\end{equation}\nfor all $\\star > 0$ and for arbitrary $q$.\nMultiplying relation~\\ref{goal2} by $\\exp[+q^2 / (4 \\psf2)]$, substituting\nprevious results for $\\sjq$ and for $\\filtsig(q)$, and\nusing $d \\filtsig(q)^2 / d\\star = 2 \\filtsig(q) \\times d\\filtsig(q)/d\\star$,\nwe obtain\n\\begin{displaymath}\n\\G3LHS =\n\\left( {1\\over 2} - \\alpha \\exp\\left[-q^2 \\over 4 \\psf2 \\right]\n\\right) \\quad - \\quad\n{k\\over 2 \\gain} \\exp\\left[-q^2 \\over 4 \\psf2 \\right] \n \\left\\{ { \\exp\\left[+q^2/6 \\psf2\\right] \\over 6 \\pi \\psf2 } -\n { \\alpha \\over \\pi \\psf2 } + \\alpha^2 \\right\\}\n \\Bigg/\n\\end{displaymath}\n\\begin{equation}\n\\left\\{\n\\skysig^2 \\left[ {1 \\over 4 \\pi \\psf2 } - { \\alpha \\over \\pi \\psf2 }\n+ \\alpha^2 \\right] + {\\star \\over \\gain} \\exp\\left[-q^2 \\over 2 \\psf2 \\right] \n\\left[ {\\exp\\left[+q^2/6 \\psf2\\right] \\over 6 \\pi \\psf2 } -\n { \\alpha \\over \\pi \\psf2 } + \\alpha^2 \\right]\n\\right\\}^{1/2} \n\\ge 0 \\label{goal3}\n\\end{equation}\nfor all $\\star > 0$.\n\nWe now assert that for well-behaved images, it is possible to choose\n$\\alpha$ so that relation~\\ref{goal3} is fulfilled as an equality for\n$\\star=0$ and $q=0$. We will justify this assertion in\nsection~\\ref{alphsec} below.\n\nTaking as a hypothesis for now that $\\G3LHS = 0$ for $\\star=0$ and\n$q=0$, we first examine the case $\\star=0$, $q > 0$. Substituting\n$\\star=0$ in equation~\\ref{goal3} and rearranging,\n\\begin{displaymath}\n1/2 \\ge \\exp\\left[ -q^2 \\over 4 \\psf2 \\right] \\left\\{ \\alpha + { \\cutoff \\over\n2 \\gain \\skysig } \\left( \\alpha^2 - {\\alpha \\over \\pi \\psf2} \\right)\n\\Bigg/ \\sqrt{ {1\\over 4 \\pi \\psf2 } -{ \\alpha \\over \\pi \\psf2 } +\n\\alpha^2 } \\right\\}\n\\end{displaymath}\n\\begin{equation} \n+ \\exp\\left[ -q^2 \\over 12 \\psf2 \\right] \\cutoff \\Bigg/ \\left\\{ 12 \\pi\n\\gain \\skysig \\psf2 \\sqrt{ {1\\over 4 \\pi \\psf2 } -{ \\alpha \\over \\pi\n\\psf2 } + \\alpha^2 } \\right\\} ~~.\n\\label{goal4}\n\\end{equation}\nWe see that the right hand side contains two exponentially decreasing\nterms. Provided both are positive, the right hand side of\nequation~\\ref{goal4} will clearly be a decreasing function of $q$ for\nall $q\\ge 0$. The second term is positive since all of its factors\nare positive by definition. Now, by hypothesis, relation~\\ref{goal4}\nis an equality for $q=0$, so that the first term in~\\ref{goal4} will also\nbe positive provided that the second is $< 1/2$ for $q=0$. This\nyields a quadratic constraint on $\\alpha$:\n\\begin{equation}\n\\alpha^2 - { \\alpha \\over \\pi \\psf2 } + {1 \\over 4 \\pi \\psf2} >\n\\left[ k \\over 6 \\pi \\gain \\skysig \\psf2 \\right]^2\n \\label{goal5}\n\\end{equation}\nThis now becomes our sufficient condition for \ninequality~\\ref{goal4} to be fulfilled for all $q$.\n\nTurning our attention to $\\star>0$, \nwe observe by inspecting~\\ref{goal3} that $\\G3LHS$ is an increasing\nfunction of $\\star$ for any fixed $q$ provided only that\n\\begin{equation}\n \\alpha^2 - { \\alpha \\over \\pi \\psf2 } + {1 \\over 6 \\pi \\psf2 } > 0 ~~.\n\\label{goal6}\n\\end{equation}\n\nThus, if we can find a value of $\\alpha$ that simultaneously fulfills\nrelation~\\ref{goal3} as an equality, and fulfills\ninequalities~\\ref{goal5} and~\\ref{goal6}, we have a convolution kernel\nthat will allow rejection of cosmic rays without any excess risk of\nrejecting a valid pixel just because it contains flux from an object.\nIn the next section, we determine the parameter space over which this\nis possible.\n\n\\subsection{The choice of $\\alpha$}\\label{alphsec}\nWe now turn to deriving the value of $\\alpha$ that fulfills our\nearlier assertion, satisfying \\ref{goal3} as an equality for\n$\\star=0$ and $q=0$. This is easier if we first define the auxiliary parameter\n$\\beta = 1/2 - \\alpha$. The intuitive significance of $\\beta$ is that\nthe expected counts in the filtered image $J$ are $S_J(0) = \\beta \\star$ at\nthe location of a star having $\\star$ counts in original image $I$.\nSubstituting $1/2-\\beta$ for $\\alpha$,\nsetting $\\star$ and $q$ to zero, and requiring exact equality,\nexpression~\\ref{goal3} becomes\n\\begin{equation}\n\\beta = {k \\over 2 \\gain \\skysig}\n { \\left(1 - {1\\over \\pi \\psf2} \\right) \\left( {1\\over 4} - \\beta\n \\right) + \\beta^2 - { 1 \\over 12 \\pi \\psf2}\n \\over \\sqrt{ \\left(1 - {1\\over \\pi \\psf2} \\right) \\left( {1\\over 4}\n - \\beta \\right) + \\beta^2 } } ~~.\n\\label{betaiter} \\end{equation}\nThis equation can be rearranged into a quartic in $\\beta$ (or\nequivalently $\\alpha$). Rather than doing so, we note that the\npresent version can be solved iteratively for $\\beta$ by calculating\nthe right hand side a few times, inserting $\\beta=0.25$ (or indeed any\nnumber in $[0,0.25]$) the first time and using the previous result at\neach successive iteration. $\\beta$ is effectively a function of two\nparameters, $k/(\\gain \\skysig)$ and $\\psfsig$. Now, for most imaging\nCCD data, we expect reasonable choices of these parameters to be $3\n\\la k \\la 5$, $1 \\la \\gain \\la 10$, $\\skysig \\gg 5/\\gain$, and\n$\\psfsig \\ga 1$ pixel. (Our estimate for $\\skysig$ is based on the\nassumption that the read noise is $\\ga 5$ electrons and the observer\nwill typically ensure that sky noise is greater than read noise.)\nThis leads to $k/(\\gain \\skysig) \\ll 1$ under typical circumstances.\nIn this limit, we expect\n\\begin{equation}\n\\beta \\approx \\betalim = {1\\over 2} \\left(k \\over \\gain \\skysig \\right) { 1/4 -\n1/(3 \\pi \\psf2) \\over 1/4 - 1/(4 \\pi \\psf2) }~~.\n\\label{betalim}\n\\end{equation}\nOne can further show that $\\beta > \\betalim$ under then nearly generic\nconditions that $0 \\le \\beta < 1/4$ and $\\beta < 1/2 - 1/(2 \\pi\n\\psf2)$. We therefore have a choice when implementing the algorithm\nbetween assuming $\\beta = \\betalim$ or solving equation~\\ref{betaiter}\niteratively.\n\nWe have not derived analytically the range of parameter space over\nwhich $\\beta$ can be found iteratively, but empirically, the iterative\nsolution will converge to a sensible result (fulfilling\nconditions~\\ref{goal3}, \\ref{goal5}, and~\\ref{goal6}) provided that $0\n< k / (\\gain \\skysig) < 2$ and\n% that $\\psfsig \\ga \\pi/(2 \\sqrt{8 \\ln(2)})$.\nthat $\\psfsig > 2/\\sqrt{3 \\pi}$.\n% (Of course, the continuous approximations to discrete sums that we\n% made in deriving $\\filtsig$ suggest that somewhat\n% larger values, $\\psfsig \\ga 1$, are more prudent.)\nThese are our final set of sufficient conditions for this algorithm to\nwork as desired. They are not as rigorously derived as conditions\n~\\ref{goal3}, \\ref{goal5}, and~\\ref{goal6}, but do provide a quick\ncheck on when the method is likely to be applicable.\nFigure~\\ref{betafig} shows contours of $\\beta$ as a function of $\\psfsig$\nand $k/(\\gain \\skysig)$.\n\n\\begin{figure}\n\\plotone{fg2.eps}\n\\caption{ Contours show the optimal choice of $\\beta =\n1/2 - \\alpha$ as a function of seeing $\\psfsig$ and the rejection\nthreshold to noise ratio $k / (\\gain \\skysig)$. Contour levels (from\ntop to bottom) are $0.20, 0.15, 0.10, 0.05, 0.025$, and $0.01$.\nConcentric semicircles at the right hand edge show the asymptotic\nvalue of $k / (\\gain \\skysig)$ for each contour curve in the limit\n$\\psfsig \\rightarrow \\infty$.}\n\\label{betafig}\n\\end{figure}\n\nGiven our formula for $\\beta$, it is now also possible to determine\n${ -\\crampj \\skysig} \\big/ {(\\crampi \\filtsig)}$\n(the multiplicative reduction in significance level of a cosmic ray after\nconvolution) as a function of $\\psfsig$ and $k/(\\gain \\skysig)$.\nFigure~\\ref{crsig_yb} shows contours of this efficiency factor.\n\n\\begin{figure}\n\\plotone{fg3.eps}\n\\caption{ Contours show the factor ${ -\\crampj \\skysig}\n\\big/ {(\\crampi \\filtsig)}$ as a function of seeing $\\psfsig$ and the\nrejection threshold to noise ratio $k / (\\gain \\skysig)$, assuming\nthat the optimal choice of $\\beta$ is used for the convolution kernel.\nContour levels (starting at lower right) are $0.98, 0.97, 0.96, 0.94,\n0.92, 0.90, 0.87, 0.84, 0.80, 0.75, 0.68, 0.60,$ and $0.50$.}\n\\label{crsig_yb}\n\\end{figure}\n\n\\section{Practical Implementation} \\label{iraf}\nWe have implemented this algorithm and applied it to several data sets\nduring the past year. In doing so, we introduced several enhancements\nof the basic algorithm that allow the method to run gracefully on our\nreal data. Two particular artifacts were addressed by these\nenhancements. First, some bad pixels in some CCD cameras give data\nvalues far below the sky level $\\sky$. If left alone, such pixels\nwill cause many of their neighbors to be flagged as cosmic rays, since\nthe wings of the convolution kernel will spread a strongly negative\npixel in image $I$ over many neighboring pixels in image $J$. Second,\ncosmic ray hits are often multiple-pixel events. In this case, a\ncosmic ray pixel may shield less strongly contaminated neighboring\ncosmic ray pixels from identification. An additional complication is\nthat the background may not be spatially uniform, which hinders\nmeasuring the noise level in an image and defining a sensible\nthreshold level for cosmic ray rejection.\n\nThe problems of low pixel values and spatially variable background\nlevels can both be handled with preprocessing steps applied prior to\nthe spatial convolution. Nonuniform sky level can be removed by\ngenerating and subtracting a smoothed map of the background intensity.\nI have chosen to use a large spatial median filter for this background\ngeneration, but any method working on larger spatial scales than the\nlargest object in the frame would work. The main caveat is that\na spatially constant rejection threshold should not be used if the\nbackground varies enough to introduce substantial spatial variations\nin the local Poisson sky noise. Low pixels can be flagged and\nreplaced before the spatial convolution, using a simple threshold\noperation. This is of course best done after any variable background\nis subtracted, since the sky level should be uniform for the\nthresholding operation to be well behaved. Any previously known bad\npixels can also be replaced with the background level or an\ninterpolation from their good neighbors at this stage.\n%\nThis approach to background estimation has yielded good results for\nour data, in which large scale intensity variations are weak ($< 10\\%$\nof $\\sky$) and due primarily to flatfielding errors. For cases where\nthe intensity level contains structure on a wide range of spatial\nscales, multiscale transform methods (Starck, Murtagh, \\& Bijaoui\n1995) can provide a natural treatment of the background level.\n\nWe estimate the variance in the input image empirically, using the\niteratively clipped sample variance of the background-subtracted image\nto determine $\\skysig$, which is taken to be spatially uniform.\nSpatial variations in the noise level could become a problem for some\nimages. Such variations can be handled with a minor modification to\nthe algorithm, by making the rejection threshold in the filtered image\ndepend on the locally measured noise, provided only that the noise\nlevel variations occur on spatial scales large compared to the\nconvolution kernel. Multiscale methods can again be used for accurate\nnoise estimation in the presence of spatially variable backgrounds or\nextended objects (Starck \\& Murtagh 1998).\n\nSome multiple-pixel cosmic ray hits will be well handled by a single\nconvolution and flagging step, provided that they remain smaller than\nthe PSF and that they are sufficiently strong (with intensities\nsubstantially exceeding the threshold for single pixel events).\nHowever, multiple-pixel events usually contain pixels with a range of\nintensities. When two contaminated pixels of very different intensity\nlie side by side, the stronger pixel will be flagged but the weaker\none will be ``shielded'' from detection by its prominent neighbor. To\nidentify such ``shielded'' cosmic ray pixels, the convolution and\nflagging algorithm can be run iteratively. After every flagging\niteration, the newly identified cosmic ray pixels are replaced with\nthe sky level, thereby exposing their less prominent neighbors to\nscrutiny. This iterative approach is highly successful at flagging\nall parts of a multi-pixel cosmic ray hit lying above the requested\ndetection threshold.\n\nWhen setting threshold levels for rejection,\nwe have chosen to use empirical measures of the sky variance in both\ninput and convolved image for convenience. Comparing the results of\nthese empirical measures to the predicted relation given by\nequation~\\ref{ssigJ} gave agreement at the $5$--$7\\%$ level for a test case\nwith $3$ pixel FWHM seeing (i.e., $\\psfsig = 1.27$), with the measured\nvariance of the convolved image slightly exceeding the prediction.\nDisagreements at this level could be due to several expected effects,\ne.g., the influence of real objects on the pixel histogram (which\nincreases after smoothing), or the continuous approximation to\ndiscrete sums made in deriving equation~\\ref{ssigJ}.\n\nThis iterative cosmic ray rejection is of course computationally\nexpensive when compared to basic image reduction steps like bias\nsubtraction and flatfielding. Presently, eight iterations of cosmic\nray rejection for a 2048$\\times$4096 pixel image requires of order 10\nminutes to run on a 295 MHz Sun Ultra-30 with 248 megabytes of main\nmemory. This speed could be improved by implementing the algorithm\nentirely in a compiled programming language (the present\nimplementation being an interpreted IRAF script).\nIt is nevertheless fast enough that I have routinely applied the\nalgorithm to large data sets (tens of $2018 \\times 4096 \\times 8$\npixel images from the Kitt Peak National Observatory CCD Mosaic camera).\n% Comment on execution time scalings?\nIn principle, the computational requirements should scale as $n\n\\log(n)$ for $n$ pixels in the large-$n$ limit, since the convolution\ncan be implemented using fast Fourier transforms, while the remaining\nsteps should all be linear in the number of pixels. Timing tests on\na 400 MHz Intel Pentium-II computer with 128 megabytes of memory\nyielded a scaling of approximately $n^{1.4}$ for images with\n$\\log_2(n) = 22 \\pm 1$ (i.e. roughly 2k by 2k pixels).\nThe difference between this scaling and the $n \\log(n)$ scaling suggested\nfrom first principles is perhaps due to the variety of different\ncomputational demands (memory, i/o, cpu speed) which can limit the\nperformance of the algorithm for different image sizes.\n\n\\section{Simulations} \\label{simulations}\nTo verify the analytical results of section~\\ref{math} and study the\neffectiveness of the iterated algorithm on multiple pixel events, we\ncarried out three types of artificial data simulations. The first\ntype tested the algorithm's detection rate for single pixel events;\nthe second tested the false alarm rate at the locations of point\nsources; and the third tested rejection of multi-pixel events. For\nboth tests of detection rates, the empirically measured detection\nthreshold was taken as the intensity of added cosmic rays for which\n50\\% of the affected pixels were correctly flagged. This is the\nappropriate cutoff because a simulated cosmic ray of precisely\nthreshold intensity will be boosted above the cutoff by Poisson noise\nhalf the time, and will fall below threshold the other half.\n\nThe cosmic ray detection rate test added single pixel cosmic ray hits\nto a noise field and counted the number of hits correctly flagged by\nthe algorithm as a function of CR intensity, rejection threshold, and\nPSF width. This allows a check of the analytic results plotted in\nfigure~\\ref{crsig_yb}. The agreement is good, with empirically\nmeasured detection thresholds falling between 100\\% and 110\\% of the\ntheoretical expectations throughout the tested parameter space. In\nparticular, the measured detection threshold is within 3\\% of the\npredicted value for $\\cutoff / ( \\gain \\skysig ) \\la 0.3$, which is\nthe regime of greatest interest for broadband astronomical imaging.\n\nAn interesting variant on the detection test is to run it on a field\nwith stars or other astronomical objects. Our tests showed an\nappreciable degradation ($\\sim 7\\%$) of the CR detection threshold\naveraged over the image in the presence of a reasonably dense star\nfield. This is expected, since the detection efficiency decreases in\nthe wings of a point source (see section~\\ref{math}). However, there\nis no good way to characterize this effect for all possible images.\nIf a precise measurement of the detection threshold in some particular\nimage is needed, it can be obtained through simulations by adding\n``cosmic ray hits'' to that exact image and studying their recovery rates.\n\nThe false alarm rate test examined the probability of rejecting a\ngiven pixel in a pure Poisson noise field with and without point\nsources. Only the central pixels of the point source locations were\nconsidered, since the wings of stellar profiles are less likely than\ntheir cores to be incorrectly rejected.\nThis test confirmed that the probability of rejecting the central\npixel of a star does not exceed the probability of rejecting an\narbitrary sky pixel under our algorithm.\n\nFinally, the multiple pixel event tests placed artificial bad columns\nonto noise fields and measured the fraction of rejected pixels. Bad\ncolumns were chosen as a suitably conservative limiting case of\nmultiple-pixel cosmic ray events, since such events usually have a\nlinear morphology. The realized rejection threshold was determined as\na function of stellar FWHM, number of adjacent bad columns, and\nrequested sigma clipping level. These simulations were run with a sky\nnoise of $41$ ADU and gain of $3$, so that they are restricted to low\nvalues of $\\cutoff / ( \\gain \\skysig )$. The general result is\n(unsurprisingly) that features comparable in size to the PSF cannot be\nrejected, while features much smaller than the PSF on only one axis\ncan be rejected with relatively modest increases in the intensity\nthreshold for rejection. Results of the multi-pixel event\nsimulations are summarized in table~\\ref{colrej_tab}.\n\n\n\\begin{table}\n\\begin{tabular}{l|l|lllllll}\nSigma & $N_{\\hbox{cols}}$ & \\multicolumn{7}{c}{Stellar FWHM} \\\\\ncutoff & & 2 & 2.52 & 3.175 & 4 & 5.04 & 6.35 & 8 \\\\\n\\hline\n3 & 1 & 0.34 & 0.57 & 0.74 & 0.80 & 0.86 & 0.90 & 0.94 \\\\\n & 2 & 0 & 0 & 0 & 0.40 & 0.56 & 0.70 & 0.80 \\\\\n & 3 & 0 & 0 & 0 & 0 & 0.19 & 0.39 & 0.58 \\\\\n & 4 & 0 & 0 & 0 & 0 & 0 & 0.12 & 0.31 \\\\\n\\hline\n4 & 1 & 0.22 & 0.53 & 0.67 & 0.76 & 0.82 & 0.86 & 0.90 \\\\\n & 2 & 0 & 0 & 0 & 0.32 & 0.49 & 0.59 & 0.70 \\\\\n & 3 & 0 & 0 & 0 & 0 & 0.09 & 0.32 & 0.38 \\\\\n & 4 & 0 & 0 & 0 & 0 & 0 & 0.07 & 0.25 \\\\\n\\hline\n5 & 1 & 0.16 & 0.52 & 0.63 & 0.73 & 0.81 & 0.85 & 0.89 \\\\\n & 2 & 0 & 0 & 0 & 0.23 & 0.43 & 0.50 & 0.63 \\\\\n & 3 & 0 & 0 & 0 & 0 & 0.06 & 0.27 & 0.36 \\\\\n & 4 & 0 & 0 & 0 & 0 & 0 & 0.04 & 0.21 \\\\\n\\hline\n%\n\\end{tabular}\n\\caption{The reduction in cosmic ray detection sensitivity for multiple\npixel events consisting of adjacent bad columns of uniform value. The\nratio of theoretical single pixel CR detection threshold to\nempirically determined multiple pixel threshold level is tabulated as\na function of sigma cutoff, transverse size of the defect in columns,\nand point spread function width.}\n\\label{colrej_tab}\n\\end{table}\n\n\\section{Summary and Discussion} \\label{theend}\nWe have presented a cosmic ray rejection algorithm based on a\nconvolution of the input image. The advantages of the method spring\nfrom the linear nature of the spatial filter, which allows us to\ndetermine the noise properties of the filtered image and so to\ncalculate and control the probability of rejecting the central pixel\n(or indeed any pixel) of a point source. This safety mechanism\nensures that cosmic ray rejection can be applied throughout the image,\nwithout special treatment for the locations of sources. The\nsensitivity to cosmic rays is of course reduced at the locations of\nobjects, because of the added Poisson noise contributed by object\nphotons and the resulting need to maintain a positive expectation\nvalue in the filtered image.\n\nWe usually apply our method conservatively, considering pixels\ninnocent until proven guilty beyond any reasonable doubt. This means\nthat given some uncertainty in the measured point spread function, we\nuse a convolution kernel that is slightly narrower than our best\nestimate of the PSF (generally by about 10\\%). This choice depends on\nthe relative importance of keeping legitimate sources and rejecting\nspurious ones for the scientific problem at hand.\n\nOur original goal in developing this algorithm was to flag and\nreplace cosmic ray hits in individual exposures that are later\naligned and stacked. The alignment procedure requires\ninterpolating the original images, and we use sinc interpolation to\npreserve the spatial resolution and noise properties of the input\nimage. However, sinc interpolation assumes well sampled data and\nresponds badly to cosmic rays, spreading their effects over many more\npixels than were originally affected and motivating us to replace them\nat an early stage. We nevertheless have a second chance to reject\ncosmic rays by looking for consistency among our different exposures\nwhen we stack them, and this second chance helps motivate our generally\nconservative approach to cosmic ray flagging.\n\nBy applying the algorithm developed here followed by sigma rejection\nduring image stacking, we exploit two distinct properties of cosmic\nrays: They are sharper than the point spread function, and they do not\nrepeat from exposure to exposure. However, we are using these two\ntests in sequence. An algorithm exploiting both\npieces of information simultaneously could potentially yield more sensitive\ncosmic ray rejection. For general data sets, such an algorithm would\nhave to handle stacks of unregistered images with different PSFs,\nmaking its development difficult but potentially rewarding. An\ninteresting effort in this regard is Freudling's (1995) algorithm,\nwhich identifies cosmic rays in the course of deconvolving and\ncoadding images with Hook \\& Lucy's (1992) method.\n\n\\acknowledgements\nThis work was supported by a Kitt Peak Postdoctoral Fellowship and\nby an STScI Institute Fellowship. Kitt\nPeak National Observatory is part of the National Optical Astronomy\nObservatories, operated by the Association of Universities for\nResearch in Astronomy (AURA) under cooperative agreement with the\nNational Science Foundation. The Space Telescope Science Institute\n(STScI) is operated by AURA under NASA contract NAS 5-26555.\nI thank an anonymous referee for their remarks.\n\n\n\\begin{references}\n% \\reference{} Croke, B. F. W. 1995, \\pasp\\ 107, 1255\n % CR identification in 2d spectroscopic data.\n\\reference{} Fischer, P. \\& Kochanski, G. P. 1994, \\aj\\ 107, 802\n\\reference{} Freudling, W. 1995, \\pasp\\ 107, 85\n % CR rejection as a step in Lucy deconvolution... opaque paper,\n % but the most interesting method in this whole bibliography\n\\reference{} Hook, R. \\& Lucy, L. B. 1992, ST-ECF Newslett., 17, 10\n\\reference{} Kendall, M. G., \\& Stuart, A. 1967, {\\it The Advanced\n Theory of Statistics}, vol. 2, 2nd edition, New York: Hafner\n % Kendall and Stuart on hypothesis testing\n\\reference{} Murtagh, F. D. 1992, ADASS 1, 265\n % Trainable classifiers (neural nets, etc)\n % for object-based CR identification in WF/PC I data\n\\reference{} Murtagh, F., \\& Adorf, H. M. 1991, {\\it 3rd ESO/ST-ECF\n Data Analysis Workshop}, P. Grosbol {\\it et al}, eds., 51\n % Intercomparison of several methods, with particular but not\n % exclusive emphasis on trainable classifiers\n\\reference{} Salzberg, S., Chandar, R., Ford, H., Murthy, S. K., \\&\n White, R. 1995, \\pasp\\ 107, 279\n % Decision trees for object-based CR identification in WF/PC I data\n\\reference{} Shaw, R. A., \\& Horne, K. 1992, ADASS 1, 311\n\\reference{} Starck, J.-L., Murtagh, F., \\& Bijaoui, A. 1995, ADASS 4, 279\n % nice review (detailed math / not much text) of a bunch of\n % multiscale transform methods for astronomical image processing.\n\\reference{} Starck, J.-L., \\& Murtagh, F. 1998, \\pasp\\ 110, 193\n % \"Automatic noise estimation from multiresolution support\"\n\\reference{} Windhorst, R. A., Franklin, B. E., \\& Neuschaefer, L. W. 1994, \n \\pasp\\ 106, 798\n\\end{references}\n\\end{document}\n\n"
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astro-ph0002042
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The Variation of Gas Mass Distribution in Galaxy Clusters: Effects of Preheating and Shocks
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[
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"author": "Yutaka Fujita\\altaffilmark{1} and Fumio Takahara"
}
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We investigate the origin of the variation of the gas mass fraction in the core of galaxy clusters, which was indicated by our work on the X-ray fundamental plane. Applying a spherical collapse model of cluster formation and considering the effect of shocks on preheated intracluster gas, we construct a simple model to predict the spatial gas distribution of clusters. As is suggested by our previous work, we assume that the core structure of clusters determined at the cluster collapse has not been much changed after that. The adopted model supposes that the gas distribution characterized by the slope parameter is related to the preheated temperature. Comparison with observations of relatively hot ($\gtrsim 3$ keV) and low redshift clusters suggests that the preheated temperature is about 0.5-2 keV, which is higher than expected from the conventional galactic wind model and possibly suggests the need for additional heating such as quasars or gravitational heating on the largest scales at high redshift. The dispersion of the preheated temperature may be attributed to the gravitational heating in subclusters. We calculate the central gas fraction of a cluster from the gas distribution, assuming that the global gas mass fraction is constant within a virial radius at the time of the cluster collapse. We find that the central gas density thus calculated is in good agreement with the observed one, which suggests that the variation of gas mass fraction in cluster cores appears to be explained by breaking the self-similarity in clusters due to preheated gas. We also find that this model does not change major conclusions on the fundamental plane and its cosmological implications obtained in previous papers, which strongly suggests that not only for the dark halo but also for the intracluster gas the core structure preserves information about the cluster formation.
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[
{
"name": "ms_prep1.tex",
"string": "%#!latex\n%\\documentclass{aastex}\n\\documentclass[preprint]{aastex}\n\\slugcomment{OU-TAP 115: ApJ in press}\n\n\\shorttitle{Variation of Gas Mass Distribution in Galaxy Clusters}\n\n\n\\begin{document}\n\n\\title{The Variation of Gas Mass\nDistribution in Galaxy Clusters: Effects of Preheating and Shocks}\n\n\\author{Yutaka Fujita\\altaffilmark{1} and Fumio Takahara}\n\\affil{Department of Earth and Space Science, Graduate School of\nScience, Osaka University, Machikaneyama-cho, Toyonaka, \nOsaka, 560-0043}\n\n\n\\altaffiltext{1}{JSPS Research Fellow}\n\n\\begin{abstract}\n We investigate the origin of the variation of the gas mass fraction in\n the core of galaxy clusters, which was indicated by our work on the\n X-ray fundamental plane. Applying a spherical collapse model of cluster\n formation and considering the effect of shocks on preheated\n intracluster gas, we construct a simple model to predict the spatial\n gas distribution of clusters. As is suggested by our previous work, we\n assume that the core structure of clusters determined at the cluster\n collapse has not been much changed after that. The adopted model\n supposes that the gas distribution characterized by the slope parameter\n is related to the preheated temperature. Comparison with observations\n of relatively hot ($\\gtrsim 3$ keV) and low redshift clusters suggests\n that the preheated temperature is about 0.5-2 keV, which is higher than\n expected from the conventional galactic wind model and possibly\n suggests the need for additional heating such as quasars or\n gravitational heating on the largest scales at high redshift. The\n dispersion of the preheated temperature may be attributed to the\n gravitational heating in subclusters. We calculate the central gas\n fraction of a cluster from the gas distribution, assuming that the\n global gas mass fraction is constant within a virial radius at the time\n of the cluster collapse. We find that the central gas density thus\n calculated is in good agreement with the observed one, which suggests\n that the variation of gas mass fraction in cluster cores appears to be\n explained by breaking the self-similarity in clusters due to preheated\n gas. We also find that this model does not change major conclusions on\n the fundamental plane and its cosmological implications obtained in\n previous papers, which strongly suggests that not only for the dark\n halo but also for the intracluster gas the core structure preserves\n information about the cluster formation.\n\\end{abstract}\n\n\\keywords{cosmology: theory --- clusters: galaxies: general --- X-rays:\ngalaxies}\n\n\n\\section{Introduction}\n\nCorrelations among physical quantities of clusters of galaxies are very\nuseful tools for studying the formation of clusters and cosmological\nparameters. Recently, we have found that clusters at low redshifts\n($z\\lesssim 0.1$) form a plane (the fundamental plane) in the three\ndimensional space represented by their core structures, that is, the\ncentral gas density $\\rho_{\\rm gas,0}$, core radius $r_c$, and X-ray\ntemperature $T_{\\rm gas}$ \\citep[Paper~I]{fuj99a}. On the other hand, a\nsimple theoretical model of cluster formation predicts that clusters\nshould be characterized by the virial density $\\rho_{\\rm vir}$ (or the\ncollapse redshift $z_{\\rm coll}$) and the virial mass $M_{\\rm vir}$\n(\\citealt{fuj99b}, Paper~II). Thus, assuming the similarity of the dark\nmatter distributions, clusters should form a plane in the three\ndimensional space of the dark matter density in the core $\\rho_{\\rm DM,\nc}$, the core radius of dark matter distribution $r_{\\rm DM, c}$, and\nthe virial temperature $T_{\\rm vir}$ \\footnote{In Paper~I, we used the\nterms ' virial density', 'virial radius', and ' virial mass' to denote\nthe dark matter density in the core, the core radius of dark matter\ndistribution, and the core mass, respectively. This is because we\nassumed that the dark matter density in the core is proportional to the\naverage dark matter density over the whole cluster (Paper II). To avoid\npossible confusions, here we use the term ' dark matter', and the term '\nvirial' will be used to represent spatially averaged quantities of\ngravitational matter (mostly dark matter) within the virialized\nregion.}. However, the relations between the two planes are not simple;\nfor example, it is found that $\\rho_{\\rm gas, 0}$ is not proportional to\n$\\rho_{\\rm DM, c}$. In Paper~I, we found that the ratio $\\rho_{\\rm\ngas,0}/\\rho_{\\rm DM, c}$ is not constant but obeys the relation of\n$\\rho_{\\rm gas,0}/\\rho_{\\rm DM, c} \\propto \\rho_{\\rm DM, c}^{-0.1}M_{\\rm\nDM, c}^{0.4}$, where $M_{\\rm DM, c}$ is the core mass.\nThis raises the question how the segregation between gas and dark\nmatter occurs.\n\nIn the hierarchical structure formation, dark halos are expected to obey\nscaling relations. In fact, numerical simulations suggest that the\ndensity distribution in dark halos take a universal form as claimed by\n\\citet{nav96, nav97}. On a cluster scale, it can be approximated by\n$\\rho_{\\rm DM}(r)\\propto r^{-2}$ for $r\\lesssim 1$ Mpc, where detailed\nX-ray observations have been done \\citep{mak98}. On the contrary,\nobservations show that the slope of the density profile of the hot\ndiffuse intracluster gas has a range of value. Radial surface brightness\nprofiles of X-ray emission are often fitted with the conventional\n$\\beta$ model as\n%\n\\begin{equation}\n\\label{eq:sur}\nI(R)=\\frac{I_0}{(1+R^2/r_c^2)^{3\\beta_{\\rm obs}-1/2}}\\;,\n\\end{equation}\n%\nwhere $\\beta_{\\rm obs}$ is the slope parameter \\citep{cav78}. If the\nintracluster gas is isothermal, equation (\\ref{eq:sur}) corresponds to\nthe gas density profile of\n%\n\\begin{equation}\n\\label{eq:gas_obs}\n\\rho_{\\rm gas}(r)=\\frac{\\rho_{\\rm gas, 0}}{(1+r^2/r_c^2)\n^{3\\beta_{\\rm obs}/2}}\\:.\n\\end{equation}\n%\nObservations show that the slope parameter takes a range $\\beta_{\\rm\nobs} \\sim 0.4-1$ \\citep{jon84, jon99}. This means that for $r>>r_{\\rm\nc}$, the density profiles range from $\\propto r^{-1.2}$ to $\\propto\nr^{-3}$, which are more diverse than those of dark matter. Moreover,\nobservations show that the clusters with large $r_c$ and $T_{\\rm gas}$\ntend to have large $\\beta_{\\rm obs}$ (e.g. \\citealt{neu99};\n\\citealt{hor99}; \\citealt{jon99}). Since the average gas fraction of\nclusters within radii much larger than $r_{\\rm c}$ should be universal\nand the dark matter distribution of clusters is also universal, the\nvariation of $\\beta_{\\rm obs}$ is expected to correlate with that of the\ngas fraction in the core region. In other words, the gas fraction at the\ncore is not the same as that of the whole cluster and is not\nproportional to the dark matter density. This fact must be taken care of\nwhen we discuss cosmological parameters using observational X-ray\ndata. Since the emissivity of X-ray gas is proportional to $\\rho_{\\rm\ngas}^2$, most of the X-ray emission of a cluster comes form the central\nregion where $\\rho_{\\rm gas}$ is large. Although in Papers I and II, we\ndid not take account of the effects of $\\beta_{\\rm obs}$, we did find\nthe gas mass fraction in the core region is diverse by analyzing the\nX-ray emission. In this paper, we reanalyze the data taking account of\n$\\beta_{\\rm obs}$ and discuss the relation between core and global gas\nmass fractions. We will also show that major conclusions on the\nfundamental relations are not changed.\n\nThe variation of gas mass fraction itself has been investigated by\nseveral authors (e.g. \\citealp{ett99, arn99}). \\citet{ett99} argue that\nit is partially explained if the dark matter has a significant baryonic\ncomponent. Another possible explanation of the diverse gas distributions\nis that intracluster gas had already been heated before the collapse\ninto the cluster; the energetic winds generated by supernovae are one\npossible mechanism to increase gas entropy (e.g. \\citealp{dek86,\nmih94}). In fact, \\citet{pon99} find that the entropy of the\nintracluster gas near the center of clusters is higher than can be\nexplained by gravitational collapse alone. In order to estimate the\neffect of the preheating on intracluster gas, we must take account of\nshocks forming when the gas collapses into the cluster; they supply\nadditional entropy to the gas. \\citet{cav97, cav98, cav99} have\ninvestigated both the effects and predicted the relation between X-ray\nluminosities and temperatures ($L_{\\rm X}-T_{\\rm gas}$ relation). They\npredicted that the gas distributions of poor clusters are flatter than\nthose of rich clusters, which results in a steeper slope of $L_{\\rm\nX}-T_{\\rm gas}$ relation for poor clusters. This is generally consistent\nwith the observations. It is an interesting issue to investigate whether\nthis scenario provides a natural explanation for the observed dispersion\nof gas mass fraction in the cluster core and whether it reproduces the\nX-ray fundamental plane we found in Paper I in our general theoretical\nscenario.\n\nIn order to clarify what determines the gas distribution, we construct\nas a simple model as possible. Although many authors have studied the\npreheating of clusters\n(\\citealt{kai91,evr91,met94,bal99,kay99,wu99,val99}), this is the first\ntime to consider the influence of the preheating and shocks on the\nfundamental plane and two-parameter family nature of clusters paying\nattention to the difference between the collapse redshift $z_{\\rm coll}$\nand the observed redshift $z_{\\rm obs}$ of clusters explicitly. In\n\\S\\ref{sec:model}, we explain the model of dark matter potential and\nshock heating of intracluster gas. In \\S\\ref{sec:result}, we use the\nmodel to predict $\\beta_{\\rm obs}-T_{\\rm gas}$ and $\\beta_{\\rm\nobs}-r_{\\rm c}$ relations, and the fundamental plane and band of\nclusters. The predictions are compared with observations.\n\n\\section{Models}\n\\label{sec:model}\n\\subsection{Dark Matter Potential}\n\\label{sec:pot}\n\nIn order to predict the relations among parameters describing a dark\nmatter potential, we use a spherical collapse model \\citep{tom69,gun72}.\nAlthough the details are described in Paper~II, we summarize them here\nfor convenience.\n\n%We assume that the characteristic density in the core region of a\n%cluster is the virial density of the cluster when the cluster collapsed\n%($z_{\\rm coll}$). \nThe virial density of a cluster $\\rho_{\\rm vir}$ at the time of the\ncluster collapse ($z_{\\rm coll}$) is $\\Delta_c$ times the critical\ndensity of a universe at $z=z_{\\rm coll}$. It is given by\n%\n\\begin{equation}\n \\label{eq:density}\n \\rho_{\\rm vir} = \\Delta_c \\rho_{\\rm crit}(z_{\\rm coll})\n = \\Delta_c \\rho_{\\rm crit,0}E(z_{\\rm coll})^2\n = \\Delta_c \\rho_{\\rm crit,0} \\frac\n {\\Omega_0 (1+z_{\\rm coll})^3}\n {\\Omega(z_{\\rm coll})} \\:,\n\\end{equation}\n%\nwhere $\\Omega(z)$ is the cosmological density parameter, and $E(z)^2 =\n\\Omega_0 (1+z)^3/\\Omega(z)$, where we do not take account of the\ncosmological constant. The index 0 refers to the values at $z=0$. Note\nthat the redshift-dependent Hubble constant can be written as $H(z) =\n100 h E(z) \\rm\\; km\\; s^{-1}\\; Mpc^{-1}$. We adopt $h=0.5$ for numerical\nvalues. In practice, we use the fitting formula of \\citet{bry98} for the\nvirial density:\n%\n\\begin{equation}\n \\label{eq:delta}\n \\Delta_c = 18\\pi^2 + 60 x - 32 x^2 \\;,\n\\end{equation}\nwhere $x = \\Omega(z_{\\rm coll})-1$. \n\nIt is convenient to relate the collapse time in the spherical model with\nthe density contrast calculated by the linear theory. We define the\ncritical density contrast $\\delta_c$ that is the value, extrapolated to\nthe present time ($t=t_0$) using linear theory, of the overdensity which\ncollapses at $t=t_{\\rm coll}$ in the exact spherical model. It is given\nby\n%\n\\begin{eqnarray}\n \\label{eq:crit}\n \\delta_c(t_{\\rm coll}) \n &=& \\frac{3}{2}D(t_0)\\left[\n 1+\\left(\\frac{t_\\Omega}{t_{\\rm coll}}\\right)^{2/3}\\right]\n \\;\\;\\;\\; (\\Omega_0 < 1) \\\\\n &=& \\frac{3(12\\pi)^{2/3}}{20}\n \\left(\\frac{t_0}{t_{\\rm coll}}\\right)^{2/3}\n \\;\\;\\;\\; (\\Omega_0 = 1) \n\\end{eqnarray}\n%\n\\citep{lac93}, where $D(t)$ is the linear growth factor given by\nequation (A13) of \\citet{lac93} and $t_\\Omega = \\pi\nH_0^{-1}\\Omega_0(1-\\Omega_0)^{-3/2}$.\n\nFor a power-law initial fluctuation spectrum $P(k)\\propto k^n$, the rms\namplitude of the linear mass fluctuations in a sphere containing an\naverage mass $M$ at a given time is $\\delta \\propto M^{-(n+3)/6}$. Thus,\nthe virial mass of clusters which collapse at $t_{\\rm coll}$ is related\nto that at $t_0$ as\n%\n\\begin{equation}\n \\label{eq:mass}\n M_{\\rm vir}(t_{\\rm coll}) \n =M_{\\rm vir, 0}\\left[\n \\frac{\\delta_c(t_{\\rm coll})}{\\delta_c(t_0)}\\right]^{-6/(n+3)}\n \\;.\n\\end{equation}\n%\nHere, $M_{\\rm vir, 0} (=M_{\\rm vir}[t_0])$ is regarded as a variable\nbecause actual amplitude of initial fluctuations has a distribution. We\nrelate $t=t_{\\rm coll}$ to the collapse or formation redshift $z_{\\rm\ncoll}$, which depends on cosmological parameters. Thus, $M_{\\rm vir}$ is\na function of $z_{\\rm coll}$ as well as $M_{\\rm vir, 0}$. This means\nthat for a given mass scale $M_{\\rm vir}$, the amplitude of initial\nfluctuations takes a range of value, and spheres containing a mass of\n$M_{\\rm vir}$ collapse at a range of redshift. In the following, the\nslope of the spectrum is fixed at $n = - 1$. It is typical of the\nscenario of standard cold dark matter for a cluster mass range, and is\nconsistent with observations as shown in Paper~II.\n\nThe virial radius and temperature of a cluster are then calculated by\n%\n\\begin{equation}\n \\label{eq:rad}\n r_{\\rm vir} = \\left(\\frac{3M_{\\rm vir}}\n {4\\pi \\rho_{\\rm vir}}\\right)^{1/3} \\:,\n\\end{equation}\n%\n\\begin{equation}\n \\label{eq:temp}\n T_{\\rm vir} = \\gamma \\frac{\\mu m_{\\rm H}}{3 k_{\\rm B}}\\frac{G M_{\\rm\n vir}}{r_{\\rm vir}} \\:,\n\\end{equation}\n%\nwhere $\\mu (=0.6)$ is the mean molecular weight, $m_{\\rm H}$ is the\nhydrogen mass, $k_{\\rm B}$ is the Boltzmann constant, $G$ is the\ngravitational constant, and $\\gamma$ is a fudge factor which typically\nranges between 1 and 1.5. In Paper~II, we adopted the value\n$\\gamma=1$. Note that the value of $\\gamma$ is applied only to dark\nmatter, but not to gas, because we do {\\em not} assume $T_{\\rm\ngas}=T_{\\rm vir}$ here. We emphasize that $M_{\\rm vir}$, $\\rho_{\\rm\nvir}$, and $r_{\\rm vir}$ are the virial mass, density, and radius at the\ntime of the cluster collapse, respectively. \n\n\\subsection{Shocks and Hydrostatic Equilibrium}\n\\label{sec:shock}\n\nTo study the effect of preheating, we here adopt a very simple model as\na first step. When a cluster collapses, we expect that a shock wave\nforms and the infalling gas is heated. In order to derive the postshock\ntemperature, we use a shock model of \\citet{cav98}. For a given preshock\ntemperature $T_1$, the postshock temperature $T_2$ can be calculated\nfrom the Rankine-Hugoniot relations. Assuming that the shock is strong\nand that the shock front forms in the vicinity of $r_{\\rm vir}$, it is\napproximately given by\n%\n\\begin{equation}\n\\label{eq:shock}\nk_{\\rm B}T_2 = -\\frac{\\phi(r_{\\rm vir})}{3}\n+\\frac{3}{2}k_{\\rm B}T_1\\:\n\\end{equation}\n%\n\\citep{cav98}, where $\\phi(r)$ is the potential at $r$. According to the\nvirial theorem and the continuity when $T_1$ approaches zero, we should\ntake $-\\phi(r_{\\rm vir})/3=k_{\\rm B}T_{\\rm vir}$. For $r<r_{\\rm vir}$,\nwe assume that the gas is isothermal and hydrostatic, and that the\nmatter accretion after the cluster collapse does not much change the\nstructure of the central region of the cluster significantly,\n%the temperature and density are unchanged, \nas confirmed by numerical simulations (e.g. \\citealt{tak98}). It is to\nbe noted that even if the density profile of dark matter is represented\nby the universal profile \\citep{nav96, nav97}, it is not inconsistent\nwith the isothermal $\\beta$ model of gas represented by equation\n(\\ref{eq:gas_obs}) (\\citealt*{mak98, eke98}) within the present\nobservational scopes. On these assumptions, the gas temperature in the\ninner region of a cluster is $T_{\\rm gas}=T_2$, and the mass within $r$\nof the cluster center $M_{\\rm DM}$ is related to the density profile of\nintracluster gas, $\\rho_{\\rm gas}$, by\n%\n\\begin{equation}\n\\label{eq:MDM}\nM_{\\rm DM}(r)= -\\frac{k_{\\rm B}T_{\\rm gas}}{\\mu m_{\\rm H}G}\\; r\n\\; \\frac{d \\ln \\rho_{\\rm gas}}{d \\ln r} \\;.\n\\end{equation}\n%\nSince $M_{\\rm DM}(r_{\\rm vir})=M_{\\rm vir}$, equations (\\ref{eq:temp})\nand (\\ref{eq:MDM}) yield\n%\n\\begin{equation}\n\\label{eq:temp2}\nT_{\\rm vir} = -\\frac{\\gamma}{3}\\: T_{\\rm gas}\n\\left.\\frac{d \\ln \\rho_{\\rm gas}}{d \\ln r}\\right|_{r=r_{\\rm vir}} \\;.\n\\end{equation}\n%\nDefining $\\beta=T_{\\rm vir}/T_{\\rm gas}$, the gas density profile is\nthus given by\n%\n\\begin{equation}\n\\label{eq:beta}\n\\rho_{\\rm gas}(r)\\propto r^{-3\\beta/\\gamma}\\:,\n\\end{equation}\n%\nas long as ($d \\ln \\rho_{\\rm gas}/d \\ln r$) is nearly constant.\n\nEquation (\\ref{eq:shock}) shows that in this model $\\beta$ is a function\nof only $T_{\\rm vir}$ when $T_1$ is regarded as an external parameter,\nthat is,\n% \n\\begin{equation}\n\\label{eq:beta2}\n\\beta=\\frac{T_{\\rm vir}}{T_{\\rm vir}+(3/2)T_1}\\:.\n\\end{equation}\n%\nSince $T_{\\rm vir}=T_{\\rm gas}\\beta$, equation (\\ref{eq:beta2}) is\nwritten as\n%\n\\begin{equation}\n\\label{eq:beta3}\n\\beta=\\frac{T_{\\rm gas}-(3/2)T_1}{T_{\\rm gas}}\\:.\n\\end{equation}\n%\nThus, the $\\beta-T_{\\rm gas}$ relation can be used to determine $T_1$ by\ncomparing with the observation. Since both $T_{\\rm vir}$ and $r_{\\rm\nvir}$ are the two-parameter families of $z_{\\rm coll}$ and $M_{\\rm vir,\n0}$ (equations [\\ref{eq:density}], [\\ref{eq:mass}],[\\ref{eq:rad}] and\n[\\ref{eq:temp}]), equation (\\ref{eq:beta2}) shows that $\\beta$ can be\nrepresented by $r_{\\rm vir}$ as $\\beta=\\beta(r_{\\rm vir}, M_{\\rm vir,\n0})$, if $T_1$ is specified. Recent numerical simulations suggest that\nthe structure of central region of clusters is related to $z_{\\rm coll}$\n\\citep{nav97}, and in particular $r_{\\rm DM, c}$ is proportional to\n$r_{\\rm vir}$ \\citep{sal98,mak98}. Therefore, if we assume that $r_{\\rm\nDM, c}=r_{\\rm c}$ and that $r_{\\rm vir}/r_{\\rm c}$ is constant as in\nPaper~II, $T_1$ can also be determined by comparing the theoretical\nprediction of the $\\beta-r_{\\rm c}$ relation with the observation. Since\na spherical collapse model predicts $r_{\\rm vir}(z_{\\rm coll}=0) \\sim 4$\nMpc and observations show that $r_{\\rm c}(z_{\\rm coll}=0)\\sim 0.5$ Mpc\n(Figure 1b in Paper~II), we adopt $r_{\\rm vir}/r_{\\rm c}=8$ from now on. \nThus, we obtain $\\beta=\\beta(8 r_{\\rm c}[z_{\\rm coll}, M_{\\rm vir, 0}],\nM_{\\rm vir, 0})$.\n\n\\section{Results and Discussion}\n\\label{sec:result}\n\\subsection{$\\beta-T_{\\rm gas}$ and $\\beta-r_{\\rm c}$ Relations}\n\nUsing the model constructed in \\S\\ref{sec:shock}, we predict relations\nbetween $\\beta$ and $T_{\\rm gas}$, and between $\\beta$ and $r_{\\rm\nc}$. \n\nIf $T_1$ is mainly determined by the energetic winds generated in the\nforming galaxies or quasars before the formation of clusters, $T_1$\nshould be constant if subsequent adiabatic heating or cooling is\nneglected. However, if, besides the winds, the gravitational energy\nreleased in the subclusters, which later merged into the observed\nclusters, contributes to $T_1$, we expect that $T_1$ has a distribution\nproduced by different merging histories. In order to determine the\ndistribution in detail, we must calculate the merging histories by Monte\nCarlo realizations as \\citet[1998]{cav97} did. In this study, however,\nwe consider the scatter by investigating a range of $T_1$ for\nsimplicity. We show in Figure \\ref{fig1} the $\\beta-T_{\\rm gas}$\nrelation for $T_1=0.5$, 1, and 2 keV. The observational data are\noverlaid. Since equation (\\ref{eq:gas_obs}) is approximated to be\n$\\rho_{\\rm gas}(r)\\propto r^{-3\\beta_{\\rm obs}}$ for $r>>r_c$, the\nrelation\n%\n\\begin{equation}\n\\label{eq:beta_beta}\n\\beta = \\gamma \\beta_{\\rm obs}\n\\end{equation}\n%\nis obtained by comparing the relation (\\ref{eq:beta}). Thus, in the\nfollowing figures, the observed values of $\\beta_{\\rm obs}$ are\nconverted by relation (\\ref{eq:beta_beta}). In Figure~\\ref{fig1} we\nassumed $\\gamma=1$. As the data, we use only relatively hot ($T_{\\rm\ngas}\\gtrsim 3$ keV) and low redshift ($z\\lesssim 0.1$) clusters obtained\nby \\citet{moh99} and \\citet{per98}. Instead of $\\beta_{\\rm obs}$,\n\\citet{per98} present velocity dispersions corresponding to\ngravitational potential well, $\\sigma_{\\rm deproj}$, derived with the\ndeprojection method, ignoring velocity dispersion anisotropies and\ngradients . Thus, for the data we assume that $k_{\\rm B}T_{\\rm vir}=\\mu\nm_{\\rm H}\\sigma_{\\rm deproj}^2$ and define $\\beta$ as $T_{\\rm\nvir}/T_{\\rm gas}$. Figure~\\ref{fig1} shows that the observational data\nare consistent with $0.5\\lesssim T_1 \\lesssim 2$ keV but it seems that a\nsingle value of $T_1$ does not represent the range of data. The\npreheating ($T_1>0$) is expected to reduce $\\beta$ of the clusters with\nsmall $T_{\\rm gas}$ (Figure~\\ref{fig1}). At first glance, no\ncorrelations between $\\beta$ and $T_{\\rm gas}$ are recognized\nobservationally in this temperature range. However, some reports on the\nexistence of a weak correlation have been made when clusters with lower\n$T_{\\rm gas}$ are included (e.g. \\citealt{hor99}). Thus, our prediction\nis not inconsistent with the observations.\n\nAs discussed in \\S\\ref{sec:shock}, the $\\beta-r_{\\rm c}$ relation is\nrepresented by two parameters $z_{\\rm coll}$ and $M_{\\rm vir, 0}$, for a\ngiven value of $T_1$. The results are shown in Figure~\\ref{fig2} for\n$\\gamma=1$. Figure~\\ref{fig2}a and ~\\ref{fig2}b are for $\\Omega_0=1$ and\n0.2, respectively. For comparison, we also present observational data\n\\citep{moh99,per98}. As was in Paper~I, for the data of \\citet{moh99} we\nuse here only the component of surface brightness reflecting the global\nstructure of clusters, although the central component (so-called cooling\nflow component) may also have formed in the scenario of hierarchical\nclustering \\citep{fuj99c}.\n\nThe mass $M_{\\rm vir, 0}$ corresponds to the mass of clusters collapsed\nat $z\\sim 0$ and takes a range of value due to the dispersion of initial\ndensity fluctuation of the universe. Since observations and numerical\nsimulations show $M_{\\rm vir, 0}\\sim 10^{15}\\;\\rm M_{\\sun}$\n\\citep{evr96}, the observational data are expected to lie between the\ntwo lines of $M_{\\rm vir, 0}=5\\times 10^{14}\\;\\rm M_{\\sun}$ (arc BC) and\n$M_{\\rm vir, 0}=5\\times 10^{15}\\;\\rm M_{\\sun}$ (arc AD) for fixed $T_1$\nin Figure~\\ref{fig2}. Note that the distribution of $M_{\\rm vir, 0}$\ndegenerates on the lines in Figure~\\ref{fig1}. In Figure~\\ref{fig2}, the\npositions along the arcs AD and BC indicate the formation redshifts of\nthe clusters. When $\\Omega_0 = 1$, most of the observed clusters should\nhave collapsed at $z\\sim 0$ because clusters continue growing even at\n$z=0$ \\citep{pee80}. Thus, the cluster data are expected to be\ndistributed along the part of the lines close to the point of $z_{\\rm\ncoll}=0$ (segment AB). In fact, calculations done by \\citet{lac93}, and\n\\citet{kit96} show that if $\\Omega_0 = 1$, most of present day clusters\n($M_{\\rm vir}\\sim 10^{14-15}\\rm\\: M_{\\sun}$) should have formed in the\nrange of $z_{\\rm coll}\\lesssim 0.5$ (parallelogram ABCD in\nFigure~\\ref{fig2}a). In contrast, when $\\Omega_0 = 0.2$, the growth rate\nof clusters decreases and cluster formation gradually ceases at $z\n\\lesssim 1/\\Omega_0-1$ \\citep{pee80}. Thus, in Figure~\\ref{fig2}b,\ncluster data are expected to be distributed between the points of\n$z_{\\rm coll}=0$ (segment AB) and $z_{\\rm coll} = 1/\\Omega_0-1$ (segment\nCD) and should have a two-dimensional distribution (parallelogram ABCD). \nThus, compared with the observations, the models in Figure~\\ref{fig2}\nshow that $T_1\\sim 1$ keV and $\\Omega_0<1$ are preferred. The latter\nresult is quite consistent with that of Paper II, where we found that\nthe $T_{\\rm gas}-r_{\\rm c}$ relation suggests $\\Omega_0<1$. Since\n$\\beta$ is related to $T_{\\rm gas}$ by equation (\\ref{eq:beta3}), the\n$\\beta-r_{\\rm c}$ relation is equivalent to the $T_{\\rm gas}-r_{\\rm c}$\nrelation for a fixed value of $T_1$. Note that in Figure~\\ref{fig2}\npredicted regions corresponding to different $T_1$ overlap each other;\nthis implies that the position of a cluster in Figure~\\ref{fig2} does\nnot uniquely correspond to $T_1$ in contrast to Figure~\\ref{fig1}. For a\ngiven $\\beta$ and $r_{\\rm c}$, larger $T_1$ corresponds to larger\n$M_{\\rm vir, 0}$ or larger amplitude of the initial fluctuation.\n\n\n%is somewhat too large for preheating\n%only by supernovae ahead of the cluster collapse ($\\sim 0.4 h^{3/2}$\n%keV; \\citealt{pon99}), \nThe dispersion of $T_1$ appears to be caused by gravitational heating in\nsubclusters that are to merge to the cluster ($T_{\\rm gas}\\gtrsim 3$\nkeV) at the time of the cluster formation. In fact, Figure~\\ref{fig2}b\nshows that observed clusters are situated close to the line of $M_{\\rm\nvir, 0}=5\\times 10^{15}\\;\\rm M_{\\sun}$ (arc AD) when $T_1\\sim 2$ keV,\nwhile they are situated close to the line of $M_{\\rm vir, 0}=5\\times\n10^{14}\\;\\rm M_{\\sun}$ (arc BC) when $0.5<T_1<1$ keV. Moreover,\nFigure~\\ref{fig1} suggests that clusters with large $T_{\\rm gas}$ favor\nlarge $T_1$. These may reflect that clusters with larger (smaller)\n$M_{\\rm vir, 0}$ or $T_{\\rm gas}$ tend to have more (less) massive\nprogenitors with larger (smaller) $T_1$, although these are only loose\ntendencies, and we need more samples and more improved models to obtain\na definite conclusion.\n\nNote that gravitational heating in subclusters itself is a self-similar\nprocess and does not modify self-similar scaling relations such as the\nluminosity-temperature relation (e.g. \\citealp{eke98}). Thus, an\nadditional entropy other than expected from purely gravitational\nassembly of a cluster must be injected into the gas. \\citet{val99}\ninvestigate the entropy evolution of intergalactic medium (IGM) and find\nthat clusters with $T_{\\rm vir}\\sim 0.5$ keV are affected by the\nadditional entropy when it is generated by quasar heating. This is\nbecause the additional entropy is comparable to the entropy generated by\ngravitational collapse of the clusters. In other words, the adiabatic\ncompression of the gas from the preheated IGM alone can heat the gas up\nto $T_{\\rm ad, cl}\\sim 0.5$ keV. Therefore, in addition to the\ngravitational processes in subclusters, the preheating may significantly\ncontribute to $T_1$, and the lower bound of which is given by $T_{\\rm\nad, cl}$. If $T_{\\rm ad, cl}\\sim 0.5$ keV, this is consistent with our\nresult (Figures \\ref{fig1} and \\ref{fig2}). \\citet{val99} also\ninvestigate the case when only supernova heating is taken into account\nand quasar heating is ignored. The result is $T_{\\rm ad, cl}< 0.1$\nkeV. In this case, and effects of the preheating is small and we expect\nthat $\\beta$ does not much depend on $T_{\\rm gas}$ and $r_{\\rm c}$,\nalthough $\\beta$ would have a scatter owing to the difference of merging\nhistory. This is inconsistent with the observations. The insufficient\npower of the supernova heating is also suggested by \\citet{wu99}\n\\citep[but see][]{loe99}. Another possible source of heating is that due\nto shocks forming at higher redshift on the largest scales, such as\nfilaments and sheets. \\citet{cen99} indicate that most of baryons at low\nredshift should have a temperature in the range of $10^5-10^7$ K. The\nrelatively large value of $T_1$ may reflect this temperature.\n%Recently, \\citet{loe99} indicates that pure preheating\n%models generally require a higher entropy floor than is observed in\n%order to reproduce the luminosity-temperature relation. However, an\n%additional entropy produced by gravitational heating in subclusters may\n%explain this discrepancy; clusters except for lowest mass ones may be\n%affected by the entropy.\n\nWe also investigate the case of $\\gamma=1.2$ and $\\Omega_0=0.2$, which\nare presented in Figure~\\ref{fig3}. In this case, the model of $T_1=0.5$\nkeV is preferred especially for the data obtained by \\citet{moh99}. This\nmeans that $\\gamma$ and $T_1$ are correlated and they cannot be\ndetermined independently. However, the model of $\\gamma> 1.2$ is\ninappropriate because $\\beta=\\gamma\\beta_{\\rm obs}$ exceeds unity for\nsome observational data while relation (\\ref{eq:beta2}) or\n(\\ref{eq:beta3}) limits $\\beta$ to less than one.\n%As can be seen, some of the observed values exceeds one.\n%the observed values of\n%$\\beta$ are larger than the predictions and $\\beta>1$ for clusters with\n%large $r_{\\rm c}$. \n%This is inconsistent with relation (\\ref{eq:beta2}) or (\\ref{eq:beta3}),\n%because it requires $\\beta<1$ regardless of $T_1$, $\\Omega_0$, and so\n%on. If a polytrope index is larger than unity and \nIf a cluster is not isothermal, the temperature in the central region\n$T_{\\rm gas}$ should be larger than $T_2$ \\citep{cav98}. In this case,\nthe discrepancy between the model and the observations is more\nsignificant. Thus, it seems to be difficult to construct a model that\npredicts $\\beta>1$.\n\n\\subsection{The Fundamental Band and Plane}\n\nIt is interesting to investigate whether the gas distribution in\nclusters derived above is consistent with the observations of central\ngas fraction, and the fundamental band and plane we found in\nPaper~I. The shapes of the band and plane are also related to the origin\nof the observed relation of $L_{\\rm X}\\propto T_{\\rm gas}^3$\n(Paper~I). We did not explore the origin of the variation of the central\ngas mass fraction in previous papers, where $\\beta_{\\rm obs}$ was\nregarded as constant. Below, we will show that this is related to the\nvariation of $\\beta$.\n\nFrom relation (\\ref{eq:beta}), the gas density at the cluster core is\napproximately given by\n%\n\\begin{equation}\n\\label{eq:rho_0_ori}\n\\rho_{\\rm gas, 0}\n=\\rho_{\\rm gas}(r_{\\rm vir})\n(r_{\\rm vir}/r_c)\n^{3\\beta/\\gamma}\\:,\n\\end{equation}\n%\nwhere $r_{\\rm vir}$ and $\\beta(T_{\\rm vir}, T_1)$ are functions of\n$z_{\\rm coll}$ and $M_{\\rm vir, 0}$ (\\S\\ref{sec:model}), and $\\rho_{\\rm\ngas}(r)$ is the gas density at radius $r$ from the cluster center. We\nassume that the profile of dark matter is isothermal ($\\rho_{\\rm\nDM}\\propto r^{-2}$) at least for $r_{\\rm c}\\lesssim r \\lesssim r_{\\rm\nvir}$, and $\\rho_{\\rm DM, c}=64 \\rho_{\\rm vir}$. Moreover, we assume\nthat the average gas fraction within radius $r_{\\rm vir}$ is $f_{\\rm\ngas}(r_{\\rm vir})=0.25$ regardless of $z_{\\rm coll}$ and $M_{\\rm vir,\n0}$. The value of $f_{\\rm gas}$ is nearly the largest gas mass fraction\nof observed clusters (e.g. \\citealt{dav95, ett99}). On these\nassumptions, the central gas density and the gas fraction at the cluster\ncore are respectively given by\n%\n\\begin{eqnarray}\n\\rho_{\\rm gas, 0}\n &=& \\left(1-\\frac{\\beta}{\\gamma}\\right)\n f_{\\rm gas}\\;\\rho_{\\rm vir}(z_{\\rm coll})\n\\left(\\frac{r_{\\rm vir}}{r_{\\rm c}}\\right)\n^{3\\beta/\\gamma} \\nonumber \\\\\n &=&0.25\\left(1-\\frac{\\beta}{\\gamma}\\right)\n \\rho_{\\rm vir}(z_{\\rm coll})\n\\;8^{3\\beta/\\gamma} \n\\:\\label{eq:rho_0}\n\\end{eqnarray}\n%\nand\n%\n\\begin{equation}\nf_{\\rm gas}(0) = 0.25\\left(1-\\frac{\\beta}{\\gamma}\\right)\n\\;8^{3(\\beta/\\gamma)-2}\\label{eq:frac}\\:, \n\\end{equation}\n%\nwhere $f_{\\rm gas}(0)\\equiv \\rho_{\\rm gas, 0}/\\rho_{\\rm DM, c}$ is the\ngas fraction at the cluster center. The above equations are valid when\n$\\beta<\\gamma$. Note that in Paper~II, we derive the central gas density\naccording to the relation $\\rho_{\\rm gas, 0}\\propto \\rho_{\\rm vir}f_{\\rm\ngas}(0)$, in which $f_{\\rm gas}(0)$ is differently determined by the\nobservations\\footnote{In Papers~I and II, we assumed that $T_{\\rm\ngas}=T_{\\rm vir}$ and did not take account of the variation of\n$\\beta_{\\rm obs}$ when we derive $f_{\\rm gas}(0)$ from observations of\n$\\rho_{\\rm gas, 0}$, $r_{\\rm c}$, and $T_{\\rm gas}$.}. In contrast, in\nequation (\\ref{eq:rho_0}), we derive $\\rho_{\\rm gas, 0}$ assuming that\n$f_{\\rm gas}(r_{\\rm vir})=constant$.\n\nThe above model values (equation [\\ref{eq:rho_0}] or [\\ref{eq:frac}])\ncan be obtained from observational data. Using equations (\\ref{eq:rad}),\n(\\ref{eq:temp}), and (\\ref{eq:beta_beta}) we obtain\n%\n\\begin{equation}\n\\label{eq:rho_vir}\n\\rho_{\\rm vir}=\\frac{9k_{\\rm B}T_{\\rm gas}}{4\\pi G\\mu m_{\\rm H}}\n\\frac{\\beta_{\\rm obs}}{(8r_{\\rm c})^2}\n\\;,\n\\end{equation}\n%\nwhere we used the relations of $T_{\\rm vir}=\\beta T_{\\rm gas}$ and\n$r_{\\rm c}=r_{\\rm vir}/8$. Thus, using equation (\\ref{eq:beta_beta}),\nthe right hand of equation (\\ref{eq:rho_0}) should be written as\n%\n\\begin{equation}\n\\label{eq:rho_model}\n\\rho_{\\rm gas, 0}^{\\rm model}\\equiv\n0.25\\beta_{\\rm obs}(1-\\beta_{\\rm obs})\n\\frac{9k_{\\rm B}T_{\\rm gas}}{4\\pi G\\mu m_{\\rm H}}\n\\frac{8^{3\\beta_{\\rm obs}}}{(8r_{\\rm c})^2}\n\\:.\n\\end{equation}\n%\nHence, $\\rho_{\\rm gas, 0}^{\\rm model}$ can be derived from the\nobservable quantities $r_{\\rm c}$, $T_{\\rm gas}$, and $\\beta_{\\rm obs}$.\nFigure~\\ref{rhorho} displays a plot of $\\rho_{\\rm gas, 0}$ and\n$\\rho_{\\rm gas, 0}^{\\rm model}$ based on the data obtained by\n\\citet{moh99}. Note that \\citet{per98} do not present $\\rho_{\\rm gas,\n0}$. We do not show the uncertainties of $\\rho_{\\rm gas, 0}^{\\rm\nmodel}$ to avoid complexity. Here we use only $\\rho_{\\rm gas, 0}$\ncorresponding to the global cluster component as we did in Paper~I.\n\nFigure~\\ref{rhorho} shows that $\\rho_{\\rm gas, 0}$ well agrees with\n$\\rho_{\\rm gas, 0}^{\\rm model}$ although $\\rho_{\\rm gas, 0}$ is slightly\nsmaller than $\\rho_{\\rm gas, 0}^{\\rm model}$ for clusters with large\n$\\rho_{\\rm gas, 0}^{\\rm model}$. Thus, we conclude that the variation of\n$f_{\\rm gas}(0)$ is due to that of the slope parameter of the gas\ndistribution $\\beta$ within $r_{\\rm vir}$. One possible reason for the\nslight disagreement between $\\rho_{\\rm gas, 0}^{\\rm model}$ and\n$\\rho_{\\rm gas, 0}$ is an uncertainty of the value of $f_{\\rm\ngas}(r_{\\rm vir})$. Another is the influence of central excess emission\nof clusters. When the distance to a cluster is relatively large, the\ncenter and global surface brightness components may not be distinguished\neven if the two components exist. In this case, the cluster may be\nconsidered that it has only a global component. However, when the\ncentral emission is strong, the fitting of the surface brightness\nprofile by one component may be affected by the central emission and may\ngive a smaller core radius than the real. This may make $\\rho_{\\rm gas,\n0}^{\\rm model}$ large for the clusters. In fact, clusters with\n$\\rho_{\\rm gas, 0}^{\\rm model}>3\\times 10^{-26}\\rm\\; g\\; cm^{-3}$ are\nregarded by \\citet{moh99} as having only one (global) component of\nsurface brightness. Note that core radii derived by \\citet{per98} may be\nless affected by the central emission because they take account of\ncooling flows and the gravitation of central cluster galaxies, which are\nresponsible for the central emission, for {\\em all} clusters they\ninvestigate (Figures \\ref{fig2} and \\ref{FB}b).\n\n%residuals of the fit done by \\citet{moh99} when they fit\n%one component $\\beta$-model to the surface brightness profiles of\n%clusters. When the central excess emission of a cluster is weak, they\n%obtain $r_{\\rm c}$ and $\\beta_{\\rm obs}$ using only one component\n%$\\beta$-model, supposing that the excess emission is regard as a biased\n%residual and that its contribution to the estimations of $r_{\\rm c}$ and\n%$\\beta_{\\rm obs}$ is small. Since they included the contribution of the\n%residual when they obtain $\\rho_{\\rm gas, 0}$ (their equation [3.8]),\n%$\\rho_{\\rm gas, 0}$ may be somewhat overestimated. In fact, most of the\n%clusters with large $\\rho_{\\rm gas, 0}/\\rho_{\\rm gas, 0}^{\\rm model}$\n%are the ones that \\citet{moh99} use only one component $\\beta$-model to\n%derive $r_{\\rm c}$ and $\\beta_{\\rm obs}$.\n\nWe present the theoretically predicted relations among $\\rho_{\\rm gas,\n0}$, $r_{\\rm vir}$, and $T_{\\rm gas}$ in Figure~\\ref{FB}. Although these\nrelations are presented in Paper~II using the observed relation between\n$f_{\\rm gas}(0)$ and $M_{\\rm DM, c}$, here we plot them by directly\nusing $\\beta$. For lines in Figure~\\ref{FB}, we use the relation $T_{\\rm\ngas}=T_{\\rm vir}/\\beta$. For comparison, we plot the observational data\nin the catalogue of \\citet{moh99} and \\citet{per98}. For the data, we\nuse the relation $r_{\\rm vir}=8 r_{\\rm c}$. Figure~\\ref{FB} shows that\nour model can well reproduce the band distribution of observational data\nin the ($\\rho_{\\rm gas, 0}, r_{\\rm c}, T_{\\rm gas}$)-space. Moreover,\nour model can explain the planar distribution of the observational data. \nIn Paper~I, we find that the observational data satisfy the relation of\nthe fundamental plane, $\\rho_{\\rm gas, 0}^{0.47}r_{\\rm c}^{0.65}T_{\\rm\ngas}^{-0.60}\\propto constant$. For $M_{\\rm vir, 0}\\sim 10^{15}\\;\\rm\nM_{\\sun}$ and $z_{\\rm coll}\\lesssim 2$, our model with $\\Omega_0=0.2$\nand $T_1=1$ keV predicts the plane of $\\rho_{\\rm gas, 0}^{0.32}r_{\\rm\nc}^{0.64}T_{\\rm gas}^{-0.70}\\propto constant$, which is approximately\nconsistent with the observation. Note that the index of $\\rho_{\\rm gas,\n0}$ is somewhat smaller than the observed value considering the\nuncertainty ($\\sim 0.1$), which may be related to the slight\ndisagreement between $\\rho_{\\rm gas, 0}^{\\rm model}$ and $\\rho_{\\rm gas,\n0}$ (Figure~\\ref{rhorho}). The plane is represented by the two\nparameters, $z_{\\rm coll}$ and $M_{\\rm vir, 0}$, as discussed in\n\\S\\ref{sec:model}. Since the cross section of the fundamental plane\ncorresponds to the observed $L_{\\rm X}-T_{\\rm gas}$ relation, and the\nfundamental plane corresponds to the observed dependence of $f_{\\rm\ngas}(0)$ on $\\rho_{\\rm DM, c}$ and $M_{\\rm DM, c}$ (Paper~I), our model\ncan also reproduce these relations. These results strengthen our\ninterpretation that the difference of gas distribution among clusters is\ncaused by heating of the gas before the cluster collapse and by shock\nheating at the time of the cluster collapse (equation [\\ref{eq:beta2}]\nor [\\ref{eq:beta3}]).\n\n\\section{Conclusions}\n\nWe have investigated the influence of heating before cluster collapse\nand shocks during cluster formation on the gas distribution in the\ncentral region of clusters of galaxies. We assumed that the core\nstructure has not much changed since the formation of a cluster. Using a\nspherical collapse model of a dark halo and a simple shock model, we\npredict the relations among the slope of gas distribution $\\beta$, the\ngas temperature $T_{\\rm gas}$, and the core radius $r_{\\rm c}$ of\nclusters. By comparing them with observations of relatively hot\n($\\gtrsim 3$ keV) and low redshift clusters, we find that the\ntemperature of the preheated gas collapsed into the clusters is about\n$0.5-2$ keV. Since the temperature is higher than that predicted by a\npreheating model of supernovae, it may reflect the heating by quasars or\ngravitational heating on the largest scales at high redshift. Moreover,\ngravitational heating in subclusters assembled when the clusters formed\nalso seems to affect the temperature of the preheated gas and produce\nthe dispersion in the preheating temperature. Assuming that the global\ngas mass fraction of clusters are constant, we predict that the gas mass\nfraction in the core region of clusters should vary correlating with\n$\\beta$ through a simple law, which is shown to be consistent with the\nobservations. Thus, we conclude that the variation of the gas mass\nfraction in the cluster core is due to the shock heating of preheated\ngas. Furthermore, we have confirmed that the observed fundamental plane\nand band of clusters are reproduced by the model even when the effects\nof preheating are taken into account. Thus, major conclusions about the\ncluster formation and cosmology obtained in our previous papers are not\nchanged.\n\n\n\\acknowledgments\n\nWe thank for A. C. Edge, C. S. Frenk, and T. Kodama for useful\ndiscussions. This work was supported in part by the JSPS Research\nFellowship for Young Scientists.\n\n\\begin{thebibliography}{}\n\n%\\bibitem[Bahcall and Lubin(1994)]{bah94}Bahcall, N. A., Lubin,\n% L. 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J. submitted to MNRAS (astro-ph/9907112)\n\n\\end{thebibliography}\n\n\n\\clearpage\n\n\\begin{figure}\n\\figurenum{1}\n\\epsscale{0.80}\n\\plotone{f1.eps}\n%\\plottwo{<epsfile>}{<epsfile>}\n\\caption{The relation between $\\beta$ and $T_{\\rm gas}$ when\n$\\gamma=1$. Dashed line: $T_1=0.5$ keV. Solid line: $T_1=1$ keV. Dotted\nline: $T_1=2$ keV. The observational data obtained by \\citet{moh99}\n(filled circles) and \\citet{per98} (open squares) are overlaid.\n\\label{fig1}}\n\\end{figure}\n\n%\\figcaption[f1.eps]{The relation between $\\beta$ and $T_{\\rm gas}$ when\n%$\\gamma=1$. Dashed line: $T_1=0.5$ keV. Solid line: $T_1=1$ keV. Dotted\n%line: $T_1=2$ keV. The observational data obtained by \\citet{moh99}\n%(filled circles) and \\citet{per98} (open squares) are overlaid.\n%\\label{fig1}}\n\n\\begin{figure}\n\\figurenum{2}\n\\epsscale{1.20}\n\\plottwo{f2a.eps}{f2b.eps}\n\\caption{Theoretical predictions of $\\beta-r_{\\rm c}$\nrelation in the case of (a) $\\Omega_0=1.0$ and $\\gamma=1$ (b)\n$\\Omega_0=0.2$ and $\\gamma=1$. Dashed line: $T_1=0.5$ keV. Solid line:\n$T_1=1$ keV. Dotted line: $T_1=2$ keV. The arcs AD and BC correspond to\n$M_{\\rm vir, 0}=5\\times 10^{15}\\rm\\; M_{\\sun}$ and $5\\times 10^{14}\\rm\\;\nM_{\\sun}$, respectively. The segments AB corresponds to $z_{\\rm coll}=0$\nand the segments CD corresponds to $z_{\\rm coll}=0.5$ in (a) and $z_{\\rm\ncoll}=4$ in (b). The observational data obtained by \\citet{moh99} (filled\ncircles) and \\citet{per98} (open squares) are overlaid.\n\\label{fig2}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\figurenum{3}\n\\epsscale{0.55}\n\\plotone{f3.eps}\n\\caption{The same as Figure~\\ref{fig2}b but for\n$\\gamma=1.2$ \\label{fig3}}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{4}\n\\epsscale{0.55}\n\\plotone{f4.eps}\n\\caption{The relation between $\\rho_{\\rm gas, 0}^{\\rm model}$\nof equation (\\ref{eq:rho_model}) and $\\rho_{\\rm gas, 0}$. The line\ncorresponds to $\\rho_{\\rm gas, 0}=\\rho_{\\rm gas, 0}^{\\rm model}$\n\\label{rhorho}}\n\\end{figure}\n\n\\newpage\n\n\\begin{figure}\n\\epsscale{1.00}\n\\plottwo{f5a.eps}{f5b.eps}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{5}\n\\epsscale{0.45}\n\\plotone{f5c.eps}\n\\caption{Theoretical predictions of (a) radius--density\nrelation (b) radius--temperature relation (c) density--temperature\nrelation when $\\gamma=1$. Solid line: $\\Omega_0=0.2$ and $M_{\\rm vir,\n0}=5\\times 10^{15}\\rm\\; M_{\\sun}$. Dotted line: $\\Omega_0=0.2$ and\n$M_{\\rm vir, 0}=5\\times 10^{14}\\rm\\; M_{\\sun}$. Dashed line:\n$\\Omega_0=1.0$ and $M_{\\rm vir, 0}=5\\times 10^{15}\\rm\\;\nM_{\\sun}$. Dash-dotted line: $\\Omega_0=1.0$ and $M_{\\rm vir, 0}=5\\times\n10^{14}\\rm\\; M_{\\sun}$. The open diamonds, triangles, and circles\ncorrespond to the collapse redshifts of $z_{\\rm coll}=0$, $z_{\\rm\ncoll}=0.5$, and $z_{\\rm coll}=4$, respectively. We assume that $r_{\\rm\nvir}=8r_{\\rm c}$. The observational data obtained by \\citet{moh99}\n(filled circles) and \\citet{per98} (open squares, only in Figure\n\\ref{FB}b) are overlaid. \\label{FB}}\n\\end{figure}\n\n\\newpage\n\n\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002042.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem[Bahcall and Lubin(1994)]{bah94}Bahcall, N. A., Lubin,\n% L. M. 1994, \\apj, 426, 513\n\n\\bibitem[Arnaud and Evrard(1999)]{arn99}Arnaud, M., Evrard, A. E. 1999,\n\\mnras, 305, 631\n\n\\bibitem[Balogh et al.(1999)]{bal99}Balogh, M., Babul, A., and Patton,\n D. R. 1999, \\mnras, 307, 463\n\n\\bibitem[Bryan and Norman(1998)]{bry98}Bryan, C. L., and Norman,\nM. L. 1998, \\apj, 495, 80\n\n\\bibitem[Cavaliere and Fusco-Femiano(1978)]{cav78}Cavaliere, A., and\n Fusco-Femiano, R. 1978, \\aap, 70, 677\n\n\\bibitem[Cavaliere et al.(1997)]{cav97}Cavaliere, A., Menci, N., and\n Tozzi, P. 1997, \\apj, 484, L21\n\n\\bibitem[Cavaliere et al.(1998)]{cav98}Cavaliere, A., Menci, N., and\n Tozzi, P. 1998, \\apj, 501, 493\n\n\\bibitem[Cavaliere et al.(1999)]{cav99}Cavaliere, A., Menci, N., and\n Tozzi, P. 1999, \\mnras, 308, 599\n\n\\bibitem[Cen and Ostriker(1999)]{cen99} Cen, R. \\& Ostriker, \nJ. P. 1999, \\apj, 514, 1\n\n\\bibitem[David et al.(1995)]{dav95}David, J. P., Jones, C., and Forman,\n W. 1995, \\apj, 445, 578\n\n\\bibitem[Dekel and Silk(1986)]{dek86}Dekel, A., and Silk, J. 1986. \\apj,\n 303, 39\n\n\\bibitem[Eke et al.(1998)]{eke98}Eke, V. R., Navarro, J. F., and Frenk,\n C. S. 1998, \\apj, 503, 569\n\n\\bibitem[Ettori and Fabian(1999)]{ett99}Ettori, S., and Fabian,\nA. C. 1999, \\mnras, 305, 834\n\n\\bibitem[Evrard and Henry(1991)]{evr91}Evrard, A. E., and Henry,\n J. P. 1991, \\apj, 383, 95\n\n\\bibitem[Evrard et al.(1996)]{evr96} Evrard, A. E., Metzler, C. A., and\nNavarro, J. F. 1996, \\apj, 469, 494\n\n\\bibitem[Fujita and Takahara(1999a)]{fuj99a}Fujita, Y., and Takahara,\n F. 1999a, \\apj, 519, L51 (Paper~I)\n\n\\bibitem[Fujita and Takahara(1999b)]{fuj99b}Fujita, Y., and Takahara,\n F. 1999b, \\apj, 519, L55 (Paper~II)\n\n\\bibitem[Fujita and Takahara(2000)]{fuj99c}Fujita, Y., and Takahara,\n F. 2000, \\pasj, in press (astro-ph/9912515)\n\n\\bibitem[Gunn and Gott(1972)]{gun72}Gunn, J. E., and Gott, J. R. 1972,\n\\apj, 176, 1 \n\n\\bibitem[Horner et al. (1999)]{hor99}Horner, D. J., Mushotzky, R. F.,\n and Scharf, C. A. 1999, \\apj, 520, 78\n\n\\bibitem[Jones and Forman(1984)]{jon84}Jones, C., and Forman, W. 1984,\n \\apj, 276, 38\n\n\\bibitem[Jones and Forman(1999)]{jon99}Jones, C., and Forman, W. 1999,\n \\apj, 511, 65\n\n\\bibitem[Kaiser(1991)]{kai91}Kaiser, N. 1991, \\apj, 383, 104\n\n\\bibitem[Kay and Bower(1999)]{kay99}Kay, S. T., and Bower, R. G. 1999,\n \\mnras, 308, 664\n\n\\bibitem[Kitayama and Suto(1996)]{kit96}Kitayama, T., and Suto, Y. 1996,\n \\apj, 469, 480\n\n\\bibitem[Lacey and Cole(1993)]{lac93}Lacey, C., and Cole, S. 1993,\n\\mnras, 262, 627\n\n\\bibitem[Loewenstein(1999)]{loe99}Loewenstein, M. 1999, \\apj, in press\n(astro-ph/9910276)\n\n\\bibitem[Makino et al.(1998)]{mak98}Makino, N., Sasaki, S., and Suto,\n Y. 1998, \\apj, 497, 555\n\n\\bibitem[Metzler and Evrard(1994)]{met94}Metzler, C. A., and Evrard,\n A. E. 1994, \\apj, 437, 564\n\n\\bibitem[Mihara and Takahara(1994)]{mih94}Mihara, K., and Takahara, F.\n1994, \\pasj, 46, 447\n\n\\bibitem[Mohr et al.(1999)]{moh99}Mohr J. J., Mathiesen B., and Evrard\nA. E. 1999, \\apj, 517, 627\n\n\\bibitem[Navarro et al.(1996)]{nav96}Navarro, J. F., Frenk, C. S., and\n White, S. D. M. 1996, \\apj, 462, 463\n\n\\bibitem[Navarro et al.(1997)]{nav97}Navarro, J. F., Frenk, C. S., and\n White, S. D. M. 1997, \\apj, 490, 493\n\n\\bibitem[Neumann and Arnaud(1999)]{neu99}Neumann, D. M., and Arnaud,\n M. 1999, 348, 711\n\n\\bibitem[Peebles(1980)]{pee80}Peebles, P. J. E. 1980, in The Large-Scale\nStructure of the Universe (Princeton; Princeton University Press)\n\n\\bibitem[Peres et al.(1998)]{per98} Peres, C. B., Fabian, A. \nC., Edge, A. C., Allen, S. W., Johnstone, R. M. \\& White, D. A. 1998, \n\\mnras, 298, 416 \n\n%\\bibitem[Ponman et al.(1996)]{pon96}Ponman, T. J., Bourner, P. D.,\n% Ebeling, H., and B\\\"{o}hringer, H. 1996, \\mnras, 283, 690\n\n\\bibitem[Ponman et al.(1999)]{pon99}Ponman, T. J., Cannon, D. B., and\n Navarro, J. F. 1999, \\nat, 397, 135\n\n%\\bibitem[Sarazin(1986)]{sar86}Sarazin, C. L. 1986, Rev. Mod. Phys. 58, 1\n\n\\bibitem[Salvador-Sol\\'{e} et al.(1998)]{sal98} Salvador-Sol\\'{e}, E.,\nSolanes, J. M., and Manrique A. 1998, \\apj, 499, 542\n\n\\bibitem[Takizawa and Mineshige(1998)]{tak98}Takizawa, M., and Mineshige,\n S. 1998, \\apj, 499, 82\n\n\\bibitem[Tomita(1969)]{tom69} Tomita, K. 1969, Prog. Thor. Phys., 42, 9\n\n\\bibitem[Valageas and Silk(1999)]{val99} Valageas, P., and Silk,\n J. 1999, \\aap, 350, 725\n\n\\bibitem[Wu et al.(1999)]{wu99} Wu, K. K. S., Fabian, A. C., and Nulsen,\n P. E. J. submitted to MNRAS (astro-ph/9907112)\n\n\\end{thebibliography}"
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astro-ph0002043
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A Search for Exozodiacal Dust and Faint Companions Near Sirius, Procyon, and Altair with the NICMOS Coronagraph\altaffilmark{1}
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"author": "Marc J. Kuchner"
}
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We observed Sirius, Altair, and Procyon with the NICMOS Coronagraph on the Hubble Space Telescope to look for scattered light from exo-zodiacal dust and faint companions within 10 AU from these stars. We did not achieve enough dynamic range to surpass the upper limits set by IRAS on the amount of exo-zodiacal dust in these systems, but we did set strong upper limits on the presence of nearby late-type and sub-stellar companions.
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"name": "paper.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\\begin{document}\n\n\\title{A Search for Exozodiacal Dust and Faint Companions Near Sirius,\nProcyon, and Altair with the NICMOS Coronagraph\\altaffilmark{1}}\n\\author{Marc J. Kuchner}\n\\affil{Palomar Observatory, California\nInstitute of Technology, Pasadena, CA 91125}\n\\authoremail{[email protected]}\n\\author{Michael E. Brown\\altaffilmark{2}}\n\\affil{Division of Geological and Planetary Sciences, California\nInstitute of Technology, Pasadena, CA 91125}\n\\altaffiltext{1}{Based on observations with the NASA/ESA Hubble Space Telescope,\nobtained at the Space Telescope Science Institute, which is operated by the\nAssociation of Universities for Research in Astronomy, Inc. under NASA\ncontract No. NAS5-26555.}\n\\altaffiltext{2}{Alfred P. Sloan Research Fellow}\n\n\n\\begin{abstract}\n\nWe observed Sirius, Altair, and Procyon with the NICMOS Coronagraph on\nthe Hubble Space Telescope to look for scattered light from exo-zodiacal\ndust and faint companions within 10 AU from these stars. We did not\nachieve enough dynamic range to surpass the upper limits set by IRAS\non the amount of exo-zodiacal dust in these systems, but we did set\nstrong upper limits on the presence of nearby late-type and sub-stellar \ncompanions. \n\n\\end{abstract}\n\n\\keywords{binaries: visual --- circumstellar matter ---\ninterplanetary medium --- stars: individual (Altair, Procyon, Sirius)\n--- stars: low mass, brown dwarfs}\n\n\\section{Introduction}\n\nSeveral main sequence stars are close enough that a large\ntelescope operating at the diffraction limit can resolve the terrestrial\nplanet-forming region within 10 AU from the star \\markcite{kuch98}\n(Kuchner, Brown \\& Koresko 1998). We used the NICMOS coronagraph\nto image three of the nearest main-sequence stars in the\nnear-infrared to look for circumstellar material---exozodiacal dust\nand faint companions---in this relatively uncharted circumstellar\nregion.\n\nAny dust orbiting close to one of our targets must have been generated\nrecently by some population of larger bodies, since dust near a\nstar quickly spirals into the star due to Poynting-Robertson drag\n(Robertson 1937). Ten micron diameter dust 3 AU from a G star spirals \ninto the star on time scales of $\\sim10^5$ years; for brighter stars,\nthis timescale is shorter. Around the sun, zodiacal dust forms when\nasteroids collide and when comets outgass; a search for exozodiacal\ndust is therefore implicitly a search for extra-solar asteroid or comet-like bodies\nthat make dust. \n\nSeveral disks around nearby main-sequence stars appear to have\nexozodiacal components. Some, such as the disk associated with\nBeta-Pictoris, reveal their warm dust as a silicate\nemission feature at 10 microns \\markcite{tele91}\n(Telesco \\& Knacke 1991). Others, like the disk around HR 4796,\nshow resolved emission at 10 microns that is interpreted as exozodiacal\n\\markcite{koer98} (Koerner et al. 1998). Dust clouds like these,\nwhich have $\\sim 1000$ times as much warm dust as our sun,\nemit thermal radiation substantially in excess of the stellar\nphotospheric emission, and can often be detected photometrically\nby studying the spectral energy distribution of the star in\nthe mid-infrared. However, many less massive exozodiacal\nclouds may never be detectable photometrically because no stellar\nspectrum is known to better than $\\sim$ 3\\% in the mid-infrared \\markcite{cohe96}(Cohen et al. 1996). We have begun to search for disk\nthat are too faint to be detected photometrically by spatially\nresolving the critical regions less than 10 AU from nearby stars.\n\nCoronagraphic images can also reveal faint companions to nearby\nstars. Such companions can go undetected by radial velocity surveys\nbecause of their small masses or long orbital periods. \nSiruis and Procyon both have white dwarf companions whose orbits\nare well studied, but analyses of the orbital motion in these\nsystems leave room for additional low mass companions.\n\nThe Sirius system in particular, so prominent in the night sky, has\nspurred much debate in the last century over its properties. Three\nanalyses of the proper motion of Sirius have suggested that there may\nbe a perturbation in the orbit of Sirius B with a $\\sim 6$ year\nperiod \\markcite{vole32}\\markcite{walb83}\\markcite{bene95}\n(Volet 1932; Walbaum \\& Duvent 1983; Benest \\& Duvent 1995).\nThese analyses do not indicate whether the perturbing body orbits\nSirius A or B, and dynamical simulations indicate that stable\norbits exist around both Sirius A and B at circumstellar distances\nup to more than half the binary's periastron separation\n\\markcite{bene89}(Benest 1989). If such a companion\nwere in a simple face-on circular orbit it would appear at a\nseparation of 4.2 AU (1.6 arcsec) from Sirius A or a separation of\n3.3 AU (1.3 arcsec) from Sirius B assuming that the masses for\nSirius A and B a are 2.1 and 1.04 M${}_{\\odot}$ respectively\n\\markcite{gate78}(Gatewood \\& Gatewood 1978). Benest \\& Duvent \\markcite{bene95}(1995) do not derive a mass for the hypothetical\ncompanion from observations of the system, but they estimate that\na perturber much more massive than 0.05 M${}_{\\odot}$ would rapidly\ndestroy the binary.\n\nPerhaps the most interesting debate about Sirius is whether or not\nthe system appeared red to ancient observers $\\sim 2000$ years ago.\nBabylonian, Graeco-Roman and Chinese texts from this time period have\nseparately been interpreted to say that Sirius was a red star\n\\markcite{brec79}\\markcite{schl85}\\markcite{bonn91}\n(Brecher 1979; Schlosser \\& Bergman 1985, Bonnet-Bidaud \\& Gry 1991).\n\\markcite{tang86}\\markcite{vang84}\\markcite{mccl87}\nTang (1986), van Gent (1984) and McCluskey (1987) have attacked\nsome of these reports, claiming that they represent mistranslations or misidentifications of the star. However, if the Sirius system did\nindeed appear red, the existence of a third star in the group\ninteracting periodically with Sirius A could explain the effect\n\\markcite{bonn91}(Bonnet-Bidaud 1991).\n\nThe low mass companions ($< 0.1$ M${}_{\\odot}$) that we could hope to\ndetect with NICMOS are late-type stars or warm brown dwarfs, shining with\ntheir own thermal power in the near-infrared. Schroeder and\nGolimowski \\markcite{schr96}(1996) recently imaged Sirius, Procyon and\nAltair at visible wavelengths with the Planetary Camera on HST in a\nsearch for faint companions. Our observations are more\nsensitive to late-type companions because of the high dynamic range\nof the NICMOS coronagraph, and because these objects are brighter in\nthe infrared than the optical. \n\n\n\\section{Observations}\n\nWe observed our target stars with the NICMOS Camera 2 coronagraph on\nfive dates during 1999 October. We used the F110 filter, the\nbluest available near-infrared filter, with an effective\nwavelength of 1.104 microns, to take advantage of the higher\ndynamic range the coronagraph has at shorter wavelengths. We took\nimages of Sirius and Procyon at two different orientations,\nrolling the telescope about the axis to the star\nby $15^{\\circ}$ between them. When we searched for faint\ncompanions in the images, we subtracted the images taken at one\nroll angle from the images taken at the other angle to cancel\nthe light in the wings from the image of the occulted star. We\nplanned to image Altair at a second roll angle, but on\nour second visit to the star the telescope's Fine Guidance Sensors\nfailed to achieve fine lock on the guide star due to ``walkdown''\nfailure.\n\nAt each roll angle we took 50 short exposures in ACCUM mode,\nlasting 0.6 seconds each, and we co-added them, for total integration\ntimes of 30 seconds. Even though we used the shortest available\nexposure times, our images saturated interior to about 1.9\narcseconds for Sirius, 1.4 arcseconds for Procyon, and 0.7\narcseconds for Altair. The actual coronagraphic hole is only 0.3\narcseconds in radius. Table 1 summarizes the timing and orientations\nof our observations.\n\nFigure 1 shows an image of Sirius taken at one roll angle. The\nwhite dwarf Sirius B appears to the left of Sirius A,\nat a separation of 3.79 arcseconds. We derived photometry of\nSirius B at 1.1 microns from the roll subtracted image of Sirius\nusing a prescription from \\markcite{riek99} Rieke (1999). We\nmeasured the flux in circular apertures with radii 7.5 pixels\naround the positive and negative images and multiplied the flux\nin those regions by an aperture correction of 1.110 to extrapolate\nto the total flux. Then we used a factor of $1.996 \\times 10^{-6}$\nJy/ADU/Sec to convert from ADU to Janskys. In this manner, we\nmeasured the flux in Sirius B to be $0.503 \\pm 0.15$ Jy. Procyon\nalso has a white dwarf companion, Procyon B, that has been\npreviously detected by HST \\markcite{prov97}(Provencal et al. 1997).\nIt is not visible in our images, because it is currently at a\nseparation of $\\sim5$ arcseconds from Procyon A.\n\n\n\\section{Exozodiacal Dust}\n\nWe compared our observations of Sirius, Procyon and Altair\nto a simple model for what our zodiacal cloud would look like if it\nwere placed aound these stars. Kelsall et al. \\markcite{kels98}(1998)\nfit an 88-parameter model of the zodiacal cloud to the maps of the\ninfrared sky made by the Diffuse Infrared Background Experiment (DIRBE)\naboard the Cosmic Background Explorer (COBE) satellite.\nWe used the smooth component of this model, which has a face-on\noptical depth of $7.11 \\times 10^{-8} (r / 1 {\\rm AU})^{-0.34}$,\nand extrapolated it to an outer radius of 10 AU. We used a\nscattering phase function consisting of a linear combination of three\nHenyey-Greenstein functions that Hong \\markcite{hong85}(1985) fit\nto visible light observations of the zodiacal cloud with the\nHelios Satellite, and we assumed an albedo of 0.2, from the Kelsall et\nal. \\markcite{kels98}(1998) fit to the 1.25 micron DIRBE maps.\n\nFor this part of our search, we could not use roll-subtraction to\ncancel the light in the images of our target stars, because this\napproach would also cancel most of the light from an exozodiacal\ndisk, even if the disk were edge-on. Instead we subtracted images\nof Altair from the images of Procyon and Sirius,\nwith the assumption that all three of our stars would not have identical circumstellar structures. We used the IDP3 data analysis software \n\\markcite{idp3}(Lytle et al. 1999) to perform sub-pixel shifts on\nthe images of Altair before we subtracted them from our images of\nSirius and Procyon to compensate for the slightly different\nrelative alignments of the three stars and the coronagraphic hole. \n\nFigures 2a and 3a show our images of Sirius and Procyon minus our\nimage of Altair. Software masks hide the regions where the images\nare saturated and the four main diffraction spikes. The bright horn\njust above the masked area in the Procyon image is a well known\nNICMOS artifact. \n\nFigures 2b and 3b show the same images plus synthesized images\nof exozodiacal clouds seen in scattered light. The\nmodels are brightest immmediately to the left and the right of the\ncircular masked regions. The symmetry planes of the model disks\nare inclined $30^{\\circ}$ from edge-on. The dust densities in these\nhave been enhanced to $ > 10^5 \\times$ solar levels so\nthey are marginally discernible from the residuals from the PSF\nsubtraction. We used these models for the sake of comparison with the\nsolar zodiacal cloud; real disks with this much dust would be\nseverely collisionally depleted in their centers, unlike the solar cloud.\nDespite the high dynamic range of the NICMOS coronagraph and our\nefforts at PSF calibration, we were not able to improve upon photometric\ndetection limits for exozodiacal dust around these stars; if the stars\nactually had this much circumstellar dust, the thermal emission from\nthe dust would have been seen as a photometric excess by IRAS.\n\nOur study demonstrates the difficulty of detecting exozodiacal dust\nin the presence of scattered light from a bright star in a single-dish\ntelescope. Faint companions can be differentiated from the wings of\nthe telescope PSF by techniques like roll subtraction, but if\nexozodiacal clouds resemble the solar zodiacal cloud, light from\nthese clouds will resemble the PSF wings. Even though coronagraphs\ncan suppress the PSF wings from an on-axis source by as much as an\norder of magnitude, the dynamic range obtainable with a coronagraph\non a large, diffraction-limited telescope in the near-infrared is far\nfrom that required to probe dust levels comparable to the solar cloud. \n\n\n\\section{Faint Companions}\n\nFor our faint companion search we created roll-subtracted images\nof Sirius and Procyon using the IDP3 software.\nTo find the detection limits for faint companions among the non-gaussian\nPSF residuals, we tested our abilities to see artificial stars\nadded to our images. We examined roughly 350 copies of\nthe PSF-subtracted images of each of Sirius, Procyon and Altair\nwith help from a few of our patient colleagues.\nTo five-sixths of the images, we added images of artificial stars,\ncopied from our image of Sirius B, at random positions and magnitudes that were unknown to the examiner. The other images were left unaltered and mixed with the images that contained artificial stars. The examiners were shown each\nimage one at at time, and asked whether they could say confidently\nthat the image they were shown had an artificial star.\nOnly 2\\% of the time did an examiner claim to see an artificial star\nwhen none had been added to the image.\nWe quote as our detection limit the threshold for finding 90\\% of\nthe artificial companions; that is, the examiners reported 90\\% of\nthe artificial companions brighter than our detection limit at a given separation. Figure 4 shows these detection limits. For\ncomparison, we plot the expected magnitudes of two kinds of\npossible companions to these objects:\nan L0 dwarf like 2MASP J0345432+254023 \\markcite{kirk99}\n(Kirkpatrick et al. 1999) and a cool brown dwarf, Gl229B\n\\markcite{matt96}(Matthews et al. 1996).\n\nOur apparent detection limits for Procyon are somewhat better than our\ndetection limits for Sirius because Procyon is almost a magnitude fainter\nin the the near infrared; the two sets of observations yielded about the\nsame dynamic range. Although Altair is fainter than Procyon, our\nabsolute detection limits for faint companions to Altair are not much\nbetter than our detection limits for companions around Procyon because\nwe have only exposures at only one roll angle for Altair. Based on\nfigure 4, we can rule out the existence of M dwarf companions farther\nthan $1.4$ arcseconds from Altair, $1.6$ arcseconds from Procyon and $1.8$ arcsecons from Sirius at greater than the 90\\% confidence level. It should be noted, however, that the coronagraph hole is only 3.5 arcseconds\nfrom the edge of the chip, and that artificial faint companions that\nwere behind one of the four main diffration spikes at one roll angle\nwere harder to detect than artificial companions at other position\nangles; figure 4 is averaged over position angle. If we compare our upper limits to the J magnitude of T Dwarf Gl229B \\markcite{matt96}(Matthews et al. 1996), we find that we can rule out dwarfs hotter than this object---including all L dwarfs---farther than $2.3$ arcseconds from Procyon and $\\sim 3.0$ arcseconds from Sirius and Altair. For comparison, note that Gl 229B was discovered 7.7 arcseconds from a M1V star with an intrinsic luminosity 5 magnitudes fainter than Sirius in\nthe J band \\markcite{naka95} (Nakajima et al. 1995).\n\n%L7 dwarf DENIS-P J0205.4-1159 \\markcite{kirk99}(Kirkpatrick et al. 1999)\n\nWe do not see any evidence for previously undetected faint companions\nin our images. If there were a low-mass companion orbiting Sirius at\n4.2 AU we could not detect it because it would lie in the saturated parts of\nour images. However, we did survey a large fraction of the space where a\ncompanion orbiting Sirius B might be found, and we could have detected a\nbrown dwarf like Gl 229B throughout most of this zone. If there is a third\nobject in the Sirius system, and it orbits Sirius B with a 6 year orbit,\nit is probably fainter than a brown dwarf. \n\n\n\n\\acknowledgments\n\nWe thank Glen Schneider and Aaron Evans for help with the data reduction,\nand Edo Berger, John Carpenter, Micol Christopher, Ulyana Dyudina, David Frayer, Roy Gal, Pensri Ho, Matthew Hunt, Shardha Jogee, Olga Kuchner, Charlie Qi, Michael Santos, Alice Shapley and David Vakil for searching for artificial stars in our data.\n\nThis research made use of the Simbad database, operated at the Centre\nde Donnees de Strasbourg (CDS), Strasbourg, France.\n \nSupport for this work was provided by NASA through grant number GO-07441.01-96A\nfrom the Space Telescope Science Institute, which is operated by AURA,\nInc., under NASA contract NAS5-26555.\n\n\n\n\\begin{references}\n\n%\\reference{auma91}Aumann, H. H. \\& Probst, R. 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C., Lindegren L., Kovalevsky J., Hog E., Bastian U., Bernacca, P.L., Creze, M., Donati, F., Grenon, M., Grewing, M., Van Leeuwen, F., Van Der Marel, L. H., Mignard, F., Murray, C.A., Le Poole, R.S., Schrijver, H., Turon, C., Arenou, F., Froeschle, M., \\& Petersen, C.S. 1997, A \\& A, 323, L49\n\n\\reference{riek99}Rieke, M. 1999, in preparation\n%photometry with NICMOS\n\n\\reference{robe37}Robertson, H. P. 1937, MNRAS, 97, 423\n\n\\reference{schl85}Schlosser, W., Bergman, W. 1985, Nature, 318, 45\n\n%\\reference{schn99}Schneider G., Smith B.A., Becklin E.E., Koerner D.W.,\n%Meier R., Hines D.C., Lowrance P.J., Terrile R.J., Thompson R.I., \\& Rieke M.\n%1999, ApJ, 513, L127\n% ``NICMOS imaging of the HR 4796A circumstellar disk''\n\n\\reference{schr96}Schroeder, D. J. \\& Golimowski, D. A. 1996, PASP, 108, 510\n%``Searching for Faint Companions to Nearby Stars with the Hubble\n% Space Telescope''\n\n\\reference{tang86}Tang, T. B. 1986, Nature, 319, 532\n\n\\reference{tele91}Telesco C. M.\\& Knacke R. F. 1991, ApJ, 372, L29\n\n\\reference{vang84}Van Gent, R. H. 1984, Nature, 312, 302\n\n\\reference{vole32}Volet, Ch. 1932, Bull. Astr. Paris, 8, 52\n\n\\reference{walb83}Walbaum, M., Duvent, J.L. 1983, l'Astronomie, 97, 277\n\n\\end{references}\n\n\\newpage\n\n\\begin{deluxetable}{cccccc}\n\\footnotesize\n\\tablewidth{0 in}\n\\tablenum{1}\n\\tablecaption{\\label{tbl-1}}\n\\tablecaption{Observations}\n\\tablehead{\\colhead{Target} & \\colhead{Spectral Type} & \\colhead{Distance (pc)\\tablenotemark{a}} & J \\tablenotemark{b} & \\colhead{UT Date} & \\colhead{Orientation} \n} \n\\startdata\n\nSirius & A1V & 2.64 & -1.34 & October 20 & 64.51${}^{\\circ}$ \\nl\n & & & & October 22 & 81.51${}^{\\circ}$ \\nl\nProcyon & F5IV & 3.50 & -0.40 & October 9 & 40.51${}^{\\circ}$ \\nl\n & & & & October 21 & 55.51${}^{\\circ}$ \\nl\nAltair & A7V & 5.14 & 0.39 &October 14 & -126.24${}^{\\circ}$ \\nl\n\n\\enddata\n\n\\tablenotetext{a}{From the Hipparcos Catalogue (Perryman et al. 1997)}\n\\tablenotetext{b}{From the SIMBAD online database}\n\n\n\\end{deluxetable}\n\n\n\\newpage\n\n\\figcaption{A coronagraphic image of the Sirius system. The white dwarf\nSirius B, appears to the left of the residual light from Sirius A. \nEven though we used the shortest available exposure time, the\nregion $< 1.9$ arcsec from Sirius A is saturated. \\label{fig1}} \n\n\\figcaption{a) An image of Sirius made using our coronagraphic image\nof Altair to cancel the wings of the occulted PSF. The saturated\nregions of the image are hiden with a software mask. b) The same image\nplus a model of the scattered light from an exozodiacal cloud similar\nto the solar zodiacal cloud but $2.5 \\times 10^5$ times as bright. \\label{fig2}}\n \n\\figcaption{a) An image of Procyon using Altair as a PSF calibrator.\nb) The same image plus a model of the scattered light for an exo-zodiacal cloud $7 \\times 10^5$ times as bright as our own zodiacal cloud. \\label{fig3}} \n\n\\figcaption{Detection limits for faint companions around our three\ntarget stars as a function of separation from the stars. The magnitudes\nof some representative cool objects, GL 229B and an L0 dwarf, are\nshown for comparison. \\label{fig4}} \n\n\n\\end{document}\n\n\\newpage\n\n"
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"name": "review.tex",
"string": "\\documentclass{elsart} %{article}\n%21 pages becomes 17 without the [12pt] - default appears to be 10pt\n%\\usepackage{elsart,}\n%\\usepackage{psfig,natbib}\n\\usepackage{epsf,graphics,natbib}\n\\begin{document}\n\\def\\fdg{\\hbox{$.\\!\\!^\\circ$}}\n\\def\\mycaption#1{\\begin{quote}\\noindent{#1}\\end{quote}}\n%\\citestyle{aa}\n\\def\\dsp{\\def\\baselinestretch{2.0}\\large\\normalsize}\n%\\dsp\n\n\\begin{center} \n{\\bf \\Large\nThe Cosmic Microwave Background Radiation\n}\n\n\\vspace{0.1 in}\n{\\large\nEric Gawiser\\footnote{current address: Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92037}}\n\\\\\n{\\normalsize\n Department of Physics, University of\nCalifornia, Berkeley, CA 94720\n}\\\\\n\\vspace{0.1 in}\n\\large\nand\\\\\nJoseph Silk\\\\\n\\normalsize \nDepartment of Physics, Astrophysics, 1 Keble Road, University of Oxford, OX1\n3NP, UK\\\\\nand\\\\ \nDepartments of Physics and Astronomy and Center for Particle \nAstrophysics, University of\nCalifornia, Berkeley, CA 94720\\\\\n\n\\vspace{0.2in}\n\n\\end{center}\n\n\n\\begin{center} \\bf Abstract\n\\end{center}\n\nWe summarize the theoretical and observational status of the study of \nthe Cosmic Microwave Background radiation. Its thermodynamic spectrum is \na robust prediction of the Hot Big Bang cosmology and has been \nconfirmed observationally. There are now 76 observations of \nCosmic Microwave Background anisotropy, which we present in a table \nwith references. We discuss the theoretical origins \nof these anisotropies and explain the standard jargon associated with \ntheir observation. \n\n\n\n\n\\section{Origin of the Cosmic Background Radiation}\n\nOur present understanding of the beginning of the universe is based upon the \nremarkably successful theory of the Hot Big Bang. We believe that our universe began about 15 billion years ago as a hot, dense, nearly uniform sea of radiation \na minute fraction of its present size (formally an infinitesimal\nsingularity).\nIf inflation occurred in the first fraction of a second, the universe became \nmatter dominated while expanding exponentially and then returned to \nradiation domination by the reheating caused by the decay of the inflaton. \nBaryonic\nmatter formed within the first second, \nand the nucleosynthesis of the lightest elements \ntook only a few minutes as the universe expanded and cooled. \nThe baryons were in the form of plasma \nuntil about 300,000 years after the Big Bang, when the universe had \ncooled to a temperature near 3000 K, sufficiently cool for \nprotons to capture free electrons and form atomic hydrogen; this process \nis referred to as recombination. The recombination epoch \noccurred at a redshift of 1100, meaning that \nthe universe has grown over a thousand times larger since then.\nThe ionization energy of a hydrogen atom is 13.6 eV, but \nrecombination did not \noccur until the universe had cooled to a characteristic temperature (kT) of\n0.3 eV \\citep{padmanabhan93}. \nThis delay had several causes. The high entropy of the universe\nmade the rate of electron capture only marginally faster than the rate of \nphotodissociation. Moreover, each electron captured directly into the ground\nstate emits a photon capable of ionizing another newly formed atom, so it \nwas through \nrecombination into excited states and the cooling of the universe to\ntemperatures below the ionization energy of hydrogen\nthat neutral matter finally condensed out of the plasma. \nUntil recombination,\nthe universe was opaque to electromagnetic radiation due to scattering \nof the photons by free electrons. As recombination occurred, the \ndensity of free electrons diminished greatly, leading to the decoupling of\nmatter and radiation as the universe became transparent to light. \n\nThe Cosmic Background Radiation (CBR) \nreleased during this era of decoupling has a mean free path long \nenough to travel almost unperturbed until the present day, where we \nobserve it peaked in the microwave region of the spectrum as the \nCosmic Microwave Background (CMB). \nWe see this radiation today coming from the surface of last \nscattering (which is really a spherical shell of finite thickness) \nat a distance of \n nearly 15 billion light years. \nThis Cosmic Background Radiation was predicted by the Hot Big Bang theory\nand discovered at an antenna temperature of 3K \nin 1964 by \\citet{penziasw65}. \nThe number density of photons in the universe at a redshift $z$ is given by \\citep{peebles93} \n\n\\begin{equation}\n n_{\\gamma} = 420 (1 + z)^{3} cm ^{-3} \n\\end{equation}\n\n\\noindent \nwhere $(1 + z)$ is the factor by which the linear scale of the \nuniverse has expanded since then. \nThe radiation temperature of the universe is given by $T = T_{0} (1 + z)$ so it\nis easy to see how the conditions in the early universe \nat high redshifts were hot and dense. \n\nThe CBR is our best probe into the conditions of the early universe. Theories\nof the formation of large-scale structure \npredict the existence of slight inhomogeneities in the distribution of \nmatter in the early universe which underwent gravitational \ncollapse to form galaxies, galaxy clusters, and superclusters. These density \ninhomogeneities lead to temperature anisotropies in the CBR \ndue to a combination of intrinsic temperature fluctuations and \ngravitational blue/redshifting of the photons leaving under/overdense \nregions. \nThe DMR (Differential Microwave Radiometer) \ninstrument of the Cosmic Background Explorer (COBE) satellite \ndiscovered primordial temperature \nfluctuations on angular scales larger than $7^\\circ$\nof order $\\Delta T/T = 10^{-5}$ \\citep{smootetal92}. \nSubsequent observations of the CMB have \nrevealed temperature anisotropies on smaller \nangular scales which correspond to the physical scale of \nobserved structures such as galaxies \nand clusters of galaxies.\n\n\\subsection{Thermalization}\n\nThere were three main processes by which this radiation interacted with matter \nin the first few hundred thousand years: Compton scattering, double Compton \nscattering, and thermal bremsstrahlung.\nThe simplest interaction of matter and radiation is Compton\nscattering of a single photon off a free electron, \n$ \\gamma + e^{-} \\rightarrow \\gamma + e^{-}$. \nThe photon will transfer\nmomentum and energy to the electron if it has significant energy in the\nelectron's rest frame. However, the scattering will be\nwell approximated by Thomson scattering if the photon's energy in \nthe rest frame of the electron is significantly less than the rest mass, \n$h \\nu \\ll m_{e}c^{2}$.\nWhen the electron is relativistic, the photon is blueshifted by \nroughly a factor \n$\\gamma$ in energy when viewed from the \nelectron rest frame, is then emitted at almost the same energy in the \nelectron rest frame, and is blueshifted by another factor of $\\gamma$\nwhen retransformed to the observer's frame. Thus, energetic \nelectrons can efficiently transfer energy \nto the photon background of the universe. \nThis process is referred to as Inverse Compton scattering.\nThe combination of cases where the photon gives energy to the electron \nand vice versa allows Compton scattering to generate thermal equilibrium \n(which is impossible in the Thomson limit of elastic scattering).\nCompton scattering conserves the number of photons.\nThere exists a similar process, double Compton scattering,\n which produces (or absorbs)\nphotons, $e^- + \\gamma \\leftrightarrow e^{-} + \\gamma + \\gamma $. \n\n\nAnother electromagnetic interaction which occurs in the plasma of the early\nuniverse is Coulomb scattering. Coulomb scattering establishes \nand maintains thermal equilibrium among the baryons of the photon-baryon \nfluid without affecting the\nphotons. However, when electrons encounter ions they experience an \nacceleration and therefore emit electromagnetic radiation. This is called \nthermal bremsstrahlung or free-free emission. For an ion $X$, \nwe have $e^{-} + X \\leftrightarrow e^{-} + X + \\gamma$. The interaction\ncan occur in reverse because of the ability of the charged particles\nto absorb incoming photons; this is called free-free absorption. Each charged\nparticle emits radiation, but the acceleration is proportional to the mass,\nso we can usually view the electron as being accelerated in the fixed Coulomb\nfield of the much heavier ion. \nBremsstrahlung is dominated by electric-dipole \nradiation \\citep{shu91} and can also \nproduce and absorb photons. \n\nThe net effect is that Compton scattering is dominant\nfor temperatures above 90 eV whereas bremsstrahlung is the primary process\nbetween 90 eV and 1 eV. At temperatures above 1 keV, double Compton \nis more efficient than bremsstrahlung. All three processes occur faster than \nthe expansion of the universe and therefore have an impact until decoupling.\nA static solution for Compton scattering \nis the Bose-Einstein distribution, \n\n\\begin{equation}\n f_{BE} = \\frac {1} {e^{x + \\mu} - 1} \n\\end{equation}\n\n\\noindent \nwhere $\\mu$ is a dimensionless chemical potential \\citep{hu95}. \nAt high optical depths, Compton scattering can exchange enough energy to \nbring the photons to this Bose-Einstein equilibrium distribution. A Planckian\nspectrum corresponds to zero chemical potential, which will occur only when \nthe number of photons and total energy are in the same proportion as they \nwould be for a blackbody. Thus, unless the photon number starts out exactly\nright in comparison to the total energy in radiation in the universe, Compton\nscattering will only produce a Bose-Einstein distribution\nand not a blackbody spectrum. It is important to note, however, that \nCompton scattering will preserve a \nPlanck distribution,\n\n\n\\begin{equation}\n f_{P} = \\frac {1}{e^{x} - 1 }. \n\\end{equation}\n\n\nAll three interactions\nwill preserve a thermal spectrum if one is achieved at any point. It has\nlong been known that the expansion of the universe serves to decrease\nthe temperature of a blackbody spectrum, \n\n\\begin{equation}\nB_{\\nu} = \\frac{2 h \\nu^{3} / c^{2}} {e^{h \\nu / k T} - 1}, \n\\end{equation}\n\n\\noindent\n but keeps it thermal \n\\citep{tolman34}. This\noccurs because both the frequency and temperature decrease as $(1 + z)$\nleaving $h \\nu / k T$ \nunchanged during expansion. Although\nCompton scattering alone cannot produce a Planck distribution, such a \ndistribution will remain unaffected by electromagnetic interactions or the \nuniversal expansion once it is achieved. \nA non-zero\nchemical potential will be reduced to zero by double Compton scattering\nand, later, bremsstrahlung which will create and absorb photons until the \nnumber density matches the energy and a thermal distribution of zero\nchemical potential is achieved. \n This results in the thermalization \nof the CBR at redshifts much greater than that of recombination.\n\n\nThermalization, of course, should only be able to create an \nequilibrium temperature over regions that are in causal contact. \nThe causal horizon at the time of last scattering was relatively small, \ncorresponding to a scale today of about 200 Mpc, or a region of \nangular extent of one degree on the sky. However, observations of the \nCMB show that it has an isotropic temperature on the sky to the \nlevel of one part in one hundred thousand! This is the origin of the \nHorizon Problem, which is that there is no physical mechanism expected \nin the early universe which can produce thermodynamic equilibrium on \nsuperhorizon scales. The inflationary universe paradigm \n\\citep{guth81,linde82,albrechts82}\nsolves the Horizon \nProblem by postulating that the universe underwent a brief phase of \nexponential expansion during the first second after the Big Bang, during \nwhich our entire visible Universe expanded out of a region small \nenough to have already achieved thermal equilibrium. \n\n\n\n\\section{CMB Spectrum}\n\n\nThe CBR \nis the most perfect blackbody ever\nseen, according to the FIRAS (Far InfraRed Absolute \nSpectrometer) instrument of COBE, which measured a temperature \nof $T_0 = 2.726 \\pm 0.010$ K \\citep{matheretal94}. \nThe theoretical prediction that the CBR will have a blackbody spectrum \nappears to be confirmed by the FIRAS observation\n (see Figure \\ref{fig:spectrum}). \nBut this is not the \nend of the story. FIRAS only observed the peak of the blackbody.\nOther experiments have mapped out the Rayleigh-Jeans part of the\nspectrum at low frequency. Most are consistent with a 2.73 K blackbody, but\nsome are not. It is in the low-frequency limit that the greatest spectral\ndistortions might occur because a Bose-Einstein distribution differs from \na Planck distribution there. However, double Compton and \nbremsstrahlung are most effective at low frequencies so \nstrong deviations\nfrom a blackbody spectrum are not generally expected.\n\nSpectral distortions in the Wien tail of the spectrum are quite difficult\nto detect due to the foreground signal from interstellar dust at those high frequencies. For example, \nbroad emission lines from electron capture at recombination are predicted\nin the Wien tail but cannot be distinguished due to foreground \ncontamination \\citep{whitess94}. However, because the energy generated \nby star formation and active galactic nuclei is absorbed by interstellar \ndust in all galaxies and then re-radiated in the far-infrared, we expect \nto see an isotropic Far-Infrared Background (FIRB) which dominates the CMB at \nfrequencies above a few hundred GHz. This FIRB has now been detected in \nFIRAS data \\citep{pugetetal96,buriganap98,fixsenetal98} and in data \nfrom the COBE DIRBE instrument \\citep{schlegelfd98, dweketal98}. \n\n%\\begin{figure}\n%\\vbox{%\n%\\begin{center}\n%\\leavevmode\n%\\hbox{%\n%angle=-90 %what command does that??\n%\\epsfxsize=7.5cm\n%\\epsffile{firas.ps}} %spectrum2 is portrait, 3 is landscape\n%\\begin{small}\n%% was \\figcaption\n%\\caption{\\small Measurements of the CMB spectrum.}\n%\\end{small}\n%\\label{fig:spectrum}\n%\\end{center}}\n%\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\rotatebox{0}{\\scalebox{0.75}{\\includegraphics{firas.ps}}}\n\\caption{\\small Measurements of the CMB spectrum.}\n\\label{fig:spectrum}\n\\end{center}\n\\end{figure}\n\n\n\n%\\begin{figure}\n%\\centerline{\\psfig{file=spectrum.ps,width=4in,angle=-90}}\n%\\caption{Measurements of the CMB spectrum.}\n%\\label{fig:spectrum}\n%\\end{figure}\n\n\nAlthough Compton, double Compton, and bremsstrahlung interactions occur \nfrequently until decoupling, the complex interplay between them required\nto thermalize the CBR spectrum is ineffective at redshifts below \n$10^7$. \nThis means that any process after that time\nwhich adds a significant portion of \nenergy to the universe \nwill lead to a spectral distortion today. Neutrino decays during this \nepoch should lead to a Bose-Einstein rather than a Planck distribution, and \nthis allows the FIRAS observations to set constraints on the decay of \nneutrinos and other particles \nin the early universe \\citep{kolbt90}. The apparent\nimpossibility of thermalizing \nradiation at low redshift makes the blackbody nature of the CBR strong \nevidence that it did originate in the early universe and as a result serves\nto support the Big Bang theory. \n\nThe process of Compton scattering can cause spectral distortions if it\nis too late for double Compton and bremsstrahlung to be effective. In general,\nlow-frequency photons will be shifted to higher frequencies, thereby \ndecreasing the number of photons in the Rayleigh-Jeans region and enhancing\nthe Wien tail. This is referred to as a Compton-{\\it y} distortion and it\nis described by the parameter\n\n\\begin{equation}\n y = \\int \\frac {T_{e}(t)} {m_{e}} \\sigma n_{e}(t) dt. \n\\end{equation}\n\n\\noindent\nThe apparent temperature drop in the long-wavelength limit is\n\n\\begin{equation}\n \\frac {\\delta T}{T} = - 2 y. \n\\end{equation}\n\n\\noindent\nThe most important example of this is Compton scattering of photons off \nhot electrons in galaxy clusters, called the Sunyaev-Zel'dovich (SZ) \neffect. The electrons transfer energy to the photons, and the spectral\ndistortion results from the sum of all of the scatterings off \nelectrons in \nthermal motion, each of which has a Doppler shift. The \nSZ effect from clusters can yield a distortion of $y \\simeq 10^{-5} - \n10^{-3}$ and these distortions have been observed in several\nrich clusters of galaxies. The FIRAS observations place \na constraint on any full-sky Comptonization by limiting the average \n$y$-distortion to $y < 2.5 \\times 10^{-5}$ \\citep{hu95}. The \nintegrated $y$-distortion predicted from the SZ effect of \ngalaxy clusters and large-scale structure is over a factor of ten lower \nthan this observational constraint \\citep{refregiersh98} \nbut that from ``cocoons'' of radio galaxies \\citep{yamadass99}\n is predicted to be of the same order. A kinematic SZ effect is caused by \nthe bulk velocity of the cluster; this is a small effect which is very \ndifficult to detect for individual clusters but will likely \nbe measured statistically by the Planck satellite. \n\n\n\n\n\n\\section{CMB Anisotropy}\n\nThe temperature anisotropy at a point on the sky $(\\theta,\\phi)$ can be \nexpressed in the basis of spherical harmonics as \n\\begin{equation}\n \\frac{\\Delta T}{T} (\\theta, \\phi) = \n\\sum_{\\ell m} a_{\\ell m} Y_{\\ell m}(\\theta, \\phi).\n\\end{equation}\n\n\\noindent\nA cosmological model predicts the variance \nof the $a_{\\ell m}$ coefficients \nover an ensemble of universes (or an ensemble of observational \npoints within one universe, if the universe is ergodic). The\nassumptions of rotational symmetry and Gaussianity allow\n us to express this ensemble \naverage in terms of the multipoles $C_{\\ell}$ as \n\\begin{equation}\n \\langle a^{*}_{\\ell m} a_{\\ell' m'} \\rangle \\equiv \nC_{\\ell} \\delta_{\\ell' \\ell} \\delta_{m' m}.\n\\end{equation}\n\n\\noindent\nThe predictions \nof a cosmological model can be expressed in terms of $C_{\\ell}$ alone if \nthat model predicts a Gaussian distribution of density perturbations, \nin which case the \n$a_{\\ell m}$ will have mean zero \nand variance $C_\\ell$. \n\n\nThe temperature anisotropies of the CMB detected by COBE are believed \nto result from inhomogeneities in the distribution of \nmatter at the epoch of recombination. Because Compton scattering is an \nisotropic process in the electron rest frame, any primordial anisotropies (as \nopposed to inhomogeneities) should have been smoothed out before\ndecoupling. This lends credence\nto the interpretation of the observed \nanisotropies as the result of density perturbations\nwhich seeded the formation of galaxies and clusters. \nThe discovery of temperature anisotropies by \nCOBE provides evidence that \nsuch density inhomogeneities existed in the early\nuniverse, perhaps caused by \nquantum fluctuations in the scalar field of inflation\nor by topological defects resulting from a phase transition \n(see \\citealp{kamionkowskik99} for a detailed review of inflationary \nand defect model predictions for CMB anisotropies). \nGravitational collapse of \nthese primordial density inhomogeneities \nappears to have formed\nthe large-scale structures of galaxies,\nclusters, and superclusters that we observe today. \n\nOn large (super-horizon) scales, the anisotropies seen in the CMB are produced \nby the Sachs-Wolfe effect \\citep{sachsw67}. \n\n\\begin{equation}\n\\left( \\frac{\\Delta T }{T}\\right )_{SW} = {\\bf v \\cdot e}|^e_o -\n\\Phi|^e_o + \\frac{1}{2} \\int^e_o h_{\\rho \\sigma , 0} n^\\rho n^\\sigma d \\xi , \n\\end{equation}\n\nwhere \nthe first term is the net \nDoppler shift of the photon \ndue to the relative motion of emitter and observer, which \nis referred to as the \nkinematic dipole. This dipole, first observed by \\citet{smootgm77}, \nis much larger than other CMB anisotropies and is believed to reflect the \nmotion of the Earth relative to the average reference frame of the CMB. \nMost of this motion is due to the peculiar velocity of the \nLocal Group of galaxies. \n The second term represents the gravitational redshift due to a \ndifference in \ngravitational potential between the site of photon emission and the \nobserver. The third term is called the Integrated \nSachs-Wolfe (ISW) effect and is caused by a non-zero time derivative of \nthe metric along the photon's path of travel due to potential decay, \ngravitational waves, or non-linear structure evolution (the Rees-Sciama \neffect). In a matter-dominated universe with scalar density \nperturbations the integral vanishes on linear scales. \nThis equation gives the redshift \nfrom emission to observation, but there is also an intrinsic $\\Delta T/T$ \non the last-scattering surface due to the local density of photons. \nFor adiabatic perturbations, we have \\citep{whiteh97} an intrinsic \n\n\\begin{equation}\n\\frac{\\Delta T }{T} = \\frac{1}{3} \\frac{\\delta \\rho}{\\rho} = \n \\frac{2}{3} \\Phi . \n\\end{equation} \n\nPutting the observer at $\\Phi=0$ (the observer's gravitational \npotential merely adds a constant energy to all CMB photons) \nthis leads to a net Sachs-Wolfe effect \nof $\\Delta T /T = - \\Phi/3$ which means that overdensities lead \nto cold spots in the CMB. \n\n\n\n\\subsection{Small-angle anisotropy}\n\n\nAnisotropy measurements on \nsmall angular scales ($0\\fdg1$ to $1^{\\circ}$) \nare expected to reveal the so-called\nfirst acoustic\n peak of the CMB power spectrum. This peak in the anisotropy power spectrum\ncorresponds \nto the scale where acoustic oscillations of the photon-baryon fluid caused\nby primordial density inhomogeneities are just reaching their maximum \namplitude at the surface of last scattering i.e. the sound horizon \nat recombination. Further acoustic \npeaks occur at scales that are reaching their second, third, fourth, etc.\nantinodes of oscillation. \n\n\n\\begin{figure}\n\\begin{center}\n\\scalebox{0.75}{\\includegraphics{hu_fig5.ps}}\n\\caption{\\small\nDependence of CMB anisotropy power spectrum on \ncosmological parameters.}\n\\label{fig:hu}\n\\end{center}\n\\end{figure}\n\n\n%\\begin{figure}\n%\\centerline{\\psfig{file=hu_fig5.ps,width=4in}}\n%\\caption{Dependence of CMB anisotropy power spectrum on \n%cosmological parameters.}\n%\\label{fig:hu}\n%\\end{figure}\n\nFigure \\ref{fig:hu} (from \\citealp{huss97})\n%Hu, Sugiyama, \\& Silk 1995) \nshows the dependence of the CMB anisotropy power spectrum on a number of cosmological parameters. The acoustic oscillations in \ndensity (light solid line) are sharp \nhere because they are really being plotted against spatial scales, which \nare then smoothed as they are projected through the last-scattering surface \nonto angular scales. The troughs in the density oscillations are filled in \nby the 90-degree-out-of-phase velocity oscillations (this is a Doppler \neffect but does not correspond to the net peaks, which\nare best referred to as acoustic peaks rather than Doppler peaks). \nThe origin of this plot\n is at a different place for different values of the matter density and the cosmological constant; the negative \nspatial curvature of an open universe makes a given spatial scale \ncorrespond to a smaller angular scale.\nThe Integrated Sachs-Wolfe (ISW) effect occurs whenever \ngravitational potentials decay due to a lack of matter dominance. Hence \nthe early ISW effect occurs just after recombination when the density \nof radiation is still considerable and serves to broaden the first \nacoustic peak at scales just larger than the horizon size at \nrecombination. And for a present-day matter density less than critical, \nthere is a late ISW effect that matters on very large angular scales - it \nis greater in amplitude for open universes than for lambda-dominated \nbecause matter domination ends earlier in an open universe for the same \nvalue of the matter density today. The late ISW effect should correlate with \nlarge-scale structures that are otherwise detectable at $z \\sim1$, and this \nallows the CMB to be cross-correlated with observations of the X-ray background to determine $\\Omega$ \n\\citep{crittendent96, kamionkowski96, boughnct98, kamionkowskikink99}\n or with observations \nof large-scale structure to determine the bias of galaxies \n\\citep{suginoharass98}.\n\nFor a given model, \nthe location of the \nfirst acoustic peak can yield information about $\\Omega$, the ratio of \nthe density of the universe to the critical density needed to stop\nits expansion. For adiabatic density perturbations, the first \nacoustic peak will occur at $\\ell = 220 \\Omega^{-1/2}$\n\\citep{kamionkowskiss94}. The ratio of $\\ell$ values of the peaks \nis a robust test of the nature of the density perturbations; for \nadiabatic perturbations these will have ratio 1:2:3:4 whereas for \nisocurvature perturbations the ratio should be 1:3:5:7 \\citep{huw96}. \nA mixture of adiabatic and isocurvature \nperturbations is possible, and this test \nshould reveal it. \n\n\nAs illustrated in Figure \\ref{fig:hu}, the amplitude of the \nacoustic peaks depends on the baryon fraction $\\Omega_b$, \nthe matter density $\\Omega_0$, and Hubble's constant \n$H_0 = 100 h$ km/s/Mpc. \nA precise measurement of all three acoustic peaks can reveal \nthe fraction of hot dark matter and even potentially the number \nof neutrino species \\citep{dodelsongs96}. \nFigure \\ref{fig:hu} shows the envelope of the \nCMB anisotropy damping tail on arcminute scales, \nwhere the fluctuations are decreased due to photon diffusion \n\\citep{silk67} as well as the finite thickness of the last-scattering \nsurface. This damping tail\n is a sensitive probe \nof cosmological parameters and has the potential to \nbreak degeneracies between models which explain the larger-scale anisotropies\n\\citep{huw97a,metcalfs98}. The characteristic angular \nscale for this damping is given by\n $1.8' \\Omega_B^{-1/2} \\Omega_0^{3/4} h^{-1/2}$ \\citep{whitess94}. \n\n\tThere is now a plethora of theoretical \nmodels which predict the development of primordial \ndensity perturbations into microwave \nbackground anisotropies. These models differ in their explanation \nof the origin of density inhomogeneities \n(inflation or topological defects), the nature of the dark matter (hot,\ncold, baryonic, or a mixture of the three), \nthe curvature of the universe ($\\Omega$), \nthe value of the cosmological constant ($\\Lambda$), \nthe value of Hubble's constant, and \nthe possibility of reionization which \nwholly or partially erased temperature anisotropies in the CMB on \nscales smaller than the horizon size. Available data does not allow \nus to constrain all (or even most) of these parameters, so analyzing \ncurrent CMB anisotropy data requires\na model-independent approach. It seems\nreasonable to view the mapping of the acoustic peaks as\na means of determining the nature of parameter space\nbefore going on to fitting cosmological parameters directly. \n\n\\subsection{Reionization}\n\nThe possibility \nthat post-decoupling interactions between ionized matter and the CBR\nhave affected the anisotropies on scales \nsmaller than those measured by COBE is of great significance\nfor current experiments. \nReionization is inevitable but its effect on anisotropies \ndepends significantly on when it occurs\n(see \\citealp{haimank99} for a review). \n Early reionization leads to \na larger optical \ndepth and therefore a greater damping of the anisotropy \npower spectrum due to the secondary scattering of CMB photons \noff of the newly free electrons. \nFor a universe with critical matter density and constant ionization fraction \n$x_e$, the optical depth as a function of redshift is given by \n\\citep{whitess94}\n\n\\begin{equation}\n\\tau \\simeq 0.035 \\Omega_B h x_e z^{3/2},\n\\end{equation}\n\nwhich allows us to determine the redshift of reionization $z_\\ast$ at \nwhich $\\tau = 1$, \n\n\\begin{equation}\nz_\\ast \\simeq 69 \\left(\\frac{h}{0.5}\\right)^{-\\frac{2}{3}} \n\\left(\\frac{\\Omega_B}{0.1}\\right)^{-\\frac{2}{3}}x_e^{-\\frac{2}{3}}\n\\Omega^{\\frac{1}{3}}, \n\\end{equation}\n\nwhere the scaling with $\\Omega$ applies to an open universe only. \nAt scales smaller than the horizon size at reionization, \n$\\Delta T/T$ is reduced by the factor $e^{-\\tau}$. \n\nAttempts to measure\nthe temperature anisotropy on angular scales of less than a degree which \ncorrespond to the size of galaxies could have led to a surprise; \nif the universe was reionized after recombination to the extent\nthat the CBR was significantly scattered \nat redshifts less than 1100, the small-scale \nprimordial anisotropies would have been washed out.\nTo have an appreciable optical depth \nfor photon-matter interaction, reionization cannot have occurred \nmuch later than a redshift of 20 \\citep{padmanabhan93}. \nLarge-scale anisotropies such as those\nseen by COBE are not expected to be affected by reionization because they \nencompass regions of the universe which were not yet in causal contact\neven at the proposed time of reionization. However, the apparently high \namplitiude of degree-scale anisotropies is a strong argument against the \npossibility of early ($z\\geq50$) reionization. \nOn arc-minute scales, the \ninteraction of photons with reionized matter is expected to have eliminated\nthe primordial anisotropies and replaced them with smaller secondary \nanisotropies from this new surface of last scattering (the \nOstriker-Vishniac effect and patchy reionization, see next section). \n\n\\subsection{Secondary Anisotropies}\n\n\n\nSecondary CMB anisotropies \noccur when the photons of the Cosmic Microwave \nBackground radiation are scattered after the original last-scattering \nsurface (see \\citealp{refregier99} for a review). \n The shape of the blackbody \nspectrum can be altered through \ninverse Compton scattering by the thermal Sunyaev-Zel'dovich (SZ) effect\n\\citep{sunyaevz72}.\n The effective temperature of \nthe blackbody can be shifted locally by \na doppler shift from the peculiar velocity of the scattering medium (the \nkinetic SZ and Ostriker-Vishniac effects, \\citealp{ostrikerv86}) \nas well as by passage through\nthe changing gravitational potential caused by the \ncollapse of nonlinear structure (the Rees-Sciama effect, \n\\citealp{reess68}) or \nthe onset of curvature or cosmological constant domination (the Integrated \nSachs-Wolfe effect). \nSeveral simulations of the impact of \npatchy reionization have been performed \n\\citep{aghanimetal96, knoxsd98, gruzinovh98, peeblesj98}.\n%(Aghanim et al. 1996, \n%Knox, Scoccimarro, \\& Dodelson 1998, Gruzinov \\& Hu 1998, Peebles \\& \n%Juskiewicz 1998). \nThe SZ effect itself is independent of redshift, so it can yield \ninformation on clusters at much higher redshift than does X-ray \nemission. However, nearly all clusters are unresolved for $10'$ resolution \nso higher-redshift clusters occupy less of the beam and therefore their SZ\neffect is in fact dimmer. In the 4.5$'$ channels of Planck this will \nno longer be true, and the SZ effect can \nprobe cluster abundance at high redshift. An additional \nsecondary anisotropy is that caused by gravitational lensing (see e.g. \n\\citealp{cayonms93, cayonms94, metcalfs97, mgsc97}). \nGravitational lensing imprints \nslight non-Gaussianity in the CMB from which it might be possible \nto determine the matter power spectrum \n\\citep{seljakz98, zaldarriagas98b}. \n\n\n\\subsection{Polarization Anisotropies}\t\n\nPolarization of the Cosmic Microwave Background radiation \n\\citep{kosowsky94, kamionkowskiks97, zaldarriagas97}\narises \ndue to local quadrupole anisotropies at each point on the surface \nof last scattering (see \\citealp{huw97b} for a review).\n Scalar (density) perturbations generate curl-free \n(electric mode) polarization only, but tensor (gravitational wave) \nperturbations can generate divergence-free (magnetic mode) polarization. \nHence the polarization of the CMB is a potentially useful probe of \nthe level of gravitational waves in the early universe\n\\citep{seljakz97, kamionkowskik98}, especially \nsince current indications are that the large-scale primary \nanisotropies seen by COBE do not contain a measurable fraction \nof tensor contributions \\citep{gawisers98}. A thorough review \nof gravity waves and CMB polarization is given by \\citet{kamionkowskik99}. \n\n\n\\subsection{Gaussianity of the CMB anisotropies}\n\nThe processes turning density inhomogeneities into CMB anisotropies \nare linear, so cosmological models that predict gaussian primordial \ndensity inhomogeneities also predict a gaussian distribution of \nCMB temperature fluctuations. Several techniques have been developed \nto test COBE and future datasets for deviations from gaussianity\n\\citep[e.g.][]{kogutetal96b, ferreiram97, ferreirams97}. Most \ntests have proven negative, but a few claims of non-gaussianity have \nbeen made. \\citet{gaztanagafe98} found a very marginal indication \nof non-gaussianity in the spread of results for degree-scale \nCMB anisotropy observations being greater than the expected sample \nvariances. \\citet{ferreiramg98} have claimed a detection of non-gaussianity \nat multipole $\\ell=16$ using a bispectrum statistic, \nand \\citet{pandovf98} find a non-gaussian wavelet coefficient correlation \non roughly $15^\\circ$ scales in the North Galactic hemisphere. Both \nof these methods produce results consistent with gaussianity, however, if \na particular area of several pixels is eliminated from the dataset \n\\citep{bromleyt99}. A true sky signal should be larger than several \npixels so instrument noise is the most likely source of the non-gaussianity. \n A different area appears to cause each detection, giving \nevidence that the COBE dataset had non-gaussian instrument noise in at \nleast two areas of the sky. \n\n \n\n\\subsection{Foreground contamination}\n\nOf particular concern in measuring CMB anisotropies is the issue of foreground\ncontamination.\nForegrounds which can affect CMB observations include\ngalactic radio emission (synchrotron and free-free), galactic infrared\nemission (dust), extragalactic radio sources (primarily elliptical galaxies, \nactive galactic nuclei, and quasars), extragalactic infrared sources (mostly\ndusty spirals and high-redshift \nstarburst galaxies), and the Sunyaev-Zel'dovich effect from \nhot gas in \ngalaxy clusters. The COBE team has gone to great lengths to analyze their\ndata for possible foreground contamination and routinely eliminates everything\nwithin about $30^{\\circ}$ of the galactic plane. \n\nAn instrument with large \nresolution such as COBE is most sensitive to the diffuse foreground emission\nof our Galaxy, but small-scale anisotropy experiments need to worry \nabout extragalactic sources as well. \nBecause foreground \nand CMB anisotropies are assumed to be uncorrelated, they should add in \nquadrature, leading to an increase in the measurement of CMB anisotropy \npower. \nMost CMB instruments, however,\n can identify foregrounds by their spectral signature\nacross multiple \nfrequencies or their display of the beam response characteristic\nof a point source. This leads to an attempt at foreground subtraction, \nwhich can cause an underestimate of CMB anisotropy if some true\nsignal is subtracted along with the foreground.\nBecause \nthey are now becoming critical, extragalactic foregrounds \nhave been studied in detail \n\\citep{toffolattietal98, refregiersh98, \ngawisers97, sokasiangs98, gawiserjs98}. \nThe Wavelength-Oriented Microwave Background Analysis Team \n(WOMBAT, see \\citealp{gawiseretal98, jaffeetal99}) has made Galactic \nand extragalactic foreground predictions and full-sky simulations of \nrealistic CMB skymaps containing foreground contamination \navailable to the public (see http://astro.berkeley.edu/wombat). \nOne of these CMB simulations is shown in Figure \\ref{fig:total}. \n\\citet{tegmarketal99} used a Fisher matrix analysis to show that \nsimultaneously estimating foreground model parameters and cosmological \nparameters can lead to a factor of a few degradation in the precision \nwith which the cosmological parameters can be determined by CMB anisotropy \nobservations, so foreground prediction and subtraction is likely to be \nan important aspect of future CMB data analysis. \n\nForeground contamination may turn out to be a serious problem for \nmeasurements of CMB polarization anisotropy. While free-free emission \nis unpolarized, synchrotron radiation displays a linear polarization \ndetermined by the coherence of the magnetic field along the \nline of sight; this is typically on the order \nof 10\\% for Galactic synchrotron and between 5 and 10\\% for flat-spectrum \nradio sources.\nThe CMB is \nexpected to show a large-angular scale linear polarization of about 10\\%, \nso the prospects for detecting polarization anisotropy are no worse than \nfor temperature anisotropy although \nhigher sensitivity is required. \nHowever, the small-angular scale electric mode of linear \npolarization which is a probe of several cosmological parameters \nand the magnetic mode that serves as a probe \nof tensor perturbations are expected to have much lower amplitude and \nmay be swamped by foreground polarization. \nThermal and spinning dust grain emission can also be polarized. \nIt may turn out that dust emission is the only significant source \nof circularly polarized microwave photons since the CMB cannot have \ncircular polarization. \n\n\n\\begin{figure}\n\\begin{center}\n\\scalebox{0.75}{\\includegraphics{total1.ps}}\n\\caption{\\small \nWOMBAT Challenge simulation of CMB anisotropy map \nthat might be observed by the MAP satellite at 90 GHz, 13' resolution, \ncontaining CMB, instrument noise, and foreground contamination. The \nresolution is degraded by the pixelization of your monitor or printer.}\n\\label{fig:total}\n\\end{center}\n\\end{figure}\n\n%\\begin{figure}\n%\\centerline{\\psfig{file=total.ps,width=5in}}\n%\\caption{Compilation of CMB Anisotropy observations.} \n%\\mycaption{WOMBAT Challenge simulation of CMB anisotropy map \n%that may be observed by the MAP satellite at 90 GHz, 13' resolution, \n%containing CMB, instrument noise, and foreground contamination.\n%}\n%\\label{fig:total}\n%\\end{figure}\n\n\n\\section{Cosmic Microwave Background Anisotropy Observations}\n\\label{sect:obs_cmb}\n\nSince the COBE DMR detection of CMB anisotropy \\citep{smootetal92}, there have\nbeen over thirty additional measurements of anisotropy on angular scales\nranging from $7^{\\circ}$ to $0\\fdg3$, and upper limits have been set\non smaller scales. \n%Shown in Figure \\ref{fig:obs_cmb} are COBE \\citep{tegmarkh97},\n%FIRS \\citep{gangaetal94},\n%Tenerife \\citep{gutierrezetal97},\n%South Pole \\citep{gundersenetal94},\n%BAM \\citep{tuckeretal97},\n%ARGO \\citep{masietal96},\n%Python \\citep{cobleetal99, plattetal97}, \n%MAX \\citep{limetal96,tanakaetal96},\n%MSAM \\citep{wilsonetal99},\n%SK \\citep{netterfieldetal97}, \n%CAT \\citep{scottetal96,bakeretal99},\n%OVRO/RING \\citep{leitchetal98},\n%WD \\citep{tuckeretal93},\n%OVRO \\citep{readheadetal89},\n%SUZIE \\citep{churchetal97},\n%ATCA \\citep{subrahmanyanetal93},\n%and VLA \\citep{partridgeetal97}. \n\n\n\n\nThe COBE DMR observations \nwere pixelized into a skymap, from which it is possible to analyze any \nparticular multipole within the resolution of the DMR. \nCurrent small angular scale \nCMB anisotropy observations are insensitive to both high $\\ell$ and \nlow $\\ell$\nmultipoles because they cannot measure features smaller than their\nresolution and are insensitive to features larger than the \nsize of the patch of sky observed.\nThe next satellite mission, NASA's \nMicrowave Anisotropy Probe \n(MAP), is scheduled for launch in Fall 2000\nand will map angular scales down to $0\\fdg2$ with high precision over most of \nthe sky. An even more precise satellite, ESA's Planck, is scheduled \nfor launch in 2007. \n Because COBE observed such large angles, the DMR data can only \nconstrain the amplitude $A$ and index $n$ of \nthe primordial power spectrum in wave number $k$, $P_p(k) = A k^{n}$, and \nthese constraints are not tight enough \nto rule out very many classes of cosmological models. \n\n\nUntil the next satellite is flown, the promise\nof microwave background anisotropy measurements to measure \ncosmological parameters rests with a series of ground-based and \nballoon-borne\nanisotropy instruments which have already published results (shown \nin Figure \\ref{fig:obs_cmb}) \nor will report results in \nthe next few years (MAXIMA, BOOMERANG, TOPHAT, ACE, MAT, VSA, CBI, DASI, see \n\\citealp{leeetal99} and \\citealp{halperns99}).\nBecause they are not satellites, these instruments face the problems of \nshorter observing times and less sky coverage, although significant \nprogress has been made in those areas. They fall into \nthree categories: high-altitude balloons, interferometers, and \nother ground-based instruments.\nPast, present, and future balloon-borne instruments are \nFIRS, MAX, MSAM, ARGO, BAM, MAXIMA, QMAP, HACME, \nBOOMERANG, TOPHAT, and ACE. Ground-based \ninterferometers include CAT, JBIAC, SUZIE, BIMA, \nATCA, VLA, VSA, CBI, and DASI, and other ground-based \ninstruments are TENERIFE, SP, PYTHON, SK, OVRO/RING, VIPER, MAT/TOCO,\nIACB, and WD. \nTaken as a whole, they have the potential to yield very useful \nmeasurements of the radiation power spectrum of the CMB on degree and \nsubdegree scales. Ground-based non-interferometers have to discard a large\nfraction of data and undergo careful further data reduction to eliminate \natmospheric contamination. Balloon-based instruments need to keep a careful \nrecord of their pointing to reconstruct it during data analysis. \nInterferometers may be the most promising technique at present but they \nare the least developed, and most instruments are at radio frequencies \nand have very narrow frequency \ncoverage, making foreground contamination a major concern. \nIn order to use small-scale CMB anisotropy measurements to constrain \ncosmological models we need to be confident of their \nvalidity and to trust the error bars. This will allow us to discard badly\ncontaminated data and to give greater weight to the more precise measurements \nin fitting models. Correlated noise is a great concern for instruments \nwhich lack a rapid chopping because the $1/f$ noise causes correlations \non scales larger than the beam \nin a way that can easily mimic CMB anisotropies.\nAdditional issues are sample variance caused by the combination of \n cosmic variance and limited sky coverage and foreground contamination.\n\n\n%[TABLE OF CMB OBSERVATIONS WITH REFERENCES]\n\n{\\small\n\\begin{table}[h] \n%\\baselinestretch{1.0}\n%\\small\n\\caption{Complete compilation of CMB anisotropy observations 1992-1999, \nwith maximum likelihood $\\Delta T$, upper and lower 1$\\sigma$ uncertainties (not \nincluding calibration uncertainty), \nthe weighted center of the window function, the $\\ell$ values where the \nwindow function falls to $e^{-1/2}$ of its maximum value, the \n1 $\\sigma$ calibration uncertainty, and references given below.}\n\\label{tab:obs}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\nInstrument & $\\Delta T$ ($\\mu$K) & +$1\\sigma(\\mu$K) & -$1\\sigma(\\mu$K) & $\\ell_{eff}$ & \n $\\ell_{min}$ & $\\ell_{max}$ & 1$\\sigma$ cal. & ref. \\\\\n\\hline\nCOBE1&\t8.5&16.0&8.5&2.1&2&2.5&0.7&1\\\\\nCOBE2&\t28.0&7.4&10.4&3.1&2.5&3.7&0.7&1\\\\\nCOBE3&\t34.0&5.9&7.2&4.1&3.4&4.8&0.7&1\\\\\nCOBE4&\t25.1&5.2&6.6&5.6&4.7&6.6&0.7&1\\\\\nCOBE5&\t29.4&3.6&4.1&8.0&6.8&9.3&0.7&1\\\\\nCOBE6&\t27.7&3.9&4.5&10.9&9.7&12.2&0.7&1\\\\\nCOBE7&\t26.1&4.4&5.3&14.3&12.8&15.7&0.7&1\\\\\nCOBE8&\t33.0&4.6&5.4&19.4&16.6&22.1&0.7&1\\\\\nFIRS&\t29.4&7.8&7.7&10&3&30&--$^a$&2\\\\\nTENERIFE&30&15&11&20&13&31&--$^a$&3\\\\\nIACB1&\t111.9&49.1&43.7&33&20&57&~20&4\\\\\nIACB2&\t57.3&16.4&16.4&53&38&75&~20&4\\\\\nSP91&\t30.2&8.9&5.5&57&31&106&~15&5\\\\\nSP94&\t36.3&13.6&6.1&57&31&106&15&5\\\\\nBAM& \t55.6&27.4&9.8&74&28&97&20&6\\\\\nARGO94&\t33&5&5&98&60&168&5 &7\\\\\nARGO96&\t48&7&6&109&53&179&10&8\\\\\nJBIAC&\t43&13&12&109&90&128&6.6&9\\\\\nQMAP(Ka1)&47.0&6&7&80&60&101&12&10\\\\\nQMAP(Ka2)&59.0&6&7&126&99&153&12&10\\\\\nQMAP(Q)&52.0&5&5&111&79&143&12&10\\\\\nMAX234&\t46&7&7&120&73&205&10&11\\\\\nMAX5&\t43&8&4&135&81&227&10&12\\\\\nMSAMI&\t34.8&15&11&84&39&130&5&13\\\\\nMSAMII&\t49.3&10&8&201&131&283&5&13\\\\\nMSAMIII&47.0&7&6&407&284&453&5&13\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n}\n\n{\\small\n\\begin{table}[h] \n%\\baselinestretch{1.0}\n%\\small\n\\setcounter{table}{0}\n%\\caption{Table 1 (cont.)}\n\\label{tab:obs2}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\footnotesize\nInstrument & $\\Delta T$ ($\\mu$K) & +$1\\sigma(\\mu$K) & -$1\\sigma(\\mu$K) & $\\ell_{eff}$ & \n $\\ell_{min}$ & $\\ell_{max}$ & 1$\\sigma$ cal. & ref. \\\\\n\\hline\nPYTHON123&60&9&5&87&49&105&20&14\\\\\nPYTHON3S&66&11&9&170&120&239&20&14\\\\\nPYTHONV1&23&3&3&50&21&94&17$^b$ &15\\\\\nPYTHONV2&26&4&4&74&35&130&17&15\\\\\nPYTHONV3&31&5&4&108&67&157&17&15\\\\\nPYTHONV4&28&8&9&140&99&185&17&15\\\\\nPYTHONV5&54&10&11&172&132&215&17&15\\\\\nPYTHONV6&96&15&15&203&164&244&17&15\\\\\nPYTHONV7&91&32&38&233&195&273&17&15\\\\\nPYTHONV8&0&91&0&264&227&303&17&15\\\\\nSK1$^c$&\t50.5&8.4&5.3&87&58&126&11&16\\\\\nSK2&\t71.1&7.4&6.3&166&123&196 &11&16\\\\\nSK3&\t87.6&10.5&8.4&237&196&266&11&16\\\\\nSK4&\t88.6&12.6&10.5&286&248&310&11&16\\\\\nSK5&\t71.1&20.0&29.4&349&308&393&11&16\\\\\nTOCO971&40&10&9&63&45&81&10&17\\\\\nTOCO972&45&7&6&86&64&102&10&17\\\\\nTOCO973&70&6&6&114&90&134&10&17\\\\\nTOCO974&89&7&7&158&135&180&10&17\\\\\nTOCO975&85&8&8&199&170&237&10&17\\\\\nTOCO981&55&18&17&128&102&161&8&18\\\\\nTOCO982&82&11&11&152&126&190&8&18\\\\\nTOCO983&83&7&8&226&189&282&8&18\\\\\nTOCO984&70&10&11&306&262&365&8&18\\\\\nTOCO985&24.5&26.5&24.5&409&367&474&8&18\\\\\nVIPER1&\t61.6&31.1&21.3&108&30&229&8&19\\\\\nVIPER2&\t77.6&26.8&19.1&173&72&287&8&19\\\\\nVIPER3&\t66.0&24.4&17.2&237&126&336&8&19\\\\\nVIPER4&\t80.4&18.0&14.2&263&150&448&8&19\\\\\nVIPER5&\t30.6&13.6&13.2&422&291&604&8&19\\\\\nVIPER6&\t65.8&25.7&24.9&589&448&796&8&19\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n}\n\n{\\small\n\\begin{table}[h] \n%\\baselinestretch{1.0}\n%\\small\n%\\setcounter{table}{0}\n%\\caption{Table 1 (cont.)}\n\\label{tab:obs3}\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\\hline\n\\footnotesize\nInstrument & $\\Delta T$ ($\\mu$K) & +$1\\sigma(\\mu$K) & -$1\\sigma(\\mu$K) & $\\ell_{eff}$ & \n $\\ell_{min}$ & $\\ell_{max}$ & 1$\\sigma$ cal. & ref. \\\\\n\\hline\nBOOM971&29&13&11&58&25&75&8.1&20\\\\\nBOOM972&49&9&9&102&76&125&8.1&20\\\\\nBOOM973&67&10&9&153&126&175&8.1&20\\\\\nBOOM974&72&10&10&204&176&225&8.1&20\\\\\nBOOM975&61&11&12&255&226&275&8.1&20\\\\\nBOOM976&55&14&15&305&276&325&8.1&20\\\\\nBOOM977&32&13&22&403&326&475&8.1&20\\\\\nBOOM978&0&130&0&729&476&1125&8.1&20\\\\\nCAT96I&\t51.9&13.7&13.7&410&330&500&10&21\\\\\nCAT96II&49.1&19.1&13.7&590&500&680&10&21\\\\\nCAT99I&\t57.3&10.9&13.7&422&330&500&10&22\\\\\nCAT99II&0.&54.6&0.&615&500&680&10&22\\\\\nOVRO/RING&56.0&7.7&6.5&589&361&756&4.3&23\\\\\nHACME&0.&38.5&0.&38&18&63&--$^a$&29\\\\\nWD& \t0.&75.0&0.&477&297&825&30&24\\\\\nSuZIE&\t16&12&16&2340&1330&3070&8&25\\\\\nVLA& \t0.&27.3&0.&3677&2090&5761&--$^a$&26\\\\\nATCA& \t0.&37.2&0.&4520&3500&5780&--$^a$&27\\\\\nBIMA&\t8.7&4.6&8.7&5470&3900&7900&--$^a$&28\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\footnotesize\nREFERENCES: 1--\\citet{tegmarkh97,kogutetal96c}\n2--\\citet{gangaetal94}\n3--\\citet{gutierrezetal99}\n4--\\citet{femeniaetal98}\n5--\\citet{gangaetal97b,gundersenetal95}\n6--\\citet{tuckeretal97}\n7--\\citet{ratraetal99}\n8--\\citet{masietal96}\n9--\\citet{dickeretal99}\n10--\\citet{docetal98b}\n11--\\citet{clappetal94, tanakaetal96}\n12--\\citet{gangaetal98}\n13--\\citet{wilsonetal99}\n14--\\citet{plattetal97}\n15--\\citet{cobleetal99}\n16--\\citet{netterfieldetal97}\n17--\\citet{torbetetal99}\n18--\\citet{milleretal99}\n19--\\citet{petersonetal99}\n20--\\citet{mauskopfetal99}\n21--\\citet{scottetal96}\n22--\\citet{bakeretal99}\n23--\\citet{leitchetal98}\n24--\\citet{ratraetal98}\n25--\\citet{gangaetal97a,churchetal97}\n26--\\citet{partridgeetal97}\n27--\\citet{subrahmanyanetal93}\n28--\\citet{holzapfeletal99}\n29--\\citet{starenetal99}\n\n$^a$Could not be determined from the literature.\n\n$^b$Results from combining the +15\\% and -12\\% \ncalibration uncertainty with the 3$\\mu$K beamwidth uncertainty. The \nnon-calibration errors on the PYTHONV\ndatapoints are highly correlated.\n\n$^c$The SK $\\Delta T$ and error bars \nhave been re-calibrated according to the \n5\\% increase recommended by \\citet{masonetal99} \nand the 2\\% decrease in $\\Delta T$ due to foreground contamination \nfound by \\citet{docetal97}.\n\\end{table}\n}\n\n\n\n\\begin{figure}\n\\begin{center}\n\\scalebox{0.75}{\\includegraphics{dT.ps}}\n\\caption{\\small Compilation of CMB Anisotropy observations. \nVertical error bars represent\n$1\\sigma$ uncertainties \nand horizontal error bars show the range from $\\ell_{min}$ to $\\ell_{max}$ \nof Table 1. The line thickness is inversely proportional to the variance \nof each measurement, emphasizing the tighter constraints. All three models \nare consistent with the upper limits at the far right, but the Open CDM \nmodel (dotted) is a poor fit to the data, which prefer models \nwith an acoustic peak near $\\ell=200$ with an amplitude close to that of \n$\\Lambda$CDM (solid).}\n\\label{fig:obs_cmb}\n\\end{center}\n\\end{figure}\n\nFigure \\ref{fig:obs_cmb}\nshows our compilation of CMB anisotropy observations without \nadding any theoretical curves to bias the eye\\footnote{This figure and \nour compilation of CMB anisotropy observations are \navailable at http://mamacass.ucsd.edu/people/gawiser/cmb.html; CMB \nobservations have also been compiled by \\citet{smoots98} and\nat http://www.hep.upenn.edu/\\~{}max/cmb/experiments.html and\\\\\nhttp://www.cita.utoronto.ca/\\~{}knox/radical.html}. \nIt is clear that a straight \nline is a poor but not implausible fit to the data. \nThere is a clear rise around $\\ell=100$ and then a \ndrop by $\\ell=1000$. This is not yet good enough to give a clear \ndetermination of \n the \ncurvature of the universe, \nlet alone fit several cosmological parameters. \nHowever, the current data prefer \nadiabatic structure formation models over isocurvature \nmodels \\citep{gawisers98}. \nIf analysis is restricted to \nadiabatic CDM models, a value of the total density near critical is \npreferred \\citep{dodelsonk99}.\n\n\n\n\\subsection{Window Functions}\n\nThe sensitivity of these instruments to various multipoles is called\ntheir window function. \n%Figure 3 shows window functions for the \n%relevant CMB anisotropy observations. \nThese window functions \nare important in analyzing anisotropy measurements because\nthe small-scale experiments do not measure enough of the sky to produce\nskymaps like COBE. Rather they yield a few \n``band-power'' measurements of rms temperature anisotropy which reflect \na convolution over the range of multipoles contained in the window \nfunction of each band. Some instruments can produce limited \nskymaps \\citep{whiteb95}. The window function $W_\\ell$ shows\nhow the total power observed is sensitive to the anisotropy on \nthe sky as a function of angular scale:\n\n\n\\begin{equation}\nPower = \\frac{1}{4 \\pi} \\sum_\\ell (2 \\ell + 1)C_\\ell W_\\ell = \\frac{1}{2}\n(\\Delta T/T_{CMB})^2 \\sum_\\ell \\frac {2 \\ell + 1}{\\ell(\\ell+1)} W_\\ell \n\\end{equation} \n\n \n\\noindent where the COBE normalization is $\\Delta T = 27.9 \\mu$K and\n$T_{CMB}=2.73$K \\citep{bennettetal96}. \nThis allows the observations of broad-band \npower to be reported as observations of $\\Delta T$, and knowing the window\nfunction of an instrument one can turn the predicted $C_\\ell$ spectrum\nof a model into the corresponding prediction for $\\Delta T$. \nThis ``band-power'' measurement \nis based on the standard definition that for a ``flat'' power spectrum,\n$\\Delta T = (\\ell (\\ell + 1) C_\\ell )^{1/2}T_{CMB}/(2\\pi)$ (flat\nactually means that $\\ell(\\ell+1)C_\\ell$ is constant). \n\n\nThe autocorrelation function for measured temperature anisotropies\nis a convolution of the true expectation values for the anisotropies \nand the window function. Thus we have \\citep{whites95}\n\n\\begin{equation}\n \\left \\langle \n\\frac{\\Delta T}{T} (\\hat{n}_{1} )\n\\frac{\\Delta T}{T} (\\hat{n}_{2} ) \\right \\rangle = \n\\frac{1}{4 \\pi} \\sum_{\\ell=1}^{\\infty} (2 \\ell + 1) C_\\ell \nW_\\ell ( \\hat{n}_{1}, \\hat{n}_{2}), \n\\end{equation}\n\n\\noindent\nwhere the symmetric beam shape that is typically assumed makes\n$W_{\\ell}$ a \nfunction of separation angle only. In general, the window function \nresults from a combination of the directional response of the antenna,\nthe beam position as a function of time, and the weighting of each \npart of the beam trajectory in producing a temperature measurement \n\\citep{whites95}. Strictly speaking, $W_\\ell$ is the diagonal part of \na filter function $W_{\\ell \\ell'}$ that reflects the coupling of \nvarious multipoles due to the non-orthogonality of the spherical \nharmonics on a cut sky and the observing strategy of the \ninstrument \n\\citep{knox99}. \nIt is standard to assume a Gaussian beam response of width $\\sigma$, \nleading to a window function \n\\begin{equation}\n W_{\\ell} = \\exp [ - \\ell ( \\ell + 1 )\\sigma^{2}]. \n\\end{equation} \nThe low-$\\ell$\ncutoff introduced by a 2-beam differencing setup comes from the window\nfunction \\citep{whitess94} \n\\begin{equation}\n W_{\\ell} = 2 [ 1 - P_{\\ell}(\\cos \\theta) ] \n\\exp [ - \\ell ( \\ell + 1 )\\sigma^{2}]. \n\\end{equation} \n\n\n\n\\subsection{Sample and Cosmic Variance}\n\n\nThe multipoles $C_\\ell$ can be related to the expected\nvalue of the spherical harmonic coefficients by \n\\begin{equation}\n \\langle \\sum_m{a_{\\ell m}^2}\\rangle = (2 \\ell + 1) C_\\ell \n\\end{equation}\nsince there are $(2 \\ell + 1)$ $a_{\\ell m}$ for each $\\ell$ and each has\nan expected autocorrelation of $C_{\\ell}$. In a theory such as inflation,\nthe temperature fluctuations follow a Gaussian distribution about \nthese expected ensemble averages. This makes the $a_{\\ell m}$ Gaussian \nrandom variables, resulting in a $\\chi^{2}_{2 \\ell + 1 }$ distribution \nfor $\\sum_m{a_{\\ell m}^2}$. The width of this distribution leads to a \ncosmic variance in the estimated $C_\\ell$ of \n$\\sigma^2_{cv} = (\\ell + \\frac{1}{2})^{-\\frac{1}{2}}C_\\ell$, \nwhich \nis much greater for small $\\ell$ than for large $\\ell$ (unless $C_\\ell$ is rising in a \nmanner highly inconsistent with theoretical expectations). So, although\n cosmic variance is an unavoidable source\nof error for anisotropy measurements,\nit is much less of a problem for small scales \nthan for COBE. \n\nDespite our conclusion that cosmic variance is a greater concern on \nlarge angular scales, Figure \\ref{fig:obs_cmb} \nshows a tremendous variation in the \nlevel of \nanisotropy measured by small-scale experiments. Is this evidence\nfor a non-Gaussian cosmological model such as topological\ndefects? Does it mean we cannot trust the data? Neither conclusion \nis justified (although both could be correct) because we do in \nfact expect a wide variation among these measurements due to their\ncoverage of a very small portion of the sky. Just as it is difficult to \nmeasure the $C_{\\ell}$ with only a few $a_{\\ell m}$, \nit is challenging to \nuse a small piece of the sky to measure multipoles whose spherical\nharmonics cover the sphere. It turns out that \nlimited sky coverage leads to a sample variance for a particular \nmultipole related to \nthe cosmic variance for any value of $\\ell$ by the simple formula \n\\begin{equation}\n \\sigma^{2}_{sv} \\simeq \\left ( \\frac {4 \\pi}{\\Omega} \\right ) \n\\sigma^{2}_{cv}, \n\\end{equation} \nwhere $\\Omega$ is the solid angle observed \\citep{scottsw94}. One caveat: \nin testing cosmological models, this cosmic and sample variance should \nbe derived from the $C_\\ell$ of the model, not the observed value of the \ndata. The difference is typically small but will bias the analysis of \nforthcoming high-precision observations if cosmic and sample variance \nare not handled properly. \n\n\n\n\\subsection{Binning CMB data}\n\nBecause there are so many measurements and the most important ones have \nthe smallest error bars, it is preferable to plot the data in some way that \navoids having the least precise measurements dominate the plot. \nQuantitative analyses should weight each datapoint by the inverse of its \nvariance. Binning the data can be useful \nfor display purposes but is dangerous for analysis, \nbecause a statistical analysis \nperformed on the binned datapoints will give different results from \none performed on the raw data. The distribution \nof the binned errors is non-Gaussian even if the original points had \nGaussian errors. Binning might improve a quantitative analysis\n if the points at a particular \nangular scale showed a scatter larger than is consistent with their error \nbars, leading one to suspect that the errors have been underestimated. \nIn this case, one could use the scatter to create a reasonable uncertainty on \nthe binned average. For the current CMB data there is no \nclear indication of scatter inconsistent with the errors so this is \nunnecessary. \n\nIf one wishes \nto perform a model-dependent analysis of the data, the simplest \nreasonable approach is to \ncompare the observations \nwith the broad-band power estimates that should have been produced given \na particular theory \n(the theory's $C_\\ell$ are not constant so the \nwindow functions must be used for this). \nCombining full raw datasets is superior but computationally \nintensive (see \\citealt{bondjk98a}). A first-order correction for the \nnon-gaussianity of the \nlikelihood function of the band-powers has been calculated by \n\\citet{bondjk98b} and is available at \nhttp://www.cita.utoronto.ca/\\~{}knox/radical.html.\n\n\\section{Combining CMB and Large-Scale Structure Observations}\n\nAs CMB anisotropy is detected on smaller angular scales and large-scale \nstructure surveys extend to larger regions, there is an increasing overlap \nin the spatial scale of inhomogeneities probed by these complementary \ntechniques. This allows us to test the gravitational instability paradigm \nin general and then move on to finding cosmological models which can \nsimultaneously explain the CMB and large-scale structure observations. \nFigure \\ref{fig:lcdm} shows this comparison for our compilation of CMB \nanisotropy observations (colored boxes) and of large-scale structure \nsurveys (APM - \\citealt{gaztanagab98}, LCRS - \\citealt{linetal96}, \nCfa2+SSRS2 - \\citealt{dacostaetal94}, PSCZ - \\citealt{tadrosetal99}, \nAPM clusters - \\citealt{tadrosed98}) including \nmeasurements of the dark matter fluctuations \nfrom peculiar velocities \\citep{kolattd97} and the abundance \nof galaxy clusters \\citep{vianal96,bahcallfc97}. Plotting CMB anisotropy \ndata as measurements of the matter power spectrum is a model-dependent \nprocedure, and the galaxy surveys must be corrected for redshift distortions, \nnon-linear evolution, and galaxy bias (see \\citealt{gawisers98} \nfor detailed methodology.) Figure \\ref{fig:lcdm} is good evidence \nthat the matter and radiation inhomogeneities had a common origin - the \nstandard $\\Lambda$CDM model with a Harrison-Zel'dovich primordial power \nspectrum predicts both rather well. On the detail level, however, the model \nis a poor fit ($\\chi^2$/d.o.f.=2.1), and no cosmological model which \nis consistent with the recent Type Ia supernovae results \nfits the data much better. Future observations will tell us if this is \nevidence of systematic problems in large-scale structure data or a fatal \nflaw of the $\\Lambda$CDM model. \n\n\n\\begin{figure}\n\\begin{center}\n\\scalebox{0.5}{\\includegraphics{lchdm00.ps}}\n\\caption{\\small \nCompilation of CMB anisotropy detections (boxes) and large-scale structure \nobservations (points with error bars) \ncompared to theoretical predictions of standard $\\Lambda$CDM model. \nHeight of boxes (and error bars) represents\n$1\\sigma$ uncertainties\nand width of boxes shows the full width \nat half maximum of each instrument's window function.}\n\\label{fig:lcdm}\n\\end{center}\n\\end{figure}\n\n\\section{Conclusions}\n\n\nThe CMB is a mature subject. The spectral distortions are well \nunderstood, and the Sunyaev-Zeldovich effect provides a unique tool for\nstudying galaxy clusters at high redshift. Global distortions will\neventually be found, most likely first at very large $l$ due to the\ncumulative contributions from hot gas heated by radio galaxies, AGN, and\ngalaxy groups and clusters. For gas at $\\sim 10^6 - 10^7$ K,\nappropriate to gas in galaxy potential wells, the thermal and kinematic\ncontributions are likely to be comparable.\n\nCMB anisotropies are a rapidly developing field, since the 1992\ndiscovery with the COBE DMR of large angular scale temperature\nfluctuations. At the time of writing, the first acoustic peak is being\nmapped with unprecedented precision that will enable definitive\nestimates to be made of the curvature parameter. More information will\ncome with all-sky surveys to higher resolution (MAP in 2000, PLANCK in 2007) \nthat will enable most of the cosmological parameters to be\nderived to better than a few percent precision if the \nadiabatic CDM paradigm proves correct. Degeneracies remain in\nCMB parameter extraction, specifically between $\\Omega_0$, $\\Omega_b$ and\n$\\Omega_{\\Lambda}$, but these can be removed via large-scale structure\nobservations, which effectively constrain $\\Omega_{\\Lambda}$ via weak\nlensing. The goal of studying reionization will be met by the\ninterferometric surveys at very high resolution ($l\\sim 10^3 - 10^4$).\n\nPolarization presents the ultimate challenge, because the foregrounds\nare poorly known. Experiments are underway to measure polarization at\nthe 10 percent level, expected on degree scales in the most optimistic\nmodels. However one has to measure polarisation at the 1 percent level to\ndefinitively study the ionization history and early tensor mode\ngeneration in the universe, and this may only be possible with long\nduration balloon or space experiments.\n\nCMB anisotropies are a powerful probe of the early universe. Not only\ncan one hope to extract the cosmological parameters, but one should be\nable to measure the primordial power spectrum of density fluctuations\nlaid down at the epoch of inflation, to within the uncertainties\nimposed by cosmic variance. In combination with new generations of\ndeep wide field galaxy surveys, it should be possible to unambiguously\nmeasure the shape of the predicted peak in the power spectrum, and\nthereby establish unique constraints on the origin of the large-scale\nstructure of the universe. \n\n\n\\small\n\n%\\nocite{*}\n%\\bibliographystyle{plain}\n\\bibliographystyle{apj}\n%\\bibliography{uctest}\n\\bibliography{apj-thesis,refs} %apj-thesis \n\n\n\\end{document}\n\n\n"
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Lett.,\n 39, 898\n\n\\bibitem[{Smoot \\& Scott(1998)}]{smoots98}\nSmoot, G.~F. \\& Scott, D. 1998, in Review of Particle Properties,\n astro-ph/9711069\n\n\\bibitem[{{Sokasian} {et~al.}(1998){Sokasian}, {Gawiser}, \\&\n {Smoot}}]{sokasiangs98}\n{Sokasian}, A., {Gawiser}, E., \\& {Smoot}, G.~F. 1998, preprint,\n astro-ph/9811311\n\n\\bibitem[{Staren {et~al.}(1999)}]{starenetal99}\nStaren, J. {et~al.} 1999, preprint, astro-ph/9912212\n\n\\bibitem[{{Subrahmanyan} {et~al.}(1993){Subrahmanyan}, {Ekers}, {Sinclair}, \\&\n {Silk}}]{subrahmanyanetal93}\n{Subrahmanyan}, R., {Ekers}, R.~D., {Sinclair}, M., \\& {Silk}, J. 1993, Mon.\n Not. R. Astron. Soc., 263, 416\n\n\\bibitem[{{Suginohara} {et~al.}(1998){Suginohara}, {Suginohara}, \\&\n {Spergel}}]{suginoharass98}\n{Suginohara}, M., {Suginohara}, T., \\& {Spergel}, D.~N. 1998, Astrophys. J.,\n 495, 511\n\n\\bibitem[{{Sunyaev} \\& {Zeldovich}(1972)}]{sunyaevz72}\n{Sunyaev}, R.~A. \\& {Zeldovich}, Y.~B. 1972, Astron. Astrophys., 20, 189\n\n\\bibitem[{{Tadros} {et~al.}(1998){Tadros}, {Efstathiou}, \\&\n {Dalton}}]{tadrosed98}\n{Tadros}, H., {Efstathiou}, G., \\& {Dalton}, G. 1998, Mon. Not. R. Astron.\n Soc., 296, 995\n\n\\bibitem[{Tadros {et~al.}(1999)}]{tadrosetal99}\nTadros, H. {et~al.} 1999, preprint, astro-ph/9901351\n\n\\bibitem[{{Tanaka} {et~al.}(1996)}]{tanakaetal96}\n{Tanaka}, S.~T. {et~al.} 1996, Astrophys. J., Lett., 468, L81\n\n\\bibitem[{Tegmark {et~al.}(1999)Tegmark, Eisenstein, Hu, \\&\n de~Oliveira-Costa}]{tegmarketal99}\nTegmark, M., Eisenstein, D.~J., Hu, W., \\& de~Oliveira-Costa, A. 1999,\n preprint, astro-ph/9905257\n\n\\bibitem[{Tegmark \\& Hamilton(1997)}]{tegmarkh97}\nTegmark, M. \\& Hamilton, A. 1997, preprint, astro-ph/9702019\n\n\\bibitem[{{Toffolatti} {et~al.}(1998){Toffolatti}, {Argueso Gomez}, {De Zotti},\n {Mazzei}, {Franceschini}, {Danese}, \\& {Burigana}}]{toffolattietal98}\n{Toffolatti}, L., {Argueso Gomez}, F., {De Zotti}, G., {Mazzei}, P.,\n {Franceschini}, A., {Danese}, L., \\& {Burigana}, C. 1998, Mon. Not. R.\n Astron. Soc., 297, 117\n\n\\bibitem[{Tolman(1934)}]{tolman34}\nTolman, R.~C. 1934, Relativity, Thermodynamics, and Cosmology (Oxford, UK:\n Clarendon Press)\n\n\\bibitem[{{Torbet} {et~al.}(1999){Torbet}, {Devlin}, {Dorwart}, {Herbig},\n {Miller}, {Nolta}, {Page}, {Puchalla}, \\& {Tran}}]{torbetetal99}\n{Torbet}, E., {Devlin}, M.~J., {Dorwart}, W.~B., {Herbig}, T., {Miller}, A.~D.,\n {Nolta}, M.~R., {Page}, L., {Puchalla}, J., \\& {Tran}, H.~T. 1999, Astrophys.\n J., Lett., 521, L79\n\n\\bibitem[{{Tucker} {et~al.}(1997){Tucker}, {Gush}, {Halpern}, {Shinkoda}, \\&\n {Towlson}}]{tuckeretal97}\n{Tucker}, G.~S., {Gush}, H.~P., {Halpern}, M., {Shinkoda}, I., \\& {Towlson}, W.\n 1997, Astrophys. J., Lett., 475, L73\n\n\\bibitem[{{Viana} \\& {Liddle}(1996)}]{vianal96}\n{Viana}, P. T.~P. \\& {Liddle}, A.~R. 1996, Mon. Not. R. Astron. Soc., 281, 323\n\n\\bibitem[{White \\& Bunn(1995)}]{whiteb95}\nWhite, M. \\& Bunn, E. 1995, Astrophys. J., Lett., 443, L53\n\n\\bibitem[{White \\& Hu(1997)}]{whiteh97}\nWhite, M. \\& Hu, W. 1997, Astron. Astrophys., 321, 8W\n\n\\bibitem[{{White} {et~al.}(1994){White}, {Scott}, \\& {Silk}}]{whitess94}\n{White}, M., {Scott}, D., \\& {Silk}, J. 1994, Ann. Rev. Astron. Astrophys., 32,\n 319\n\n\\bibitem[{White \\& Srednicki(1995)}]{whites95}\nWhite, M. \\& Srednicki, M. 1995, Astrophys. J., 443, 6\n\n\\bibitem[{Wilson {et~al.}(1999)}]{wilsonetal99}\nWilson, G.~W. {et~al.} 1999, preprint, astro-ph/9902047\n\n\\bibitem[{Yamada {et~al.}(1999)Yamada, Sugiyama, \\& Silk}]{yamadass99}\nYamada, M., Sugiyama, N., \\& Silk, J. 1999, Astrophys. J., 522, 66\n\n\\bibitem[{{Zaldarriaga} \\& {Seljak}(1997)}]{zaldarriagas97}\n{Zaldarriaga}, M. \\& {Seljak}, U. 1997, Phys. Rev. D, 55, 1830\n\n\\bibitem[{Zaldarriaga \\& Seljak(1998)}]{zaldarriagas98b}\nZaldarriaga, M. \\& Seljak, U. 1998, preprint, astro-ph/9810257\n\n\\end{thebibliography}\n"
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astro-ph0002045
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Conservation of circulation in magnetohydrodynamics
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We demonstrate, both at the Newtonian and (general) relativistic levels, the existence of a generalization of Kelvin's circulation theorem (for pure fluids) which is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
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"name": "astro-ph0002045.tex",
"string": "\\documentstyle[aps,pre,eqsecnum,12pt]{revtex}\n\n\\begin{document}\n\\tighten\n\\title{Conservation of circulation in magnetohydrodynamics }\n\n \\author{ Jacob D. Bekenstein\\thanks{Electronic mail:\n [email protected]} and Asaf\nOron\\thanks{Electronic mail:[email protected]}}\n\n\\address{\\it The Racah Institute of Physics, Hebrew University of\nJerusalem,\\\\ Givat Ram, Jerusalem 91904, Israel}\n\n\\date{\\today}\n\n\\maketitle\n%\\tableofcontents{}\n\n\\begin{abstract}\nWe demonstrate, both at the Newtonian and (general) relativistic levels, the\nexistence of a generalization of Kelvin's circulation theorem (for pure fluids)\nwhich is applicable to perfect magnetohydrodynamics. The argument is based on\nthe least action principle for magnetohydrodynamic flow. Examples of the new\nconservation law are furnished. The new theorem should be helpful in\nidentifying new kinds of vortex phenomena distinct from magnetic ropes or\nfluid vortices.\n\\end{abstract}\n \\section{Introduction}\n\nKelvin's theorem on the conservation of circulation of a simple perfect\nfluid has played an important role in the development of hydrodynamics. For\ninstance, it shows that potential flows are possible, that isolated\nvortices can exist, that they obey the Helmholtz laws, etc. Kelvin's\ntheorem is valid only for flows in which the body force per unit mass is a\ngradient; mostly this includes incompressible or isentropic flows of\none--component fluids.\n\nMost flows in geophysics and astrophysics are more complicated. In\nparticular, many fluids in the real world carry magnetic fields: they are\nmagnetofluids. Yet the Lorentz force per unit mass on a\nmagnetofluid is almost {\\it never\\/} a perfect gradient. Thus the circulation\ntheorem in its original form is almost never true in magnetohydrodynamics\n(MHD). Must we then surrender the many insights that Kelvin's theorem\nconferred on pure hydrodynamics ? \n\nNot necessarily. One might speculate that a suitable combination of fluid\nvelocity ${\\bf v}$ and magnetic induction ${\\bf B}$ may inherit the\nproperty of having a ``circulation'' on a closed curve which is preserved as\nthat curve is dragged with the magnetofluid. Such conserved circulation\nmight play as useful a role in MHD as has Kelvin's circulation in pure\nfluid dynamics. For example, it might help characterize a set of\nmagnetoflows as being potential in some sense, with consequent\nsimplification of this intricate subject. Or it might help to characterize\na new type of vortex, a hybrid vorticity--magnetic rope. In view of the\nimportance of the vortex phenomenon in contemporary physics, this last\npossibility is by itself ample reason to delve into the subject.\n\nTwo decades ago, E. Oron\\cite{bekenstein1} discovered, with the formalism\nof relativistic perfect MHD, a circulation theorem of the above kind.\nAlthough some of its consequences for new helicity conservation laws have\nbeen explored\\cite{bekenstein2}, this new conserved circulation has remained\nobscure. Contributing to this, no doubt, is the fact that it has only\nbeen derived relativistically, and that this derivation is an intricate one,\neven for relativistic MHD. In addition, Oron's derivation assumes both\nstationary symmetry and axisymmetry, while it is well known that Kelvin's\ntheorem requires neither of these.\n\nIn the present paper we use the least action principle to give a rather\nstraightforward existence proof for a generically conserved hybrid\nvelocity--magnetic field circulation within the framework of perfect MHD\nwhich does not depend on spacetime symmetries. We do this both at the\nNewtonian (Sec.II) and general relativistic (Sec.III) levels; the importance\nof MHD effects in pulsars, active galactic nuclei and cosmology underscores\nthat this last arena is not just of academic importance.\n\nAs mentioned, we approach the whole problem not from equations of motion,\nbut from the least action principle. Lagrangians for nonrelativistic pure\nperfect flow have been proposed by Herivel\\cite{herivel},\nEckart\\cite{eckart}, Lin\\cite{lin}, Seliger and Witham\\cite{seliger},\nMittag, Stephen and Yourgrau\\cite{mittag} and others. Many of the proposed\nLagrangians necessarily imply irrotational flow, {\\it i.e.\\/} not to\ngeneric flow, a deficiency which is often missed by the authors. \nLin\\cite{lin} introduced a device that allows vortical flows to be\nencompassed. This device is used by Seliger and Witham. Lagrangians\nfor nonrelativistic perfect MHD flow in Eulerian coordinates have been \nproposed by Eckart\\cite{eckart2}, Henyey\\cite{henyey}, Newcomb\\cite{newcomb},\nLundgren\\cite{lundgren} and others.\n\nIn special relativity Penfield\\cite{penfield} proposed a perfect\nfluid Lagrangian which admits vortical isentropic flow. The early\ngeneral relativistic Lagrangian of Taub\\cite{taub1,taub2} as well\nas the more recent one by Kodama et. al\\cite{kodama} describe only\nirrotational perfect fluid flows. The Lin device is incorporated by\nSchutz\\cite{schutz}, whose perfect fluid Lagrangian admits vortical as\nwell as irrotational flows in general relativity. Carter\n\\cite{carter1,carter2} introduced Lagrangians for particle-like motions from\nwhich can be inferred the properties of fluid flows, including vortical\nones. Achterberg\\cite{achterberg} proposed a general relativistic MHD action,\nwhich, however, describes only ``irrotational'' flows. Thompson\n\\cite{thompson} used this Lagrangian in the extreme relativistic\nlimit. Heyl and Hernquist \\cite{heyl} modified it to include QED\neffects. In this paper we follow mostly Seliger and Witham\\cite{seliger} \nand Schutz\\cite{schutz}.\n\nIn Sec.~II.A we propose a nonrelativistic MHD Lagrangian, and show in\nSec.~II.B and II.C that it gives rise to the correct equations of motion for\nthe density, entropy, velocity and magnetic fields in Newtonian MHD. \nIn Sec.~II.D we derive from it the conserved circulation, defined in terms\nof a new vector field ${\\bf R}$, and discuss its invariance under\nredefinition of ${\\bf R}$. Sec.~II.E furnishes two examples of the\nconserved circulation in action. In Sec.~III.A we collect all the equations\nof motion of general relativistic MHD, and propose a general relativistic\nMHD Lagrangian in Sec.~III.B. Secs.~III.C and III.D recover all the\nrelativistic MHD equations of motion from it. Finally in Sec.~III.E we\ngeneralize the conserved MHD circulation to the general relativistic case. \n\n\\section{Variational Principle in Eulerian Coordinates}\n\n\\subsection{The Lagrangian Density}\n\nPerfect MHD describes situations where the flow is nondissipative, and, in\nparticular, when the magnetoflow has ``infinite conductivity'', and where\nMaxwell's displacement current may be neglected in Ampere's equation. We\nshall adopt this approximation. We work in eulerian coordinates: all\nphysical quantities are functions of coordinates $x_i$ or $ {\\bf r}$ which\ndescribe a fixed point in space. We first summarize the MHD equations. We\nwork in units for which $c=1$.\n\nFirst of all, the fluid obeys the equation of continuity ($\\partial_t\\equiv\n\\partial/\\partial t)$\n\\begin{equation}\n\\label{continu}\n\\partial_t \\rho +\\nabla \\cdot \\left( \\rho {\\bf v}\\right) =0,\n\\end{equation}\nwhere $\\rho( {\\bf r}, t)$ is the mass density per unit volume of the fluid\nand ${\\bf v}( {\\bf r}, t)$ is the fluid's velocity field. Second, since\nthere is no dissipation, $s$, the entropy per unit mass, must be conserved\nalong the flow:\n\\begin{equation}\n\\label{adiabatic0}\nDs\\equiv\\partial_t s +{\\bf v}\\cdot\\nabla s =0.\n\\end{equation}\nHere we have defined the convective derivative $D$, which in Cartesian\ncoordinates has the same form for scalars or vectors. With the help of\nEq.~(\\ref{continu}) this equation can be written as\n\\begin{equation}\n\\label{adaibatic1}\n\\partial_t {(\\rho s)}+\\nabla \\cdot \\left( \\rho s{\\bf v}\\right) =0.\n\\end{equation}\nThird, ``infinite conductivity\" implies that ${\\bf E} + ({\\bf v}/c) \\times\n{\\bf B}=0$, where ${\\bf E}$ and ${\\bf B}$ are the electric and magnetic\nfields, respectively. Combining this with Faraday's equation yields the so\ncalled field-freezing equation\n\\begin{equation}\n\\label{ff}\n\\partial_t {\\bf B}=\\nabla \\times \\left( {\\bf v}\\times {\\bf B}\\right),\n\\end{equation}\nwhich implies Alfven's law of conservation of the magnetic flux\nthrough a closed loop moving with the flow.\nFinally, the evolution of the velocity field is governed by the MHD Euler\nequation,\n\\begin{equation}\n\\label{mag_euler}\n\\rho D{\\bf v}=-\\nabla p-\\rho\\nabla U +{(\\nabla\\times{\\bf B})\\times{\\bf\nB}\\over 4\\pi},\n\\end{equation}\nwhere $p$ is the fluid's pressure (here assumed isotropic), and $U({\\bf r},t)$\nis the gravitational potential.\n\nThe least action principle is in general\n\\begin{equation}\n \\delta S[f_a] \\equiv \\delta \\int dt \\int d^3r\\, {\\cal L}(f_a,\\partial_t\nf_a,\\nabla f_a) =0.\n\\label{action}\n\\end{equation}\nHere the action $S$ is a functional of various fields $f_a({\\bf r},t)$,\n$a=1, 2, \\cdots$. One varies each $f_a$, transfers time and space\nderivatives of each variation $\\delta f_a$ to the adjacent factor by\nintegration by parts, and sets to zero the overall coefficient of the bare\n$\\delta f_a$. This gives us the Lagrange--Euler equation\n\\begin{equation}\n\\partial_t\\left({\\partial {\\cal L}\\over \\partial (\\partial_t\nf_a)}\\right) + \\nabla\\cdot \\left({\\partial {\\cal L}\\over \\partial \\nabla\nf_a}\\right) -{\\partial {\\cal L}\\over \\partial f_a}=0.\n\\label{EL}\n\\end{equation}\nIt is usually more convenient to get the equation for each $f_a$ {\\it ab\ninitio\\/} by the above procedure, rather than by using Eq.~(\\ref{EL}).\n\n We now propose the following Lagrangian {\\it density\\/} for\nMHD flow of perfect infinitely conducting fluid which incorporates\nEqs.(\\ref{continu}-\\ref{ff}), as three Lagrange constraints\n\\begin{eqnarray}\n{\\cal L}&=&\\rho {\\bf v}^{2}/2-\\rho\n\\epsilon\n\\left(\n\\rho ,s\\right) -\\rho U -{\\bf B}^{2}/(8\\pi) +\n\\nonumber \\\\\n&+&\\phi \\left[ \\partial_t\\rho +\\nabla \\cdot \\left[ \\rho\n{\\bf v}\\right) \\right]\n+ \\eta \\left[ \\partial_t{(\\rho s)}+\\nabla \\cdot\n\\left(\\rho s{\\bf v}\\right)\n \\right]\n\\nonumber\\\\\n&+&\\lambda \\left[ \\partial_t{(\\rho\\gamma)} +\\nabla \\cdot\n\\left(\n\\rho\n\\gamma {\\bf v}\\right)\n \\right]\n+{\\bf K}\\cdot \\left[\\partial_t{\\bf B} -\\nabla \\times\n\\left( {\\bf v}\\times {\\bf B}\\right) \\right].\n\\label{le1}\n\\end{eqnarray}\nIn the above $\\epsilon \\left(\\rho,s\\right)$ is the thermodynamic\ninternal energy per unit mass; in the total Lagrangian the corresponding\ntotal internal energy enters as a potential energy. The magnetic energy, the\nvolume integral of ${\\bf B}^2/(8\\pi)$, also enters the total Lagrangian as a\npotential energy.\n\nIn Eq.~(\\ref{le1}) $\\phi$, $ \\eta $ are Lagrange\nmultiplier fields which locally enforce the conservation laws\n(\\ref{continu}-\\ref{adiabatic0}), as may be verified by varying with respect\nto these multipliers. ${\\bf K}$ is a triplet of Lagrange multiplier fields\nwhich enforce the field--freezing constraint Eq.~(\\ref{ff}): varying\nwith respect to ${\\bf K}$ reproduces Eq.~(\\ref{ff}) at every point and time.\nFinally, $\\lambda$ is a Lagrange multiplier field which enforces the Lin\nconstraint on a new field, $\\gamma$:\n\\begin{equation}\n\\partial_t(\\rho\\gamma)+\\nabla\\cdot(\\rho{\\bf v}\\gamma) = 0\\qquad {\\rm\nor}\\qquad D\\gamma = 0.\n\\label{Lin}\n\\end{equation}\nHere we have used Eq.~(\\ref{continu}) to reduce to the second form.\nLin's field $\\gamma$, like $s$, is conserved along the flow, but\nunlike $s$ it does not occur elsewhere in the Lagrangian. Lin interprets\n$\\gamma({\\bf r}, t)$ as one of the three initial {\\it Lagrangian\\/} coordinates\nwhich label each fluid element. But whatever the interpretation, the\ncondition~(\\ref{Lin}) is essential so that the flow can be vortical also\nin the limit ${\\bf B}\\rightarrow 0$. This matter is further discussed in\nthe following section.\n\n\\subsection{The Equations of Motion}\n\nCan our proposed Lagrangian density reproduce all the equations of motion of\nperfect MHD flow ? We have already seen that it does reproduce\nEqs.~(\\ref{continu}-\\ref{adiabatic0}) and (\\ref{ff}). Let us now vary\n$\\gamma$ to get\n\\begin{equation}\n\\label{le4}\nD\\lambda = 0,\n\\end{equation}\nso that $\\lambda$, like $\\gamma$, is conserved with the flow. Both this and\nEq.~(\\ref{Lin}) will be essential in demonstrating the existence of the new\nconserved circulation. Next we vary\n$s$; remembering that $(\\partial \\epsilon/ \\partial\ns)_\\rho$ is just the fluid's temperature $T$, we have\n\\begin{equation}\n\\label{le6}\nD\\eta=-T,\n\\end{equation}\nwhich establishes that $\\eta$ decreases along the flow. The next variation\nis one with respect to $\\rho$. Recalling that $(\\partial \\epsilon/ \\partial\n\\rho)_s=p/\\rho^2$, introducing the enthalpy per unit mass\n$w=\\epsilon+p/\\rho$, and using Eqs.~(\\ref{le4}-\\ref{le6}) we get\n\\begin{equation}\n\\label{le7}\nD\\phi=v^{2}/2-w+T- U.\n\\label{phi}\n\\end{equation}\n\nWhen we vary ${\\bf v}$ in the action we may take advantage of the identity\n$\\nabla\\cdot({\\bf A}\\times{\\bf B})={\\bf B}\\cdot\\nabla\\times {\\bf A}-{\\bf\nA}\\cdot\\nabla\\times {\\bf B}$ and Gauss' theorem to flip the curl operation\nfrom $\\delta{\\bf v}\\times {\\bf B}$ onto ${\\bf K}$. Then the identity ${\\bf\nA}\\cdot{\\bf B}\\times{\\bf C}=-{\\bf B}\\cdot{\\bf A}\\times{\\bf C}$ helps to\nshift the $\\delta{\\bf v}$ into the position of a factor in a scalar product.\nWe may then factor out the common $\\delta{\\bf v}$ and isolate the vector\nequation\n\\begin{eqnarray}\n\\label{le3}\n{\\bf v}&=&\\nabla \\phi +\\gamma \\nabla \\lambda +s\\nabla \\eta + {\\bf Q}\n\\\\\n\\label{me3}\n{\\bf Q} &\\equiv& {\\bf B}\\times{\\bf R}/\\rho.\n\\end{eqnarray}\nwhere $ {\\bf R}\\equiv \\nabla \\times {\\bf K}$. This is neither a solution for\n${\\bf v}$ ($\\lambda$ and $\\eta$ not known), nor an equation of motion (${\\bf\nv}$ appears undifferentiated). In the next subsection we show that this\nprescription for ${\\bf v}$ leads to the MHD Euler equation (\\ref{mag_euler}).\n\n\nExpression (\\ref{le3}) shows the importance of including Lin's field\n$\\gamma$. For suppose we consider an unmagnetized fluid in isentropic ($s=$\nconst.) flow. Without $\\gamma$ the expression for ${\\bf v}$ is a perfect\ngradient, which means the proposed Lagrangian density describes only\nirrotational flows, a small subset of all possible ones. It is well known\n\\cite{seliger,mittag} that this problem does not appear when one\ncouches the problem in Lagrangian coordinates because one gets then an\nequation, not for $ {\\bf v}$, but for the fluid's acceleration.\nLin's\\cite{lin} way out of this difficulty is to remember that\nthe initial coordinates of the fluid element are maintained throughout its\nflow. These coordinates ``label'' the element, and this can be interpreted\nas a triplet of constraints (one for each coordinate) of the form $\n\\lambda _i\\left( {\\partial b_i}/{\\partial t}+\\nabla b_i\\right), $ where\n${\\bf b}$ is the initial vector coordinate for the element in question.\nLundgren\\cite{lundgren} used this triplet form for the MHD case. It was\nlater shown (see for example\\cite{seliger}) that the triplet can be reduced\nto a single constraint with the help of Pfaff's theorem. One thus returns\nto form (\\ref{le1}) of the Lagrangian density and Eq.~(\\ref{le3}) for the\nfluid velocity. The vorticity is now (still excluding ${\\bf B}$)\n\\begin{equation}\n\\label{le13}\n{\\bf \\omega }=\\nabla \\times {\\bf v}= \\nabla \\gamma\n\\times \\nabla \\lambda +\\nabla s\\times \\nabla \\eta,\n\\end{equation}\nso we see that isentropic vortical flow is possible.\n\nIn the MHD case, the magnetic term in Eq.~(\\ref{le3}) contributes to the\nvorticity. Henyey\\cite{henyey}, who suggested a Lagrangian density similar\nto ours, occasionally dropped the Lin term in the MHD case. However, we shall\nretain the Lin term throughout. It might seem peculiar at first that adding a\nconstraint like Lin's permits the appearance of solutions (vortical) which\nwere forbidden before it was imposed. But we must remember that we add to the\nLagrangian not only a constraint, but also a new degree of freedom,\n$\\gamma({\\bf r},t)$, and it is natural that with more degrees of freedom the\nclass of allowed flows will expand.\n\nFinally, we vary ${\\bf B}$ in the action; by similar manipulation to those\nwhich gave Eq.~(\\ref{le3}) we get\n\\begin{equation}\n\\label{le8}\n\\partial_t{\\bf K}={\\bf v} \\times {\\bf R}\n-{\\bf B}/(4\\pi).\n\\end{equation}\nTaking the curl of this equation we get the more convenient one\n\\begin{equation}\n\\partial_t{\\bf R}=\\nabla \\times [ {\\bf v}\n\\times {\\bf R}-{\\bf B}/(4\\pi)]=\\nabla \\times ( {\\bf v}\\times {\\bf R})-{\\bf J}.\n\\label{dR}\n\\end{equation}\nHere ${\\bf J}= \\nabla \\times {\\bf B} / 4 \\pi $ is the\nelectric current density coming from Ampere's equation. Notice the similarity\nbetween Eq.~(\\ref{dR}) and~(\\ref{ff}). Eq.~(\\ref{dR}) says that\nthe rate of change of the flux of ${\\bf R}$ through the surface spanning a\nclosed curve carried with the flow equals minus the flux of the\nelectric current density through that curve.\n\n\\subsection{The MHD Euler equation}\n\nWe now show that the Lagrangian density (\\ref{le1}) yields the correct\nMHD Euler equation. We first operate with the convective derivative $D$ on\nEq.~(\\ref{le3}) remembering that $Ds=0$ and $D\\gamma=0$:\n\\begin{equation}\n\\label{me0}\nD{\\bf v}=D\\nabla\\phi+\\gamma D\\nabla\\lambda+sD\\nabla\\eta +D{\\bf Q}.\n\\end{equation}\nWe now use the identity\n\\begin{equation}\n\\label{me4}\nD\\nabla=\\nabla D - (\\nabla{\\bf v}) \\cdot \\nabla,\n\\end{equation}\nwhere in Cartesian coordinates\n\\begin{equation}\n\\label{tensor}\n[(\\nabla{\\bf v}) \\cdot \\nabla]_i \\equiv \\sum_j {\\partial v_j\\over \\partial\nx_i}{\\partial\\over\\partial x_j},\n\\label{grad_v}\n\\end{equation}\nin conjunction with Eqs.~(\\ref{le4}-\\ref{le7}) to transform Eq.~(\\ref{me0})\ninto\n\\begin{eqnarray}\nD{\\bf v}&=&\\nabla (v^{2}/2-w+Ts-U)-s\\nabla T\n-s(\\nabla{\\bf v})\\cdot \\nabla\\eta\n\\nonumber\n\\\\\n\\label{me5}\n&-&(\\nabla{\\bf v}) \\cdot \\nabla\\phi-\\gamma(\\nabla{\\bf v}) \\cdot\n\\nabla\\lambda + D{\\bf Q}.\n\\end{eqnarray}\n\nFrom the thermodynamic identity $dw = T ds + dp/\\rho$ we infer\n\\begin{equation}\n\\label{me7}\n-\\nabla w + T\\nabla s = -\\nabla p/\\rho,\n\\end{equation}\nand we also have $\\nabla v^2/2 =\n(\\nabla{\\bf v})\\cdot {\\bf v}$, where the meaning of the right hand side is\nclear by analogy with Eq.~(\\ref{grad_v}). Thus Eq.~(\\ref{me5}) turns into\n\\begin{equation}\nD{\\bf v} = -\\nabla p/\\rho -\\nabla U + (\\nabla{\\bf v})\\cdot({\\bf v} -\\nabla\n\\phi- s\\nabla \\eta -\\gamma\\nabla\\lambda) + D{\\bf Q}.\n\\label{semifinal}\n\\end{equation}\nFinally comparing with Eq.~(\\ref{le3}) we see that the last brackets stand\nfor ${\\bf Q}$ so that\n\\begin{equation}\nD{\\bf v} = -\\nabla p/\\rho -\\nabla U + (\\nabla{\\bf v})\\cdot{\\bf Q} + D{\\bf\nQ}.\n\\label{final}\n\\end{equation}\nThus, magnetic term aside, we have recovered the Euler equation\n(\\ref{mag_euler}).\n\nWe now go on to calculate the ${\\bf Q}$ dependent terms. We may rewrite\nthe equation of continuity (\\ref{continu}) as\n\\begin{equation}\n\\label{me9}\nD\\rho=-\\rho \\nabla \\cdot {\\bf v},\n\\end{equation}\nWith this, the Gauss law $\\nabla\\cdot{\\bf B}=0$ and the identity\n$\\nabla\\times({\\bf A}\\times{\\bf B})={\\bf B}\\cdot\\nabla{\\bf A}-{\\bf\nB}\\nabla\\cdot{\\bf A}-{\\bf A}\\cdot\\nabla{\\bf B}+{\\bf\nA}\\nabla\\cdot{\\bf B}$, Eq.~(\\ref{ff}) may be recast in the well known form\n\\begin{equation}\n\\label{Btransport}\nD({\\bf B}/\\rho)=\\left(({\\bf B}/\\rho)\\cdot\\nabla\\right) {\\bf v}.\n\\end{equation}\nAnalogously, because $\\nabla\\cdot{\\bf R}=0$, Eq.~(\\ref{dR}) may be put in\nthe form\n\\begin{equation}\n\\label{Rtransport}\nD{\\bf R}=({\\bf R}\\cdot\\nabla) {\\bf v}-{\\bf R}\\nabla\\cdot{\\bf v}-{\\bf J}.\n\\end{equation}\nTherefore,\n\\begin{eqnarray}\n\\nonumber\n(\\nabla{\\bf v})\\cdot{\\bf Q} + D{\\bf\nQ}&=& -(\\nabla{\\bf v})\\cdot({\\bf R}\\times{\\bf B}/\\rho) -D{\\bf R}\\times{\\bf\nB}/\\rho-{\\bf R}\\times D({\\bf B}/\\rho)\n\\\\\n&=& -(\\nabla{\\bf v})\\cdot({\\bf R}\\times{\\bf B}/\\rho) -\\left(({\\bf\nR}\\cdot\\nabla){\\bf v}\\right)\\times({\\bf B}/\\rho)\n\\nonumber\n\\\\\n&+& (\\nabla\\cdot{\\bf v}){\\bf\nR}\\times({\\bf B}/\\rho) -{\\bf R}\\times\\left(({\\bf\nB}/\\rho)\\cdot\\nabla\\right){\\bf v}+{\\bf J}\\times{\\bf B}/\\rho.\n\\label{distrib}\n\\end{eqnarray}\n\nThe four terms in the second version of Eq.~(\\ref{distrib}) involving\nderivatives of ${\\bf v}$ can be shown to cancel out by\nexpanding them out in Cartesian coordinates. Hence, Eq.~(\\ref{final}) is the\nmagnetic Euler equation with the usual Lorentz force per unit mass, ${\\bf\nJ}\\times{\\bf B}/\\rho$, in addition to the pure fluid terms. The fact that we\nobtain the correct MHD equations (\\ref{continu}-\\ref{adiabatic0}), (\\ref{ff})\nand (\\ref{mag_euler}) is testament to the correctness of our proposed\nLagrangian density Eq.~(\\ref{le1}). Note that Lin's field $\\gamma$ has\ndisappeared from the final equation of motion.\n\n\\subsection{Circulation Conservation Law}\n\\label{circ}\n\nWith the help of the above formalism, we can now prove the existence of\na generalization of Kelvin's circulation theorem applicable to perfect MHD. \nLet us calculate the line integral of the vector\n\\begin{equation}\n\\label{mke1}\n{\\bf Z}={\\bf v}+{\\bf R}\\times{\\bf B}/\\rho\n\\end{equation}\nalong a closed curve $ {\\cal C} $ drifting with the fluid:\n\\begin{equation}\n\\label{mke2}\n\\Gamma =\\oint _{{\\cal C}}{\\bf Z}\\cdot d {\\bf r}.\n\\end{equation}\nAccording to Eq.~(\\ref{le3}) this integral is\n\\begin{equation}\n\\label{mke3}\n\\Gamma =\\oint_{{\\cal C}}\\nabla \\phi\\cdot d {\\bf r} +\\oint _{{\\cal\nC}}\\gamma \\nabla \\lambda \\cdot d {\\bf r}+\n\\oint _{{\\cal C}}s\\nabla \\eta\\cdot d {\\bf r}.\n\\end{equation}\nThe term involving $\\phi$ obviously vanishes (we assume all the Lagrange\nmultipliers are single valued). For like reason so does the term involving\n$\\eta$ in the isentropic ($s=$ const ) case as\n$s$ can be taken out of the integral. The\nmiddle integral can be written $\\oint_{{\\cal C}}\\gamma\\,d\\lambda$,\nwhere $d\\lambda\\equiv \\nabla\\lambda\\cdot d{\\bf r}$. But\nEqs.~(\\ref{Lin}-\\ref{le4}) tell us that both\n$\\gamma$ and $\\lambda$ are conserved along the flow. Hence $\\Gamma$ remains\nconstant as ${\\cal C}$ drifts along with the flow. Since in the limit\n${\\bf B}\\rightarrow 0$, $\\Gamma$ becomes Kelvin's circulation, we\nhave found an extension of Kelvin's theorem to perfect MHD. Obviously\nthe conservation of $\\Gamma$ implies the conservation of the flux of $\\nabla\n\\times {\\bf Z} $ through ${\\cal C}$.\n\nThe vector field ${\\bf R}$ is not unique for a given physical situation. For\nexample, the change ${\\bf R}\\rightarrow {\\bf R}+ k {\\bf B}$ ($k$ a real\nconstant) leaves invariant all equations of motion,\nEqs.~(\\ref{Lin}-\\ref{me3}), (\\ref{dR}), and (\\ref{final}), as well as the\nconserved circulation expressions (\\ref{mke1}-\\ref{mke2}). In addition, \nsuppose that at time\n$t=0$ we define an arbitrary solenoidal (divergence--free) field\n${\\bf b}$ all over the flow, and then evolve it in time as a passive\nvector, i.e., in accordance with the frozen--in field equation (\\ref{ff}). \nComparing with Eq.~(\\ref{dR}) we see that ${\\bf R}+k{\\bf b}$ and ${\\bf R}$\nobey the same equation, and both are permanently solenoidal [this property is\nobviously preserved by Eqs.~(\\ref{ff}) and (\\ref{dR}) in the MHD\napproximation]. \n\nIf in ${\\bf Z}$ we use ${\\bf R}+k {\\bf\nb}$ in lieu of ${\\bf R}$ to construct the conserved circulation, $\\Gamma$\ngets the additional contribution\n\\begin{equation}\n\\Delta\\Gamma=k\\oint _{\\cal C}\\left({\\bf b}\\times {\\bf\nB}/\\rho\\right)\n\\cdot d {\\bf r} =k \\oint _{{\\cal C}} {\\bf B}\\cdot \\left(d{\\bf r}\\times{\\bf\nb/\\rho}\\right)\n\\label{DGamma}\n\\end{equation}\nHere we have used a well known vector identity. Now by analogy with ${\\bf\nB}$, ${\\bf b}$ obeys Eq.~(\\ref{Btransport}) which tells us that any two\nelements of the fluid permanently lie on one and the same line of ${\\bf\nb}/\\rho$, and their distance, if small, is proportional to $|{\\bf\nb}|/\\rho$\\cite{LL}. We can always make ${\\bf b}$ small. Then $d{\\bf\nr}\\times{\\bf b/\\rho}$ is a vectorial element of area of a narrow closed\nstrip carried along by the fluid, one of whose edges coincides with ${\\cal\nC}$. The integral in Eq.~(\\ref{DGamma}) is just the flux of magnetic\ninduction through this strip (not through the space bounded by the strip),\nand we know this is conserved by virtue of Alfven's law. \n\nThus with the change ${\\bf R}\\rightarrow {\\bf R}+k{\\bf b}$\nwe added some conserved magnetic flux to $\\Gamma$, and did not get a new\nconserved circulation. The MHD flow $\\{ {\\bf B}, {\\bf v}, \\rho, p\\}$ is\nevidently unchanged because the MHD Euler equation (\\ref{mag_euler}) does\nnot contain ${\\bf R}$, so we must conclude that in the expression for ${\\bf\nv}$, Eq.~(\\ref{le3}-\\ref{me3}), the change of the ${\\bf Q}$ term\nmust be compensated by suitable changes in the Lagrange multipliers\n$\\phi+s\\eta$ and $\\lambda$ (recall that we are working with $s={\\rm\nconst.}$). Indeed, the initial choice of ${\\bf b}$ involves a choice of two\nfunctions because of the $\\nabla\\cdot{\\bf b}=0$ constraint, so that the two\nfunctions $\\phi+s\\eta$ and $\\lambda$ are just enough to absorb the change\n${\\bf R}\\rightarrow {\\bf R}+k {\\bf b}$ thus\ngenerated and leave ${\\bf v}$ unchanged. It is not possible to eliminate\n${\\bf R}$ altogether by the change ${\\bf R}\\rightarrow {\\bf R}+k {\\bf b}$\nbecause ${\\bf R}$ and ${\\bf b}$ obey different equations. This means the\ncirculation conservation law we have found cannot be reduced to an Alfven\ntype law; it is a new law. \n\nIn Sec.\\ref{last_sec} we shall discuss the freedom inherent in\n${\\bf R}$ by a covariant procedure. Fixing the freedom is a necessary\nstep in any attempt to exhibit explicitly the conserved circulation.\n\n\\subsection{Examples}\n\nFirst consider a situation where the fluid is isentropic but not flowing:\n${\\bf v}=0$. It follows from Eq.~(\\ref{continu}) that $\\rho=\\rho_0({\\bf r})$, \nand from Eq.~(\\ref{ff}) that ${\\bf B} = {\\bf B}_0({\\bf r})$. From these facts\nand Eq.~(\\ref{dR}) we see that\n\\begin{equation}\n{\\bf R}=-t\\ \\nabla\\times{\\bf B}_0({\\bf r})/(4\\pi)+ {\\bf R}_0({\\bf r}).\n\\end{equation}\nAlthough the physical quantities are stationary, ${\\bf R}$ is not. This is\nso because like the electromagnetic potential, ${\\bf R}$ is not a measurable\nquantity, being subject to ``gauge changes'' ${\\bf R}\\rightarrow {\\bf R}+{\\bf\nb}$ as already discussed. According to Eq.~(\\ref{mke1}) the conserved\ncirculation (around a contour fixed in space because ${\\bf v}=0$) should be\n\\begin{equation}\n\\Gamma= -t\\oint _{{\\cal C}} {(\\nabla\\times{\\bf B}_0)\\times{\\bf B}_0\\over\n4\\pi\\rho_0}\\cdot d{\\bf r} +\n\\oint _{{\\cal C}} {{\\bf R}_0\\times {\\bf B}_0\\over 4\\pi\\rho_0}\\cdot d{\\bf r}.\n\\end{equation}\nOn the face of it, the time dependence of the first term in this\nsimple situation puts the claimed circulation conservation law in jeopardy.\nHowever, according to the magnetic Euler equation (\\ref{mag_euler}), the\nfirst integrand here is equal to $\\nabla U+\\nabla p/\\rho_0$ which, by\nvirtue of Eq.~(\\ref{me4}) and the isentropic nature of the fluid, is a\nperfect gradient (for isentropic flow $\\nabla p / \\rho_0 = \\nabla w $). Hence\nthe first integral vanishes, and the circulation is indeed time independent as\nrequired by our theorem.\n\nAs a second example consider an axisymmetric differentially\nrotating fluid exhibiting a purely poloidal magnetic field. Let the\nflow also be isentropic and stationary. We choose to work in\ncylindrical coordinates $\\{\\varrho,\\phi,z\\}$; the hat symbol will denote a\nunit vector in the stated direction. It then follows that\n$\\rho=\\rho_0({\\bf r})$, ${\\bf B} = {\\bf B}_0({\\bf r})$ and ${\\bf\n v}=\\Omega \\varrho \\hat{\\phi}$, where $\\Omega (\\varrho,z)$ is the angular\nvelocity of the fluid. It is well known \\cite{chandra,mestel}\nthat for axisymmetric fields the curl of a poloidal field is a toroidal\none, and the toroidal field has only a $\\hat{\\phi}$ component. Therefore, the\nelectric current density ${\\bf J} = \\nabla \\times {\\bf B}/(4 \\pi)$, is\neverywhere collinear with ${\\bf v}$ and time independent. Since the\nproblem is stationary, $\\Omega$ satisfies Ferraro's \\cite{ferraro,mestel} law \nof isorotation ${{\\bf B} \\cdot \\nabla \\Omega = 0}$. In addition the\nfield must be torque-free \\cite{mestel} i.e. no Lorentz force in the\n$\\hat{\\phi}$ direction. This condition is identically satisfied for a purely\npoloidal field. Combining all of the above we get the following solution of\nEq.~(\\ref{dR}):\n\\begin{equation}\n\\label{ex_1}\n{\\bf R}=-t {\\bf J}\n\\end{equation}\n\nAccording to Eq.~(\\ref{mke1}) the conserved circulation should be\n\\begin{equation}\n\\label{ex_2}\n\\Gamma= \\oint _{{\\cal C}} \\Omega\n\\varrho^2 d \\phi -t\\oint _{{\\cal C}} \n{{\\bf J} \\times{\\bf B}_0\\over\n4\\pi\\rho_0}\\cdot d{\\bf r}\n\\end{equation}\nwhere we have exploited the axisymmetry to rewrite the first term.\nWe now verify that this circulation is indeed conserved. Because of the\ndifferential rotation, the contour ${\\cal C}$ is gradually deformed in the\nazimuthal direction. The difference $d \\phi$ in the azimuthal\ncoordinates between two infinitesimally close fluid elements lying on\n$\\cal C$ can be written as\n$d\\phi = d\\phi_0 + t\\, d\\Omega$ where $d\\phi_0$ is the initial difference\nin azimuthal coordinates while $d \\Omega $ is the difference between the\nelements' angular velocities. Hence we have\n\\begin{equation}\n\\label{ex_4}\n\\oint _{{\\cal C}} \\Omega\n\\varrho^2 d \\phi = \\oint _{{\\cal C}} \\Omega\n\\varrho^2 d \\phi_0 +t\\oint _{{\\cal C}} \\Omega\n\\varrho^2 d \\Omega.\n\\end{equation}\nNote that the first term is time independent while the second one is linear in\ntime. \n\nThe magnetic Euler equation (\\ref{mag_euler}) in cylindrical coordinate reads\n\\begin{equation}\n\\label{ex_5}\n-{\\Omega ^ 2}\\varrho \\hat \\varrho = -{\\nabla p \\over \\rho_0} - \\nabla U + \n{{\\bf J}\n \\times\n {\\bf B}_0 \\over 4 \\pi \\rho_0}.\n\\end{equation}\nAgain, by the isentropic condition we can write $\\nabla p/\\rho_0 =\\nabla w$. \nTaking the integral round $\\cal C$ of both sides of Eq.~(\\ref{ex_5}) we have\n\\begin{equation}\n\\label{ex_6}\n -\\oint_{{\\cal C}} {\\Omega ^ 2}\\varrho d\\varrho =\\oint _{{\\cal C}} {{\\bf J}\n\\times{\\bf B}_0\\over\n 4\\pi\\rho_0}\\cdot d{\\bf r}.\n\\end{equation}\nSubstituting from Eq.~(\\ref{ex_6}) and Eq.~(\\ref{ex_4}) into Eq.~(\\ref{ex_2})\nwe get\n\\begin{eqnarray}\n\\label{ex_gamma}\n\\Gamma &=& \\oint _{{\\cal C}} \\Omega \\varrho^2 d \\phi_0 + t\\oint _{{\\cal C}}\n\\Omega \\varrho^2 d \\Omega + t \\oint_{{\\cal C}} {\\Omega ^2}\\varrho d\\varrho\n\\nonumber\n\\\\\n&=& \\oint _{{\\cal C}} \\Omega \\varrho^2 d \\phi_0 +{t \\over 2} \\oint _{{\\cal C}}\nd(\\Omega^2 \\varrho^2)\n = \\oint _{{\\cal C}} \\Omega \\varrho^2 d \\phi_0 ,\n\\end{eqnarray}\nand $\\Gamma$ is indeed time independent.\nNote that it is possible to add to ${\\bf R}$ in Eq.~(\\ref{ex_1}) an arbitrary\ntime independent solenoidal vector field ${\\bf R}_0({\\bf r})$ which satisfies\n${\\bf R}_0 \\times {\\bf v} = \\nabla \\chi $. However, as already stressed in the\nprevious subsection, this will only add to $\\Gamma$ a time independent\nquantity.\n\nIt is important to note that although the example specifically relates\nto an axisymmetric problem, Eq.~(\\ref{ex_1}) applies to all stationary MHD \nflows which have ${\\bf J}$ collinear with ${\\bf v}$. Accordingly,\n$\\Gamma$ will be conserved in all such flows.\n\n\n\n\\section{Relativistic Variational principle}\n\nIn this section we formulate a Lagrangian density for MHD flow\nin the framework of general relativity (GR). \nGreek indices run from 0 to 3. The coordinates are denoted\n$x^\\alpha=\\left(x^0,x^1,x^2,x^3\\right)$; $x^0$ stands for time. A comma\ndenotes the usual partial derivative; a semicolon covariant\ndifferentiation. Our signature is $\\{-,+,+,+\\}$. We continue to take $c=1$.\n\n\\subsection{Relativistic MHD Equations}\nThe general relativistic (GR) equations for MHD were formulated by\nLichnerowicz\\cite{lichnerowicz}, Novikov and Thorne\\cite{novikov},\nCarter\\cite{carter1}, Bekenstein and Oron\\cite{bekenstein1} and others. The\nrole of the mass conservation equation (\\ref{continu}) is taken over by\nthe law of particle number conservation,\n\\begin{equation}\n\\label{gr4}\nN^\\alpha{}_{;\\alpha }=\\left( nu^{\\alpha }\\right) _{;\\alpha }=0,\n\\end{equation}\nwhere $N^\\alpha$ is the particle number 4--current density, $n$ the particle\nproper number density and $u^\\alpha$ the fluid 4--velocity field normalized by\n$u^\\alpha u_\\alpha=-1$. If $s$ represents the entropy per particle (not per\nunit mass as in Sec.~II), then the assumption of ideal adiabatic flow,\nEq.~(\\ref{adiabatic0}), can be put in the form\n\\begin{equation}\n\\label{gr_entropy}\n\\left( sN^{\\alpha }\\right) _{;\\alpha }=0\\qquad {\\rm or} \\qquad u^\\alpha\ns_{,\\alpha}=0.\n\\end{equation}\n\nBecause the flow is assumed adiabatic, the energy momentum tensor for the\nmagnetized fluid is that of an ideal fluid augmented by the electromagnetic\nenergy--momentum tensor:\n\\begin{equation}\n\\label{gr5}\nT^{\\alpha \\beta }=pg^{\\alpha \\beta }+\\left( p+\\rho \\right) u^{\\alpha }\nu^{\\beta }+ (F^{\\alpha\\gamma} F^\\beta{}_\\gamma - {\\scriptstyle 1\\over\n\\scriptstyle 4} F^{\\gamma\\delta} F_{\\gamma\\delta}\\, g^{\\alpha\\beta})/(4\\pi).\n\\end{equation}\nHere $\\rho$ represents the fluid's energy proper density (including rest\nmasses) and $p$ the scalar pressure (again assumed isotropic), while\n$F^{\\alpha\\beta}$ denotes the electromagnetic field tensor. As usual the\ncovariant divergence\n$T^{\\alpha \\beta }{}_{;\\beta}$ must vanish (energy--momentum conservation). In\nconsequence\n$T^{\\alpha \\beta}{}_{;\\beta} +u^\\alpha u_\\gamma T^{\\gamma \\beta\n}{}_{;\\beta} = 0 $ which can be recast as\n\\begin{equation}\n\\label{em_conservation}\n(\\rho+p)u^\\beta u^\\alpha{}_{;\\beta} = - (g^{\\alpha\\beta}+u^\\alpha\nu^\\beta)p_{,\\beta} + F^{\\alpha\\beta} F_{\\beta}{}^\\gamma{}_{;\\gamma}/(4\\pi).\n\\end{equation}\nThe term $a^\\alpha\\equiv u^\\beta u^\\alpha{}_{;\\beta}$ stands for the fluid's\nacceleration 4--vector. The effects of gravitation are automatically\nincluded by the appeal to curved metric and covariant derivatives. This\nequation parallels Eq.~(\\ref{mag_euler});as usual in GR the\npressure contributes alongside the energy density to the inertia. The\nelectromagnetic field tensor is subject to Maxwell's equations\n\\begin{eqnarray}\n\\label{Maxwell1}\nF^{\\alpha\\beta}{}_{;\\beta} &=& 4\\pi j^\\alpha\n\\\\\n F_{\\alpha\\beta,\\gamma} +\nF_{\\beta\\gamma,\\alpha}+F_{\\gamma\\alpha,\\beta} &=& 0.\n\\label{Maxwell2}\n\\end{eqnarray}\nwhere $j^\\alpha$ denotes the electric 4--current density.\nPutting all this together we have the GR MHD Euler equation\n\\begin{equation}\n\\label{grmag_euler}\n(\\rho+p)a^\\alpha = - h^{\\alpha\\beta} p_{,\\beta} +\nF^{\\alpha\\beta} j_\\beta,\n\\end{equation}\nwhere we have introduced the projection tensor\n\\begin{equation}\n\\label{h}\n h^{\\alpha\\beta}\\equiv g^{\\alpha\\beta} + u^\\alpha u^\\beta.\n\\end{equation}\n\nThe above equations do not completely specify MHD flow (as opposed to flow\nof a generic magnetofluid). For any flow carrying an electromagnetic field,\nthe (antisymmetric) Faraday tensor $F_{\\alpha \\beta }$ may be split into\nelectric and magnetic vectors with respect to the flow:\n\\begin{eqnarray}\n\\label{gr1}\nE_{\\alpha }&=&F_{\\alpha \\beta }u^{\\beta }\n\\\\\n\\label{gr2}\nB_{\\alpha }&=&{}^*F_{\\beta\\alpha}u^\\beta\\equiv {\\scriptstyle\n1\\over\\scriptstyle 2}\\epsilon_{\\beta\\alpha\n\\gamma \\delta }\\,F^{\\gamma \\delta } u^{\\beta }.\n\\end{eqnarray}\nHere $ \\epsilon _{\\alpha \\beta \\gamma \\delta } $ is the\nLevi-Civita totally antisymmetric tensor ($\\epsilon_{0123}=(-g)^{1/2}$ with\n$g$ denoting the determinant of the metric $g_{\\alpha\\beta}$) and\n${}^*F_{\\alpha\\beta}$ is the dual of $F_{\\alpha\\beta}$. In the frame moving\nwith the fluid, these 4--vectors have only spatial parts which correspond to\nthe usual ${\\bf E}$ and ${\\bf B}$, respectively. The inversion of\nEqs.~(\\ref{gr1}-{\\ref{gr2}) is\n\\begin{equation}\nF_{\\alpha\\beta}=u_\\alpha E_\\beta - u_\\beta E_\\alpha\n+\\epsilon_{\\alpha\\beta\\gamma\\delta}u^\\gamma B^\\delta\n\\label{inversion}\n\\end{equation} \nFor an infinitely conducting (perfect\nMHD) fluid, the electric field in the fluid's frame must vanish, i.e., \n\\begin{equation}\n\\label{gr3}\nE_{\\alpha }=F_{\\alpha \\beta } u^\\beta = 0.\n\\label{freeze}\n\\end{equation}\nThis corresponds to the usual MHD condition ${\\bf E} + {\\bf v} \\times {\\bf\nB}=0$.\n\n\\subsection{Relativistic Lagrangian Density }\n\\label{rel_lagrangian}\n\nInspired by Schutz's\\cite{schutz} Lagrangian density for\npure fluids in GR, we now propose a Lagrangian density for GR MHD\nflow which reproduces Eqs.~(\\ref{gr4}-\\ref{gr_entropy}),\n(\\ref{Maxwell1}-\\ref{grmag_euler}) and (\\ref{gr3}). Like Schutz we include\nLin's term, which proves essential to our subsequent proof of the existence\nof a circulation theorem. The proposed Lagrangian density is\n\\begin{equation}\n\\label{rl_1}\n{\\cal L}=-\\rho(n,s) -F_{\\alpha \\beta }F^{\\alpha \\beta }/(16\\pi)+\n\\phi N^{\\alpha }{}_{;\\alpha }+\\eta \\left( sN^{\\alpha }\\right) _{;\\alpha\n}+\\lambda \\left( \\gamma N^{\\alpha }\\right) _{;\\alpha }+\\tau^{\\alpha\n}F_{\\alpha\\beta }N^{\\beta }.\n\\label{Lagrangian}\n\\end{equation}\nNow in GR the scalar density ${\\cal L}\\,(-g)^{1/2}$ replaces ${\\cal L}$\nin the action (\\ref{action}), and is what enters in the Euler--Lagrange\nequations (\\ref{EL}). The covariant derivatives cause no problem; for\nexample $(-g)^{1/2}\\phi N^\\alpha{}_{;\\alpha}\n=\\phi[(-g)^{1/2}N^\\alpha]_{,\\alpha}$, whose variation with respect to\n$N^\\alpha$ is easily integrated by parts.\n\nAs in the nonrelativistic case, $\\phi $ is the Lagrange multiplier\nassociated with the conservation of particle number constraint,\nEq.~(\\ref{gr4}), $\n\\eta $ is that multiplier associated with the adiabatic flow constraint,\nEq.~(\\ref{gr_entropy}), and $\\lambda $ is that associated with the\nconservation along the flow of Lin's quantity $\\gamma$. We view $\\gamma$,\n$N^\\alpha$ and $s$ as the independent fluid variables, while $n$ and\n$u^\\alpha$ are determined by the obvious relations\n\\begin{equation}\n\\label{grem0}\n-N^{\\alpha }N_{\\alpha }=n^2; \\qquad u^\\alpha = n^{-1}\\,N^\\alpha.\n\\end{equation}\nStrictly speaking, one should include in ${\\cal L}$ a new Lagrange\nmultiplier times the constrained expression $N^{\\alpha }N_{\\alpha }+n^2$.\nRather than clutter up ${\\cal L}$ further, we enforce this constraint\nbelow by hand. \n\nAs usual, we view the vector potential $A_\\alpha$, rather than the\nelectromagnetic field tensor $F_{\\alpha\\beta} = A_{\\beta;\\alpha} -\nA_{\\alpha;\\beta} = A_{\\beta,\\alpha} -A_{\\alpha,\\beta}$, as the independent\nelectromagnetic variable. In consequence, the Maxwell Eqs.~(\\ref{Maxwell2})\nare satisfied as identities. The last term in ${\\cal L}$ enforces the\n``vanishing of electric field'' constraint, Eq.~(\\ref{gr3}); $ \\tau^{\\alpha }\n$ is a Lagrange multiplier 4--vector field. Because here we enforce the\n``vanishing of electric field'' rather than the equivalent flux freezing\ncondition (\\ref{ff}), the $\\tau^\\alpha$ is more like ${\\bf R}$ of Sec.~II.B.\nthan like ${\\bf K}$. Not all of $\\tau^\\alpha$ is physically meaningful. For\nsuppose we add an arbitrary function $f(x^\\beta)$ multiplied by $N^\\alpha$ to\n$\\tau^\\alpha$. This increments the Lagrangian density by $f\nN^\\alpha F_{\\alpha\\beta} N^\\beta$ which vanishes identically by the\nantisymmetry of $F_{\\alpha\\beta}$. So $\\tau^\\alpha$ and $\\tau^\\alpha+f\nN^\\alpha$ are physically equivalent. We shall exploit this to substract from\n$\\tau^\\alpha$ its component along $u^\\alpha$. So henceforth we may take it\nthat $\\tau^\\alpha u_\\alpha=0$. \n\nMuch freedom is still left in $\\tau^\\alpha$. Suppose we add\nto it a term proportional to $n^{-1}\\,B^\\alpha$. By\nEqs.~(\\ref{gr1}-\\ref{inversion}), this adds to the Lagrangian density the\nterm $ E_\\alpha B^\\alpha$. Of course we cannot take this to\nvanish at the Lagrangian's level because we have not yet obtained the\nfreezing-in condition (\\ref{freeze}) from it. However, it is known that\n$B^\\alpha E_\\alpha={\\scriptstyle 1\\over\\scriptstyle\n4}\\epsilon^{\\alpha\\beta\\gamma\\delta} F_{\\alpha\\beta} F_{\\gamma\\delta}$. By\nintroducing the potential $A_\\alpha$ we can write this as $ {\\scriptstyle\n1\\over\\scriptstyle 2}\\left[\\epsilon^{\\alpha\\beta\\gamma\\delta} F_{\\alpha\\beta}\nA_{\\gamma}\\right]_{;\\delta} - {\\scriptstyle 1\\over\\scriptstyle\n2}\\epsilon^{\\alpha\\beta\\gamma\\delta} F_{\\alpha\\beta;\\delta} A_\\gamma$,\nwhere we have used the fact that\n$\\epsilon^{\\alpha\\beta\\gamma\\delta}$ has vanishing covariant derivatives. \nObviously the last term vanishes by virtue of Maxwell's equations\n(\\ref{Maxwell2}) which are identities in the present approach. When\nmultiplied by $(-g)^{1/2}$, the first term becomes a perfect\nderivative. Such term, when added to the integral forming the Lagrangian,\nis known not to affect its physical content. Thus $\\tau^\\alpha$ and\n$\\tau^\\alpha+{\\rm const.}\\hskip-3pt\\times n^{-1}\\,B^\\alpha$ are physically\nequivalent, and this transformation respects the condition $\\tau_\\alpha\nu^\\alpha=0$ because $B_\\alpha u^\\alpha=0$ [see (\\ref{gr2})]. However,\nthere is not enough freedom in the constant to allow us to eliminate the\ncomponent of $\\tau^\\alpha$ along $B^\\alpha$. But in Sec.\\ref{last_sec} we\nshall exploit what we have just found. \n\n\\subsection{Equations of Motion}\n\nWe can now derive the equations of motion. Variation of $\\phi$\nrecovers the conservation of particles $N^\\alpha{}_{;\\alpha}$. Variation of\n$\\lambda$ with subsequent use of the previous result yields\n\\begin{equation}\n\\gamma_{,\\alpha }u^{\\alpha }=0.\n\\label{gr_lambda}\n\\end{equation}\nIf we vary $ \\gamma $ we get\n\\begin{equation}\n\\lambda_{,\\alpha }u^{\\alpha }=0.\n\\label{gr_gamma}\n\\end{equation}\nThese two results are precise analogs of Eqs.~(\\ref{Lin}) and (\\ref{le4});\nthey inform us that $\\gamma$ and $\\lambda$ are both locally conserved with\nthe flow. In view of the thermodynamic relation\n$n^{-1}(\\partial \\rho/\\partial s)_n = T$, with $T$ the locally\nmeasured fluid temperature, variation of\n$s$ gives\n\\begin{equation}\nu^{\\alpha }\\eta _{,\\alpha }=-T;\n\\label{gr_s}\n\\end{equation}\nthis is the analogue of Eq.~(\\ref{le6}).\n\nWe now vary $N^\\alpha$ using the obvious consequence of Eq.~(\\ref{grem0}),\n\\begin{equation}\n\\label{grem2}\n\\delta n=-u_{\\alpha }\\delta N^{\\alpha },\n\\end{equation}\ntogether with the thermodynamic relation\\cite{novikov} involving the\nspecific enthalpy $\\mu$,\n\\begin{equation}\n\\label{gr_mu1}\n\\mu \\equiv (\\partial\\rho/\\partial n)_s =n^{-1}\\,(\\rho +p);\n\\end{equation}\nwe get the GR analog of Eq.~(\\ref{le3}),\n\\begin{equation}\n\\mu u_{\\alpha }=\\phi _{,\\alpha }+s\\eta _{,\\alpha }+\\gamma\n\\lambda _{,\\alpha }+\n\\tau^{\\beta }F_{\\alpha\\beta }.\n\\label{gr_varu}\n\\end{equation}\nThe importance of Lin's $\\gamma$ is again clear here; in the pure\nisentropic fluid case ($F^{\\alpha\\beta}=0$ and $s=$ const.), the\nKhalatnikov vorticity tensor given by\n\\begin{equation}\n\\label{gr_vor2}\n\\omega _{\\alpha \\beta }=\\left( \\mu u_{\\beta }\\right) _{,\\alpha }-\n\\left( \\mu u_{\\alpha }\\right) _{,\\beta }\n=\\left( \\gamma \\lambda _{,\\beta }\\right) _{,\\alpha }-\n\\left( \\gamma \\lambda _{,\\alpha }\\right) _{,\\beta }\n\\end{equation}\nwould vanish in the absence of $\\gamma$, thus constraining us to discuss\nonly irrotational flow.\n\nBy contracting Eq.~(\\ref{gr_varu}) with $u^\\alpha$ and using $u_\\alpha\nu^\\alpha=-1$ as well as Eqs.~(\\ref{gr3}) and\n(\\ref{gr_gamma}-{\\ref{gr_s}), we get the following GR version of\nEq.~(\\ref{le7}):\n\\begin{equation}\n\\phi_{,\\alpha}u^\\alpha = - \\mu + Ts.\n\\label{gr_phi}\n\\end{equation}\nThus the proper time rate of change of $\\phi$ along the flow is just minus the\nspecific Gibbs energy or chemical potential. The apparent difference\nbetween the result here and Eq.~(\\ref{le7}) stems from the fact that proper\ntime rate (here) and coordinate time rate (there) differ by gravitational\nredshift and time dilation effects. These effects are not noticeable when\none compares Eqs.~(\\ref{gr_s}) with (\\ref{le6}) because the first refers to\nlocally measured temperature and the second to global temperature; these two\ntemperatures differ by the same factors as do proper and coordinate time.\n\nTurn now to the variation of $A_\\alpha$. Because of the antisymmetry of\n$F_{\\alpha\\beta}$, the last term of the Lagrangian, Eq.~(\\ref{rl_1}), can\nbe written as $(\\tau^\\beta N^\\alpha-\\tau^\\alpha N^\\beta)A_{\\alpha,\\beta}$.\nThe variation of $A_\\alpha$ in the corresponding term in the action\nproduces, after integration by parts, the term $\\big[(-g)^{1/2}(\\tau^\\alpha\nN^\\beta-\\tau^\\beta N^\\alpha)\\big]_{,\\beta}\\, \\delta A_\\alpha$. Because\nfor any antisymmetric tensor $t^{\\alpha\\beta}$,\n$(-g)^{1/2}t^{\\alpha\\beta}{}_{;\\beta} = [(-g)^{1/2}\nt^{\\alpha\\beta}]_{,\\beta}$, this finally leads to the equation\n\\begin{equation}\n\\label{gr_mag2}\nF^{\\alpha \\beta }{}_{;\\beta } =4\\pi\\left( \\tau^{\\alpha }N^{\\beta }\n- \\tau^{\\beta }N^{\\alpha }\\right) _{;\\beta }.\n\\label{tau}\n\\end{equation}\nComparison with Eq.~(\\ref{Maxwell1}) shows that this result gives us a\nrepresentation of the electric current density $j^\\alpha$ as the\ndivergence of the bivector $ \\tau^{\\alpha }N^{\\beta }- \\tau^{\\beta }\nN^{\\alpha}$. Such representation makes the conservation of charge\n($j^\\alpha{}_{;\\alpha}=0) $ an identity because the divergence of the\ndivergence of any antisymmetric tensor vanishes. This equation is the GR\nanalogue of Eq~(\\ref{dR}). Formally Eq.~(\\ref{tau}) determines the Lagrange \nmultiplier 4--vector $\\tau^\\alpha$, modulo the freedom inherent in it.\n\n \n\\subsection{MHD Euler Equation in General Relativity}\n\nOur central task now is to show that the equations in Sec.~III.C\nlead uniquely to the GR MHD Euler equation (\\ref{grmag_euler}). We begin by\nwriting the Khalatnikov vorticity $\\omega_{\\beta\\alpha}$ in two forms,\n\\begin{equation}\n\\omega_{\\beta\\alpha} = \\mu_{,\\beta} u_\\alpha - \\mu_{,\\alpha} u_\\beta\n +\\mu u_{\\alpha;\\beta} - \\mu u_{\\beta;\\alpha},\n\\end{equation}\nas well as by means of Eq.~(\\ref{gr_varu})\n\\begin{eqnarray}\n\\label{gr_mgel2}\n\\omega_{\\beta\\alpha} &=& s_{,\\beta }\\eta _{,\\alpha }-s_{,\\alpha }\\eta\n_{,\\beta}+\\gamma _{,\\beta }\\lambda _{,\\alpha }-\\gamma _{,\\alpha }\\lambda\n_{,\\beta }\n \\nonumber \\\\\n&+&\\tau^{\\delta }{}_{;\\beta }F_{\\alpha \\delta }-\\tau^{\\delta }{}_{;\\alpha\n}F_{\\beta\\delta }+\\tau^{\\delta }F_{\\alpha \\delta ;\\beta }-\\tau^{\\delta\n}F_{\\beta\n\\delta;\\alpha }.\n\\end{eqnarray}\nContracting the left hand side of the first with $ N^{\\alpha } $, recalling\nEq.~(\\ref{grem0}) and that by normalization $ u^{\\alpha }u_{\\alpha ;\\beta\n}=0 $ whereas $ u^{\\beta }u_{\\alpha ;\\beta }=a_\\alpha $, the fluid's\n4--acceleration, we get\n\\begin{equation}\n\\label{gr_mgel3}\n\\omega_{\\beta\\alpha} N^\\alpha =-n\\mu _{,\\beta }-n\\mu _{,\\alpha }u^{\\alpha\n}u_{\\beta }-n\\mu a_\\beta = -n h_\\beta{}^\\alpha\\mu_{,\\alpha} - n \\mu a_\\beta.\n\\end{equation}\n\nNow contracting Eq.~(\\ref{gr_mgel2}) with $ N^{\\alpha } $ and using\nEqs.~(\\ref{gr_lambda}-\\ref{gr_s}) and (\\ref{gr3}) to drop a number of terms\nwe get\n\\begin{equation}\n\\label{gr_mgel6}\n\\omega_{\\beta\\alpha} N^\\alpha =-nTs_{,\\beta }-\\tau^{\\delta }{}_{;\\alpha\n}F_{\\beta \\delta }N^{\\alpha }+\\tau^{\\delta }F_{\\alpha \\delta ;\\beta\n}N^{\\alpha}-\\tau^{\\delta }F_{\\beta \\delta ;\\alpha }N^{\\alpha }.\n\\end{equation}\nBy virtue of Eq.~(\\ref{gr_entropy}), $-nTs_{,\\beta}$ is the same as\n$-n T h_\\beta{}^\\alpha s_{,\\alpha}$. It is convenient to use\nthe thermodynamic identity $d\\mu =n^{-1}\\,dp+Tds$, which follows from\nEq.~(\\ref{gr_mu1}) and the first law $d(\\rho/n)= Tds -pd(1/n)$, to replace\nin Eq.~(\\ref{gr_mgel6}) $-nTs_{,\\beta}$ by\n$h_\\beta{}^\\alpha (-n\\mu_{,\\alpha}+p_{,\\alpha})$. Equating our two\nexpressions for $\\omega_{\\beta\\alpha} N^\\alpha$ gives, after a cancellation,\n\\begin{equation}\n\\label{gr_mgel9}\n-\\left( n\\mu a_{\\beta }+h_{\\beta }{}^{\\alpha }p_{,\\alpha }\\right) =\n-\\tau^{\\delta }{}_{;\\alpha }F_{\\beta \\delta }N^{\\alpha }+\\tau^{\\delta\n}F_{\\alpha\\delta ;\\beta }N^{\\alpha }-\\tau^{\\delta }F_{\\beta \\delta ;\\alpha\n}N^{\\alpha }.\n\\end{equation}\n\nThe last two terms in this equation can be combined into a single one by\nvirtue of Eq.~(\\ref{Maxwell2}), which, as well known, can be written with\ncovariant as well as ordinary derivatives. Further, by Eq.~(\\ref{gr_mu1})\nwe may replace\n$n\\mu$ by $\\rho+p$. In this manner we get\n\\begin{equation}\n\\left( \\rho +p\\right) a_{\\beta }=-h_{\\beta }{}^{\\alpha }p_{,\\alpha }+\nF_{\\beta \\alpha ;\\delta }\\tau^{\\delta }N^{\\alpha }+F_{\\beta \\delta\n}\\tau^{\\delta }{}_{;\\alpha}N^{\\alpha }.\n\\end{equation}\nThe term $ \\tau^{\\delta }{}_{;\\alpha }N^{\\alpha } $ here can be replaced by\ntwo others with help of Eq.~(\\ref{gr_mag2}) if we take into\naccount that $N^\\beta{}_{;\\beta}=0$:\n\\begin{equation}\n\\label{gr_mgel12}\n\\left( \\rho +p\\right) a_{\\beta }=-h_{\\beta }{}^{\\alpha }p_{,\\alpha }+\nF_{\\beta \\delta }F^{\\delta \\alpha }{}_{;\\alpha }/(4\\pi)+F_{\\beta \\alpha\n;\\delta }\\tau^{\\delta }N^{\\alpha }+F_{\\beta \\delta }\\left( \\tau^{\\alpha\n}N^{\\delta}\\right) _{;\\alpha }.\n\\end{equation}\nWe note that the last two terms on the right hand side combine into $\\left(\nF_{\\beta \\alpha }N^{\\alpha }\\tau^{\\delta }\\right) _{;\\delta }$ which\nvanishes by Eq.~(\\ref{gr3}). Now substituting from the\nMaxwell equations (\\ref{Maxwell1}) we arrive at the final equation\n\\begin{equation}\n\\label{gr_mgel15}\n\\left( \\rho +p\\right) a_{\\beta }=-h_{\\beta }{}^{\\alpha }p_{,\\alpha }+\nF_{\\beta \\delta }j^{\\delta },\n\\end{equation}\nwhich is the correct GR MHD Euler equation (\\ref{grmag_euler}). We have not\nused any information about $\\tau^\\alpha$ beyond Eq.~(\\ref{tau}); hence\nEuler's equation is valid for all choices of $\\tau^\\alpha$. Since we\nare able to obtain all equations of motion for GR MHD from our Lagrangian\ndensity, we may regard it as correct, and go on to look at some consequences.\n\n\\subsection{New Circulation Conservation Law}\n\\label{last_sec}\n\nEqs.~(\\ref{gr_varu}) and (\\ref{gr_lambda}-\\ref{gr_gamma}) allow us to\ngeneralize the conserved circulation of Sec.~II.D to relativistic perfect\nMHD. Let\n$ \\Gamma $ be the line integral\n\\begin{equation}\n\\label{gr_kel1}\n\\Gamma =\\oint_{{\\cal C}}z_{\\alpha }dx^{\\alpha },\n\\end{equation}\nwhere $ {\\cal C} $ is, again, a closed curve drifting with the fluid, and\n\\begin{equation}\n\\label{gr_kel2}\nz_\\alpha \\equiv {\\mu}u_{\\alpha }-\\tau^{\\beta }F_{\\alpha \\beta }.\n\\end{equation}\nAccording to Eq.~(\\ref{gr_varu}), $ z_{\\alpha }=\\phi _{,\\alpha }+s\\eta\n_{,\\alpha }+\\gamma \\lambda _{,\\alpha }$. Since $ \\phi _{,\\alpha } $ is a\ngradient, its contribution to $\\Gamma $ vanishes. Likewise, for isentropic\nflow ($ s=$ const.) the term involving $ s\\eta _{,\\alpha } $ makes no\ncontribution to $\\Gamma$. Thus\n\\begin{equation}\n\\label{gr_kel3}\n\\Gamma =\\oint_{{\\cal C}}\\gamma \\lambda_{,\\alpha} dx^\\alpha = \\oint_{{\\cal\nC}}\\gamma\\, d\\lambda.\n\\end{equation}\nBy Eqs.~(\\ref{gr_lambda}-\\ref{gr_gamma}) both $\\gamma$ and $ \\lambda$ are\nconserved with the flow. Thus $ \\Gamma $ is conserved along the flow. \nNote that by virtue of $\\gamma$'s presence, $\\Gamma$ need not vanish. \n\nIn the absence of electromagnetic fields and in the nonrelativistic limit\n$(\\mu\\rightarrow m$ where $m$ is a fluid particle's rest mass), $\\Gamma $\nfor a curve ${\\cal C}$ taken at constant time reduces to Kelvin's\ncirculation. On this ground our result can be considered a generalization\nof Kelvin's circulation theorem to general relativistic\nMHD. We have gone here beyond Oron's original result\\cite{bekenstein1} in\nthat no symmetry is necessary for the circulation to be conserved.\n\nTo manifestly exhibit the conserved circulation, one has to know\n$\\tau^\\alpha$ explicitly. The first step is to understand the\nfreedom left in $\\tau^\\alpha$ beyond that discussed in\nSec.~\\ref{rel_lagrangian}. The second is to determine\n$\\tau^\\alpha$ in a specific flow exploiting for this the symmetries and\nother information. Below we address the first step; the second is left\nmainly to future publications. \n\nGiven a specific MHD flow as background, let us at define a generic test field\n$f_{\\alpha\\beta}=-f_{\\beta\\alpha}$ which satisfies Maxwell's homogeneous\nequations (\\ref{Maxwell2}) as well as the freezing-in condition\n(\\ref{freeze}), e.g. $e_\\alpha \\equiv f_{\\alpha\\beta}u^\\beta=0$. We think\nof $f_{\\alpha\\beta}$ as very weak, so that it does not disturb the MHD flow\nor the spacetime geometry; it is a passive tensor. Because\n$f_{\\alpha\\beta}u^\\beta=0$, $f_{\\alpha\\beta}$ has only three independent\ncomponents. Therefore, its full content is reflected in the ``magnetic\n4-vector'' $b_{\\alpha}\\equiv{\\scriptstyle 1\\over\\scriptstyle\n2}\\epsilon_{\\beta\\alpha \\gamma \\delta }\\, f^{\\gamma \\delta }u^{\\beta }$,\nwhich is obviously orthogonal to $u_\\alpha$. The transformation\n$\\tau^\\alpha\\rightarrow \\tau^\\alpha +k n^{-1}\\,b^\\alpha$ ($k$ a real\nconstant) is not a symmetry of the Lagrangian. However, it does not disturb\nthe inhomogeneous Maxwell equations (\\ref{Maxwell1},\\ref{tau}). This is\nbecause the change in $\\tau^\\alpha$ merely adds to the electric current the\nterm $\\left( b^{\\alpha }u^{\\beta } - b^{\\beta }u^{\\alpha }\\right)_{;\\beta\n}=(-g)^{-1/2}\\left[ (-g)^{1/2} (b^{\\alpha }u^{\\beta } - b^{\\beta }u^{\\alpha\n})\\right]_{,\\beta }$. Because of the condition $e^\\alpha = 0$, we may easily\ninvert the analog of (\\ref{inversion}) to get $b^{\\alpha }u^{\\beta } -\nb^{\\beta }u^\\alpha = {\\scriptstyle 1\\over \\scriptstyle\n2}\\epsilon^{\\alpha\\beta\\gamma\\delta} f_{\\gamma\\delta}$. But since\n$(-g)^{1/2}\\epsilon^{\\alpha\\beta\\gamma\\delta}$ is just the constant\nantisymmetric symbol, our assumed equations $f_{\\alpha\\beta,\\gamma}\n+f_{\\gamma\\alpha,\\beta}+f_{\\beta\\gamma,\\alpha}=0$ imply that $\\left(\nb^{\\alpha }u^{\\beta } - b^{\\beta }u^{\\alpha }\\right)_{;\\beta}=0$ so that the\nMaxwell equations (\\ref{tau}) are invariant under $\\tau^\\alpha\\rightarrow\n\\tau^\\alpha +k n^{-1}\\,b^\\alpha$. So is the Euler\nequation since its derivation used only the information about\n$\\tau^\\alpha$ inherent in (\\ref{tau}). \n\nThe expression for $u_\\alpha$, (\\ref{gr_varu}), does seem to change under\n$\\tau^\\alpha\\rightarrow \\tau^\\alpha +k n^{-1}\\,b^\\alpha$, and we also note\nthat $\\Gamma\\rightarrow \\Gamma+k \\oint n^{-1}\\,b^\\beta F_{\\alpha\\beta}\\,\ndx^\\alpha$. Now since the ``magnetic 4-vector'' $b^\\alpha$ is frozen in,\nlike any such {\\it infinitesimal\\/} field, it evolves in such a way that\n$n^{-1}\\,b^\\alpha$ gives for all time that part of the spacetime separation\nof two neighboring fluid elements which is orthogonal to\n$u^\\alpha$\\cite{bekenstein1}, {\\it c.f.\\/} discussion after\nEq.~(\\ref{DGamma}). Thus\n$n^{-1}\\,b^\\alpha$ can be employed to define a thin closed strip dragged with\nthe fluid such that one of its edges coincides with the curve ${\\cal C}$. \nTherefore, the increment $\\oint n^{-1}\\,b^\\beta F_{\\alpha\\beta}\\, dx^\\alpha$\nis just the conserved magnetic flux through this strip. Evidently the\ntransformation $\\tau^\\alpha\\rightarrow \\tau^\\alpha +k n^{-1}\\,b^\\alpha$\nhas not changed the nature of the conservation law for $\\Gamma$, but only\nadded a trivially conserved quantity to it.. \n\nNow the MHD flow $\\{ B^\\alpha, u^\\alpha, n, \\rho, \\mu\\}$ is evidently\nunchanged because neither the MHD Euler equation (\\ref{em_conservation}) nor\nMaxwell's equations were changed, so we must conclude that in the expression\nfor $u^\\alpha$, Eq.~(\\ref{gr_varu}), the change of the $\\tau^\\beta\nF_{\\alpha\\beta}$ term must be compensated by suitable changes in the pair of\nLagrange multipliers $\\phi+s\\eta$ and $\\lambda$ (since we are assuming $s={\\rm\nconst.}$). They are capable of this because $b^\\alpha$ has only two\nindependent components. For the condition $b^\\alpha u_\\alpha=0$ eliminates\none of the four. In addition $b^\\alpha$ comes from $f_{\\alpha\\beta}$ which\nsatisfies Eqs.~(\\ref{Maxwell2}); in particular, $f_{12,3}+f_{31,2}+f_{23,1}=0$\nin the chosen coordinates. But since no time derivatives appear in it, this\nlast equation serves as an initial constraint on $b^\\alpha$ just as\nthe Gauss equation $\\nabla\\cdot{\\bf B}=0$ does for the true magnetic field. \nAccordingly, one further relation exists between components of $b^\\alpha$ so\nthat the generic $b^\\alpha$ contains only two free functions. Thus the\nchange in $\\tau^\\beta F_{\\alpha\\beta}$ can be taken up by changes in the two\nfunctions $\\phi+s\\eta$ and $\\lambda$ so that $\\mu u_\\alpha$ is unchanged. \n \nNote that it is not possible to ``get rid'' of $\\tau^\\alpha$ by means of\nthe transformation $\\tau^\\alpha\\rightarrow \\tau^\\alpha +k n^{-1}\\,b^\\alpha$ \nbecause, as we shall make clear presently, $\\tau^\\alpha$ and $b^\\alpha$ obey\ndifferent equations of motion. Thus there must be a residual part of\n$\\tau^\\alpha$ which is not changed by the transformations. It is this part\nwhich is responsible for the conserved circulation, so that the conservation\nof $\\Gamma$ cannot be reduced to magnetic flux conservation.\n\nThe following algorithm can be used to find $\\tau^\\alpha$. Maxwell's\ninhomogeneous equations (\\ref{tau}) which say that the divergence of a\ncertain tensor vanishes can always be ``solved'' by the prescription\n\\begin{equation}\nF^{\\alpha\\beta}-4\\pi(\\tau^\\alpha N^\\beta-\\tau^\\beta N^\\alpha)={\\scriptstyle\n1\\over\\scriptstyle 2}\\epsilon^{\\alpha\\beta\\gamma\\delta}{\\cal F}_{\\gamma\\delta}\n\\label{prescription}\n\\end {equation}\nwhere the new field ${\\cal F}_{\\gamma\\delta}$ just has to satisfy Maxwell's\nhomogeneous equations (\\ref{Maxwell2}), i.e. ${\\cal F}_{\\gamma\\delta}\\equiv\n{\\cal A}_{\\delta,\\gamma}-{\\cal A}_{\\gamma,\\delta}$. Taking the dual of\nEq.~(\\ref{prescription}) with help of the identity\n$\\epsilon_{\\gamma\\delta\\alpha\\beta}\\epsilon^{\\alpha\\beta\\mu\\nu}=\n-2(\\delta_\\gamma{}^\\mu\\delta_\\delta{}^\\nu\n-\\delta_\\gamma{}^\\nu\\delta_\\delta{}^\\mu)$ gives\n\\begin{equation}\n{}^*F_{\\gamma\\delta}-4\\pi\\epsilon_{\\gamma\\delta\\alpha\\beta} \\tau^\\alpha\nN^\\beta=-{\\cal F}_{\\gamma\\delta}\n\\label{dual}\n\\end {equation}\nContracting this equation with $u^\\gamma$ gives the further requirement on\n${\\cal F}_{\\alpha\\beta}$:\n\\begin{equation}\n{\\cal F}_{\\delta\\gamma} u^\\gamma=B_\\delta,\n\\label{requirement}\n\\end {equation}\nwhere we have used Eq.~(\\ref{gr2}). The ${\\cal F}_{\\delta\\gamma}$ can\nalways be solved for: because of gauge freedom there are three independent\ncomponents in ${\\cal A}_\\alpha$, and this is enough to find a solution for\nan arbitrary field $B_\\delta$ obeying $B_\\alpha u^\\alpha=0$ (thus three\ncomponents at most). If fact, $B_\\delta$ does not determine\n${\\cal F}_{\\delta\\gamma}$ uniquely: if one adds to this last one of the\nfrozen-in\n$f_{\\gamma\\delta}$ we discussed earlier in this section (which also satisfy\nthe homogeneous Maxwell equations), Eq.~(\\ref{requirement}) is still\nsatisfied because $f_{\\delta\\gamma}u^\\gamma=0$. \n\nWe get $\\tau^\\alpha$ by contracting Eq.~(\\ref{prescription}) by $u_\\beta$ and\nremembering that $F^{\\alpha\\beta}u_\\beta=0$ and $\\tau^\\beta u_\\beta=0$. Thus\n\\begin{equation}\n\\tau^\\alpha=(8\\pi n)^{-1}\\epsilon^{\\alpha\\beta\\gamma\\delta}{\\cal\nF}_{\\gamma\\delta}\\,u_\\beta\n\\end{equation}\nIt is interesting that $B_\\delta$ plays the role of electric part of ${\\cal\nF}_{\\delta\\gamma}$ while $\\tau^\\alpha$ enters like the magnetic part of this\ntensor, {\\it c.f.\\/} Eq.~(\\ref{gr2}) (but because ${\\cal F}_{\\delta\\gamma}\nu^\\gamma\\neq 0$, $\\tau^\\alpha$ evolves differently from a magnetic type field\nlike $B^\\alpha$ or the $b^\\alpha$). It should also be clear now that the\nfreedom in redefining ${\\cal F}_{\\gamma\\delta}\\rightarrow {\\cal\nF}_{\\gamma\\delta}+f_{\\gamma\\delta}$ is equivalent to the changes\n$\\tau^\\alpha\\rightarrow \\tau^\\alpha +k n^{-1}\\,b^\\alpha$ we considered\nearlier in this section. This freedom can be exploited together with the\nsymmetries to simplify the problem of solving explicitly for\n$\\tau^\\alpha$ in any specific MHD flow. \n \n\n\n%----------------------------------------------------------&\n\\begin{thebibliography}{99}\n\n\\bibitem{bekenstein1}J. D. Bekenstein and E. Oron, Phys. Rev. D {\\bf\n18},1809 (1978).\n\n\\bibitem{bekenstein2}J. D. Bekenstein, Astrophys, Journ. {\\bf 319}, 207\n(1987).\n\n\\bibitem{herivel}J. W. Herivel, Proc. Camb. Phil Soc. {\\bf 51}, 344 (1955).\n\n\\bibitem{eckart}C. Eckart, Physics of Fluids, {\\bf 3},421 (1960).\n\n\\bibitem{lin}C. C. Lin, in {\\it Liquid Helium\\/}, Proceedings of the\nInternational School of Physics ``Enrico Fermi', Course XXI, edited by G.\nCareri (Academic Press, New York, 1963).\n\n\\bibitem{seliger}R. L. Seliger and F.R.S. Witham, Proc. Roy. Soc. A {\\bf\n305}, 1 (1968).\n\n\\bibitem{mittag}L. Mittag, M. J. Stephen and W. Yourgrau, in W.\nYourgrau and S. Mandelstam, {\\it Variational Principles in Dynamics and\nQuantum Theory} (Dover, New York 1968). \n\n\\bibitem{eckart2}C. Eckart, Phys. Rev. {\\bf 54}, 920 (1938).\n\n\\bibitem{henyey}F. S. Henyey, Phys. Rev. A {\\bf 26}, 480 (1982).\n\n\\bibitem{newcomb}W. A. Newcomb, {\\it Nuclear Fusion Supplement\\/}, {\\bf 2},\n451 (1962).\n\n\\bibitem{lundgren}T. S. Lundgren, Physics of Fluids, {\\bf 6},1313\n(1963).\n\n\\bibitem{penfield}P. Penfield, Jr., {\\it Physics of Fluids\\/} {\\bf\n 9}, 1184 (1966).\n\n\\bibitem{taub1}A. H. Taub, Phys. Rev. {\\bf 94},1468 (1954).\n\n\\bibitem{taub2}A. H. Taub , Commun. Math. Phys. {\\bf 15}, 235 (1969).\n\n\\bibitem{kodama}T. Kodama, Th.-H. Elze, Y. Hama, M. Makler and J. Rafelski,\nJ. Phys. G {\\bf 25} 1935 (1999).\n\n\\bibitem{schutz}B. F. Schutz, Phys. Rev. D {\\bf 2}, 2762 (1970).\n\n\\bibitem{carter1}B. Carter, in {\\it Active Galactic Nuclei\\/}, edited by\nC.Hazard and S.Mitton (Cambridge University Press, Cambridge 1977).\n\n\\bibitem{carter2}B. Carter, in {\\it Topological Defects and Nonequilibrium\nDynamics of Symmetry Breaking Phase Transitions\\/}, edited by Y. Bunkov and H.\nGodfrin (Kluwer, Dordrecht 2000).\n\n\\bibitem{achterberg}A. Achterberg, Phys. Rev. A {\\bf 28}, 2449 (1983).\n\n\\bibitem{thompson}C. Thompson, Phys. Rev. D {\\bf 57}, 3219 (1998).\n\n\\bibitem{heyl}J. S. Heyl and L. Hernquist, Phys.Rev.D {\\bf 59}, 045005\n (1999).\n\n\\bibitem{LL}L. D. Landau and E. M. Lifshitz, {\\it Electrodynamics of\nContinuous Media\\/}, 2nd ed. (Pergamon, Oxford 1984), p. 227.\n\n\\bibitem{chandra}S. Chandrasekhar, {\\it Hydrodynamic and Hydromagnetic\nInstability\\/} (Clarendon Press, Oxford, 1961).\n\n\\bibitem{mestel}L. Mestel, {\\it Stellar Magnetism } (Clarendon Press, Oxford,\n1999).\n\n\\bibitem{ferraro}V. C. A. Ferraro, MNRAS, {\\bf 97}, 458 (1937).\n\n\n\\bibitem{lichnerowicz}A. Lichnerowicz, {\\it Relativistic Hydrodynamics and \nMagnetohydrodynamics\\/} (Benjamin, New York, 1967).\n\n\\bibitem{novikov}I. D. Novikov and K. S. Thorne, in {\\it Black Holes\\/},\nedited by B. S. DeWitt and C. M. DeWitt (Gordon and Breach, New York, 1973).\n\n\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002045.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{bekenstein1}J. D. Bekenstein and E. Oron, Phys. Rev. D {\\bf\n18},1809 (1978).\n\n\\bibitem{bekenstein2}J. D. Bekenstein, Astrophys, Journ. {\\bf 319}, 207\n(1987).\n\n\\bibitem{herivel}J. W. Herivel, Proc. Camb. Phil Soc. {\\bf 51}, 344 (1955).\n\n\\bibitem{eckart}C. Eckart, Physics of Fluids, {\\bf 3},421 (1960).\n\n\\bibitem{lin}C. C. Lin, in {\\it Liquid Helium\\/}, Proceedings of the\nInternational School of Physics ``Enrico Fermi', Course XXI, edited by G.\nCareri (Academic Press, New York, 1963).\n\n\\bibitem{seliger}R. L. Seliger and F.R.S. Witham, Proc. Roy. Soc. A {\\bf\n305}, 1 (1968).\n\n\\bibitem{mittag}L. Mittag, M. J. Stephen and W. Yourgrau, in W.\nYourgrau and S. Mandelstam, {\\it Variational Principles in Dynamics and\nQuantum Theory} (Dover, New York 1968). \n\n\\bibitem{eckart2}C. Eckart, Phys. Rev. {\\bf 54}, 920 (1938).\n\n\\bibitem{henyey}F. S. Henyey, Phys. Rev. A {\\bf 26}, 480 (1982).\n\n\\bibitem{newcomb}W. A. Newcomb, {\\it Nuclear Fusion Supplement\\/}, {\\bf 2},\n451 (1962).\n\n\\bibitem{lundgren}T. S. Lundgren, Physics of Fluids, {\\bf 6},1313\n(1963).\n\n\\bibitem{penfield}P. Penfield, Jr., {\\it Physics of Fluids\\/} {\\bf\n 9}, 1184 (1966).\n\n\\bibitem{taub1}A. H. Taub, Phys. Rev. {\\bf 94},1468 (1954).\n\n\\bibitem{taub2}A. H. Taub , Commun. Math. Phys. {\\bf 15}, 235 (1969).\n\n\\bibitem{kodama}T. Kodama, Th.-H. Elze, Y. Hama, M. Makler and J. Rafelski,\nJ. Phys. G {\\bf 25} 1935 (1999).\n\n\\bibitem{schutz}B. F. Schutz, Phys. Rev. D {\\bf 2}, 2762 (1970).\n\n\\bibitem{carter1}B. Carter, in {\\it Active Galactic Nuclei\\/}, edited by\nC.Hazard and S.Mitton (Cambridge University Press, Cambridge 1977).\n\n\\bibitem{carter2}B. Carter, in {\\it Topological Defects and Nonequilibrium\nDynamics of Symmetry Breaking Phase Transitions\\/}, edited by Y. Bunkov and H.\nGodfrin (Kluwer, Dordrecht 2000).\n\n\\bibitem{achterberg}A. Achterberg, Phys. Rev. A {\\bf 28}, 2449 (1983).\n\n\\bibitem{thompson}C. Thompson, Phys. Rev. D {\\bf 57}, 3219 (1998).\n\n\\bibitem{heyl}J. S. Heyl and L. Hernquist, Phys.Rev.D {\\bf 59}, 045005\n (1999).\n\n\\bibitem{LL}L. D. Landau and E. M. Lifshitz, {\\it Electrodynamics of\nContinuous Media\\/}, 2nd ed. (Pergamon, Oxford 1984), p. 227.\n\n\\bibitem{chandra}S. Chandrasekhar, {\\it Hydrodynamic and Hydromagnetic\nInstability\\/} (Clarendon Press, Oxford, 1961).\n\n\\bibitem{mestel}L. Mestel, {\\it Stellar Magnetism } (Clarendon Press, Oxford,\n1999).\n\n\\bibitem{ferraro}V. C. A. Ferraro, MNRAS, {\\bf 97}, 458 (1937).\n\n\n\\bibitem{lichnerowicz}A. Lichnerowicz, {\\it Relativistic Hydrodynamics and \nMagnetohydrodynamics\\/} (Benjamin, New York, 1967).\n\n\\bibitem{novikov}I. D. Novikov and K. S. Thorne, in {\\it Black Holes\\/},\nedited by B. S. DeWitt and C. M. DeWitt (Gordon and Breach, New York, 1973).\n\n\n\\end{thebibliography}"
}
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astro-ph0002046
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Effects of massive star formation on the ISM of dwarf galaxies
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[
{
"author": "Suzanne C. Madden"
}
] |
We are studying star formation effects on the properties of the ISM in low metallicity environments using mid-infrared (MIR) and far-infrared (FIR) observations of starbursting dwarf galaxies taken with the Infrared Space Observatory (ISO) and the Kuiper Airborne Observatory (KAO). Effects of the hard pervasive radiation field on the gas and dust due to the dust-poor environments are apparent in both the dust and gas components. From a 158 $\mu$m [CII] survey we find enhanced I[CII]/FIR ratios in dwarf galaxies and I[CII]/I(CO) ratios up to 10 times higher than those for normal metallicity starburst galaxies. We consider MIR observations in understanding the star formation properties of dwarf galaxies and constraints on the stellar SED. Notably, the strong MIR [NeIII]/[NeII] ratios reveal the presence of current massive stellar populations $<$ 5 My old in NGC~1569, NGC~1140 and IIZw40. The MIR unidentified infrared bands (UIBs) are weak, if present at all, as a general characteristic in low metallicity environments, revealing the destruction of the smallest carbon particles (e.g. PAHs) over large spatial scales. This is confirmed with our dust modeling: mass fractions of PAHs are almost negligible compared to the larger silicate grains emitting in the FIR as well as the small carbon grains emitting in the MIR, which appear to be the source of the photoelectric gas heating in these galaxies, in view of the [CII] cooling.
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[
{
"name": "toulouse.tex",
"string": "\\documentclass{elsart}\n%\\usepackage{natbib}\n\\usepackage{graphicx}\n\\begin{document}\n\\runauthor{Madden}\n\\begin{frontmatter}\n%\\title{Effects of massive star formation on the ISM of dwarf galaxies}\n\\title{Effects of massive star formation on the ISM of dwarf galaxies\\thanksref{X}}\n\\author{Suzanne C. Madden}\n\\address{CEA, Saclay, Service d'Astrophysique, France, [email protected]}\n\\thanks[X]{\\emph{Proceedings for The Interplay between Massive Stars and the ISM \\\\ New Astronomy Reviews, Eds. D. Schaerer \\& R. Delgado-Gonzalez}}\n%\\thanks[email]{\\emph{email: [email protected]}}\n\\begin{abstract}\nWe are studying star formation effects on the properties of the ISM in\nlow metallicity environments using mid-infrared (MIR) and far-infrared\n(FIR) observations of starbursting dwarf galaxies taken with the\nInfrared Space Observatory (ISO) and the Kuiper Airborne Observatory\n(KAO). Effects of the hard pervasive radiation field on the gas and\ndust due to the dust-poor environments are apparent in both the dust\nand gas components. From a 158 $\\mu$m [CII] survey we find enhanced\nI[CII]/FIR ratios in dwarf galaxies and I[CII]/I(CO) ratios up to 10\ntimes higher than those for normal metallicity starburst galaxies. We\nconsider MIR observations in understanding the star formation\nproperties of dwarf galaxies and constraints on the stellar\nSED. Notably, the strong MIR [NeIII]/[NeII] ratios reveal the presence\nof current massive stellar populations $<$ 5 My old in NGC~1569,\nNGC~1140 and IIZw40. The MIR unidentified infrared bands (UIBs) are\nweak, if present at all, as a general characteristic in low\nmetallicity environments, revealing the destruction of the smallest\ncarbon particles (e.g. PAHs) over large spatial scales. This is confirmed with our\ndust modeling: mass fractions of PAHs are almost negligible compared\nto the larger silicate grains emitting in the FIR as well as the small\ncarbon grains emitting in the MIR, which appear to be the source of\nthe photoelectric gas heating in these galaxies, in view of the [CII]\ncooling.\n\\end{abstract}\n\\begin{keyword}\ndwarf galaxies; dust;\nphotodissociation regions; ISO\n\\end{keyword}\n\\end{frontmatter}\n\\section{Introduction}\n\\typeout{SET RUN AUTHOR to \\@runauthor}\n%hello\\footnote{A footnote}\nTo construct a comprehensive picture of a galaxy's history,\nunderstanding the distribution of its energy budget is a fundamental\nstep. For this we must consider observations covering several\ncharacteristic wavelength regimes, thus, sampling the various\ncomponents of the interstellar medium (ISM). While the UV to NIR\nwavelength continua give us relatively direct probes of the stellar\npopulations, this radiation is subject to varying amounts of\nabsorption before we view it. Some of this energy is absorbed by the\ngas directly in HII regions or transferred to the gas in\nphotodissociation regions (PDRs) and reemitted as molecules, bands and\natomic ionic and recombination lines, from wavelengths covering the UV\nto FIR and beyond. Some of the stellar energy is absorbed by the dust,\nrevealed through extinction, and reradiated in MIR to submillimeter\nwavelengths as thermal emission. Therefore, models of the ISM in\ngalaxies must consider these interdependent processes and be\nself-consistent. Our knowledge of the wavelength window from the MIR\nto the FIR has been limited by the low spatial and spectral resolution\nprovided by IRAS, and has been rather sketchy when it comes to\ndetailed studies of the ISM of individual galaxies. The Infrared Space\nObservatory (ISO) \\cite{kessler96} has been a recent turning point in\nthis effort, providing high spectral and spatial resolution and\nunprecedented sensitivity in the MIR to FIR. We are incorporating our\nMIR and FIR observations in a study of the energy redistribution in\nstarburst galaxies to understand the effects of the star formation on\nthe surrounding gas and dust. Here we report the progress to date in\nour study of star forming low-metallicity dwarf galaxies, which, in\nthe absence of major dynamical complications, allow us to `simplify'\nmodel assumptions and the interpretation of observations.\n\\section{Far-infrared observations: the [CII] cooling line}\nAs an indirect probe of the star formation activity, we have obtained\nKAO (Kuiper Airborne Observatory) and ISO observations of the 158\n$\\mu$m $^2P_{3/2} - ^2P_{1/2}$ far infrared [CII] fine structure line\nemission in a sample of 15 dwarf galaxies \\cite{jones97} with\nmetallicities ranging from 0.1 to 0.5 solar. As the ionization\npotential of carbon is 11.3 eV, less than that of HI, photons escaping\nthe HII regions, dissociate CO, and ionize carbon in the\nphotodissociation regions (PDRs) on the surfaces of nearby molecular\nclouds exposed to the stellar UV radiation. The observed [CII]\nintensity can be traced back to the radiation source due to the fact\nthat the UV photons heat the dust which emits thermal radiation in the\nMIR to submillimeter wavelengths. Energetic electrons, ejected from\nthe dust through the photoelectric effect, heat the gas. The gas\nsubsequently cools via emission from molecules and atomic fine\nstructure lines, predominantly the 158 $\\mu$m [CII] and the 63 $\\mu$m\n[OI] transitions in PDRs. There has been a long history of development\nof PDR models which provide tools to differentiate physical\nproperties, such as density (n), radiation field strength (G$_{0}$)\nand filling-factors in galaxies (see review and references in\n\\cite{hollenbach97}).\n\\subsection{[CII] Survey of Dwarf Galaxies}\nThe ratio of I[CII]/I(CO) is a useful measure of the PDR emission\nrelative to the molecular core emission and is an indicator of the\ndegree of star formation activity in galaxies. Active galaxies have a\nratio of I[CII]/I(CO) $\\sim$ 6300, which is 3 times greater than that\nobserved in more quiescent galaxies \\cite{stacey91}. Our [CII] survey\nshows that for dwarf galaxies, this ratio ranges from 6000 to 70,000,\nwhich is up to 10 times greater than those for normal metallicity\nstarburst galaxies (Figure \\ref{cii}) \\cite{jones97}. We also observe\nan overall enhancement in the I[CII]/FIR ratios (where FIR is defined\nas the sum of the IRAS 60 and 100 $\\mu$m bands) in these regions\ncompared to those in normal metallicity galaxies, which was also noted\nin the LMC \\cite{mochizuki94} \\cite{poglitsch95}\n\\cite{pak98}. The ratio of I[CII]/FIR is a direct measure of the\nfraction of UV energy reemerging in the [CII] cooling line, and is\nusually between 0.1\\% and 1\\% for normal metallicity galaxies\n\\cite{stacey91}, while we find up to 2\\% for dwarf galaxies.\nObservations of CO in dwarf galaxies have been very challenging and\nthe glaring underabundance of observed CO in dwarf galaxies and\nrelatively high FIR/CO luminosities have often been interpreted as\nunusually high star formation efficiency. While all these\nobservational effects are a consequence of the lower metal abundance\nand decreased dust to gas ratio, we do not find an unambiguous direct\ncorrelation of the I[CII]/I(CO) and I[CII]/FIR ratios in our surveys\nwith metallicity.\n\\begin{figure*}\n\\includegraphics[width=13cm]{fig1.ps}\n\\caption{[CII] survey results: comparing normal metallicity regions with low-metallicity galaxies. Lines of constant I[CII]/I(CO) ratios run diagonally across the plot and range from $\\sim$ 2000 for quiescent galaxies and Galactic molecular cloud regions \\cite{stacey91} up to $\\sim$ 70,000 for some dwarf galaxies \\cite{jones97}. The ratios of both axes are normalized to the local interstellar radiation field (1.3x10$^{-4}$ erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$)}\n\\label{cii}\n\\end{figure*}\nThe reduced dust abundance in these environments allows the UV\nradiation to penetrate deeper, leaving a smaller CO core surrounded by\na larger C$^{+}$- emitting region, thus enhancing the I[CII]/I(CO)\nratios \\cite{maloney88}. Consequently, as the FUV flux travels further,\nthe intensity becomes geometrically diluted, resulting in a lower\nbeam-averaged FIR flux, accounting for the increased I[CII]/FIR ratios\n\\cite{israel96}.\n\nUsing the results of recent PDR models that consider the effects of\nreduced metallicity \\cite{kaufman99}, we can find solutions for the\ndwarf galaxies for clouds in our beam described by 2 different\ncases. One possible solution (case A) is for clouds with low A$_{v}$\n($\\sim$3) and equal densities (n) in the CO and C$^{+}$- emitting\nregions with n ranging from 10$^{3}$ to 10$^{4.5}$ cm$^{-3}$ and low\nto moderate G$_{o}$ (normalized to the local interstellar radiation\nfield intensity, 1.3x10$^{-4}$ erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$)\nranging from 10$^{1.5}$ to 10$^{3}$. Another possible solution (case\nB) is a higher A$_{v}$ ($\\sim$10) with the density of the CO-emitting\nregion (n$_{CO}$) $>$ the density of the C$^{+}$- emitting region\n(n$_{CII}$) which gives higher ranges of G$_{o}$ ($\\sim$ 10$^{2.5}$ to\n10$^{3.5}$). We can put further constraints on these solutions through\nstellar population modeling. Based on our modeled SED for IIZw40, for\nexample, case A is a solution (section 4.1). Arguments for molecular cloud stability\npoint toward case B for the LMC \\cite{kaufman99}. Decreasing the A$_{v}$\n(case A) or increasing the n$_{CO}$ relative to n$_{CII}$ (case B) has\nthe similar effect of reducing the CO-emitting core and increasing the\nC$^{+}$- emitting zone and increasing the CO-to-H$_{2}$ conversion\nfactor\n\\cite{kaufman99}. Based on [CII] observations in IC10, for example, we speculated\nthat up to 100 times more H$_2$ may be `hidden' in a C$^+$-emitting\nregions compared to that deduced only from CO observations and using\nthe Galactic CO-to-H$_{2}$ conversion factor \\cite{madden97}. The\npresence of H$_2$ in the C$^+$- emitting region is due to the\nself-shielding of H$_2$ from UV photons or shielding by dust\n\\cite{burton90}\n\\cite{pak98} \\cite{kaufman99}. \n\\section{Mid-Infrared Observations}\nWe are studying some of these galaxies in our [CII] survey with\nfollowup MIR observations. In Figure \\ref{cvfs} we show ISOCAM\n\\cite{ccecarsky96} spectra covering 5 to 17 $\\mu$m for 3 galaxies from\nour [CII] survey, IIZw40, NGC~1140 and NGC~1569 along with that of\nthe notoriously metal-poor SBS0335-052 \\cite{thuan99a}. The\nspectra represent the total emission from the galaxies except in the\ncase of the NGC~1569 spectra, which samples the region around the\nH$\\alpha$ peak $\\#$2 (see\n\\cite{waller91}). As often seen in starburst galaxies\n(e.g. \\cite{dudley99} \\cite{laurent00}), the MIR spectra are dominated\nby steeply rising continua longward of $\\sim$ 10 $\\mu$m, as evident in\nNGC~1569, IIZw40 and SBS0335-052 (Figure \\ref{cvfs}). Thermal\nemission from hot small grains with mean temperatures of the order of\n100's of K are responsible for the MIR continuum emission. The\nunidentified infrared bands (UIBs) at 6.2, 7.7, 8.6, 11.3 and 12.6\n$\\mu$m, are proposed to be due to aromatic hydrocarbon particles\nundergoing stochastic temperature fluctuations (i.e, PAHs\n\\cite{leger84} \\cite{allaman89}; coal grains\n\\cite{papou91}) and are observed to peak on the PDR zones around\nthe HII regions but are destroyed deep within HII regions\n\\cite{vertraete96} \\cite{dcesarsky96} \\cite{tran98}. While the UIBs are not obvious in the spectra of IIZw40 and SBS0335-052, and are only very weakly present NGC~1569, they can be distinguished in the spectrum of NGC~1140. Several ground state fine-structure\nnebular lines are present also in 3 of the spectra, the most prominent\nbeing 15.6 $\\mu$m [NeIII] (energy potential $\\sim$ 41 eV) and 10.5 $\\mu$m [SIV] (energy potential $\\sim$ 35 eV).\nWeaker, lower energy lines may also present, such as the 8.9 $\\mu$m\n[ArIII] line and the [NeII] 12.8 $\\mu$m line, which can be blended\nwith the 12.6 $\\mu$m UIB. All of these spectra look very\ndifferent from one another and all differ significantly from those of\nnormal metallicity starburst galaxies. Normal starburst galaxies show\nprominent UIBs, in contrast to AGNs, which are devoid of UIBs\n(e.g. \\cite{roche91} \\cite{dudley99} \\cite{laurent00}). When compared to spectra characteristic of PDRs and HII regions, ie, M17 \\cite{dcesarsky96} \\cite{vertraete96}, IIZw40 is remarkably similar to that of an HII region. In contrast,\nNGC~1140, which has a very flat continuum, yet very strong [NeIII]\nline, does have a more obvious contribution from PDR regions in its\nspectra. The MIR spectra of N66, the most prominent HII region in the\nSMC, also shows a scarcity of UIBs in the vicinity of the most massive\ncentral cluster \\cite{contoursi99}, as does the low metallicity source\nNGC~5253 \\cite{crowther99}. \n\\begin{figure*}\n\\includegraphics[scale=.6,viewport=0 0 630 630, clip]{fig2.eps}\n\\caption{ISOCAM MIR spectra of dwarf galaxies: IIZw40, NGC~1569, NGC~1140 and SBS0335-052. The horizontal lines in SBS0335-052 are broad band measurements; the dashed line is a blackbody with A$_{v}$ $\\sim$ 20 \\cite{thuan99a}. Note the absorption attributed to amorphous silicates at $\\sim$ 9 and 18 $\\mu$m.}\n\\label{cvfs}\n\\end{figure*}\nIn some starburst galaxies, amorphous silicate is seen in absorption\ncentered at 9 and 18 $\\mu$m (e.g. \\cite{roche91}, \\cite{dudley99},\n\\cite{laurent00}). We can fit the MIR region of the IIZw40 \nspectrum with a blackbody of 193 K and and an absorption equivalent to\nA$_{v}$ $\\sim$ 4. We caution interpretation of the dust temperature we\nderive assuming a blackbody, since the dust emitting in the MIR is\nexpected to be undergoing stochastic heating events, rather than being\nin thermal equilibrium with the radiation field. The amount of\nabsorption in IIZw40 (A$_{v}$ $\\sim$ 4) has yet to be confirmed. In\nSBS0335-052, a very low metallicity galaxy (1/40 solar), A$_{v}$ $\\sim$\n20 deduced from the absorption in the ISOCAM MIR spectra (Figure \\ref{cvfs})\n\\cite{thuan99a}. The presence of a significant amount of dust in\nsuch a low metallicity galaxy is surprising, since star formation in SBS0335-052 began as recently as 100 Myr ago \\cite{papader98}\n\\cite{thuan99b}. Such high extinction implies that the current star\nformation rate, hidden by dust, can be underestimated by at least 50\\%\n\\cite{thuan99a}\n\\subsection{Effects of the starburst activity on the dwarf galaxy MIR spectra}\nAs a consequence of the decreased dust abundance in dwarf galaxies, the\nISM throughout the galaxies is effected globally by the hard radiation\nfield of the massive stellar clusters. These galaxies contain evidence\nfor Wolf-Rayet stars {\\cite{schaerer99} and super star clusters have\nbeen detected in NGC~1140 \\cite{hunter94}, NGC~1569 \\cite{oconnell94}\nand SBS0335-052\n\\cite{thuan97}. The harsh radiation field, which more easily permeates the\nISM compared to normal metallicity environments, can destroy the UIB\ncarriers, for example, over very extensive spatial areas. The effect of the\npervasive radiation field can be witnessed in NGC~1569 (Figure\n\\ref{n1569_image}). Photodissociation occurs on global scales. Violent activity is revealed by the H$\\alpha$ distribution \\cite{waller91} \\cite{martin98} and the 15.8 $\\mu$m [NeIII] emission,\nwith giant streamers suspected to originate from the energetic winds\nof the super star clusters A \\& B, (shown in the figure as white\nstars). The UIBs, [SIV] and [NeIII] emission seem to avoid the super\nstar clusters, which blow out much of the gas and dust on relatively\nshort time scales. This effect is also seen in the CO \\cite{taylor99},\nHI \\cite{israel90} and the H$\\alpha$ \\cite{waller91}\ndistribution. Likewise we see the destruction of the UIBs in the beam-\naveraged spectrum of the entire galaxy of IIZw40 and SBS0335-052 (due\nto our lack of spatial resolution we do not see the details within\nthese galaxies in the MIR).\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[scale=0.6,viewport=97 176 471 571, clip]{fig3.eps}\n\\caption{NGC~1569: H$\\alpha$ (image) \\cite{waller91} and 15.8 $\\mu$m [NeIII] emission (contours). Note the extended [NeIII] filaments as also seen in H$\\alpha$. The 2 white stars mark the positions of the super star clusters A and B \\cite{oconnell94} which are void of[NeIII] emission.}\n\\label{n1569_image}\n\\end{center}\n\\end{figure*}\n\\section{Spectral Energy Distribution}\nWe compile broad-band data from the literature for IIZw40, NGC~1569\nand NGC~1140, and together with our MIR data, construct stellar\nspectral energy distributions (SEDs). In doing so, we fit the observed optical\nand NIR data with stellar evolution models of PEGASE \\cite{fioc97},\ntaking into account the results of photoionization\nmodeling of the MIR line emission using CLOUDY \\cite{ferland96}. This\nis an attempt to reconstruct the input stellar spectra consistent from\nthe viewpoints of both the stellar evolution and\nphotoionization.\n\\subsection{Combined stellar evolution and photoionization model results} \nUsing PEGASE with an instantaneous star formation rate, metallicity\n0.2 solar and a Salpeter IMF (with upper and lower mass cut offs of .1\nand 120 solar masses), we find solutions to observed broad band\nstellar light for various ages and ionization parameters. Diagnostic\noptical and NIR lines in the literature exist for all of these sources for a\nvariety of apertures. The ISOCAM MIR observations also provide\nimportant diagnostic lines of neon, sulphur and argon, and has been\nrecently addressed by others, including \\cite{lutz98}\n\\cite{crowther99} \\cite{schaerer99b}\n\\cite{genzel98}. For example, the [NeIII]/[NeII] ratio, is a measure of T$_{eff}$, the hardness of the radiation field, and therefore traces the massive\nstellar population. For the dwarf galaxies, we find [NeIII]/[NeII]\nratios in the range of 5 to 10 - much higher than those for normal\nmetallicity galaxies ($\\leq$1) \\cite{thornley00}. The extreme values\nof the [NeIII]/[NeII] ratios are due to effects of the\nlow-metallicities of the systems: the T$_{eff}$ of the stars increases\nas the metallicity decreases for a specific stellar age. High ratios\nof [NeIII]/[NeII] and the prominent [SIV] in these spectra limit the\nage of the present star formation to $<$ 5 Myr. Beyond this age, the\nmassive stars have died and the [NeIII]/[NeII] ratio drops\ndramatically. The high excitation 24.9 $\\mu$m [OIV] line, covered by\nthe ISO SWS data, is observed in some dwarf galaxies\n\\cite{lutz98} and has been proposed to be due to the presence of Wolf-Rayet\nstars \\cite{schaerer99b}. For NGC~1569, NGC~1140 and IIZw40, we\nconstruct composite stellar SEDs that require a 75\\% to 95 \\% mass\nfraction of an 'older' population ranging in age from about 10 Myr to\n30 Myr along with 5\\% to 30\\% of a very young population, $<$ 5\nMyr. The broad band optical and NIR data alone reveal predominantly\nthe older population in our apertures. Figure \\ref{sed}\nshows an example of the resultant composite SED obtained for IIZw~40,\nand the extreme-ultraviolet (EUV) radiation which the young, massive\nstellar population traces. Observational evidence for the presence of\nWolf-Rayet stars also indicates a very young stellar population \\cite{vacca92}.\n\\begin{figure*}\n\\includegraphics[width=\\textwidth, viewport=0 0 670 495, clip]{fig4.eps}\n\\caption{IIZw40 SED. The synthetic stellar spectra are fit for the extinction-corrected optical to NIR data from the literature for a 12'' aperture using PEGASE. The 12, 25, 60 and 100 $\\mu$m data are from IRAS and the 7 and 15 $\\mu$m data points are integrated over 5.0 to 8.5 $\\mu$m and 12.0 to 17 $\\mu$m bands, respectively, using the ISOCAM spectrum (Figure \\ref{cvfs}).}\n\\label{sed}\n\\end{figure*}\n\\section{Dust modeling}\nHaving modeled the radiation field above, we next use the stellar\nspectra of IIZw40, NGC~1569 and NGC~1140 as input to a dust model to\ndeduce the nature of the various dust components emitting in the MIR\nand the FIR. This is an important step since dust plays a major role\nin influencing the chemical and physical state of the ISM. We use the\nD\\'esert et al. model\n\\cite{desert90}, which calculates the IR emission from large silicate\ngrains (BGs), very small amorphous carbon grains (VSGs), and\nstochastically-heated polycyclic aromatic hydrocarbons (PAHs), for\nvarious grain size distributions. This model is rather empirical in\nits approach and thus does not give an exact fit to the details of the\nobserved spectrum. For example, the 8.6~$\\mu$m UIB is not well-matched\nand no emission from bands at wavelengths longer than 11.3~$\\mu$m are\nincluded. The model is currently in the process of modification using\nup-to-date laboratory-measured optical constants for a wide range of\nlikely interstellar grain materials.\n\\subsection{Dust in low-metallicity galaxies}\nIn Figure \\ref{dust_model} we show, as an example, the ISOCAM MIR\nspectrum and the IRAS data points for IIZw40 and NGC~1569, where we\nhave plotted the emission from the PAH (dashed line), VSG (dotted\nline) and BG (dashed-dotted line) components. In these galaxies the\nMIR spectrum is clearly dominated by emission from VSGs with very\nlittle PAH emission. The BG component dominantes the overall dust\nemission with mass fractions ranging from 93\\% to 99\\% for the 3\ngalaxies, while the PAH mass fraction is relatively insignificant - 5\norders of magnitude lower. This model gives a PAH/VSG mass ratio for\nNGC~1569 and IIZw 40 of 2 to 3x10$^{-4}$ and 10 times this for\nNGC~1140. The D\\'esert et al. model applied to the Galactic cirrus\ngives PAH/VSG mass ratio $\\sim 1$. Thus, even compared to the VSG\npopulation, we find an insignificant mass fraction of PAHs, reflecting\nthe fact that the PAHs are destroyed in the hard radiation fields\nin these galaxies. PAHs are thought to be the primary particles\nresponsible for the photoelectric heating process \\cite{bakes94} and\nare incorporated in PDR models\n\\cite{kaufman99}. Our preliminary results, while not statistically\nrobust at this stage, suggest that even in the absence of PAHs, the\nphotoelectric effect is efficient, as both IIZw40 and NGC~1569 are\nrelatively prominent [CII] sources from our survey. On the contrary,\nin NGC~1140, where PAHs are more obvious in the MIR spectra (Figure\n\\ref{cvfs}), we do not detect [CII]. VSGs (sizes determined from model $\\sim$40 to 300A), which are very abundant relative to the PAHs in NGC~1569 and IIZw40, and less so in NGC~1140, may therefore, be the more efficient\nsources of photoelectric gas heating in these environments, rather\nthan PAHs. More detailed studies of these galaxies will be carried out\nusing the analytical dust model of V\\'arosi and Dwek \\cite{varosi99},\nwhich takes into account radiative transfer in a two-phase clumpy\nenvironment and considers various geometries.\n\\begin{figure*}\n\\begin{center}\n\\includegraphics[width=\\textwidth,viewport = 23 307 716 590,clip]{fig5.eps}\n\\caption{Model results for the dust components in IIZw40 (left) and NGC~1569 (right) fitted to the ISOCAM MIR spectra and the IRAS data (boxes) Component are from the D\\'esert et al. model \\cite{desert90} (see text for model explanation)}\n\\end{center}\n\\label{dust_model}\n\\end{figure*}\n\\section{Summary}\nTracers of various components of the ISM show evidence of effects of\nthe hard stellar radiation field in dwarf galaxies on the\nsurrounding ISM due to the decreased dust abundace, allowing\nphotoionization over large galactic scales to occur. From our survey\nof the 158 $\\mu$m [CII] PDR cooling line in dwarf galaxies, we observe\nan increased penetration of the FUV radiation field which enhances the\nI[CII]/I(CO) emission in dwarf galaxies up to a factor of 10 more than\nin normal metallicity star burst galaxies. We also find a small\nenhancement in the I[CII]/FIR ratio in dwarf galaxies. Followup MIR\nISOCAM spectroscopy provides details of ionic lines, UIBs and small\nhot small grain emission distribution in dwarf galaxies. The strong\nMIR [NeIII]/[NeII] ratios are signatures of the hard radiation fields\nand indicate the presence of young massive stellar populations in\ndwarf galaxies. Because of the increase in T$_{eff}$ in low\nmetallicity environments, this ratio is enhanced at least 5 to 10\ntimes more in dwarf galaxies than in normal metallicity galaxies. The\npenetrating radiation field also effects the dust components,\ndestroying the UIBs in some dwarf galaxies on global scales, as\nis evident in the MIR spectra and in the dust modeling.\n\\section{Acknowledgements}\nThis work, still in progress, results from a series of observations\nfrom ISO and the KAO and includes a number of collaborators such as\nS. Colgan, N. Geis, M. Haas, D. Hollenbach, A. Jones, P. Maloney,\nA. Poglitsch, D. Ragaigne, B. Smith and M. Wolfire. I have benefited\nfrom invaluable discussions with E. Dwek and A. Jones on dust\nmodeling. I thank W. Waller for his H$\\alpha$ image of NGC 1569.\n\\begin{thebibliography}{999}\n\\bibitem{kessler96} M.F. Kessler et al., {\\em A\\&A\\/} {\\bf 315} (1996) L27.\n\\bibitem{jones97} A.P. Jones, S.C. Madden, S.W.J. Colgan, N. Geis, M. Haas, P. Maloney, T. Nikola, A. Poglitsch, {\\em Extragalactic Astronomy in the Infrared\\/}, (1997) G. Mamon, T. Thuan, J.Tran Than, eds, Editions Fronti\\`eres, Paris, 1997, p.101.\n\\bibitem{hollenbach97} D. Hollenbach, A.G.G.M. Tielens, {\\em Ann. Rev. Astron. Astrophys\\/} {\\bf 35} (1997) 179.\n\\bibitem{stacey91} G.J. Stacey, N. Geis, R. Genzel, J.B. Lugten, A. Poglitsch, A. Sternberg, C.H. Townes, {\\em ApJ\\/} {\\bf 373} (1991) 423.\n\\bibitem{mochizuki94} K. Mochizuki et al, {\\em ApJ\\/} {\\bf 430} (1994) L37.\n\\bibitem{poglitsch95} A. Poglitsch, A. Krabbe, S.C. Madden, T. Nikola, N. Geis, L.E.B. Johansson, G.J. Stacey, A. Sternberg, {\\em ApJ\\/} {\\bf 454} (1995) 293.\n\\bibitem{pak98} S. Pak, D.T. Jaffe, E. F. van Dishoeck, L.E.B. Johansson, R.S. Booth, {\\em ApJ\\/} {\\bf 498} (1998) 735.\n\\bibitem{maloney88} P. Maloney, J.H. Black {\\em APJ\\/} {\\bf 325} (1988) 389.\n\\bibitem{israel96} F.P. Israel, P.R. Maloney , N. Geis, F. Herrmann, S.C. Madden, A. Poglitsch, G.J. Stacey, {\\em ApJ\\/} {\\bf 465} (1996) 738.\n\\bibitem{kaufman99} M.J. Kaufman, M.G. Wolfire, D.J. Hollenbach, M.L. Luhman, {\\em ApJ\\/} (1999) in press.\n\\bibitem{madden97} S.C. Madden, A. Poglitsch, N. Geis, G.J. Stacey, C.H. Townes , {\\em ApJ\\/} {\\bf 483} (1997) 200.\n\\bibitem{burton90} M.G. Burton, D.J. Hollenbach, A.G.G.M. Tielens, {\\em ApJ\\/} {\\bf 365} (1990) 620.\n\\bibitem{ccecarsky96} C.J. Cesarsky et al., {\\em A\\&A\\/} {\\bf 315} (1996) 32.\n\\bibitem{thuan99a} T.X. Thuan, M. Sauvage, S.C. Madden, {\\em ApJ\\/} {\\bf 516} (1999) 783.\n\\bibitem{waller91} W.H. Waller, {\\em ApJ\\/} {\\bf 370} (1991) 144.\n\\bibitem{dudley99} C.C. Dudley, {\\em MNRAS\\/} {\\bf 304} (1999) 549.\n\\bibitem{laurent00} O. Laurent, I.F. Mirabel, V. Charmandaris, P. Gallais, S.C. Madden, M. Sauvage, L. Vigroux, C. Cesarsky, {\\em A\\&A\\/} (2000) submitted.\n\\bibitem{leger84} A. L\\'eger, J.-L. Puget, {\\em A\\&A\\/} {\\bf 137} (1984) L5.\n\\bibitem{allaman89} L.J. Allamandola, A.G.G.M.. Tielens, J.R. Barker, {\\em ApJS\\/} {\\bf 71} (1989) 733.\n\\bibitem{papou91} R. Papoular, C. Reynaud, I. Nenner, {\\em A\\&A\\/} {\\bf 247} (1991) 215. \n\\bibitem{vertraete96} L. Verstraete, J.L. Puget, E. Falgarone, S. Drapatz, C.M. Wright, R. Timmermann, {\\em A\\&A \\/} {\\bf 315} (1996) L337.\n\\bibitem{dcesarsky96} D. Cesarsky, J. Lequeux, A. Abergel, M. Perault, E. Palazzi, S.C. Madden, D. Tran, {\\em A\\&A\\/} {\\bf 315} (1996) L309.\n\\bibitem{tran98} D. Tran, {\\em Ph. D. Thesis\\/}, 1998, Universit\\'e Paris XI.\n\\bibitem{roche91} P.F. Roche, D.K. Aitken, C.H. Smith, M.J. Ward, {\\em MNRAS\\/} {\\bf 248} (1991) 606.\n\\bibitem{contoursi99} A. Contursi, J. Lequeux, D. Cesarsky, F. Boulanger, M. Rubio, M. Hanus, M. Sauvage, D. Tran, A. Bosma, S.C. Madden, L. Vigroux, {\\em A\\&A\\/} {\\bf 315} (2000) submitted.\n\\bibitem{crowther99} P.A. Crowther, S.C. Beck, A.J. Willis, P.S. Conti, P.W. Morris, R.S. Sutherland, {\\em MNRAS\\/} {\\bf 304} (1999) 645.\n\\bibitem{papader98} P. Papaderos, Y.I. Izotov, K.J. Fricke, T.X. Thuan, N.G. Guseva, {\\em A\\&A\\/} {\\bf 338} (1998) 43.\n\\bibitem{thuan99b} T.X. Thuan, Y.I. Izotov, C.B. Foltz {\\em ApJ\\/} {\\bf 525} (1999) 105..\n\\bibitem{schaerer99} D. Schaerer, T. Contini, M. Pindao, {\\em A\\&AS\\/} {\\bf 136} (1999) 35.\n\\bibitem{hunter94} D.A. Hunter, R.W. O'Connell, J.S. Gallagher, {\\em AJ\\/} {\\bf 108} (1994) 84.\n\\bibitem{oconnell94} R.W. O'Connell, J.S. Gallagher, D.A. Hunter, {\\em ApJ\\/} {\\bf 443} (1994) 65.\n\\bibitem{thuan97} T.X. Thuan, Y.I. Izotov, V.A. Lipovetsky, {\\em ApJ\\/} {\\bf 477} (1997) 661.\n\\bibitem{martin98} C.L. Martin, {\\em ApJ\\/} {\\bf 506} (1998) 222.\n\\bibitem{taylor99} C.L. Taylor, S. H\\\"uttemeister, U. Klein, A. Greve, {\\em A\\&A\\/} {\\bf 349} (1999) 424.\n\\bibitem{israel90} F.P. Israel, W. van Driel, {\\em A\\&A\\/} {\\bf 236} (1990) 323.\n\\bibitem{fioc97} M. Fioc, B. Rocca-Volmerange, {\\em A\\&A} {\\bf 326} (1997) 950.\n\\bibitem{ferland96} G.J. Ferland, {\\em Int.Rep. Dept. of Physics, U. Kentucky} (1996).\n\\bibitem{lutz98} D. Lutz, D. Kunze, H.W.W. Spoon, M.D. Thornley, {\\em A\\&A\\/} {\\bf 333} (1998) L75.\n\\bibitem{schaerer99b} D. Schaerer, G. Stasi\\'nska, {\\em A\\&A\\/} {\\bf 345} (1999) L17.\n\\bibitem{genzel98} R. Genzel et al., {\\em A\\&A\\/} {\\bf 335} (1998) 161.\n\\bibitem{thornley00} M. D. Thornley, N.M. F\\\"orster Schreiber, D. Lutz, R. Genzel, H.W.W. Spoon, D. Kunze, A. Sternberg, {\\em ApJ\\/} (2000) submitted.\n\\bibitem{vacca92} W.D. Vacca, P.S. Conti, {\\em ApJ\\/} {\\bf 401} (1992) 543.\n\\bibitem{desert90} F.-X. D\\'esert, F. Boulanger, J.-L. Puget, {\\em A\\&A\\/} {\\bf 237} (1990) 215.\n\\bibitem{bakes94} E.L.O. Bakes, A.G.G.M. Tielens, {\\em ApJ\\/} {\\bf 427} (1994) 822.\n\\bibitem{varosi99} F. V\\'arosi, E. Dwek, {\\em ApJ\\/} {\\bf 523} (1999) 265.\n\n\\end{thebibliography}\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002046.extracted_bib",
"string": "\\begin{thebibliography}{999}\n\\bibitem{kessler96} M.F. Kessler et al., {\\em A\\&A\\/} {\\bf 315} (1996) L27.\n\\bibitem{jones97} A.P. Jones, S.C. Madden, S.W.J. Colgan, N. Geis, M. Haas, P. Maloney, T. Nikola, A. Poglitsch, {\\em Extragalactic Astronomy in the Infrared\\/}, (1997) G. Mamon, T. Thuan, J.Tran Than, eds, Editions Fronti\\`eres, Paris, 1997, p.101.\n\\bibitem{hollenbach97} D. Hollenbach, A.G.G.M. Tielens, {\\em Ann. Rev. Astron. Astrophys\\/} {\\bf 35} (1997) 179.\n\\bibitem{stacey91} G.J. Stacey, N. Geis, R. Genzel, J.B. Lugten, A. Poglitsch, A. Sternberg, C.H. Townes, {\\em ApJ\\/} {\\bf 373} (1991) 423.\n\\bibitem{mochizuki94} K. Mochizuki et al, {\\em ApJ\\/} {\\bf 430} (1994) L37.\n\\bibitem{poglitsch95} A. Poglitsch, A. Krabbe, S.C. Madden, T. Nikola, N. Geis, L.E.B. Johansson, G.J. Stacey, A. Sternberg, {\\em ApJ\\/} {\\bf 454} (1995) 293.\n\\bibitem{pak98} S. Pak, D.T. Jaffe, E. F. van Dishoeck, L.E.B. Johansson, R.S. Booth, {\\em ApJ\\/} {\\bf 498} (1998) 735.\n\\bibitem{maloney88} P. Maloney, J.H. Black {\\em APJ\\/} {\\bf 325} (1988) 389.\n\\bibitem{israel96} F.P. Israel, P.R. Maloney , N. Geis, F. Herrmann, S.C. Madden, A. Poglitsch, G.J. Stacey, {\\em ApJ\\/} {\\bf 465} (1996) 738.\n\\bibitem{kaufman99} M.J. Kaufman, M.G. Wolfire, D.J. Hollenbach, M.L. Luhman, {\\em ApJ\\/} (1999) in press.\n\\bibitem{madden97} S.C. Madden, A. Poglitsch, N. Geis, G.J. Stacey, C.H. Townes , {\\em ApJ\\/} {\\bf 483} (1997) 200.\n\\bibitem{burton90} M.G. Burton, D.J. Hollenbach, A.G.G.M. Tielens, {\\em ApJ\\/} {\\bf 365} (1990) 620.\n\\bibitem{ccecarsky96} C.J. Cesarsky et al., {\\em A\\&A\\/} {\\bf 315} (1996) 32.\n\\bibitem{thuan99a} T.X. Thuan, M. Sauvage, S.C. Madden, {\\em ApJ\\/} {\\bf 516} (1999) 783.\n\\bibitem{waller91} W.H. Waller, {\\em ApJ\\/} {\\bf 370} (1991) 144.\n\\bibitem{dudley99} C.C. Dudley, {\\em MNRAS\\/} {\\bf 304} (1999) 549.\n\\bibitem{laurent00} O. Laurent, I.F. Mirabel, V. Charmandaris, P. Gallais, S.C. Madden, M. Sauvage, L. Vigroux, C. Cesarsky, {\\em A\\&A\\/} (2000) submitted.\n\\bibitem{leger84} A. L\\'eger, J.-L. Puget, {\\em A\\&A\\/} {\\bf 137} (1984) L5.\n\\bibitem{allaman89} L.J. Allamandola, A.G.G.M.. Tielens, J.R. Barker, {\\em ApJS\\/} {\\bf 71} (1989) 733.\n\\bibitem{papou91} R. Papoular, C. Reynaud, I. Nenner, {\\em A\\&A\\/} {\\bf 247} (1991) 215. \n\\bibitem{vertraete96} L. Verstraete, J.L. Puget, E. Falgarone, S. Drapatz, C.M. Wright, R. Timmermann, {\\em A\\&A \\/} {\\bf 315} (1996) L337.\n\\bibitem{dcesarsky96} D. Cesarsky, J. Lequeux, A. Abergel, M. Perault, E. Palazzi, S.C. Madden, D. Tran, {\\em A\\&A\\/} {\\bf 315} (1996) L309.\n\\bibitem{tran98} D. Tran, {\\em Ph. D. Thesis\\/}, 1998, Universit\\'e Paris XI.\n\\bibitem{roche91} P.F. Roche, D.K. Aitken, C.H. Smith, M.J. Ward, {\\em MNRAS\\/} {\\bf 248} (1991) 606.\n\\bibitem{contoursi99} A. Contursi, J. Lequeux, D. Cesarsky, F. Boulanger, M. Rubio, M. Hanus, M. Sauvage, D. Tran, A. Bosma, S.C. Madden, L. Vigroux, {\\em A\\&A\\/} {\\bf 315} (2000) submitted.\n\\bibitem{crowther99} P.A. Crowther, S.C. Beck, A.J. Willis, P.S. Conti, P.W. Morris, R.S. Sutherland, {\\em MNRAS\\/} {\\bf 304} (1999) 645.\n\\bibitem{papader98} P. Papaderos, Y.I. Izotov, K.J. Fricke, T.X. Thuan, N.G. Guseva, {\\em A\\&A\\/} {\\bf 338} (1998) 43.\n\\bibitem{thuan99b} T.X. Thuan, Y.I. Izotov, C.B. Foltz {\\em ApJ\\/} {\\bf 525} (1999) 105..\n\\bibitem{schaerer99} D. Schaerer, T. Contini, M. Pindao, {\\em A\\&AS\\/} {\\bf 136} (1999) 35.\n\\bibitem{hunter94} D.A. Hunter, R.W. O'Connell, J.S. Gallagher, {\\em AJ\\/} {\\bf 108} (1994) 84.\n\\bibitem{oconnell94} R.W. O'Connell, J.S. Gallagher, D.A. Hunter, {\\em ApJ\\/} {\\bf 443} (1994) 65.\n\\bibitem{thuan97} T.X. Thuan, Y.I. Izotov, V.A. Lipovetsky, {\\em ApJ\\/} {\\bf 477} (1997) 661.\n\\bibitem{martin98} C.L. Martin, {\\em ApJ\\/} {\\bf 506} (1998) 222.\n\\bibitem{taylor99} C.L. Taylor, S. H\\\"uttemeister, U. Klein, A. Greve, {\\em A\\&A\\/} {\\bf 349} (1999) 424.\n\\bibitem{israel90} F.P. Israel, W. van Driel, {\\em A\\&A\\/} {\\bf 236} (1990) 323.\n\\bibitem{fioc97} M. Fioc, B. Rocca-Volmerange, {\\em A\\&A} {\\bf 326} (1997) 950.\n\\bibitem{ferland96} G.J. Ferland, {\\em Int.Rep. Dept. of Physics, U. Kentucky} (1996).\n\\bibitem{lutz98} D. Lutz, D. Kunze, H.W.W. Spoon, M.D. Thornley, {\\em A\\&A\\/} {\\bf 333} (1998) L75.\n\\bibitem{schaerer99b} D. Schaerer, G. Stasi\\'nska, {\\em A\\&A\\/} {\\bf 345} (1999) L17.\n\\bibitem{genzel98} R. Genzel et al., {\\em A\\&A\\/} {\\bf 335} (1998) 161.\n\\bibitem{thornley00} M. D. Thornley, N.M. F\\\"orster Schreiber, D. Lutz, R. Genzel, H.W.W. Spoon, D. Kunze, A. Sternberg, {\\em ApJ\\/} (2000) submitted.\n\\bibitem{vacca92} W.D. Vacca, P.S. Conti, {\\em ApJ\\/} {\\bf 401} (1992) 543.\n\\bibitem{desert90} F.-X. D\\'esert, F. Boulanger, J.-L. Puget, {\\em A\\&A\\/} {\\bf 237} (1990) 215.\n\\bibitem{bakes94} E.L.O. Bakes, A.G.G.M. Tielens, {\\em ApJ\\/} {\\bf 427} (1994) 822.\n\\bibitem{varosi99} F. V\\'arosi, E. Dwek, {\\em ApJ\\/} {\\bf 523} (1999) 265.\n\n\\end{thebibliography}"
}
] |
astro-ph0002047
|
THE PRIMORDIAL HELIUM ABUNDANCE: TOWARDS UNDERSTANDING AND REMOVING THE COSMIC SCATTER IN THE $dY/dZ$ RELATION
|
[
{
"author": "D. R. Ballantyne\\altaffilmark{1}"
},
{
"author": "G. J. Ferland\\altaffilmark{2} and P. G. Martin"
}
] |
We present results from photoionization models of low-metallicity \h regions. These nebulae form the basis for measuring the primordial helium abundance. Our models show that the helium ionization correction factor (ICF) can be non-negligible for nebulae excited by stars with effective temperatures larger than 40,000~K. Furthermore, we find that when the effective temperature rises to above 45,000~K, the ICF can be significantly negative. This result is independent of the choice of stellar atmosphere. However, if an \h region has an \3/\1 ratio greater than 300, then our models show that, regardless of its metallicity, it will have a negligibly small ICF. A similar, but metallicity dependent, result was found using the \3/H$\beta$ ratio. These two results can be used as selection criteria to remove nebulae with potentially non-negligible ICFs. Using our metallicity independent criterion on the data of \citet{izo98} results in a 20\% reduction of the rms scatter about the best fit $Y-Z$ line. A fit to the selected data results in a slight increase of the value of the primordial helium abundance.
|
[
{
"name": "ms.tex",
"string": "\\documentclass[preprint]{aastex}\n\n\\newcommand{\\h}{H\\scriptsize II \\normalsize}\n\\newcommand{\\etal}{et al.}\n\\newcommand{\\3}{[O III]~$\\lambda$5007}\n\\newcommand{\\1}{[O I]~$\\lambda$6300}\n\n\\begin{document} \n\n\\title{THE PRIMORDIAL HELIUM ABUNDANCE: TOWARDS UNDERSTANDING AND\nREMOVING THE COSMIC SCATTER IN THE $dY/dZ$ RELATION}\n\n\\author{D. R. Ballantyne\\altaffilmark{1}, G. J. Ferland\\altaffilmark{2} \nand P. G. Martin}\n\\affil{Canadian Institute for Theoretical Astrophysics, University of\nToronto, Toronto, ON, Canada~M5S~3H8; ballanty, ferland and\[email protected]}\n\n\\altaffiltext{1}{Current address: Institute of Astronomy, \nMadingley Road, Cambridge, United Kingdom CB3 0HA}\n\n\\altaffiltext{2}{Also: Department of Physics and Astronomy, \nUniversity of Kentucky, Lexington, KY 40506-0055 USA} \n\n\\begin{abstract}\nWe present results from photoionization models of low-metallicity \\h\nregions. These nebulae form the basis for measuring the primordial helium abundance.\nOur models show that the helium ionization correction factor (ICF) can be non-negligible\nfor nebulae excited by stars with effective temperatures larger than 40,000~K. \nFurthermore, we find that when the effective temperature rises to above 45,000~K, the\nICF can be significantly negative. This result is independent of the choice of stellar\natmosphere. However, if an \\h region has an \\3/\\1 ratio greater than 300, then our \nmodels show that, regardless of its metallicity, it will have a negligibly small ICF. \nA similar, but metallicity dependent, result was found using the \\3/H$\\beta$ ratio. These\ntwo results can be used as selection criteria to remove nebulae with potentially \nnon-negligible ICFs. Using our metallicity independent criterion on the data of\n\\citet{izo98} results in a 20\\% reduction of the rms scatter about the best fit \n$Y-Z$ line. A fit to the selected data results in a slight increase of the value \nof the primordial helium abundance. \n\n\\end{abstract}\n\n\\keywords{galaxies: abundances --- galaxies: ISM --- \\h regions --- ISM: abundances}\n\n\\section{INTRODUCTION}\n\\label{sec:intro}\n\nAn accurate measurement of the primordial helium abundance would be\nan important test of standard big bang nucleosynthesis \\citep{oli97}, and\nwould also constrain the values of the photon-to-baryon ratio and $\\Omega_b$\n \\citep{oli99}. The traditional procedure to measure the primordial helium\nabundance is to make use of the correlation between the helium mass fraction\n ($Y$) and metal abundance ($Z$). This correlation is then extrapolated\nto zero metallicity to estimate the primordial mass fraction of helium, \n$Y_p$. Spectroscopic observations of bright, low-metallicity extragalactic \n\\h regions provide the data for these studies \\cite[e.g.,][]{oli95,oli97,\nizo94,izo97,izo98,tor89,skil98}. \n\nTo be cosmologically useful the value of $Y_p$ has to be determined to better\nthan 5\\%. Fortunately, abundance determinations from measurements of line ratios\n is relatively straightforward \\citep{pei75,ben99}, and can, {\\it in theory}, \ngive the desired accuracy. However, to reach the needed level of precision, any\nsystematic errors involved with target selection, observations, and data \nanalysis must be identified and corrected. Many such systematic \nerrors have already been identified\n\\citep{dav85,din86,pag92,skil94,pei96,izo97,ste97,skil98}, but any errors resulting \nfrom the so-called ``ionization correction factor'' (ICF) have so far been \nassumed to be small. The ICF corrects for the fact that some amount of atomic \n(i.e., unseen) helium might be present in ionized regions of hydrogen \n\\citep{ost89,pei75}. This correction traditionally has been assumed to be \nzero because measurements of the primordial helium abundance employ \nobservations of bright extragalactic \\h regions. These regions are excited by \nclusters of young stars with effective temperatures greater than\n40,000~K. Calculations by \\citet{sta90} and \\citet{pag92} showed that the\nhelium ICF should be negligibly small for these \\h regions. As a result, \nrecent determinations of $Y_p$ have assumed that the helium ICF is small.\n\nVery recently, \\citet{arm99} presented calculations that showed that\n\\h regions excited by stars with temperatures greater than 40,000~K can\nhave non-negligible ICFs. \\citet{arm99} found that the ICFs were often negative \n(i.e., the helium ionized zone is {\\bf larger} than the hydrogen one; \n\\citet{sta80,sta82}, \\citet{pen86}) for the hardest \nstellar continua. These results were confirmed by \\citet{vie99}. \nIn this paper, we follow up on the work of \\citet{arm99}, and develop observational \ndiagnostics of when the He ICF is important and when it can be ignored. We then \napply these diagnostics to the data of \\cite{izo98} to illustrate how our technique\n can improve the precision of the measurement of $Y_p$. \n\nWe describe our calculations in \\S~\\ref{sec:calc}, and our results in\n\\S~\\ref{sec:results}. The main results are summarized in \\S~\\ref{sec:concl}.\n\n\\section{DESCRIPTION OF CALCULATIONS}\n\\label{sec:calc}\n\nIn order to investigate the effects of a non-negligible ICF on the determination of the \nprimordial helium abundance, we ran photoionization models of \\h regions and extracted \nthe ICF for each nebula. These calculations are very similar to ones presented by \n\\citet{arm99} and \\citet{bot98}, and were made with the development version \nof Cloudy, last described by \\citet{fer98}.\n\nSince we are modeling \\h regions, our models use the ISM abundances and grain model that \nwere used and described by \\citet{arm99}. However, we scaled both the metal \nand grain abundances to lower values because, in this case, we are most interested in \nlower metallicity nebulae. The scaling was implemented so that all metals and grains\nwere varied together relative to hydrogen and helium, but the He/H ratio was held\nconstant. We modeled nebulae at three different metallicities: O/H=32, 64, and 128 \nparts per million [ppm] ($Z=Z_{\\odot}/23, Z_{\\odot}/12$, and $Z_{\\odot}/6$ respectively). \nFor each metallicity, 1936 models were computed for each\nof the following spectral energy distributions: the LTE plane-parallel\natmospheres of \\citet{kur91}, the non-LTE, wind-blanketed, solar\nabundance CoStar atmospheres of \\citet{sc96a,sc96b}, the earlier NLTE\natmospheres of \\citet{mih72}, and for completeness blackbodies. We also\nran models using the subsolar-abundance CoStar atmospheres which are\nspectrally slightly harder than the solar abundance ones. These models\nresulted in slightly more negative ICFs, but the values of the line\nratio cutoffs (\\S~\\ref{sub:zdep} \\& \\S~\\ref{sub:zindep}) were not\nchanged from the ones calculated with a solar abundance atmosphere.\n\nFor each atmosphere we computed models with 10~cm$^{-3} \\leq n_H \\leq 10^6$~cm$^{-3}$, \n10$^{-4} \\leq U \\leq 10^{-0.25}$, and 40,000~K$ \\leq T_{eff} \\leq 50,000$~K, where\n$U$ is the ionization parameter defined as in Eq.~4 of \\citet{arm99}. Giant \nextragalactic \\h regions that are observed are generally excited by large clusters, so this \nrange of parameters should cover all such nebulae. We modeled the nebulae as\nplane-parallel constant density slabs, a simple way to characterize blister \\h regions.\nOur proposed diagnostic indicators are the \\3 and \\1 lines (\\S~\\ref{sub:zdep} \\& \n\\S~\\ref{sub:zindep}), and these should be fairly independent of the\nassumed geometry (sphere, sheet, or evaporating blister). The \\3/H$\\beta$\nratio represents the cooling per recombination (the Stoy ratio) and so is\nprimarily sensitive to the stellar temperature \\citep{sto33,kal78}\nrather than geometry. Similarly, the \\1/H$\\beta$ intensity ratio mostly\nmeasures the \"softness\" of the hydrogen ionization front (where the line\nforms - Netzer \\& Davidson 1979).\n\n\\section{RESULTS}\n\\label{sec:results}\n\\subsection{Temperature Dependence}\n\\label{sub:temp}\n\nFigure~\\ref{fig:temp-icf} plots the ICF calculated from the Kurucz and CoStar models \nversus the stellar temperature. Note that we define the ICF such that an ICF of zero \ncorresponds to zero correction:\n\\begin{equation}\n\\label{eq:ICF}\n\\mathrm{ICF}={\\left < \\mathrm{H^{+}}\\!/\\,\\mathrm{H} \\right > \\over \\left < \n\\mathrm{He^{+}}\\!/\\,\\mathrm{He} \\right > } - 1,\n\\label{eq:icf}\n\\end{equation}\nwhere the angle brackets denote the volume mean ionization fraction. This definition\ntakes into account the presence of any He$^{+2}$ in the nebula. \nFigure~\\ref{fig:temp-icf} clearly \nshows that one can obtain a non-negligible ICF for stars with temperatures greater \nthan 40,000~K. The harder CoStar atmospheres give preferentially negative ICFs, which, \nif not taken into account, would result in a overestimate of the helium abundance. The \nsame is true of the Mihalas atmospheres (not shown). These results agree with the \ncalculations of \\citet{arm99} and \\citet{vie99}. The softer Kurucz atmospheres result in \npreferentially positive ICFs (i.e., the helium ionized zone is smaller than the hydrogen one), \nalthough, at temperatures greater than 45,000~K, they can \nalso give negative ICFs. The blackbody atmospheres, the least realistic, are softer still, \nbut even they can produce negative ICFs in some models at the highest temperatures. \nTherefore, negative ICFs seem to be found at high stellar temperatures {\\it independent \nof the type of stellar atmosphere}.\n\n\\subsection{Metallicity Dependent Cutoff Criterion}\n\\label{sub:zdep}\n\nA negative ICF occurs as the results of penetrating high-energy photons \npreferentially ionizing helium, due to its large photoionization cross section. \nThis tends to be important for lower ionization parameter models, since these have\nsignificant regions where H and He are partially ionized. We expect these nebula to be\ncharacterized by lower \\3/H$\\beta$ ratios (a measure of excitation) and larger\n\\1/H$\\beta$ ratios (since \\1 is formed in warm atomic regions).\n\nThe results presented in \\S~\\ref{sub:temp} show that it is not appropriate to simply \nassume that the ICF is zero when a nebula is excited by a star with a temperature \ngreater than 40,000~K. However, it would be important to develop observational \ndiagnostics for when the ICF is important and when it is not. Figure~\\ref{fig:o3-icf} \nshows such a diagnostic. A plot of ICF versus \\3/H$\\beta$ shows that beyond a line \nratio of about 3--4 the ICF is negligible (for clarity results are shown for Kurucz \nand CoStar atmospheres only; a plot for blackbody and Mihalas atmospheres is very\nsimilar). However, the value of the cutoff will depend on metallicity. We found very \nsmall ICFs for line ratios greater than the following cutoff:\n\\begin{equation}\n\\label{eq:zcutoff}\n\\left (\\mathrm{[O\\ III]}\\ \\lambda 5007/\\mathrm{H}\\beta \\right )_{\\mathrm{Cutoff}} =\n(0.025 \\pm 0.004)\\mathrm{O/H}+(1.139 \\pm 0.306),\n\\end{equation}\nwhere O/H is measured in parts per million. \\h regions which have an \\3/H$\\beta$\nratio less than the cutoff for their metallicity might be subject to an ICF \ncorrection. Unless this correction can be made (and, in general, it cannot) these\n\\h regions should be removed from the abundance analysis, as they will increase the\nscatter in the $dY/dZ$ relation used to determine the primordial helium abundance.\n\n\\subsection{Metallicity Independent Cutoff Criterion}\n\\label{sub:zindep}\n\nOne can improve the above result by finding emission line ratios that should be\nindependent of metallicity. Figure~\\ref{fig:o3o1-icf} plots the helium ICF versus\nthe \\3/\\1 ratio. The figure shows that the ICF is negligible for a line ratio greater\nthan about 300. Not surprisingly, this result is {\\it independent of metallicity}. \n\nThere are some Kurucz and blackbody models which result in a non-negligible ICF at line \nratios larger than this cutoff. These models had low stellar temperatures \n(40,000--42,000~K), and were found over a narrow range in both $\\log U$ ($-1.5$ to $-2.25$) \nand $\\log n_H$ (1.0--3.0). Their positive ICF is a result of combining the low stellar\ntemperatures and the softness of their atmospheres; their large \\3/\\1 ratio is a result\nof combining the fairly high ionization parameter with the low density. CoStar and Mihalas \nmodels, which are considered more ``realistic'', result in only very small ICFs in this \nregion.\n\nTherefore, we find that any \\h region, regardless of its metallicity, that has an\n\\3/\\1 ratio less than about 300 might be subject to an ICF correction and should not \nbe used to determine the primordial helium abundance.\n\n\\subsection{Application to Real Data}\n\\label{sub:apply}\n\nTo see how these new results affect the determination of $Y_p$, we applied the\nmetallicity independent rejection criteria to the data of \\citet{izo98}, and the\nresults are shown in Figure~\\ref{fig:o3o1-y}. There are a number of points to note\nfrom this Figure:\n\\begin{enumerate}\n\n\\item Our criterion rejects points over the entire range of metallicity, so there is\nno metallicity bias. The rejected points also fall evenly over the range of $Y$ values,\nwhich implies that there is no correlation between $Y$ and the \\3/\\1 ratio.\n\n\\item At an \\3/\\1 cutoff of 300 there is a 20\\% reduction in the weighted rms scatter \nabout the best fit line. This is encouraging evidence that part of the scatter was\ndue to the ICF, and the situation has indeed improved by the implementation of the\ncutoff.\n\n\\item The negative slopes predicted by using a\ncutoff$\\ \\geq$ 300 result from weighted fits to the small number of data\nthat remain after applying the cutoff, and are probably not\nrealistic. Given the current data, a cutoff value greater than 300 is\ntoo severe (not practical).\n\n\\item Despite the increased errors in the slope and the intercept, we find that\nimplementing our cutoff will result in a larger value of $Y_p$. Specifically, we\nfind $Y_p = 0.2489 \\pm 0.0030$ when the cutoff is taken at a \\3/\\1 ratio of 300. \n\\cite{izo98} find $0.2443 \\pm 0.0015$ (our fit gives $0.2443 \\pm 0.0013$ with no cutoff), \nso the two results are barely consistent at the 1$\\sigma$ level. This result is \nin the opposite direction of the shift predicted by the Monte Carlo simulations of \n\\citet{vie99}, but moves the value of $Y_p$ closer to the theoretically predicted \nvalues \\citep{oli95}.\n\n\\end{enumerate}\n\nThere is always the possibility that systematic errors are introduced whenever data\nare rejected by a certain criterion. The above selection criterion preferentially\nselects \\h regions that have large \\3/\\1 ratios. This ratio is generally large \nwhenever the \\3 line is strong (this is consistent with our metallicity dependent \ncriterion). The \\3 line is a major source of cooling in a nebula, and so by selecting \n\\h regions with strong \\3 lines we are selecting regions ionized by hotter stars. Since \nthese large extragalactic \\h regions are generally ionized by clusters, ones with \nstrong \\3 lines are preferentially younger. However, this is unlikely to introduce a \nsystematic error in the primordial helium abundance determination, as young clusters \ncan form at any metallicity. Indeed, Figure~\\ref{fig:o3o1-y} shows that the points \nrejected by applying the cutoff span the entire range of metallicity.\n\nThere is also the possibility that physical conditions within the \\h regions\nmay bias our results. For example, in some nebulae the intensity of the \\1 line \ncould be enhanced due to shock heating. This would lower the measured \\3/\\1 ratio,\nand could move it below our selection criterion. However, shock heating would not\nchange the ICF of the nebula, so even though application of our criterion might\nreject such a \\h region, it will not bias the determination of $Y_p$. \n\nAnother potential situation in \\h regions is that the nebula may be matter\nbounded (i.e., optically thin to the Lyman continuum) in certain solid\nangles or sectors. Because there will be no hydrogen ionization front in such\nsectors, and therefore no \\1 line emission, the presence of such sectors\nwill increase the measured \\3/\\1 ratio, possibly pushing it above our selection \ncriterion. However, these sectors will also have little or no neutral helium \nwithin them, and so will have no ICF. Therefore, although the\nother, ionization bounded, sectors of the \\h region could have a\nnon-negligible ICF, this will be diluted by the matter bounded sectors.\nWe anticipate that even if such an \\h region were shifted into our\nselected data, there ought not be a large effect on determining $Y_p$. According\nto Fig.~\\ref{fig:o3o1-icf}, to severely bias the results a number of points would have \nto shift rightward in \\3/\\1 by a factor larger than ten; but such a large shift in \nthe line ratio would probably result in a large dilution in the ICF. More modeling \nwould be needed to quantify how little an impact matter bounded sectors would have on \nthe \\3/\\1 ratio and ICFs.\n\n\\section{CONCLUSIONS}\n\\label{sec:concl}\nIn this paper we have shown the following:\n\\begin{enumerate}\n\n\\item There can be a non-negligible ICF correction for \\h regions excited by stars with\ntemperatures greater than 40,000~K. At temperatures higher than 45,000~K, the ICF is\npreferentially negative. This result is independent of the atmosphere of the O star.\n\n\\item There is a simple procedure to determine if an ICF correction needs to be made for\na given \\h region. If the \\3/\\1 ratio is greater than 300, then no correction is needed.\nThis criterion is independent of metallicity. If the \\1 line cannot be measured, then \nthere is a metallicity dependent cutoff (Eq.~\\ref{eq:zcutoff}) that can be used \nwith the \\3 line.\n\n\\item Applying the metallicity independent criterion to the data of \\citet{izo98}\nresults in reducing the rms scatter about the best fit $Y-Z$ line by 20\\%. \nThis will help remove systematic errors relating to unrecognized ICF effects, and ought to \nimprove the reliability of the $Y_p$ determination. Furthermore, an analysis of the \nselected data gives a larger value of $Y_p$ than was originally measured, which is \ncloser to the theoretically expected value.\n\\end{enumerate} \n\n\\acknowledgements\n\nG.J.F.\\ thanks CITA for its hospitality during a sabbatical year and acknowledges\nsupport from the Natural Science and Engineering Research Council of Canada through\nCITA. D.R.B.\\ also acknowledges financial support from NSERC. We acknowledge useful\ncomments from an anonymous referee.\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\\bibitem[Armour \\etal (1999)]{arm99} Armour, M-H., Ballantyne, D. R., \nFerland, G. J., Karr, J. \\& Martin, P. G. 1999, \\pasp, 111, 1251.\n\\bibitem[Benjamin, Skillman \\& Smits(1999)]{ben99} Benjamin, R. A., Skillman, E. D. \n\\& Smits, D. P. 1999, \\apj, 514, 307.\n\\bibitem[Bottorff \\etal (1998)]{bot98} Bottorf, M., Lamothe, J., Momjian, E.,\nVerner, E., Vinkovic, D. \\& Ferland, G. J. 1998, \\pasp, 110, 1040.\n\\bibitem[Davidson \\& Kinman(1985)]{dav85} Davidson, K. \\& Kinman, T. D. 1985, \n\\apjs, 58, 321.\n\\bibitem[Dinerstein \\& Shields(1986)]{din86} Dinerstein, H. L. \\& Shields, G. A. 1986,\n\\apj, 311, 45.\n\\bibitem[Ferland \\etal (1998)]{fer98} Ferland, G. J., Korista, K. T.,\nVerner, D. A., Ferguson, J. W., Kingdon, J. B., \\& Verner, E. W. 1998,\n\\pasp, 110, 761.\n\\bibitem[Izotov, Thuan \\& Lipovetsky(1994)]{izo94} Izotov, Y. I., Thuan, T. X. \\&\nLipovetsky, V. A. 1994, \\apj, 435, 647.\n\\bibitem[Izotov, Thuan \\& Lipovetsky(1997)]{izo97} Izotov, Y. I., Thuan, T. X. \\&\nLipovetsky, V. A. 1997, \\apjs, 108, 1.\n\\bibitem[Izotov \\& Thuan(1998)]{izo98} Izotov, Y. I. \\& Thuan, T. X. 1998, \n\\apj, 500, 188.\n\\bibitem[Kaler(1978)]{kal78} Kaler, J. B. 1978, \\apj, 220, 887.\n\\bibitem[Kurucz(1991)]{kur91} Kurucz, R. L. 1991, in Proceedings of the \nWorkshop on Precision Photometry: Astrophysics of the Galaxy, eds. Davis \nPhilip, A. C., Upgren, A. R., \\& James, K. A. (Schenectady: Davis), p. 27.\n\\bibitem[Mihalas(1972)]{mih72} Mihalas, D. 1972, Non-LTE Atmospheres for B and O Stars,\nNCAR-TN/STR-76.\n\\bibitem[Netzer \\& Davidson(1979)]{net79} Netzer, H. \\& Davidson, K. 1979, \\mnras,\n187, 871.\n\\bibitem[Olive \\& Steigman(1995)]{oli95} Olive, K. A. \\& Steigman, G. 1995, \\apjs,\n 97, 490.\n\\bibitem[Olive, Steigman \\& Skillman(1997)]{oli97} Olive, K. A., Steigman,\n G. \\& Skillman, E. D. 1997, \\apj, 483, 788.\n\\bibitem[Olive, Steigman \\& Walker(1999)]{oli99} Olive, K. A., Steigman, G. \\&\nWalker, T. P. 1999, \\physrep, in press (astro-ph/9905320)\n\\bibitem[Osterbrock(1989)]{ost89} Osterbrock, D. E. 1989, Astrophysics of Gaseous\nNebulae and Active Galactic Nuclei (Mill Valley: University Science Books).\n\\bibitem[Pagel \\etal (1992)]{pag92} Pagel, B. E. J., Simonson, E. A., Terlevich, R. J.\n \\& Edmunds, M. 1992, \\mnras, 255, 325.\n\\bibitem[Peimbert(1975)]{pei75} Peimbert, M. 1975, \\araa, 13, 11.\n\\bibitem[Peimbert(1996)]{pei96} Peimbert, M. 1996, Rev. Mex. Astr. Astrofis., \nSerie de Conferencias, 4, 55.\n\\bibitem[Pe\\~{n}a(1986)]{pen86} Pe\\~{n}a, M. 1986, \\pasp, 98, 1061. \n\\bibitem[Schaerer \\etal (1996a)]{sc96a} Schaerer, D., de Koter, A., Schmutz, W.\n \\& Maeder, A. 1996a, \\aap, 310, 837.\n\\bibitem[Schaerer \\etal (1996b)]{sc96b} Schaerer, D., de Koter, A., Schmutz, W.\n \\& Maeder, A. 1996b, \\aap, 312, 475.\n\\bibitem[Skillman \\etal (1994)]{skil94} Skillman, E. D., Terlevich, R. J., \nKennicutt, R. C., Garnett, D. R. \\& Terlevich, E. 1994, \\apj, 431, 172.\n\\bibitem[Skillman, Terlevich \\& Terlevich(1998)]{skil98} Skillman, E. D., \nTerlevich, E. \\& Terlevich, R. 1998, Space Sci. Rev., 84, 105.\n\\bibitem[Stasinska(1980)]{sta80} Stasinska, G. 1980, \\aap, 84, 320.\n\\bibitem[Stasinska(1982)]{sta82} Stasinska, G. 1982, \\aaps, 41, 513.\n\\bibitem[Stasinska(1990)]{sta90} Stasinska, G. 1990, \\aaps, 83, 501.\n\\bibitem[Steigman, Viegas \\& Gruenwald(1997)]{ste97} Steigman, G., Viegas, S. M. \\&\nGruenwald, R. 1997, \\apj, 490, 187.\n\\bibitem[Stoy(1933)]{sto33} Stoy, R. H. 1933, \\mnras, 93, 588. \n\\bibitem[Torres-Peimbert, Peimbert \\& Fierro(1989)]{tor89} Torres-Peimbert, S., \nPeimbert, M. \\& Fierro, J. 1989, \\apj, 345, 186.\n\\bibitem[Viegas, Gruenwald \\& Steigman(2000)]{vie99} Viegas, S. M., Gruenwald, R. \\& \nSteigman, G. 2000, \\apj, in press (astro-ph/9909213). \n\n\\end{thebibliography}\n\n\\clearpage\n\n% Figure Captions - actual figure files are separate from MS\n\n\\figcaption{A plot of the He ICF values obtained from the CoStar and Kurucz \nphotoionization models versus stellar temperature of the atmospheres. Only points \nwith ICF between $\\pm$10\\% are plotted. There are non-negligible ICFs at all values\nof stellar temperature. The CoStar atmospheres generally result in negative ICFs, \nwhile the softer Kurucz atmospheres give positive ICFs for temperatures less than about\n45,000~K. These models were run with a metallicity of (O/H)=64 ppm. \\label{fig:temp-icf}}\n\n\\figcaption{A plot of He ICF vs. \\3/H$\\beta$ using data from the CoStar and \nKurucz grids run at (O/H)=64 ppm. Only points with ICF between $\\pm$10\\% were \nplotted. At this metallicity the ICF-related cutoff is at a relative line strength of \nabout 3--4. See the text for discussion on how cutoff varies with metallicity. \n\\label{fig:o3-icf}} \n\n\\figcaption{ a) A plot of He ICF vs. \\3/\\1 with data obtained from the\nCoStar and Kurucz model grids run at (O/H)=64 ppm. The ideal ICF-related\ncutoff here is at a line ratio of 300. This cutoff is {\\it independent}\nof metallicity. The Kurucz models that have positive ICFs in the allowed\nzone are models with a particular combination of parameters (see text). \nb) Like a) but for Mihalas and blackbody atmospheres.\n\\label{fig:o3o1-icf}}\n\n\\figcaption{This figure shows the effects of applying the metallicity independent\nrejection criterion to the data of Izotov \\& Thuan (1998). The solid line is a \nweighted least-squares fit to the selected data points shown by the solid symbols. \nThe open symbols are the rejected points. For reference, the dashed line is the fit \nwith no cutoff applied. Note that as the \\3/\\1 cutoff becomes larger, the scatter of \nthe points about the best-fit line becomes smaller (there is a 20\\% reduction in\nthe rms scatter when the cutoff is 300). This procedure also shows that the value of \n$Y_p$ determined by Izotov \\& Thuan (1998) might be an underestimate. \n\\label{fig:o3o1-y}}\n\n\\clearpage\n\n\n\\end{document}\n"
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"string": "\\begin{thebibliography}{}\n\\bibitem[Armour \\etal (1999)]{arm99} Armour, M-H., Ballantyne, D. R., \nFerland, G. J., Karr, J. \\& Martin, P. G. 1999, \\pasp, 111, 1251.\n\\bibitem[Benjamin, Skillman \\& Smits(1999)]{ben99} Benjamin, R. A., Skillman, E. D. \n\\& Smits, D. P. 1999, \\apj, 514, 307.\n\\bibitem[Bottorff \\etal (1998)]{bot98} Bottorf, M., Lamothe, J., Momjian, E.,\nVerner, E., Vinkovic, D. \\& Ferland, G. J. 1998, \\pasp, 110, 1040.\n\\bibitem[Davidson \\& Kinman(1985)]{dav85} Davidson, K. \\& Kinman, T. D. 1985, \n\\apjs, 58, 321.\n\\bibitem[Dinerstein \\& Shields(1986)]{din86} Dinerstein, H. L. \\& Shields, G. A. 1986,\n\\apj, 311, 45.\n\\bibitem[Ferland \\etal (1998)]{fer98} Ferland, G. J., Korista, K. T.,\nVerner, D. A., Ferguson, J. W., Kingdon, J. B., \\& Verner, E. W. 1998,\n\\pasp, 110, 761.\n\\bibitem[Izotov, Thuan \\& Lipovetsky(1994)]{izo94} Izotov, Y. I., Thuan, T. X. \\&\nLipovetsky, V. A. 1994, \\apj, 435, 647.\n\\bibitem[Izotov, Thuan \\& Lipovetsky(1997)]{izo97} Izotov, Y. I., Thuan, T. X. \\&\nLipovetsky, V. A. 1997, \\apjs, 108, 1.\n\\bibitem[Izotov \\& Thuan(1998)]{izo98} Izotov, Y. I. \\& Thuan, T. X. 1998, \n\\apj, 500, 188.\n\\bibitem[Kaler(1978)]{kal78} Kaler, J. B. 1978, \\apj, 220, 887.\n\\bibitem[Kurucz(1991)]{kur91} Kurucz, R. L. 1991, in Proceedings of the \nWorkshop on Precision Photometry: Astrophysics of the Galaxy, eds. Davis \nPhilip, A. C., Upgren, A. R., \\& James, K. A. (Schenectady: Davis), p. 27.\n\\bibitem[Mihalas(1972)]{mih72} Mihalas, D. 1972, Non-LTE Atmospheres for B and O Stars,\nNCAR-TN/STR-76.\n\\bibitem[Netzer \\& Davidson(1979)]{net79} Netzer, H. \\& Davidson, K. 1979, \\mnras,\n187, 871.\n\\bibitem[Olive \\& Steigman(1995)]{oli95} Olive, K. A. \\& Steigman, G. 1995, \\apjs,\n 97, 490.\n\\bibitem[Olive, Steigman \\& Skillman(1997)]{oli97} Olive, K. A., Steigman,\n G. \\& Skillman, E. D. 1997, \\apj, 483, 788.\n\\bibitem[Olive, Steigman \\& Walker(1999)]{oli99} Olive, K. A., Steigman, G. \\&\nWalker, T. P. 1999, \\physrep, in press (astro-ph/9905320)\n\\bibitem[Osterbrock(1989)]{ost89} Osterbrock, D. E. 1989, Astrophysics of Gaseous\nNebulae and Active Galactic Nuclei (Mill Valley: University Science Books).\n\\bibitem[Pagel \\etal (1992)]{pag92} Pagel, B. E. J., Simonson, E. A., Terlevich, R. J.\n \\& Edmunds, M. 1992, \\mnras, 255, 325.\n\\bibitem[Peimbert(1975)]{pei75} Peimbert, M. 1975, \\araa, 13, 11.\n\\bibitem[Peimbert(1996)]{pei96} Peimbert, M. 1996, Rev. Mex. Astr. Astrofis., \nSerie de Conferencias, 4, 55.\n\\bibitem[Pe\\~{n}a(1986)]{pen86} Pe\\~{n}a, M. 1986, \\pasp, 98, 1061. \n\\bibitem[Schaerer \\etal (1996a)]{sc96a} Schaerer, D., de Koter, A., Schmutz, W.\n \\& Maeder, A. 1996a, \\aap, 310, 837.\n\\bibitem[Schaerer \\etal (1996b)]{sc96b} Schaerer, D., de Koter, A., Schmutz, W.\n \\& Maeder, A. 1996b, \\aap, 312, 475.\n\\bibitem[Skillman \\etal (1994)]{skil94} Skillman, E. D., Terlevich, R. J., \nKennicutt, R. C., Garnett, D. R. \\& Terlevich, E. 1994, \\apj, 431, 172.\n\\bibitem[Skillman, Terlevich \\& Terlevich(1998)]{skil98} Skillman, E. D., \nTerlevich, E. \\& Terlevich, R. 1998, Space Sci. Rev., 84, 105.\n\\bibitem[Stasinska(1980)]{sta80} Stasinska, G. 1980, \\aap, 84, 320.\n\\bibitem[Stasinska(1982)]{sta82} Stasinska, G. 1982, \\aaps, 41, 513.\n\\bibitem[Stasinska(1990)]{sta90} Stasinska, G. 1990, \\aaps, 83, 501.\n\\bibitem[Steigman, Viegas \\& Gruenwald(1997)]{ste97} Steigman, G., Viegas, S. M. \\&\nGruenwald, R. 1997, \\apj, 490, 187.\n\\bibitem[Stoy(1933)]{sto33} Stoy, R. H. 1933, \\mnras, 93, 588. \n\\bibitem[Torres-Peimbert, Peimbert \\& Fierro(1989)]{tor89} Torres-Peimbert, S., \nPeimbert, M. \\& Fierro, J. 1989, \\apj, 345, 186.\n\\bibitem[Viegas, Gruenwald \\& Steigman(2000)]{vie99} Viegas, S. M., Gruenwald, R. \\& \nSteigman, G. 2000, \\apj, in press (astro-ph/9909213). \n\n\\end{thebibliography}"
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The calculations in Thomas-Fermi approximation show that in a gravitational field each cell of ultra dense matter inside celestial bodies obtains a very small positive electric charge. A celestial body is electrically neutral as a whole, because the negative electric charge exists on its surface. On the order of magnitude the positive volume charge is very small ($10^{-18}e$ only). But it is sufficient to explain the occurrence of magnetic fields of celestial bodies and the existence of a discrete spectrum of steady-state values of masses of stars and pulsars.
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"string": "\\documentstyle[epsfig,12pt]{article}\n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n Submitted to \"Il Nuovo Cimento C\"\n\\begin{center}\n\n{\\bf\n\n\\title \"GYRO-MAGNETIC RELATIONS AND MASSES OF STARS}\n\n\\author \"B.V.Vasiliev\n\nInstitute in Physical and Technical Problems,Dubna,Russia,141980\n\n$e-mail: [email protected]$\n\n\\end{center}\n\n\\begin{abstract}\nThe calculations in Thomas-Fermi approximation show that in a\ngravitational field each cell of ultra dense matter inside\ncelestial bodies obtains a very small positive electric charge. A\ncelestial body is electrically neutral as a whole, because the\nnegative electric charge exists on its surface. On the order of\nmagnitude the positive volume charge is very small ($10^{-18}e$\nonly). But it is sufficient to explain the occurrence of magnetic\nfields of celestial bodies and the existence of a discrete\nspectrum of steady-state values of masses of stars and pulsars.\n\n\\end{abstract}\n\nPACS: 64.30.+i; 95.30.-k; 97.10.-q\n\n\\clearpage\n\n\\section{}\n\n\nWe cannot measure magnetic fields of the majority of stars, which\nare distant far from us. Therefore, the existence of magnetic\nfields for the majority of stars can be considered only\nhypothetically. However, the magnetic field of the Sun is known\nover than a hundred years, and in the last decades the astronomers\nmanaged to measure magnetic fields for a number of stars\n(so-called $A_{p}$-stars) \\cite{1} and some pulsars \\cite{2}. It\nis interesting to construct a model describing the generation of\nmagnetic fields by stars and to compare it with the data of the\nastronomers. The mechanism examined below is based on the\ngravity-induced electric polarization of matter. It is capable to\nexplain also the generation of magnetic fields by planets\n\\cite{3}, however, in the case of stars, this mechanism works in\nthe purest manner.\n\n\n\\section{}\nThe action of gravity on metals has often been a topic of\ndiscussion before \\cite{4}-\\cite{9}. The basic result of these\nresearches is reduced to the statement that gravity induces inside\na metal an electric field with an intensity\n\n\\begin{equation}\n\\vec{E}\\simeq\\frac{m_{i}\\vec{g}}{e},\\label{1010}\n\\end{equation}\n\nwhere $m_{i}$ is the mass of an ion,\n\n$\\vec{g}$ is gravity acceleration,\n\n$e$ is the electron charge.\n\nThis field is so small that it is not possible to measure it\nexperimentally. It is a direct consequence of the presence of an\nion lattice in a metal. This lattice is deformed by gravity and\nthen the electron gas adapts its density to this deformation. The\nresulting field becomes very small.\n\nUnder superhigh pressure, all substances transform into ultradense\nmatter usually named nuclear-electron plasma \\cite {10}. It occurs\nwhen external pressure enhances the density of matter several\ntimes \\cite{10,11}. Such values of pressure exist inside celestial\nbodies.\n\nIn nuclear-electron plasma the electrons form the degenerated\nFermi gas. At the same time, the positively charged ions form\ninside plasma a dense packing lattice \\cite{12},\\cite{13}. As\nusually accepted, this lattice may be replaced by a lattice of\nspherical cells of the same volume. The radius $r_{s}$ of such a\nspherical cell in plasma of the mass density $\\gamma$ is given by\n\n\n\\begin{equation}\n\\frac{4\\pi}{3}r_{s}^{3}=\\biggl(\\frac{\\gamma}{m_{i}}\\biggr)^{-1}=\n\\frac{Z}{n},\\label{1020}\n\\end{equation}\n\n\nwhere Z is the charge of the nucleus, $m_{i}=Am_{p}$ is the mass\nof the nucleus, A is the atomic number of the nucleus, $m_{p}$ is\nthe mass of a proton, and n is the electron number density\n\n\\begin{equation}\nn=\\frac{3Z}{4\\pi{r_{s}^{3}}}.\\label{1030}\n\\end{equation}\n\nThe equilibrium condition in matter is described by the constancy\nof its electrochemical potential \\cite{10}. In plasma, the direct\ninteraction between nuclei is absent, therefore the equilibrium in\na nuclear subsystem of plasma (at $T=0$) looks like\n\n\\begin {equation}\n\\mu_{i}=m_{i}\\psi+Ze\\varphi=const.\\label{1040}\n\\end {equation}\n\nHere $\\varphi$ is the potential of an electric field and $\\psi$ is\nthe potential of a gravitational field.\n\nThe direct action of gravitation on electrons can be neglected.\nTherefore, the equilibrium condition in the electron gas is\n\n\\begin {equation}\n\\mu_{e}=\\frac{p_{F}^{2}}{2m_{e}}-(e-\\delta{q})\\varphi=const,\\label{1050}\n\\end {equation}\n\nwhere $m_{e}$ is the mass of an electron and $p _ {F} $ is the\nFermi momentum.\n\nBy introducing the charge $\\delta {q}$, we take into account that\nthe charge of the electron cloud inside a cell can differ from\n$e$. A small number of electrons can stay on the surface of a\nplasma body where the electric potential is absent. It results\nthat the charge in a cell, subjected to the action of the electric\npotential, is effectively decreased on a small value $ \\delta\n{q}$.\n\nThe electric polarization in plasma is a result of changing in\ndensity of both nuclear and electron gas subsystems. The\nelectrostatic potential of the arising field is determined by the\nGauss' law\n\n\n\\begin{equation}\n\\nabla^{2}\\varphi=\\frac{1}{r^{2}}\\frac{d}{dr}\\biggl[r^{2}\\frac{d}\n{dr}\\varphi\\biggr]= -4\\pi\\biggl[Ze\\delta(r)-en\\biggr],\\label{1060}\n\\end{equation}\n\nwhere the position of nuclei is described by the function\n$\\delta(r)$.\n\nAccording to the Thomas - Fermi method, $n$ is approximated by\n\n\\begin{equation}\nn=\\frac{8\\pi}{3h^{3}}p^{3}_{F}.\\label{1070}\n\\end{equation}\n\nWith this substitution, Eq.({\\ref{1060}}) is converted into a\nnonlinear differential equation for $\\varphi$, which for $r>0$ is\ngiven by\n\n\\begin{equation}\n\\frac{1}{r^{2}}\\frac{d}{dr}\\left(r^{2}\\frac{d}{dr}\\varphi(r)\\right)=\n4\\pi\\left[\\frac{8\\pi}{3h^{3}}\\right] \\left[2m_{e}(\\mu_{e}+(e-\n\\delta{q})\\varphi)\\right]^{3/2}.\\label{1080}\n\\end{equation}\n\n\nIt can be simplified by introducing the following variables\n\\cite{10}:\n\n\n\\begin{equation}\n\\mu_{e}+(e-\\delta{q})\\varphi=Ze^{2}{\\frac{u}{r}}\\label{1090}\n\\end{equation}\n\n\nand $r=ax$,\n\nwhere\n\n$a=\\{\\frac{9\\pi^{2}}{128Z}\\}^{1/3}a_{0}$\n\nwith $ a_{0}=\\frac{\\hbar^{2}}{m_{e}e^{2}}=$ Bohr radius.\n\n\nWith the account of Eq.({\\ref{1040}})\n\n\\begin{equation}\nZe^{2}{\\frac{u}{r}}= const\n-\\frac{m_{i}\\psi}{Z}-\\delta{q}\\varphi.\\label{1092}\n\\end{equation}\n\n\n\nThen Eq.({\\ref{1080}}) gives\n\n\\begin{equation}\n\\frac{d^{2}u}{dx^{2}}=\\frac{u^{3/2}}{x^{1/2}}.\\label{1100}\n\\end{equation}\n\nIn terms of u and x, the electron density within a cell is given\nby \\cite{10}\n\n\\begin{equation}\nn_{TF}=\\frac{8\\pi}{3h^{3}}p^{3}_{F}=\n\\frac{32Z^{2}}{9\\pi^{3}a^{3}_{0}}\n\\biggl(\\frac{u}{x}\\biggr)^{3/2}.\\label{1110}\n\\end{equation}\n\nUnder the influence of gravity the charge of the electron gas in a\ncell becomes equal to\n\n\\begin{equation}\nQ_{e}=4\\pi{e}\\int^{r_{s}}_{0}n(r)r^{2}dr=\\frac{8\\pi{e}}{3h^{3}}\n\\biggl[2m_{e}\\frac{Ze^{2}}{a}\\biggr]^{3/2}4\\pi{a}^{3}\n\\int^{x_{s}}_{0}x^{2}dx\\biggl[\\frac{u}{x}\\biggr]^{3/2}.\\label{1140}\n\\end{equation}\n\nUsing Eq.({\\ref{1100}}), we obtain\n\n\n\\begin{equation}\nQ_{e}=Ze\\int^{x_{s}}_{0}xdx\\frac{d^{2}u}{dx^{2}}=\nZe\\int^{x_{s}}_{0}dx\\frac{d}{dx}\\biggl[x\\frac{du}{dx}-u\\biggr]=\nZe\\biggl[x_{s}\\frac{du}{dx}\\bigg|_{x_{s}}-u(x_{s})+u(0)\\biggr].\n\\label{1150}\n\\end{equation}\n\nAt $ r\\rightarrow0 $ the electric potential is due to the nucleus\nalone $ \\varphi{(r)} \\rightarrow\\frac {Ze} {r} $. It means that $\nu(0)\\rightarrow1 $ and each cell of plasma obtains a small charge\n\n\n\\begin{equation}\n\\delta{q}=Ze\\biggl[{x_{s}}\\frac{du}{dx}\\bigg|_{x_{s}}-u(x_{s})\\biggr]=\nZe{x_{s}}^2\\biggl[\\frac{d}{dx}\\biggl(\\frac{u}{x}\\biggr)\\biggr]_{x_{s}}.\n\\label{1160}\n\\end{equation}\n\nFor a cell placed in a point $R$ inside a star\n\n\\begin{equation}\n\\delta{q}=Zer_{s}^2\\biggl[\\frac{d}{dR}\n\\biggl(\\frac{u}{r}\\biggr)\\biggr]\\biggl[\\frac{dR}{dr_{s}}\\biggr].\n\\label{1170}\n\\end{equation}\n\nConsidering that gravity acceleration $\\vec{g}=-\\frac{d\\psi}{dR}$\nand the electric field intensity $\\vec{E}=-\\frac{d\\varphi}{dR}$\n\n\n\n\\begin{equation}\n\\frac{dr_{s}}{dR}=\\frac{r_{s}^2}{e}\\biggl[\\frac{\\frac{m_{i}}{Z}\\vec{g}\n+\\delta{q}\\vec{E}}{\\delta{q}}\\biggr].\\label{1180}\n\\end{equation}\n\nThis equation has the following solution\n\n\\begin{equation}\n\\frac{dr_{s}}{dR}=0\\label{1190}\n\\end{equation}\n\nand\n\n\\begin{equation}\n\\frac{m_{i}}{Z}\\vec{g}+\\delta{q}\\vec{E}=0.\\label{1200}\n\\end{equation}\n\nIn plasma, the equilibrium value of the electric field on nuclei\naccording to Eq.({\\ref{1040}}) is determined by Eq.({\\ref{1010}})\nas well as in a metal. But there is one more additional effect in\nplasma. Simultaneously with the supporting of nuclei in\nequilibrium, each cell obtains an extremely small positive\nelectric charge.\n\nAs $div{\\vec{g}}=-4\\pi{G}{n}m_{i}$ and\n$div{\\vec{E}}=4\\pi{n}\\delta{q}$, the gravity-induced electric\ncharge in a cell\n\n\\begin{equation}\n\\delta{q}=\\sqrt{G}\\frac{m_{i}}{Z}\\simeq{10^{-18}e},\\label{1210}\n\\end{equation}\n\nwhere $G$ is the gravity constant.\n\nHowever, because the sizes of bodies may be very large, the\nelectric field intensity may be very large as well\n\n\\begin{equation}\n\\overrightarrow{E}=\\frac{\\overrightarrow{g}}{\\sqrt{G}}.\\label{2050}\n\\end{equation}\n\nIn accordance with Eqs.({\\ref{1190}},{\\ref{1200}}), the action of\ngravity on matter is compensated by the electric force and the\ngradient of pressure is absent.\n\nThus, a celestial body is electrically neutral as a whole, because\nthe positive volume charge is concentrated inside the charged core\nand the negative electric charge exists on its surface and so one\ncan infer gravity-induced electric polarization of a body.\n\n\n\\section{}\n\nAt the surface of the core, the electric field intensity reduces\nto zero. The jump in electric field intensity is accompanied at\nthe surface of the core by the pressure jump $\\Delta p(R_{N})$. It\nleads to the redistribution of the matter density inside a star.\nIn a celestial body consisting of matter with an atomic structure,\ndensity and pressure grow monotonously with depth. In a celestial\nbody consisting of electron-nuclear plasma, the pressure gradient\ninside the polarized core is absent and the matter density is\nconstant. Pressure affecting the matter inside this body is equal\nto the pressure jump on the surface of the core\n\n\\begin{equation}\np=\\Delta p(R_{N})=\\frac{E(R_{N})^{2}}{8\\pi }=\\frac{2\\pi}{9}G\\gamma\n^{2}R_{N}^{2}, \\label{210}\n\\end{equation}\n\nwhere R$_{N}$ is the radius of the core.\n\nOne can say that this pressure jump is due to the existence of the\npolarization jump or, which is the same, the existence of the\nbound surface charge formed by an electron pushed out from the\ncore and making the total charge of the celestial body equal to\nzero.\n\nBecause the electron subsystem of plasma inside a star is the\nrelativistic Fermi gas, we can write its equation of state\n\\cite{10}\n\n\n\\begin{equation}\np=\\frac{(3\\pi^{2})^{1/3}}{4}\\frac{{\\hbar}c\\gamma^{4/3}}{{m_{p}}^\n{4/3}\\beta^{4/3}}\\label{220}\n\\end{equation}\n\nwhere $\\beta\\cdot{m_{p}}$ is the mass of the matter related to one\nelectron of the Fermi gas system, and\n\n$m_{p}$ is the proton mass.\n\nBecause of the electroneutrality, one proton should be related to\nelectron of the Fermi gas of plasma. The existence of one neutron\nper proton is characteristic for a substance consisting of light\nnuclei. The quantity of neutrons grows approximately to 1.8 per\nproton for the heavy nuclei substance. Therefore, it is necessary\nto expect that inside stars\n\n\\begin{equation}\n2<\\beta<2.8 .\\label{222}\n\\end{equation}\n\n\nAs pressure inside a star is known (Eq.({\\ref{210}})), from\nEq.({\\ref{220}}) it is possible to determine a steady-state value\nof mass of a star\n\n\\begin{equation}\nM_{\\star}=\\zeta{A_{\\star}^{3/2}}\\frac{m_{p}}{\\beta^2}.\\label{230}\n\\end{equation}\n\nThis mass is expressed by dimensionless constants only\n\n\\begin{equation}\nA_{\\star}=\\biggl(\\frac{\\hbar{c}}{G{m_{p}}^2}\\biggr)=1.54\\cdot{10^{38}}\\label{240}\n\\end{equation}\n\n$\\zeta=(1.5^5\\pi)^{1/2}\\simeq{5}$,\n\nand the slowly varying parameter $\\beta$ (Eq.({\\ref{222}})).\n\nThe masses of stars can be measured with a considerable accuracy,\nif these stars compose a binary system. There are almost 200\ndouble stars whose masses are known with the required accuracy\n\\cite{15}. Among these stars there are giants, white dwarfs, and\nstars of the main sequence. Their averaged mass is described by\nthe equality\n\n\\begin{equation}\n\\langle M_{\\star}\\rangle =\\left( 1.36\\pm 0.05\\right) M_{\\odot },\n\\label{250}\n\\end{equation}\n\nwhere $M_{\\odot }$ is the mass of the Sun.\n\nThe center of this distribution (Fig.1) corresponds to\nEq.({\\ref{230}}) at $\\beta \\simeq 2.6$.\n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig4c.EPS}\n\\vspace{11cm}\n\\caption{Mass distributions of stars and pulsars\nfrom the binary systems \\cite{15},\\cite{17}. The curve shows\nEq.({\\ref{230}}).} \\label{fig1}\n\\end{center}\n\\end{figure}\n\n\n\n\nIt is interesting to note that the \"biography\" of such a star\nappears much poorer than in the Chandrasecar model.\n\nTemperature does not influence the parameters of relativistic\nplasma. Therefore, a star with a mass close to the steady-state\nvalue (Eq.({\\ref{230}})) is in a stable equilibrium not depending\non temperature. It should not collapse with a temperature\ndecreasing. The instability of a star can arise with burning out\nof light nuclei - deuterium and helium - and with a related\nincreasing of $\\beta$. This growth leads to the reduction of a\nsteady-state value of mass (Eq.({\\ref{230}})) and, probably, to\nthe distraction of stars with greater masses.\n\n\\section{}\n\nAs the density of matter inside a relativistic star is constant,\nit is possible to assume that it equals the mean density of the\nSun and to estimate a star radius\n\n\\begin{equation}\nR\\simeq\\biggl(\\frac{M_{\\star}}{\\frac{4\\pi}{3}\n{\\gamma_{\\odot}}}\\biggr)^{1/3},\\label{310}\n\\end{equation}\n\nwhere $\\gamma_{\\odot}$ is the mean density of the Sun.\n\nIt allows one to calculate the momentum of a star as the momentum\nof a sphere with a constant density\n\n\\begin{equation}\nI=\\frac{2}{5}M_{\\star}{R^2}\\label{320}\n\\end{equation}\n\nand at a known frequency of rotation $\\Omega$ to calculate its\nangular momentum\n\n\\begin{equation}\nL=\\frac{2}{5}M_{\\star}\\Omega{R^2}.\\label{330}\n\\end{equation}\n\nIn this model the magnetic moment of a star is created by the\nrotation of a star as a whole. Thus, it is composed of two parts.\nOne is the magnetic moment of the layer of electrons placed on the\nexternal surface of a star\n\n\\begin{equation}\n\\mu_{-}=-\\frac{1}{3}\\biggl({\\frac{4\\pi}{3}\\rho{R^3}}\\biggr)\\Omega{R^2}.\\label{340}\n\\end{equation}\n\nThe second component of the magnetic moment is created by the\npositively charged core\n\n\n\\begin{equation}\n\\mu_{+}=\\frac{1}{5}\\biggl({\\frac{4\\pi}{3}\\rho{R^3}}\\biggr)\\Omega{R^2}.\\label{350}\n\\end{equation}\n\n\nThe summary moment is\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig2.EPS}\n\\vspace{11cm} \\caption{The observed values of the magnetic moments\nof celestial bodies vs. their angular momenta. On the ordinate,\nthe logarithm of the magnetic moment over $Gs\\cdot{cm^3}$ is\nplotted; on the abscissa the logarithm of the angular momentum\nover $erg\\cdot{s}$ is shown. The solid line illustrates\nEq.({\\ref{370}}). The dash-dotted line is the fitting of the\nobserved values.} \\label{fig2}\n\\end{center}\n\\end{figure}\n\n\n\\begin{equation}\n\\mu_{\\Sigma}=-\\frac{2}{15}\\biggl({\\frac{4\\pi}{3}\\rho{R^3}}\\biggr)\n\\Omega{R^2}.\\label{360}\n\\end{equation}\n\n\nIt is remarkable that the gyromagnetic relation of a star, i.e.,\nthe relation of its magnetic moment to the angular momentum, is\nexpressed through world constants only\n\n\n\\begin{equation}\n\\vartheta=\\frac{\\mu_{\\Sigma}}{L}=\\frac{\\sqrt{G}}{3c}.\\label{370}\n\\end{equation}\n\nThe measurements permit us to define the frequency of rotation and\nmagnetic fields for a number of stars \\cite {1}. It appears enough\nto check up the considered theory, since masses of stars and their\nmomenta are determined inside the theory (Eq.({\\ref{250}}) and\n(Eq.({\\ref{330}}))). The magnetic moments as functions of their\nangular momenta for all celestial objects (for which they are\nknown today) are shown in Fig.2. The data for planets are taken\nfrom \\cite{16}, the data for stars are taken from \\cite{1}, and\nfor pulsars - from \\cite{2}. As it can be seen from this figure\nwith the logarithmic accuracy, all celestial bodies - stars,\nplanets, and pulsars - really have the gyromagnetic ratio close to\nthe universal value (Eq.({\\ref{370}})). Only the data for the Moon\nfall out, because its size is too small to create an electrically\npolarized core.\n\n\n\n\n\n\\section{}\n\nApparently, the considered theory is quite true for pulsars which\nconsist, as it is supposed, from the neutron substance with an\naddition of electrons and protons \\cite{10}. As this substance is\na relativistic one, there is a fair definition of a steady-state\nvalue of mass Eq.({\\ref{230}}). The astronomers measured masses of\n16 radio-pulsars and 7 x-ray pulsars included in a double system\n\\cite {17}. According to this data, the distribution of masses of\npulsars is\n\n\\begin{equation}\n\\langle M_{pulsar}\\rangle=(1.38\\pm{0.03})M\\odot.\\label{380}\n\\end{equation}\n\nThe center of this distribution corresponds to Eq.({\\ref{230}}) at\n$\\beta \\simeq 2.6$.\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[5cm,14cm][17cm,2cm]{ae-fig5.EPS}\n\\vspace{14cm} \\caption{The estimated values of the magnetic\nmoments of pulsars \\cite{18} vs. their angular momenta. Solid line\nis Eq.({\\ref{370}}). Axes are like in Fig.2.} \\label{fig3}\n\\end{center}\n\\end{figure}\n\nThe gyromagnetic relations are measured for three pulsars only\n\\cite {2}. These values are in a quite satisfactory agreement with\nEq.({\\ref{370}})(Fig.2). For the majority of pulsars \\cite{18},\nthere are estimations of magnetic fields obtained using a number\nof model assumptions \\cite{2}. It is impossible to consider these\ndata as the data of measurements, but nevertheless they also are\nin some agreement with Eq.({\\ref{370}}), (Fig.3).\n\n\nFor planets the situation is more difficult. First, inside planets\nthe substance forms not relativistic electron-nuclear plasma, but\nnonrelativistic electron-ion plasma. It has different equation of\nstate \\cite{10} leading to a more complex expression for the\nstable mass of a planet core than the expression of\nEq.({\\ref{230}}) for stars. Second, a noncharged layer at the\nsurface of the core can take a significant part of a planet's\nvolume and it is impossible to neglect a role of this stratum.\nHowever, it can be seen from Fig.2 that the gyromagnetic relations\nof planets are also in the quite satisfactory agreement with\nEg.({\\ref{370}}). The detailed calculation for the Earth \\cite{3}\ngives for the magnetic moment $4\\cdot{10^{25}} Oe\\cdot{cm^3}$,\nwhich is almost exactly twice smaller than the measured value\n$8.05\\cdot{ 10^{25} Oe\\cdot{cm^3}}$. Thus, it is possible to\nassume that the basic component of the magnetic moment of planets\nis induced by the same mechanism which is working in stars.\n\n\n\\clearpage\n\n\n\n\\begin{thebibliography}{18}\n\n\\bibitem {1} Borra E.F. and Landstreet J.D. - The Astrophysical Journ, Suppl., 1980, v.42, 421-445.\n\\bibitem {2} Beskin V.S.,Gurevich, A.V., Istomin Ya.N. - Physics of the Pulsar Magnetosphere, Cambridge University Press, 1993.\n\\bibitem {3} Vasiliev B.V. - Nuovo Cimento B,1999,v.114,pp.291-300.\n\\bibitem {4} Shiff L.I. and Barnhill M.V. - Phys.Rev.,1968,v.151,pp.1067-1071.\n\\bibitem {5} Dressler A.I. a.o. -Phys.Rev.,1968,v.168,pp.737-743.\n\\bibitem {6} Riegel T.J. - Phys. Rev.B,1970,v. 2,pp.825-828.\n\\bibitem {7} Kumar N. and Naddini R. - Phys. Rev.D.,1973,v.7,pp.1067-1071.\n\\bibitem {8} Leung M.C. et al. - Canad.Journ. of Phys.,1971,v.49,pp.2754-2767.\n\\bibitem {9} Leung M.C. - Nuovo Cimento,1972,v.76,pp.825-929.\n\\bibitem {10} Landau L.D. and Lifshits E.M. - Statistical Physics,1980, vol.1, 3rd edition,Oxford:Pergamon.\n\\bibitem {11} Vasiliev B.V. and Luboshits V.L. - Physics-Uspekhi,1994,v.37,pp.345-351.\n\\bibitem {12} Kirzhnitz D.A. - JETP, 1960, v.38, pp.503-508.\n\\bibitem {13} Abrikosov A.A. - JETP, 1960, v.39, pp.1797-1805.\n\\bibitem {14} Leung Y.C. - Physics of Dense Matter, 1984, Science\n\\bibitem {15} Heintz W.D. - Double stars,1978, Geoph. and Astroph.monographs, vol.15, D.Reidel Publ.Comp.\n\\bibitem {16} Sirag S.-P. - Nature,1979,v.275,pp.535-538.\n\\bibitem {17} Thorsett S.E. and Chakrabarty D. - E-preprint: astro-ph/9803260, 1998, 35pp.\n\\bibitem {18} Taylor J.H., Manchester R.N., Lyne A.G., Camilo F., Catalog of 706 pulsars,\n 1995, pulsar.prinston.edu\n\n\\end{thebibliography}\n\n\\clearpage\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002048.extracted_bib",
"string": "\\begin{thebibliography}{18}\n\n\\bibitem {1} Borra E.F. and Landstreet J.D. - The Astrophysical Journ, Suppl., 1980, v.42, 421-445.\n\\bibitem {2} Beskin V.S.,Gurevich, A.V., Istomin Ya.N. - Physics of the Pulsar Magnetosphere, Cambridge University Press, 1993.\n\\bibitem {3} Vasiliev B.V. - Nuovo Cimento B,1999,v.114,pp.291-300.\n\\bibitem {4} Shiff L.I. and Barnhill M.V. - Phys.Rev.,1968,v.151,pp.1067-1071.\n\\bibitem {5} Dressler A.I. a.o. -Phys.Rev.,1968,v.168,pp.737-743.\n\\bibitem {6} Riegel T.J. - Phys. Rev.B,1970,v. 2,pp.825-828.\n\\bibitem {7} Kumar N. and Naddini R. - Phys. Rev.D.,1973,v.7,pp.1067-1071.\n\\bibitem {8} Leung M.C. et al. - Canad.Journ. of Phys.,1971,v.49,pp.2754-2767.\n\\bibitem {9} Leung M.C. - Nuovo Cimento,1972,v.76,pp.825-929.\n\\bibitem {10} Landau L.D. and Lifshits E.M. - Statistical Physics,1980, vol.1, 3rd edition,Oxford:Pergamon.\n\\bibitem {11} Vasiliev B.V. and Luboshits V.L. - Physics-Uspekhi,1994,v.37,pp.345-351.\n\\bibitem {12} Kirzhnitz D.A. - JETP, 1960, v.38, pp.503-508.\n\\bibitem {13} Abrikosov A.A. - JETP, 1960, v.39, pp.1797-1805.\n\\bibitem {14} Leung Y.C. - Physics of Dense Matter, 1984, Science\n\\bibitem {15} Heintz W.D. - Double stars,1978, Geoph. and Astroph.monographs, vol.15, D.Reidel Publ.Comp.\n\\bibitem {16} Sirag S.-P. - Nature,1979,v.275,pp.535-538.\n\\bibitem {17} Thorsett S.E. and Chakrabarty D. - E-preprint: astro-ph/9803260, 1998, 35pp.\n\\bibitem {18} Taylor J.H., Manchester R.N., Lyne A.G., Camilo F., Catalog of 706 pulsars,\n 1995, pulsar.prinston.edu\n\n\\end{thebibliography}"
}
] |
astro-ph0002049
|
Compton dragged gamma--ray bursts: the spectrum
|
[
{
"author": "Gabriele Ghisellini$^1$"
},
{
"author": "Davide Lazzati"
},
{
"author": "$^{1,2}$ Annalisa Celotti$^3$ and Martin J. Rees$^{4}$"
},
{
"author": "$^1$ Osservatorio Astronomico di Brera"
},
{
"author": "Via Bianchi 46"
},
{
"author": "I--23807 Merate (Lc)"
},
{
"author": "Italy"
},
{
"author": "$^2$ Dipartimento di Fisica"
},
{
"author": "Universit\\`a degli Studi di Milano"
},
{
"author": "Via Celoria 16"
},
{
"author": "I--20133 Milano"
},
{
"author": "$^3$ SISSA"
},
{
"author": "Via Beirut 2--4"
},
{
"author": "I--34014 Trieste"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge"
}
] |
We calculate the spectrum resulting from the interaction of a fireball with ambient soft photons. These photons are assumed to be produced by the walls of a funnel in a massive star. By parameterizing the radial dependence of the funnel temperature we calculate the deceleration of the fireball self--consistently, taking into account the absorption of high energy $\gamma$--rays due to interaction with the softer ambient photons. The resulting spectrum is peaked at energies in agreement with observations, has a $\nu^2$ slope in the X--ray band and a steep power--law high energy tail.
|
[
{
"name": "ghisellini.tex",
"string": "\\documentstyle[psfig]{mn}\n\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\lsim{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\gsim{\\lower.5ex\\hbox{\\gtsima}}\n\n\\begin{document}\n\n\\title[Compton dragged gamma--ray bursts: the spectrum]\n{Compton dragged gamma--ray bursts: the spectrum}\n\\author[Ghisellini, Lazzati, Celotti and Rees]\n{Gabriele Ghisellini$^1$, Davide Lazzati,$^{1,2}$\nAnnalisa Celotti$^3$ and Martin J. Rees$^{4}$\\\\ \n$^1$ Osservatorio Astronomico di Brera, Via Bianchi 46, I--23807\nMerate (Lc), Italy \\\\\n$^2$ Dipartimento di Fisica, Universit\\`a degli Studi di Milano,\nVia Celoria 16, I--20133 Milano, Italy \\\\\n$^3$ SISSA, Via Beirut 2--4, I--34014 Trieste, Italy \\\\\n$^4$ Institute of Astronomy, Madingley Road, Cambridge\\\\\nE--mail: {\\tt [email protected]}, {\\tt [email protected]}, \n{\\tt [email protected]}, {\\tt [email protected]}\n}\n\n\n\\maketitle\n\n\\begin{abstract}\nWe calculate the spectrum resulting from the interaction of a \nfireball with ambient soft photons.\nThese photons are assumed to be produced by the walls of a funnel in a\nmassive star.\nBy parameterizing the radial dependence of the funnel temperature we\ncalculate the deceleration of the fireball self--consistently, taking\ninto account the absorption of high energy $\\gamma$--rays due to\ninteraction with the softer ambient photons.\nThe resulting spectrum is peaked at energies in agreement with\nobservations, has a $\\nu^2$ slope in the X--ray band and a steep\npower--law high energy tail.\n\\end{abstract}\n\n\\begin{keywords}\ngamma rays: bursts --- X--rays: general --- radiation mechanisms:\nnon--thermal\n\\end{keywords}\n\n\\section{Introduction}\n\nWe have recently proposed (Lazzati et al. 2000, hereafter Paper I)\nthat the gamma--ray burst (GRB) phenomenon originates from the\ninteraction of a relativistic fireball with a dense photon\nenvironment, leading to Compton drag.\nOn one hand this is an inevitable effect if the progenitors of GRBs\nare massive stars which are about to explode or have just exploded as\nsupernovae; on the other hand this mechanism greatly alleviates the\nefficiency problem faced by the standard internal shock scenario\n(Lazzati, Ghisellini \\& Celotti 1999; Panaitescu, Spada \\& Meszaros\n1999; Kumar 1999).\nIn Paper I we have discussed the basic Compton drag scenario, showing\nhow this process can convert bulk motion energy directly into\nradiation with a remarkable high efficiency and, on the basis of\nsimple estimates, how the resulting spectrum should peak, in a $\\nu\nF(\\nu)$ representation, around $\\sim$1 MeV, as observed.\n\nHere we quantitatively and self--consistently estimate the predicted\nspectrum, assuming that the fireball propagates in a funnel inside a\nmassive star, and show that, independently of the details of the model, \nit satisfactorily resembles what observed. \nSince the funnel walls emit a blackbody spectrum and the scattered\nphotons are boosted by the square of the Lorentz factor ($\\Gamma$) of\nthe fireball, the local spectrum has a blackbody shape, at a\ntemperature enhanced by $\\Gamma^2$.\nHowever, the observed spectrum, convolution of all the locally emitted\nspectra, is not a blackbody, due to four main effects:\ni) the funnel walls would not be at a uniform temperature, but there should\nbe a gradient between the internal and external parts;\nii) if the Compton drag process is efficient, the fireball decelerates;\niii) the very high energy emission produced in the internal regions\ncan interact with the ambient photons, producing electron--positron pairs;\niv) the fireball may become optically thin to scattering outside the funnel,\nwhere the ambient photons are characterized by the same \ntemperature, but their energy density is progressively diluted with distance. \n\n\\section{Basic assumptions}\n\nWe postulate that the fireball propagates with a bulk Lorentz factor\n$\\Gamma$ inside a funnel cavity, whose walls emit blackbody radiation\nat a temperature $T$, of conical shape with semi--aperture angle\n$\\psi$.\nThe calculation starts at the distance $z_0$, assumed to be the end of\nthe acceleration phase and, for consistency, we verify that the power\nemitted at $z<z_0$ is negligible.\n\nWe assume that the fireball is and remains cold\nin the comoving frame.\nAt $z_0$, in fact, the internal energy has been already used\nto accelerate the fireball, and thus protons are\nsub--relativistic. On the other hand leptons might be still hot \nat $z_0$ and/or being re-heated \nwhen the bulk scattering process starts to be efficient. However, \nin a few (Compton) cooling timescales they would \nreach the (sub-relativistic) Compton temperature. It is thus \nreasonable to treat also the leptonic component as cold\nin the estimate of both the dynamics and resulting spectrum.\n\n\n\nThe initial Lorentz factor (at $z_0$) is indicated as $\\Gamma_0$, and the \nfireball energy is therefore $E_f=\\Gamma_0 M_f c^2$, \nwhere $M_f$ is its rest mass.\nFor simplicity, the dependence of the temperature on $z$,\nbetween $z_0$ and the radius of the star $z_*$,\nhas been parameterized by a power law:\n%\n\\begin{equation}\nT(z)\\, =\\, T_0 \\left( z\\over z_0 \\right)^{-b}\\, =\\,\nT_* \\left( z\\over z_* \\right)^{-b}\n\\end{equation}\n%\nwhere $T_*$ is the temperature at the top of the funnel.\n\nInside it, we approximate the local radiation energy density \nof the ambient photons as $U(z)= a T^4(z)$.\nBeyond $z_*$, and in the region where the fireball remains optically\nthick (i.e. for $z<z_T$, see below), $U(z)$ is characterized by\nthe same temperature, but decreases. \nAs the relevant quantity is \nthe amount of radiation which is indeed scattered by the fireball, \nwe parameterize the dependence on $z$ of the \nproduct $U(z) \\times$ (the scattering rate) as $(z/z_*)^{-g}$.\n\nWe consider $g$ a free parameter. \nInside the funnel $g=0$, while outside it \na value $g>2$ can account for a decrease in the scattering rate\ndue to the changing of the typical scattering angle (photons come\npreferentially at smaller angles as $z$ increases).\nAs the scattering rate is $\\propto (1-\\beta\\cos\\theta)$, where $\\theta$ \nis the angle between the photon and the electron directions,\nfar from the star surface $(1-\\beta\\cos\\theta) \\propto\n(z/z_*)^{-2}$, corresponding to $g\\sim 4$.\nFurthermore some of the radiation produced by the massive star \ncould be reflected and re--isotropized by scattering material, of unknown \nradial density profile, likely surrounding the massive star progenitor. \nIn particular if this forms a wind with a $z^{-2}$ profile, \nthe energy density of the re--isotropized radiation scales as $z^{-3}$,\nand dominates the seed photon distribution at large distances.\nIn this case \n$U(z)\\times$(the scattering rate)\n can have a complex profile,\nbeing flat in the vicinity of the surface of the star, then decreasing\nas $z^{-2}$ and as $z^{-4}$ for increasing $z$,\nto become flatter when the component associated with the\nre--isotropized photons dominates.\nIt is also possible that, as a result of intermittent stellar activity,\nthe stellar wind is not continuous.\nIn this case a single shell may dominate the scattering, producing a\nhomogeneous and isotropic scattered radiation field, dominating\nthe total radiation energy density beyond some critical distance.\n\n\nThe distance $z_T$ at which the fireball becomes optically thin to\nscattering is\n%\n\\begin{equation}\nz_T = \\left({\\sigma_T E_f \\over \\pi \\psi^2 m_p c^2 \\Gamma_0}\\right)^{1/2}\n\\sim \n3.7\\times 10^{14} \\psi_{-1}^{-1}\nE_{f,51}^{1/2} \\Gamma_{0,2}^{-1/2} {\\rm cm}\n\\end{equation}\n%\nwhere the conventional representation $Q = Q_x 10^x$ and c.g.s. units \nare adopted. \nIt is then likely that the fireball becomes transparent at $z>z_*$ \n(since the radius of red supergiants is $z_*\\lsim 10^{13}$ cm).\n\nAs long as the fireball is opaque to scattering, the interaction \nwith photons boosts their energy by a factor $\\sim 2\\Gamma^2$.\nTherefore the (local) total energy emitted by\nthe fireball through the Compton drag process (over a distance $dz$) is\n%\n\\begin{equation}\ndE(z) \\, = \\, 2 \\pi \\psi^2 z^2 aT_0^4\\left({z\\over z_0}\\right)^{-4b} \n\\Gamma^2 dz \\quad z<z_*\n\\end{equation}\n%\n%\n\\begin{equation}\ndE(z) \\, = \\, 2 \\pi \\psi^2 z^2 aT_*^4 \n\\left({ z\\over z_*}\\right)^{-g}\\, \\Gamma^2 dz \\quad z>z_*.\n\\end{equation}\n%\nThe factor 2 in front of the RHS of these equations takes into account\nthat the preferred scattering angle is $\\sim 90^\\circ$, corresponding\nto an average energy boost of $2\\Gamma^2$.\n\n\nLet us now consider the spectral shape.\nFor this it is convenient to use dimensionless photon energies and\ntemperatures, defined as $x\\equiv h\\nu/(m_e c^2)$ and $\\Theta \\equiv\nkT/(m_ec^2)$, respectively.\n\nThe resulting Compton spectrum has a blackbody shape, of effective\ntemperature $T_c = 2\\Gamma^2 T$ (or $\\Theta_c = 2\\Gamma^2 \\Theta$),\ni.e. the local spectral distribution produced within $dz$ is given by:\n%\n\\begin{eqnarray}\ndE(z, x)&=&\\pi^2 \\psi^2 {z^2 \\over \\Gamma^6}\nm_ec^2 \\left({m_e c\\over h}\\right)^3 { x^3 \\over e^{x/\\Theta_c}-1} dz; \\,\n\\nonumber \\\\ &\\, & \\qquad \\qquad \\qquad\\qquad \\qquad\\qquad z<z_*\n\\end{eqnarray}\n%\n%\n\\begin{eqnarray}\ndE(z, x)&=&\\pi^2 \\psi^2 {z^2 (z/z_*)^{-g}\\over \\Gamma^6} \nm_ec^2 \\left({m_e c\\over h}\\right)^3\n{ x^3 \\over e^{x/\\Theta_{c,*}}-1} dz; \\nonumber \\\\ \n&\\, & \\qquad \\qquad \\qquad\\qquad \\qquad\\qquad z>z_*,\n\\end{eqnarray}\n%\nwhere $\\Theta_{c,*}=2\\Gamma^2\\Theta_*$.\nEquations (5) and (6) are correctly normalized, i.e. the integrated \nenergies correspond to those expressed in (3) and (4).\n\n\n\n\\section{The fireball dynamics}\n\nAs long as the fireball remains optically thick for scattering\nand this occurs in the Thomson regime, the dynamics (deceleration) \nof the fireball due to the radiative drag, obeys: \n%\n\\begin{equation}\nM_f c^2 \\, {d\\Gamma \\over dz}\\, = \\, -\\, 2\\pi \\psi^2 z^2 aT^4 \\Gamma^2.\n\\end{equation}\n%\nAssuming the temperature profile of equation (1) we obtain:\n%\n\\begin{eqnarray}\n\\Gamma &=& {\\Gamma_0 \\over 1+ 2\\pi \\psi^2 aT_0^4 \\Gamma_0^2 z_0^3 \n[(z/z_0)^{3-4b}-1]/[E_f(3-4b)]}; \n\\nonumber \\\\ &\\, & \\qquad \\qquad \\qquad\\qquad \\qquad\\qquad z_0<z<z_*, \n\\end{eqnarray}\n%\nand thus the deceleration radius, $z_d$, defined as the distance at which \n$\\Gamma$ is halved, corresponds to:\n%\n\\begin{eqnarray}\nz_d\\, &=&\\, \nz_o\\, \\left[ 1+ { E_f (3-4b) \\over \n2\\pi\\psi^2 aT_0^4\\Gamma_0^2 z_0^3}\\right]^{1/(3-4b)}\\, \\nonumber \\\\\n&=& \\, \nz_o\\, \\left[ 1+ { E_f (3-4b) \\over \n2\\pi\\psi^2 aT_*^4\\Gamma_0^2 (z_*/z_0)^{4b}z_0^3}\\right]^{1/(3-4b)}\n\\end{eqnarray}\n%\nBeyond $z_d$, the Lorentz factor decreases with distance as a power\nlaw, whose slope is determined by the temperature profile.\n\nOutside the star radius ($z>z_*$) the Lorentz factor follows:\n%\n\\begin{eqnarray}\n\\Gamma &=& {\\Gamma_* \\over 1+ 2\\pi \\psi^2 aT_*^4 \\Gamma_0\\Gamma_* z_*^3 \n[(z/z_*)^{3-g}-1]/[E_f(3-g)]};\n\\nonumber \\\\ &\\, & \\qquad \\qquad \\qquad\\qquad \\qquad\\qquad \\,\\, z_*<z<z_T.\n\\end{eqnarray}\n%\nNote that Klein-Nishina effects are important for incoming photon energies \nsuch that $x \\Gamma>1$, i.e. when $\\Theta>1/(3\\Gamma)$.\nFor simplicity, we neglect interactions in this regime when\ncalculating $\\Gamma(z)$, but we assume no scattering events when\n$\\Theta>1/(3\\Gamma)$ in calculating the spectrum.\nThis simplification is justified as long as most of the fireball energy\nis lost in the Thomson scattering regime (see Fig. 2, which shows\nthat $\\Gamma$ starts to decrease at distances where the temperature\nis small enough to ensure scatterings entirely in the Thomson regime).\n\n \nWhen the fireball becomes optically thin, the amount of scattered\nphotons is correspondingly reduced, and the process becomes\nless efficient. \nAs shown by equation (2), this is likely to happen at some\ndistance from the star surface, where the photon density is also\nreduced, thus further decreasing the efficiency of the process.\nIn the numerical calculations we have however included the optically\nthin scattering regime, and one can see its contribution in Fig. 1\n(dotted line).\n\n\n\n\n\n\\section{Pair production}\n\nA further effect which may strongly affect both the observed \nspectrum and the dynamics of the fireball is the production of\nelectron--positron pairs through photon-photon interactions.\nLet us thus consider in turn the role of scattered and funnel\nradiation as seed photons for this process.\n\n\\subsection{Interaction among photons in the beam}\n\nThe threshold energy for interaction between photons of energies $x$\nand $x_T$ is $x_T > 2/[x(1-\\cos\\theta)]\\sim 4\\Gamma^2/x$, \n where all quantities are calculated in the observer frame.\nThe\nlatter expression takes into account that the high energy photons\nproduced by the Compton drag are highly collimated, within a typical\nangle $\\sin\\theta\\sim 1/\\Gamma$.\nAs the bulk of the scattered photons have energies $x\\sim 2\\Gamma^2\n(3\\Theta)$, pair production would occur if $\\Gamma\\Theta > 1/3$.\n\nHowever this also implies that the scattering process\nis in the Klein Nishina\nregime, and we can therefore conclude that photon--photon collisions\namong photons in the beam can only affect the high energy tail of the\nspectrum produced at each radius, while the emission at the peak is\nunaltered. We therefore neglect this effect.\n\n\\subsection{Interaction between beam photons and funnel radiation}\n\nThe interaction between the $\\gamma$--rays produced by the Compton\ndrag process and photons emitted by the funnel walls would occur at \nlarge angles, resulting in an average energy threshold $x_T>1/x$.\nSince $x\\le\\Gamma_0$, this absorption mechanism would be significant\nas long as the funnel walls produce a sufficient number of photons \nwith energies $x_T > 1/\\Gamma_0$.\n\nLet us then estimate the photon--photon optical depth\n$\\tau_{\\gamma\\gamma}$, by integrating the product of the\nphoton--photon cross section $\\sigma_{\\gamma\\gamma}(x,x_T)$ and the\nphoton density above threshold $n_\\gamma(x)$ over the $\\gamma$--ray\npath, i.e. from the site of creation, $z_1$, to infinity, and over the\nphoton energies:\n%\n\\begin{equation}\n\\tau_{\\gamma\\gamma}(z_1,x) \\, =\\, \n\\int_{x_T}^{\\infty}dx^\\prime\\int_{z_1}^{\\infty}\n\\sigma_{\\gamma\\gamma}(x^\\prime,x) n_\\gamma(z, x^\\prime) dz.\n\\end{equation}\n%\nSince $\\sigma_{\\gamma\\gamma}(x^\\prime,x)$ is peaked at the threshold\nenergy, equation (11) can be simplified (Svensson 1984, 1987) as\n%\n\\begin{eqnarray}\n\\tau_{\\gamma\\gamma}(z_1, x) \\, = {\\sigma_T \\over 5 m_ec^2} \n\\int_{z_1}^{\\infty} x_T U(z, x_T) dz,\n\\end{eqnarray}\n%\nwhere $U(z, x_T) = m_e c^2 n_\\gamma(z, x_T)$ is the photon energy \ndensity at threshold, at the location $z$, i.e. \n%\n\\begin{equation}\nU(z_1,x_T)\\, =\\, {8\\pi h\\over c^3}\\, \\left( {m_ec^2\\over h}\\right)^4\n\\, { x_T^3 \\over \\exp[x_T/\\Theta(z_1)] -1}.\n\\end{equation}\n%\nThe radiation flux produced at the location $z_1$ is then decreased\nby the factor $\\exp[-\\tau_{\\gamma\\gamma}(z_1, x)]$ while crossing the \nfunnel.\n\nThe absorbed radiation will be reprocessed by the pairs,\nand re--distributed in energy.\nEach electron and positron will have an energy $\\gamma\\sim x/2$\nat birth, and will cool due to the Compton drag process.\nThe positrons will then annihilate in collisions with the electrons \nin the fireball, producing a Doppler blueshifted annihilation line at\n$x\\sim \\Gamma$.\nWe have neglected these reprocessing mechanisms, since, as can be seen \nin Fig. 1, the amount of energy absorbed in $\\gamma$--$\\gamma$ collisions\nis small, amounting to a few per cent at most.\n\n\n\\begin{figure}\n\\vskip -0.5 true cm\n\\psfig{figure=sum_new.ps,width=10cm}\n\\vskip -2.5 true cm\n\\caption{{Example of spectra produced by Compton drag.\nThe thick solid lines correspond to the sum of the radiation produced\ninside the funnel (thin solid lines) and outside it (dashed and dotted lines).\nThe thin solid lines at the highest energies correspond\nto the emission neglecting photon--photon absorption, to show the\nimportance of this process.\nThe dotted line (only shown for the $\\Gamma_0=30$ case) is\nthe spectrum produced by the fireball once it becomes optically thin.\nThe model parameters are for all cases:\n$E_f=5\\times 10^{51}$ erg; $\\psi=0.2$; $b=0.5$;\n$g=2$; $z_*=10^{13}$ cm and $T_*=3\\times 10^5$ K.\nThe three cases differ for the assumed initial bulk Lorentz factor\nand $z_0$, i.e. $\\Gamma_0=30$, $100$, $300$ and\n$z_0=3\\times 10^8$, $10^9$, $3\\times 10^9$ cm, respectively.\nThe two vertical dashed lines mark 10 and 150 keV, the range of the\nforeseen hard X--ray detector onboard the Swift mission.}\n\\label{figuno}}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{figure=cool.ps,width=9cm}\n\\vskip -3 true cm\n\\caption{{The profile of the bulk Lorentz factor $\\Gamma$ \ncorresponding to the cases shown in Fig.~1. \nThe vertical dotted line marks $10^{13}$ cm, the top of the funnel.}\n\\label{figdue}}\n\\end{figure}\n\n\\begin{figure}\n\\vskip -0.5 true cm\n\\psfig{figure=sumt.ps,width=9cm}\n\\vskip -2 true cm\n\\caption{Spectra produced by Compton drag\nfor three different choices of the temperature\nof the surface of the massive star (as labeled).\nFor all cases \n$E_f=5\\times 10^{51}$ erg; $\\psi=0.2$; $b=0.5$;\n$g=2$; $z_*=10^{13}$ cm, $\\Gamma_0=100$ and $z_0=10^9$ cm.}\n\\end{figure}\n\n\\section{The spectrum}\n\nThe observed total spectrum can be computed by integrating equations \n(3) and (4) over $z$, taking into account photon--photon absorption.\nThe contribution produced within the star is given by: \n%\n\\begin{eqnarray}\nE(x) &=& \\pi^2 \\psi^2 m_ec^2 \\left({m_e c\\over h}\\right)^3 \n\\int_{z_0}^{z_*}{z^2 \\over \\Gamma^6}\\, \n{ x^3 e^{-\\tau_{\\gamma\\gamma}(z, x)}\\over e^{x/\\Theta_c}-1}\n\\, dz;\n\\nonumber \\\\ &\\, & \\qquad \\qquad \\qquad\\qquad \\qquad \\,\\,\nz_0<z<z_*, \n\\end{eqnarray}\n%\nwhile beyond $z_*$ the number of target photons able to interact with \nhigh energy $\\gamma$--rays to produce pairs is negligible, and thus,\nignoring photon--photon absorption, we obtain:\n%\n\\begin{eqnarray}\nE(x)&=&\\pi^2 \\psi^2 m_ec^2 \\left({m_e c\\over h}\\right)^3 \n\\int_{z_*}^{z_T}{z^2 (z/z_*)^{-g} x^3\\over \\Gamma^6(e^{x/\\Theta_{c,*}}-1) }\ndz; \n\\nonumber \\\\ \n&& \\qquad \\qquad \\qquad\\qquad \\quad \\,\\,\n z_*<z<z_T.\n\\end{eqnarray}\n%\nIn Fig.~1 we show three examples of the predicted spectrum\ncorresponding to different values of the initial bulk Lorentz\nfactors.\nTo illustrate the main features of the model and\nthe importance of photon--photon absorption, this is \ncalculated both with and without the photon--photon absorption\nterm. \nTogether with the total spectrum, the separate \ncontributions for $z<z_*$ and for $z_T<z<z_*$ are reported.\nIn Fig. 2 we show the corresponding $\\Gamma$ profiles.\nThe effect of the star surface temperature (and of the entire funnel, since the\nparameter $b$ is assumed to be the same for all cases) can be clearly seen \nin Fig. 3.\nNote the $\\nu^{-1/2}$ power law shape in the X--ray band for the\nhigh temperature case.\nThe extension of this power law branch depends on the value of $g$. \nIn the case shown ($g=2$) the radiation energy density outside the funnel\nremains sufficiently large to cause the deceleration of the fireball,\nand this is responsible for the power law tail between 10 and 100 keV.\nFor larger $g$ the extension of this power law would decrease.\nThis effect can also be seen for the high $\\Gamma_0$ case in Fig. 1.\n\n\nIn order to determine the general features of the predicted spectrum\nand thus assess its robustness against the parameters of the model, we\nalso derived analytical (although approximated) expressions for the\nspectral energy distribution.\n\n\\subsection{Analytical approximations}\n\nFirst, let us approximate the blackbody spectral form with its \nRayleigh--Jeans part, and let us neglect photon--photon absorption.\nIn this case, for $x<6\\Theta\\Gamma^2$ we have:\n%\n\\begin{eqnarray}\ndE(z,x) \\, &\\propto& \\, {T\\over \\Gamma^4} z^2 dz;\n\\quad \\quad {\\rm for}\\,\\, z_o<z<z_* \\nonumber \\\\\n&\\propto &\\, {T\\over \\Gamma^4} z^{2-g} dz;\n\\quad {\\rm for}\\,\\, z_*<z<z_T.\n\\end{eqnarray}\n%\n\nThree regimes occur at different distances:\n\n\\noindent\n${\\mathbf z_0<z<z_d}$: ---\nin this case $\\Gamma=$ const, and integration over $z$ yields:\n%\n\\begin{equation}\nE(x) \\, \\propto \\, x^{-(3-3b)/b};\n\\quad {\\rm for}\\, z>z_d\n\\end{equation}\n%\nwhich, for $b=0.5$, gives $E(x)\\propto x^{-3}$.\n\n\\noindent\n${\\mathbf z_d<z<z_*}$: ---\nhere $\\Gamma$ decreases as $(z/z_0)^{-(3-4b)}$ and thus:\n%\n\\begin{equation}\nE(x) \\, \\propto \\, x^{-3(1-b)/(6-7b)}\n\\quad {\\rm for}\\, z_d<z<z_*;\n\\end{equation}\n%\nwhich, for $b=0.5$, results in $E(x)\\propto x^{-3/5}$.\n\n\\noindent\n${\\mathbf z_*<z<z_T}$: ---\nat these distances \nthe ambient radiation energy density decreases as $(z/z_0)^{-g}$.\nIf $\\Gamma$ remains constant (= $\\Gamma_*$), the spectrum\n$E(x)\\propto x^2$, while, for $\\Gamma$ decreasing as\n$\\Gamma\\propto (z/z_0)^{-(3-g)}$\n%\n\\begin{equation}\nE(x) \\, \\propto \\, x^{-1/2}\n\\quad {\\rm for}\\, z_*<z<z_T, \n\\end{equation}\n%\nwhich is independent of $g$.\n\nIn conclusion, in the case of efficient Compton drag, and\nindependently of the particular choice of parameters, the predicted\nspectrum is always characterized (in order of decreasing energy) by: a \nsteep high energy tail; a first\nbreak flagging the deceleration of the fireball; a second break\ncorresponding to radiation produced at the top of the funnel -- above\nwhich the temperature of the ambient photons remains constant; a third\nbreak, below which the spectrum $\\propto x^{-1/2}$, corresponding to\nthe deceleration of the fireball due to the isothermal photon bath;\nand finally a fourth break, below which the spectrum $F(x)\\propto x^2$.\nOne obtains such a hard spectrum, instead of the familiar \nslope $F(x) \\propto x$ corresponding to scatterings of isotropically \ndistributed electrons and seed photons, because only\nthe photons scattered along the forward direction are observed\n\\footnote{This can be seen by integrating Eq. 7.23 of Rybicki \n\\& Lightman (1979), \nin the angle range [$0<\\theta_1< 1/\\Gamma$]}.\n \n \n \n\\section{Discussion}\n\nIf the fireball propagates in a dense photon environment the\nCompton drag effect must necessarily be taken into account,\nand it may even be the dominant emission mechanism,\nable to decelerate the fireball without the need of internal\nshocks and without invoking the build--up of large magnetic fields.\n\nIn this letter we have shown that the predicted spectrum, rather than being\nsimply a black body spectrum boosted in energy, has a complex\nshape, with power law segments corresponding to the decrease in \ntemperature of the funnel, deceleration of the fireball, and dilution\nof the radiation energy density as the fireball propagates outside\nthe funnel while remaining optically thick.\n\nThe general features of the predicted spectrum qualitatively \nagree with observations,\nsince they can explain the steep power law high energy tail,\nthe peak of the emission, and a hard tail in the X--ray band.\nThe latter feature is particularly interesting, since other models\nmade different predictions.\nIn the standard internal shock synchrotron model, in fact, \nthe spectrum cannot be harder than $\\nu^{1/3}$ in the thin part,\nand it is very unlikely that self--absorption can take place\nin the X--ray band (Granot, Piran \\& Sari 2000).\nThis would in fact imply a huge density of relativistic particles,\nmaking the inverse Compton effect largely dominate the total\nradiation output.\nThis radiation would be emitted at higher and yet unobserved frequencies,\nand would then worsen the already severe efficiency problem.\n\nIn the quasi--thermal Comptonization model, on the other hand, the \ntypical predicted spectral shape in the X--ray band is $\\propto \\nu^0$,\ndown to the typical frequencies of the seed soft photons,\ni.e. the IR--optical band (Ghisellini \\& Celotti 1999; \nMeszaros \\& Rees 2000).\n\nThe existing observations of a significant fraction\nof burst spectra harder than $\\nu^{1/3}$\n(Preece et al., 1999a,b; Crider et al., 1997)\nare therefore already\na challenge to existing models, and may suggest a Compton\ndrag origin of this portion of the spectrum.\nHowever the situation is not already a clear--cut because,\nto receive enough photons to study the spectral shape, integration\ntimes are much longer than the dynamical time--scales of the system,\nwith the spectrum rapidly evolving in time.\nMore sensitive instruments, such as the Burst Alert Telescope (BAT,\na coded mask detector more sensitive than BATSE) onboard the\nforeseen Swift satellite will probably overcome this limitation.\n\nWe must also stress that the Compton drag scenario is not alternative\nto the more conventional internal shock one. Indeed, the front of the\nfireball will decelerate first, plausibly causing subsequent \nun-decelerated parts to shock even if the central engine is\nworking in a continuous way. This would produce additional radiation,\neither by the synchrotron and inverse Compton processes or by\nquasi--thermal Comptonization, depending on the details of the\nparticle acceleration mechanism (see Ghisellini \\& Celotti 1999). We\nthen expect spectral evolution: since the latter radiation mechanisms\nproduce a steeper low energy tail, a hard--to--soft transition\n(i.e. from $\\nu^2$ to $\\nu^{1/3}$ or $\\nu^0$) would occur.\n\n\nIn this paper, we have considered the illustrative case of a single fireball\nmoving out through an extended stellar envelope, along a funnel which is empty\nof matter but pervaded by thermal radiation from the funnel walls. \nThe fireball itself (for typical parameters) remains optically \nthick until it expands beyond the stellar surface. \nA burst with complex time-structure could be modeled by a series of \nfireballs or expanding shells. \nHowever, in this more general case,\nthe later shells would suffer less drag, since not enough time may \nhave elapsed\nto replenish the entire funnel cavity with seed photons.\nIndeed one expects the spikes to be more powerful \nthe longer is the time interval \nbetween them, as more seed photons could pervade the cavity. \nThis, besides causing internal shocks with the first shell\nwhich has been efficiently decelerated by Compton drag,\nwill also result in a distribution of $\\Gamma$--factors:\nthey will become greater on axis, where few seed photons can efficiently\nCompton drag the shells, and smaller towards the border of the funnel,\nwhere seed photons can be replenished by the funnel walls.\n\nWe plan to investigate these possibilities and their consequences on the \nassociated predicted afterglows in future work.\n\n\\section*{Acknowledgments}\nAC acknowledges the Italian MURST for financial support. \n\n\\begin{thebibliography}{}\n\\bibitem []{} Crider A. et al., 1997, ApJ, 479, L39\n\\bibitem []{} Ghisellini G., Celotti A., 1999, ApJ, 511, L93 \n\\bibitem []{} Granot J., Piran T., Sari R., 2000, ApJ, 534, L163\n\\bibitem []{} Kumar P., 1999, ApJ, 523, L113\n\\bibitem []{} Lazzati D., Ghisellini G., Celotti A. \\& Rees M.J., 2000,\n ApJ, 529, L17 (Paper I)\n\\bibitem []{} Lazzati D., Ghisellini G. \\& Celotti A., 1999. MNRAS, 309, L13 \n\\bibitem []{} Meszaros P. \\& Rees M.J., 2000, ApJ in press, astro--ph/9908126\n\\bibitem []{} Panaitescu A., Spada M. \\& Meszaros P., 1999, ApJ, 522, L105\n\\bibitem []{} Preece R.D. et al., 1998a, ApJ, 496, 849\n\\bibitem []{} Preece R.D. et al., 1998b, ApJ, 506, L23\n\\bibitem []{} Rybicki G.B. \\& Lightman A.P., 1979, Radiative Processes in\n Astrophysics, J. Wiley \\& Sons (New York)\n\\bibitem []{} Svensson R., 1984, MNRAS, 209, 175\n\\bibitem []{} Svensson R., 1987, MNRAS, 227, 403\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n\n\n\n"
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[
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"name": "astro-ph0002049.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem []{} Crider A. et al., 1997, ApJ, 479, L39\n\\bibitem []{} Ghisellini G., Celotti A., 1999, ApJ, 511, L93 \n\\bibitem []{} Granot J., Piran T., Sari R., 2000, ApJ, 534, L163\n\\bibitem []{} Kumar P., 1999, ApJ, 523, L113\n\\bibitem []{} Lazzati D., Ghisellini G., Celotti A. \\& Rees M.J., 2000,\n ApJ, 529, L17 (Paper I)\n\\bibitem []{} Lazzati D., Ghisellini G. \\& Celotti A., 1999. MNRAS, 309, L13 \n\\bibitem []{} Meszaros P. \\& Rees M.J., 2000, ApJ in press, astro--ph/9908126\n\\bibitem []{} Panaitescu A., Spada M. \\& Meszaros P., 1999, ApJ, 522, L105\n\\bibitem []{} Preece R.D. et al., 1998a, ApJ, 496, 849\n\\bibitem []{} Preece R.D. et al., 1998b, ApJ, 506, L23\n\\bibitem []{} Rybicki G.B. \\& Lightman A.P., 1979, Radiative Processes in\n Astrophysics, J. Wiley \\& Sons (New York)\n\\bibitem []{} Svensson R., 1984, MNRAS, 209, 175\n\\bibitem []{} Svensson R., 1987, MNRAS, 227, 403\n\n\\end{thebibliography}"
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astro-ph0002050
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A Test of the Collisional Dark Matter Hypothesis from Cluster Lensing
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[
{
"author": "Jordi Miralda-Escud\\'e$^{1}$"
}
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Spergel \& Steinhardt proposed the possibility that the dark matter particles are self-interacting, as a solution to two discrepancies between the predictions of cold dark matter models and the observations: first, the observed dark matter distribution in some dwarf galaxies has large, constant-density cores, as opposed to the predicted central cusps; and second, small satellites of normal galaxies are much less abundant than predicted. The dark matter self-interaction would produce isothermal cores in halos and expel the dark matter particles from dwarfs orbiting in large halos. Another consequence of the model is that halos should become spherical once most particles have interacted. Several observations show that the mass distribution in relaxed clusters of galaxies is elliptical. Here, I discuss in particular gravitational lensing in the cluster MS2137-23, where the ellipticity of the dark matter distribution can be measured to a small radius, $r\sim 70$ kpc, suggesting that most dark matter particles in clusters outside this radius do not collide during the characteristic age of clusters. If true, this implies that any dark matter self-interaction with a cross section independent of velocity is too weak to have affected the observed density profiles in the dark-matter dominated dwarf galaxies, or to have facilitated the destruction of dwarf satellites in galactic halos. If $s_x$ is the cross section and $m_x$ the mass of the dark matter particle, then $s_x/m_x < 10^{-25.5} \cm^2/\gev$.
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"name": "p62b.tex",
"string": "\\documentclass[12pt,preprint]{aastex}\n%\\documentstyle[11pt,aaspp4]{article}\n\\begin{document}\n\\newcommand{\\msun}{M_{\\odot}}\n\\newcommand{\\kms}{\\, {\\rm km\\, s}^{-1}}\n\\newcommand{\\cm}{\\, {\\rm cm}}\n\\newcommand{\\gm}{\\, {\\rm g}}\n\\newcommand{\\gev}{\\, {\\rm GeV}}\n\\newcommand{\\erg}{\\, {\\rm erg}}\n\\newcommand{\\kpc}{\\, {\\rm kpc}}\n\\newcommand{\\mpc}{\\, {\\rm Mpc}}\n\\newcommand{\\seg}{\\, {\\rm s}}\n\\newcommand{\\kev}{\\, {\\rm keV}}\n\\newcommand{\\hz}{\\, {\\rm Hz}}\n\\newcommand{\\nhi}{N_{\\hi}}\n\\newcommand{\\etal}{et al.\\ }\n\\newcommand{\\yr}{\\, {\\rm yr}}\n\\newcommand{\\eq}{eq.\\ }\n\\def\\arcsec{''\\hskip-3pt .}\n\n\\title{A Test of the Collisional Dark Matter Hypothesis from Cluster\nLensing}\n\\author{Jordi Miralda-Escud\\'e$^{1}$}\n\\affil{The Ohio State University, Dept. of Astronomy,\nMcPherson Labs.,\n140 W. 18th Ave., Columbus, OH 43210}\n\\authoremail{[email protected]}\n\\affil{$^{1}$ Alfred P. Sloan Fellow}\n\n\\begin{abstract}\n\n Spergel \\& Steinhardt proposed the possibility that the dark matter\nparticles are self-interacting, as a solution to two discrepancies\nbetween the predictions of cold dark matter models and the observations:\nfirst, the observed dark matter distribution in some dwarf galaxies has\nlarge, constant-density cores, as opposed to the predicted central\ncusps; and second, small satellites of normal galaxies are much less\nabundant than predicted. The dark matter self-interaction would produce\nisothermal cores in halos and expel the dark matter particles from\ndwarfs orbiting in large halos. Another consequence of the model is that\nhalos should become spherical once most particles have interacted.\nSeveral observations show that the mass distribution in relaxed clusters\nof galaxies is elliptical. Here, I discuss in particular gravitational\nlensing in the cluster MS2137-23, where the ellipticity of the dark\nmatter distribution can be measured to a small radius, $r\\sim 70$ kpc,\nsuggesting that most dark matter particles in clusters outside this\nradius do not collide during the characteristic age of clusters. If\ntrue, this implies that any dark matter self-interaction with a cross\nsection independent of velocity is too weak to have affected the\nobserved density profiles in the dark-matter dominated dwarf galaxies,\nor to have facilitated the destruction of dwarf satellites in galactic\nhalos. If $s_x$ is the cross section and $m_x$ the mass of the dark\nmatter particle, then $s_x/m_x < 10^{-25.5} \\cm^2/\\gev$.\n\n\\end{abstract}\n\n\\keywords{dark matter - galaxies: clusters: general - galaxies: formation\n - large-scale structure of universe}\n\n\\section{Introduction}\n\n The Cold Dark Matter (CDM) model of structure formation in\nthe universe has been tremendously successful in accounting for a huge\nvariety of available observations (e.g., the Cosmic Background fluctuations,\nthe abundances of clusters of galaxies, peculiar velocity fields,\nthe Ly$\\alpha$ forest), provided that the mean density of matter\nis only a fraction $ \\Omega_m \\simeq 0.3$ of the critical density, and\nthe existence of vacuum energy with a negative pressure equation of\nstate is allowed to make the universe spatially flat (e.g.,\n\\cite{kp00}; \\cite{ptw99}; \\cite{bops99}; \\cite{sw95}; \\cite{ecf96};\n\\cite{crofta99}).\n\n A possible problem of this model has emerged when comparing the\ndensity profiles of dark matter halos predicted in numerical\nsimulations, with observations of the rotation curves in dwarf galaxies\n(\\cite{m94}; \\cite{fp94}; \\cite{nfw96}; \\cite{moorea98}; \\cite{kkbp98};\n\\cite{moorea99}). Whereas the observations show linearly rising rotation\ncurves out to core radii greater than $1 \\kpc$ in certain dwarf galaxies\nwhere the density is dominated by dark matter everywhere (indicating\nthat the dark matter has a constant density core), the simulations\npredict that the collapse of collisionless particles of cold dark matter\nproduces cuspy halo density profiles, with a logarithmic slope\n$-d\\log\\rho / d\\log r > 1$ down to the smallest resolved radius. A\nsecond problem is that the number of dwarf galaxies observed in the\nLocal Group is much smaller than the total number predicted from\nnumerical simulations (\\cite{kkvp99}; \\cite{moorea99}).\n\n A solution to this discrepancy has been proposed by\nSpergel \\& Steinhardt (2000): if the dark matter is self-interacting,\nwith large enough cross section to make most particles in the inner core\nof a dwarf galaxy interact among themselves over a Hubble time, then an\nisothermal core will be produced. A clear prediction of this hypothesis\nis that when most of the particles of a halo within some radius $r_c$\nhave interacted, then the halo should be close to spherical inside\n$r_c$, or else be supported by rotation, because the velocity dispersion\ntensor should become isotropic. This paper examines the consequence of\nthis prediction for the inner parts of rich clusters of galaxies, where\nhighly magnified images of background galaxies are occasionally\nobserved. We will find that severe restrictions on the\ncollisional dark matter hypothesis are obtained.\n\n\\section{The Collisional Radius in Dwarf Galaxies and in Galaxy Clusters}\n\n We assume that a halo of self-interacting dark matter has an initial\ndensity profile equal to the one for the case of collisionless dark\nmatter, and is thereafter modified by the effects of the collisions.\nNumerical simulations of collisionless CDM models have shown that halos\nhave a characteristic density profile, with a logarithmic slope that\nincreases gradually with radius (Navarro, Frenk, \\& White 1996, 1997;\nMoore \\etal 1999b). We define the radius $r_h$ where the logarithmic\nslope is equal to 2, so that\n$ | d\\log\\rho/d\\log r | < 2$ at $r < r_h$, and \n$ | d\\log\\rho/d\\log r | > 2$ at $r > r_h$.\nThe particles closest to the center will be the first ones to collide,\nowing to the higher density. We define the collisional radius, $r_c$, as\nthe radius within which more than half the particles have interacted.\nThe effects of the collisions will be to change the velocity distribution\nof the particles inside the collisional radius toward a Maxwellian\ndistribution, with constant velocity dispersion. This implies that the\ndensity profile within the collisional radius will be altered toward\nthat of an isothermal sphere with finite core. The core radius produced\nby the collisions can obviously not be larger than the collisional\nradius, but it can be much smaller than the collisional radius if the\ninitial slope of the halo profile inside $r_c$ was already close to\nisothermal, because the total energy needs to be conserved. Several\nnumerical simulations have recently been done to model this effect\n(e.g., Burkert 2000, Yoshida \\etal 2000, Dav\\'e \\etal 2001).\n\n In the initial density profile, the velocity dispersion should clearly\ndecrease toward the center at $r < r_h$: as long as the density profile\nhas a central power-law cusp, and the orbits are not all highly radial\nnear the center, then $\\sigma^2(r) \\propto \\rho(r) r^2$. The collisions\nwill therefore transport heat to the colder central particles from the\nhotter exterior, destroying the cusp and slowly increasing the core of\nthe isothermal sphere as the collisional radius increases. However, the\nparticles at $r> r_h$ should have a decreasing velocity dispersion with\nradius in their initial configuration, so when $r_c > r_h$ heat starts\nto be transported outward and the isothermal core shrinks as more\nparticles are slung to the outer parts of the halo (or to unbound\norbits), leading eventually to core collapse. As discussed by Spergel \\&\nSteinhardt (2000), the cross section should be low enough so that the core\ncollapse of the dark matter has not taken place in any halos up to the\npresent time.\n\n How should the collisional radius vary with the velocity dispersion\nof a dark matter halo? We assume that the cross section for the elastic\ncollisions in the dark matter is independent of velocity, as expected\nin the low energy limit when the cross section is dominated by the\ns-wave contribution (e.g., Landau \\& Lifshitz 1977).\nThen, the rate of interaction of a particle\nis proportional to the dark matter density, $\\rho$, times the velocity\ndispersion $\\sigma$. Hence, $\\rho\\, \\sigma\\, t = {\\rm constant}$, where\n$t$ is the age of the halo (or the time since the last merger which\ndetermined an initial density profile). Assuming that the core of the\nhalo is not larger than the collisional radius, dynamical equilibrium\nimplies $\\rho(r_c) \\propto \\sigma^2/r_c^2$, and therefore,\n\\begin{equation}\n r_c \\propto \\sigma^{3/2}\\, t^{1/2} ~.\n\\label{colprop}\n\\end{equation}\nThis implies that {\\it if the core radii in dwarf galaxies are caused by\ndark matter collisions within a larger collisional radius, then all the\ngalactic and cluster dark matter halos should have much larger\ncollisional radii as their velocity dispersion increases.}\n\n Typically, the constant density cores of dwarf galaxy halos measured\nfrom the kinematics of the HI gas extend out to\na few kpc, and a typical velocity dispersion is $50 \\kms$. As a few\nexamples, the rotation curves of the dwarfs DDO 154, DDO 170, and\nDDO 236 yield fits for their dark matter halos with velocity\ndispersion $\\sigma=(28,52,45) \\kms$, and core radii $(3,2.5,6) \\kpc$\n(\\cite{cb89}; \\cite{lsv90}; \\cite{jc90}), with assumed distances of\n$(4, 15, 1.7) \\mpc$, respectively.\n\n If we wish to explain the sizes of these dark matter cores in dwarf\ngalaxies as the result of collisional dark matter, then the collisional\nradii of the halos of these dwarfs must be larger than the observed\ncore radii, and the collisional radii in rich clusters of galaxies must\nbe much larger, according to (\\ref{colprop}). Using the conservative\nvalues of $r_c=2 \\kpc$ and $\\sigma=50 \\kms$ for a typical dwarf galaxy,\nand assuming that a typical rich cluster is about a third as old as a\ndwarf galaxy (since massive halos have collapsed more recently than\ndwarf galaxies; see Fig. 10 of Lacey \\& Cole 1993), we infer that the\ncollisional radius of a typical rich cluster with velocity dispersion\n$\\sigma = 1000 \\kms$ should be at least $r_c > 100 \\kpc$.\n\n Within the collisional radius, the halo potential should be very\nnearly spherical because the collisions should make the velocity\ndispersion tensor of the dark matter particles isotropic (unless\nthe core is rapidly rotating, which is highly unlikely as will be\ndiscussed in \\S 4). This is most easily seen for a finite system,\nusing the tensor virial theorem: the potential energy tensor (which\nreflects the shape of the mass distribution) will become diagonal\nover the same timescale as the kinetic energy tensor.\nThe next section discusses the evidence from\ngravitational lensing showing that cluster cores are elliptical in\ntheir inner parts, focusing in particular on the example of\nMS2137-23.\n\n\\section{The core of the cluster MS2137-23 is elliptical}\n\n Highly magnified images of background galaxies (or ``arcs'') produced\nby gravitational lensing have been observed in many clusters of\ngalaxies. In general, models that reproduce the positions and shapes of\nthese images assume the presence of elliptical clumps of dark matter\ncentered on the most luminous galaxies in the cluster, with the\nellipticity being oriented along the same axis as the optical light.\nExamples of clusters that have been modeled in this way\ninclude A370 (\\cite{kmfm93}), A2218 (\\cite{kneiba95}), MS2137-23\n(\\cite{mfk93}), and A2390 (\\cite{pierrea96}).\nIt should be noted that the optical isophotes of the\ncentral cluster galaxies generally extend out to the radius where the\ngravitationally lensed images are observed, where the potential is\nstrongly dominated by the dark matter. The regular elliptical\nisophotes of the distribution of stars implies that the gravitational\npotential has the same shape, and this is confirmed by the lensing\nmodels that reproduce the positions and shapes of the multiple images\nof background galaxies.\n \n We note here the intriguing fact that the isophotes of central\ncluster galaxies tend to show a decrease of the ellipticity toward the\ncenter, within radii $\\lesssim 10 \\kpc$ (Porter \\etal 1991). This might\nplausibly be an indication of the effects of self-interacting dark\nmatter at this small radius, making the potential more spherical;\nhowever, other dynamical effects associated with the formation of these\ngalaxies from mergers\nmight also explain this if the dark matter is collisionless. In this\npaper, we will discuss the evidence that if there is self-interacting\ndark matter, the collisional radius in rich clusters of galaxies should\nbe smaller than $\\sim 100$ kpc, leaving the question of whether there\nmight a smaller collisional radius for future work.\n\n Here, we shall focus on the cluster MS2137-23. This cluster has\nseveral characteristics that make it particularly useful for our\npurpose. First, the central region of the cluster appears to be well\nrelaxed as shown from both the optical image, dominated by the central\ngalaxy, and the X-ray emission, centered on the galaxy and with an\nellipticity and position angle similar to that of the central galaxy\n(\\cite{hammera97}). In clusters with substructure, the presence of\nmultiple mass clumps requires models of the mass distribution with many\nparameters, making it difficult to constrain the ellipticity of each\nmass clump. Second, a total of five gravitationally lensed images \narising from two sources are observed in MS2137-23, providing many\nconstraints for the lensing model. Although redshifts for these five\nimages have not yet been measured, their morphologies and colors provide\nstrong evidence for the lensing interpretation (\\cite{hammera97}).\nOne source produces a long, tangential arc and two other arclets,\nand the second source gives rise\nto a radially elongated image near the center and another arclet\n(where ``arclet'' refers to images that are not magnified by very\nlarge factors, but still show a characteristic stretching effect\ndue to lensing).\n\n The positions and relative sizes and shapes of these five\nimages can be reproduced in an extremely simple model: an elliptical\nmass clump centered on the central galaxy, with the same ellipticity\nand position angle (\\cite{mfk93}; \\cite{m95}).\nThis model needs only two free parameters for the radial density\nprofile (the velocity dispersion of the cluster and the core radius).\nSince the positions of the five images alone already provide 6\nconstraints (ten coordinates of the five images minus 4 for the unknown\npositions of the two sources), and in addition the relative sizes and\norientations of each image are also reproduced, this should be\nconsidered as strong evidence that the potential of the dark matter\nis elliptical, just like the stellar isophotes, and has not been\nsignificantly circularized by dark matter collisions at the radius\nwhere the images are observed. This radius is 15'' for the longest\ntangential arc, which corresponds to 70 kpc (for\n$H_0=70\\kms\\mpc^{-1}$). The radially elongated image is only 5'' from\nthe cluster center; however, if the potential became spherical only\nat this small radius, this radial image would not be significantly\naltered.\n\n Could other perturbations to the potential, arising from\nsubstructure (which causes external shear), mimic the effect of\nellipticity if the true potential was spherical within $\\sim 100$ kpc?\nThere are two arguments against this possibility. First, \nan external shear would be roughly constant within the region of the\nmultiple images, whereas an elliptical potential causes a variable\nshear and convergence that depend on the density profile\n(see eqs. 2 to 8 below). Second, there would be no reason why the external\nshear should be aligned with the major axis of the galaxy. While\nsubstructure is common in many clusters, the central parts of MS2137-23\nappear relaxed, as discussed above.\n\n Although the fact that the simple elliptical potential, with constant\nellipticity as a function of radius, fits the observed positions\nand shapes of the five images can already be considered as persuasive\nevidence that the potential cannot be spherical within $\\sim 100 \\kpc$,\nit will be useful to show analytically why an ellipticity is required\nin a model-independent manner. We will\nfocus here on the radial image and its counterimage. These two images\nof the same source are labeled as A1 and A5 in Mellier \\etal (1993),\nand in Figure 1 of Miralda-Escud\\'e (1995), and as AR and A5 in\nthe HST image presented in Hammer \\etal (1997).\n\n\\begin{figure}\n\\plotone{f1.eps}\n\\caption{Schematic representation of the lensing configuration\nin the cluster MS2137-23 discussed in \\S 3. The lens center is at $C$,\nthe source is located at $S$, and its two images are observed at\n$R$ (which is the image on the radial critical line) and $I$. The angle\nof misalignment $\\gamma$ between the two images relative to the center\nwould be zero for a spherical potential. The radial and azimuthal\ncomponents of the deflection angles ($\\alpha_{\\theta}$ and $\\alpha_{\\phi}$)\nare indicated.}\n\\end{figure}\n\n A schematic representation of the lensing of the source on the radial\ncaustic is shown in Figure 1, which defines the notation that will be\nused here. The point labeled $C$ is the center of the cluster,\nand $S$ is the position of\nthe source that gives rise to the radial image at $R$ and the\ncounterimage at $I$ (the entire lensing configuration in this system,\nwith the critical lines and caustics of a simple elliptical potential,\nis shown in Fig. 1 of Miralda-Escud\\'e 1995).\nWe use polar coordinates on the image\nplane: $\\theta$, the angular distance from the center $C$, and $\\phi$,\nthe azimuthal angle. The light ray observed at $R$ is deflected by\nan angle $\\alpha_{\\theta R}$ in the radial direction, and\n$\\alpha_{\\phi R}$ in the azimuthal direction, and the same for the\nlight ray observed at $I$.\n\n The specific observed quantity that we will relate to the ellipticity\nof the potential is the angle $\\gamma$ of misalignment between the\nimages $R$ and $I$, relative to the center of the lens. In a spherical\npotential, the images $R$ and $I$ should lie on a straight line passing\nthrough $C$. The observed angle is $\\gamma = 19^\\circ$, indicating that\nthe potential is elliptical. In principle, this misalignment could\nalso be caused by substructure in the cluster, but this is unlikely\nin view of the relaxed appearance of the cluster.\n\n We now relate the angle $\\gamma$ to the ellipticity and the density\nprofile of the potential. If the ellipticity $\\epsilon$ is small, \nthe projected potential is adequately approximated with a quadrupole\nterm (e.g., \\cite{m95}),\n\\begin{equation}\n\\psi(\\theta,\\phi) = \\psi_0(\\theta) - {\\epsilon\\over 2} \\,\n\\psi_1(\\theta) \\, \\cos(2\\phi) ~,\n\\end{equation}\nwhere\n\\begin{equation}\n\\psi_0(\\theta) = \\int_0^\\theta d\\theta ' \\, \\alpha_0(\\theta ') ~,\n\\end{equation}\n\\begin{equation}\n\\alpha_0(\\theta) = {2\\over \\theta}\\, \\int_0^{\\theta '} d\\theta ' \\,\n\\theta ' \\, \\kappa_0(\\theta ') \\equiv \\theta \\bar\\kappa_0(\\theta ') ~,\n\\end{equation}\n\\begin{equation}\n\\psi_1(\\theta) = {2\\over \\theta^2}\\,\n\\int_0^\\theta d\\theta ' \\, \\theta '^3 \\, \\kappa_0(\\theta ') ~,\n\\label{psi1eq}\n\\end{equation}\nand where the surface density of the lens is\n\\begin{equation}\n\\kappa(\\theta,\\phi) = \\kappa_0(\\theta) - {\\epsilon\\over 2} \\,\n\\theta\\, {d\\kappa_0\\over d\\theta} \\, \\cos(2\\phi) ~.\n\\end{equation}\nHere, $\\kappa_0(\\theta)$ is the azimuthally averaged surface density\nprofile, and $\\bar\\kappa_0(\\theta)$ is the averaged surface density\nwithin $\\theta$. The deflection angle is given by the gradient of the\npotential,\n\\begin{equation}\n\\alpha_{\\theta} = \\theta \\bar\\kappa_0(\\theta) +\n\\theta \\left[ \\kappa_0(\\theta) + {\\psi_1(\\theta)\\over \\theta^2 } \\right] \\,\n\\epsilon \\cos(2\\phi) ~,\n\\end{equation}\n\\begin{equation}\n\\alpha_{\\phi} = { \\psi_1(\\theta)\\over \\theta } \\, \\epsilon \\sin(2\\phi) ~.\n\\end{equation}\n\n In the limit of a small ellipticity of the potential, the angle of\nmisalignment $\\gamma$ is given by (using the notation in Fig. 1),\n\\begin{equation}\n\\gamma = \\beta_I\\, {\\alpha_{\\theta I}\\over \\theta_I - \\alpha_{\\theta I} }\n+ \\beta_R\\, { \\alpha_{\\theta R} \\over \\alpha_{\\theta R} - \\theta_R } =\n{ \\alpha_{\\phi I} \\over \\theta_I - \\alpha_{\\theta I} } + \n{ \\alpha_{\\phi R} \\over \\alpha_{\\theta R} - \\theta_R } ~.\n\\end{equation}\n\n Using the condition that the rays at images $R$ and $I$ are deflected\nto the same position $S$, which is simply\n$\\theta_i - \\alpha_{\\theta I} = \\alpha_{\\theta R} - \\theta_R$\n(the ellipticity introduces only second order corrections here),\nwe obtain\n\\begin{equation}\n\\gamma = \\left[ { \\psi_1(\\theta_R) \\over \\theta_R } + \n{ \\psi_1(\\theta_I) \\over \\theta_I } \\right ] \\,\n{\\epsilon \\sin (2\\phi_I) \\over \\theta_I - \\alpha_{\\theta I} } ~.\n\\end{equation}\n\n We now want to find a lower limit to the ellipticity necessary to\ngenerate the observed angle $\\gamma$. For this purpose, it will be\nconvenient to replace the function $\\psi_1(\\theta)/\\theta)$ by an upper\nlimit. Using equation (\\ref{psi1eq}), we find that if the $\\kappa_0$ is\nconstant within $\\theta$, then $\\psi_1(\\theta)/\\theta = \\theta\\,\n\\bar\\kappa_0(\\theta) / 2$, while in any profile where $\\kappa_0$\ndecreases with radius, we have $\\psi_1(\\theta)/\\theta < \\theta\\,\n\\bar\\kappa_0(\\theta) / 2$, because the integral of equation\n(\\ref{psi1eq}) weights more heavily the surface density near $\\theta$\nthan at smaller angular radius. Therefore,\n\\begin{equation}\n\\gamma < { \\left[ \\theta_R \\bar\\kappa_0(\\theta_R) +\n\\theta_I \\bar\\kappa_0(\\theta_I) \\right] \\, \\epsilon \\sin(2\\phi_I) \\over\n 2 \\, \\theta_I \\, \\left[ 1 - \\bar\\kappa(\\theta_I) \\right] } =\n{ (1 + \\theta_R / \\theta_I) \\, \\epsilon \\sin(2\\phi_I) \\over\n 2\\, \\left[ 1 - \\bar\\kappa(\\theta_I) \\right] } ~.\n\\end{equation}\nWe can now substitute the observed values $\\theta_I=22\\arcsec 5$\n(\\cite{flhc92}), and $\\theta_R = 5\\arcsec 2$ (\\cite{hammera97}):\n\\begin{equation}\n\\gamma < 0.62\\, {\\epsilon \\cos(2\\phi_I) \\over 1-\\bar\\kappa_0(\\theta_I) } ~.\n\\label{glt2}\n\\end{equation}\nTo obtain a lower limit to $\\epsilon$, we need to assume an upper limit\nfor $1-\\bar\\kappa(\\theta_I)$. Because the two images $R$ and $I$ result\nfrom radial (rather than tangential) magnification, there is no reason\nwhy $\\bar\\kappa$ needs to be particularly close to unity at either\nimage. Given the relation $[\\bar\\kappa_0(\\theta_R) - 1 ] / [1 -\n\\bar\\kappa_0(\\theta_I) ] = \\theta_I /\\theta_R = 4.3$, the quantity $1 -\n\\bar\\kappa(\\theta_I)$ could be very small only if the surface density\nprofile was very flat between the angular radii $\\theta_R$ and\n$\\theta_I$. This is very unlikely because the velocity dispersion\nimplied for the cluster for an Einstein radius close to $\\theta_I =\n22\\arcsec 5$ is already larger than $1000 \\kms$ (see \\cite{m95}, Figs. 8\nand 9), and it would increase to a much higher value at large radius if\nthe slope of the density profile was much shallower than isothermal at\n$\\theta\\sim \\theta_I$.\n\n As a reasonable limit on how flat the $\\bar\\kappa$ profile could\nbe from $\\theta_R$ to $\\theta_I$, we will assume here\n$\\bar\\kappa(\\theta_R) / \\bar\\kappa(\\theta_I) > 2$ (remember that\n$\\theta_I/\\theta_R = 4.3$). This corresponds to\n$1-\\bar\\kappa_0(\\theta_I) > 0.16$, implying that the image $I$ is\nnot tangentially magnified by more than a factor 6, which is reasonable\ngiven the length of the image $I$ (called A5 in \\cite{hammera97}),\n$\\sim 3''$, and its axis ratio of $\\sim 3$.\n\n With this condition, and using also $\\cos(2\\phi_I)\\simeq 0.7$\n(e.g., Mellier \\etal 1993; we assume the major axis of the potential\nis aligned with that of the central galaxy), and $\\gamma = 0.33$, the\nlower limit on the ellipticity from equation (\\ref{glt2}) is\n\\begin{equation}\n\\epsilon > 0.77\\, [1-\\bar\\kappa(\\theta_I) ] \\gtrsim 0.1 ~.\n\\end{equation}\n\n This is only a lower limit that we have obtained using only one\nobservational constraint, the misalignment of two images relative to\nthe center. The models that reproduce also the three images of the\nother source require an ellipticity $\\epsilon \\simeq 0.2$. \n\n There are other clusters that show little substructure in their\ninner parts and are well modelled by an elliptical potential with\nthe major axis coinciding with that of the central galaxy: one is\nA2218 (Kneib \\etal 1995), which requires two clumps in the model, but\nwith the dominant agreeing in position and ellipticity with the\ncentral cluster galaxy. Another is A963, which shows two\ntangential arcs around the central giant elliptical (Lavery \\& Henry\n1988). In the case of\nA963 the ellipticity is difficult to constrain because there are only\ntwo images which could be from the same source or two different sources. \n\n\\section{Discussion}\n\n The modeling of multiple images of background galaxies produced by\ngravitational lensing in clusters of galaxies require elliptical models\nof the mass distribution in order to reproduce their positions and\nmagnifications successfully (\\cite{kmfm93}; \\cite{mfk93}; \\cite{kneiba95}).\nThe last section discussed the specific\nexample of MS2137-23, where the misalignment in the position of two\nimages relative to the cluster center can be used to constrain the\nellipticity in a model-independent way: the ellipticity of the dark\nmatter halo around the central galaxy must be greater than $0.1$ within\nthe image $I$, which is at $22\\arcsec 5$ from the cluster center,\ncorresponding to a distance of $65 h^{-1} \\kpc$. The fact that the\ndark matter halos of galaxy clusters are elliptical within this small\nradius implies that the dark matter particles have not collided over\nthe age of the cluster. As shown in \\S 2, this also implies that the\nobserved cores of the dark matter halos in dwarf galaxies are too big\nto have been caused by dark matter self-interaction, as proposed by\nSpergel \\& Steinhardt (2000).\n\n Further evidence supporting that cluster dark matter halos are\nelliptical at radii $\\sim 100$ kpc comes from the similarity with the\nellipticity of the optical isophotes of the central cluster galaxies in\nboth the magnitude of the ellipticity and the orientation of the major\naxis (\\cite{mfk93}; \\cite{kmfm93}; \\cite{kneiba95}). If the underlying\ndark matter distribution became spherical due to the collisions, the\nellipticity of the stellar distribution would be reduced (although not\neliminated, owing to the anisotropy in the velocity dispersion tensor).\nAccording to Hammer \\etal (1997), the central galaxy in MS2137-23 has\nellipticity $\\epsilon = 0.16 \\pm 0.02$ beyond the radius of the radial\narc, and the best fit ellipticity for the lens model is $\\epsilon =\n0.18$ (see also \\cite{kneiba95} for similar conclusions obtained in the\ncluster A2218). We note again that the ellipticities of the optical\nisophotes decline at a radius smaller than that probed by gravitational\nlensing (Porter \\etal 1991).\n\n The ellipticity of the cluster halo can be used to place an upper\nlimit on the interaction rate of the dark matter, in terms of the cross\nsection $s_x$ and mass $m_x$ of the dark matter particle. We assume here\nthat the collisional radius must be smaller than the distance from the\ncenter to the long tangential arc and two other arclets\n(these images are A01-A02, A2 and A4 in \\cite{hammera97},\nand they also require an ellipticity similar to that of the central\ngalaxy in the lensing models), which is about $70 \\kpc$. The dark matter\ndensity at this radius is $\\rho \\simeq \\Sigma_{crit}/2r$, where\nthe critical surface density is $\\Sigma_{crit}\\simeq 1\\gm\\cm^{-2}$\nfor a source at $z_s=1$. Assuming also a cluster velocity dispersion\n$\\sigma=1000 \\kms$ (roughly the minimum value required given the\nEinstein radius of the cluster), and a cluster age\n$t_c = 5\\times 10^9$ years, we obtain the upper limit\n\\begin{equation}\n{s_x \\over m_x} < {1 \\over \\rho\\, 2^{1/2}\\sigma\\, t_c } \\simeq\n10^{-25.5} { \\cm^2 \\over m_p } \\simeq 0.02 {\\cm^2 \\over \\gm} ~.\n\\end{equation}\nFor the dwarf galaxies DDO 154, DDO 170, and DDO 236 mentioned in \\S 2,\nwith velocity dispersion $\\sigma=(28,52,45) \\kms$, and core radii\n$(3,2.5,6) \\kpc$, the time it would take for the collisional radius to\nreach the value of their core radii if $s_x/m_x$ were equal to the above\nupper limit is $t = (40,5,40)\\times 10^{10}$ years, respectively [where\nwe have used the relation $t \\propto \\sigma^3/r_c^2$, from eq.\\\n(\\ref{colprop}) ].\n\n The limit we have obtained on the self-interaction of the dark matter\nalso rules it out as an explanation for the low abundance of dwarf\ngalaxies in the Local Group, compared to the predictions of halo\nsatellites abundances from numerical simulations (\\cite{kkvp99};\n\\cite{mooreb99}). In order to strike out the dark matter particles, the\nsatellite halos must be moving in an orbit inside the collisional\nradius. For example, in the Milky Way halo (with $\\sigma \\simeq 150\n\\kms$), the collisional radius cannot be greater than about $6 \\kpc$, if\n$r_c < 100 \\kpc$ in a cluster with $\\sigma = 1000 \\kms$ (where we use\nthe scaling $r_c \\propto \\sigma^{3/2}$).\n\n Finally, we mention three ways by which the collisional dark\nmatter hypothesis might still remain viable as an explanation of the\nconstant density cores observed in some dwarf galaxies. A first\npossibility is that the presence of substructure in the mass\ndistribution of MS2137-23, or of other massive structures projected on\nthe line of sight of the cluster, introduces an external shear that\nwould modify the positions of the images. However, this seems unlikely\nas discussed in \\S 3, because elliptical models fit the observed\npositions and shapes of the images remarkably well with fewer model\nparameters than observational constraints, and an external shear\ninduces a lensing potential different than a constant ellipticity, and\nwould not generally be aligned with the major axis of the galaxy. \nThe second possibility is that the ellipticity of the dark matter could\nbe supported by rotation, instead of anisotropic velocity dispersion.\nHowever, halos formed by collisionless collapse are known to rotate very\nslowly (\\cite{be87}; \\cite{wqsz92}), and the collisions would further\nslow down the rotation of the central parts of the halo by enforcing\nsolid body rotation. Finally, there is the possibility that the cross\nsection for the dark matter interaction decreases with velocity. 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Lett., 83, 670\n\n\\bibitem[Pierre \\etal 1996]{pierrea96}\nPierre, M., Le Borgne, J. F., Soucail, G., \\& Kneib, J. P. 1996,\nA\\& A, 311, 413\n\n\\bibitem[Porter, Schneider, \\& Hoessel 1991]{psh91}\nPorter, A. C., Schneider, D. P., \\& Hoessel, J. G. 1991, AJ, 101, 1561\n\n\\bibitem[Spergel \\& Steinhardt 2000]{ss00}\nSpergel, D. N., \\& Steinhardt, P. J. 1999, Phys. Rev. Lett. 84, 3760\n\n\\bibitem[Strauss \\& Willick 1995]{sw95}\nStrauss, M. A., \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[Warren \\etal 1992]{wqsz92} Warren, M. S., Quinn, P. J.,\nSalmon, J. K., \\& Zurek, W. H. 1992, ApJ 399, 405\n\n\\bibitem[Yoshida \\etal 2000]{yoshidaa2000}\nYoshida, N., Springel, V., White, S. D. M., \\& Tormen, G. 2000,\nApJ, 544, L87\n\n\\end{thebibliography}\n\n\\end{document}\n"
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"name": "astro-ph0002050.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Bahcall et al. 1999]{bops99}\nBahcall, N., Ostriker, J. P.,\nPerlmutter, S., \\& Steinhardt, P. J. 1999, Science, 284, 1481\n\n%\\bibitem[Bahcall, Lubin, \\& Dorman 1995]{bld95}\n%Bahcall, N. A., Lubin, L. M., \\& Dorman, V. 1995, ApJ, 447, L81\n%\n%\\bibitem[Bahcall \\& Fan 1998]{bf98}\n%Bahcall, N. A., \\& Fan, X. 1998, ApJ, 504, 1\n\n\\bibitem[Barnes \\& Efstathiou 1987]{be87}\nBarnes, J., \\& Efstathiou, G. 1987, ApJ, 319, 575\n\n\\bibitem[Burkert 2000]{burkert00}\nBurkert, A. 2000, ApJ, 534, L143\n\n\\bibitem[Carignan \\& Beaulieu 1989]{cb89}\nCarignan, C., \\& Beaulieu, S. 1989, ApJ, 347, 760\n\n\\bibitem[Croft \\etal 1999]{crofta99} Croft, R. A. C., Weinberg, D. H.,\nPettini, M., Hernquist, L., \\& Katz, N. 1999, ApJ, 520, 1\n\n\\bibitem[Dav\\'e \\etal 2001]{davea00}\nDav\\'e, R., Spergel, D. N., Steinhardt, P. J., \\& Wandelt, B. D. 2001,\nApJ, 547, 574\n\n\\bibitem[Eke, Cole, \\& Frenk 1996]{ecf96}\nEke, V. R., Cole, S., \\& Frenk, C. S, 1996, MNRAS, 282, 263\n\n\\bibitem[Firmani \\etal 2001]{fdcha01}\nFirmani, C., D'Onghia, E., Chincarini, G., Hern\\'andez, X., \\& Avila-Reese, V.\n2001, MNRAS, 321, 723\n\n\\bibitem[Flores \\& Primack 1994]{fp94}\nFlores, R. A., \\& Primack, J. A. 1994, ApJ, 427, L1\n\n\\bibitem[Fort \\etal 1992]{flhc92}\nFort, B., Le F\\`evre, O., Hammer, F., \\& Cailloux, M. 1992, ApJ, 399, L125\n\n\\bibitem[Hammer \\etal 1997]{hammera97} Hammer, F., Gioia, I. M., Shaya, E. J.,\nTeyssandier, P., Le F\\`evre, O., \\& Luppino, G. A. 1997, ApJ, 491, 477\n\n\\bibitem[Jobin \\& Carignan 1990]{jc90}\nJobin, M., \\& Carignan, C. 1990, AJ, 100, 648\n\n\\bibitem[Klypin \\etal 1999]{kkvp99} Klypin, A. A., Kravtsov, A. V.,\nValenzuela, O., \\& Prada, F. 1999, ApJ, 522, 82\n\n\\bibitem[Kneib \\etal 1993]{kmfm93}\nKneib, J. P., Mellier, Y., Fort, B., \\& Mathez, G. 1993, A\\& A, 273, 367\n\n\\bibitem[Kneib \\etal 1995]{kneiba95}\nKneib, J. P., Mellier, Y., Pell\\'o, R., Miralda-Escud\\'e, J.,\nLe Borgne, J.-F., B\\\"ohringer, H., \\& Picat, J.-P. 1995, A\\&A, 303, 27\n\n\\bibitem[Knox \\& Page 2000]{kp00} Knox, L., \\& Page, L. 2000,\nPhys. Rev. Lett., 85, 1366\n\n\\bibitem[Kravtsov \\etal 1998]{kkbp98} Kravtsov, A. V., Klypin, A. A.,\nBullock, J. S., \\& Primack, J. R. 1998, ApJ, 502, 48\n\n\\bibitem[Lacey \\& Cole 1993]{lc93}\nLacey, C., \\& Cole, S. 1993, MNRAS, 262. 627\n\n\\bibitem[Lake, Schommer, \\& van Gorkom 1990]{lsv90}\nLake, G., Schommer, R. A., \\& van Gorkom, J. A. 1990, AJ, 99. 547\n\n\\bibitem[Landau \\& Lifshitz 1977]{ll77}\nLandau, L. D., \\& Lifshitz, E. M. 1977, {\\it Quantum Mechanics\n(Non-Relatistic Theory)} (Pergamon Press).\n\n\\bibitem[Lavery \\& Henry 1988]{lh88}\nLavery, R. J., \\& Henry, J. P. 1988, ApJ, 329, L21\n\n\\bibitem[Mellier, Fort, \\& Kneib 1993]{mfk93}\nMellier, Y., Fort, B., \\& Kneib, J. P. 1993, ApJ, 407, 33\n\n\\bibitem[Miralda-Escud\\'e 1995]{m95}\nMiralda-Escud\\'e, J. 1995, ApJ, 438, 514\n\n\\bibitem[Moore 1994]{m94} Moore, B. 1994, Nat, 370, 629\n\n\\bibitem[Moore \\etal 1998]{moorea98} Moore, B., Governato, F., Quinn, T.,\nStadel, J., \\& Lake, G. 1998, ApJ, 499, L5\n\n\\bibitem[Moore \\etal 1999a]{mooreb99} Moore, B., Ghigna, S., Governato, F.,\nLake, G., Quinn, T., Stadel, J., \\& Tozzi, P. 1999, ApJ, 524, L19\n(astro-ph/9907411)\n\n\\bibitem[Moore \\etal 1999b]{moorea99} Moore, B., Quinn, T., Governato, F.,\nStadel, J., \\& Lake, G. 1999, MNRAS, 310, 1147\n\n\\bibitem[Navarro, Frenk, \\& White 1996]{nfw96}\nNavarro, J. F., Frenk, C. S., \\& White, S. D. M. 1996, ApJ, 462, 563\n\n\\bibitem[Navarro, Frenk, \\& White 1997]{nfw97}\nNavarro, J. F., Frenk, C. S., \\& White, S. D. M. 1997, ApJ, 490, 493\n\n\\bibitem[Perlmutter, Turner, \\& White 1999]{ptw99} Perlmutter, S., Turner,\nM. S., \\& White, M. 1999, Phys. Rev. Lett., 83, 670\n\n\\bibitem[Pierre \\etal 1996]{pierrea96}\nPierre, M., Le Borgne, J. F., Soucail, G., \\& Kneib, J. P. 1996,\nA\\& A, 311, 413\n\n\\bibitem[Porter, Schneider, \\& Hoessel 1991]{psh91}\nPorter, A. C., Schneider, D. P., \\& Hoessel, J. G. 1991, AJ, 101, 1561\n\n\\bibitem[Spergel \\& Steinhardt 2000]{ss00}\nSpergel, D. N., \\& Steinhardt, P. J. 1999, Phys. Rev. Lett. 84, 3760\n\n\\bibitem[Strauss \\& Willick 1995]{sw95}\nStrauss, M. A., \\& Willick, J. A. 1995, Phys. Rep., 261, 271\n\n\\bibitem[Warren \\etal 1992]{wqsz92} Warren, M. S., Quinn, P. J.,\nSalmon, J. K., \\& Zurek, W. H. 1992, ApJ 399, 405\n\n\\bibitem[Yoshida \\etal 2000]{yoshidaa2000}\nYoshida, N., Springel, V., White, S. D. M., \\& Tormen, G. 2000,\nApJ, 544, L87\n\n\\end{thebibliography}"
}
] |
astro-ph0002051
|
The intragroup medium in loose groups of galaxies
|
[
{
"author": "School of Physics and Astronomy"
},
{
"author": "Edgbaston"
},
{
"author": "Birmingham B15 2TT"
},
{
"author": "UK"
}
] |
\noindent We have used the {ROSAT} PSPC to study the properties of a sample of 24 X-ray bright galaxy groups, representing the largest sample examined in detail to date. Hot plasma models are fitted to the spectral data to derive temperatures, and modified King models are used to characterise the surface brightness profiles. In agreement with previous work, we find evidence for the presence of two components in the surface brightness profiles. The extended component is generally found to be much flatter than that observed in galaxy clusters, and there is evidence that the profiles follow a trend with system mass. We derive relationships between X-ray luminosity, temperature and optical velocity dispersion. The relation between X-ray luminosity and temperature is found to be $L_X \propto T^{4.9}$, which is significantly steeper than the same relation in galaxy clusters. These results are in good agreement with preheating models, in which galaxy winds raise the internal energy of the gas, inhibiting its collapse into the shallow potential wells of poor systems.
|
[
{
"name": "loosegrp.tex",
"string": "\\documentstyle[general_cite,psfig]{mn}\n\\bibliographystyle{mnras}\n\\title{The intragroup medium in loose groups of galaxies}\n\\author[Stephen F. Helsdon and Trevor J. Ponman]\n {Stephen F. Helsdon\\thanks{E-mail: [email protected]} and Trevor J.\n Ponman \\\\\n School of Physics and Astronomy, University of\n Birmingham, Edgbaston, Birmingham B15 2TT, UK\\\\}\n \\date{Accepted 1999 ??.\n Received 1999 ??;\n in original form 1999 ??}\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{1998}\n\n% A few definitions for symbols - degrees, greater than or approx eq, less\n % than or approx eq\n\\def\\deg{\\hbox{$^\\circ$}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\gtsim{$\\mathrel{\\spose{\\lower 3pt\\hbox{$\\sim$}}\n \\raise 2.0pt\\hbox{$>$}}$} \n\\def\\ltsim{$\\mathrel{\\spose{\\lower 3pt\\hbox{$\\sim$}}\n \\raise 2.0pt\\hbox{$<$}}$}\n\n\\begin{document}\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\n\n \\noindent We have used the {\\it ROSAT} PSPC to study the properties of a\n sample of 24 X-ray bright galaxy groups, representing the largest sample\n examined in detail to date. Hot plasma models are fitted to the spectral\n data to derive temperatures, and modified King models are used to\n characterise the surface brightness profiles.\n \n In agreement with previous work, we find evidence for the presence of two\n components in the surface brightness profiles. The extended component is\n generally found to be much flatter than that observed in galaxy clusters,\n and there is evidence that the profiles follow a trend with system mass.\n We derive relationships between X-ray luminosity, temperature and optical\n velocity dispersion. The relation between X-ray luminosity and\n temperature is found to be $L_X \\propto T^{4.9}$, which is significantly\n steeper than the same relation in galaxy clusters. These results are in\n good agreement with preheating models, in which galaxy winds raise the\n internal energy of the gas, inhibiting its collapse into the shallow\n potential wells of poor systems.\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: clusters: general -- intergalactic medium -- X-rays: galaxies\n\\end{keywords}\n\n\\section{Introduction}\n\\label{sec:intro}\n\nThe majority of galaxies in the universe are found in galaxy groups\n\\cite{tully87}. These collections of between 3 and about 30 galaxies trace\nlarge scale structure (Ramella, Geller \\& Huchra 1990)\\nocite{ramella90}\nand probably contain a large fraction of the total baryonic mass in the\nuniverse (Fukugita, Hogan \\& Peebles 1998)\\nocite{fukugita98}. However\ndespite their abundance and importance, galaxy groups have received\nrelatively little attention until recently. The main problem has been the\nidentification of the groups themselves. Even when redshift information is\navailable, it is difficult to identify whether a group is truly bound, due\nto the problems of small number statistics and chance superpositions. In\ncontrast, galaxy clusters which are easier to identify due to the larger\nnumber of members, have been extensively studied.\n\nThe detection of extended X-ray emission from hot gas in the group\npotential well provides the best evidence that a group is truly\ngravitationally bound. The study of this hot intragroup gas can provide\nimportant insights into the evolution and dynamics of the group and its\nmember galaxies. Samples of X-ray bright groups were originally studied\nusing the {\\it Einstein} satellite (e.g. \\pcite{price91}), but the\nintroduction of the {\\it ROSAT} satellite with its improved sensitivity and\nresolution, allowed a more thorough analysis of these systems. Since the\n{\\it ROSAT} PSPC was first used to study X-ray bright groups\n\\cite{mulchaey93,ponman93a} a number of collections of groups have been\nstudied (e.g.\n\\pcite{doe95,ponman96a,burns96,mulchaey96,mahdavi97,mulchaey98b}).\nHowever, none of these studies provides a uniform, detailed analysis of a\nreasonable sized sample of groups, based on high quality data. The largest\nsamples have all been based on {\\it ROSAT} All Sky Survey (RASS) data, in\nwhich case properties other than the luminosities are difficult to\ndetermine, due to poor statistics resulting from the short exposures.\n\nThe study of \\scite{ponman96a} used a mixture of RASS and pointed data and\nidentified 22 X-ray bright groups. These were all compact groups from the\ncatalogue of \\scite{hickson82}. Such compact groups have the advantage that\nthey can be easily identified on the sky due to the high projected\nover-densities of galaxies within them, but may be unrepresentative of\ngroups as a whole. The X-ray properties of these Hickson compact groups\n(HCGs) showed systematic departures from those of clusters, leading to the\nsuggestion that they might be displaying the marks of energy injection into\nthe intergalactic medium due to galaxy winds.\n\n\\scite{mulchaey98b} (henceforth MZ98) used pointed PSPC data to study\ngroups of both loose and compact morphology. With a sample of only nine\ngroups they were unable to derive reliable statistical results, however\nthey found that properties such as the $L:T$ relation and surface\nbrightness slope were indistinguishable from those of clusters, in\ncontradiction to the results of \\scite{ponman96a}. If this is true, it\nsuggests a fundamental difference between the properties of loose and\ncompact groups. The main aim of the present work is to establish the X-ray\nproperties of loose groups by means of a careful and uniform study of a\nlarger sample of systems, and to establish whether they do, in fact, differ\nfrom compact groups in their X-ray properties. To allow direct comparison\nwith the results of MZ98, their sample has been included within ours.\n\nIn \\S~\\ref{sec:sample_selection} we describe the sample selection and\ninitial identification of the X-ray bright groups. The spectral and spatial\nanalyses of the X-ray emission are described in\n\\S~\\ref{sec:spectral_analysis} and \\S~\\ref{sec:spatial_analysis}. Results\nof the analysis, including correlations between the derived parameters, are\npresented in \\S~\\ref{sec:Distributionsandcorrelations}. These results are\ncompared with those of MZ98 in \\S~\\ref{Comparison}, and discussed in\n\\S~\\ref{Discussion}. Finally, our conclusions are summarized in\n\\S~\\ref{Conclusions}. Throughout this paper we use H$_0$~=~50~km~s$^{-1}$\nMpc$^{-1}$.\n\n\\section{Sample Selection and Data Reduction}\n\\label{sec:sample_selection}\n\nThe primary aim of this work is to study the properties of a number of\nX-ray bright groups, as such it was necessary to initially compile such a\nsample. Three different sources were used for this purpose, the optical\ncatalogue of \\scite{nolthenius93}, the sample of \\scite{ledlow96} and the\nX-ray bright groups from MZ98. The catalogue of \\scite{nolthenius93}\ncontains 173 groups, with three or more members, selected from the CfA1\ngalaxy redshift catalogue using a friends of friends algorithm with a\ndensity enhancement of 15. The \\scite{ledlow96} sample contains 71 groups\nselected from the Zwicky Catalogue of Galaxies and Clusters of Galaxies,\nusing a friends of friends algorithm with a surface density enhancement of\n46.4, each group having at least 4 members and galactic latitude $|b|~\\geq\n30\\deg$.\n\nCross-correlation of the \\scite{nolthenius93} and \\scite{ledlow96} samples\nwith the {\\it ROSAT} observing log, identified groups which had been\nobserved by the {\\it ROSAT} PSPC during its programme of pointed\nobservations. We further restricted ourselves to groups which had been\nobserved within 20$'$ of the centre of the PSPC. The nine X-ray bright\ngroups from MZ98 were all known to have been observed by the {\\it ROSAT}\nPSPC and were added to the sample. Groups identified as being part of\nknown bright galaxy clusters such as Coma were also excluded at this stage.\nThis resulted in a potential sample of 37 galaxy groups, which are listed\nin Table~\\ref{tab:allgroups}.\n\nBefore the X-ray data can be used it is necessary to identify and exclude\nsources of contamination. These include particle events and solar X-ray\nemission scattered from the Earth's atmosphere into the telescope.\nDetectors on board the spacecraft identify and exclude over 99\\% of the\nparticle events that would be recorded as X-rays. These particle events are\nrecorded as the master veto rate. At values of the master veto rate of\nabove 170 count s$^{-1}$ the contamination by particles is significant, and\nthese times are excluded from our analysis. Reflected solar X-rays can be\nidentified by an increase in the total X-ray event rate. To remove this\ncontamination, times where the total event rate deviated by more than\n2$\\sigma$ from the mean were excluded. Typically this resulted in the\nremoval of a few percent of each observation.\n\nA standard reduction of the data was then carried out to produce an image\nand background for each group. The statistical significance of any emission\nwithin distances of 50~kpc and 200~kpc from the optical centre of each of\nthe groups was then calculated. This was used along with a smoothed image\nand a profile of the group to identify the presence of extended emission\nabove a 5$\\sigma$ detection threshold. It was also apparent that in a few\ncases diffuse X-ray emission was centred on a galaxy within the PSPC ring,\neven though the catalogued optical centre of the group was outside the\nring. These groups were also included, and are identified with an asterisk\nin Table~\\ref{tab:allgroups}. This resulted in a final sample of 24 X-ray\nbright galaxy groups, which are identified in Table~\\ref{tab:allgroups}. As\nthe table shows, those systems span a considerable range in catalogued\noptical richness ($N_{gal} = 3-45$). A more reliable measure of the total\nmass of each group is given by the X-ray temperatures derived below. Our\nsample should not be regarded as being statistically complete in any way,\nbut rather a reasonably representative sample of X-ray bright groups.\n\n\\input{table1}\n\n\\section{Spectral analysis}\n\\label{sec:spectral_analysis}\n\nEvents surviving the initial screening process were binned into a\n3-dimensional $x,y,Energy$ data cube. An estimate of the background was\ngenerated from an annulus at r=0.6-0.7\\deg with the PSPC support spokes\nremoved. The dataset was then background subtracted, and point sources\nidentified using a maximum likelihood source searching program. Point\nsources within the background annulus were removed to 1.2 times the 95\\%\nradius for 0.5~keV photons. The background was then recalculated and the\nimage once again searched for point sources. Other more extended sources,\nsuch as background galaxy clusters not associated with the group emission,\nwere also manually identified and excluded at this point. This process of\nidentifying and removing point sources to produce a better estimate of the\nbackground was repeated until the same number of point sources was\nidentified each time. Typically this took 4-5 iterations for each dataset.\n\nThe final background subtracted data were then corrected for dead time\neffects and vignetting, and then divided by the effective exposure time to\ngive a map of spectral flux. A circular region around each of the groups\nwas used to extract a spectrum. The size of this region was determined by\nexamination of a smoothed image and a surface brightness profile of the\ngroup. The region was selected to include all the emission that could be\nobserved in the smoothed image and profile; its size for each of the groups\nis shown in Table~\\ref{tab:allgroups}. Point sources, and other sources as\nidentified above, were removed from the spectral image, along with the\nsupport structure and the data outside the radius of interest. The spectrum\nfor each group was then obtained by collapsing the spectral image along the\n$x$ and $y$ axes.\n\nEach spectrum was fitted with a MEKAL hot plasma model (Mewe, Lemen \\& van\nden Oord 1986)\\nocite{mewe86a} with a hydrogen absorbing column frozen at a\nvalue determined from radio surveys \\cite{stark92a}. For two of the groups\nit was also necessary to fix the abundance to obtain a sensible fit. A\nvalue of 0.3 solar was used for this purpose. In this way we derived\ntemperature, abundance and bolometric flux for each group.\n\nFor hot spectra, the limited spectral band of {\\it ROSAT} makes temperature\ndetermination subject to systematic errors in the high energy response of\nthe PSPC, and there is evidence that {\\it ROSAT} temperatures are\nsystematically lower than those from hard X-ray instruments such as {\\it\nGinga} and {\\it ASCA}. A comparison of {\\it ROSAT} and {\\it ASCA}\ntemperatures by \\pcite{hwang99} showed that this temperature bias amounts\nto $\\sim 30$\\% in hot systems, but that there is no evidence of any\nsystematic offset below an {\\it ASCA} derived temperature of 2keV, where\nthe {\\it ROSAT} band covers the spectrum adequately. We therefore expect\nthe {\\it ROSAT}-determined temperatures for the systems in our sample\n(which have $T<1.7$~keV) to be free from serious bias.\n\nThe distribution of group temperatures in the present sample occupies a\nrather small range around 1~keV. For the 22 groups in which metallicities\nwere derived, the overall weighted mean metallicity is $0.19 \\pm 0.01$\nsolar, whilst the median is 0.42 solar. A trend is observed in clusters for\nhigher metallicity in lower temperature systems \\cite{arnaud94}. This would\nlead one to expect a typical metallicity of $\\approx$ 0.6 solar in systems\nwith $T \\approx 1$ keV. However there is evidence that there may be\nabundance gradients in cool clusters which result in an increased abundance\nat the centre (e.g. \\pcite{xu97,ikebe97,fukazawa98,finoguenov99}) and\ncould account for the observed trend. In any case, results obtained here\nfor the group metallicities must be viewed with caution, since {\\it ROSAT}\nis unable to resolve individual emission lines, and metallicities can be\nstrongly biased when a variable temperature plasma is fitted with an\nisothermal model (e.g. Buote \\& Fabian 1998\\nocite{buote98}, Finoguenov \\&\nPonman 1999).\n\nFor each of the groups in the sample we also derived simple projected\ntemperature profiles. In each case spectra in several annuli were extracted\nand fitted with a MEKAL model as described above. In each annulus the\nhydrogen column and abundance were frozen at the global values. The\nresulting temperature profiles of all groups are shown in\nFig.\\ref{fig:profiles}. Some of the profiles shown are not particularly\ninformative due to a combination of large errors on the temperatures and a\nsmall number of annuli. However it is clear that approximately half of the\ngroups show evidence of a temperature drop in the central regions,\nindicating the presence of a cooler component. Also, approximately half of\nthe profiles show evidence of a decline in temperature at large radii.\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=tempprof.ps,angle=0,width=16cm}\n\\caption{\\label{fig:profiles}Temperature profiles from an annular analysis\n of the 24 groups in this sample. A number of the groups show a\n temperature drop in the central regions and/or at large radii.}\n\\end{figure*}\n\n\n\\section{Surface Brightness profiles and Group Luminosities}\n\\label{sec:spatial_analysis}\n\nObservations of galaxy clusters across a wide range in virial temperature\nappear to indicate a flattening of the profiles in lower mass systems\n(\\pcite{arnaud99}; Ponman, Cannon \\& Navarro 1999\\nocite{ponman99}) -- a\nresult consistent with expectations if the intergalactic gas has been\nsubject to preheating by galaxy winds \\cite{metzler99,cavaliere99}.\nHowever, MZ98 found for their sample of groups that surface brightness\nprofiles did not differ significantly from those in clusters, once the\npresence of central components was properly allowed for. We set out to\nexamine the surface brightness profiles of our group sample in an attempt\nto resolve this issue.\n\nFollowing initial reduction, an image was extracted in the 0.5 - 2 keV\nband, and corrected for vignetting using an energy dependent exposure map\n(see \\scite{snowden94a} for description). Point sources identified in the\nspectral analysis were removed from the image along with any other\nunrelated extended sources. Only the data within the region from which each\ngroup spectrum was extracted, were used for the spatial analysis. It has\nbeen shown that the centroid of the X-ray emission often lies at the\nposition of the brightest group galaxy (MZ98), and as such any emission\ncentred on this galaxy may be associated with the group potential as a\nwhole. For this reason any source associated with the centre of the X-ray\nemission was not removed. Use of the energy dependent exposure map to\ncorrect for vignetting, results in a constant background level across the\nimage, therefore a flat background was also determined and subtracted from\nthe data.\n\nFor each group the 2-dimensional surface brightness profile was modelled\nwith a modified King function (or '$\\beta$-profile')of the form:\\\\\n\n\\noindent\n\\begin{math}\nS(r)=S_0(1+(r/r_{core})^{2})^{-3\\beta_{fit}+0.5}\n\\end{math}\n\\\\\n\nModels were convolved with the PSPC point spread function at an energy\ndetermined from the mean photon energy of the group spectrum, and fitted to\nthe data. The free parameters were the central surface brightness $S_0$,\nthe core radius $r_{core}$, the index $\\beta_{fit}$ and the $x$ and $y$\nposition of the centre of the emission. Both spherical and elliptical fits\nwere carried out on the data, with the major to minor axis ratio and the\nposition angle being extra free parameters in the elliptical fits.\n\nThe use of 2-dimensional datasets to fit the surface brightness\ndistribution results in a low number of counts in many of the data bins.\nUnder these conditions chi-squared ($\\chi^2$) fitting performs poorly, so\nmaximum likelihood fitting, using the Cash statistic, was used instead. The\nCash statistic \\cite{cash79} is defined as $-2{\\rm ln}L$ where $L$ is the\nlikelihood function (in this case derived from the Poisson distribution).\nThus the most likely model has a minimum Cash statistic. Differences in the\nCash statistic are $\\chi^2$ distributed, so confidence intervals may be\ncalculated in the same way as for a conventional $\\chi^2$ fit.\n\nUnfortunately the Cash statistic by itself gives no indication of the\nquality of a fit; hence it was necessary to obtain some other estimate of\nthe fit quality. A Monte Carlo approach was used, in which the best fit\nmodel was used to simulate 1000 images of the group. Poisson noise was\nadded to each of these images, and they were then compared to the original\nmodel, and the Cash statistic for each image determined. Thus, for a\nparticular model we were able to obtain a distribution showing the range of\nCash values expected for datasets generated from this model. A Gaussian was\nthen fitted to this distribution to obtain the width and central value. By\ncomparing the Cash statistic for the real dataset with this distribution,\nit was possible to determine the probability that the model could have\nproduced the data. This probability is recorded in\nTable~\\ref{tab:2kingfit}, as the number of standard deviations that the\nreal value lies from the centre point of the distribution. If the value of\nthe real Cash statistic lay more than 2$\\sigma$ from the peak of the\ndistribution then the fit was regarded as `poor'.\n\nAs can be seen in Table~\\ref{tab:2kingfit}, the single-component fits\nprovide an adequate description of the data in a few cases. However for\nmost groups the single-component fits are poor. It has been suggested that\nthere are typically two components in the surface brightness profiles of\ngalaxy groups (MZ98), a central component associated with a central galaxy,\ncooling flow or AGN, and a more extended component associated with the\ngroup potential. To check this, models comprising of two superposed\n$\\beta$-profiles were also fitted to those datasets with poor\nsingle-component fits and greater than $\\approx900$ total counts. Below\nthis number of source counts, statistics were found to be too poor to\nconstrain the more complicated two-component models. To limit the number of\nfree parameters, the central component was constrained to be spherical\nwhile the outer component was allowed to vary in ellipticity.\n\nIn three of the groups (NGC4065, NGC4073 and NGC7619) the emission was\nbimodal, so that the two-component models fitted with the centres of the\ntwo components significantly offset from one another (e.g. see\nFig.\\ref{fig:ovly1}). As a result, it is not sensible to define one\ncomponent as extended, and the other as the central component. In these\ncases both of the components were constrained to be spherical.\n\n\\begin{figure}\n\\hspace{0cm}\n\\psfig{file=ovly1.ps,angle=-90,width=8cm}\n\\caption{\\label{fig:ovly1}Contours of adaptively smoothed X-ray emission\n from the group NGC4065, overlaid on an optical image. It is clear that\n there are two distinct centres of emission in this system.}\n\\end{figure}\n\n\\input{table2}\n\nThe fitted parameters of the two-component King profiles are also shown in\nTable~\\ref{tab:2kingfit}, along with an estimate of the goodness of fit.\nThe errors quoted are 1$\\sigma$ for one interesting parameter. Note that\nthese errors are only reliable for reasonable fits (see final column in\nTable~\\ref{tab:2kingfit}). The best fitting surface brightness profiles\nwere also used to correct the derived group fluxes for the diffuse emission\nlost when point sources are removed. A model image for the group was\nproduced, and from the ratio of the number of counts in the model image to\nthat in the same image with `holes' punched at the positions of detected\nsources, a correction factor for the fluxes was obtained. The luminosity of\neach group was then calculated using distances corrected for infall to\nVirgo and the Great Attractor \\cite{fixsen96,burstein90}, which are listed\nin Table~\\ref{tab:groupspec}.\n\nIn the case of groups with a detected central component, we checked for the\npossibility that this might arise from a nuclear source in the central\ngalaxy. Fits with Gaussian models for the central component show that it is\nextended at $>99$\\% confidence in all cases except NGC 5353, where\nstatistics are too poor to constrain the extent of the central source. For\neach of these systems a search for radio sources associated with the\nbrightest group galaxies was carried out using NED and the \\pcite{burns87}\nradio survey of groups, which has some overlap with this sample. This\nsearch identified radio sources associated with six of the brightest group\ngalaxies: NGC 383, NGC 741, NGC 4261, NGC 4636, NGC 5353 and NGC 6338.\n\\pcite{hwang99} have studied three of these using ASCA spectra. Two showed\nno significant improvement in fit statistic when a powerlaw component was\nadded to the spectral model. For the third, NGC 6338, \\pcite{hwang99} find\nevidence that there may be contamination by an AGN, although in our data\nthe spatial extent of the central component in this, and almost all the\nother systems rules out a large AGN component. The only system that may be\ncontaminated (as indicated by the spatial extent of the central component)\nis NGC 5353. For this system we fitted the spectral data for this group\nwith an added power-law component of index 1.7. We then calculated the\nrelative contributions from the power-law and hot plasma components in the\n{\\it ROSAT} band. This showed that even for the 90\\% upper limit of the\npower-law component the emission was dominated by the hot plasma component.\nOur conclusion from these spatial and spectral studies is that any AGN\ncontribution to the central components in these systems appears to be\nminor.\n\nWe were also interested in the way in which the luminosity of groups varies\nwith radius. The model images were therefore used to calculate luminosities\nwithin radii of 200~kpc, 500~kpc, 1/3 of the virial radius and the virial\nradius ($R_V$). Note that $R_V$ lies well beyond the radius to which\nsignificant X-ray emission can actually be detected in our data, in almost\nall cases. It can be seen in Table~\\ref{tab:2kingfit} that the\ntwo-component models provide good descriptions of the data in the majority\nof cases. However even in the cases where the two-component fit is not\nacceptable it is significantly better than the single-component model, thus\nwhere possible, the two-component models are used for the purposes of\ncalculating the effects of extrapolating to different radii. The virial\nradii of the groups were determined using the relation obtained from\nsimulations by Navarro, Frenk \\& White (1995)\\nocite{navarro95a}. This is\ngiven (for H$_0$~=~50~km~s$^{-1}$ Mpc$^{-1}$) by,\\\\\n\n\\noindent\n\\begin{math}\nR_V = 2.57(\\frac{T}{5.1KeV})^{\\frac{1}{2}} \\textrm{ Mpc.}\n\\end{math}\n\\\\\n\nLuminosities and temperatures derived in this study are generally similar\nto those from earlier studies\n\\cite{doe95,ponman96a,mulchaey96,burns96,mulchaey98b}. The small\ndifferences in the luminosities of groups common to both this sample and\nthat of \\scite{burns96} are most likely primarily due to the fact that\n\\scite{burns96} use a spectral model with a temperature of 1 keV to derive\nall luminosities, whereas the luminosities derived here use fitted spectral\nmodels, and thus should be more reliable.\n\n\\input{table3}\n\\section{Results}\n\\label{sec:Distributionsandcorrelations}\n\nThroughout the following sections, the luminosities quoted are extracted\nfrom within the radius given in Table~\\ref{tab:groupspec}. Corrections for\nremoved point sources have been made using the best model derived for each\ngroup; either two-component or (elliptical) single-component.\n\n\\subsection{X-ray profiles}\n\n\\begin{figure}\n\\hspace{0cm}\n\\psfig{file=sbprof.ps,angle=0,width=8.5cm}\n\\caption{\\label{fig:sbprofs}1D surface brightness profiles for the groups NGC\n 2563 and NGC 3091. The overall best fit two component models are shown as\n the solid lines, with the dotted line representing the central component\n and the dashed line the extended. Data points are shown as crosses. For\n comparison the single component elliptical models are marked as the\n dot-dashed lines. This is steeper than the extended component in NGC 3091\n but slightly flatter than it in NGC 2563. $r_{core}$ marks the core\n radius of the extended component and $r_x$ the crossover radius, as\n defined in the text.}\n\\end{figure}\n\nThe surface brightness profiles for our 24 systems break down into 12\ntwo-component, 9 single-component and 3 bimodal cases. However, note that\nthe nine single-component systems include the eight groups with the lowest\nsource counts in the sample, so it is likely that the majority of these\nsingle-component fits appear to be adequate only because of poor\nstatistics. Two examples of radial profiles are shown in\nFig.\\ref{fig:sbprofs}. These 1D profiles only give an approximate\nrepresentation of our 2D models, but the centres of the two components\nalmost coincide in the two cases shown, and profiles for both data and\nmodel components have been derived about the centre of the more compact\ncomponent. A distinct `shoulder' in the observed profile indicates the need\nfor two components in the model, as noted by MZ98.\n\nThe median value of $\\beta_{fit}$ obtained for the extended group component\nin our sample (from two-component fits where available, or else\nsingle-component fits), is $\\beta_{fit}=0.46$, and the weighted mean is\n$0.42\\pm0.06$ (where the error is derived from the scatter of the values\nabout the mean). This value of $\\beta_{fit}$ can be compared with the\ntypical value for rich clusters, $\\beta_{fit}\\approx 2/3$\n(\\pcite{arnaud99}; Mohr, Mathiesen \\& Evrard 1999)\\nocite{mohr99}),\nindicating that the surface brightness profiles of the groups in this\nsample are generally significantly flatter than those of clusters.\n\nIn the case of a number of the groups, the core radius derived for the\nextended group component is smaller than the resolution of the {\\it ROSAT}\nPSPC. Such a small core radius means essentially that the group emission\nhas been fitted with a power law model. In such cases, the derived core\nradii are unreliable, particularly if an additional central component is\npresent. To investigate the effect of a small core radius on the other\nderived parameters, in particular the slope, $\\beta_{fit}$, we varied the\ncore radii in a number of groups which fitted with two components and a\nsmall core radius for the extended component. It was found that varying the\ncore radii between 0.1 and 1.0 arcmin typically changes the value of\n$\\beta_{fit}$ by less than 5\\%. Values of the index and core radius of the\ncentral component also varied only within 1$\\sigma$ of their best fit\nvalues. Hence uncertainties in core radius in such cases do not seriously\ncompromise our results for other parameters.\n\nWe define the `cross-over radius', $r_x$, to be the radius within which the\ncentral component dominates the surface brightness. We derived values for\n$r_x$ for the twelve groups for which two-component fits were available,\nbut the emission was not bimodal. The mean cross-over radius for these\nsystems was $r_x=35 \\pm 6$~kpc. Groups with two-component profiles which\nhave $r_{core}<r_x$ are deemed to have poorly determined core radii. In\norder to gain some insight into the typical core radii of galaxy groups,\nthe median value was determined, using $r_x$ as an upper limit for those\ngroups with $r_{core}<r_x$. Under these assumptions the median core radius\nof the twelve groups was found to be 60 kpc.\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=betat1.ps,angle=-90,height=9cm,width=13cm}\n\\caption{\\label{fig:beta_temp_1}The relationship between\n $\\beta_{fit}$ and temperature for the whole group sample compared to\n cluster data from Arnaud \\& Evrard (1999). Values from groups with\n single-component fits are shown as plain crosses, those from\n two-component fits as crosses with central squares. The cluster data are\n marked as crosses with central circles.}\n\\end{figure*}\n\\nocite{arnaud99}\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=betat2.ps,angle=-90,height=9cm,width=13cm}\n\\caption{\\label{fig:beta_temp_2}The relation between $\\beta_{fit}$\n and temperature for a subsample of the groups with the best two-component\n models, and the cluster data. Symbols are the same as in the previous\n figure. The triangle marks the new value of the one discrepant group\n value when its central component was refitted with a Gaussian.}\n\\end{figure*}\n\nThe relationship between the integrated temperature of the intragroup gas\nand the best obtained $\\beta_{fit}$ value for each of the groups is plotted\nin Fig.\\ref{fig:beta_temp_1}. Also shown are cluster data from\n\\scite{arnaud99} (data points with circles). The group data are split into\ntwo categories: single-component (plain crosses) and the extended component\nfrom the two-component fits (points with square in centre). As can be seen,\nthe general trend in clusters is for $\\beta_{fit}$ to drop with decreasing\ntemperature. In the region of the graph containing the group data it is\nclear that the majority of the groups have low $\\beta_{fit}$ values, but\nthere is also a large amount of scatter, in particular amongst the groups\nwith single-component fits.\n\nFig.\\ref{fig:beta_temp_1} also includes the three bimodal groups.\nExcluding these three groups, the single-component fits and the\ntwo-component fits whose quality of fit (from the Monte Carlo simulations)\nis poor, greatly reduces the scatter in the group results. The outcome is a\nmuch clearer trend in $\\beta_{fit}$ with temperature, as can be seen in\nFig.\\ref{fig:beta_temp_2}. The combined groups and cluster data are\nsignificantly correlated with a Kendall's rank correlation coefficient (a\ndistribution free test for correlation) of K=4.05 (P=0.00006 of chance\noccurrence). The one group point that conflicts with the general trend\n(NGC533) is, in fact, the only group in the sample which has a flatter\n$\\beta_{fit}$ value for its central component than for the extended\ncomponent. This means that the central component has a significant effect\nbeyond the central region. Hence the {\\it shape} of this component could\naffect the parameters obtained for the extended component. To test this, we\nrefitted the surface brightness profile with a Gaussian model for the\ncentral component, in place of the previous King model. The $\\beta_{fit}$\nvalue for the extended component changed markedly, and the new value is\ndenoted by the triangle in Fig.\\ref{fig:beta_temp_2}. As can be seen, this\npoint is now much closer to the trend described by the other groups.\n\n\n\\subsection{Luminosity, temperature and velocity dispersion}\n\n\\subsubsection{X-ray luminosities}\n\nBolometric luminosities for each group, derived from within the extraction\nradius as described in section~3, are given in Table~\\ref{tab:groupspec},\nalong with best fit spectral properties. The tabulated luminosities are\nthose of the intragroup gas only. Errors on the luminosities are derived\nfrom Poisson errors on the data combined with errors arising from\nuncertainties in the fitted surface brightness profiles, which are used to\ncorrect for flux lost where contaminating sources have been excluded.\n\nThe flat surface brightness profiles of groups imply that a significant\nfraction of their luminosity derives from large radii. To quantify this, we\nused our best fit surface brightness models to derive bolometric\nluminosities extrapolated to $R_V$, and the fraction of this luminosity\nrepresented by the luminosity derived from within the extraction radius is\nshown for each group in Table~\\ref{tab:groupspec}. This may be as low as\n$\\sim$30\\% in some cases.\n\nThe effect of scaling the luminosities to different radii is shown in more\ndetail in Fig.\\ref{fig:fraction}. This analysis is based on the eight\nsystems with well-fitting two-component profiles. These have been binned\ninto three temperature bins to reduce fluctuations from system to system\nand show trends more clearly. The luminosity as a fraction of that within\n$R_V$ is shown at three radii for the systems within each temperature bin.\nPoints marked by triangles (dash-dot-dot line) show these ratios at a\nradius of 200~kpc, squares (dashed line) at the radius out to which\nemission could be detected, and crossed circles (solid line) at one third\nof the virial radius of the group. As can be seen the luminosity is\nsignificantly underestimated in all cases. In particular, for groups\nmeasured to a fixed radius of 200~kpc, and for the coolest groups at the\nextraction radius, one may underestimate $L_X$ by factor of more than two.\n\n\\begin{figure}\n\\hspace{0cm}\n\\psfig{file=fraction.ps,angle=-90,height=8cm,width=8cm}\n\\caption{\\label{fig:fraction}Fraction of the total\n luminosity observed within three different radii, as deduced from best\n fitting surface brightness models, for systems of different temperature.\n Squares show the luminosity within the radius to which emission could be\n observed, circles the luminosity within $R_V/3$, and triangles the\n luminosity within a fixed radius of 200~kpc.}\n\\end{figure}\n\n\\subsubsection{Correlations}\n\nThe well-known relation between X-ray luminosity and temperature is\napparent in our sample. The two parameters are significantly correlated\n(K=4.81, P$<$0.00001) and the relation between them is shown in\nFig.\\ref{fig:L:T}. Neither the errors on $L_X$ or $T$ are negligible, and a\ndoubly weighted technique made available through the \\textsc{odrpack}\npackage was used in this and following plots to determine the best fit\nline,\\\\\n\n\\noindent\n\\begin{math}\n\\log L_X = (42.98 \\pm 0.08) + (4.9 \\pm 0.8) \\log T\n\\end{math}\n.\n\\\\\n\nThis relationship is marked with its 1$\\sigma$ error bounds in\nFig.\\ref{fig:L:T}. A best fit to the cluster $L:T$ relation has been\nderived by White, Jones \\& Forman (1997)\\nocite{white97}. They obtain $\\log\nL_X = 42.67 + 2.98 \\log T$, which is marked as the heavy dashed line in\nFig.\\ref{fig:L:T}. This line is much flatter than the best trend fit for\nthe loose groups.\n\nThe luminosities used in this plot are those within the radius of\nextraction. Fig.\\ref{fig:fraction} shows that at this radius the\nluminosities will be underestimated, with the effect being greatest in the\nsmaller mass systems. This means that if luminosities extrapolated to the\nvirial radius were used, the $L:T$ slope should be slightly flatter. This\nis indeed found to be the case, with a best fitting relation of $\\log L_X =\n(43.17 \\pm 0.07) + (4.2 \\pm 0.7) \\log T$, although the difference in slope\nfrom the previous relation is not formally significant.\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=lxvstemp.ps,angle=-90,height=9cm,width=13cm}\n\\caption{\\label{fig:L:T}The relation between X-ray\n luminosity and temperature for our group sample. The solid line shows the\n best fit relation to our data, with one sigma error bounds marked by\n dotted lines. The extrapolation of the best fitting cluster relation\n (White et al. 1997) is shown as the dashed line.}\n\\end{figure*}\n\\nocite{white97}\n\nIf galaxy systems scaled with mass in a self-similar way, then one would\nexpect $L_X \\propto T^2$. The cluster relation is steeper than this, and\nour result for groups is steeper still. However, the relationships derived\nby \\scite{white97} do not take into account the effects of cluster cooling\nflows, and recent work suggests that the $L:T$ relation may be flattened\ntowards $L_X \\propto T^2$ when the effects of cooling flows are allowed for\n\\cite{allen98,markevitch98}. Such a flattening of the relation for\nclusters would raise its extrapolation at low temperatures, accentuating\nthe disagreement with the low luminosities observed in groups.\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=lxvssig.ps,angle=-90,height=9cm,width=13cm}\n\\caption{\\label{fig:L:v}The relationship between X-ray luminosity and group\n velocity dispersion, $\\sigma$. The best fit to the data is shown as the\n solid line with the one sigma error bounds marked by the dotted lines.\n The extrapolation of the cluster relation (White et al. 1997) is shown as the\n dashed line.}\n\\end{figure*}\n\\nocite{white97}\n\nIn Fig.\\ref{fig:L:v}, velocity dispersion is plotted against the X-ray\nluminosity for our sample. A strong correlation can be seen between these\ntwo parameters (K=3.97, P=0.00006). A regression line fitted to the data\ngives \\\\\n\n\\noindent\n\\begin{math}\n\\log L_X = (31.3 \\pm 2.8) + (4.5 \\pm 1.1) \\log \\sigma\n\\end{math}\n,\n\\\\\n\n\\noindent which is marked in Fig.\\ref{fig:L:v} with its 1$\\sigma$ error\nbounds. This relationship is somewhat flatter than the cluster trend given\nby \\scite{white97} of $\\log L_X = 25.84 + 6.38 \\log \\sigma$ (bold dashed\nline in Fig.\\ref{fig:L:v}). Dell'Antonio, Geller \\& Fabricant\n(1994)\\nocite{dellantonio94} found evidence that the $L:\\sigma$ relation\nmay flatten below $\\sigma \\approx$ 300 km s$^{-1}$. However they did not\nremove the galaxy contribution from the X-ray emission, and suggest that\ntheir flattening may arise from the galaxy contribution becoming\nsignificant at low luminosities. This flattening has also been confirmed\nby \\scite{mahdavi97}. In the work presented here, contaminating sources\nwere removed, but a flatter relation than clusters is still seen. Our\nresult is actually consistent with that expected from self similar scaling\nof clusters, i.e. $L_X \\propto \\sigma^4$. However, errors are large and\nthere is a good deal of scatter, so that the disagreement with the cluster\nresult is not highly significant, and requires further confirmation.\n\n\\begin{figure*}\n\\hspace{0cm}\n\\psfig{file=sigvtemp.ps,angle=-90,height=9cm,width=13cm}\n\\caption{\\label{fig:v:T}The relationship between group velocity dispersion,\n $\\sigma$ and temperature. The best fit to the data is shown as the solid\n line with the one sigma error bounds marked by the dotted lines. The\n extrapolation of the cluster relation (White et al. 1997) is shown as the\n dashed line. The dot-dashed line shows the locus along which\n $\\beta_{spec}=1$.}\n\\end{figure*}\n\\nocite{white97}\n\nA strong correlation between $\\sigma$ and $T$ is shown in Fig.\\ref{fig:v:T}\n(K=3.82, P=0.0001). A regression line fitted to the data gives \\\\\n\n\\noindent\n\\begin{math}\n\\log \\sigma = (2.57 \\pm 0.03) + (1.1 \\pm 0.2) \\log T\n\\end{math}\n,\\\\\n\n\\noindent which is shown in Fig.\\ref{fig:v:T} with its 1$\\sigma$ error\nbounds. Also shown in Fig.\\ref{fig:v:T} is the line $\\beta_{spec}=1$, where\n$\\beta_{spec}$ is defined as the ratio of the specific energy in the\ngalaxies to that in the gas. As can be seen, this $\\beta_{spec}=1$ line is\nflatter than the relation for the loose group sample. However it is\ninteresting to note that the higher temperature groups appear to be\nconsistent with $\\beta_{spec}=1$, while the lower temperature groups appear\nto fall well below this relation. The extension of the best fit relation\nfor galaxy clusters as determined by \\scite{white97} is shown as the dashed\nline in Fig.\\ref{fig:v:T}. This line, given by $\\log \\sigma = 2.53 + 0.6\n\\log T$, is also significantly flatter than the relation determined for the\nloose group sample.\n\nThe unweighted mean value of $\\beta_{spec}$ for our sample is $0.86 \\pm\n0.13$. However, with one exception, it is clear that $\\beta_{spec}$ is\ndecreasing in the lower temperature (i.e. lower mass) systems. These\nresults are in good agreement with those of Bird, Mushotzky \\& Metzler\n(1995)\\nocite{bird95}, who predict a trend towards lower $\\beta_{spec}$ in\nsmaller systems.\n\nThe one low temperature point (NGC 3607) that has a high velocity\ndispersion is also deviant in the $L:\\sigma$ plot. Examination of the group\nmembers reveals that, of the three catalogued members, one is a large\nangular distance from the remaining two, and has a large difference in\nrecession velocity. Also there is a further bright galaxy at the redshift\nof the group, which is very close to two of the catalogued members. The\nrecession velocity of this galaxy is between those of the two catalogued\ngalaxies, and is almost certainly a group member, although it was not\nclassified as such by \\scite{nolthenius93}. These two effects combined\nindicate that the true velocity dispersion of the group is probably\nconsiderably lower than our estimate, which is taken from\n\\scite{nolthenius93}.\n\n\\section{Comparison with Mulchaey and Zabludoff}\n\\label{Comparison}\nAs discussed in the introduction, we have included the X-ray bright systems\nstudied by MZ98, in order to allow a direct comparison of our results with\ntheirs. This is important, since our conclusions about $\\beta_{fit}$,\n$\\beta_{spec}$ and the $L:T$ relation all differ from MZ98. In\nTable~\\ref{tab:MZgroups} we show the best fit parameters as determined by\nMZ98 for the groups that both they and we fit with two-component models\n(Note that they also fit two component models to NGC~4325 and NGC~5129,\nwhilst we find that single component elliptical models provide an adequate\nrepresentation of our data for these systems). Whilst we confirm their\nconclusion that two-component fits are required to adequately represent\nmost systems, it can be seen there are some significant differences between\nthe two sets of results.\n\n\\input{table4}\n\nThe fitting techniques used by MZ98 differ from those used in this work.\nSince they work with radial profiles, their fits are necessarily 1D models,\nwith both components centred at the same point. Their method firstly\ninvolved excluding the central region and fitting for the outer component\nonly. The central component was then fitted with the extended component\nfixed at the values derived from the previous fit. Thus at no stage were\nthe two components allowed to fit simultaneously. The 2D models fitted in\nthis work allow the positions of the two components to vary and also permit\nelliptical models to be used. Parameters for the two components were also\noptimised simultaneously. The lower number of counts in each bin forced us\nto use maximum likelihood fitting rather than $\\chi^2$ fitting, but the\nquality of the fits were checked using the Monte Carlo approach as\ndescribed above.\n\nTo demonstrate the dangers of a 1D approach to fitting the surface\nbrightness profiles we simulated an image of a group, in which the outer\ncomponent was elliptical (axis ratio=1.5), and offset a short distance (3\narcmin) from the central component. These values were chosen to construct a\nfairly elongated and offset system to make any biases more obvious. A 2D\nfit successfully recovered the slope of the outer component\n($\\beta_{fit}$=0.4). We then attempted to fit the data using a 1D approach.\nWe initially extracted a profile centered on the brightest point in the\ngroup (the central component). This gave a profile with a shoulder and a\nclear central excess. This profile was fitted using \\textsc{qdp} with a\n$\\beta$-profile plus a constant background. Initially we fitted to the full\nprofile, giving a value of $\\beta_{fit}\\approx0.7$. We then progressively\nexcluded the central regions and refitted the data. The fitted value of\n$\\beta_{fit}$ rose to a peak of $\\approx0.9$ before dropping as a larger\ncentral region was excluded. Thus it is possible, with the 1D approach used\nby MZ98, to significantly overestimate the true value of $\\beta_{fit}$.\n\nTo decide whether the models of MZ98 referred to in\nTable~\\ref{tab:MZgroups} provide an acceptable fit to our data, we carried\nout a series of two-component fits with the index and core radius frozen at\nthe MZ98 values. The components were also constrained to be circular and\ncentred in the same place. The Cash values for these models were then\ncompared to the best fitting values derived earlier. The differences\nbetween the Cash statistic values are shown in the final column of\nTable~\\ref{tab:MZgroups}. As can be seen, the models using the MZ98\nparameters generally fall well outside the 99\\% confidence regions of our\nbest fitting models (which corresponds to $\\Delta$C=-20.1). Hence it\nappears that our more sophisticated models do represent the data\nsignificantly better.\n\nThe most important difference in the surface brightness results is apparent\nin the $\\beta_{fit}$ value of the extended component. MZ98 obtain values\nconsistent with $\\beta_{fit} \\approx 1$ whereas the values obtained here\nmostly lie in the region 0.4-0.5, with a median value for the extended\ncomponent of $\\beta_{fit}=0.46$.\n\nMZ98 obtain lower values of $\\beta_{fit}$ when fitting single-component\nmodels, but find that the extended components fit with systematically\nhigher $\\beta_{fit}$ when a second component is included (this sort of\neffect was reproduced in our simulations mentioned earlier). The same\neffect is noted for a sample of clusters by \\scite{mohr99}, who give a\nuseful discussion of the effect. Since core radius and $\\beta_{fit}$ are\nstrongly positively correlated when fitting (i.e. models with larger cores\nand higher $\\beta_{fit}$ can give rather similar profiles to those with\nlower values of both parameters), the presence of a central excess will\nforce $r_{core}$ towards lower values and hence decrease $\\beta_{fit}$,\nunless an additional component is included in the model to account for the\ncentral excess.\n\nInterestingly, we do not find this to be the case in general, for our\nanalysis. For the subset of our groups with two-component fits, the median\nvalue of $\\beta_{fit}$ for the single-component fits is 0.47 (i.e. just\nsteeper than for the two-component fits). Individually, some groups (e.g.\nNGC533) have a steeper profile when the two-component model is used, and\nsome (e.g. NGC4761) have a flatter profile. The distinction appears to be\nthat the argument of \\scite{mohr99} applies to systems for which the {\\it\nextended} component dominates over most of the range of the fitted data.\nIn this case, the presence of a central component acts to slightly modify\nthe extended component fit, by reducing both $r_{core}$ and $\\beta_{fit}$.\nNGC2563 in Fig.\\ref{fig:sbprofs} is such an example. However, for systems\nwhere the {\\it central} component is more dominant, such as NGC3091 in\nFig.\\ref{fig:sbprofs}, the single component fit is a compromise between a\nsteeper central component, and a flatter extended one, so that the result\nis to {\\it increase} $\\beta_{fit}$, relative to the extended component.\n\nFig.\\ref{fig:betacomp} shows the relationship between the $\\beta_{fit}$\nvalues from one and two-component models for the eight systems from our\nsample with well-fitting two-component profiles. The solid line splits the\ngraph into two areas. In the upper left area the two-component fit has a\nsteeper profile than the single-component fit, in the lower right area the\nreverse is true. As can be seen, the single-component fits lead to\noverestimates and underestimates of $\\beta_{fit}$, relative to the\ntwo-component results, in equal numbers of cases. The two dashed lines\ndelineate the region in which the two-component fit differs from the\nsingle-component fit by less than $\\pm50\\%$. As can be seen the\ntwo-component models generally have $\\beta_{fit}$ values for the extended\ncomponent within 50\\% of the single-component fit. The small nominal errors\non the single-component $\\beta_{fit}$ values in the figure are misleading,\nsince they result from calculating errors on a poor fit.\n\n\\begin{figure}\n\\hspace{0cm}\n\\psfig{file=betacomp.ps,angle=0,height=8cm,width=8cm}\n\\caption{\\label{fig:betacomp}Relationship between the single-component\n $\\beta_{fit}$ value and the extended component $\\beta_{fit}$ value from\n the two-component fit. The groups shown are the eight systems with the\n best fitting two-component models.}\n\\end{figure}\n\nThe slope of the $L:T$ relation for our group sample is significantly\nsteeper than the cluster relation. This is in contrast to the results of\nMZ98, who find that the $L:T$ relation for their sample of nine groups is\nconsistent with the cluster relation. However they had too few points to\nfit to the group sample alone, so they added a large cluster sample in\norder to determine the best fit line. If the $L:T$ relation is turning over\nat a temperature of $\\approx$ 1 keV, as is suggested by Fig.\\ref{fig:L:T},\nthen it is to be expected that the line fitted through a combined group and\ncluster sample would not differ greatly from the cluster relation.\n\nValues of $\\beta_{spec}$ derived by MZ98 for their groups lead them to\nconclude that $\\beta_{spec} \\sim 1$, whereas we see evidence for a drop in\n$\\beta_{spec}$ for low temperature systems (Fig.~\\ref{fig:v:T}). This\ndifference appears to result from two factors. Firstly, four of the nine\ncommon groups are found in the region ($T$\\gtsim 1~keV) where our groups\nare generally consistent with $\\beta_{spec} \\sim 1$. So this only leaves\nfive systems in which MZ98 could have noted a drop in $\\beta_{spec}$.\nSecondly, our values of $\\beta_{spec}$ appear to be typically about 10\\%\nlower than those of MZ98. For the nine groups in common, we derive a mean\nvalue of $<$$\\beta_{spec}$$>$~=~0.78 compared to\n$<$$\\beta_{spec}$$>$~=~0.87 for MZ98. Since we use the same velocity\ndispersions, the difference results from the derived gas temperatures. This\ndifference may arise from the fact that for most groups MZ98 extract their\nspectral data from within a larger radius, and given the tendency towards a\ndecline in temperature with radius apparent in many systems in\nFig.\\ref{fig:profiles}, this should result in temperatures somewhat lower\nthan ours. This interpretation is supported by the fact that our\ntemperatures are in good agreement with those derived in the study of\n\\scite{mulchaey96}, in which similar extraction radii were used for systems\ncommon to the two studies.\n\n\n\\section{Discussion}\n\\label{Discussion}\nThis survey of X-ray bright, loose galaxy groups represents the largest\ndetailed study of their properties to date. This allows a comparison with\nthe properties of richer clusters, and we have been able to show that three\neffects are apparent in low temperature systems: steepening of the $L:T$\nrelation, steepening of the $\\sigma$:T relation (i.e. lower $\\beta_{spec}$\nvalues in groups), and flatter surface brightness profiles in groups. We\nfind that the contrary results of MZ98 appear to be due to the small size\nof their sample, coupled with their somewhat less sophisticated analysis of\nthe surface brightness distributions.\n\nThe general nature of these three departures from cluster trends are in\ngood agreement with the expectations from preheating models, in which\nenergetic winds from forming galaxies raise the entropy of intergalactic\ngas and inhibit its collapse into the smaller potential wells of galaxy\ngroups (\\pcite{metzler94}; Cavaliere, Menci \\& Tozzi 1997; Cavaliere, Menci\n\\& Tozzi 1999; \\nocite{cavaliere97,cavaliere99}\\pcite{ponman99,metzler99};\nBalogh, Babul \\& Patton 1999\\nocite{balogh99}). This increase in gas\nentropy primarily acts to reduce the gas density in the central regions of\nlow mass systems, flattening their surface brightness profiles and reducing\ntheir X-ray luminosity. The enhanced entropy also leads to some increase in\ngas temperature, resulting in a value of $\\beta_{spec}$ less than unity.\n\nThe slope of the $L:T$ relation, $L\\propto T^{4.9\\pm0.8}$, is flatter than\nthe index of $8.2\\pm2.7$ derived for Hickson groups by \\scite{ponman96a},\nhowever the error from the HCG sample was very large, so the difference in\nslopes is not significant (1.2$\\sigma$). The present, much more accurate\ndetermination of the $L:T$ slope, is in excellent agreement with the\nasymptotic relation $L\\propto T^5$ derived in the low temperature limit by\nthe semi-analytical models of \\scite{cavaliere97} and \\scite{balogh99}.\nThese two treatments make somewhat different simplifying assumptions about\nthe physics of the heating of the intracluster gas, but both obtain similar\nslopes in the limit of isentropic gas (i.e. where shock heating becomes\nnegligible).\n\nThis result has to be quite robust to detailed model assumptions, since an\napproximate result $L \\propto T^{4.5} \\Lambda(T)$, where $\\Lambda(T)$ is\nthe cooling function, is easily derived by combining the scaling relations\n$T\\propto M/R$ (from hydrostatic equilibrium), $M\\propto R^3$ (for systems\nvirialising at a given epoch), $\\rho_{gas}\\propto T^{3/2}$ (for constant\nentropy gas) and $L\\propto \\rho_{gas}^2 \\Lambda(T) R^3$. For\nbremsstrahlung, $\\Lambda(T)\\propto T^{1/2}$, so that one obtains $L \\propto\nT^5$. In practice, at $T\\sim 1$~keV the cooling function is flatter than\n$T^{1/2}$, due to the increasing contribution of metal lines at low\ntemperatures, and so the expected relation flattens somewhat towards\n$L\\propto T^{4.5}$. The good agreement between this isentropic result and\nour observations lends strong support to the result of \\scite{ponman99},\nthat the gas entropy tends towards a constant `floor' value, set by\npreheating, in low temperature systems.\n\nWithin the above picture, the significant scatter seen in our $L:T$\nrelation is expected to be primarily due to different star formation and\nmerging histories of the groups. It has also been shown \\cite{fabian94}\nthat scatter in the cluster $L:T$ relation is correlated with the strength\nof the emission associated with a cooling flow. Lower temperature gas (at a\ngiven density) has a shorter cooling time, and it is apparent from\nFig.\\ref{fig:profiles} that many of these groups do contain cooling flows.\nHence some $L:T$ scatter can also be attributed to the presence of cooling\nflows in the sample.\n\nAnother consequence of the effect of galaxy winds is that if winds have\ninjected extra energy into the intragroup medium then a greater proportion\nof the energy of the system should be found in this hot gas. However, this\nextra energy could manifest itself in the form of extra thermal energy, or\nhigher gravitational potential energy of the gas. The models of\n\\scite{cavaliere99} and \\scite{balogh99}, and the N-body+hydrodynamical\nsimulations of \\scite{metzler99}, all indicate that for systems with\n$T>1$~keV, the energy is taken up in flattening the gas distribution, with\nvery little effect on gas temperature. Unfortunately, the simulations of\n\\scite{metzler99} do not extend to lower temperatures, but the models of\n\\scite{cavaliere99} and \\scite{balogh99} both predict that at\nT\\ltsim$0.8$~keV, systems depart rather suddenly from the cluster $M:T$\nrelation, with $T$ flattening out at a minimum value. This must\nnecessarily happen, since (in the absence of significant cooling) the gas\ntemperature cannot drop below the level to which it was preheated, since\nits density will have increased as it settles into the group potential.\n\nThe observed $\\sigma$:T relation for our groups (Fig.\\ref{fig:v:T}), is\nnoisy, but there is a rather clear pattern whereby $\\beta_{spec}\\approx 1$\nfor $T$\\gtsim 1~keV, but drops to lower values for cooler systems. For\nexample, the median $\\beta_{spec}$ for our nine groups with $T<0.8$~keV is\n0.44. This behaviour is just what the models predict for preheating\ntemperatures $\\sim 0.5$~keV.\n\nThe $L:\\sigma$ relation for our group sample is slightly flatter than the\ncluster relation as determined by \\scite{white97}, although the errors on\nthe slope of the loose group sample are large and as a result the\ndifference is not statistically significant. This might suggest that the\ngroup L:$\\sigma$ relation is an extension of the cluster trend. However,\nif as argued above, preheating has substantially reduced the luminosity of\nthe groups, then the velocity dispersion must also be lower than expected,\notherwise a steepening of the $L:\\sigma$ relation, similar to that seen in\n$L:T$, would be observed.\n\n\\scite{bird95} have suggested that velocity dispersion should be reduced\nfor lower mass systems due to the effects of dynamical friction, which is\nmore effective in lower mass systems due to their lower velocity\ndispersion. Loss of orbital energy will lead to a reduction in orbital\nvelocity provided that the potential is less steep than a singular\nisothermal potential in the inner regions. This would be the case for\neither a King-like potential, with a flat core, or for potentials of the\nform introduced by Navarro, Frenk \\& White (1997)\\nocite{navarro97}, which\ntend to $\\rho \\propto r^{-1}$ at small radii. However it must be remembered\nthat the velocity dispersions of the groups in this sample are drawn from\nthree different sources, and may be based on only a small number of group\ngalaxies, so that statistical errors are large. \\scite{mulchaey98a} find\nthat when they add the velocities of fainter group galaxies to their\nredshift samples, the velocity dispersions they derive may increase by a\nfactor of 1.5 or more. This is qualitatively consistent with expectations\nfrom dynamical friction, since the orbits of more massive galaxies should\ndecay more quickly, and hence their velocity dispersion would drop below\nthat of fainter group members.\n\nThe results on the asymptotic slope of the X-ray surface brightness in\ngroups derived here, confirms and quantifies the result of\n\\scite{ponman99}, who showed that surface brightness is progressively\nflattened in low temperature systems. This trend is in accord with\npreheating models, as discussed above, although our median value of\n$\\beta_{fit}=0.46$ is a little lower than the values $\\beta_{fit}\\approx\n0.5$-0.6 predicted by the models of \\scite{metzler99} and\n\\scite{cavaliere99} for $T\\sim 1$~keV.\n\nThe situation in clusters is still a matter of debate. \\scite{arnaud99}\ncollect together results from the literature, and find a clear trend in\n$\\beta_{fit}$ with temperature, as can be seen in\nFig.\\ref{fig:beta_temp_1}. However, \\scite{mohr99} find that two-component\nfits are required to adequately represent most cluster profiles, and that\nthe results from such fits show no trend in the value of $\\beta_{fit}$ for\nthe extended cluster component. They conclude that results such as those of\n\\scite{arnaud99} arise from biases due to the inappropriate use of single\n$\\beta$-model profiles. On the other hand, we {\\it have} accounted for the\ncentral component, but still find that $\\beta_{fit}$ is substantially lower\nin groups that the value of $2/3$ found for clusters by \\scite{mohr99}.\n\nThe resolution of this situation probably lies in the temperature ranges\ncovered. The analysis of \\scite{ponman99} is model-independent, in that it\ninvolved simply overlaying the scaled surface brightness profiles. This\nshows that flattening of the profiles sets in at temperatures $T$\\ltsim\n3~keV. Since the sample of \\scite{mohr99} includes only a single cluster\nwith $T<3$~keV, the lack of trend in $\\beta_{fit}$ observed within their\nsample, and the much flatter profiles observed in our sample, are both\nconsistent with the \\scite{ponman99} results.\n\nFinally, we wish to emphasize that an important implication of the flat\nX-ray profiles of groups, coupled with their generally low surface\nbrightness compared to clusters, is that one must be very careful in\ndrawing conclusions about properties such as gas mass, gas fraction etc. on\nthe basis of analyses confined to `detection radii'. For example\n\\scite{mulchaey96} conclude that masses of gas in groups are typically\nlower than the mass in galaxies, on the basis of analyses within the region\nof detectable X-ray emission, which in many cases is only $\\sim 200$~kpc.\nSuch results have important implications. For example, \\scite{renzini97}\nhas used them to argue that the iron mass to light ratio in groups is much\nlower than that in clusters, and that it is therefore difficult to explain\nhow clusters can be assembled through group mergers.\n\nIt can be seen from Fig.\\ref{fig:fraction} that under the assumption that\nour $\\beta$-model fits can be extrapolated to $R_V$, less than 50\\% of the\nX-ray luminosity of the system is contained within 200~kpc for typical\ngroups. Now the asymptotic power law behaviour of surface brightness at\nlarge $r$ is $S(r) \\propto r^{1-6\\beta}$, whilst the corresponding density\nprofile (in the approximation of isothermal gas) is $\\rho_{gas}\\propto\nr^{-3\\beta}$. Hence the density profile is even flatter, and the fraction\nof the total gas mass contained within $r=$200~kpc will be considerably\n{\\it less} than 50\\%. The flat gas profiles mean that the gas fractions of\ngroups rise strongly with radius, so that very different results might be\nobtained if our instruments were sufficiently sensitive to detect group\nemission out to $R_V$, a possibility which should be realised with the\nlaunch of XMM.\n\n\n\\section{Conclusions}\n\\label{Conclusions}\n\nWe have carried out detailed analysis of {\\it ROSAT} PSPC data for 24 X-ray\nbright galaxy groups. Temperatures and bolometric luminosities have been\nderived for each group, and surface brightness profiles modelled in some\ndetail. In agreement with previous studies we find evidence for the\npresence of two components in the surface brightness profiles of many of\nthe groups. When present, the central component is coincident with the\nposition of a central galaxy, suggesting that it may be due to the halo of\nthe galaxy, or to a cooling flow focused onto the central galaxy.\n\nThe surface brightness profiles of groups are significantly flatter than\nthose of galaxy clusters. For a subsample of the groups with the best data,\nthe steepness of the surface brightness profiles, as measured by the\nparameter $\\beta_{fit}$, appear to show a trend with mass when combined\nwith cluster data. This result is consistent with the idea that galaxy\nwinds have significantly affected the state of the intergalactic medium in\nlow mass systems.\n\nThe relation between the X-ray luminosity and temperature for galaxy groups\nis also derived. This relation is found to be significantly steeper than\nthat derived for galaxy clusters. The action of galaxy winds flattening\nsurface brightness profiles would reduce the luminosity of the gas, due to\nthe luminosity dependance on the square of the density, thus causing a\nsteepening of the $L:T$ relation for lower mass systems. Further evidence\nfor this scenario is provided in the relation between velocity dispersion\nand temperature. The $\\sigma:T$ relation shows that for lower mass systems\nthe specific energy in the gas is greater than the specific energy in the\ngalaxies, suggesting that there has been energy injection in these systems.\nAn encouraging level of agreement is apparent between our results and\nrecent models and simulations of the effects of preheating by galaxy winds.\n\n\\section{Acknowledgements}\nWe thank Alex Deakin for his work in the early stages of this project,\nJohn Mulchaey for interesting discussions about the X-ray properties of\ngroups, and the referee for suggesting several improvements to the paper.\nEdward Lloyd-Davies and Bruce Fairley provided help and advice\non the data analysis and read several versions of this\nmanuscript.\n\nSFH acknowledges financial support from the University of Birmingham. This\nwork made use of the Starlink facilities at Birmingham, the LEDAS database\nat Leicester, the NASA/IPAC Extragalactic Database (NED), and images from\nthe STScI Digitized Sky Survey.\n\n\\bibliography{reffile}\n\\label{lastpage}\n\n\n\\end{document}\n\n\n\n\n\n\n"
},
{
"name": "table1.tex",
"string": "\\begin{table*}\n\\begin{minipage}[c]{17cm}\n\\caption{\\label{tab:allgroups}Listed are the groups in which a\n search for extended X-ray emission was carried out. Groups with a 1 in\n the comments column have properties taken from Nolthenius (1993), those\n identified with a 2 are from Ledlow et al. (1996) and those marked with a\n 3 are from Mulchaey \\& Zabludoff (1998). Asterisks indicate groups in\n which emission was identified within the PSPC support ring, but whose\n catalogued optical positions were outside the ring. Groups with detected\n X-ray emission are listed in the top half of the table along with the\n radius to which emission was observed. Groups that were not used are\n given in the lower region of the table along with the reason for\n exclusion.} \\center{\n\\begin{tabular}{llccrrclc}\n\\hline\nName & Alt. Name & RA(2000) & Dec(2000) & $N_{gal}$ & $\\sigma$ (km s$^{-1}$) & z & Comments & R$_{ext}$ ($'$) \\\\\n\\hline \nNGC 315 & Nol 6 & 00 58 25.0 & +30 39 11 & 4 & 122 & 0.0164 & 1 $\\ast$ & 6.0\\\\\nNGC 383 & S34-111 & 01 07 27.7 & +32 23 59 & 29 & 466 & 0.0173 & 2 & 30.0 \\\\\nNGC 524 & Nol 11 & 01 24 01.6 & +09 27 37.7 & 8 & 205 & 0.0083 & 1 & 10.6 \\\\\nNGC 533 & & 01 25 29.1 & +01 48 17 & 36 & 464 & 0.0181 & 3 & 20.3 \\\\\nNGC 741 & S49-140 & 01 57 00.7 & +05 40 00 & 41 & 432 & 0.0179 & 3 & 16.0 \\\\\nNGC 1587 & Nol 33 & 04 30 46.1 & +00 24 25.7 & 4 & 106 & 0.0122 & 1 & 6.0 \\\\\nNGC 2563 & NGC 2563 & 08 20 24.4 & +21 05 46 & 29 & 336 & 0.0163 & 3 & 17.6 \\\\\nNGC 3091 & HCG 42 & 10 00 13.1 & -19 38 24 & 22 & 211 & 0.0128 & 3 & 8.9 \\\\\nNGC 3607 & Nol 65 & 11 17 55.9 & +18 07 35.8 & 3 & 421 & 0.0037 & 1 & 9.6 \\\\\nNGC 3665 & Nol 68 & 11 23 30.6 & +38 43 31.6 & 4 & 29 & 0.0069 & 1 & 6.0 \\\\\nNGC 4065 & N79-299A,Nol 91 & 12 04 09.5 & +20 13 18 & 9 & 495 & 0.0235 & 2 & 15.0 \\\\\nNGC 4073 & N67-335 & 12 04 21.7 & +01 50 19 & 22 & 607 & 0.0204 & 2 & 18.0 \\\\\nNGC 4261 & Nol 99,N67-330 & 12 20 02.3 & +05 20 24 & 33 & 465 & 0.0071 & 1 & 15.0 \\\\\nNGC 4325 & NGC 4325 & 12 23 18.2 & +10 37 19 & 18 & 256 & 0.0252 & 3 & 10.2 \\\\\nNGC 4636 & Nol 104 & 12 42 57.2 & +02 31 34.3 & 12 & 463 & 0.0044 & 1 & 21.6 \\\\\nNGC 4761 & HGC62 & 12 52 57.9 & -09 09 26 & 45 & 376 & 0.0146 & 3 & 15.6 \\\\\nNGC 5129 & Nol 117 & 13 24 36.0 & +13 55 40 & 33 & 294 & 0.0232 & 3 & 9.0 \\\\\nNGC 5171 & N79-296 & 13 29 22.3 & +11 47 31 & 8 & 424 & 0.0232 & 2 & 10.8 \\\\\nNGC 5353 & Nol 124,N79-286,HCG68 & 13 51 37.0 & +40 32 12& 15 & 174 & 0.0081 & 1 $\\ast$ & 9.6\\\\\nNGC 5846 & Nol 146 & 15 05 47.0 & +01 34 25 & 20 & 368 & 0.0063 & 3 & 15.0 \\\\\nNGC 6338 & N34-175 & 17 15 21.4 & +57 22 43 & 7 & 589 & 0.0283 & 2 & 13.8 \\\\\nNGC 7176 & HCG90 & 22 02 31.4 & -32 04 58 & 16 & 193 & 0.0085 & 3 & 13.5 \\\\\nNGC 7619 & Nol 164 & 23 20 32.1 & +08 22 26.5 & 7 & 253 & 0.0111 & 1 & 24.0 \\\\\nNGC 7777 & Nol 170$^{\\ast}$ & 23 53 33.0 & +28 34 42 & 4 & 116 & 0.0229 & 1 $\\ast$ & 6.6 \\\\\n\\hline\nNGC 7819 & Nol 173 & 00 02 28.0 & +31 28 42.1 & 3 & 71 & 0.0164 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 43 & Nol 1 & 00 13 05.8 & +30 58 40.8 & 3 & 63 & 0.0160 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 2769 & Nol 35 & 09 10 22.8 & +50 23 45.3 & 3 & 125 & 0.0166 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 3839 & Nol 82,N67-312 & 11 42 04.6 & +10 18 20.0 & 9 & 177 & 0.0206 & \\multicolumn{2}{l}{2 background clusters} \\\\\nNGC 4168 & Nol 98 & 12 13 38.9 & +13 01 19.3 & 4 & 152 & 0.0077 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 4360 & Nol 101 & 12 25 44.6 & +09 07 23.5 & 3 & 289 & 0.0245 & \\multicolumn{2}{l}{1 behind Virgo emission} \\\\\nNGC 4615 & Nol 108 & 12 41 16.0 & +26 13 33.2 & 3 & 47 & 0.0158 & \\multicolumn{2}{l}{1 too few counts} \\\\\nNGC 5386 & Nol 129 & 13 58 00.1 & +06 15 25.1 & 3 & 9 & 0.0143 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 5775 & Nol 143 & 14 53 24.9 & +03 29 47.5 & 5 & 88 & 0.0051 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 5866 & Nol 147 & 15 16 23.5 & +56 25 01.9 & 4 & 74 & 0.0022 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 5970 & Nol 154 & 15 36 16.2 & +12 02 07.7 & 3 & 81 & 0.0064 & \\multicolumn{2}{l}{1 no detection} \\\\\nNGC 7448 & Nol 160,S49-143 & 23 01 48.9 & +15 58 09.0 & 8 & 153 & 0.0077 & \\multicolumn{2}{l}{2 no detection} \\\\\n\\hline\n\\end{tabular}\n}\n\\end{minipage}\n\\end{table*}\n\n\\nocite{nolthenius93,ledlow96,mulchaey98b}\n\n\n\n"
},
{
"name": "table2.tex",
"string": "\\begin{table*}\n\\begin{minipage}[c]{18cm}\n \\center{\\caption{\\label{tab:2kingfit}Results of the surface brightness\n fits for elliptical and two-component models. If two models are shown\n for a group, the first is the elliptical model and the second the the\n two-component model. Models marked with an $\\ast$ are groups in which\n two separate centres of emission could be observed. The goodness of\n fit is as described in the main body of the text. All errors are\n $1\\sigma$ for one interesting parameter.}}\n\\begin{tabular}{lcccccccc}\n\\hline\n & & Extended & component & & & Central & component & \\\\\n\\cline{2-5} \\cline{7-8}\nGroup & $\\beta_{fit}$ & Core radius & Axis ratio & Position angle & & Core radius & $\\beta_{fit}$ & Goodness \\\\ \n & &(arcmin) & &(degrees) & & & & of fit \\\\\n\\hline \nNGC 315 & 1.37 $\\pm$ 0.36 & 0.42 $\\pm$ 0.10 & 1.08 $\\pm$ 0.13 & 141 $\\pm$ 65 & & - & - & -0.5 \\\\ \nNGC 383 & 0.362 $\\pm$ 0.003 & 0.43 $\\pm$ 0.06 & 1.34 $\\pm$ 0.05 & 166 $\\pm$ 4 & & - & - & 8.2 \\\\ \n & 0.48 $\\pm$ 0.02 & 6.9 $\\pm$ 0.9 & 1.19 $\\pm$ 0.04 & 156 $\\pm$ 6 & & 0.01 $\\pm$ 0.03 & 0.48 $\\pm$ 0.02 & 5.2 \\\\ \nNGC 524 & 0.45 $\\pm$ 0.01 & 0.01 $\\pm$ 0.01 & 1.41 $\\pm$ 0.22 & 143 $\\pm$ 16 & & - & - & 18.2 \\\\ \nNGC 533 & 0.482 $\\pm$ 0.005 & 0.40 $\\pm$ 0.03 & 1.60 $\\pm$ 0.06 & 77 $\\pm$ 3 & & - & - & 14.2 \\\\ \n & 0.75 $\\pm$ 0.14 & 10.2 $\\pm$ 2.8 & 1.89 $\\pm$ 0.04 & 49 $\\pm$ 2 & & 0.02 $\\pm$ 0.02 & 0.54 $\\pm$ 0.02 & -0.23 \\\\ \nNGC 741 & 0.465 $\\pm$ 0.008 & 0.37 $\\pm$ 0.05 & 1.35 $\\pm$ 0.09 & 74 $\\pm$ 6 & & - & - & 11.2 \\\\ \n & 0.391 $\\pm$ 0.009 & 0.10 $\\pm$ 0.13 & 1.24 $\\pm$ 0.11 & 174 $\\pm$ 11 & & 0.17 $\\pm$ 0.09 & 0.9 $\\pm$ 0.3 & 0.20 \\\\ \nNGC 1587 & 0.47 $\\pm$ 0.06 & 0.34 $\\pm$ 0.27 & 1.4 $\\pm$ 0.5 & 35 $\\pm$ 22 & & - & - & -0.1 \\\\ \nNGC 2563 & 0.369 $\\pm$ 0.003 & 0.01 $\\pm$ 0.02 & 1.28 $\\pm$ 0.04 & 88 $\\pm$ 7 & & - & - & 4.6 \\\\ \n & 0.400 $\\pm$ 0.004 & 2.6 $\\pm$ 0.6 & 1.31 $\\pm$ 0.06 & 95 $\\pm$ 7 & & 0.2 Fixed & 1.0 Fixed & 1.54 \\\\ \nNGC 3091 & 0.60 $\\pm$ 0.02 & 0.48 $\\pm$ 0.06 & 1.64 $\\pm$ 0.09 & 14 $\\pm$ 4 & & - & - & 10.0 \\\\ \n & 0.41 $\\pm$ 0.02 & 0.1 $\\pm$ 0.05 & 4.3 $\\pm$ 1.3 & 184 $\\pm$ 4 & & 0.3 $\\pm$ 0.07 & 0.66 $\\pm$ 0.05 & 0.82 \\\\ \nNGC 3607 & 0.52 $\\pm$ 0.18 & 4.8 $\\pm$ 1.2 & 3.4 $\\pm$ 0.7 & 20 $\\pm$ 3 & & - & - & 3.2 \\\\ \n$\\ast$ & 0.45 $\\pm$ 0.04 & 0.28 $\\pm$ 0.16 & 1.0 Fixed & 0.0 Fixed & & 0.01 $\\pm$ 0.04 & 0.38 $\\pm$ 0.03 & 0.63 \\\\ \nNGC 3665 & 0.49 $\\pm$ 0.03 & 0.13 $\\pm$ 0.12 & 1.4 $\\pm$ 0.2 & 63 $\\pm$ 19 & & - & - & 0.2 \\\\ \nNGC 4065 & 0.47 $\\pm$ 0.04 & 4.1 $\\pm$ 0.6 & 3.6 $\\pm$ 0.4 & 7 $\\pm$ 1 & & - & - & 8.9 \\\\ \n$\\ast$ & 0.41 $\\pm$ 0.01 & 0.05 $\\pm$ 0.06 & 1.0 Fixed & 0.0 Fixed & & 4.3 $\\pm$ 1.4 & 0.8 $\\pm$ 0.2 & 2.49 \\\\ \nNGC 4073 & 0.431 $\\pm$ 0.002 & 0.10 $\\pm$ 0.01 & 1.25 $\\pm$ 0.02 & 103 $\\pm$ 3 & & - & - & 2.5 \\\\ \n & 0.46 $\\pm$ 0.01 & 2.14 $\\pm$ 0.26 & 1.28 $\\pm$ 0.04 & 102 $\\pm$ 4 & & 0.34 $\\pm$ 0.05 & 0.73 $\\pm$ 0.06 & 1.64 \\\\ \nNGC 4261 & 0.446 $\\pm$ 0.004 & 0.01 $\\pm$ 0.01 & 1.34 $\\pm$ 0.09 & 47 $\\pm$ 5 & & - & - & 13.6 \\\\ \n & 0.35 $\\pm$ 0.03 & 3.3 $\\pm$ 1.0 & 1.22 $\\pm$ 0.13 & 156 $\\pm$ 17 & & 0.28 $\\pm$ 0.01 & 1.0 Fixed & -1.20 \\\\ \nNGC 4325 & 0.60 $\\pm$ 0.01 & 0.32 $\\pm$ 0.03 & 1.17 $\\pm$ 0.05 & 11 $\\pm$ 8 & & - & - & 1.3 \\\\ \nNGC 4636 & 0.476 $\\pm$ 0.003 & 0.268 $\\pm$ 0.014 & 1.09 $\\pm$ 0.08 & 17 $\\pm$ 7 & & - & - & 17.0 \\\\ \n & 0.373 $\\pm$ 0.008 & 0.013 $\\pm$ 0.006 & 1.15 $\\pm$ 0.06 & 167 $\\pm$ 9 & & 0.92 $\\pm$ 0.11 & 0.81 $\\pm$ 0.06 & 6.39 \\\\ \nNGC 4761 & 0.502 $\\pm$ 0.005 & 0.30 $\\pm$ 0.02 & 1.33 $\\pm$ 0.04 & 16 $\\pm$ 3 & & - & - & 19.3 \\\\ \n & 0.364 $\\pm$ 0.006 & 0.10 $\\pm$ 0.04 & 1.17 $\\pm$ 0.09 & 72 $\\pm$ 14 & & 0.49 $\\pm$ 0.06 & 0.85 $\\pm$ 0.04 & 1.28 \\\\ \nNGC 5129 & 0.44 $\\pm$ 0.01 & 0.15 $\\pm$ 0.06 & 1.30 $\\pm$ 0.16 & 28 $\\pm$ 13 & & - & - & -0.7 \\\\ \nNGC 5171 & 0.34 $\\pm$ 0.03 & 0.84 $\\pm$ 0.71 & 2.7 $\\pm$ 0.9 & 171 $\\pm$ 6 & & - & - & 0.8 \\\\ \nNGC 5353 & 0.58 $\\pm$ 0.03 & 1.35 $\\pm$ 0.17 & 1.34 $\\pm$ 0.11 & 129 $\\pm$ 7 & & - & - & 71.0 \\\\ \n & 0.44 $\\pm$ 0.02 & 0.29 $\\pm$ 0.13 & 1.8 $\\pm$ 0.2 & 25 $\\pm$ 5 & & 0.01 $\\pm$ 0.01 & 1.0 Fixed & 6.39 \\\\\nNGC 5846 & 0.66 $\\pm$ 0.02 & 1.43 $\\pm$ 0.08 & 1.70 $\\pm$ 0.05 & 246 $\\pm$ 2 & & - & - & 106.9 \\\\ \n & 0.58 $\\pm$ 0.01 & 0.84 $\\pm$ 0.07 & 1.16 $\\pm$ 0.03 & 47 $\\pm$ 7 & & 0.27 $\\pm$ 0.04 & 1.0 Fixed & 3.48 \\\\ \nNGC 6338 & 0.423 $\\pm$ 0.004 & 0.06 $\\pm$ 0.01 & 1.24 $\\pm$ 0.06 & 24 $\\pm$ 7 & & - & - & 21.9 \\\\ \n & 0.52 $\\pm$ 0.04 & 2.6 $\\pm$ 0.4 & 1.29 $\\pm$ 0.07 & 23 $\\pm$ 6 & & 0.42 $\\pm$ 0.03 & 1.0 Fixed & 1.40 \\\\ \nNGC 7176 & 1.07 $\\pm$ 0.29 & 8.0 $\\pm$ 4.2 & 1.6 $\\pm$ 0.2 & 139 $\\pm$ 10 & & - & - & 2.3 \\\\ \nNGC 7619 & 0.458 $\\pm$ 0.006 & 1.42 $\\pm$ 0.08 & 1.93 $\\pm$ 0.07 & 210 $\\pm$ 1 & & - & - & 22.7 \\\\ \n$\\ast$ & 0.78 $\\pm$ 0.08 & 0.26 $\\pm$ 0.05 & 1.0 Fixed & 0.0 Fixed & & 0.01 $\\pm$ 0.01 & 0.40 $\\pm$ 0.01 & 6.27 \\\\\nNGC 7777 & 0.35 $\\pm$ 0.02 & 0.01 $\\pm$ 0.01 & 1.0 Fixed & 0.0 Fixed & & - & - & 1.1 \\\\\n\\hline\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n"
},
{
"name": "table3.tex",
"string": "\\begin{table*}\n\\begin{minipage}[c]{18cm}\n \\center{\\caption{\\label{tab:groupspec}Results of the spectral fitting are\n shown along with the derived luminosities for each of the groups. The\n distance to each of the groups is calculated after allowances for\n infall to Virgo and the Great Attractor. The luminosities are those\n derived within the radius to which emission could be observed. The\n final column shows what fraction of the luminosity as extrapolated to\n the virial luminosity is observed within the stated radius. All\n errors are $1\\sigma$.}}\n\\begin{tabular}{lcccccccc}\n\\hline\n & & & & & & Radius of & Physical & Fraction of \\\\\nGroup name & N$_H$ & Temperature & Abundance & Distance & log L & extraction & radius & virial \\\\ \n & (1.0$^{21}$ cm$^{-2}$) & (keV) & (Solar) & (Mpc) & (erg s$^{-1}$) & (arcmin) & (kpc) & luminosity \\\\\n\\hline \nNGC 315 & 0.588 & 0.85 $\\pm$ 0.07 & 0.12 $\\pm$ 0.05 & 96.4 & 42.15 $\\pm$ 0.15 & 6.0 & 168 & 1.00$\\ast$\\\\ \nNGC 383 & 0.54 & 1.53 $\\pm$ 0.07 & 0.40 $\\pm$ 0.09 & 101.8 & 43.31 $\\pm$ 0.02 & 30.0 & 889 & 0.76\\\\ \nNGC 524 & 0.467 & 0.56 $\\pm$ 0.08 & 0.35 $\\pm$ 0.43 & 49.9 & 41.37 $\\pm$ 0.11 & 10.6 & 153 & 0.59\\\\ \nNGC 533 & 0.305 & 1.06 $\\pm$ 0.04 & 0.82 $\\pm$ 0.19 & 106.8 & 42.95 $\\pm$ 0.02 & 20.3 & 630 & 0.91\\\\ \nNGC 741 & 0.442 & 1.08 $\\pm$ 0.06 & 0.48 $\\pm$ 0.18 & 106.0 & 42.66 $\\pm$ 0.03 & 16.0 & 494 & 0.59\\\\ \nNGC 1587 & 0.692 & 0.92 $\\pm$ 0.15 & 0.3 Fixed & 77.1 & 41.50 $\\pm$ 0.18 & 6.0 & 134 & 0.46\\\\ \nNGC 2563 & 0.424 & 1.06 $\\pm$ 0.04 & 0.56 $\\pm$ 0.14 & 106.7 & 42.79 $\\pm$ 0.02 & 17.6 & 546 & 0.57\\\\ \nNGC 3091 & 0.478 & 0.71 $\\pm$ 0.03 & 0.95 $\\pm$ 1.08 & 90.6 & 42.20 $\\pm$ 0.03 & 8.9 & 236 & 0.81\\\\ \nNGC 3607 & 0.156 & 0.41 $\\pm$ 0.04 & 0.05 $\\pm$ 0.02 & 33.1 & 41.59 $\\pm$ 0.03 & 9.6 & 92 & 0.34\\\\ \nNGC 3665 & 0.204 & 0.45 $\\pm$ 0.11 & 0.17 $\\pm$ 0.14 & 52.5 & 41.36 $\\pm$ 0.10 & 6.0 & 92 & 0.66\\\\ \nNGC 4065 & 0.239 & 1.22 $\\pm$ 0.08 & 0.80 $\\pm$ 0.36 & 151.3 & 42.99 $\\pm$ 0.04 & 15.0 & 660 & 0.76\\\\ \nNGC 4073 & 0.190 & 1.59 $\\pm$ 0.06 & 0.94 $\\pm$ 0.12 & 135.9 & 43.70 $\\pm$ 0.01 & 18.0 & 711 & 0.75\\\\ \nNGC 4261 & 0.156 & 0.94 $\\pm$ 0.03 & 0.20 $\\pm$ 0.02 & 53.0 & 42.32 $\\pm$ 0.02 & 15.0 & 231 & 0.26\\\\ \nNGC 4325 & 0.223 & 0.86 $\\pm$ 0.03 & 2.01 $\\pm$ 1.09 & 162.6 & 43.35 $\\pm$ 0.03 & 10.2 & 482 & 0.95\\\\ \nNGC 4636 & 0.179 & 0.72 $\\pm$ 0.01 & 0.51 $\\pm$ 0.04 & 32.8 & 42.48 $\\pm$ 0.01 & 21.6 & 206 & 0.46\\\\ \nNGC 4761 & 0.297 & 1.04 $\\pm$ 0.02 & 0.36 $\\pm$ 0.04 & 104.7 & 43.16 $\\pm$ 0.01 & 15.6 & 475 & 0.59\\\\ \nNGC 5129 & 0.176 & 0.81 $\\pm$ 0.06 & 0.51 $\\pm$ 0.22 & 149.9 & 42.78 $\\pm$ 0.04 & 9.0 & 393 & 0.65\\\\ \nNGC 5171 & 0.193 & 1.05 $\\pm$ 0.11 & 0.40 $\\pm$ 0.20 & 150.1 & 42.92 $\\pm$ 0.05 & 10.8 & 472 & 0.39\\\\ \nNGC 5353 & 0.0973 & 0.68 $\\pm$ 0.05 & 0.30 $\\pm$ 0.07 & 58.0 & 41.76 $\\pm$ 0.03 & 9.6 & 162 & 0.46\\\\\nNGC 5846 & 0.428 & 0.70 $\\pm$ 0.02 & 0.43 $\\pm$ 0.10 & 42.3 & 42.36 $\\pm$ 0.02 & 15.0 & 185 & 0.88\\\\ \nNGC 6338 & 0.256 & 1.69 $\\pm$ 0.16 & 0.06 $\\pm$ 0.04 & 171.2 & 43.93 $\\pm$ 0.01 & 13.8 & 687 & 0.79\\\\ \nNGC 7176 & 0.163 & 0.53 $\\pm$ 0.11 & 0.3 $\\pm$ 0.6 & 50.6 & 41.47 $\\pm$ 0.11 & 13.5 & 199 & 0.90\\\\ \nNGC 7619 & 0.496 & 1.00 $\\pm$ 0.03 & 0.44 $\\pm$ 0.09 & 64.9 & 42.62 $\\pm$ 0.02 & 24.0 & 453 & 0.59\\\\\nNGC 7777 & 0.500 & 0.62 $\\pm$ 0.15 & 0.3 Fixed & 133.4 & 41.75 $\\pm$ 0.20 & 6.6 & 256 & 0.32\\\\\n\\hline \n\\end{tabular}\n\\\\\n$\\ast$ NGC 315 fits with a high $\\beta_{fit}$ and it is possible that for\nthis group the emission may be due to a extensive elliptical galaxy halo\nrather than genuine group emission.\n\\end{minipage}\n\\end{table*}\n"
},
{
"name": "table4.tex",
"string": "\\begin{table*}\n\\begin{minipage}[c]{13cm}\n \\center{\\caption{\\label{tab:MZgroups}A comparison of the two-component\n models fitted by Mulchaey \\& Zabludoff (1998) with those from this\n work. $\\beta_{fit}$ and core radius values of the extended component\n for both sets of models are listed. The final column gives the\n difference in Cash statistic between the two models as fitted to our\n data; the negative sign indicating that the model fitted here gives\n the better fit.}}\n\\begin{tabular}{lccccl}\n\\hline\n & M\\&Z & M\\&Z & This work & This work & \\\\\nGroup & $\\beta_{fit}$ & core radius & $\\beta_{fit}$ & core radius & $\\Delta$C\\\\ \n & & (arcmin) & & (arcmin) & \\\\\n\\hline \nNGC 533 & 0.83 & 8.15 & 0.74 & 10.2 & -122.5 \\\\ \nNGC 741 & 1.00 & 14.08 & 0.39 & 0.1 & -45.1 \\\\ \nNGC 2563 & 0.86 & 11.15 & 0.40 & 2.6 & -26.4 \\\\ \nNGC 3091 & 0.68 & 3.61 & 0.41 & 0.1 & -41.0 \\\\ \nNGC 4761 & 0.63 & 9.00 & 0.36 & 0.1 & -129.2\\\\ \nNGC 5846 & 0.83 & 13.93 & 0.58 & 0.84 & -263.7\\\\ \n\\hline\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\n\\nocite{mulchaey98b}"
}
] |
[
{
"name": "loosegrp.bbl",
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}
] |
astro-ph0002052
|
Relativistic Effects in the Pulse Profile of the 2.5 msec X-Ray Pulsar SAX~J1808.4-3658
|
[
{
"author": "Eric C. Ford"
}
] |
We analyze the properties of the pulsed emission from the accreting millisecond pulsar \saxpsr in observations of its April 1998 outburst by the Rossi X-Ray Timing Explorer. Pulse phase spectroscopy shows that the emission evolves from a hard spectrum (power law with photon index $2.39\pm0.06$) to a soft spectrum (index $3.39\pm0.24 $). This softening is also observable as a phase lag in the fundamental of low-energy photons with respect to high-energy photons. We show that this lag is roughly constant over ten days of the outburst. We fit these data with a model where the pulse emission is from a hot spot on the rotating neutron star and the flux as a function of phase is calculated including the effects of general relativity. The energy-dependent lags are very well described by this model. The harder spectra at earlier phases (as the spot approaches) are the result of larger Doppler boosting factors which are important for this fast pulsar.
|
[
{
"name": "ford1808.tex",
"string": "% Relativistic Effects in SAX J1808.4-3658\n% Eric C. Ford \n% submitted to ApJ, 2 February 2000\n% uses AAS preprint style sheets version 5.01\n\n% note this file uses BibTeX, citations defined in refs.bib\n\n\\documentclass[preprint2,11pt]{aastex}\n%\\documentclass{aastex}\n\n% Put a space after macro unless followed by punctuation\n%\n\\newcommand\\puncspace{\\ifmmode\\,\\else{\\ifcat.\\C{\\if.\\C\\else\\if,\\C\\else\\if?\\C\\else%\n\\if:\\C\\else\\if;\\C\\else\\if-\\C\\else\\if)\\C\\else\\if/\\C\\else\\if]\\C\\else\\if'\\C%\n\\else\\space\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi}%\n\\else\\if\\empty\\C\\else\\if\\space\\C\\else\\space\\fi\\fi\\fi}\\fi}\n\\newcommand\\SP{\\let\\\\=\\empty\\futurelet\\C\\puncspace}\n\n% commands for this article\n\\newcommand{\\Msun}{{\\rm M}_\\sun\\SP}\n\\newcommand{\\mdot}{$\\dot{M}$\\SP}\n\\newcommand{\\lx}{$L_x$\\SP}\n\\newcommand{\\freq}{$\\nu_{kHz}$\\SP}\n\\newcommand{\\mm}{M\\'endez }\n%\\newcommand{\\sax1808}{SAX J1808.4-3658\\SP} %doesn't work\n\\newcommand{\\saxpsr}{SAX J1808.4-3658\\SP}\n\n\\citestyle{aa} % make citations look right\n\n\\slugcomment{Submittted to ApJ Letters: 2 February 2000}\n\n\\shorttitle{Relativistic Effects in SAX~J1808.4-3658}\n\\shortauthors{Ford}\n\n\\begin{document}\n\n\\title{Relativistic Effects in the Pulse Profile of the 2.5\nmsec X-Ray Pulsar SAX~J1808.4-3658}\n\n\\author{Eric C. Ford}\n%\\author{Eric C. Ford\\altaffilmark{1}}\n\n\\affil{Astronomical Institute, ``Anton Pannekoek'', University of Amsterdam}\n\\affil{Kruislaan 403, 1098 SJ Amsterdam, The Netherlands}\n\\email{[email protected]}\n\n%\\altaffiltext{1}{Astronomical Institute, ``Anton Pannekoek'',\n%University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam,\n%The Netherlands}\n\n\\begin{abstract}\n\nWe analyze the properties of the pulsed emission from the accreting\nmillisecond pulsar \\saxpsr in observations of its April 1998 outburst\nby the Rossi X-Ray Timing Explorer. Pulse phase spectroscopy shows\nthat the emission evolves from a hard spectrum (power law with photon\nindex $2.39\\pm0.06$) to a soft spectrum (index $3.39\\pm0.24 $). This\nsoftening is also observable as a phase lag in the fundamental of\nlow-energy photons with respect to high-energy photons. We show that\nthis lag is roughly constant over ten days of the outburst. We fit\nthese data with a model where the pulse emission is from a hot spot on\nthe rotating neutron star and the flux as a function of phase is\ncalculated including the effects of general relativity. The\nenergy-dependent lags are very well described by this model. The\nharder spectra at earlier phases (as the spot approaches) are the\nresult of larger Doppler boosting factors which are important for this\nfast pulsar.\n\n\\end{abstract}\n\n\\keywords{accretion --- black holes -- stars: neutron --- X--rays: stars}\n\n\\section{Introduction}\n\nStrong X-ray pulsations with a 2.49 msec period were discovered from\n\\saxpsr in an April 1998 observation with the Rossi X-ray Timing\nExplorer \\citep{wk98}. The pulsar is a member of an accreting binary\nsystem with an orbital period of 2.01 hour and a low-mass companion\n\\citep{cm98}. Though similar to other low-mass X-ray binaries in its\ntiming and spectral properties \\citep[e.g.][]{wk99,hs98}, \\saxpsr is\nunique for its X-ray pulsations. No other such binary has shown\ncoherent pulsations in its persistent flux despite of careful searches\n\\citep[][and references therein]{vaughan94a}.\n\nAs such, \\saxpsr is the fastest rotating accreting neutron star.\nIf the pulsations are due to modulated emission from one hot spot on\nthe neutron star surface, the 2.49 msec period corresponds to an\nequatorial speed of approximately 0.1c. With these high speeds,\n\\saxpsr offers an excellent system for studying relativistic effects.\n\nOne such effect may be the observed lag of low-energy photons relative\nto high-energy photons in the pulse discovered by\n\\citet{cmt98}. \\citet{cmt98} suggest that the lags are due to\nComptonization in a relatively cool surrounding medium. Alternatively,\nthe lags may be the result of a relativistic effect: the high-energy\nphotons are preferentially emitted at earlier phases due to Doppler\nboosting along the line of sight. This possibility was suggested for\nthe similar lags in the 549~Hz oscillations in an X-ray burst of\nAql~X-1 \\citep{ford99}, where a simple model showed that the delays\nroughly match those expected.\n\nIn the following, we present new measurements of the pulsed emission\nfrom \\saxpsr. We show that the energy-dependent phase lags are\nequivalent to a hardening pulse profile. We model this behavior in\nterms of a hot spot on the neutron star, including relativistic\neffects.\n\n\\section{Observations \\& Analysis}\n\nWe have used publicly available data from the proportional counter\narray (PCA) on board RXTE in an `event' mode with high time resolution\n(122$\\mu$sec) and high energy resolution (64 channels). The\nobservations occurred from April 10 1998 to May 7 1998, when the source\nwas in outburst.\n\nWe generate folded lightcurves in each PCA channel. This is\naccomplished with the fasebin tool in FTOOLS version 4.2, which\napplies all known XTE clock corrections and corrects photon arrival\ntimes to the solar system barycenter using the JPL DE-200 ephemeris,\nyielding a timing accuracy of several $\\mu$sec (much less than the\nphase binning used here). As a check, we have applied this method to\nCrab pulsar data and the results are identical to \\citet{pravdo97}.\nTo produce pulse profiles in the neutron star rest frame, we use the\n\\saxpsr orbital ephemeris found by \\citet{cm98}. An example folded\nlightcurve is shown in Figure~\\ref{lc} (top) for the observation of\nApril 18 1998 14:05:40 to April 19 1998 00:51:44 UTC.\n\nTo study the energy spectra at each phase bin, we take the rates at\npulse minimum and subtract it from the rest of the data at other\nphases. This effectively accomplishes background subtraction and\neliminates the unpulsed emission which we do not wish to\nconsider. Note, however, that the pulsed emission may have some\ncontribution even at the pulse minimum and this subtraction scheme\nrepresents only a best approximation to the true pulse emission. We\ngenerate detector response matrices appropriate to the observation\ndate and data mode using pcarsp v2.38, and use XSPEC v.10.0 to fit\nmodel spectra.\n\nWe fit the spectrum here with a simple powerlaw function. Though the\nfunction itself is not meant to be a physical description, the\npowerlaw index provides a good measure of the spectral hardness. Fits\nin each phase bin have reduced $\\chi^2$ of 0.7 to 1.6. Including an\ninterstellar absorption does not substantially affect these results.\nThe powerlaw index clearly increases through the pulse phase\n(Figure~\\ref{lc}, bottom), i.e. spectrum evolves from hard to soft.\n\nWe also fit the profiles of the folded lightcurves in each channel\nusing Fourier functions at the fundamental frequency and its\nharmonics. From these fits we determine the phase lag in each channel\nrelative to the fits in some baseline channel range. Results for the\n18 April 1998 observation are shown in Figure~\\ref{lags} as solid\nsymbols. Note that negative numbers indicate that high-energy photons\nprecede low-energy photons. We are also able to measure lags in the\nfirst harmonic, and find that they are opposite in sign to the\nfundamental, i.e. low-energy photons precede high-energy photons in\nthe first harmonic. No lags are measurable in the other harmonics.\n\nAnother way to measure energy-dependent phase lags is by Fourier\ncross-correlation analysis. This is the method used for \\saxpsr by\n\\citet{cmt98} and for other timing signals as well, e.g. kilohertz\nQPOs \\citep[e.g.][]{kaaret99a}. For a description of cross\ncorrelation analysis see e.g. \\citet{vaughan94b}. From the PCA event\nmode data we calculate Fourier spectra in various channel ranges with\nNyquist frequency of 2048 Hz and resolution of 0.25 Hz. We then\ncalculate cross spectra defined as $C(j) = X_1^{*}(j)X_2(j)$, where\n$X$ are the complex Fourier coefficients for two energy bands at the\npulsar frequency $\\nu_j$. The phase lag between the two energy bands\nis given by the argument of $C$. We measure all phase delays relative\nto the unbinned channels range 5 to 8, i.e. 1.83 to 3.27 keV for 5\ndetector units in PCA gain epoch 3 (April 15 1996 to March 22\n1999). The results for the 18 April 1998 observation, are shown in\nFigure~\\ref{lags} by the open symbols. The phase lags are consistent\nwith those calculated from the lightcurve fitting. From the\ncross-correlation spectra we are not able to measure lags in the much\nweaker harmonics.\n\n% zero-band = orig chan 5-8: 1.83 - 3.27 keV\n% based on E-C conversion of \n% http://heasarc.gsfc.nasa.gov/docs/xte/e-c_table.html\n% for epoch 3 = 4/15/96 to 3/22/99\n\nWe have calculated phase lag spectra also for other RXTE observations\nduring the April 1998 outburst. These spectra are similar to that in\nFigure~\\ref{lags}. To quantify the trends, we compute an average phase\ndelay, $\\phi_{avg}$, over all energies for each observation. We also\nfit a broken powerlaw function to each phase delay spectrum:\n$\\phi=E^{-\\alpha}$ below a break energy, $E_{b}$, and\n$\\phi=\\phi_{max}$ above this energy. Figure~\\ref{lags_v_time} shows\nthe quantities $\\phi_{avg}$, $E_{b}$ and $\\phi_{max}$ versus the\ntime of each observation.\n\nThere is a clear connection between the results of the two analyses\npresented here. The phase resolved spectroscopy shows that the\nspectrum softens and correspondingly the peak of the pulse profile\nappears slightly earlier in phase for higher energies\n(Figure~\\ref{lc}). The method of measuring phase delays shows the same\nbehavior: higher-energy photons preferentially lead lower-energy\nphotons in the fundamental and the magnitude of this phase delay\nincreases with energy (Figure~\\ref{lags}). In the following we discuss\na model that can account for the phase delays/spectral softening\nmeasured here.\n\n\\section{Model}\n\nWe calculate the expected luminosity as a function of phase in a\nmanner similar to \\citet{pfc83,stroh92} but including Doppler effects\n\\citep{cs89} and time of flight delays \\citep{fkp86}. This treatment\nis based on a Schwarzschild metric, where the photon trajectories are\ncompletely determined by the compactness, $R/M$. The predicted\nluminosity as a function of phase from our code matches the results of\n\\citet{pfc83} and \\citet{cs89} for the various choices of parameters.\n\\citet{brr00} recently developed a model for pulse profiles using a\nslightly different approach.\n\nThe parameters in the model are the speed at the equator of the\nneutron star, $v$, the mass of the neutron star, $M$, the compactness,\n$R/M$, the angular size of the cap, $\\alpha$, and the viewing angles,\n$\\beta$ (the angle between the rotation axis and the cap center) and\n$\\gamma$ (rotation axis to line of sight). Another ingredient is the\nemission from the spot, which we take as isotropic and isothermal. The\nspectrum of energy emitted from the spot is another important\ninput. Note that if the emitted spectrum is power law like, the\nobserved spectrum will not evolve with phase, since Doppler\ntransformation preserves the shape \\citep[see][]{cs89}. The intrinsic\nspectrum must therefore have some shape that transforms to match the\nobserved hardening and phase lags; we use a blackbody spectrum with\ntemperature $kT_0$.\n\nA fit from the model is shown in Figure~\\ref{lags}. This fit uses the\nfollowing model parameters: $R/M=5$, $M=1.8\\Msun$, $kT_0=0.6$ keV,\n$v=0.1$, $\\beta=\\gamma=10^{\\rm o}$, $\\alpha=10^{\\rm o}$. To derive\ncount rates, we use table models in XSPEC and the appropriate response\nfiles as discussed above. The fit for this single set of parameters\nis good; we find $\\chi^2=5.3$ from the Fourier cross-correlation data\nor a reduced $\\chi^2$ of 0.8 for all the parameters fixed.\n\nA full exploration of the parameter space of the model is beyond the\nscope of this letter. We note the following trends, however. The\nmagnitude of the phase lags depends sensitively on $v$ and\n$kT_0$. Larger delays result from higher speeds, because the pulses\nbecome increasingly asymmetric due to Doppler boosting. This asymmetry\nis also energy dependent, so there is a dependence on $kT_0$ as well\n\\citep[see][]{cs89}. The lags also depend on $\\beta$ and $\\gamma$,\nespecially at higher energies where there is the turn-over noted\nabove. The phase lags are less sensitive to $R/M$ and $\\alpha$. We\nhave tested the assumption of isotropic emission and found that the\nphase lags depend only weakly on the beaming.\n\n\\section{Discussion}\n\nThe pulsed emission from \\saxpsr evolves through its phase from a\nrelatively hard to a soft spectrum, as shown by our phase resolved\nspectroscopy (Figure~\\ref{lc}). This evolution can also be thought of,\nand measured as, an energy-dependent phase lag in the fundamental\n(Figure~\\ref{lags}), i.e. higher-energy photons emerging earlier in\nphase than lower-energy photons.\n\nWe have applied a model to the data which consists of a hot spot on\nthe rotating neutron star under a general relativistic treatment. The\ndominant effect accounting for energy-dependent delays is Doppler\nboosting, the larger boosting factors at earlier phases giving harder\nspectra. The model fits the data quite well. The model also provides\na stable mechanism for generating the phase delays, which meshes with\nthe fact that the characteristic delays remain stable in time to\nwithin 25\\% (Figure~\\ref{lags_v_time}) even as there is a factor of\ntwo decrease in the X-ray flux, a possible tracer of accretion\nrate. As noted in \\citet{ford99}, in addition to explaining the\nenergy-dependent phase lags in \\saxpsr, this mechanism may also\naccount for the lags in the burst oscillations of Aql X-1\n\\citep{ford99} and kilohertz QPOs \\citep{vaughan98,kaaret99a}. Phase\nresolved spectroscopy has not yet been possible in these signals.\n\nThe model offers a new means of measuring the neutron star mass and\nradius, a notoriously difficult problem in accreting binary\nsystems. The radius is directly related to $v$, the equatorial speed\n($v=\\Omega_{\\rm spin} R$). The fits also depend on the model\nparameters $M$ and $R/M$, though the lag spectra are less sensitive to\nthese quantities. The model could be independently constrained by\nfuture optical spectroscopy of the companion which could provide\ninformation on $M$ and the viewing angles, $\\alpha$ and $\\beta$.\n\n\\acknowledgments\n\nWe acknowledge stimulating discussions with the participants of the\nAugust 1999 Aspen workshop on Relativity where an early version of\nthis work was presented. We thank Michiel van der Klis, Mariano\nM\\'{e}ndez and Luigi Stella for helpful discussions. This work was\nsupported by NWO Spinoza grant 08-0 to E.P.J.van den Heuvel, by the\nNetherlands Organization for Scientific Research (NWO) under contract\nnumber 614-51-002, and by the Netherlands Researchschool for Astronomy\n(NOVA). This research has made use of data obtained through the High\nEnergy Astrophysics Science Archive Research Center Online Service,\nprovided by the NASA/Goddard Space Flight Center.\n\n%\\bibliographystyle{apj}\n%\\bibliography{apj-jour,refs} %apj-hour.bib is an astronat distrib. file\n\n\\begin{thebibliography}{16}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{{Braje} {et~al.}(2000){Braje}, {Romani}, \\& {Rauch}}]{brr00}\n{Braje}, T., {Romani}, R., \\& {Rauch}, K. 2000, ApJ in press\n\n\\bibitem[{{Chakrabarty} \\& {Morgan}(1998)}]{cm98}\n{Chakrabarty}, D. \\& {Morgan}, E.~H. 1998, \\nat, 394, 346\n\n\\bibitem[{{Chen} \\& {Shaham}(1989)}]{cs89}\n{Chen}, K. \\& {Shaham}, J. 1989, \\apj, 339, 279\n\n\\bibitem[{{Cui} {et~al.}(1998){Cui}, {Morgan}, \\& {Titarchuk}}]{cmt98}\n{Cui}, W., {Morgan}, E.~H., \\& {Titarchuk}, L.~G. 1998, \\apjl, 504, L27\n\n\\bibitem[{{Ford}(1999)}]{ford99}\n{Ford}, E.~C. 1999, \\apjl, 519, L73\n\n\\bibitem[{{Ftaclas} {et~al.}(1986){Ftaclas}, {Kearney}, \\& {Pechenick}}]{fkp86}\n{Ftaclas}, C., {Kearney}, M.~W., \\& {Pechenick}, K. 1986, \\apj, 300, 203\n\n\\bibitem[{{Heindl} \\& {Smith}(1998)}]{hs98}\n{Heindl}, W.~A. \\& {Smith}, D.~M. 1998, \\apjl, 506, L35\n\n\\bibitem[{{Kaaret} {et~al.}(1999){Kaaret}, {Piraino}, {Ford}, \\&\n {Santangelo}}]{kaaret99a}\n{Kaaret}, P., {Piraino}, S., {Ford}, E.~C., \\& {Santangelo}, A. 1999, \\apjl,\n 514, L31\n\n\\bibitem[{{Pechenick} {et~al.}(1983){Pechenick}, {Ftaclas}, \\& {Cohen}}]{pfc83}\n{Pechenick}, K.~R., {Ftaclas}, C., \\& {Cohen}, J.~M. 1983, \\apj, 274, 846\n\n\\bibitem[{{Pravdo} {et~al.}(1997){Pravdo}, {Angelini}, \\& {Harding}}]{pravdo97}\n{Pravdo}, S.~H., {Angelini}, L., \\& {Harding}, A.~K. 1997, \\apj, 491, 808+\n\n\\bibitem[{{Strohmayer}(1992)}]{stroh92}\n{Strohmayer}, T.~E. 1992, \\apj, 388, 138\n\n\\bibitem[{{Vaughan} {et~al.}(1994{\\natexlab{a}}){Vaughan}, {van Der Klis},\n {Lewin}, {Wijers}, {van Paradijs}, {Dotani}, \\& {Mitsuda}}]{vaughan94b}\n{Vaughan}, B., {van Der Klis}, M., {Lewin}, W. H.~G., {Wijers}, R. A. M.~J.,\n {van Paradijs}, J., {Dotani}, T., \\& {Mitsuda}, K. 1994{\\natexlab{a}}, \\apj,\n 421, 738\n\n\\bibitem[{{Vaughan} {et~al.}(1998){Vaughan}, {van der Klis}, {M\\'endez}, {van\n Paradijs}, {Wijnands}, {Lewin}, {Lamb}, {Psaltis}, {Kuulkers}, \\&\n {Oosterbroek}}]{vaughan98}\n{Vaughan}, B.~A., {van der Klis}, M., {M\\'endez}, M., {van Paradijs}, J.,\n {Wijnands}, R. A.~D., {Lewin}, W. H.~G., {Lamb}, F.~K., {Psaltis}, D.,\n {Kuulkers}, E., \\& {Oosterbroek}, T. 1998, \\apjl, 509, L145\n\n\\bibitem[{{Vaughan} {et~al.}(1994{\\natexlab{b}}){Vaughan}, {van Der Klis},\n {Wood}, {Norris}, {Hertz}, {Michelson}, {van Paradijs}, {Lewin}, {Mitsuda},\n \\& {Penninx}}]{vaughan94a}\n{Vaughan}, B.~A., {van Der Klis}, M., {Wood}, K.~S., {Norris}, J.~P., {Hertz},\n P., {Michelson}, P.~F., {van Paradijs}, J., {Lewin}, W. H.~G., {Mitsuda}, K.,\n \\& {Penninx}, W. 1994{\\natexlab{b}}, \\apj, 435, 362\n\n\\bibitem[{{Wijnands} \\& {van der Klis}(1998)}]{wk98}\n{Wijnands}, R. \\& {van der Klis}, M. 1998, \\nat, 394, 344\n\n\\bibitem[{{Wijnands} \\& {van der Klis}(1999)}]{wk99}\n---. 1999, \\apj, 514, 939\n\n\\end{thebibliography}\n\n\n\\onecolumn\n\n%% FIG 1: folded lightcurves with spectral fits\n\\begin{figure}[h]\n\\begin{center}\n% need rescaling in preprint mode\n\\epsscale{0.7}\n\\plotone{f1.ps} %only works in AASTeX v 5.0.1 or higher\n\\caption{Folded lightcurve in example low (top) and high (middle)\nenergy bands and index of the power law of spectral fit (bottom). The\nprofile is repeated twice for clarity.}\n\\label{lc}\n\\end{center}\n\\end{figure}\n% from: /d1/ecford/xte/sax1808/spec/18b/plot2lcalpha2.f\n\n%% FIG 2: phase lags\n\\begin{figure}[h]\n\\begin{center}\n% need rescaling in preprint mode\n\\epsscale{0.7}\n\\plotone{f2.ps} %only works in AASTeX v 5.0.1 or higher\n\n\\caption{Phase delays in the fundamental of SAX~J1808.4-3658 relative\nto the 1.83 - 3.27 keV band. A negative number indicates that\nhigh-energy photons precede low-energy photons. Solid symbols indicate\nmeasurements from fitting the folded lightcurves, open symbols are\ndata from Fourier cross-correlation analysis. The line shows the model\nfor parameters $R/M=5$, $M=1.8{\\rm M}_\\sun$, $kT_0=0.6$ keV, $v=0.1$\nc, and $\\beta=\\gamma=10^{\\rm o}$ as described in the text.}\n\n\\label{lags}\n\\end{center}\n\\end{figure}\n%R/M=5$, $M=1.8\\Msun$, }\n% from: /d1/ecford/xte/sax1808/spec/18b/plot_lag_fund2.f\n\n%% FIG 3: lags vs time\n\\begin{figure}[h]\n\\begin{center}\n% need rescaling in preprint mode\n\\epsscale{0.8}\n\\plotone{f3.ps} %only works in AASTeX v 5.0.1 or higher\n\\caption{Parameters of the Fourier phase delay spectra for each\nobservation. Plotted are average phase delay over all energies (top),\nthe break energy (middle) and the maximum phase delay (bottom).}\n\\label{lags_v_time}\n\\end{center}\n\\end{figure}\n% from: /d1/ecford/xte/sax1808/fitplot\n\n%%% FIG 4: coordinate system\n%\\begin{figure}[h]\n%\\begin{center}\n%% need rescaling in preprint mode\n%\\epsscale{0.4}\n%\\plotone{coord.eps} %only works in AASTeX v 5.0.1 or higher\n%\\caption{Coordinate systems. The observer looks at the neutron star\n%along the $z$-axis. The viewing angle $\\beta$ and the cap-rotation\n%angle $\\gamma$ are fixed.}\n%\\label{coord}\n%\\end{center}\n%\\end{figure}\n\n\\end{document}\n% LocalWords: AAS ECF BibTeX refs Pannekoek Kruislaan SJ accreting msec wk hs\n% LocalWords: vaughan cmt Comptonization Aql wml brr PCA RXTE sec unbinned keV\n% LocalWords: UTC orig chan html powerlaw lightcurves fasebin FTOOLS XTE JPL\n% LocalWords: barycenter binning pravdo lightcurve unpulsed pcarsp XSPEC pfc\n% LocalWords: stroh cs Schwarzschild pfk QPOs kaaret Michiel der Klis Mariano\n% LocalWords: ndez Luigi NWO Spinoza Heuvel Researchschool fkp\n"
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"string": "\\begin{thebibliography}{16}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{{Braje} {et~al.}(2000){Braje}, {Romani}, \\& {Rauch}}]{brr00}\n{Braje}, T., {Romani}, R., \\& {Rauch}, K. 2000, ApJ in press\n\n\\bibitem[{{Chakrabarty} \\& {Morgan}(1998)}]{cm98}\n{Chakrabarty}, D. \\& {Morgan}, E.~H. 1998, \\nat, 394, 346\n\n\\bibitem[{{Chen} \\& {Shaham}(1989)}]{cs89}\n{Chen}, K. \\& {Shaham}, J. 1989, \\apj, 339, 279\n\n\\bibitem[{{Cui} {et~al.}(1998){Cui}, {Morgan}, \\& {Titarchuk}}]{cmt98}\n{Cui}, W., {Morgan}, E.~H., \\& {Titarchuk}, L.~G. 1998, \\apjl, 504, L27\n\n\\bibitem[{{Ford}(1999)}]{ford99}\n{Ford}, E.~C. 1999, \\apjl, 519, L73\n\n\\bibitem[{{Ftaclas} {et~al.}(1986){Ftaclas}, {Kearney}, \\& {Pechenick}}]{fkp86}\n{Ftaclas}, C., {Kearney}, M.~W., \\& {Pechenick}, K. 1986, \\apj, 300, 203\n\n\\bibitem[{{Heindl} \\& {Smith}(1998)}]{hs98}\n{Heindl}, W.~A. \\& {Smith}, D.~M. 1998, \\apjl, 506, L35\n\n\\bibitem[{{Kaaret} {et~al.}(1999){Kaaret}, {Piraino}, {Ford}, \\&\n {Santangelo}}]{kaaret99a}\n{Kaaret}, P., {Piraino}, S., {Ford}, E.~C., \\& {Santangelo}, A. 1999, \\apjl,\n 514, L31\n\n\\bibitem[{{Pechenick} {et~al.}(1983){Pechenick}, {Ftaclas}, \\& {Cohen}}]{pfc83}\n{Pechenick}, K.~R., {Ftaclas}, C., \\& {Cohen}, J.~M. 1983, \\apj, 274, 846\n\n\\bibitem[{{Pravdo} {et~al.}(1997){Pravdo}, {Angelini}, \\& {Harding}}]{pravdo97}\n{Pravdo}, S.~H., {Angelini}, L., \\& {Harding}, A.~K. 1997, \\apj, 491, 808+\n\n\\bibitem[{{Strohmayer}(1992)}]{stroh92}\n{Strohmayer}, T.~E. 1992, \\apj, 388, 138\n\n\\bibitem[{{Vaughan} {et~al.}(1994{\\natexlab{a}}){Vaughan}, {van Der Klis},\n {Lewin}, {Wijers}, {van Paradijs}, {Dotani}, \\& {Mitsuda}}]{vaughan94b}\n{Vaughan}, B., {van Der Klis}, M., {Lewin}, W. H.~G., {Wijers}, R. A. M.~J.,\n {van Paradijs}, J., {Dotani}, T., \\& {Mitsuda}, K. 1994{\\natexlab{a}}, \\apj,\n 421, 738\n\n\\bibitem[{{Vaughan} {et~al.}(1998){Vaughan}, {van der Klis}, {M\\'endez}, {van\n Paradijs}, {Wijnands}, {Lewin}, {Lamb}, {Psaltis}, {Kuulkers}, \\&\n {Oosterbroek}}]{vaughan98}\n{Vaughan}, B.~A., {van der Klis}, M., {M\\'endez}, M., {van Paradijs}, J.,\n {Wijnands}, R. A.~D., {Lewin}, W. H.~G., {Lamb}, F.~K., {Psaltis}, D.,\n {Kuulkers}, E., \\& {Oosterbroek}, T. 1998, \\apjl, 509, L145\n\n\\bibitem[{{Vaughan} {et~al.}(1994{\\natexlab{b}}){Vaughan}, {van Der Klis},\n {Wood}, {Norris}, {Hertz}, {Michelson}, {van Paradijs}, {Lewin}, {Mitsuda},\n \\& {Penninx}}]{vaughan94a}\n{Vaughan}, B.~A., {van Der Klis}, M., {Wood}, K.~S., {Norris}, J.~P., {Hertz},\n P., {Michelson}, P.~F., {van Paradijs}, J., {Lewin}, W. H.~G., {Mitsuda}, K.,\n \\& {Penninx}, W. 1994{\\natexlab{b}}, \\apj, 435, 362\n\n\\bibitem[{{Wijnands} \\& {van der Klis}(1998)}]{wk98}\n{Wijnands}, R. \\& {van der Klis}, M. 1998, \\nat, 394, 344\n\n\\bibitem[{{Wijnands} \\& {van der Klis}(1999)}]{wk99}\n---. 1999, \\apj, 514, 939\n\n\\end{thebibliography}"
}
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astro-ph0002053
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Black hole X-ray binaries:\\ A new view on soft-hard spectral transitions
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[
{
"author": "F. Meyer \\inst{1}"
},
{
"author": "B.F. Liu \\inst{1}\\inst{,2}"
},
{
"author": "E. Meyer-Hofmeister \\inst{1}"
}
] |
The theory of coronal evaporation predicts the formation of an inner hole in the cool thin accretion disk for mass accretion rates below a certain value ($\approx$ 1/50 of the Eddington mass accretion rate) and the sudden disappearance of this hole when the mass accretion rate rises above that value. The inner edge of the standard thin disk then suddenly shifts inward vvvvfrom about a few hundred Schwarzschild radii to the last stable orbit. This appears to quantitatively account for the observed transitions between hard and soft spectral states at critical luminosities. Due to the evaporation process the matter accreting in the geometrically thin disk changes to a hot coronal flow which proceeds towards the black hole as an advection-dominated accretion flow (ADAF; for a review see Narayan et al. 1998). \keywords{accretion disks -- black hole physics -- X-rays: stars -- stars: individual: Cygnus X-1, Nova Muscae 1991}
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[
{
"name": "LBm102.tex",
"string": "\\documentclass{aa} % <-- \"class\" anstelle von \"style\"\n\\usepackage{amssymb,graphicx} % <-- \"graphicx\" fuer Bilder, \"amssymb\"\n\t\t\t % fuer einige besondere\n\t\t\t % mathematische Symbole\n\n\\sloppy\n\n\\begin{document}\n\n\\thesaurus{06 (02.01.2 - 08.02.1 - 02.02.1 - 13.25.5 - 08.09.2 A0620-00)}\n\n\\title{Black hole X-ray binaries:\\\\\n A new view on soft-hard spectral transitions}\n\\author{F. Meyer \\inst{1}, B.F. Liu \\inst{1}\\inst{,2}, E. Meyer-Hofmeister \\inst{1}\n}\n\\offprints{Emmi Meyer-Hofmeister}\n\\institute{Max-Planck-Institut f\\\"ur Astrophysik, Karl\nSchwarzschildstr.~1, D-85740 Garching, Germany\n\\and\nYunnan Observatory, Academia Sinica. P.O.Box 110, Kunming 650011, China\n} \n\n% figures cygx1_bw.ps, fig_1_ws_new.eps, fig_2_ws_new.eps\n% figures LBm102.f1 LBm102.f2 LBm102.f3\n\\date{Received:s / Accepted:}\n\\titlerunning {Black hole X-ray binaries:soft-hard spectral transitions}\n\\maketitle\n\n\\begin{abstract}\n\nThe theory of coronal evaporation predicts the formation of an\ninner hole in the cool thin accretion disk for mass accretion rates\nbelow a certain value ($\\approx$ 1/50 of the Eddington mass\naccretion rate) and the sudden disappearance of this hole when\nthe mass accretion rate rises above that value.\nThe inner edge of the standard thin disk then suddenly shifts inward\nvvvvfrom about a few hundred Schwarzschild radii to the last stable orbit.\nThis appears to quantitatively account for the observed transitions\nbetween hard and soft spectral states at critical luminosities.\nDue to the evaporation process the matter accreting in the geometrically\nthin disk changes to a hot coronal flow which proceeds towards the\nblack hole as an advection-dominated accretion flow (ADAF; for a\nreview see Narayan et al. 1998). \n\\keywords{accretion disks -- black hole physics --\n X-rays: stars -- stars: individual: Cygnus X-1, Nova Muscae 1991}\n\\end{abstract}\n\n\n\\section{Introduction}\nFor a decade it has been known that the spectra of X-ray novae\nshow changes from a soft state at high luminosity to a hard \nstate when the luminosity has declined during the outburst\n(Tanaka 1989). The persistent canonical black hole\nsystem Cyg X-1 also undergoes occasional transitions between its standard low\nluminosity (hard) state and a soft state (see Fig. 1). Such changes\nbetween the two spectral states have been observed for several\nsystems, regardless of whether the compact object is a neutron star\n(Aql X-1, 1608-522) or a black hole (GS/GRS 1124-684, GX 339-4)\n(Tanaka \\& Shibazaki 1996). Here we concentrate on black hole sources. \nObservations show that the phenomenon always occurs at a luminosity around\n$10^{37}\\rm{erg/s}$, which corresponds to a mass accretion rate of\nabout $10^{17}\\rm{g/s}$ (Tanaka 1999).\n\nThe two spectral states are thought to be related to different states\nof accretion:\n(1) the soft spectrum originates from a thin disk which extends down\nto the last stable orbit plus a corona above the disk, \n(2) the hard spectrum originates from a thin disk outside a\ntransition radius $r_{tr}$ and a coronal flow/ ADAF\ninside. The spectral\ntransitions of Nova Muscae 1991 and Cygnus X-1 were modelled based on\nthis picture by Esin et al. (1997, 1998). The value of $r_{tr}$ was\ntaken as the maximal distance $r$ for which an ADAF with that accretion\nrate can exist (``strong ADAF proposal\", Narayan \\& Yi 1995). \nWe determine the location of the inner edge of the thin disk from the\nequilibrium between it and the corona above. \n\n\\section{Generation of the coronal flow}\n\\subsection{Evaporation}\nThe equilibrium between the cool accretion disk and the corona\nabove (Meyer \\& Meyer-Hofmeister 1994) is established in the following\nway. Frictional heat released in the\ncorona flows down into cooler and denser transition layers. There it\nis radiated away if the density is sufficiently high. If the density is\ntoo low, cool matter is heated up and evaporated into the corona until\nan equilibrium density is established (Meyer 1999).\n\n\n\nMass drained from the corona by an inward drift is replaced by mass\nevaporating from the thin disk as the system establishes a stationary state.\nWhen the evaporation rate exceeds the mass flow rate in the cool disk\nthe disk terminates. Inside only a hot coronal flow exists.\n\n\\begin{figure}[ht]\n\\includegraphics[width=8.3cm]{LBm102.f1}\n\\caption{Transition from the hard spectrum on 26/3/1996 to a soft\nspectrum on 30/5/1996, observed for Cygnus X-1 (from M. Gilfanov,\nE. Churazov, M.G. Revnivtsev, in preparation)}\n\\end{figure}\n\n\n\\subsection{Physics of the corona}\nMass flow in the corona is similar to that in the thin disk.\nDifferential (Kepler-like) rotation causes transfer of angular momentum\noutwards and mass flow inwards. The corona is geometrically much\nthicker than the disk underneath. Therefore sidewise energy\ntransport is not negligible. Sidewise advection, heat conduction\ndownward, radiation from the hot optically thin gas flow and \nwind loss are all important for the equilibrium between corona and thin\ndisk. A detailed description would demand the solution of a set of partial\ndifferential equations in radial distance $r$ and vertical height $z$.\nIn particular a sonic transition requires treatment of a free\nboundary condition on an extended surface. \n\n\nFrom simplified modelling and analysis we find the\nfollowing pattern of coronal flow. When a hole in the thin disk\nexists there are three regimes with increasing distance from the black hole.\n(1) Near the inner edge of the thin disk\nthe gas flows towards the black hole. (2) At\nlarger $r$ wind loss is important taking away about 20\\% of the total\nmatter inflow. (3) At even larger distances some matter\nflows outward in the corona as a consequence of conservation of angular\nmomentum. One might compare this with the\nflow in a ``free'' thin disk without the tidal forces acting in a\nbinary. In such a disk matter flows inward in the inner region and\noutward in the outer region, with conservation of the total mass and\nangular momentum (Pringle 1981). \n\n\n\\subsection{Model}\nWe model the equilibrium between corona and thin disk in a simplified\nway. This is possible since the evaporation process is concentrated\nnear the inner edge of the thin disk. Thus the corona above the\ninnermost zone of the disk dominates the global structure. Further\ninward there is no thin disk anymore. The representative dominant region\nfrom $r$ to $r$+$\\Delta r$ has to be chosen such that evaporation\nfurther outward is not important. One incorporates the effects of\nfrictional heat generation, conduction, radiation, sidewise loss of\nenergy and wind loss at large height into this one zone\n( ``one-zone-model''). A set of ordinary differential equations for mass,\nmotion, and energy with boundary conditions at the bottom (downward\nthermal flux \\,-\\, pressure relation) and at the top (sonic\ntransition) {\\it{uniquely}}\ndetermine mass accretion rate, wind loss and temperature in the corona\nas a function of radius. We restrict the analysis to a stationary corona.\n\n\nThe evaporation process was first investigated for disks in dwarf nova\nsystems (Meyer \\& Meyer-Hofmeister 1994, Liu et al 1995). The\nsituation is similar for disks around black holes (Meyer 1999). The\ncoronal gas flowing into the hole and replaced by evaporation from the\ndisk is understood as the supply for an ADAF which was used successfully to\nmodel the spectra of several black hole sources. A recent review by\nNarayan et al. (1998) gives a detailed description of accretion in the\nvicinity of a black hole.\n \n\n\\section{Computational results}\n\n\\subsection{The critical mass flow rate ${\\dot M_{\\rm{crit}}}$} \nWe use the same equations as Liu et al. (1995).\nThe efficiency of evaporation at given distance $r$ from the\ncompact star determines the location of the inner edge of the thin\ndisk $r_{\\rm{tr}}$. The relation between the mass flow rate ${\\dot M}$\nin the disk and $r_{\\rm{tr}}$ was now computed also for black\nhole systems. In Fig. 2 we show this relation for a 6 $M_\\odot$\nblack hole (viscosity parameter $\\alpha$=0.3). \n\n\nUp to now only the decreasing branch was known and investigated.\nThe interesting new feature is that the efficiency\nof evaporation reaches a maximum. This means that as the mass\naccretion rate in the disk is increased the inner edge moves inward, but\nif the rate exceeds a critical value $\\dot M_{\\rm{crit}}$ the\nthin disk can no longer be fully depleted by evaporation (for this accretion rate the\ninner disk edge is at about 340 Schwarzschild radii). The thin disk then\nextends inward towards the last stable orbit.\n\n\\begin{figure}[ht]\n\\includegraphics[width=7.5cm]{LBm102.f2}\n\\caption{\nSolid lines: rate of inward mass flow $\\dot M$(in g/s) in the\ncorona (= evaporation rate), maximum temperature in the corona and $h/r$\n(h pressure scaleheight) at the inner edge $r$=$r_{\\rm{tr}}$ of the\nstandard thin disk. Dashed line: virial temperature.}\n\\end{figure}\n\nThe temperature in the corona increases with decreasing radius, but\nreaches a saturation value where the coronal mass flow reaches maximum.\nThe value h in Fig. 2 is the height where the pressure has\ndecreased by 1/e.\n\n\\subsection{What causes the maximum of the coronal mass flow rate?}\nA change in the physical process that removes the heat released by friction\nis the cause for the maximum of the coronal mass flow rate seen in\nFig. 2. A dimensional analysis of the equations\nyields the following result. \nFor large inner radii coronal heating is balanced by inward advection \nand wind loss. This fixes the coronal temperature at about 1/8 of the\nvirial temperature $T_{\\rm{v}}$\n($\\Re T_{\\rm v}/\\mu=GM/r$, $\\Re$ gas constant, $\\mu$ molecular weight,\n$G$ gravitational constant) (see Fig. 2). Downward heat conduction and\nsubsequent radiation \nin the denser lower region play a minor role for the energy loss though \nthey always establish the equilibrium density in the corona above the \ndisk.\n\nWith rising temperature, thermal heat conduction removes an increasing\npart of the energy released and finally becomes dominant.\nFor optically thin bremsstrahlung the temperature saturates at a\nuniversal value defined by a combination of conductivity and\nradiation coefficients, the Boltzmann and the gas constant, and the\nnon-dimensional $\\alpha$-parameter of friction, (see Fig. 2). Dimensional\nanalysis of the equations yields the rate of mass accretion through the \ncorona as a function of temperature divided by the\nKepler frequency $(GM/r^3)^{1/2}$. For small radii this gives the \n$r^{3/2}$ law in Fig. 2. \n\n\nThe maximum accretion rate occurs where the \nsub-virial temperature for large radii reaches the saturation temperature \nfor small radii. Since the virial temperature is proportional to $M/r$, \nthis radius $r_{\\rm{crit}}$ is proportional to $M$. Then the\naccretion rate, proportional to the inverse of the Kepler frequency, also \nbecomes proportional to $M$. \n\n\n\\subsection{Approximations used for our model} \nSynchrotron and Compton cooling have been left out. Synchrotron cooling\nis non-dominant as long as the magnetic energy density stays below roughly\n1/3 of the pressure. Compton cooling and heating by photons from the\ndisk surface and from the accretion centre are non-dominant at all\ndistances larger than that of the peak of the coronal mass flow rate,\n$r\\ge r_{\\rm{crit}}$ ($\\approx 340 {R_s}$, Fig. 2). They become\nimportant for smaller radii.\n\nThe conductive flux remains small compared to the upper limit,\nthe transport by free streaming electrons, so that classical\nthermal heat conduction is a good approximation.\nWe have neglected lateral heat inflow by thermal conduction. \nThis term is small compared to the dominant advective and wind\nlosses at large radii, and vanishes\nwhen the temperature becomes constant at small radii. \n\nTemperature equilibrium between electrons and ions requires that\nthe collision times between them remains shorter than \nthe heating timescale. This holds for $r\\ge r_{\\rm{crit}}$, but\nthe condition fails for $r < r_{\\rm{crit}}$ where a two temperature\ncorona can develop.\n\n\nTangled coronal magnetic fields\ncould reduce electron thermal conductivity. We note\nhowever that reconnection and evaporation tend to establish a rather\ndirect magnetic path between disk and corona.\n\n \n\\section{Spectral transitions}\n\n\\subsection{Predictions from the evaporation model}\nAt maximum luminosity of an X-ray nova outburst the mass accretion\nrate is high and the thin disk extends inward to the last stable\norbit. A corona exists above the thin disk, but the mass flow in the\nthin disk is so high that no hole appears.\nIn decline from outburst the mass accretion rate decreases. When\n${\\dot M_{\\rm{crit}}}$ is reached a hole forms at $\\approx$\n340 ${R_s}$ and the transition soft/hard occurs.\nIf the mass accretion rate varies up and down as in high-mass X-ray\nbinaries we expect hard/soft and soft/hard transitions. \nIn Fig. 3 we show the expected behaviour schematically.\n\n\nThe descending branch for smaller $r$ indicates the possibility that an\ninterior disk could form. We note that a gap exists between the exterior\nstandard thin disk and an interior disk. In this gap the flow assumes\nthe character of an ADAF with different temperature of ions and\nelectrons, due to its high temperature and poor collisional\ncoupling. This provides the possibility that the interior disk fed by\nthis flow has a two temperature corona on top, different from a\nstandard thin disk plus corona in the high state. We will discuss this\nin a further investigation.\n\n\\begin{figure}[ht]\n\\includegraphics[width=8.3cm]{LBm102.f3}\n\\caption{\nEvaporation rate ${\\dot M(r)}$ as in Fig. 2. Inward extension of the standard\nthin disk for 3 different mass flow rates ${\\dot M}$ in the thin\ndisk (schematic). Note\nthat the standard thin disk reaches inward towards the black hole if \n${\\dot M} \\ge {\\dot M_{\\rm{crit}}}$. Shown also the type of spectrum,\nsoft or hard, related to ${\\dot M}$}.\n\\end{figure}\n\n\n\\subsection{Comparison with observations}\n\nThe three persistent (high-mass) black hole X-ray sources LMC X-1,\nLMC X-3 and Cyg X-1 show a different behaviour. LMC X-1 is always \nin the soft state (Schmidtke et al. 1999). For LMC X-3, most of the time in the\nsoft state, recently recurrent hard states have been detected \n(Wilms et al. 1999). Cyg X-1 spends most of its time in the hard\nstate with occasional transitions to the soft state (see e.g. Fig. 1).\nThis can be interpreted as caused by different long-term mean mass transfer\nrates: the highest rate (scaled to Eddington luminosity) in LMC X-1,\nthe lowest in Cyg X-1, and in between in LMC X-3.\nTransient sources show a soft/hard transition during the decay from\noutburst. The best studied source is the X-ray Nova Muscae 1991\n(Cui et al. 1997).\n\nThe transition always occurs around $L_X\\approx10^{37}$ erg/s (Tanaka 1999).\nOur value for the critical mass accretion rate for a 6 $M_\\odot$ black\nhole, $10^{17.2}$g/s, corresponds to a standard accretion disk\nluminosity of about $10^{37.2}$ erg/s. This is very close agreement.\n\nFor accretion rates below ${\\dot M_{\\rm{crit}}}$ the location of the\ninner edge of the standard thin disk derived from the evaporation\nmodel also agrees with observations (Liu et al. 1999).\n\nAt the moment of spectral transition our model predicts the inner edge\nnear 340 Schwarzschild radii. The observed timescale for the spectral\ntransition of a few days (Zhang et al. 1997) agrees with the time one\nobtains for the formation of a disk at 340 ${R_s}$ with an accretion\nrate ${\\dot M_{\\rm{crit}}}$. \n\n \nBut even in the low state X-ray observations of a reflecting component\nindicates the existence of a disk further inward, at 10 to 25 ${R_s}$\n(Gilfanov et al. (1998), Zycki et al. (1999)). This might point to\na non-standard interior disk as discussed above and explain why the\nspectral transitions in Cygnus X-1 could be well fitted by Esin et\nal. (1998) with a disk reaching inward to $\\le 100 {R_s}$. \n\n\n\\section{Conclusions}\n\nWe understand the spectral transition as related to a critical mass\naccretion rate. For rates ${\\dot M} \\ge {\\dot M_{\\rm{crit}}}$ \n(the peak coronal mass flow rate) the standard disk reaches inward\nto the last stable orbit and the spectrum is soft. Otherwise the ADAF\nin the inner accretion region provides a hard spectrum.\nAt ${\\dot M_{\\rm{crit}}}$ the transition between dominant advective\nlosses further out and\ndominant radiative losses further in occurs. Except for the difference\nbetween the sub-virial temperature of the corona and the\ncloser-to-virial temperature of an ADAF of the\nsame mass flow rate, this same critical radius is predicted by the\n``strong ADAF proposal\"\n(Narayan \\& Yi (1995). In general however, the strong ADAF\nproposal results in an ADAF region larger than that which the evaporation\nmodel yields.\n\n\nThe transition between the two spectral states has been observed\nfor black hole and neutron star systems, in persistent and transient\nsources (Tanaka \\& Shibazaki 1996, Campana et al.1998). This\npoints to similar physical accretion processes. Menou et al. (1999) already\ndiscussed the accretion via an ADAF in neutron star transient\nsources. Our results should also be applicable.\n\nThe relations for a 6 $M_\\odot$ black hole plotted in Fig. 2 can be\nscaled to other masses: in units of\nSchwarzschild radii and Eddington accretion rates the plot is\nuniversal. The application to disks around supermassive black holes\nimplies interesting conclusions for AGN. \n\n\n\n\\begin{acknowledgements}\nWe thank Marat Gilfanov, Eugene Churazov and Michael Revnivtsev for the\nspectral data of Cygnus X-1.\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}\n{}\n\\bibitem{ref:5} Campana S., Colpi M., Mereghetti S., 1998, A\\&A\nRev. 8, 269\n\\bibitem{ref:10} Cui W., Zhang S.N., Focke W. et al., 1997, ApJ 484,383\n\\bibitem{ref:19} Esin A.A., McClintock J.E, Narayan R., 1997, ApJ 489,\n865\n\\bibitem{ref:30} Esin A.A., Narayan R., Cui W. et al., 1998, ApJ\n505, 854\n\\bibitem{ref:33} Gilfanov M., Churazov E., Sunyaev R., 1998, in: 18th\nTexas Symposium on Relativistic Astrophysics and Cosmology, eds.\nA.V. Olinto et al.; World Scientific, p.735\n\\bibitem{ref:35} Liu B.F., Yuan W., Meyer F. et al., 1999, ApJ 527, L17\n\\bibitem{ref:40} Liu F.K., Meyer F., Meyer-Hofmeister E., 1995, A\\&A\n300, 823\n\\bibitem{ref:50} Menou K., Esin A., Narayan R. et al., 1999, ApJ \n520, 276\n\\bibitem{ref:52} Meyer F., 1999, in: Proc. of Disk Instabilities,\neds. S. Mineshige and J.C. Wheeler, Univ. Academic Press, Kyoto, p.209 \n\\bibitem{ref:55} Meyer F., Meyer-Hofmeister E. 1994, A\\&A 288, 175\n\\bibitem{ref:81} Narayan R., Mahadevan R., Quartaert E., 1998, in:\nThe Theory of Black Hole Accretion Discs, eds. M.A. Abramowicz et al.,\nCambridge University Press, p.148\n\\bibitem{ref:82} Narayan R., Yi, 1995, ApJ 452, 710\n\\bibitem{ref:83} Pringle J.,1981, Ann. Rev. Astron. Astrophys. 137\n\\bibitem{ref:831} Schmidtke P.C., Ponder A.L., Cowley A.P., 1999,\nAstron.J., 117, 1292\n\\bibitem{ref:84} Tanaka Y.,1989, in: Proc. 23rd ESLAB Symp. Two-Topics\nX-Ray Astronomy, Bologna ESA SP-296, p.3\n\\bibitem{ref:85} Tanaka Y.,1999, in: Proc. of Disk\nInstablities in Close Binary Systems, eds. S. Mineshige and\nJ.C. Wheeler, Universal Academic Press, Kyoto, p.21\n\\bibitem{ref:87} Tanaka Y., Shibazaki N., 1996, ARA\\&A, 34, 607\n\\bibitem{ref:90} Wilms J., Nowak M.A., Pottschmidt K., et al. 1999,\nastro-ph 9910508\n%in: Proc. ESO Workshop on Black Holes in Binaries and Galactic Nuclei,\n%eds. L. Kaper, et al., Lecture Notes in Physics, in print \n\\bibitem{ref:95} Zhang S.N., Cui W., Harmon B.A. et al., 1997, ApJ\n477, L95\n\\bibitem{ref:100} Zycki T., Done C., Smith D.A., 1999, MNRAS 305, 231\n\n\\end{thebibliography}\n \n\\end{document}\n\n\n\n"
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"name": "astro-ph0002053.extracted_bib",
"string": "\\begin{thebibliography}\n{}\n\\bibitem{ref:5} Campana S., Colpi M., Mereghetti S., 1998, A\\&A\nRev. 8, 269\n\\bibitem{ref:10} Cui W., Zhang S.N., Focke W. et al., 1997, ApJ 484,383\n\\bibitem{ref:19} Esin A.A., McClintock J.E, Narayan R., 1997, ApJ 489,\n865\n\\bibitem{ref:30} Esin A.A., Narayan R., Cui W. et al., 1998, ApJ\n505, 854\n\\bibitem{ref:33} Gilfanov M., Churazov E., Sunyaev R., 1998, in: 18th\nTexas Symposium on Relativistic Astrophysics and Cosmology, eds.\nA.V. Olinto et al.; World Scientific, p.735\n\\bibitem{ref:35} Liu B.F., Yuan W., Meyer F. et al., 1999, ApJ 527, L17\n\\bibitem{ref:40} Liu F.K., Meyer F., Meyer-Hofmeister E., 1995, A\\&A\n300, 823\n\\bibitem{ref:50} Menou K., Esin A., Narayan R. et al., 1999, ApJ \n520, 276\n\\bibitem{ref:52} Meyer F., 1999, in: Proc. of Disk Instabilities,\neds. S. Mineshige and J.C. Wheeler, Univ. Academic Press, Kyoto, p.209 \n\\bibitem{ref:55} Meyer F., Meyer-Hofmeister E. 1994, A\\&A 288, 175\n\\bibitem{ref:81} Narayan R., Mahadevan R., Quartaert E., 1998, in:\nThe Theory of Black Hole Accretion Discs, eds. M.A. Abramowicz et al.,\nCambridge University Press, p.148\n\\bibitem{ref:82} Narayan R., Yi, 1995, ApJ 452, 710\n\\bibitem{ref:83} Pringle J.,1981, Ann. Rev. Astron. Astrophys. 137\n\\bibitem{ref:831} Schmidtke P.C., Ponder A.L., Cowley A.P., 1999,\nAstron.J., 117, 1292\n\\bibitem{ref:84} Tanaka Y.,1989, in: Proc. 23rd ESLAB Symp. Two-Topics\nX-Ray Astronomy, Bologna ESA SP-296, p.3\n\\bibitem{ref:85} Tanaka Y.,1999, in: Proc. of Disk\nInstablities in Close Binary Systems, eds. S. Mineshige and\nJ.C. Wheeler, Universal Academic Press, Kyoto, p.21\n\\bibitem{ref:87} Tanaka Y., Shibazaki N., 1996, ARA\\&A, 34, 607\n\\bibitem{ref:90} Wilms J., Nowak M.A., Pottschmidt K., et al. 1999,\nastro-ph 9910508\n%in: Proc. ESO Workshop on Black Holes in Binaries and Galactic Nuclei,\n%eds. L. Kaper, et al., Lecture Notes in Physics, in print \n\\bibitem{ref:95} Zhang S.N., Cui W., Harmon B.A. et al., 1997, ApJ\n477, L95\n\\bibitem{ref:100} Zycki T., Done C., Smith D.A., 1999, MNRAS 305, 231\n\n\\end{thebibliography}"
}
] |
astro-ph0002054
|
Thomson Thick X-ray Absorption in a Broad Absorption Line Quasar PG0946+301
|
[
{
"author": "S. Mathur\\altaffilmark{1,2}"
},
{
"author": "P. J. Green\\altaffilmark{2}"
},
{
"author": "N. Arav\\altaffilmark{3}"
},
{
"author": "M. Brotherton\\altaffilmark{4}"
},
{
"author": "M. Crenshaw\\altaffilmark{5}"
},
{
"author": "M. deKool\\altaffilmark{6}"
},
{
"author": "M. Elvis\\altaffilmark{2}"
},
{
"author": "R. W. Goodrich\\altaffilmark{7}"
},
{
"author": "F. Hamann\\altaffilmark{8}"
},
{
"author": "D. C. Hines\\altaffilmark{9}"
},
{
"author": "V. Kashyap\\altaffilmark{2}"
},
{
"author": "K. Korista\\altaffilmark{10}"
},
{
"author": "B. M. Peterson\\altaffilmark{1}"
},
{
"author": "J. Shields\\altaffilmark{11}"
},
{
"author": "I. Shlosman\\altaffilmark{12}"
},
{
"author": "W. van Breugel\\altaffilmark{13} M. Voit\\altaffilmark{14}"
}
] |
We present a deep ASCA observation of a Broad Absorption Line Quasar (BALQSO) PG0946+301. The source was clearly detected in one of the gas imaging spectrometers, but not in any other detector. If BALQSOs have intrinsic X-ray spectra similar to normal radio-quiet quasars, our observations imply that there is Thomson thick X-ray absorption (N$_H$\gax$10^{24}$ cm$^{-2}$) toward PG0946+301. This is the largest column density estimated so far toward a BALQSO. The absorber must be at least partially ionized and may be responsible for attenuation in the optical and UV. If the Thomson optical depth toward BALQSOs is close to one, as inferred here, then spectroscopy in hard X-rays with large telescopes like XMM would be feasible.
|
[
{
"name": "astro-ph0002054.tex",
"string": "%%\n%% Beginning of file 'sample.tex'\n%%\n%% Modified 03 Nov 99\n%%\n%% This is a sample manuscript marked up using the\n%% AASTeX v5.0 LaTeX 2e macros.\n\n%% The first piece of markup in an AASTeX v5.0 document\n%% is the \\documentclass command. LaTeX will ignore\n%% any data that comes before this command.\n\n%% The command below calls the default manuscript style,\n%% which will produce a double-spaced document on one column.\n%% Examples of commands for other substyles follow. Use\n%% whichever is most appropriate for your purposes.\n\n% \\documentclass{aastex}\n\n%% preprint produces a one-column, single-spaced document:\n\n% \\documentclass[preprint]{aastex}\n\n%% preprint2 produces a double-column, single-spaced document:\n\n \\documentclass[preprint2]{aastex}\n\n%% If you want to create your own macros, you can do so\n%% using \\newcommand. Your macros should appear before\n%% the \\begin{document} command.\n%%\n%% If you are submitting to a journal that translates manuscripts\n%% into SGML, you need to follow certain guidelines when preparing\n%% your macros. See the AASTeX v5.0 Author Guide\n%% for information.\n\n%\\newcommand{\\vdag}{(v)^\\dagger}\n%\\newcommand{\\myemail}{[email protected]}\n\n\\def\\lax {${_<\\atop^{\\sim}}$}\n\\def\\gax {${_>\\atop^{\\sim}}$}\n\\def\\aox {$\\alpha_{ox}$}\n\\def\\etal {{\\it et al.}~}\n\\def\\lya {Ly$\\alpha$}\n\\def\\kms {km s$^{-1}$}\n\n%% You can insert a short comment on the title page using the command below.\n\n%\\slugcomment{Not to appear in Nonlearned J., 45.}\n\n%% If you wish, you may supply running head information, although\n%% this information may be modified by the editorial offices.\n%% The left head contains a list of authors,\n%% usually a maximum of three (otherwise use et al.). The right\n%% head is a modified title of up to roughly 44 characters. Running heads\n%% will not print in the manuscript style.\n\n\\shorttitle{Mathur et al.}\n\\shortauthors{Thomson Thick Absorption in a BALQSO}\n\n\n%% This is the end of the preamble. Indicate the beginning of the\n%% paper itself with \\begin{document}.\n\n\\begin{document}\n\n%% LaTeX will automatically break titles if they run longer than\n%% one line. However, you may use \\\\ to force a line break if\n%% you desire.\n\n\\title{Thomson Thick X-ray Absorption in a Broad Absorption Line Quasar\nPG0946+301 }\n\n\n%% Use \\author, \\affil, and the \\and command to format\n%% author and affiliation information.\n%% Note that \\email has replaced the old \\authoremail command\n%% from AASTeX v4.0. You can use \\email to mark an email address\n%% anywhere in the paper, not just in the front matter.\n%% As in the title, you can use \\\\ to force line breaks.\n\n\\author{S. Mathur\\altaffilmark{1,2}, P. J. Green\\altaffilmark{2},\nN. Arav\\altaffilmark{3},\nM. Brotherton\\altaffilmark{4},\nM. Crenshaw\\altaffilmark{5},\n M. deKool\\altaffilmark{6},\nM. Elvis\\altaffilmark{2},\nR. W. Goodrich\\altaffilmark{7},\nF. Hamann\\altaffilmark{8},\n D. C. Hines\\altaffilmark{9},\nV. Kashyap\\altaffilmark{2},\nK. Korista\\altaffilmark{10},\n B. M. Peterson\\altaffilmark{1},\nJ. Shields\\altaffilmark{11},\n I. Shlosman\\altaffilmark{12},\n W. van Breugel\\altaffilmark{13}\nM. Voit\\altaffilmark{14}\n}\n\n\n%\\author{C. D. Biemesderfer\\altaffilmark{4,5}}\n%\\affil{National Optical Astronomy Observatories, Tucson, AZ 85719}\n%\\email{[email protected]}\n\n%\\and\n\n%\\author{R. J. Hanisch\\altaffilmark{5}}\n%\\affil{Space Telescope Science Institute, Baltimore, MD 21218}\n\n%% Notice that each of these authors has alternate affiliations, which\n%% are identified by the \\altaffilmark after each name. Specify alternate\n%% affiliation information with \\altaffiltext, with one command per each\n%% affiliation.\n\n\\altaffiltext{1}{The Ohio State Univ., [email protected]}\n\\altaffiltext{2}{Harvard Smithsonian Center for Astrophysics}\n\\altaffiltext{3}{University of California, Berkeley}\n\\altaffiltext{4}{NOAO, Tucson, Arizona}\n\\altaffiltext{5}{Catholic\nUniversity of America and NASA's Goddard Space Flight Center}\n\\altaffiltext{6}{RSAA, ANU, Australia}\n\\altaffiltext{7}{The W. M. Keck Observatory, Hawaii}\n\\altaffiltext{8}{University of Florida}\n\\altaffiltext{9}{Steward Observatory, The University of Arizona}\n\\altaffiltext{10}{Western\nMichigan University}\n\\altaffiltext{11}{Ohio University}\n\\altaffiltext{12}{University of Kentucky}\n\\altaffiltext{13}{LLNL}\n\\altaffiltext{14}{Space Telescope Science Institute}\n\n\n%% Mark off your abstract in the ``abstract'' environment. In the manuscript\n%% style, abstract will output a Received/Accepted line after the\n%% title and affiliation information. No date will appear since the author\n%% does not have this information. The dates will be filled in by the\n%% editorial office after submission.\n\n\\begin{abstract}\n\n We present a deep ASCA observation of a Broad\n Absorption Line Quasar (BALQSO) PG0946+301. The source was clearly detected\n in one of the gas imaging spectrometers, but not in any other\n detector. If BALQSOs have intrinsic X-ray spectra similar to normal\n radio-quiet quasars, our observations imply that there is Thomson\n thick X-ray absorption (N$_H$\\gax$10^{24}$ cm$^{-2}$) toward\n PG0946+301. This is the largest column density estimated so far\n toward a BALQSO. The absorber must be at least partially ionized and\n may be responsible for attenuation in the optical and UV. If the\n Thomson optical depth toward BALQSOs is close to one, as inferred here,\n then spectroscopy in hard X-rays with large telescopes like XMM would\n be feasible.\n\n\\end{abstract}\n\n%% Keywords should appear after the \\end{abstract} command. The uncommented\n%% example has been keyed in ApJ style. See the instructions to authors\n%% for the journal to which you are submitting your paper to determine\n%% what keyword punctuation is appropriate.\n\n\\keywords{galaxies: active---quasars: absorption lines---quasars:\nindividual (PG0946+301)---X-rays: galaxies}\n\n\n%% From the front matter, we move on to the body of the paper.\n%% In the first two sections, notice the use of the natbib \\citep\n%% and \\citet commands to identify citations. The citations are\n%% tied to the reference list via symbolic KEYs. The KEY corresponds\n%% to the KEY in the \\bibitem in the reference list below. We have\n%% chosen the first three characters of the first author's name plus\n%% the last two numeral of the year of publication as our KEY for\n%% each reference.\n\n\\section{Introduction}\n\n About 10 - 15\\% of optically selected QSOs have optical/UV spectra\nshowing deep absorption troughs displaced blueward from the\ncorresponding emission lines.\n% in the high ionization transitions of\n% C\\,IV, Si\\,IV, N\\,V, and O\\,VI.\nThese broad absorption lines (BALs)\nare commonly attributed to material flowing toward the observer with\nvelocities of up to $\\sim 50,000~$ \\kms. BALQSOs are probably normal\nQSOs viewed at a fortuitous orientation passing through a BAL outflow,\nthus implying a BAL ``covering factor'' at least 10 - 15\\% in all\nQSOs. BALQSOs thus provide a unique probe of conditions near the\nnucleus of most QSOs. The absorbing columns typically inferred from\nthe UV spectra for the BAL clouds themselves are $N_{\\rm H}\\sim 10^{20-21}$\ncm$^{-2}$\n(Korista \\etal 1993). It has been noted, however, that UV studies\nunderestimate the BAL column densities because of saturation (Korista\n\\etal 1993, Arav 1997, Hamann 1998). BALQSOs, as a class, show higher\noptical/UV polarization than other radio-quiet QSOs (Schmidt \\&\nHines 1999, Ogle \\etal 1999). Polarization studies reveal multiple\nlines of sight through high column density gas (Goodrich \\& Miller\n1995, Cohen \\etal 1995).\n\n With the absorbing column densities as estimated from the earlier UV studies,\nwe\nwould have expected very little soft X-ray absorption in the BALQSOs.\nHowever, BALQSOs are found to be markedly underluminous in X-rays\ncompared to their non-BALQSO counterparts (Bregman 1984, Singh \\etal\n1987, Green et al. 1995). Green \\& Mathur (1996, here after GM96)\nstudied 11 BALQSOs observed with ROSAT and found that just one was\ndetected with \\aox \\footnote{The slope of a hypothetical power law\nconnecting 2500\\,\\AA~ and 2~keV is defined as \\aox\\, = $0.384~{\\rm\nlog} L_{opt}/L_x $, so that \\aox\\, is larger for objects with weaker\nX-ray emission relative to optical.} about 2. BALQSOs thus have unusually weak\nsoft X-ray emission, as evidenced by large \\aox (\\gax\n1.9. c.f. \\aox=1.51$\\pm0.01$, from Laor \\etal 1997, for radio-quiet\nquasars). If BALQSOs are indeed normal radio-quiet QSOs, then their\nweak X-ray flux is most likely due to strong\nabsorption. Unfortunately, due to the low observed flux, there are no\nobserved X-ray spectra of BALQSOs to confirm the absorption scenario,\nwith one exception, the archetype BALQSO PHL5200 (Mathur, Elvis \\&\nSingh 1995, here after MES95). The ASCA spectrum of PHL5200 is best\nfit by a power-law typical for non-BALQSOs in the 2--10 keV range,\nwith intrinsic absorption 2 to 3 orders of magnitude higher than\ninferred from UV spectra alone (MES95). However, the PHL5200 spectrum\nsuffers from a low signal to noise ratio, and while the above was a\npreferred fit, a model with no intrinsic absorption also fits the\ndata. Recently Gallagher \\etal (1999, hereafter G99) studied a sample\nof six new BALQSOs with ASCA, of which two were detected. G99 derived\ncolumn densities of \\gax 5$\\times 10^{23}$ cm$^{-2}$ to explain the\nnon-detections, even higher than the ROSAT estimates (assuming a neutral\nabsorber with solar abundances unless stated otherwise).\n\nHow are the X-ray and UV absorbers related to each other? Are they\nboth part of the same outflow? If so, then the kinetic energy carried\nout is a significant fraction of bolometric luminosity of the quasar\n(see Mathur, Elvis \\& Wilkes 1995 for a discussion). With all QSOs\nlikely to contain a BAL outflow, it becomes very important to measure the\nabsorbing column density accurately to understand the energetics and\ndynamics of quasars. We attempt this with a deep ASCA observation\nof a typical BALQSO, PG0946+301.\n\n\\section{Observations and Data Analysis}\n\n\\subsection{Observations}\n\n We observed PG0946+301 with ASCA (Tanaka \\etal 1994) on 1998 November\n 12. ASCA contains two sets of two detectors, SIS (Solid-state\nImaging Spectrometer) and GIS (Gas Imaging Spectrometer). The\neffective exposure times in SIS0, SIS1, GIS2 and GIS3 were 72,024\nseconds, 69,668 seconds, 80,910 seconds and 80,896 seconds\nrespectively. SIS was operated in 1CCD mode with the target in the\nstandard 1CCD mode position. GIS was operated in pulse height (PH)\nmode. The data were reduced and analyzed using FTOOLS and XSELECT in a\nstandard manner (see ASCA Data Reduction Guide or MES95 and G99 for\ndetails of data reduction).\n\n\\subsection{Image Analysis}\n\n\\subsubsection{XSELECT Analysis}\n\n We used XSELECT to create full and hard (2--9.5 keV) band images of\n for each of the four detectors. We also created combined SIS and GIS\n images. We looked for the target in these images displayed with\n SAOIMAGE. While there were sources seen within the GIS field of view,\n there was no obvious source seen at the target position in any of the\n four detectors. We then smoothed the images with a Gaussian function\n of $\\sigma=$ 1--2 pixels. A faint source at the position of the\n target was then evident in GIS3 hard band image and a trace of a\n source was seen in the full GIS image, but not in any other\n image. Note that for a standard pointing position the target lies\n closest to the optical axis in SIS0 and GIS3. GIS3 is more sensitive\n in hard X-rays than SIS0. The fact that the source is seen by eye in\n the GIS3 detector only suggests that the source is faint with flux\n mainly in the hard band.\n\n We extracted the total counts in a circular region with a\n3$^{\\prime}$ radius centered on the source position. Because our\nsource is observed to be so faint, background subtraction is crucial\nin determining the net source count rate, so we have done careful\nbackground subtraction using different background estimates.\nBackground counts were extracted in two different ways: (1) from a\nsource-free region on the detector and (2) from exactly the same\nregion as the source in the blank sky background files provided by the\nASCA guest observer facility. The significance of the source\ndetection was therefore different for different background\nestimates. For SIS, the blank sky background is underestimated because\nit is available in the BRIGHT mode only, while the source counts were\nextracted in the BRIGHT2 mode. So the SIS detections are less reliable\nwith background (2). We found that the source was detected in GIS3 and\nGIS3 hard band, and is marginally detected in SIS0 (2$\\sigma$). It\nwas not detected in any other detector in either bandpass. The\nsignificance of detection for the source in different detectors and\nthe resulting net count rate is given in Table 1. For non-detections,\nwe give a 3$\\sigma$ upper limit of the count rate (see G99 for exact\nformulation of the detection and corresponding count rate estimate).\n\n\\subsubsection{XIMAGE Analysis}\n\nDetermination of whether or not the source is detected is extremely\nimportant to our results. As an independent check, we performed image\nanalysis with XIMAGE (Giommi, Angellini, \\& White 1997) which is\ndesigned for detailed image analysis. The $\\sf detect$ algorithm in\nXIMAGE locates point sources in an image by means of a sliding-cell\nmethod. We used $\\sf detect$ on all of our images and looked for a\nsource at the position of the target. Again, we found the source to be\ndetected in GIS3 hard band. To minimize the number of spurious sources\ndetected, the threshold used by $\\sf detect$ is somewhat\nconservative. As a result, sources with intensity just above the image\nbackground can be missed. We found that the source was detected in the\nfull band GIS image if we lowered the detection threshold.\n The source was not detected in other detectors. These\nresults are consistent with those from the XSELECT analysis discussed\nabove.\n\n\\subsubsection{CIAO Analysis}\n\nWe applied more sophisticated wavelet-based techniques (Freeman \\etal 2000) to\nprovide\nindependent support to the above detections. Software developed for\n{\\sl Chandra Interactive Analysis of Observations} (CIAO) allows us to\ndecompose the image such that structures at different scales are\nenhanced. We analyzed the central $20'$ region of GIS3 images in both\nthe full spectral range and in the harder range. Wavelet analysis of\nthe GIS image at scales approximating the size of the point spread\nfunction shows that detection of PG0946+301 is complicated by the\npresence of a strong nearby source $\\sim 5'$ away. In the GIS hard\nband image, this source is significantly weaker, and we detect\nPG0946+301 at a probability of spurious detection of $10^{-4}$, with a\nnet count rate of $(1.26 \\pm 0.25) \\times 10^{-3}$ counts s$^{-1}$ (90\\%\nconfidence). This is consistent with the results discussed above.\n\n\n\\subsection{Column Density Constraints}\n\nConsistency among the methods discussed above gives us confidence\nin our measurements and in our resulting detections in GIS3 and\nnon-detections in other detectors. If the low observed X-ray count\nrate is due to intrinsic absorption, we can estimate the absorbing\ncolumn density in PG0946+301. Since the source did not yield enough\nnet counts in any detector to perform spectral analysis, we use the\nmethod discussed in GM96 to determine the column density. We first\ncalculate the flux from the source if there was no intrinsic\nabsorption. This was done using the observed $\\it B$ magnitude of the source\n($\\it B=16.0$ mag.) and assuming \\aox=1.6. Redshift of the source (z=1.216)\nand\nthe Galactic column density (N$_H=1.6\\times 10^{20}$ atoms cm$^{-2}$,\nMurphy \\etal 1996) were taken into account to predict the 2--10 keV\nflux in the observed band (=7.2$\\times 10^{-13}$ erg s$^{-1}$\ncm$^{-2}$). A power-law slope with photon index $\\Gamma=1.7$ was\nused. We then entered this model into the X-ray spectral analysis\nsoftware XSPEC (Arnaud 1996), with normalization consistent with the\nexpected flux and simulated spectra using SIS and GIS response\nmatrices. The response of the telescope and detectors was taken into\naccount as well.\n%by generating ``arf'' files with ``ascaarf'' using the same\n%region as used for the extraction of the source counts.\nThe column\ndensity at the redshift of the source was an additional parameter used\nin the simulation. If there was no intrinsic absorption, then the\npredicted count rate was found to be typically an order of magnitude\nlarger than the observed one. We then varied the value of the\nintrinsic absorption, keeping the normalization constant, until the\npredicted and observed column densities matched. The values of\nintrinsic column density estimated in this way are given in Table 2.\n\n This estimate of $N_{\\rm H}$ depends upon $\\Gamma$ and \\aox. Given the\n observed range of \\aox ($\\S1$), our adopted value of \\aox=1.6 gives\n conservative estimates of column densities. X-ray spectral slopes\n also vary among quasars. So we have estimated N$_H$ for $\\Gamma=2.0$\n as well as $\\Gamma=1.7$. Flatter spectra result in even higher\n derived column densities. As shown in Table 2, even the\n conservative estimate results in Thomson thick X-ray absorption in\n PG0946+301, i.e. N$_{\\rm H}$\\gax$10^{24}$ cm$^{-2}$. The column density\n estimates are consistent with the detection in GIS3 and non detection\n in SIS0.\n\nAlternatively, is it possible that PG0946+301 (and BALQSOs in general)\nis intrinsically X-ray weak? Earlier work (GM96, G99) could not rule\nout this possibility. To test this, we estimated the observed SIS0 hard band\ncount rate for flux consistent with detection in GIS3 hard band, but\nno intrinsic absorption. We find that the source would have been\ndetected in SIS0 hard band at $>8\\sigma$ (with $\\Gamma=1.7$;\n$>7\\sigma$ with $\\Gamma=2.0$). So we conclude that the observed X-ray\nweakness of BALQSOs is due to absorption, and not due to intrinsic\nweakness. We cannot, however, rule out the possibility that the source\nis intrinsically X-ray weak with an unusual spectral shape\n(turning up at around 10 keV, rest frame). It is also possible that\nthe observed flux is only the scattered component, from a line of\nsight different from the absorbing material. This is unlikely in\nPG0946+301 which not strongly polarized (Schmidt \\& Hines\n1999). However, if true, it again implies the existence of X-ray thick\nmatter along the direct line of sight.\n\n\n\n\\section{Discussion}\n\n We have clearly detected the quasar PG0946+301 in our deep ASCA\n observation and we infer that there is Thomson thick X-ray absorption\n ($N_{\\rm H}$\\gax$10^{24}$ cm$^{-2}$) toward this BALQSO. The use of a\n detection, rather than upper limits, to determine the absorption is\n highly significant. In earlier work, GM96 and G99 had estimated\n absorbing column densities of a few times $10^{22}$ cm$^{-2}$ and\n $10^{23}$ cm$^{-2}$ respectively. However these were based on\n non-detections only and hence yielded only lower limits to the column\n density. A detection provides a much stronger estimate.\n\n Assuming that there is indeed Thomson thick matter covering the X-ray\n source, can we infer its ionization state? The X-ray absorber will\n cover the optical and UV continuum sources as well, at least\n partially. If the absorber is completely neutral, it will result in\n significant HI opacity, which is not observed (Arav \\etal\n 1999). If the absorber is completely ionized, then the opacity due to\n Thomson scattering would be the same in the optical, UV and X-rays\n (up to $m_ec^2$). Thus this scenario by itself cannot account for\n the unusually large values of \\aox. ~If, on the other hand, the\n hydrogen is mostly ionized, but there are still some hydrogen-like\n and helium-like heavy elements, then photoelectric absorption would\n still be the dominant mechanism in X-rays. In the optical/UV, a\n Thomson opacity of one would result in attenuation by a factor of\n 2.7. Such attenuation is inferred from polarization studies (Goodrich\n 1997, Schmidt \\& Hines 1999). The X-ray absorber thus must be at\n least partially ionized and may be responsible for attenuation in the\n optical and UV.\n\n Whether the X-ray absorber has an ionization state overlapping the\n range of UV BALs and if it outflows with similar velocity remain\n outstanding questions. It is possible that the X-ray absorber is\n stationary, at the base of winds producing BALs. X-ray continuum\n source might be preferentially covered. X-ray spectroscopy is\n necessary to better probe the nuclear region in BALQSOs. For\n PG0946+301, we predict about 0.015 counts s$^{-1}$ with the XMM PN. A\n reasonable spectrum may be obtained in about 70 ks.\n\n% In a model by Murray \\etal\n% (1995), high column density gas responsible for X-ray absorption lies\n% at the base of the outflowing wind responsible for UV absorption\n% lines. The present observations are consistent with this scenario. We\n% are going to observe PG0946+301 with HST STIS as well. Results from\n% both X-ray and UV data will shed more light on nuclear region in\n% PG0946+301, and BALQSOs in general.\n\n%% In this section, we use the \\subsection command to set off\n%% a subsection. \\footnote is used to insert a footnote to the text.\n\n%% Observe the use of the LaTeX \\label\n%% command after the \\subsection to give a symbolic KEY to the\n%% subsection for cross-referencing in a \\ref command.\n%% You can use LaTeX's \\ref and \\label commands to keep track of\n%% cross-references to sections, equations, tables, and figures.\n%% That way, if you change the order of any elements, LaTeX will\n%% automatically renumber them.\n\n%% This section also includes several of the displayed math environments\n%% mentioned in the Author Guide.\n\n\n\\acknowledgments\nWe thank K. Arnaud and L. Angelini for help with\nXIMAGE. This work is supported in part by NASA grants NAG5-8360 (PJG,\nSM), NAG5-3249 (SM), NAG5-3841 (IS). The work by W.v.B. at IGPP/LLNL was performed\nunder the auspices of the US Department of Energy under contract\nW-7405-ENG-48.\n\n\n%% Appendix material should be preceded with a single \\appendix command.\n%% There should be a \\section command for each appendix. Mark appendix\n%% subsections with the same markup you use in the main body of the paper.\n\n%% Each Appendix (indicated with \\section) will be lettered A, B, C, etc.\n%% The equation counter will reset when it encounters the \\appendix\n%% command and will number appendix equations (A1), (A2), etc.\n\n\n%% The reference list follows the main body and any appendices.\n%% Use LaTeX's thebibliography environment to mark up your reference list.\n%% Note \\begin{thebibliography} is followed by an empty set of\n%% curly braces. If you forget this, LaTeX will generate the error\n%% \"Perhaps a missing \\item?\".\n%%\n%% thebibliography produces citations in the text using \\bibitem-\\cite\n%% cross-referencing. Each reference is preceded by a\n%% \\bibitem command that defines in curly braces the KEY that corresponds\n%% to the KEY in the \\cite commands (see the first section above).\n%% Make sure that you provide a unique KEY for every \\bibitem or else the\n%% paper will not LaTeX. The square brackets should contain\n%% the citation text that LaTeX will insert in\n%% place of the \\cite commands.\n\n%% We have used macros to produce journal name abbreviations.\n%% AASTeX provides a number of these for the more frequently-cited journals.\n%% See the Author Guide for a list of them.\n\n%% Note that the style of the \\bibitem labels (in []) is slightly\n%% different from previous examples. The natbib system solves a host\n%% of citation expression problems, but it is necessary to clearly\n%% delimit the year from the author name used in the citation.\n%% See the natbib documentation for more details and options.\n\n\\begin{thebibliography}{}\n\\bibitem[]{}Arav, N., 1997 in Mass Ejection from AGN, ASP Conference\nSeries, Vol. 128, ed. N. Arav, I. Shlosman, and R. J. Weymann, p. 208\n%\\bibitem[]{}Arav, N., Li, Z.-Y., \\& Begelman, M. C. 1994, ApJ, 432, 62\n\\bibitem[]{}Arav, N., Korista, K.T., de Kool, M., Junkkarinen, V.T., \\&\nBegelman, M.C.,\n1999, ApJ, 516, 27\n\\bibitem[]{}Arnaud, K. A. 1996 in ASP Conf. Ser. 101 Astronomical Data\nAnalysis Software and Systems V, ed. G. Jacoby \\& J. Barnes (San Fracisco:\nASP), 17\n\\bibitem[]{}Bregman, J. M. 1984, ApJ, 276, 423\n\\bibitem[]{}Cohen et al. 1995, ApJL, 448,77\n\\bibitem[]{}Freeman, P.E., Kashyap, V., Rosner, R., \\& Lamb, D.Q.\\ 2000, ApJ,\nsubmitted\n\\bibitem[]{} Gallagher, S., Brandt, W. N., Sambruna, R., Mathur, S., \\&\nYamasaki, N. 1999, ApJ, 519, 549 (G99)\n\\bibitem[]{}Giommi, P., Angelini, L. \\& White, N. 19997, The XIMAGE Users'\nGuide (Greenbelt:NASA/GSFC)\n\\bibitem[]{}Goodrich, R. \\& Miller, 1995, ApJ, 448, 73L\n\\bibitem[]{}Goodrich, R. 1997, ApJ, 474, 606\n\\bibitem[]{}Green, P. J. \\etal 1995 ApJ, 450, 51\n\\bibitem[]{}Green, P. J. \\& Mathur, S. 1996 ApJ, 462, 637 (GM96)\n%\\bibitem[]{} Hamman, F., \\& Ferland, G. J. 1993, 418, 11\n\\bibitem[]{} Hamman, F. 1998 ApJ 500, 798\n\\bibitem[]{}Korista, K. T., Voit, G. M., Morris, S. L., \\& Weymann, R.\nJ. 1993, ApJS, 88, 357\n\\bibitem[]{}Laor, A., Fiore, F., Elvis, M., Wilkes, B. J.\n \\& McDowell, J. C. 1994, ApJ, 435, 611\n\\bibitem[]{} Mathur, S., Elvis, M., \\& Singh, K. P. 1995, ApJ, 455, L9 (MES95)\n\\bibitem[]{} Mathur, S., Elvis, M., \\& Wilkes, B. 1995, ApJ, 452, 230\n%\\bibitem[]{} Murray, N., Grossman, S. A., Chiang, J.,\n%\\& Voit, M. 1995, ApJ\n\\bibitem[]{}Ogle, P. et al. 1999, ApJS, 125, 1\n\\bibitem[]{}Schmidt, G. \\& Hines, D. C. 1999, ApJ, 512, 125\n\\bibitem[]{}Singh,~K.~P., Westergaard, N.~J., \\& Schnopper,\nH.~W., 1987, A \\& A, 172, L11\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\n\\end{thebibliography}\n\n\n%% Generally speaking, only the figure captions, and not the figures\n%% themselves, are included in electronic manuscript submissions.\n%% Use \\figcaption to format your figure captions. They should begin on a\n%% new page.\n\n\\clearpage\n\n%% No more than seven \\figcaption commands are allowed per page,\n%% so if you have more than seven captions, insert a \\clearpage\n%% after every seventh one.\n\n%% There must be a \\figcaption command for each legend. Key the text of the\n%% legend and the optional \\label in curly braces. If you wish, you may\n%% include the name of the corresponding figure file in square brackets.\n%% The label is for identification purposes only. It will not insert the\n%% figures themselves into the document.\n%% If you want to include your art in the paper, use \\plotone.\n%% Refer to the on-line documentation for details.\n\n\\clearpage\n\\thispagestyle{empty}\n\n%% If you use the table environment, please indicate horizontal rules using\n%% \\tableline, not \\hline.\n%% Do not put multiple tabular environments within a single table.\n%% The optional \\label should appear inside the \\caption command.\n\n\\begin{table}[h]\n\\caption{ASCA Count Rates for PG0946+301$^a$ (10$^{-3}$) photons s$^{-1}$}\n%\\vspace*{8.5in}\n%{\\bf Table 1:}\n\\begin{tabular}{|lcccccc|}\n\\tableline\\tableline\n & SIS0 & SIS0 hard & SIS1 & GIS2 & GIS3 & GIS3 hard\\\\\n\\tableline\nBackground$^b$ 1 & $0.855 (2\\sigma)$ & $<0.74$& $<1.2$ & $<0.75$ & $1.84\n(7.9\\sigma)$ & $1.4 (8.7\\sigma)$\\\\\n & $<1.2$ && $$ & $$ & $$ &\\\\\nBackground$^c$ 2 & $1.29 (3\\sigma)$ &$0.51 (2\\sigma)$& $<1.2$ & $<0.75$ & $0.52\n(2\\sigma)$ & $0.48 (2\\sigma)$\\\\\n & &$<0.74$& $$ & $$ & $<0.83$ & $<0.63$\\\\\n\\tableline\n\\end{tabular}\n\\small\n\\noindent\n\\newline\na. Significance of detection is given in brackets. For non-detections,\n3$\\sigma$ upper limit is given. For $2\\sigma$ detections, $3\\sigma$\nupper limit is given as well. For SIS0 and GIS3, hard band count rates are\ngiven as well.\n\\\\\nb. With background from a source free\nregion on the detector. \\\\\nc. With background from blank sky\nobservations. \\\\\n\\end{table}\n\n\\begin{table}[h]\n\\caption{Column Density Constraints ($10^{24}$ atoms cm$^{-2}$) }\n%\\vspace*{8.5in}\n%{\\bf Table 1:}\n\\begin{tabular}{|lcccc|}\n\\tableline\\tableline\n Detector & $\\Gamma$ & Detection$^a$ & $3\\sigma$ Lower Limit$^b$ & $2\\sigma$\nDetection \\\\\n\\tableline\nGIS3 &1.7 & 0.95 & 2.1 & 3.3\\\\\n &2.0 & 0.52 & 1.2 & 1.95 \\\\\nGIS3 hard &1.7 & 1.2 & 2.55 & 3.2\\\\\n &2.0 & 0.67& 1.55 & 1.95 \\\\\nSIS0 &1.7 &1.4 & 1.42 & 1.95\\\\\n &2.0 & 0.9 & 0.92 & 1.3 \\\\\nSIS0 hard &1.7 & & 2.12& 2.73 \\\\\n &2.0 & & 1.42& 1.86 \\\\\n\\tableline\n\\end{tabular}\n\\small\n\\noindent\n\\newline\na. If $3\\sigma$ or better detection (Table 1). \\\\\nb. Upper limit on count rate gives lower limit on the column density. \\\\\n\\end{table}\n\n\n%% If the table is more than one page long, the width of the table can vary\n%% from page to page when the default \\tablewidth is used, as below. The\n%% individual table widths for each page will be written to the log file; a\n%% maximum tablewidth for the table can be computed from these values.\n%% The \\tablewidth argument can then be reset and the file reprocessed, so\n%% that the table is of uniform width throughout. Try getting the widths\n%% from the log file and changing the \\tablewidth parameter to see how\n%% adjusting this value affects table formatting.\n\n%% In this example, we have used the optional * argument to \\\\ to\n%% instruct LaTeX to keep rows together on the same page. (See the\n%% lines following the \\cutinhead.) Using \\\\* to group together table\n%% rows on the same page affects how the table breaks. Try taking\n%% the *'s out and LaTeXing again to see the difference.\n\n\n\\clearpage\n\n\n%% Tables may also be prepared as separate files. See the accompanying\n%% sample file table.tex for an example of an external table file.\n%% To include an external file in your main document, use the \\input\n%% command. Uncomment the line below to include table.tex in this\n%% sample file.\n\n% \\input{table}\n\n\n%% The following command ends your manuscript. LaTeX will ignore any text\n%% that appears after it.\n\n\\end{document}\n\n%%\n%% End of file `sample.tex'.\n"
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[
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"string": "\\begin{thebibliography} is followed by an empty set of\n%% curly braces. If you forget this, LaTeX will generate the error\n%% \"Perhaps a missing \\item?\".\n%%\n%% thebibliography produces citations in the text using \\bibitem-\\cite\n%% cross-referencing. Each reference is preceded by a\n%% \\bibitem command that defines in curly braces the KEY that corresponds\n%% to the KEY in the \\cite commands (see the first section above).\n%% Make sure that you provide a unique KEY for every \\bibitem or else the\n%% paper will not LaTeX. The square brackets should contain\n%% the citation text that LaTeX will insert in\n%% place of the \\cite commands.\n\n%% We have used macros to produce journal name abbreviations.\n%% AASTeX provides a number of these for the more frequently-cited journals.\n%% See the Author Guide for a list of them.\n\n%% Note that the style of the \\bibitem labels (in []) is slightly\n%% different from previous examples. The natbib system solves a host\n%% of citation expression problems, but it is necessary to clearly\n%% delimit the year from the author name used in the citation.\n%% See the natbib documentation for more details and options.\n\n\\begin{thebibliography}{}\n\\bibitem[]{}Arav, N., 1997 in Mass Ejection from AGN, ASP Conference\nSeries, Vol. 128, ed. N. Arav, I. Shlosman, and R. J. Weymann, p. 208\n%\\bibitem[]{}Arav, N., Li, Z.-Y., \\& Begelman, M. C. 1994, ApJ, 432, 62\n\\bibitem[]{}Arav, N., Korista, K.T., de Kool, M., Junkkarinen, V.T., \\&\nBegelman, M.C.,\n1999, ApJ, 516, 27\n\\bibitem[]{}Arnaud, K. A. 1996 in ASP Conf. Ser. 101 Astronomical Data\nAnalysis Software and Systems V, ed. G. Jacoby \\& J. Barnes (San Fracisco:\nASP), 17\n\\bibitem[]{}Bregman, J. M. 1984, ApJ, 276, 423\n\\bibitem[]{}Cohen et al. 1995, ApJL, 448,77\n\\bibitem[]{}Freeman, P.E., Kashyap, V., Rosner, R., \\& Lamb, D.Q.\\ 2000, ApJ,\nsubmitted\n\\bibitem[]{} Gallagher, S., Brandt, W. N., Sambruna, R., Mathur, S., \\&\nYamasaki, N. 1999, ApJ, 519, 549 (G99)\n\\bibitem[]{}Giommi, P., Angelini, L. \\& White, N. 19997, The XIMAGE Users'\nGuide (Greenbelt:NASA/GSFC)\n\\bibitem[]{}Goodrich, R. \\& Miller, 1995, ApJ, 448, 73L\n\\bibitem[]{}Goodrich, R. 1997, ApJ, 474, 606\n\\bibitem[]{}Green, P. J. \\etal 1995 ApJ, 450, 51\n\\bibitem[]{}Green, P. J. \\& Mathur, S. 1996 ApJ, 462, 637 (GM96)\n%\\bibitem[]{} Hamman, F., \\& Ferland, G. J. 1993, 418, 11\n\\bibitem[]{} Hamman, F. 1998 ApJ 500, 798\n\\bibitem[]{}Korista, K. T., Voit, G. M., Morris, S. L., \\& Weymann, R.\nJ. 1993, ApJS, 88, 357\n\\bibitem[]{}Laor, A., Fiore, F., Elvis, M., Wilkes, B. J.\n \\& McDowell, J. C. 1994, ApJ, 435, 611\n\\bibitem[]{} Mathur, S., Elvis, M., \\& Singh, K. P. 1995, ApJ, 455, L9 (MES95)\n\\bibitem[]{} Mathur, S., Elvis, M., \\& Wilkes, B. 1995, ApJ, 452, 230\n%\\bibitem[]{} Murray, N., Grossman, S. A., Chiang, J.,\n%\\& Voit, M. 1995, ApJ\n\\bibitem[]{}Ogle, P. et al. 1999, ApJS, 125, 1\n\\bibitem[]{}Schmidt, G. \\& Hines, D. C. 1999, ApJ, 512, 125\n\\bibitem[]{}Singh,~K.~P., Westergaard, N.~J., \\& Schnopper,\nH.~W., 1987, A \\& A, 172, L11\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\\bibitem[]{}\n\n\\end{thebibliography}"
}
] |
astro-ph0002055
|
Gravitational waves from cosmological compact binaries
|
[
{
"author": "R. Schneider$^1$"
},
{
"author": "V. Ferrari$^1$"
},
{
"author": "S. Matarrese$^{2,3}$ and S. F. Portegies Zwart$^{4,5}$"
},
{
"author": "$^{1}$Dipartimento di Fisica ``G. Marconi\""
},
{
"author": "Universit\\'a degli Studi di Roma"
},
{
"author": "``La Sapienza\" and Sezione INFN ROMA1"
},
{
"author": "piazzale Aldo Moro 5"
},
{
"author": "00185 Roma"
},
{
"author": "Italy"
},
{
"author": "$^2$Dipartimento di Fisica ``Galileo Galilei \""
},
{
"author": "Universit\\'a degli Studi di Padova and Sezione INFN PADOVA"
},
{
"author": "via Marzolo 8"
},
{
"author": "35131 Padova"
},
{
"author": "$^3$Max-Planck-Institut f\\\"ur Astrophysik"
},
{
"author": "Karl-Schwarzschild-Strasse 1"
},
{
"author": "D-85748 Garching - Germany"
},
{
"author": "725 Commonwealth Ave."
},
{
"author": "Boston"
},
{
"author": "MA 02215"
},
{
"author": "USA"
},
{
"author": "$^5$ Hubble Fellow"
}
] |
We consider gravitational waves emitted by various populations of compact binaries at cosmological distances. We use population synthesis models to characterize the properties of double neutron stars, double black holes and double white dwarf binaries as well as white dwarf-neutron star, white dwarf-black hole and black hole-neutron star systems. \\ We use the observationally determined cosmic star formation history to reconstruct the redshift distribution of these sources and their merging rate evolution.\\ The gravitational signals emitted by each source during its early-inspiral phase add randomly to produce a stochastic background in the low frequency band with spectral strain amplitude between $\sim 10^{-18} \, \mbox{Hz}^{-1/2}$ and $\sim 5 \times 10^{-17}\,\mbox{Hz}^{-1/2}$ at frequencies in the interval $[\sim 5 \times 10^{-6}-5 \times 10^{-5}]$~Hz. The overall signal which, at frequencies above $10^{-4}$~Hz, is largely dominated by double white dwarf systems, might be detectable with LISA in the frequency range $[1-10]$~mHz and acts like a confusion limited noise component which might limit the LISA sensitivity at frequencies above 1~mHz.
|
[
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Schneider, V. Ferrari, S. Matarrese and S. F. Portegies Zwart]\n {R. Schneider$^1$, V. Ferrari$^1$, S. Matarrese$^{2,3}$ and \nS. F. Portegies Zwart$^{4,5}$\\\\\n $^{1}$Dipartimento di Fisica ``G. Marconi\",\nUniversit\\'a degli Studi di Roma, ``La Sapienza\"\nand Sezione INFN ROMA1,\\\\ piazzale Aldo Moro\n5, 00185 Roma, Italy\\\\\n $^2$Dipartimento di Fisica ``Galileo Galilei \",\nUniversit\\'a degli Studi di Padova\nand Sezione INFN PADOVA,\\\\ via Marzolo 8, 35131 Padova, Italy \\\\\n$^3$Max-Planck-Institut f\\\"ur Astrophysik, \nKarl-Schwarzschild-Strasse 1, D-85748 Garching - Germany \\\\\n$^4$Institute for Astrophysical research,\n\t\t Boston University,\n\t\t 725 Commonwealth Ave.,\n\t\t Boston, MA 02215, USA\\\\\n$^5$ Hubble Fellow}\n\n\\date{January 2000}\n\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{2000}\n\\begin{document}\n\n\\maketitle\n\\label{firstpage}\n\n\\begin{abstract}\nWe consider gravitational waves emitted by various populations of \ncompact binaries at cosmological distances. We use population \nsynthesis models to characterize the properties of double neutron stars,\ndouble black holes and double white dwarf binaries as well as white \ndwarf-neutron star, white dwarf-black hole and black hole-neutron star\nsystems. \\\\\nWe use the observationally determined cosmic star formation history \nto reconstruct the redshift distribution of these sources \nand their merging rate evolution.\\\\\nThe gravitational signals emitted by each source during its early-inspiral\nphase add randomly to produce a stochastic background in the low frequency\nband with spectral strain amplitude \nbetween $\\sim 10^{-18} \\, \\mbox{Hz}^{-1/2}$ and\n$\\sim 5 \\times 10^{-17}\\,\\mbox{Hz}^{-1/2}$ at frequencies in the interval\n$[\\sim 5 \\times 10^{-6}-5 \\times 10^{-5}]$~Hz.\n\nThe overall signal which, at frequencies above $10^{-4}$~Hz, \nis largely dominated by double white dwarf \nsystems, might be detectable with LISA in the frequency range $[1-10]$~mHz\nand acts like\na confusion limited noise component which might limit the LISA sensitivity\nat frequencies above 1~mHz.\n\\end{abstract}\n\n\\begin{keywords}\ngravitation -- stars: formation -- stars: binaries--gravitational waves.\n\\end{keywords}\n\n\\section{Introduction}\n\nBinaries with two compact stars are the most promising sources for\ngravitational radiation. The final phase of spiral in may be detected\nwith ground-based (LIGO, VIRGO, GEO and TAMA) and space-borne laser\ninterferometers (LISA). \nThis has motivated researchers to model\ngravitational waveforms and to develop population synthesis codes to\nestimate the properties and formation rates of possible sources for\ngravitational wave radiation.\n \nSince there is not yet a single prescription for calculating the\ngravitational emission from a compact binary system, it is customary\nto divide the gravitational waveforms in two main pieces: the inspiral\nwaveform, emitted before tidal distortions become noticeable, and the\ncoalescence waveform, emitted at higher frequencies during the epoch\nof distortion, tidal disruption and/or merger (Cutler \\etal 1993). \n\nAs the binary, driven by gravitational radiation reaction, spirals in,\nthe frequency of the emitted wave increases until the last 3 orbital cycles\nprior to complete merger.\n\nWith post-Newtonian expansions of the equations of motion for two\npoint masses, the waveforms can be computed fairly accurately in the\nrelatively long phase of spiral in (see, for a recent review, Rasio \\&\nShapiro 2000 and references therein).\nConversely, the gravitational waveform from the coalescence can only \nbe obtained from extensive numerical calculations\nwith a fully general relativistic treatment. Such calculations \nare now well underway (Brady, Creighton \\& Thorne 1998; Damour, Iyer \\& \nSathyaprakash 1998; Rasio \\& Shapiro 1999). \n \nIn this paper, we consider the low frequency signal from the early phase of the\nspiral in, which is of interest for space-borne antennas, such as LISA.\nFor this purpose, we use the leading order expression for the single\nsource emission spectrum, obtained using the quadrupole approximation.\nOur analysis includes various populations of compact binary systems:\nblack hole-black hole (bh, bh), neutron star-neutron star (ns, ns),\nwhite dwarf-white dwarf (wd, wd) as well as mixed systems such as\n(ns, wd), (bh, wd) and (bh, ns).\n\nFor some of these sources [(ns, ns), (wd, wd) and (ns, wd)],\nstatistical information on the event rate can be inferred from\nelectromagnetic observations. In particular, there are several\nobservational estimates of the (ns, ns) merger rate obtained from\nstatistics of the known population of binary radio pulsars (Narayan, Piran\n\\& Shemi 1991; Phinney 1991).\n\nA rather large number of close white dwarf binaries have recently been\nfound (see Maxted \\&\nMarsh 1999 and Moran 1999). However, it is customary to\nconstrain the (wd, wd) merger rate from the observed SNIa rate (see\nPostnov \\& Prokhorov 1998). Also the population of binaries where a\nradio pulsar is accompanied by a massive unseen white dwarf may be\nconsiderably higher than hitherto expected (Portegies Zwart \\&\nYungelson 1999).\n\n\n\nSince most stars are members of binaries and the formation rate of\npotential sources of gravitational waves may be abundant in the Galaxy,\nthe gravitational-wave signal emitted by such binaries might produce a\nstochastic background. This possibility has been explored by various\nauthors, starting from the earliest work of Mironovskij (1965) and Rosi\n\\& Zimmermann (1976) until the more recent investigations of Hils,\nBender \\& Webbink (1990), Lipunov \\etal (1995), Bender \\& Hils\n(1997), Giazotto, Bonazzola \\& Gourgoulhon (1997),\nGiampieri (1997), Postnov \\& Prokhorov (1998), and Nelemans,\nPortegies Zwart \\&\nVerbunt (1999). This background, which acts like a noise component\nfor the interferometric detectors, has always been viewed as a\npotential obstacle for the detection of gravitational wave backgrounds\ncoming from the early Universe.\n\nIn this paper we extend the investigation of compact binary systems to\nextragalactic distances, accounting for the binaries which have been\nformed since the onset of galaxy formation in the Universe. Following\nFerrari, Matarrese \\& Schneider (1999a, 1999b: hereafter referred as FMSI\nand FMSII, respectively), we modulate the binary formation rate in the\nUniverse with the cosmic star formation history derived from\nobservations of field galaxies out to redshift $z \\sim 5$ (see \\eg Madau,\nPozzetti \\& Dickinson 1998b; Steidel \\etal 1999).\n\nThe magnitude and frequency distribution of the integrated\ngravitational signal produced by the cosmological population of\ncompact binaries is calculated from the distribution of binary\nparameters (masses and types of both stars, orbital separations and\neccentricities). These orbital parameters characterize the \ngravitational-wave signal which we observe on Earth.\n\nDetailed information for the properties of the binary population may\nbe obtained through population synthesis. We use the binary\npopulation synthesis code {\\sf SeBa} to simulate the characteristics\nof the binary population in the Galaxy (Portegies Zwart \\& Verbunt\n1996; Portegies Zwart \\& Yungelson 1998). The characteristics of the\nextragalactic population are derived from extrapolating these results\nto the local Universe.\n\n\nThe paper is organized as follows: in Section~2 we describe the\npopulation synthesis calculations. Section~3 deals with the energy\nspectrum of a single source followed, in Section~4, by the derivation of\nthe extragalactic backgrounds for the different binary populations. \nIn Sections~3 and~4 we also give details on the adopted astrophysical and \ncosmological properties of the systems. \nIn Section~5, we compute the spectral strain amplitude\nproduced by each cosmological population and investigate its\ndetectability with LISA. Finally, in Section~6 we\nsummarize our main results and compare them with other previously\nestimated astrophysical background signals.\n\n\n\\section{Population synthesis model}\n\\label{sec:popSeBa}\n\nIn order to characterize the main properties of different compact\nbinary systems, we use the binary population synthesis program {\\sf\nSeBa} of Portegies Zwart \\& Yungelson (1998). Details of the code can\nbe found in (Portegies Zwart \\& Yungelson 1998). Here, we simply\nrecall the main assumptions of their adopted model B, which\nsatisfactorily reproduces the properties of observed high-mass binary\npulsars (with neutron star companions).\n\nThe following initial conditions were assumed: the mass of the primary\nstar $m_1$ is determined using the mass function described by Scalo\n(1986) between 0.1 and 100 $\\msun$. For a given $m_1$, the mass of the\nsecondary star $m_2$ is randomly selected from a uniform distribution\nbetween a minimum of 0.1 $\\msun$ and the mass of the primary star. The\nsemi-major axis distribution is taken flat in $\\log a$ (Kraicheva\n\\etal 1978) ranging from Roche-lobe contact up to $10^6$~R$_\\odot$\n(Abt \\& Levy 1978; Duquennoy \\& Mayor 1991). The initial eccentricity\ndistribution is independent of the other orbital parameters, and is\n$\\Xi(e) = 2 e$.\n\nNeutron stars receive a velocity kick upon birth. Following Hartman\n\\etal (1997), model B assumes the distribution for isotropic kick\nvelocities (Paczy{\\'n}ski 1990),\n\\begin{equation}\nP(u)du = {4\\over \\pi} \\cdot {du\\over(1+u^2)^2},\n\\label{eqkick}\\end{equation}\nwith $u=v/\\sigma$ and $\\sigma = 600 \\,\\,\\mbox{km}\\,\\mbox{s}^{-1}$.\n\nThe birthrate of the various compact binaries is normalized to the\nType II+Ib/c supernova rate \n(see Portegies Zwart \\& Verbunt 1996). The supernova rate of \n0.01 per year was assumed to be constant over the lifetime of\nthe galactic disc ($\\sim 10$~Gyr).\n\nWhen computing the birth and merger-rates we account for the \ntime-delay between the formation of the progenitor system and that \nof the corresponding degenerate binary, $\\tau_s$. Its value is \nset by the time it takes for the least massive between the two companion\nstars to evolve on the main sequence. For (bh, bh), (ns, ns) and\n(bh, ns) systems $\\tau_s \\lsim 50$~Myr and it is negligible\ncompared to the assumed lifetime of the galactic disc. Conversely, \n(wd, wd), (ns, wd) and (bh, wd) binaries follow a slower evolutionary clock \nand $\\tau_s$ can be considerably larger. The cumulative\nprobability distribution, $P(<\\tau_s)$, predicted \nby the population synthesis code is shown in Fig.~1. For these\nsystems $\\tau_s$ can be as large as 10~Gyr although all systems are predicted\nto have $\\tau_s\\leq 10$~Gyr.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=tscum_log.ps,angle=270,width=8cm}\n\\caption{The cumulative probability distribution for the time delay $\\tau_s$\n(in Myr) between the formation of the progenitor system and the formation of\nthe corresponding degenerate binary \nobtained for the (bh, wd), (ns, wd) and (wd, wd) samples.}\n\\end{center} \n\\label{fig:ts}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \nAfter the degenerate binary has formed, its further evolution is\ndetermined by the time it takes to radiate away its orbital energy in\ngravitational waves. The time between the formation of the degenerate\nsystem and its final coalescence, $\\tau_m$, depends on the orbital\nconfiguration and on the mass of the two companion stars. The\npredicted cumulative probability distribution is shown in\nFig.~2 for the (wd, wd), (ns, ns) and (ns, wd) samples. We\nsee from the figure that there is a significant fraction of systems\nwhich does not merge in 10~Gyr. For (bh, bh) binaries and mixed\nsystems with one black hole companion the population synthesis code\npredicts very long merger times. In particular, all (bh, bh) systems\nappear to have $\\tau_m$ greater than 15 Gyr. The reason for these\nlarge merger times is that binaries with a black hole companion are\ncharacterized by very large initial orbital separations (see \\eg\nFig.~3). In fact, bh progenitors are very massive stars\nand have a very strong stellar wind. For this reason they do not\neasily reach Roche-lobe over-flow and rarely experience a phase of\nmass transfer, which is required to reduce the orbital separation of\nthe stars. Unfortunately, the evolution (especially the amount of mass\nloss in the stellar winds) of high mass stars is rather uncertain\n(Langer \\etal 1994). The result that we obtain at least indicates\nthat it will be very rare to observe any of these bh mergers. Recently\nPortegies Zwart \\& McMillan (1999) however identified a new channel\nfor producing black hole binaries which are eligible to mergers on a\nrelatively short time scale.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=tmcum_log.ps,angle=270,width=8cm}\n\\caption{The cumulative probability distribution for the merger time $\\tau_m$\n(in Myr) is shown for the (ns, ns), (ns, wd) and (wd, wd) samples.} \n\\end{center}\n\\label{fig:tm}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\psfig{figure=bhbhorbit.ps,angle=270,width=7.cm}\n\\psfig{figure=nsnsorbit.ps,angle=270,width=7.cm}\n\\caption{The probability distribution for the orbital parameters\nof (bh, bh) systems ({\\bf left} panel) is compared to that obtained for\nthe (ns, ns) ({\\bf right} panel) population.} \n\\label{fig:orbit}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nIn Table~\\ref{galacticrates}, we summarize the results for all \nbinary types that we have investigated. \n\n \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}\n\\caption{The galactic birthrates, $R_{X,gal}$, and merger rates, \n$R^{mrg}_{X,gal}$, obtained for\neach compact binary type $X$ using model B of (Portegies Zwart \\& \nYungelson 1998), see text. The rates are normalized to the core-collapse\nsupernova rate of $0.01 \\,\\,\\mbox{yr}^{-1}$ and 100\\% binarity.\nMerger rates are computed after 10~Gyr of the evolution of the Galaxy with\na constant supernova rate.}\n\\begin{tabular}{@{}ccc@{}}\nBinary Type $X$ & $R_{X,gal}\\mbox{yr}^{-1}$& \n$R^{mrg}_{X,gal}\\mbox{yr}^{-1}$ \\\\\\hline\n & & \\\\[1pt]\n(bh, bh) & $6.3 \\times 10^{-5}$ & NA\\\\\n(bh, ns) & $1.0 \\times 10^{-5}$ & $1.0 \\times 10^{-6}$ \\\\ \n(bh, wd) & $4.4 \\times 10^{-5}$ & $10^{-7}$ \\\\\n(ns, ns) & $3.6 \\times 10^{-5}$ & $2.5 \\times 10^{-5}$ \\\\\n(ns, wd) & $3.6 \\times 10^{-4}$ & $1.6 \\times 10^{-4}$ \\\\\n(wd, wd) & $4.4 \\times 10^{-2}$ & $4.8 \\times 10^{-3}$ \\\\ \n\\end{tabular}\n\\label{galacticrates}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\section{Inspiral energy spectrum of single sources}\n\\label{sec:single}\n\nAssuming that the orbit of the binary system has already been circularized by \ngravitational radiation reaction, the inspiral \nspectrum $dE/d{\\nu}$ emitted by a single source \ncan be obtained using the quadrupole approximation \n(Misner, Thorne \\& Wheeler 1995). The resulting expression,\nin geometrical units (G=c=1), can be written as,\n\\be\n\\frac{dE}{d\\nu}=\\frac{\\pi}{3}\\,\\frac{{\\cal M}^{5/3}}{(\\pi \\nu)^{1/3}}\n\\label{singlespectrum}\n\\ee \nwhere ${\\cal M}=\\mu^{3/5} M^{2/5}$ is the so-called chirp mass,\n$M=m_1+m_2$ stands for the total mass and $\\mu=m_1\\,m_2/M$ is the \nreduced mass.\n\nThe frequency $\\nu$ at which gravitational waves are emitted is twice the \norbital frequency and depends on the time left to the merger event through,\n\\be\n(\\pi \\nu)^{-8/3} = (\\pi \\nu_{max})^{-8/3} + \n\\frac{256}{5}\\, {\\cal M}^{5/3} \\,(t_c -t)\n\\label{eq:emissionfreq}\n\\ee\nwhere $t_c$ is the time of the final coalescence and we terminate the\ninspiral spectrum at a frequency $\\nu_{max}$. \nWhen Post-Newtonian expansion terms are included, it is customary to\nconsider the inspiral spectrum as a good approximation all the way up to\n$\\nu_{LSCO}$, \\ie the frequency of the quadrupole waves \nemitted at the last stable circular orbit (LSCO) (see \\eg Flanagan \\& Hughes 1998).\nHowever, for the purposes of our study, we neglect \npost-Newtonian terms\nand we set the value of $\\nu_{max}$ to correspond to the quadrupole\nfrequency emitted when the orbital separation is roughly 3 times the\nseparation at the LSCO. \n\nThe value of the orbital separation at the LSCO depends on the mass\nratio of the two stellar components and varies between $5 M-6 M$. The\nlower limit is obtained in the test particle approximation ($m_1 \\gg\nm_2$), whereas the upper value corresponds to the equal-mass case\n($m_1 \\sim m_2$) (see Kidder, Will \\& Wiseman 1993). If we consider\nthe equal-mass limit, which is more conservative for constraining the\nmaximum frequency, $\\nu_{LSCO} \\sim 0.022/M$ and $\\nu_{max} \\sim\n0.19\\,\\, \\nu_{LSCO}$.\n\nFor (wd, wd) binaries and binaries with one wd companion, \nthe maximum frequency, \\ie the minimum distance\nbetween the two stellar components, is set in order to cut-off the \nRoche-lobe contact stage. In fact, the mass transfer from one component \nto its companion transforms the original detached binary into a semi-detached\nbinary. This process can be accompanied by the loss of angular momentum with \nmass loss from the system and the above description cannot be applied. \nThus, for closed white dwarf binaries we require that the \nmimimum orbital separation is given by $r_{wd}(m_1)+r_{wd}(m_2)$ \nwhere \n\\be\nr_{wd}(m)=0.012 R_{\\odot} \\sqrt{\\left(\\frac{m}{1.44 M_{\\odot}}\\right)^{-2/3} -\n\\,\\,\\left(\\frac{m}{1.44 M_{\\odot}}\\right)^{2/3}} \n\\ee\nis the approximate formula for the radius of a white dwarf from \nNauenberg (1972) (see also Portegies Zwart \\& Verbunt 1996). \n\nConsider now sources at cosmological distances. The locally measured \naverage energy flux emitted by a source at redshift $z$ is,\n\\be\nf(\\nu)= \\int \\frac{d\\Omega}{4 \\pi}\\, \\frac{dE}{d\\Sigma d\\nu}(\\nu) =\n\\frac{(1+z)^2}{4 \\pi d_{L}(z)^2} \\,\\,\\frac{c^3}{G} \\,\\,\n\\frac{dE_e}{d\\nu_e}[\\nu (1+z)]\n\\label{fluxsingle}\n\\ee\nwhere $d_{L}(z)$ is the luminosity distance to the source,\n$\\nu=\\nu_e \\,(1+z)^{-1}$ is the observed frequency and the factor $c^3/G$\nis needed in order to change from geometrical to physical units. \nThus, the emission spectrum can be written as,\n\\be\n\\frac{dE_e}{d\\nu_e}[\\nu (1+z)]=\\frac{\\pi}{3}\\frac{{\\cal M}^{5/3}}{[\\pi\\,\n\\nu (1+z)]^{1/3}} \n\\label{cosmicspectrum}\n\\ee\nwhere $\\nu$ is the observed frequency emitted by a system at time $t(z)$\n\\beq\n\\label{freinterval}\n(\\pi \\nu)^{-8/3}=(\\pi \\nu_{max})^{-8/3}(1+z)^{8/3} + \n\\frac{256}{5} \\, {\\cal M }^{5/3} \\, \\\\ \n\\left[t(z_f)+ \\tau_m -t(z)\\right](1+z)^{8/3} \\nonumber\n\\eeq\nand we have written the time of the final coalescence $t_c=t(z_c)$ in terms \nof the time of formation $t(z_f)$ and of the merger-time \n$\\tau_m = t(z_c) - t(z_f)$. \n\n\n\\section{Extragalactic backgrounds from different binary populations} \n\nOur main purpose is to estimate the stochastic background signal\ngenerated by different populations of compact binary systems at\nextragalactic distances. \n\nThese gravitational sources have\nbeen forming since the onset of galaxy formation in the Universe\nand for each binary type $X$ [(ns, ns); (wd, wd); (bh, bh); (ns, wd); \n(bh, wd); (bh, ns)]\nwe should think of a large ensemble of unresolved and uncorrelated \nelements, each characterized by its masses $m_1$ and $m_2$ (or $M$ and $\\mu$),\nby its redshift and by its time-delays $\\tau_s$ and $\\tau_m$ \n[see eqns~(\\ref{cosmicspectrum}) and~(\\ref{freinterval})]. \n\nThus, in order to consider all contributions from different elements of \nthe ensemble $X$, we must integrate the single source emission spectrum over \nthe distribution functions for the masses $M$ and $\\mu$, for the time-delays \nand for the redshifts.\n\nThe distribution functions for $\\tau_s$ and $\\tau_m$ depend on the\nbinary type $X$ and have been derived from the population synthesis code\ndiscussed in the previous section. \nThe distribution function for ${\\cal M}$ can be similarly estimated. \n\nHowever, $\\tau_s$, $\\tau_m$ and ${\\cal M}$ are not \nindependent random variables.\nIn particular, $\\tau_m$ and ${\\cal M}$ are correlated because ${\\cal M}$ \ndefines the rate of orbital decay, once the degenerate system has formed.\nThus, for each binary population $X$, we consider the joint probability\ndistribution for $\\tau_s$, $\\tau_m$ and ${\\cal M}$,\n\\be\np_X(\\tau_s, \\tau_m, {\\cal M})\\,\\, d \\tau_m \\,\\,d\\tau_s \\,\\,d{\\cal M}.\n\\ee\n \nConversely, the redshift distribution function, \\ie the evolution of the\nformation rate for each binary type $X$, can be deduced from the \nobserved cosmic star formation history out to $z \\sim 5$. \n\nIn the following subsections, we illustrate the procedure we have\nfollowed to derive the birth and merger-rates for all binary populations\nand to compute the spectra of the corresponding stochastic gravitational \nbackgrounds. \n \n\\subsection{Cosmic star formation rate}\n\nIn the last few years, the extraordinary advances attained in observational\ncosmology have led to the possibility of identifying actively \nstar forming galaxies at increasing cosmological look-back times \n(see, for a thorough review, Ellis 1997).\nUsing the rest-frame UV-optical luminosity as an indicator of the star\nformation activity and integrating on the overall galaxy population,\nthe data obtained with the {\\it Hubble Space Telscope} (HST Madau \\etal 1996,\nConnolly \\etal 1997, Madau \\etal 1998a) Keck and\nother large telescopes (Steidel \\etal 1996, 1999) \ntogether with the \ncompletion of several large redshift surveys \n(Lilly \\etal 1996, Gallego \\etal 1995, Treyer \\etal 1998)\nhave enabled, for the first time, to derive coherent models for\nthe star formation rate evolution throughout the Universe. \\\\\nA collection of some data obtained at different redshifts \nis shown in the left panel of Figure~\\ref{sfr} for a flat cosmological\nbackground model with $\\Omega_{\\Lambda}=0$, $h=0.5$ and a Scalo (1986) IMF \nwith masses in the range $0.1-100 \\msun$. \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\psfig{file=sfr_nodc.ps,angle=270,width=7.cm}\n\\psfig{file=sfr_dckennfinal.ps,angle=270,width=7.cm}\n\\caption{The Log of the star formation rate density in units of \n$\\msun \\mbox{yr}^{-1} \\mbox{Mpc}^{-3}$ as a function of redshift for a \ncosmological background model with $\\Omega_{M}=1$, $\\Omega_{\\Lambda}=0$,\n$H_0=50 \\,\\mbox{km}\\mbox{s}^{-1} \\mbox{Mpc}^{-1}$ and a \nScalo (1986) IMF. {\\bf Left}: The data points correspond to \nUV, H$\\alpha$ and IR observations of field galaxies. ({\\bf Filled dots}) \nUV observations of Treyer \\etal (1998), Lilly \\etal (1996), \nConnolly \\etal (1997), HDF Madau \\etal (1996), Steidel \\etal (1996),(1999); \n({\\bf asterisks}) H$\\alpha$ observations of Gallego \\etal 1995, Gronwall\n1999, Tresse \\& Maddox 1998, Glazebrook \\etal 1998, Yan \\etal 1999); ({\\bf triangles}): ISO IR observations (Flores \\etal 1999) and the lower limit\nof SCUBA data (Hughes \\etal 1998). ({\\bf Right}):\nThe dust-corrected SFR density as derived from UV\ndata in the two models most favoured by observations predicted by \nCalzetti \\& Heckman ({\\bf asterisks}) and by Pei, Fall \\&\nHauser {\\bf filled dots} (see text).} \n\\label{sfr}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nAlthough the strong luminosity \nevolution\nobserved between redshift 0 and 1-2 is believed to be quite firmly established,\nthe behaviour of the\nstar formation rate at high redshift is still relatively uncertain.\nIn particular, the decline of the star formation rate density implied by\nthe $ \\lanlge z \\ranlge\\, \\sim 4$ point of the {\\it Hubble Deep Field} \n(HDF, see Fig.~\\ref{sfr}) \nis now\ncontradicted by the star formation rate density derived from a new \nground-based sample of Lyman break galaxies with $\\langle z \\rangle\\,=4.13$ \n(Steidel \\etal 1999) which, instead, seems to indicate that the star\nformation rate density remains substantially constant at $z>1-2$.\nIt has been suggested that this discrepancy might be caused by problems\nof sample variance in the HDF point at $\\lanlge z \\ranlge\\,=4$ \n(Steidel \\etal 1999). \\\\\n\nBecause dust extinction can lead to\nan underestimate of the real UV-optical emission and, ultimately, of the \nreal star formation activity, the data shown in the left panel \nof Fig.~\\ref{sfr} need to be corrected\nupwards according to specific models for the evolution of dust opacity\nwith redshift. In the right panel of Fig.~\\ref{sfr}, the data have been\ndust-corrected according to factors obtained by Calzetti \\& Heckman (1999)\nand by Pei, Fall \\& Hauser (1999). Using different approaches, these authors \nhave recently investigated the cosmic histories of stars, gas, heavy elements \nand dust in galaxies using as inputs the available data from quasar\nabsorption-line surveys, optical and UV imaging of field galaxies, \nredshift surveys and the COBE DIRBE and FIRAS measurements of the cosmic IR \nbackground radiation. \nThe solutions they obtain appear to reproduce remarkably well a variety of \nobservations that were not used as inputs, among which the SFR at various \nredshifts from H$\\alpha$, mid-IR and submm\nobservations and the mean abundance of heavy elements at various epochs \nfrom surveys of damped Lyman-$\\alpha$ systems.\n\nAs we can see from the right panel of Fig.~\\ref{sfr}, spectroscopic and \nphotometric surveys in different wavebands point to a consistent picture \nof the low-to-intermediate redshift evolution:\nthe SFR density rises rapidly as we go from the local value\nto a redshift between $\\sim 1-2$ and remains roughly flat between \nredshifts $\\sim 2-3$. At higher redshifts, two different\nevolutionary tracks seem to be consistent with the data: \nthe SFR density might remain substantially constant at $z \\gsim 2$\n(Calzetti \\& Heckman 1999) \nor it might decrease again out to a redshift of \n$\\sim 4$ (Pei, Fall \\& Hauser 1999). Hereafter, we always indicate the\nformer model as 'monolithic scenario' and the latter as 'hierarchical\nscenario' although this choice is only ment to be illustrative. In fact,\npreliminary considerations have pointed out that a constant SFR activity\nat high redshifts might not be unexpected in hiererachical structure \nformation models (Steidel \\etal 1999). \n\nThus, we have updated the star formation rate model that we have \nconsidered in previous analyses (FMSI, FMSII), even though the\ngravitational wave backgrounds are more contributed by low-to-intermediate\nredshift sources than by distant ones. In addition,\nif a larger dust correction factor should be applied at intermediate\nredshifts, this would result in a similar amplification of the \ngravitational background spectra.\n\n\\subsection{Birth and merger rate evolution}\n\nFollowing the method we have previously proposed (FMSI, FMSII), \nfor each binary type $X$ the birth and merger-rate evolution could be\ncomputed from the observed star formation rate evolution.\nHowever, this procedure proves to be unsatisfactory because it fails\nto provide a fully consistent normalization. \nIts main weakness is that, even if we assume 100\\% of binarity, \\ie that\nall stars are in binary systems, the star formation histories that we have\ndescribed above are not corrected for the presence of secondary stars.\nFor the mass distributions that we have considered,\nsecondary stars are expected to give a significant contribution \nto the observed UV luminosity as they account for $\\sim 1/3$ of the \nfraction of mass in stars more massive than $8 \\,\\msun$. \n\nIn order to circumvent the necessity of extrapolating \nthe UV luminosity indication of massive star formation to the full\nrange of stellar masses predicted by the model, \nwe could directly normalize to the rate of core-collapse supernovae.\nThis is consistent with the adopted normalization for galactic rates. \n\nThe core-collapse supernova rate can be directly \nderived from the observed UV luminosity at each redshift, as stars\nwhich dominate the UV emission from a galaxy are the same stars which,\nat the end of the nuclear burning, explode as Type II+Ib/c SNae. \nMoreover, the supernova rate is observed independently of the SFR. Therefore\nit can be used as an alternative normalization.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=SNaeIIrate.ps,angle=270,width=8cm}}\n\\caption{The rest-frame frequency of core-collapse SNae \nvs redshift predicted by the monolithic and \nhierarchical models. The predictions are consistent\nwith the observed value for the present-day galaxy population (see text).} \n\\label{sneII}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe rates of core-collapse supernovae predicted by the models shown in\nFig.~\\ref{sfr} are shown \nin Fig.~\\ref{sneII} assuming a \nflat cosmological background model with zero cosmological constant \nand $h=0.5$.\n\nIn the same figure, we have plotted the available observations for the \ncore-collapse supernova frequency in the local Universe\n(Cappellaro \\etal 1997, Tamman \\etal 1994, Evans \\etal 1989, \nsee also Madau \\etal 1998b).\n\nThe binary birthrate per entry per year and comoving\nvolume $\\dot{\\eta}(z)$ can be related to the core-collapse supernova rate \n$\\dot{n}_{[SNae II+Ib/c]}(z)$ shown in Fig.~\\ref{sneII} in the following way,\n\\be\n\\dot{\\eta}(z)=\\frac{\\dot{n}_{[SNae II+Ib/c]}(z)}{N_{[SNae II+Ib/c]}}\n\\label{eq:norm}\n\\ee\nwhere $N_{[SNae II+Ib/c]}$ is the total number of core-collapse supernovae that\nwe find in the simulation.\n\nIn order to estimate, from $\\dot{\\eta}(z)$, \nthe birth and merger-rate evolution \nof a degenerate binary population $X$, we need to multiply \neq.~(\\ref{eq:norm})\nby the number of type $X$ systems in the simulated samples, $N_X$, \nand we also need to properly account for both $\\tau_s$ and\n$\\tau_m$. \n\nWe shall assume that the redshift at the onset of galaxy formation \nin the Universe\nis $z_F=5$ and that a zero-age main sequence binary forms at a redshift $z_s$.\nAfter a time interval $\\tau_s$, the system has evolved into a \ndegenerate binary. Then, \nthe redshift of formation of the degenerate binary system, $z_f$, \nis defined as $t(z_f)=t(z_s)+\\tau_s$. \nThe system then evolves \naccording to gravitational wave reaction until, \nafter a time interval $\\tau_m$, it finally merges. \nThus, the redshift at which coalescence occurs, $z_c$, is given by \n$t(z_c)=t(z_f)+\\tau_m$.\n\nThis simple picture implies that the number of $X$ systems formed\nper unit time and comoving volume at redshift $z_f$ is\n\\beq\n\\dot{n}_{X}(z_f)&=&\\int\\!\\! d\\tau_m \\, d{\\cal M}\\int_{0}^{t(z_f)-t(z_F)} \\!\\!d\\tau_s\\,\\, f_{X} \\\\ \n& &\\frac{\\dot{n}_{[SNae II+Ib/c]}(z_s)}{(1+z_s)}\n\\,p_{X}(\\tau_s,\\tau_m, {\\cal M}) \\nn\n\\eeq\nwhere $f_{X}=N_{X}/N_{[SNae II+Ib/c]}$ and \n$z_s$ is defined by $t(z_s)=t(z_f)-\\tau_s$.\n\nIf we write, \n\\be\n\\label{eq:deltaprob}\np_{X}(\\tau_s,\\tau_m, {\\cal M})=\\frac{1}{N_{X}} \\sum_{i}^{N_{X}}\n\\,\\delta(\\tau_s -\\tau_{s,i})\\,\\delta(\\tau_m - \\tau_{m,i})\\,\\delta({\\cal M}-\n{\\cal M}_i)\n\\ee\nwhere $\\tau_{s,i}$, $\\tau_{m,i}$ and ${\\cal M}_i$ indicate the time delays \nand the chirp mass for the $i^{th}$ \nelement of the ensemble $X$, the birthrate reads,\n\\beq\n\\label{eq:birthrate}\n\\dot{n}_{X}(z_f)&=&\\frac{1}{N_{[SNae II+Ib/c]}} \\,\\,\\sum_{i}^{N_{X}}\\,\n\\frac{\\dot{n}_{[SNae II+Ib/c]}(z_s)}{(1+z_s)}\\\\ \n& &\\Theta[t(z_f)-t(z_F)-\\tau_{s,i}] \\nn\n\\eeq\nwhere $\\Theta(x)$ is the step-function.\n\nSimilarly, the number of $X$ systems per unit time and comoving volume \nwhich merge at redshift $z_c$ is,\n\\beq\n\\dot{n}^{mrg}_{X}(z_c)=\\int_{0}^{t(z_c)-t(z_F)}\\!\\! d\\tau_m \n\\int_{0}^{t(z_c)-\\tau_m-t(z_F)}\\!\\! d\\tau_s \\,\\,\\, f_{X} \\\\ \n\\frac{\\dot{n}_{[SNae II+Ib/c]}(z_s)}{(1+z_s)}\\int d{\\cal M} \\,\\, \np_{X}(\\tau_s,\\tau_m, {\\cal M}) \\nn\n\\eeq\nwhere $z_s$ is defined by $t(z_s)=t(z_c)-\\tau_m-\\tau_s$. \nIf we apply eq.~(\\ref{eq:deltaprob}), we can write the merger-rate in a form \nsimilar to eq.~(\\ref{eq:birthrate}), \\ie\n\\beq\n\\label{eq:mergerate}\n\\dot{n}^{mrg}_{X}(z_c)&=&\\frac{1}{N_{[SNae II+Ib/c]}}\\,\\, \\sum_{i}^{N_{X}}\n\\, \\frac{\\dot{n}_{[SNae II+Ib/c]}(z_s)}{(1+z_s)}\\\\ \n& & \\Theta[t(z_c)-t(z_F)-\\tau_{s,i}-\\tau_{m,i}]. \\nn\n\\eeq \n\nUsing this procedure, we compute the birth and merger-rates for all\nthe synthetic binary populations. The results are presented in \nFigs.~6,~7 and~8.\n\nDue to their relatively small $\\tau_s$ \ncompared to the\ncosmic time, the birthrates of (bh, bh), (ns, ns) and (bh, ns) systems\nclosely trace the UV-luminosity evolution, although with different\namplitudes. Our simulation suggests that (bh, bh) systems are more \nnumerous than (ns, ns) or (bh, ns) (see Fig.~6).\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=bhbirth_hier_Flat.ps,angle=270,width=8cm}\n\\psfig{figure=bhbirth_mon_Flat.ps,angle=270,width=8cm}\n\\caption{The formation rate of (bh, bh) ({\\bf asterisks}), (ns, ns) ({\\bf dots}) and (bh, ns) ({\\bf triangles}) binaries as a function of $z$ is\nshown for hierarchical ({\\bf upper} panel) and monolithic ({\\bf lower} panel) scenarios for \na flat cosmological background.} \n\\end{center}\n\\label{birthrate1}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nConversely, Fig.~7 shows that the birthrates of \n(wd, wd), (ns, wd) and (bh, wd) systems misrepresent the original\nUV-luminosity evolution as a consequence of their large $\\tau_s$. \nThe largest is the characteristic time-delay\n$\\tau_s$, the more the maximum is shifted versus lower redshifts because\nthe intense star formation activity observed at $z\\gsim2$, especially for\nmonolithic scenarios, boosts\nthe formation of degenerate systems at $z\\lsim2$. \nFor hierarchical scenarios,\nif the redshift at which significant star formation begins to occur is\n$z_F \\sim 5$, the birthrate of degenerate systems at redshifts $\\gsim4$\nis almost negligible.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=wdbirth_hier_Flat.ps,angle=270,width=8cm}\n\\psfig{figure=wdbirth_mon_Flat.ps,angle=270,width=8cm}\n\\caption{The formation rate of (wd, wd) ({\\bf asterisks}), (ns, wd)\n({\\bf dots}) and (bh, wd) ({\\bf triangles}) binaries as a function of $z$ is\nshown for hierarchical ({\\bf upper} panel) and monolithic ({\\bf lower} panel) scenarios for \na flat cosmological background.}\n\\end{center} \n\\label{birthrate2}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\nFinally, in Fig.~8, we have shown the predicted \nmerger-rate for (wd, wd), (ns, ns) and (ns, wd) systems. In this case,\nthe distortion of the original UV-luminosity evolution is even more apparent, \nparticularly for monolithic scenarios. The redshift at which the \nmaximum merger-rate occurs as well as the high redshift tail reflects\nthe different $\\tau_m$ distributions of these populations. \nWe have not shown the merger-rates for \n(bh, bh), (bh, wd) and (bh, ns) binaries because, as we have discussed\nin the previous section, these systems are predicted to have\nmerger-rates consistent with zero throughout the history of the Universe\nas a consequence of their very large initial orbital separations.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\begin{center}\n\\psfig{figure=wdmerger_hier_Flat.ps,angle=270,width=8cm}\n\\psfig{figure=wdmerger_mon_Flat.ps,angle=270,width=8cm}\n\\caption{The merger-rate of (wd, wd) ({\\bf asterisks}), (ns, ns) ({\\bf\ndots}) and (ns, wd) ({\\bf triangles}) binaries as a function of $z$ is\nshown for hierarchical ({\\bf upper} panel) and monolithic ({\\bf lower} panel) scenarios for \na flat cosmological background.}\n\\end{center} \n\\label{mergerate}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\n\\subsection{Stochastic backgrounds}\n\nHaving characterized each ensemble $X$ by the distribution of chirp mass \nand time delays, $p_X(\\tau_s, \\tau_m, {\\cal M})$, \nand by the birthrate density evolution per entry $\\dot{\\eta}(z)$, we can sum up\nthe gravitational signals coming from all the elements of the ensemble. \nThe spectrum of the resulting stochastic background, for a binary\ntype $X$ and at a given observation frequency $\\nu$, is\ngiven by the following expression,\n \n\\beq\n\\label{eq:BINenergydensity}\n\\frac{dE}{d\\Sigma dt d\\nu}[\\nu] &=&\\int_0^{z_F}\\!\\!dz_f \\int_{0}^{t(z_f)-t(z_F)}\n\\!\\!\\!d\\tau_s \\frac{ N_X \\, \\dot{\\eta}(z_s)}{(1+z_s)} \\\\ \n& & \\int_0^{\\infty}\\!\\!d{\\cal M} \\,d\\tau_m\\, \np_X(\\tau_s, \\tau_m, {\\cal M}) \\, \\frac{dV}{dz_e^*} \\, f[\\nu, z_e^*] \\nn\n\\eeq\nwhere $z_F$ is the redshift of the onset of star formation in the Universe, \n$z_f$ is the redshift of formation of the degenerate binary systems,\n$z_s$ is the redshift of formation of the corresponding progenitor system\ndefined by $t(z_s)=t(z_f)-\\tau_s$, $f[\\nu, z_e^*]$ is given by eq.~(5) and \n$z_e^*$ is the redshift of emission that an element of the ensemble \nmust have in order to contribute to the energy density at the observation \nfrequency $\\nu$.\n\nIt follows from eq.~(\\ref{freinterval}) that, for a given observation \nfrequency $\\nu$, $z_e^*$ is a function of $z_f$, $\\tau_m$, ${\\cal M}$ and $\\nu_{max}$.\nIn principle, an inspiraling compact binary system emits a continuous\nsignal from its formation to its final coalescence thus,\n$z_c \\le z_e \\le z_f$.\nHowever, in eq.~(\\ref{eq:BINenergydensity}) we do not restrict to systems \nwhich reach their final coalescence at $z_c\\geq0$ as we are interested to\n{\\it any} source between $z=0$ and $z=z_F$ emitting gravitational\nwaves during its early inspiral phase. Therefore, the signals which contribute\nto the local energy density at observation frequency $\\nu$ might be emitted\nanywhere between $\\sup[0,z_c] \\le z_e^* \\le z_f$, provided that, \n\\beq\n\\label{eq:bin_freconstraint}\n(\\pi \\nu)^{-8/3}=(\\pi \\nu_{max})^{-8/3}(1+z_e^*)^{8/3} + \n\\frac{256}{5} \\, {\\cal M}^{5/3} \\\\ \n\\left[t(z_f)+ \\tau_m -t(z_e^*)\\right](1+z_e^*)^{8/3}. \\nn \n\\eeq\nSubstituting eq.~(\\ref{eq:deltaprob}) in eq.~(\\ref{eq:BINenergydensity}),\nwe can write the background energy density generated by a population $X$ in the\nform, \n\\beq\n\\frac{dE}{d\\Sigma dt d\\nu}[\\nu] &=&\\int_0^{z_F}\\!\\! dz_f \\sum_{i}^{N_{X}}\n\\frac{\\dot{\\eta}(z_s)}{(1+z_s)}\\\\ \n& &\\Theta[t(z_f)-t(z_F)-\\tau_{s,i}]\\,\n\\frac{dV}{dz_e^*} \\, f[\\nu, z_e^*] \\nn\n\\eeq\nwhere $z_e^*$ satisfies eq.~(\\ref{eq:bin_freconstraint}).\n\nThe predicted spectral energy densities for the populations of degenerate binary types \nthat we have considered are plotted in Fig.~9.\nFor each binary type, we show the results obtained assuming both monolithic\nand hierarchical scenarios for the evolution of the underlying galaxy population.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=bhbh_spe.ps,angle=270,width=7.cm}\n\\psfig{figure=wdwd_spe.ps,angle=270,width=7.cm}\n\\psfig{figure=nsns_spe.ps,angle=270,width=7.cm}\n\\psfig{figure=bhns_spe.ps,angle=270,width=7.cm}\n\\psfig{figure=bhwd_spe.ps,angle=270,width=7.cm}\n\\psfig{figure=nswd_spe.ps,angle=270,width=7.cm}\n\\caption{The spectral energy density of the gravitational background\nproduced by various extragalactic populations of degenerate binaries in \nmonolithic and hierarchical scenarios assuming a flat cosmological\nbackground with zero cosmological constant.} \n\\end{center}\n\\label{fig:bin_spectra}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe spectral energy densities are characterized by the presence of a sharp\nmaximum which, depending on the\nbinary population, has an amplitude spanning about two orders of magnitudes, \nin the frequency range $[10^{-5}-10^{-4}]$~Hz. In the following, we refer to\nthis part of the signal as 'primary' component. At higher frequencies, a\n'secondary' component appears for all but (bh, bh) systems. The frequency\nwhich marks the transition between primary and secondary components as\nwell as their relative amplitudes depend sensitively on the population.\n\nThe reason why (bh, bh) systems do not show a secondary component is that\nthis is entirely contributed by sources which merge before $z=0$. Conversely,\nthe low-frequency part of the spectrum is dominated by systems with \nmerger-times larger than a Hubble time. \nThese sources are observed at very low\nfrequencies because the value of the minimum frequency \n(which is emitted at formation, $z_f$) is set by the amplitude of the\nmerger-time [see eq.~(16)]. The larger is the merger-time, the smaller the\nminimum frequency at which the in-spiral waves are emitted. Moreover, \neq.~(6) shows that the flux emitted by each source decreases with frequency.\nThis explains the larger amplitude of primary components with respect to\nsecondary ones. \nFor systems with merger-times larger than a Hubble time, the largest \nfrequency is emitted at $z=0$ by binaries which form at $z_f \\sim z_F$.\nNo contribution from such objects can be observed above this critical \nfrequency and the primary component falls rapidly to zero. \n\nThe amplitude of secondary components reflects the number of systems\nwith moderate merger-times. The maximum frequency which might be observed is\nemitted by systems which are very close to their coalescence at $z=0$.\nSince $\\nu_{max}$ is larger for (ns, ns) than for (wd, wd), the secondary\ncomponent produced by double neutron stars extends up to $\\sim10^2$~Hz.\n\nIt is interesting to note is that monolithic scenarios predict a \nmaximum amplitude which is a factor $\\sim$ 20-25\\% larger than the\nhierarchical case. This difference is much larger than what has been \npreviously obtained for other extragalactic backgrounds (see \\eg FMSI), \nindicating that\nthe energy density produced by extragalactic compact binaries is substantially\ncontributed by sources which form at redshifts $\\gsim 1-2$. It is quite \ndifficult to\nunveil the origin of this effect because of the large number of parameters which\ndetermine the appearance of the final energy density. However, a plausible explanation\nmight be that, depending on its specific time-delays $\\tau_s$ and $\\tau_m$, each\nsystem emits the signal at redshifts which can be substantially smaller than the\nformation redshift of the corresponding progenitor system. Thus, although the \nbackground signal is mostly emitted at low-to-intermediate redshifts, the sources\nwhich produce these signals might have been formed at higher redshifts and \nreflect the state of the Universe at earlier times, when the differences among\nhierarchical and monolithic scenarios are more significant. \nComparing the different panels of Fig.~9, we conclude\nthat the background produced by (bh, bh) binaries has the largest amplitude\nbut it is concentrated at frequencies below $\\sim 2\\times 10^{-5}$~Hz. At\nhigher frequencies, which are more interesting from the point of view of \ndetectability, the dominant contribution comes from (wd, wd) systems.\nThis is consistent with what has already been found for the galactic \npopulations (Hils, Bender \\& Webbink 1990).\n\n>From the background spectrum it is possible to compute the closure density\n$\\Omega_{gw} \\, h^2$ and the spectral strain amplitude of the signal $S_h$,\n\\beq\nS_h(\\nu)& =& \\frac{2 G}{\\pi c^3} \\,\\,\\frac{1}{\\nu^2} \\,\\,\\frac{dE}{dSdtd{\\nu}}({\\nu}), \\\\\n\\Omega_{gw}(\\nu)&=& \\frac{\\nu}{c^3 \\rho_{cr}}\\, \\frac{dE}{dt dS\nd\\nu}(\\nu).\n\\eeq \nThe results are shown in Figs.~10 and~11\nfor all binary types within monolithic and hierarchical scenarios.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=bhbh_sh.ps,angle=270,width=7.cm}\n\\psfig{figure=wdwd_sh.ps,angle=270,width=7.cm}\n\\psfig{figure=nsns_sh.ps,angle=270,width=7.cm}\n\\psfig{figure=bhns_sh.ps,angle=270,width=7.cm}\n\\psfig{figure=bhwd_sh.ps,angle=270,width=7.cm}\n\\psfig{figure=nswd_sh.ps,angle=270,width=7.cm}\n\\caption{The strain amplitude of the gravitational background\nproduced by various extragalactic populations of degenerate binaries in\nmonolithic and hierarchical scenarios assuming a flat cosmological background\nmodel with zero cosmological constant.} \n\\end{center}\n\\label{fig:bin_sh}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nThe strain amplitude of the backgrounds has a maximum amplitude\nbetween $\\sim 10^{-18} \\, \\mbox{Hz}^{-1/2}$ and\n$\\sim 5 \\times 10^{-17}\\,\\mbox{Hz}^{-1/2}$ at frequencies in the interval\n$[\\sim 5 \\times 10^{-6}-5 \\times 10^{-5}]$~Hz.\nThe function $S_h$ is more sensitive to the low frequency part of the\nenergy density. \nTherefore, its shape reflects \nmainly the primary components of the corresponding \nenergy density. In all but the (bh, bh) population,\nit is evident the presence of a tail at frequencies above\nthe maximum which is the secondary component of the energy density: \nin the next section we compare this part of the\nbackground signal with the LISA sensitivity to assess the possibility of\na detection. Still, it is clear that the prominent part of the background\nsignals produced by extragalactic populations of degenerate binaries \ncould be observed with a detector sensitive to smaller frequencies than LISA.\n\nConversely, $\\Omega_{gw} \\, h^2$ is mostly dominated by secondary components.\nWe can compare the predictions for (bh, bh), (wd, wd) and (ns, ns)\nsystems. Contrary to what has been found for the spectral energy density\nor for the strain amplitude of the signal, the largest $\\Omega_{gw} \\, h^2$\nis produced by (ns, ns), as a consequence of \nthe high amplitude of the secondary component. \nIn particular, no significant contribution\nfrom the primary component appears.\nFor (wd, wd), instead, the contribution of the primary component\nis relevant, although its amplitude is roughly half that of the secondary\ncomponent.\nFinally, for (bh, bh) no secondary component is produced and thus the \namplitude of the closure density is very low and at very low frequencies.\nMixed binary types have different properties, depending on the\nrelative importance of the above effect. \nFor instance, (bh, wd) produce a secondary component but the amplitude is\nso small to be comparable with that of the primary. \n\n\nWe stress that the value of $\\nu_{max}$ is quite uncertain as it\ndefines the boundary between the early inspiral phase and the highly \nnon-linear merger. Clearly, the more we get closer to this boundary, the\nless accurate is the Newtonian description of the orbit as post-Newtonian\nterms start to be relevant. Therefore, we believe that the most reliable \npart of the binary background signal is the low frequency part, \\ie the\npart which mostly contributes to the strain amplitude $S_h$.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure*}\n\\begin{center}\n\\leavevmode\n\\psfig{figure=bhbh_home.ps,angle=270,width=7.cm}\n\\psfig{figure=wdwd_home.ps,angle=270,width=7.cm}\n\\psfig{figure=nsns_home.ps,angle=270,width=7.cm}\n\\psfig{figure=bhns_home.ps,angle=270,width=7.cm}\n\\psfig{figure=bhwd_home.ps,angle=270,width=7.cm}\n\\psfig{figure=nswd_home.ps,angle=270,width=7.cm}\n\\caption{The function $\\Omega_{gw}\\, h^2$ of the gravitational background\nproduced by various extragalactic populations of degenerate binaries in \nmonolithic and hierarchical scenarios assuming a flat cosmological\nbackground model with zero cosmological constant.} \n\\end{center}\n\\label{fig:bin_omega}\n\\end{figure*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\n\\section{Confusion noise level and detectability by LISA} \n\n\nTo have some confidence in the detection of \na stochastic gravitational background with LISA it is necessary \nto have a sufficiently large $\\SNR$. The standard choice made by\nthe LISA collaboration is $\\SNR=5$ which, in turn, yields a \nminimum detectable amplitude of a stochastic signal of \n(see Bender 1998 and references therein),\n\\be\nh^2 \\, \\Omega_{gw}[\\nu = 1\\,\\mbox{mHz}] \\simeq 10^{-12}.\n\\ee\n \nThis value already accounts for the angle between the arms ($60^\\circ$)\nand the effect of LISA motion. It shows the remarkable sensitivity\nthat would be reached in the search for stochastic signals at low \nfrequencies. Table~\\ref{tbl:minima} shows that the backgrounds\ngenerated by (wd, wd) and (ns, ns) \nextragalactic binary populations exceed this minimum\nvalue and LISA might be able to detect these signals.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{table}\n\\centering\n\\begin{tabular}{|c|cc|} \\hline \\hline \n$\\nu=$1~mHz & (wd, wd) & (ns, ns) \\\\\n\\hline \n$\\Omega_{gw}\\,h^2$& $6 \\times 10^{-12}$ & $1.1 \\times 10^{-12}$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\caption{The values of the closure density at 1~mHz obtained for \n(wd, wd) and (ns, ns) extragalactic binary populations investigated. \nAll these values\nare larger than the minimum detectable value of $\\Omega_{gw}\\,h^2(1\\mbox{mHz})$ predicted by the LISA team for a $\\SNR=5$ and after 1 year of observation.}\n\\label{tbl:minima}\n\\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nWe plot in Fig.~\\ref{fig:hrms} the predicted sensitivity of LISA to a stochastic\nbackground after 1 year of observation (Bender 1998).\nOn the vertical axis it is shown $h_{\\rms}$, defined as,\n\\be\nh_{\\rms} = [2\\,\\nu\\, S_n(\\nu)]^{1/2} \\, \\left(\\frac{\\Delta \\nu}{\\nu}\\right)^{1/2}\n\\ee\nwhere $S_n(\\nu)$ is the predicted spectral noise density and the factor \n$(\\Delta \\nu/\\nu)^{1/2}$ is introduced to account for the frequency\nresolution $\\Delta \\nu = 1/T$ attained after a total observation time \n$T$.\\\\\nOn the same plot we show the equivalent $h_{\\rms}$ levels predicted \nfor different extragalactic binary populations and for the galactic \npopulation of close white dwarfs binary considered by Bender \\& Hils\n(1997).\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\n\\psfig{figure=hrms.ps,angle=270,width=8cm}}\n\\caption{The sensitivity of LISA to a stochastic background of gravitational\nwaves after one year of observation. The extragalactic backgrounds from\n(wd, wd), (ns, ns), (ns, wd) and (bh, ns) systems \nmight be observable at frequencies between $\\sim 1$ and $\\sim10$~mHz.} \n\\label{fig:hrms}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nWe see that the extragalactic backgrounds might be observable at frequencies\nbetween $\\sim 1$ and $\\sim 10$~mHz. \n\nThese background signals represent\nadditional noise components to the LISA sensitivity curve when\nsearching for signals from individual sources. \n\nIn particular, backgrounds from unresolved astrophysical sources represent\na confusion limited noise. In fact, unless the signal emitted\nby an individual source has a much higher amplitude, the background signal\nprevents the individual source to be resolved. Clearly, the magnitude of this\neffect depends on the frequency resolution of the instrument, \\ie on the\nobservation time. The $h_{\\rms}$ noise levels produced by extragalactic \ncompact binaries shown in Fig.~\\ref{fig:hrms} have been computed assuming\n$T=1$~yr. For the same total observation time we show, \nin Fig.~\\ref{fig:numbin}, the number of extragalactic (wd, wd) and (ns, ns) \nobserved in each frequency resolution bin. At frequencies were these \nbackgrounds might be relevant (between 1 and 10~mHz), the number of sources\nper bin is $\\gg 1$, representing a relevant confusion limited noise component.\nThe critical frequency above which the number of sources per bin is lower\nthan 1 occurs at $\\sim 0.1$~Hz for (wd, wd) and outside LISA sensitivity \nwindow for (ns, ns). However, at these frequencies \nthe dominant noise component is the instrumental noise. \n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\n\\psfig{figure=numbin.ps,angle=270,width=8cm}}\n\\caption{The number of extragalactic (wd, wd) and (ns, ns) binaries per\nresolution bin after a total observation time of 1yr.} \n\\label{fig:numbin}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Conclusions}\n\nIn this paper we have obtained estimates for the stochastic\nbackground of gravitational waves emitted by cosmological populations of compact binary\nsystems during their early-inspiral phase.\n\nSince we have restricted our investigation to frequencies well below the \nfrequency emitted when each system approaches its last stable circular\norbit, we have characterized the single source emission \nusing the quadrupole approximation. \n\nOur main motivation was to develop a simple method to estimate the \ngravitational signal produced by populations of binary systems at \nextragalactic distances. This method relies on three main pieces of \ninformation:\n\\begin{enumerate}\n\\item\nthe theoretical description of gravitational waveforms to \ncharacterize the single source contribution to the overall background \n\\item\nthe predictions of binary population synthesis codes to characterize the \ndistribution of astrophysical parameters (masses of the stellar components, \norbital parameters, merger times etc.) among each ensemble of binary systems\n\\item \na model for the evolution of the cosmic star formation history derived from\na collection of observations out to $z \\sim 5$ to infer the evolution of the\nbirth and merger rates for each binary population throughout the Universe.\n\\end{enumerate}\nAs we have considered only the early-inspiral phase of the binary evolution,\nour predictions for the resulting gravitational signals are restricted to the\nlow frequency band $10^{-5}-1$~Hz. The stochastic background signals produced\nby (wd, wd) and (ns, ns) might be observable with LISA and \nadd as confusion limited noise components to the LISA instrumental noise \nand to the signal produced by binaries within our own Galaxy. \nThe extragalactic contributions are dominant at frequencies in the range \n$1-10$~mHz and limit the performances expected for LISA in the\nsame range, where the previously estimated sensitivity curve was attaining\nits mimimum. \n\nWe plan to extend further this preliminary study and to consider more\nrealistic waveforms so as to enter a frequency region interesting for\nground-based experiments.\n\nFinally, in Fig.~\\ref{fig:extragal}\nwe show the spectral densities of the extragalactic backgrounds that have\nbeen investigated so far. \nThe high frequency band appears to be dominated by the stochastic\nsignal from a population of rapidly rotating neutron stars via the r-mode \ninstability (see FMSII). For comparison, \nwe have shown the overall signal emitted during\nthe core-collapse of massive stars to black holes (see FMSI). \nIn this case, the amplitude\nand frequency range depend sensitively on the fraction of progenitor \nstar which participates to the collapse. \nThe signal indicated with BH corresponds to the\nconservative assumption that the core mass is $\\sim 10 \\%$ of the \nprogenitor's (see FMSI).\nRecent numerical simulations of core-collapse supernova\nexplosions (Fryer 1999) appear to indicate that for progenitor\nmasses $>40 \\msun$ no supernova explosion occurs and the star directly \ncollapses to form a black hole. The final mass of this core depends \nstrongly on the relevance of mass loss caused by stellar winds \n(Fryer \\& Kalogera 2000). \nIf massive black holes are formed the resulting background would have\na larger amplitude and the relevant signal would be shifted towards \nlower frequencies, more interesting for ground-based interferometers\n(Schneider, Ferrari \\& Matarrese 1999).\n\nIn the low frequency band, we have plotted only the backgrounds produced by \n(bh, bh), (ns, ns) and (wd, wd) binaries because their signals largely \noverwhelm those from other degenerate binary types. \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}\n\\centerline{\\psfig{figure=extragalactic.ps,angle=270,width=8cm}}\n\\caption{The predicted strain amplitude of the stochastic backgrounds \nproduced by extragalactic populations of gravitational sources. In the high\nfrequency band, we show the estimates for the background produced by \nrotating neutron \nstars via r-mode instability, and two possible signals emitted by populations\nof massive stars collapsing to black holes (see text). In the \nlow frequency band, we plot the background predicted \nfor three different populations of binary systems.}\n\\label{fig:extragal}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \nWe find that both in the low and in the high frequency band, \nextragalactic populations generate a signal which is comparable to and,\nin some cases, larger than the\nbackgrounds produced by populations of sources within our Galaxy \n(Giazotto, Bonazzola \\& Gourgoulhon 1997; Giampieri 1997; Postnov 1997;\nHils, Bender \\& Webbink 1990; Bender \\& Hils\n1997; Postnov \\& Prokhorov 1998; Nelemans, Portegies Zwart \\& Verbunt 1999).\nIt is important to stress that even if future\ninvestigations reveal that the amplitude of galactic \nbackgrounds might be higher than presently conceived,\ntheir signal could still be discriminated from that generated by\nsources at extragalactic distance. In fact, the signal produced within the\nGalaxy shows a characteristic amplitude modulation\nwhen the antenna changes its orientation with respect to fixed stars\n (Giazotto, Bonazzola \\& Gourgoulhon 1997; Giampieri 1997). \n\n\nThe same conclusions can be drawn when the extragalactic backgrounds are \ncompared to the stochastic relic gravitational signals predicted by\nsome classical early Universe scenarios. \nThe relic gravitational\nbackgrounds suffer of the many uncertainties which characterize our\npresent knowledge of the early Universe. According to\nthe presently conceived typical spectra, we find that their detectability\nmight be severely limited by the amplitude of the more recent astrophysical\nbackgrounds, especially in the high frequency band. \n\n\n\n\n\n\\section*{Acknowledgments}\nWe acknowledge Bruce Allen, Pia Astone, Andrea Ferrara, Sergio Frasca, Piero Madau and Lucia \nPozzetti for useful conversations and fruitful insights in various aspects\nof the work.\n\nSPZ thank Gijs Nelemans and Lev Yungelson for discussions and\ncode developement. This work was supported by NASA through Hubble\nFellowship grant HF-01112.01-98A awarded (to SPZ) by the Space\nTelescope Science Institute, which is operated by the Association of\nUniversities for Research in Astronomy, Inc., for NASA under contract\nNAS\\, 5-26555. Part of the calculations are performed on the\nOrigin2000 SGI supercomputer at Boston University. SPZ is grateful to\nthe University of Amsterdam (under Spinoza grant 0-08 to Edward\nP.J. van den Heuvel) for their hospitality.\n\n\\newpage\n\n\\begin{thebibliography}{99}\n\n\n\n\n\n\\bibitem{}\nAbt H.A., Levy S.G., 1978, ApJSS, 36, 241 \n\n\\bibitem{} \nBender P. L. \\& Hils D., 1997, Class. Quant. Gravity,\n14, 1439 \n\n\\bibitem{}\nBender P.L. for the LISA SCIENCE TEAM, 1998, {\\em LISA Pre-Phase Report},\nsecond edition \n\n\\bibitem{DC}\nCalzetti D., 1997, AJ 113, 162 \n\n\\bibitem{} \nCalzetti D., Heckman T. M., 1999, ApJ, 519, 27\n\n\\bibitem{}\nCarraro G., Chiosi G., 1994, A\\&A, 287, 761\n\n\\bibitem{} \nCappellaro E., Turatto M., Tsvetkov D.Y., Bartunov O.S., \nPollas C., Evans R., Hamuy M., 1997, A\\&A, 322,431\n\n\\bibitem{} \nConnolly A.J., Szalay A.S., Dickinson M., SubbaRao M.U., Brunner R.J., 1997, \nApJ, L11\n\n\n\\bibitem{}\nCutler C. \\etal, 1993, Phys. Rev. Lett., 70, 2984 \n\n\n\\bibitem{}\nDamour T., Iyer B.R., Sathyaprakash B.S., \n1998, in the Second Amaldi Conference\non Gravitational Waves, E. Coccia, G. Pizzella, G. Veneziano eds., \n(World Scientific, Singapore)\n\n\n\n\n\n\\bibitem{} Danzmann K. for the LISA Study Team, 1997, Class. Quant. Gravity,\n14, 1399\n\n\n\\bibitem{}\nDuquennoy A., Mayor M., 1991, A\\&A, 248, 485\n\n\n\n\\bibitem{} \nEllis R.S., 1997, A.R.A.A., 35, 389 \n\n\n\\bibitem{} \nFerrari V., Matarrese S., Schneider R., 1999a, MNRAS, 303, 247 (FMSI)\n\n\n\\bibitem{} \nFerrari V., Matarrese S., Schneider R., 1999b, MNRAS, 303, 258 (FMSII)\n\n\n\\bibitem{}\nFixsen D.J., Dwek E., Mather J.C., Bennett C.L., Shafer R.A.,1998, ApJ, 508, 123\n\n\n\\bibitem{}\nFlanagan E.E. \\& Hughes S.A., 1998, Phys. Rev. D57, 4535\n\n\n\n\\bibitem{}\nFlores H., Hammer F., Thuan T.X., C\\'esarsky C., Desert F.X., Omont A., Lilly S.J., Eales S., Crampton D. and Le F\\'evre O., 1999, 517, 148\n\n\n\n\\bibitem{}\nFryer C.L., 1999, ApJ, 522, 413\n\n\\bibitem{}\nFryer C.L., Kalogera V., 2000, submitted to ApJ, pre-print (astro-ph/9911312) \n\n\n\\bibitem{}\nGallego J., Zamorano J., Ar\\'agon-Salamanca A., Rego M., 1995, ApJ, 455, L1\n\n\\bibitem{}\nGiampieri G., 1997, MNRAS, 292, 218\n\n\\bibitem{}\nGiazotto A., Bonazzola S., Gourgoulhon E., 1997, Phys. Rev. D55, 2014\n\n\n\n\\bibitem{}\nGlazebrook K., Blake C., Frossie E., Lilly S., Colless M., 1999, \nMNRAS, 306, 843\n\n\\bibitem{}\nGronwall, 1999, {\\em \nAfter the Dark Ages: When Galaxies were Young (the Universe at $2<z<5$)},\n 9th Annual October Astrophysics Conference in Maryland, S. Holt, E. Smith eds., American Institute of Physics Press, pg. 335\n\n\n\n\\bibitem{}\nHartman J.W., Bhattacharya D., Wijers R.A.M.J.,Verbunt F., 1997, A\\&A, 322, \n477\n\n\\bibitem{}\nHils D.L., Bender P., Webbink R.F., 1990, ApJ, 360, 75\n\n\\bibitem{}\nHughes D. H. and the UK Submillimeter Survey Consortium, 1998,\nNature, 394, 241\n\n\n\\bibitem{}\nKidder L.E., Will C.M., Wiseman A.G., 1993, Phys. Rev. D47, 3281\n\n\n\\bibitem{}\nKosenko, D.I. \\& Postnov, K.A., 1998, A\\&A, 336, 786\n\n\\bibitem{}\nKraicheva, Z.T., Popova, E.I., Tutukov, A.V., Yungelson, L.R., 1978,\nAZh. 55, 1176 \n\n\n\\bibitem{}\nLanger, N., Hamann, W.~R., Lennon, M., et al.\\,\nNajarro, F., Pauldrach, A. W.~A., Puls, J. \n1994, A\\&Ap 290, 819\n\n\n\n\\bibitem{} \nLilly S.J., Le F\\'{e}vre O., Hammer F., Crampton D., 1996, ApJ, 460, L1 \n\n\n\\bibitem{} \nLipunov V.M., Nazin S.N., Panchenko I.E., Postnov K.A., Prokhorov M.E., 1995,\nA\\&A, 298, 677\n\n\n\\bibitem{} \nLipunov V.M., 1997, invited review at the XXIII General Assembly of IAU\n``High Energy Transients'', Kyoto, 1997 pre-print (astro-ph/9711270).\n\n\n\n\\bibitem{}\nLISA: Jafry,\nY. R., Cornelisse, J., Reinhard, R., 1994, ESA Journal (ISSN\n0379-2285), vol. 18, no. 3, p. 219-228\n\n\n\n\\bibitem{} \nMadau P., Ferguson H.CC., Dickinson M.E., Giavalisco M.,\nSteidel C.C., Fruchter A., 1996, MNRAS, 283, 1388\n\n\n\\bibitem{} \nMadau P., Pozzetti L., Dickinson M., 1998a, ApJ, 498, 106\n\n\n\\bibitem{}\nMadau P., Della Valle M., Panagia N., 1998b, MNRAS, 297, L17 \n\n\n\n\\bibitem{}\nMao S., Yi I., 1994, ApJ, 424, L131\n\n\n\\bibitem{}\nMeynet G., Mermilliod J.C., Maeder A., 1993, A\\&AS, 98, 477 \n\n\n\\bibitem{} \nMironovskij V.N., 1966, Sov. Astr.- AJ, 9 752\n\n\n\n\\bibitem{}\nMisner C. W., Thorne K. S., Wheeler J.A., {\\em Gravitation},\nNineteenth printing, 1995, W.H. Freeman \\& Co., New York\n\n\n\n\\bibitem{}\nNarayan, R.,\nPiran, T., Shemi, A., 1991, ApJ 379, L17--21\n\n\n\n\\bibitem{}\nNauenberg, M., 1972, ApJ, 175, 417\n\n\n\n\\bibitem{}\nNelemans G., Portegies Zwart S.F. \\& Verbunt F., 1999, \nto appear in the proceedings of the XXXIVth Rencontres de Moriond on \n\"Gravitational Waves and Experimental Gravity\", pre-print (astro-ph/9903255)\n\n\n\\bibitem{}\nPaczy{\\'n}ski B., 1986, ApJ, 308, L43\n\n\n\\bibitem{}\nPaczy{\\'n}ski B., 1990, ApJ, 348, 485\n\n\\bibitem{} \nPain R., \\etal 1997, ApJ, 473, 356\n\n\\bibitem{} \nPei Y.C., Fall S.M., 1995, ApJ, 454, 69\n\n\\bibitem{} \nPei Y.C., Fall S.M., Hauser M.G., 1999, ApJ, 522, 604\n\n\\bibitem{} \nPerlmutter S., \\etal 1998, Nature, 391, 51\n\n\n\\bibitem{} \nPeters, Mathews, 1963, Phys. Rev., 131, 435\n\n\n\\bibitem{}\nPiran E.S., 1996, in Compact stars in binaries, ed. J. van Paradijs, \nE.P.J. van den Heuvel, E. Kuulkers (Dordrecht: Kluwer), p. 489\n\n\n\\bibitem{}\nPortegies Zwart S.F. \\& Verbunt F., 1996, A\\&A, 309, 179\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& Yungelson, L.R., 1998, A \\& A 332, 173\n\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& Yungelson, L.R., 1999, MNRAS, 309, L26\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& McMillan S.L.W., 1999, ApJ {\\em in press}\n\n\\bibitem{} \nPostnov, K.A. \\& Prokhorov, M.E., 1998, ApJ 494, 674\n\n\\bibitem{}\nRasio, F.A., Shapiro, S.L., 2000, invited Topical Review to appear in\nClassical and Quantum Gravity, pre-print (gr-qc/9902019) \n\n\n\n\\bibitem{}\nRosi, L.A., Zimmermann, R.L., 1976, ApJSS 45, 447\n\n\n\\bibitem{}\nScalo, J.M., 1986, Fund. of Cosm. Phys. 11,1\n\n\\bibitem{}\nSchneider R., Ferrari V., Matarrese S., 1999, in preparation\n\n\n\\bibitem{} \nSteidel C.C., Giavalisco M., Pettini M., Dickinson M., Adelberger K.L., \n1996, ApJ, 462L, 17\n\n\n\\bibitem{} \nSteidel C.C., Adelberger K.L., Giavalisco M., Dickinson M., Pettini M., \n1999, ApJ, 519, 1\n\n\n\n\\bibitem{}\nTammann G.A., L\\\"{o}ffler W., Schr\\\"{o}der A., 1994, ApJS, 92, 487 \n\n\n\\bibitem{} \nTreyer, M.A., Ellis, R.S., Milliard, B., Donas, J., Bridges, T.J., 1998,\nMNRAS 300,303 \n\n\\bibitem{} \nTresse L., Maddox S.J., 1998, ApJ, 495, 691\n\n\n\\bibitem{}\nvan den Bergh, S., Tamman, G.A., 1991, ARA\\&A 29, 363 \n\n\\bibitem{}\nvan den Heuvel, E.P.J., Lorimer, D.R., 1996, MNRAS 283, L37\n\n\n\\bibitem{}\nvan den Hoek, B., 1997, PhD Thesis, U. Amsterdam \n\n\\bibitem{}\nvan den Hoek, B., de Jong, T., 1997, A\\&A 318, 231\n\n\n\n\n\n\n\\end{thebibliography}\n\n\n\\label{lastpage}\n\n\\end{document}\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002055.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\n\n\n\n\\bibitem{}\nAbt H.A., Levy S.G., 1978, ApJSS, 36, 241 \n\n\\bibitem{} \nBender P. L. \\& Hils D., 1997, Class. Quant. Gravity,\n14, 1439 \n\n\\bibitem{}\nBender P.L. for the LISA SCIENCE TEAM, 1998, {\\em LISA Pre-Phase Report},\nsecond edition \n\n\\bibitem{DC}\nCalzetti D., 1997, AJ 113, 162 \n\n\\bibitem{} \nCalzetti D., Heckman T. M., 1999, ApJ, 519, 27\n\n\\bibitem{}\nCarraro G., Chiosi G., 1994, A\\&A, 287, 761\n\n\\bibitem{} \nCappellaro E., Turatto M., Tsvetkov D.Y., Bartunov O.S., \nPollas C., Evans R., Hamuy M., 1997, A\\&A, 322,431\n\n\\bibitem{} \nConnolly A.J., Szalay A.S., Dickinson M., SubbaRao M.U., Brunner R.J., 1997, \nApJ, L11\n\n\n\\bibitem{}\nCutler C. \\etal, 1993, Phys. Rev. Lett., 70, 2984 \n\n\n\\bibitem{}\nDamour T., Iyer B.R., Sathyaprakash B.S., \n1998, in the Second Amaldi Conference\non Gravitational Waves, E. Coccia, G. Pizzella, G. Veneziano eds., \n(World Scientific, Singapore)\n\n\n\n\n\n\\bibitem{} Danzmann K. for the LISA Study Team, 1997, Class. Quant. Gravity,\n14, 1399\n\n\n\\bibitem{}\nDuquennoy A., Mayor M., 1991, A\\&A, 248, 485\n\n\n\n\\bibitem{} \nEllis R.S., 1997, A.R.A.A., 35, 389 \n\n\n\\bibitem{} \nFerrari V., Matarrese S., Schneider R., 1999a, MNRAS, 303, 247 (FMSI)\n\n\n\\bibitem{} \nFerrari V., Matarrese S., Schneider R., 1999b, MNRAS, 303, 258 (FMSII)\n\n\n\\bibitem{}\nFixsen D.J., Dwek E., Mather J.C., Bennett C.L., Shafer R.A.,1998, ApJ, 508, 123\n\n\n\\bibitem{}\nFlanagan E.E. \\& Hughes S.A., 1998, Phys. Rev. D57, 4535\n\n\n\n\\bibitem{}\nFlores H., Hammer F., Thuan T.X., C\\'esarsky C., Desert F.X., Omont A., Lilly S.J., Eales S., Crampton D. and Le F\\'evre O., 1999, 517, 148\n\n\n\n\\bibitem{}\nFryer C.L., 1999, ApJ, 522, 413\n\n\\bibitem{}\nFryer C.L., Kalogera V., 2000, submitted to ApJ, pre-print (astro-ph/9911312) \n\n\n\\bibitem{}\nGallego J., Zamorano J., Ar\\'agon-Salamanca A., Rego M., 1995, ApJ, 455, L1\n\n\\bibitem{}\nGiampieri G., 1997, MNRAS, 292, 218\n\n\\bibitem{}\nGiazotto A., Bonazzola S., Gourgoulhon E., 1997, Phys. Rev. D55, 2014\n\n\n\n\\bibitem{}\nGlazebrook K., Blake C., Frossie E., Lilly S., Colless M., 1999, \nMNRAS, 306, 843\n\n\\bibitem{}\nGronwall, 1999, {\\em \nAfter the Dark Ages: When Galaxies were Young (the Universe at $2<z<5$)},\n 9th Annual October Astrophysics Conference in Maryland, S. Holt, E. Smith eds., American Institute of Physics Press, pg. 335\n\n\n\n\\bibitem{}\nHartman J.W., Bhattacharya D., Wijers R.A.M.J.,Verbunt F., 1997, A\\&A, 322, \n477\n\n\\bibitem{}\nHils D.L., Bender P., Webbink R.F., 1990, ApJ, 360, 75\n\n\\bibitem{}\nHughes D. H. and the UK Submillimeter Survey Consortium, 1998,\nNature, 394, 241\n\n\n\\bibitem{}\nKidder L.E., Will C.M., Wiseman A.G., 1993, Phys. Rev. D47, 3281\n\n\n\\bibitem{}\nKosenko, D.I. \\& Postnov, K.A., 1998, A\\&A, 336, 786\n\n\\bibitem{}\nKraicheva, Z.T., Popova, E.I., Tutukov, A.V., Yungelson, L.R., 1978,\nAZh. 55, 1176 \n\n\n\\bibitem{}\nLanger, N., Hamann, W.~R., Lennon, M., et al.\\,\nNajarro, F., Pauldrach, A. W.~A., Puls, J. \n1994, A\\&Ap 290, 819\n\n\n\n\\bibitem{} \nLilly S.J., Le F\\'{e}vre O., Hammer F., Crampton D., 1996, ApJ, 460, L1 \n\n\n\\bibitem{} \nLipunov V.M., Nazin S.N., Panchenko I.E., Postnov K.A., Prokhorov M.E., 1995,\nA\\&A, 298, 677\n\n\n\\bibitem{} \nLipunov V.M., 1997, invited review at the XXIII General Assembly of IAU\n``High Energy Transients'', Kyoto, 1997 pre-print (astro-ph/9711270).\n\n\n\n\\bibitem{}\nLISA: Jafry,\nY. R., Cornelisse, J., Reinhard, R., 1994, ESA Journal (ISSN\n0379-2285), vol. 18, no. 3, p. 219-228\n\n\n\n\\bibitem{} \nMadau P., Ferguson H.CC., Dickinson M.E., Giavalisco M.,\nSteidel C.C., Fruchter A., 1996, MNRAS, 283, 1388\n\n\n\\bibitem{} \nMadau P., Pozzetti L., Dickinson M., 1998a, ApJ, 498, 106\n\n\n\\bibitem{}\nMadau P., Della Valle M., Panagia N., 1998b, MNRAS, 297, L17 \n\n\n\n\\bibitem{}\nMao S., Yi I., 1994, ApJ, 424, L131\n\n\n\\bibitem{}\nMeynet G., Mermilliod J.C., Maeder A., 1993, A\\&AS, 98, 477 \n\n\n\\bibitem{} \nMironovskij V.N., 1966, Sov. Astr.- AJ, 9 752\n\n\n\n\\bibitem{}\nMisner C. W., Thorne K. S., Wheeler J.A., {\\em Gravitation},\nNineteenth printing, 1995, W.H. Freeman \\& Co., New York\n\n\n\n\\bibitem{}\nNarayan, R.,\nPiran, T., Shemi, A., 1991, ApJ 379, L17--21\n\n\n\n\\bibitem{}\nNauenberg, M., 1972, ApJ, 175, 417\n\n\n\n\\bibitem{}\nNelemans G., Portegies Zwart S.F. \\& Verbunt F., 1999, \nto appear in the proceedings of the XXXIVth Rencontres de Moriond on \n\"Gravitational Waves and Experimental Gravity\", pre-print (astro-ph/9903255)\n\n\n\\bibitem{}\nPaczy{\\'n}ski B., 1986, ApJ, 308, L43\n\n\n\\bibitem{}\nPaczy{\\'n}ski B., 1990, ApJ, 348, 485\n\n\\bibitem{} \nPain R., \\etal 1997, ApJ, 473, 356\n\n\\bibitem{} \nPei Y.C., Fall S.M., 1995, ApJ, 454, 69\n\n\\bibitem{} \nPei Y.C., Fall S.M., Hauser M.G., 1999, ApJ, 522, 604\n\n\\bibitem{} \nPerlmutter S., \\etal 1998, Nature, 391, 51\n\n\n\\bibitem{} \nPeters, Mathews, 1963, Phys. Rev., 131, 435\n\n\n\\bibitem{}\nPiran E.S., 1996, in Compact stars in binaries, ed. J. van Paradijs, \nE.P.J. van den Heuvel, E. Kuulkers (Dordrecht: Kluwer), p. 489\n\n\n\\bibitem{}\nPortegies Zwart S.F. \\& Verbunt F., 1996, A\\&A, 309, 179\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& Yungelson, L.R., 1998, A \\& A 332, 173\n\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& Yungelson, L.R., 1999, MNRAS, 309, L26\n\n\\bibitem{}\nPortegies Zwart, S.F. \\& McMillan S.L.W., 1999, ApJ {\\em in press}\n\n\\bibitem{} \nPostnov, K.A. \\& Prokhorov, M.E., 1998, ApJ 494, 674\n\n\\bibitem{}\nRasio, F.A., Shapiro, S.L., 2000, invited Topical Review to appear in\nClassical and Quantum Gravity, pre-print (gr-qc/9902019) \n\n\n\n\\bibitem{}\nRosi, L.A., Zimmermann, R.L., 1976, ApJSS 45, 447\n\n\n\\bibitem{}\nScalo, J.M., 1986, Fund. of Cosm. Phys. 11,1\n\n\\bibitem{}\nSchneider R., Ferrari V., Matarrese S., 1999, in preparation\n\n\n\\bibitem{} \nSteidel C.C., Giavalisco M., Pettini M., Dickinson M., Adelberger K.L., \n1996, ApJ, 462L, 17\n\n\n\\bibitem{} \nSteidel C.C., Adelberger K.L., Giavalisco M., Dickinson M., Pettini M., \n1999, ApJ, 519, 1\n\n\n\n\\bibitem{}\nTammann G.A., L\\\"{o}ffler W., Schr\\\"{o}der A., 1994, ApJS, 92, 487 \n\n\n\\bibitem{} \nTreyer, M.A., Ellis, R.S., Milliard, B., Donas, J., Bridges, T.J., 1998,\nMNRAS 300,303 \n\n\\bibitem{} \nTresse L., Maddox S.J., 1998, ApJ, 495, 691\n\n\n\\bibitem{}\nvan den Bergh, S., Tamman, G.A., 1991, ARA\\&A 29, 363 \n\n\\bibitem{}\nvan den Heuvel, E.P.J., Lorimer, D.R., 1996, MNRAS 283, L37\n\n\n\\bibitem{}\nvan den Hoek, B., 1997, PhD Thesis, U. Amsterdam \n\n\\bibitem{}\nvan den Hoek, B., de Jong, T., 1997, A\\&A 318, 231\n\n\n\n\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002056
|
The Light Elements Be and B as Stellar Chronometers in the Early Galaxy
|
[
{
"author": "Timothy C. Beers"
}
] |
Recent detailed simulations of Galactic Chemical Evolution have shown that the heavy elements, in particular [Fe/H], are expected to exhibit a weak, or absent, correlation with stellar ages in the early Galaxy due to the lack of efficient mixing of interstellar material enriched by individual Type II supernovae. A promising alternative ``chronometer'' of stellar ages is suggested, based on the expectation that the light elements Be and B are formed primarily as spallation products of Galactic Cosmic Rays.
|
[
{
"name": "beers.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Beers, Suzuki, \\& Yoshii}{The Light Elements as Chronometers}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{The Light Elements Be and B as Stellar Chronometers in the Early Galaxy}\n \\author{Timothy C. Beers}\n\\affil{Michigan State University, Dept. of Physics \\& Astronomy, E. Lansing, MI\n 48824 USA}\n\\author{Takeru K. Suzuki}\n\\affil{University of Tokyo, Dept. of Astronomy, School of Science,\nUniversity of Tokyo; Theoretical\nAstrophysics Division, National \nAstronomical Observatory, Mitaka, Tokyo, 181-8588 Japan}\n\\author{Yuzuru Yoshii}\n\\affil{University of Tokyo, Institute of Astronomy, School of Science, \nUniversity of Tokyo, Mitaka, Tokyo, 181-8588 Japan; \nResearch Center for the Early Universe, School \nof Science, University of Tokyo Japan}\n\n\\begin{abstract}\nRecent detailed simulations of Galactic Chemical Evolution have shown that the\nheavy elements, in particular [Fe/H], are expected to exhibit a weak, or\nabsent, correlation with stellar ages in the early Galaxy due to the lack of\nefficient mixing of interstellar material enriched by individual Type II\nsupernovae. A promising alternative ``chronometer'' of stellar ages is\nsuggested, based on the expectation that the light elements Be and B are formed\nprimarily as spallation products of Galactic Cosmic Rays.\n\\end{abstract}\n\n\\section{Introduction}\n\nIt has become clear, from a number of lines of recent evidence, that the early\nevolution of the Galaxy is best thought of as a stochastic process. Within\nthe first 0.5-1 Gyr following the start of the star formation process, chemical\nenrichment does not operate within a well-mixed uniform environment, as was\nassumed in the simple one-zone models that were commonly used in past\ntreatments of this problem. Rather, the very first generations of stars are\nexpected to have their abundances of heavy elements set by local conditions,\nwhich are likely to have been dominated by the yields from individual SNeII.\n\nThe seeds of this paradigm shift can be found in the observations,\ninterpretations, and speculations of McWilliam et al. (1995), Audouze \\& Silk\n(1995), and Ryan, Norris, \\& Beers (1996). Models which attempt to incorporate\nthese ideas into a predictive formalism have been put forward by Tsujimoto,\nShigeyama, \\& Yoshii (1999; hereafter TSY), and Argast et al. (2000).\nAlthough they differ in the details of their implementation, and in a number of\ntheir assumptions, both of these models rely on the idea of enhanced star\nformation in the high-density shells of SN remnants, and the interaction of\nthese shells of enriched material with a local ISM. The predictions which\nresult are similar as well: (1) Both models are capable of reproducing the\nobserved distributions of abundance (e.g., [Fe/H]) for stars in the tail of the\nhalo metallicity distribution function (Laird et al. 1988; Ryan \\& Norris 1991;\nBeers 1999), and (2) Both models predict that the abundances of heavy elements,\nsuch as Fe, are not expected to show strong correlations with the ages of the\nfirst stars, at least up until an enrichment level on the order of [Fe/H]$ \\sim\n-2.0$ is reached, i.e., at the time when mixing on a Galactic scale is possible\n(roughly 1 Gyr following the initiation of star formation).\n\nSuzuki, Yoshii, \\& Kajino (1999; hereafter SYK, see also Suzuki, Yoshii, \\&\nKajino, this volume) have extended the SN-induced chemical evolution model of\nTSY to include predictions of the evolution of the light element species\n$^9$Be, $^{10}$B, and $^{11}$B, based on secondary processes involving\nspallative reactions with Galactic Cosmic Rays (hereafter GCRs). Recently,\nSuzuki, Yoshii, \\& Beers (2000) have considered the extension of this model to\nthe prediction of $^6$Li and $^7$ Li, and demonstrate that they naturally\nreproduce the recently detected slope in the abundance of Li in extremely\nmetal-poor stars noted by Ryan, Norris, \\& Beers (1999; see also Ryan this\nvolume). It is particularly encouraging that the same stochastic\nstar-formation models which reproduce the observed trends of some (but not all)\nheavy elements, such as Eu, Fe, etc., also obtain predictions of the light\nelement abundance distributions that match the available observations quite\nwell, with a minimum of parameter tweaking.\n\nIn this contribution we summarize one of the more interesting predictions of\nthe TSY/SYK class of models, that the abundances of the light elements Be and B\n(hereafter, BeB) might be useful as stellar chronometers in the early Galaxy (a\ntime when the heavy element ``age-metallicity'' relationships are not operating\ndue to the lack of global mixing). It appears possible that, with refinement\nof the modeling, and adequate testing, observations of BeB for metal-poor\nstars may provide a chronometer with ``time resolution'' on scales of tens\nof Myrs.\n\t\t\n\\section{The Essence of the Model}\n\n\nIn this section we would like to briefly explain our model of SN-induced\nstar formation and chemical evolution. After formation of the very FIRST\ngeneration of (Pop. III) stars, with atmospheres containing gas of primordial\nabundance, the most massive of these stars exhaust their core H, and explode as\nSNeII. Following the explosion a shock is formed, because the velocity of the\nejected material exceeds the local sound speed. Behind the shock the\nswept-up ambient material in the ISM accumulates to form a high-density shell.\nThis shell cools in the later stages of the lifetime of a given SN remnant\n(SNR) and is a suitable site for the star formation process to occur. The\nSNR shells are expected to be distributed randomly throughout the early and\nrapidly evolving halo, and the shells do not easily merge with one another\nbecause of the large available volume. As a result, each SNR keeps its\nidentity and the stars which form there reflect the abundances of material\ngenerated by their ``parent'' SN. TSY present this model, and describe the\ninput assumptions, in more quantitative detail. Figure 1 provides a cartoon\nillustration of the processes which we discuss herein.\n\n\\begin{figure}\n%\\epsfxsize=11cm\n%\\epsfysize=13cm\n%\\epsfbox{beersf1.eps}\n\\plotfiddle{beersf1.eps}{11cm}{0.}{65.}{65.}{-215.}{-33.}\n\\caption{A simplified view of the early stages of chemical evolution in \nthe Galactic halo. In the lower cutout we show star formation \nbeing triggered in SNR shells. See text for more detail.} \n\\end{figure}\n\nOne of the most important results of the TSY model is that stellar metallicity,\nespecially [Fe/H], cannot be employed as an age indicator at these early\nepochs. Thus, to consider the expected elemental abundances of the metal-poor\nstars which form at a given time, a {\\it distribution} of stellar abundances\nmust be constructed, rather than adopting a global average abundance under the\nassumption that the gas of the ISM is well mixed. SYK constructed such a\nmodel, coupled with the model of SN-induced chemical evolution, which considers\nthe evolution of the light elements.\n\nSYK proposed that GCRs arise from the mixture of elements of individual SN\nejecta and their swept-up ISM, with the acceleration being due to the shock\nformed in the SNR. GCRs originating from SNeII propagate faster than the\nmaterial trapped in the clouds of gas making up the early halo. As a result,\nGCRs are expected to achieve uniformity throughout the halo faster than\nthe general ISM, with its patchy structure. It follows that the abundances of\nBeB, which are mainly produced by spallation processes of CNO elements\ninvolving GCRs, are expected to exhibit a much tighter correlation with time\nthan those of heavy elements, synthesized through stellar evolution and SN\nexplosions.\n\nWe note that alternative models for the origin of spallative nucleosynthesis\nproducts have been developed which rely on the existence of {\\it spatially\ncorrelated} SNeII in superbubbles of the early ISM (see Parizot \\& Drury\n1999, and this volume). The superbubble model predicts a locally homogeneous\nproduction of both heavy and light elements, and the variety of stellar\nabundances which are observed are explained by the differing diffusion\nprocesses of metal-rich ([Fe/H] $\\sim -1$) shells swept-up by the bubble and\nmixed with a metal-poor ([Fe/H] $\\sim -4$) ISM. Tests of the ``isolated'' SN\nmodels vs. the superbubble models are expected to be conducted in the near\nfuture. \n \n\\section{Abundance Predictions of the Model}\n\nFigure 2 shows the predicted behavior of the abundance of [Fe/H], log(Be/H),\nand log(B/H), as a function of time, over the first 0.6 Gyrs of the evolution\nof the early Galaxy, according to the model of SYK. At any given time (note\nthat ``zero time'' is set by the onset of star formation, not the beginning of\nthe Universe) the range of observed BeB is substantially less than that of Fe,\nowing to the global nature of light element production. For example, at time\n0.2 Gyrs, the expected stellar [Fe/H] extends over a range of 50, while that of\nlog (BeB/H) is on the order of 3--7.\n\nDuring early epochs Fe is produced {\\it only} by SNeII, and most of the Fe\nobserved in stars formed in SNR shells originates from that contributed by the\nparent SN, because of uniformly low Fe abundance in the ISM at that time.\nThus, the expected [Fe/H] of stars born at that time will exhibit a rather\nlarge range, reflecting differences in Fe yields associated with the different\nmasses of the progenitor stars. On the other hand, according to the SYK model,\nmost of the BeB is produced by spallation reactions of CNO nuclei involving\nglobally transported GCRs. The observed abundances of BeB in metal-poor stars\nwhich formed at this time should reflect the global nature of their production,\nand the correlation between time and BeB abundance is expected to be much\nbetter than that found for heavier species.\n\n\\begin{figure}\n%\\epsfxsize=15cm\n%\\epsfysize=6cm\n%\\epsfbox{beersf2.eps}\n\\plotfiddle{beersf2.eps}{5cm}{0.}{82.}{85}{-234.}{-55.}\n\\caption{Predicted distribution of abundance for three elements, relative to H,\nfor long-lived stars born at the indicated time {\\it following} the initiation\nof star formation. The distributions have been convolved with Gaussians with\n$\\sigma = 0.15$ dex to take into account expected observational errors. The\ntwo contours, from the inside to the outside, correspond to probability density\n$10^{-3}$ and $10^{-5}$ within the unit area $\\Delta t = 10({\\rm Myr})\\times\n\\Delta \\log {\\rm (element/H)} = 0.1$. The solid lines show the predicted ISM\ngas abundances of each element.}\n\\end{figure}\n\nIn Table 1, we use the predictions from SYK, and the stellar abundance data\nfrom Boesgaard et al. (1999) for Be, to put forward ``bold'' estimates of\nstellar ages (since the onset of star formation). We note that these numbers\nare meant to be indicative, not definitive, predictions, as further tests of\nthe model and its underlying assumptions still remain to be carried out. We\nhave ordered the table according to estimated (Be) time since the onset of star\nformation in the early Galaxy.\n\n\n\\begin{table}\n\\begin{center}\n\\caption{Predictions of Stellar ``Ages'' Based on Be Abundance}\n\\begin{tabular}{lccc}\n\\tableline\nStar\t\t& [Fe/H] \t& log(Be/H)\t& Be ``age'' (Gyr) \\cr\n\\tableline\nBD$-$13:3442\t& $-$3.02\t& $-$13.49 &\t0.22 ($-$0.07,+0.03) \\cr \nBD+03:740\t& $-$2.89\t& $-$13.33 &\t0.26 ($-$0.05,+0.03) \\cr\nHD 140283\t& $-$2.56\t& $-$13.08 &\t0.32 ($-$0.05,+0.02) \\cr \nBD+37:1458\t& $-$2.14\t& $-$13.07 &\t0.32 ($-$0.05,+0.02) \\cr\nHD 84937\t& $-$2.20\t& $-$12.94 &\t0.35 ($-$0.05,+0.03) \\cr\nBD+26:3578\t& $-$2.32\t& $-$12.79 &\t0.39 ($-$0.05,+0.03) \\cr\nBD+02:3375\t& $-$2.39\t& $-$12.80 &\t0.39 ($-$0.05,+0.03) \\cr\nBD$-$04:3208\t& $-$2.35\t& $-$12.69 &\t0.41 ($-$0.05,+0.03) \\cr\nHD 19445\t& $-$2.10\t& $-$12.55 &\t0.45 ($-$0.04,+0.03) \\cr\nHD 64090\t& $-$1.77\t& $-$12.49 &\t0.46 ($-$0.04,+0.03) \\cr\nBD+20:3603\t& $-$2.22\t& $-$12.47 &\t0.46 ($-$0.04,+0.03) \\cr\nBD+17:4708\t& $-$1.81\t& $-$12.40 &\t0.48 ($-$0.04,+0.03) \\cr\nHD 219617\t& $-$1.58\t& $-$12.15 &\t0.54 ($-$0.04,+0.02) \\cr\nHD 74000\t& $-$2.05\t& $-$12.10 &\t0.55 ($-$0.04,+0.02) \\cr\nHD 103095\t& $-$1.37\t& $-$12.04 &\t0.56 ($-$0.04,+0.02) \\cr\nHD 194598\t& $-$1.25\t& $-$11.88 &\t0.59 ($-$0.03,+0.01) \\cr\nBD+23:3912\t& $-$1.53\t& $-$11.92 &\t0.59 ($-$0.03,+0.01) \\cr\nHD 94028\t& $-$1.54\t& $-$11.55 &\t$> 0.60$\t \\cr \n\\tableline\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nIt is interesting to consider the implications of this strong age-abundance\nrelationship for individual stars which have been noted in the literature as\nhaving ``peculiar'' BeB (or $^7$Li for that matter) abundances, at least as\ncompared to otherwise similar stars of the same [Fe/H], T$_{\\rm eff}$, and log\ng. The set of ``twins'' G64-12 and G64-37 have been noted as one example of\nstars with very low metallicity, and apparently similar T$_{\\rm eff}$ and log\ng, which never-the-less, exhibit rather different abundances of $^7$Li. Could\nthis difference be accounted for by a difference in AGE of these stars ?\nAnswering this question is of great importance, and hopefully will be resolved\nin the near future.\n\n\\section{Can we Test This Model ?}\n\nYes, but it will take some hard work. Obviously, if there exists an\nindependent method with which to verify the relative age determinations\npredicted by this model, that would be ideal. Fortunately, there have been\nnumerous refinements in models of stellar atmospheres, and their\ninterpretation, which may make this feasible (see Fuhrmann 2000). In order to\napply the methods described by Fuhrmann, one requires high-resolution, high-S/N\nspectroscopy of individual stars. It is imperative that the present-generation\n8m telescopes (VLT, SUBARU, GEMINI, HET) obtain this data, so that this, and\nother related questions, may be addressed with the best possible information.\n\nAnother feasible test would be to compare the abundances of BeB with [Fe/H],\nand other heavy elements, for a large sample of stars with [Fe/H] $< -2.0$. If\nthe superbubble model is the correct interpretation, with an implied\nlocally homogeneous production of the light elements, then one might expect to\nfind correlations between the abundances of various heavy element species\n(including those other than Fe and O) and BeB. Simultaneous observations of\nlight and heavy elements for stars of extremely low abundance are planned with\nall the major 8m telescopes, so it should not be too long before a sufficiently\nlarge sample to carry out this test is obtained.\n\nOne can also seek, as we have, confirmatory evidence in the predicted behavior\nof $^7$Li vs. [Fe/H] (Suzuki et al. 2000).\n\n\\section{Other Uses for This Model}\n\nIf the model we have considered here can be shown to be correct, there are\nseveral new avenues of investigation which are immediately opened.\nFor example, if one were able to ``age rank'' stars on the basis of their BeB\nabundances, one could refine alternative production mechanisms for the light\nelement Li which are not driven by GCR spallation, including the SN\n$\\nu-$process and/or production via a giant-branch Cameron-Fowler mechanism\n(see Castilho et al. , this volume), in stellar flares, etc..\n\nFurthermore, since BeB nuclei are more difficult to burn than Li nuclei, one\ncould imagine a powerful test for the extent to which depletion of Li has\noperated in metal-poor dwarfs, with important implications for the Li\nconstraint on Big Bang Nucleosynthesis (BBN). Realistic modeling of BeB\nevolution at early epochs may also help distinguish between predictions of\nstandard BBN, non-standard BBN, and the accretion hypothesis (see Yoshii,\nMathews, \\& Kajino 1995).\n\nAn age ranking of metal-poor stars based on their BeB abundances, in\ncombination with measurements of their alpha, iron-peak, and neutron-capture\nelements, would open the door for an unraveling of the mass spectrum of the\nprogenitors of first generation SNeIIs, and allow one to obtain direct\nconstraints on their elemental yields as a function of mass, a key component to\nmodels of early nucleosynthesis.\n\n\\acknowledgements\n\nTCB expresses gratitude to the IAU for support which enabled his attendance at\nthis meeting, and acknowledges partial support from the National Science\nFoundation under grant AST 95-29454. TCB also wishes to express his\ncongratulations to the LOC and SOC for a well-run, scientifically stimulating,\nand marvelously located meeting. YY acknowledges a Grant-in-Aid from the\nCenter of Excellence (COE), 10CE2002, awarded by the Ministry of Education,\nScience, and Culture, Japan.\n\n\\begin{references}\n\n\\reference Argast D., Samlund, M., Gerhard, O.E., \\& Thielemann, F.-K. 2000,\n\\aap, in press\n\\reference Audouze J., \\& Silk, J. 1995, \\apj , 451, L49 \n\\reference Beers, T.C. 1999, in Third Stromlo Symposium: The Galactic Halo,\neds. B. Gibson, T. Axelrod, \\& M. Putman, (ASP, San Francisco), 165, p. 206 \n\\reference Boesgaard, A.M., Deliyannis, C.P., King, J.R., Ryan, S.G., Vogt,\nS.S., \\& Beers, T.C. 1999, \\aj , 117, 1549\n\\reference Fuhrmann, K. 2000, in The First Stars, Proceedings of the Second\nMPA/ESO Workshop, eds. A. Weiss, T. Abel, \\& V. Hill (Springer, Heidelberg), in\npress\n\\reference Laird, J.B., Carney, B.W., Rupen, M.P., \\& Latham, D.W. 1988, \\aj, \n96, 1908\n\\reference McWilliam, A., Preston, W., Sneden, C., \\& Searle, L. 1995, \\aj ,\n109, 2757\n\\reference Ryan, S.G., Norris, J.E., \\& Beers, T.C. 1996, \\apj , 471, 254\n\\reference Ryan, S.G., Norris, J.E., \\& Beers, T.C. 1999, \\apj, 523, 654 \n\\reference Ryan, S.G., \\& Norris, J.E. 1991, \\aj, 101, 1865\n\\reference Suzuki, T.K., Yoshii, Y., \\& Kajino, T. 1999, \\apj , 522, L125 \n(SYK)\n\\reference Suzuki, T.K., Yoshii, Y., \\& Beers, T.C. 2000, \\apjl , submitted\n\\reference Tsujimoto, T., Shigeyama, T., \\& Yoshii, Y. 1999, \\apj , 519,\nL63 (TSY) \n\\reference Yoshii, Y., Mathews, G.J., \\& Kajino, T. 1995, \\apj, 447, 184\n\\end{references}\n\n\\end{document}\n\n"
}
] |
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astro-ph0002057
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The Warp of the Galaxy and the Orientation of the LMC Orbit
|
[
{
"author": "I. Garc\\'{\\i}a-Ruiz$^1$"
},
{
"author": "K. Kuijken$^1$"
},
{
"author": "J. Dubinski$^2$"
},
{
"author": "Postbus 800"
},
{
"author": "9700 AV Groningen"
},
{
"author": "The Netherlands"
},
{
"author": "$^2$Department of Astronomy and CITA"
},
{
"author": "60 St. George Street"
},
{
"author": "Toronto"
},
{
"author": "Ontario M5S 3H8"
},
{
"author": "Canada"
}
] |
After studying the orientation of a warp generated by a companion satellite, we show that the Galactic Warp would be oriented in a different way if the Magellanic Clouds were its cause. We have treated the problem analytically, and complemented it with numerical N-Body simulations.
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Garc\\'{\\i}a-Ruiz$^1$, K. Kuijken$^1$, J. Dubinski$^2$\\\\\n$^1$Kapteyn Astronomical Institute, Postbus 800, 9700 AV Groningen,\nThe Netherlands\\\\\n$^2$Department of Astronomy and CITA, University of Toronto, 60 St. George\nStreet, Toronto, Ontario M5S 3H8, Canada}\n\\maketitle\n\n\\begin{abstract}\nAfter studying the orientation of a warp generated by a companion\nsatellite, we show that the Galactic Warp would be oriented in a\ndifferent way if the Magellanic Clouds were its cause. We have\ntreated the problem analytically, and complemented it with numerical\nN-Body simulations. \n\\end{abstract}\n\n\\begin{keywords}\ngalaxies:kinematics and dynamics -- Galaxy:structure -- Magellanic Clouds\n\\end{keywords}\n\n\n\\section{Introduction}\n\nThe disk of the Milky Way is remarkably flat out to 10 kpc, \nwhere it starts to bends in\nopposite directions in the southern and northern parts. The cause of it\nis still a puzzle: for a review, see Binney \\shortcite{b92}.\n\nOne possibility is that the Magellanic Clouds\ndistort the Galactic disk in the observed way. The fact\nthat the direction of the maximum warping lies very close to the\ngalactocentric longitude of the Clouds makes this hypothesis tempting. \n\nThe problem with this scenario is that the Clouds are not massive\nenough to generate the warp amplitudes that\nwe observe at their present distance. This was noticed by the first\nresearches in this field \\cite{bu57,ke57}, and later by Hunter \\&\nToomre (1969). A remedy which might allow this\nscenario to work was to suppose that the Clouds are currently not at the\npericenter of their orbit, so that they have been much closer to the\nGalactic disk in a previous epoch ($\\simeq 20$ kpc is what was needed).\nHowever, \nlater work by Murai \\& Fujimoto (1986) determined the orbit of the Clouds,\nand proved that the Clouds are actually at their pericenter, with an\napocenter close to 100 kpc, so the problem of the small amplitude\nstill remains if the Clouds are to be blamed as the cause of the\nGalactic warp. \n\nRecently a mechanism for amplifying the\neffect of a satellite has been proposed by Weinberg \\shortcite{w98}.\nHe describes a calculation in which a disk\ngalaxy surrounded by a dark halo is perturbed by a massive satellite,\nsimilar to the LMC. By means of a linear perturbation analysis, he\nfollows the perturbation (wake) created by the satellite in the halo,\nincluding its self-gravity. He finds that the torque exerted on the\ndisk is several times larger than that due directly to the satellite:\nthe latter is amplified because (i) the satellite-induced wake in the\nhalo itself exerts a torque, roughly in phase with that from the\nsatellite; and (ii) the wake itself further perturbs the halo,\nresulting in a torque that is larger again. Under circumstances in\nwhich the satellite orbital frequency is close to the natural\nprecession frequency of the disk (i.e., the warp mode frequency of\nSparke \\& Casertano \\shortcite{sc}), a significant amplitude can\nresult. A calculation by Lynden-Bell \\shortcite{lb85} of a similar\nscenario gives comparable results, as does a simple model described by\nKuijken \\shortcite{k97}.\n\nIn this paper, we focus on the orientation of a warp generated by a\nmassive orbiting satellite with less emphasis on the amplitude of the\nwarp. In \\S2 we discuss a simple analytic model in\nwhich the disk and halo are rigid: this establishes the baseline\nresponse of a disk to satellite tides, and its orientation with\nrespect to the satellite orbital plane. As we show, this orientation\nis different from that of the Galactic warp to the LMC orbit. \\S3\ncontains a description of the N-body code used, and \\S4 to \\S6 the results of\nour N-body simulations, showing that the orientation problem remains. In\n\\S7 we give our conclusions.\n\n\\section{Analytic results with a simplified model}\n\nA simple model serves as a reference for the warp response of the disk\nto an orbiting satellite. Consider a rigid disk, embedded in a rigid\nhalo potential, and subjected to the potential of an orbiting\nsatellite. The evolution of the disk is governed by the combined\ntorque from halo and satellite. A stellar or gaseous disk is floppy,\nand so will warp when tilted, since it is not able to generate the\nstresses that would be required to keep it flat; however the overall\nre-alignment of the disk angular momentum should be comparable between\nthe rigid and floppy cases.\n\nThe angles used in this paper related to the satellite, and the\ndefinition of our coordinate system are illustrated in\nFigure~\\ref{fig:coord}. The tilting of the disk is measured by the\nangle between the $z$ axis and the angular momentum of the disk. The\nlongitude of this vector is the same as the longitude of the maximum\nof the warp when looking at the disk from the North Galactic Pole.\n\n\\begin{figure}\n\\plotone{fig1.ps}\n\\caption{Definition of the coordinate system, satellite angles, and\n orientation of the disk of the Galaxy. The disk lies on the $z=0$\n plane. The sun is on the left, and the galactic plane is viewed from\n the South Galactic Pole so that the disk rotates counterclockwise\n (indicated by an arrow).} \n\\label{fig:coord}\n\\end{figure}\n\nThe Lagrangian for a rigidly spinning, axisymmetric object is\n\\newcommand{\\half}{\\textstyle{\\frac12}}\n\\begin{equation}\n{\\cal L}=\\half I_1(\\dot\\theta^2 + \\dot\\phi^2 \\sin^2\\theta)\n+ \\half I_3(\\dot\\phi\\cos\\theta + \\dot\\psi)^2 \n-V(\\theta,\\phi)\n\\end{equation}\nwhere $(\\theta,\\phi,\\psi)$ are the Euler angles, and $I_3$ and $I_1$\nare the moments of inertia of the object about its symmetry axis\nand about orthogonal directions. $V$ is the potential energy of the\nbody in the halo plus satellite potential. The $\\psi$-equation of\nmotion leads to the conserved quantity\n$S=I_3(\\dot\\phi\\cos\\theta+\\dot\\psi)$, the spin, and the other two\nequations of motion then become\n\\begin{equation}\nI_1\\ddot\\theta-I_1\\dot\\phi^2\\sin\\theta\\cos\\theta\n+S\\dot\\phi\\sin\\theta+{\\partial V\\over\\partial\\theta}=0\n\\label{eq:theq}\n\\end{equation}\nand\n\\begin{equation}\nI_1{{\\rmn d}\\over{\\rmn d}t}({\\dot\\phi\\sin^2\\theta})\n+{\\partial V\\over\\partial\\phi}=0.\n\\label{eq:pheq}\n\\end{equation}\nFor small deviations from the equator ($\\theta=0$), we can expand\nthese equations in terms of $x=\\sin\\theta\n\\cos\\phi\\simeq\\theta\\cos\\phi$, $y=\\sin\\theta\n\\sin\\phi\\simeq\\theta\\sin\\phi$. In these terms the equations of motion\nbecome\n\\begin{equation}\nI_1\\ddot{x}+S \\dot{y} +{\\partial V\\over\\partial x}=0,\n\\end{equation}\n\\begin{equation}\nI_1\\ddot{y}-S \\dot{x} +{\\partial V\\over\\partial y}=0.\n\\end{equation}\nFor small $x,y$, the potential energy of the disk due to the flattened\nhalo will have the form $\\half V_{\\rmn H}(x^2+y^2)$, and that due to\nthe satellite at position $\\theta_{\\rmn S},\\phi_{\\rmn S}$ will be\n$-V_{\\rmn S}(\\sin^2\\theta_{\\rmn S} - x\\sin2\\theta_{\\rmn\n S}\\cos\\phi_{\\rmn S} - y\\sin2\\theta_{\\rmn S}\\sin\\phi_{\\rmn S})$ where\n$V_{\\rmn H}$ and $V_{\\rmn S}$ are constants representing the strengths\nof the halo \ntorque and of the quadrupole of the tidal field from the satellite,\nrespectively. Hence we find\n\\begin{equation} \nI_1\\ddot{x}+S \\dot{y} + V_{\\rmn H}x +\nV_{\\rmn S}\\sin2\\theta_{\\rmn S}\\cos\\phi_{\\rmn S}=0, \n\\end{equation}\n\\begin{equation}\nI_1\\ddot{y}-S \\dot{x} + V_{\\rmn H}y +\nV_{\\rmn S}\\sin2\\theta_{\\rmn S}\\sin\\phi_{\\rmn S}=0.\n\\end{equation}\nIf furthermore the satellite orbit is circular and polar in the $x=0$ plane, \n$\\theta_{\\rmn S}=\\Omega_{\\rmn S}t$, $\\phi_{\\rmn S}=90$, \nand the solution to the equations of motion is \n\\begin{equation}\nx={2\\Omega_{\\rmn S}S\\over\\Delta}V_{\\rmn S}\\cos2\\Omega_{\\rmn S} t;\n\\quad\ny={4I_1\\Omega_{\\rmn S}^2 - V_{\\rmn H}\\over\\Delta}V_{\\rmn S}\\sin2\\Omega_{\\rmn S}t\n\\label{eq:rigidsol}\n\\end{equation}\nplus free precession and nutation terms, where $\\Delta=(V_{\\rmn\nH}-4I_1\\Omega_{\\rmn S}^2)^2-4\\Omega_{\\rmn S}^2S^2$. (A more general\nquasiperiodic satellite orbit yields a solution which can be written\nas a sum of such terms.) Notice that the satellite provokes an\nelliptical precession about the halo symmetry axis, with axis ratio\ndependent on the halo flattening and on the satellite orbit\nfrequency. For example, for an exponential disk of mass $M$, scale\nlength $h$ and with a flat rotation curve of amplitude $v$,\n$I_3=2I_1=6Mh^2$ and $S=2hvM$. For such a disk in a spherical (or\nabsent) halo ($V_{\\rmn H}=0$), a satellite orbiting at radius $r_{\\rmn\nS}$ has frequency $\\Omega_{\\rmn S}=v/r$, and hence the axis ratio of\nthe forced precession is $(x:y)=r_{\\rmn S}/3h$. Hence the response of\nthe disk to a distant satellite is mainly to nod perpendicular to the\nsatellite orbit plane. This result can be understood as the classic\northogonal response of a gyroscope to an external torque: a distant\nsatellite has a sufficiently low orbital frequency that the disk\nresponds as if the torque were static.\n\nFor a slightly flattened potential of the form $\\half\nv^2\\ln[R^2+(z/(1-\\epsilon))^2]$, $V_{\\rmn H}=Mv^2\\epsilon$. With\nnon-zero $\\epsilon$, the axis ratio of the precession cone \nbecomes $[(4h/r_{\\rmn S}) / (\\epsilon-12h^2/r_{\\rmn S}^2)]$: again the\noscillation in $x$ is larger than that in $y$ except for very\nflattened halos.\n\nThe amplitudes generated by tidal perturbation from a satellite such\nas the LMC are small, less than a degree. The largest amplitude of\noscillation is in the $y$-direction. The potential energy of the disk\ndue to the tidal field of the satellite can be shown to be (see\nAppendix)\n\\begin{equation}\nV_{\\rmn S}={3GM_{\\rmn S}I_1\\over2r_{\\rmn S}^3}.\n\\end{equation}\nHence equation~\\ref{eq:rigidsol} yields, to leading order in\n$h/r_{\\rmn S}$, an $x$-amplitude of \n\\begin{equation}\n\\frac98 \\frac{GM_{\\rmn S}}{v^2 r_{\\rmn S}}\\frac{h}{r_{\\rmn\nS}}\n\\simeq 0.09^\\circ\n\\end{equation}\nfor the LMC (orbital radius about $50\\,\\rmn kpc$, and $r_{\\rmn\nS}/h\\simeq15$). This number increases only slightly (a factor 2) for\nhalo flattenings up to 0.2 (see Figure~\\ref{fig:rigidtilt}).\n\n\\begin{figure}\n\\plotone{fig2.ps}\n\\caption{The oscillation of the axis of a rigid exponential disk\nsubjected to the tidal field of an orbiting satellite. The amplitude\nis calculated assuming a satellite of mass $1.5\\times10^{10}M_\\odot$,\norbiting at radius $54\\rmn kpc$ in the $z=0$ plane. The direction of\nthe tilt of the Galactic disk with respect to the Magellanic Clouds'\norbital plane is indicated by the arrow. The dots mark the expected\nposition of the disk axis given the current phase of the LMC orbit for\n(bottom to top) halo potential ellipticities\n$\\epsilon=0$ (solid symbol),$0.05,0.1,0.15$ and 0.2 (open circles).}\n\\label{fig:rigidtilt}\n\\end{figure}\n\nIt is clear from this calculation that simple tidal tilting of a disk\nby an LMC-like satellite does not provide a good model for the warping\nin the Galaxy, because the orientation of the warp is not perpendicular\nto the orbital plane of the LMC. This constraint is independent of\nthe strength of the perturbation $V_{\\rmn S}$.\n\nThe amplitudes are much too small, but we have only considered the\ntilting of a rigid disk, and the situation can change when the\nfloppiness of the disk is considered.\n\n\\section{Simulation details}\n\nTo test this scenario, and in particular to get beyond the rigid\ntilting considered above, we have performed some N-body\nsimulations. We assume the halo to be a background potential which\ndoes not respond to the disk or the satellite.\n\nThe N-body code used for this work models the disk as a set of\nconcentric spinning rings embedded in a spherical, rigid halo. This\ndescription allows warps to be described, but not in-plane distortions\nof the disk such as bars or lopsidedness.\n\n\\subsection{Initial conditions}\n\nWe have performed simulations with two types of disks: a rigid\ndisk and a exponential disk. The rigid disk run tells us how good the\nanalytic predictions are, and the exponential disk\nis used later for a more realistic approach. \n\nWe use a King model for the halo, in order to obtain a reasonable flat\nrotation curve (Figure~\\ref{fig:rc}). This is accomplished with\na model of $\\Psi_0/{{\\sigma}_0}^2 = -6$, a tidal radius of 44 (200\nkpc. for a 4.5 kpc scale-length disk), and mass of 10 disk masses. \n\nEach of the disks is made of 1000 rings, each of them consisting of 36\nparticles. Various runs where made with more rings and more particles\nper ring, without important changes in the results described below.\n\n\\begin{figure}\n\\plotone{fig3.ps}\n\\caption{{Rotation curve showing the contribution from the disk\n (dotted) and halo (dashed) to the total (solid)}}\n\\label{fig:rc}\n\\end{figure}\n\nThe satellite is modelled as having a Plummer distribution. To avoid\nrelative movements of the galaxy with respect to the satellite we\nhave used two satellites instead of one, symmetrically placed with\nrespect to the centre of the halo-disk system. This causes the dipole\nterm of the tidal field to be zero, avoiding relative movements of the\ngalaxy with respect to the satellites. It is equivalent to only\nkeeping the even-$l$ \nterms in the potential of the satellite, neglecting the\ndipole, $l=1$, terms in the potential, and concentrating on the warp\n(which result from the quadrupole, $l=2$ terms).\n\nThe first run was made with a satellite in a circular orbit, to try to\nreproduce the predictions in \\S2. Later a non-circular orbit is\nconsidered, and the difference between both simulations analysed. The\nnon-circular orbit has a pericenter at 50 kpc and apocenter at 100\nkpc, consistent with recent determination of the orbit of the\nClouds \\cite{lin}. In the non-circular simulations the satellite\nstarts at its apocenter at the beginning of the simulation, where the\nperturbation on the disk is the smallest possible.\n\nThe units of the model translate to the Galaxy (disk scale-length\n$4.5\\,\\rmn kpc$, and the rotation velocity at $8.5\\,\\rmn kpc$ of\n$220\\,\\rmn km\\,s^{-1}$) as follows: length unit = $4.5\\,\\rmn kpc$,\nvelocity unit = 340 $\\rmn km\\,s^{-1}$, time unit = $1.30 \\times\n10^7\\,$years, mass unit= $1.20 \\times 10^{11}\\rmn M_{\\odot}$. With\nthese numbers, the disk mass of our model is $6.1 \\times 10^{10}\\rmn\\,\nM_{\\odot}$, and the satellite (LMC) has a mass of $1.5 \\times 10^{10}\\rmn\\,\nM_{\\odot}$, the biggest current mass estimate for the Clouds\n\\cite{so92}. \nIn the coordinate system of the simulations, the $z=0$ is the disk\nplane, and the orbit of the satellite lies in the $x=0$ plane.\n\n\\subsection{Code used to evolve the system}\n\nThe disk is modelled as a system of pivoted spinning rings, fixed at\nthe centre of the halo. Each ring is realized as 36 azimuthally-spaced\nparticles, and the potential generated by the rings is calculated with\na tree code \\cite{bh86}. The forces on the individual\n``ring-particles'' are used to calculate the torque on each ring. The\nforce exerted by a satellite on the ring particles was evaluated\ndirectly using the Plummer law. \n\nThe Euler equations for rings and axisymmetric bodies can be rewritten in a\nform so that the time derivatives of the instantaneous angular velocities\nabout the body axes are linear combinations of the angular velocities, \ntorques and body normal vector components. This allows the derivation of a\nsecond order explicit time-centred leapfrog integration scheme that\ncan be used to solve the coupled equations for the rings and make it easy\nto merge with an N-body code \\cite{du00}.\n\n\n\\section{Rigid Disk}\n\nAs a first approach, we have evolved a rigid disk and analysed its\nevolution under the influence of an orbiting satellite. The result of\nour simulation is in good agreement with the analytic\npredictions. The disk wobbles under the influence of the satellite,\ndescribing an ellipse elongated in the direction perpendicular\nto the satellite's orbital plane. The path followed by the disk is\nplotted in Figure~\\ref{fig:rigidrun}, where it can be seen that most\nof the time the maximum of the warp is located in the direction\nperpendicular to the orbital plane of the satellite ($l=0^\\circ$ and\n$l=180^\\circ$). The ellipse isn't as regular as in\nFigure~\\ref{fig:rigidtilt} for two reasons: the assumption that the disk is\nmuch smaller than the orbital radius of the satellite is not\ncompletely fulfilled; and there are some transient terms present\nbecause of the initial conditions of the simulation. This are also the\ncause for the precession ellipse of the disk not to be centred in the\norigin. \n\nThe position of the warp when the satellite is at the location of the\nLMC is indicated by the dots in Figure~\\ref{fig:rigidrun}, and the\nlocation of them resembles the predicted one in\nFigure~\\ref{fig:rigidtilt} (for $\\epsilon_{halo}=0$) remarkably well.\n\n\\begin{figure}\n\\plotone{fig4.ps}\n\\caption{Precession path followed by the rigid disk:\n $x=\\theta\\cos\\phi$, $y=\\theta\\sin\\phi$. The dots indicate the disk's\n state when the satellite has the LMC's orbital phase. } \n\\label{fig:rigidrun}\n\\end{figure}\n\n\\section{Exponential self-gravitating Disk}\n\nWe now consider a more realistic disk: an exponential disk model, in\nwhich we have considered also the disk's self-gravity. The first thing\nthat draws our attention in this simulation is a peak we see in the\ninclination at around 6.5 scale-lengths. Simulations done with a\ndifferent rotation curve showed that this peak occurs at the locations\non the disk that satisfy $\\Omega_s/w_z=2,3,...$, that are caused by\nresonances with the satellite's orbital frequency. This happens\nbecause the non-linear behaviour of the outer parts of the disk, where\nthe assumption $r_s \\gg r_{disk}$ is worse than it is further in.\n\nThis is not the kind of warp we are looking for, due to the fact that\nit is the result of a satellite with a single frequency, and in the\nreal case the eccentric orbit of the satellite will wash out this\npeak. Looking at the evolution of the disk it is clear that the warp\nlooses its coherence at a radius about 4.5 scale-lengths (at larger\nradius the line of nodes winds up), so we will measure the warp\nproperties considering that the disk finishes there. \n \n\\begin{figure*}\n\\plotnine{fig5.ps}\n\\caption{Warp orientation\n followed by the Exponential Disk:\n $x=\\theta\\cos\\phi$, $y=\\theta\\sin\\phi$. The dots indicate the disk's\n state when the satellite has the LMC's orbital phase.}\n\\label{fig:exprun}\n\\end{figure*}\n\nIn the case of a floppy disk it is not \nstraight-forward to define a single inclination and position\nangle. We have separated the disk into two components: the inner disk\nand the outer (warped) disk. The inner disk consists on the first 2\nscale-lengths, and remains practically flat along the simulation. The\nwarping angle is then calculated as the angle between the inner and\nouter disk vectors. We have chosen to use the disk vectors and not\nthe angular momentum, for example, not to penalise the outer less\nmassive rings. The results presented here do not change significantly\nwhen the definition of the inner disk is altered.\n\nIt has to be kept in mind that the warping angles quoted here are\ndifferent than the maximum amplitude of the warp, who usually are\nlarger by a factor not greater than 5.\n\nUsing this method we obtain a plot similar to\nFigure~\\ref{fig:rigidrun} for the exponential disk, which is\nshown in Figure~\\ref{fig:exprun}. Only the path after t=160 is shown,\nthat is the moment when the disk behaviour reaches an equilibrium.\n\nNote that the predictions for the Galactic Warp don't really change\nwith the floppiness of the disk: it is clearly close to $l=0^\\circ$,\nas chapter \\S2 predicted, and not at $l=\\simeq 90^\\circ$, as we\nobserve it in the Galaxy. \n\n\\section{Non-circular orbit, and flattened halos}\n\nWe also considered non-circular orbits, to allow for the fact that the\norbit derived for the Clouds has a pericenter of 50 kpc and an\napocenter of 100 kpc \\cite{mf80}. The changing radius of the satellite causes a\nfluctuating tidal field amplitude, which could be important for the\ndynamics of the disk. Here we show that in fact the effect does not\nchange our conclusions materially.\n\nFirst, to have an idea of what to expect, we integrated the analytic\nequations of section \\S2 with a satellite in this kind of orbit. The\nresult was, as before, that the disk's precession path was contained\nwithin an ellipse, elongated along the direction perpendicular to the\nsatellite's plane. This causes the warp maxima to be most of the time\nclose to the direction perpendicular to the satellite's orbit.\n\nWe then performed simulations with this type of orbits. The first thing we\nobserve in these simulations is that the resonance peak we\nfound in the circular orbit simulation has disappeared. Now the\nsatellite doesn't have a single frequency, so the result is not\nsurprising. The energy of the resonance gets distributed along\ndifferent parts of the disk now, and no coherent pattern can be\nmaintained across the disk, winding up the outer parts of the\ndisk. When we look at the inner 4.5 scale-lengths as before, the\nprecession pattern remains similar to the simulation with the circular\norbit, so does the prediction of the warp's longitude at LMC's actual\norbital phase. So our conclusions are not modified by the\nnon-circularity of the orbit.\n\nThe halos considered in all these simulations are spherical, which\nmeans that they don't contribute to the generation of torques on the\ndisk. We know that halos are not spherical, which creates a\npreferred plane in which the disk settles. Ellipticities of the order\nof 0.05 in the potential make the precession paths described before yet\nmore elongated, which would make the chances of finding the warp\nmaxima in the satellites' direction even more unlikely.\n\n\\section{Conclusion}\n\nWe show by means of analytic work and N-body simulations that the\nprecession path of a warp generate by an orbiting satellite galaxy is\nelongated along the direction perpendicular to the satellite's orbital\nplane. Applying our result to the Milky Way, if the Galactic Warp is\ngenerated by the Magellanic Clouds, the direction of maximum amplitude\nof the warp would lie close to $l \\simeq 0^\\circ$, as compared to\nthe observed direction of $\\simeq 90^\\circ$. Even if the halo's\nself-gravitating tidal response to the satellite amplifies the effect\nof the satellite~\\cite{w98}, this response will be mostly in phase\nwith the satellite, and the alignment problems will persist. Possibly\nthe Sagittarius dwarf galaxy, whose orbit lies at 90$^\\circ$ to that\nof the LMC, can be the cause of the warp instead~\\cite{ibata}. \n\nA limitation of the present work is that the halo has not been\nconsidered as a live, self-gravitating component. It has been\nshown~\\cite{dk,nt} that the back-reaction of the halo on a\nre-aligning disk can have important consequences. Such effects will be\nthe subject of a further paper.\n\n\\appendix\n\n\\section{Potential of axisymmetric disk due to a satellite}\n\nThe potential energy of an disk of surface density $\\Sigma(r)$ and in\nthe gravitational field due to a satellite at position ${\\bmath\nr}_{\\rmn S}$ is given by\n\\begin{equation}\nV=-\\int {\\rmn d}^2{\\bmath r}\\,G\\Sigma(r)\n{M_{\\rmn S}\\over|{\\bmath r}-{\\bmath r}_{\\rmn S}|}.\n\\end{equation}\nChoosing spherical coordinates for the satellite's position (see\nFigure~\\ref{fig:coord}), and Cartesian coordinates in the disk plane so\nthat the satellite has $x=0$, we have \n\\begin{equation}\nV=-GM_{\\rmn S}\\int \\Sigma{\\rmn d}x\\,{\\rmn d}y\\,\n(r_{\\rmn S}^2-2yr_{\\rmn S}\\sin\\theta_{\\rmn S}+x^2+y^2)^{-1/2}.\n\\end{equation}\nAssuming that the disk is small compared to $r_{\\rmn S}$, we can\nexpand the integrand in $x$ and $y$. For an axisymmetric disk the\nsecond-order terms are the first ones that generate a potential\ngradient: they are\n\\begin{equation}\nV=-{GM_{\\rmn S}\\over r_{\\rmn S}^3}\\int\\Sigma{\\rmn d}x\\,{\\rmn d}y\\,\n[-\\half(1-3\\sin^2\\theta_{\\rmn S}) y^2-\\half x^2]\n\\end{equation}\nwhich results in \n\\begin{equation}\nV=-{3GM_{\\rmn S}I_1\\over 2r_{\\rmn S}^3}\\sin^2\\theta_{\\rmn S}+\\hbox{constant}.\n\\end{equation}\n\n\n\\newcommand{\\apj}{ApJ}\n\\newcommand{\\mnras}{MNRAS}\n\n\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{Barnes \\& Hut }1986]{bh86}\nBarnes, J., Hut, P., 1986, Nature, 324, 446\n\\bibitem[\\protect\\citename{Binney }1992]{b92}\nBinney, J., 1992, Annu. Rev. Astron. Astrophysics, 30, 51\n\\bibitem[\\protect\\citename{Burke }1957]{bu57}\nBurke, B. F., 1957, AJ, 62, 90\n\\bibitem[\\protect\\citename{Dubinski }2000]{du00}\nDubinski, J., 2000, in preparation.\n\\bibitem[\\protect\\citename{Dubinski \\& Kuijken }1995]{dk}\nDubinski, J., Kuijken, K., 1995, ApJ, 442, 492 \n\\bibitem[\\protect\\citename{Hunter \\& Toomre }1969]{ht69}\nHunter, C., Toomre, A., 1969, ApJ, 155, 747\n\\bibitem[\\protect\\citename{Ibata \\& Razoumov }1998]{ibata}\nIbata, R. A., Razoumov, A. O., 1998, A\\&A, 336, 130 \n\\bibitem[\\protect\\citename{Kerr }1957]{ke57}\nKerr, F. J., 1957, AJ, 62, 93\n\\bibitem[\\protect\\citename{Kuijken }1997]{k97}\nKuijken, K., 1997, in ASP Conference Series, Vol. 117, Dark and\nVisible Matter in Galaxies, ed. Massimo Persic and Paolo Salucci, pp. 220\n\\bibitem[\\protect\\citename{Lin, Jones \\& Klemola }1995]{lin}\nLin, D. N. C., Jones, B. F., Klemola, A. R., 1995, ApJ, 439, 652\n\\bibitem[\\protect\\citename{Lynden-Bell }1985]{lb85}\nLynden-Bell, D. 1985, in The Milky Way Galaxy, ed. H. van Woerden\n (Dordrecht: Reidel), 461\n\\bibitem[\\protect\\citename{Murai \\& Fujimoto }1980]{mf80}\nMurai, T., Fujimoto, M., 1980, Publ. Astron. Soc. Japan, 32, 581\n\\bibitem[\\protect\\citename{Nelson \\& Tremaine }1995]{nt}\nNelson, R. W., Tremaine, S., 1995, MNRAS, 275, 897\n\\bibitem[\\protect\\citename{Schommer et al. }1992]{so92}\nSchommer, R. A., Olszewski, E. W., Suntzeff, N. B., Harris, H. C.,\n1992, AJ, 103, 447\n\\bibitem[\\protect\\citename{Sparke \\& Casertano }1988]{sc}\nSparke, L. S., Casertano, S., 1988, MNRAS, 234, 873\n\\bibitem[\\protect\\citename{Weinberg }1998]{w98}\nWeinberg, M. D., 1998, MNRAS, 299, 499 \n\\end{thebibliography}\n\n\\end{document}\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002057.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{Barnes \\& Hut }1986]{bh86}\nBarnes, J., Hut, P., 1986, Nature, 324, 446\n\\bibitem[\\protect\\citename{Binney }1992]{b92}\nBinney, J., 1992, Annu. Rev. Astron. Astrophysics, 30, 51\n\\bibitem[\\protect\\citename{Burke }1957]{bu57}\nBurke, B. F., 1957, AJ, 62, 90\n\\bibitem[\\protect\\citename{Dubinski }2000]{du00}\nDubinski, J., 2000, in preparation.\n\\bibitem[\\protect\\citename{Dubinski \\& Kuijken }1995]{dk}\nDubinski, J., Kuijken, K., 1995, ApJ, 442, 492 \n\\bibitem[\\protect\\citename{Hunter \\& Toomre }1969]{ht69}\nHunter, C., Toomre, A., 1969, ApJ, 155, 747\n\\bibitem[\\protect\\citename{Ibata \\& Razoumov }1998]{ibata}\nIbata, R. A., Razoumov, A. O., 1998, A\\&A, 336, 130 \n\\bibitem[\\protect\\citename{Kerr }1957]{ke57}\nKerr, F. J., 1957, AJ, 62, 93\n\\bibitem[\\protect\\citename{Kuijken }1997]{k97}\nKuijken, K., 1997, in ASP Conference Series, Vol. 117, Dark and\nVisible Matter in Galaxies, ed. Massimo Persic and Paolo Salucci, pp. 220\n\\bibitem[\\protect\\citename{Lin, Jones \\& Klemola }1995]{lin}\nLin, D. N. C., Jones, B. F., Klemola, A. R., 1995, ApJ, 439, 652\n\\bibitem[\\protect\\citename{Lynden-Bell }1985]{lb85}\nLynden-Bell, D. 1985, in The Milky Way Galaxy, ed. H. van Woerden\n (Dordrecht: Reidel), 461\n\\bibitem[\\protect\\citename{Murai \\& Fujimoto }1980]{mf80}\nMurai, T., Fujimoto, M., 1980, Publ. Astron. Soc. Japan, 32, 581\n\\bibitem[\\protect\\citename{Nelson \\& Tremaine }1995]{nt}\nNelson, R. W., Tremaine, S., 1995, MNRAS, 275, 897\n\\bibitem[\\protect\\citename{Schommer et al. }1992]{so92}\nSchommer, R. A., Olszewski, E. W., Suntzeff, N. B., Harris, H. C.,\n1992, AJ, 103, 447\n\\bibitem[\\protect\\citename{Sparke \\& Casertano }1988]{sc}\nSparke, L. S., Casertano, S., 1988, MNRAS, 234, 873\n\\bibitem[\\protect\\citename{Weinberg }1998]{w98}\nWeinberg, M. D., 1998, MNRAS, 299, 499 \n\\end{thebibliography}"
}
] |
astro-ph0002058
|
Death of Stellar Baryonic Dark Matter
|
[
{
"author": "Katherine Freese\\inst{1}"
},
{
"author": "Brian Fields\\inst{2}"
},
{
"author": "David Graff\\inst{3}"
}
] |
The nature of the dark matter in the haloes of galaxies is one of the outstanding questions in astrophysics. All stellar candidates, until recently thought to be likely baryonic contributions to the Halo of our Galaxy, are shown to be ruled out. Faint stars and brown dwarfs are found to constitute only a few percent of the mass of the Galaxy. Stellar remnants, including white dwarfs and neutron stars, are shown to be very constrained as well. High energy gamma-rays observed in HEGRA data place the strongest constraints, $\Omega_{WD} < 3 \times 10^{-3} h^{-1}$, where $h$ is the Hubble constant in units of 100 km s$^{-1}$ Mpc$^{-1}$. Hence one is left with several unanswered questions: 1) What are MACHOs seen in microlensing surveys? 2) What is the dark matter in our Galaxy? Indeed a nonbaryonic component in the Halo seems to be required.
|
[
{
"name": "freese.tex",
"string": "\\documentclass{cl2emult}\n\n\\usepackage{makeidx} % allows index generation\n\\usepackage{graphicx} % standard LaTeX graphics tool\n % for including eps-figure files\n\\usepackage{subeqnar} % subnumbers individual equations\n % within an array\n\\usepackage{multicol} % used for the two-column index\n\\usepackage{cropmark} % cropmarks for pages without\n % pagenumbers\n\\usepackage{eso} % placeholder for figures\n\\makeindex % used for the subject index\n % please use the style sprmidx.sty with\n % your makeindex program\n\n\n\n\\begin{document}\n\n\\def\\omegam{\\Omega_{\\rm Macho}}\n\\def\\omegab{\\Omega_{\\rm B}}\n\\def\\lya{Ly$\\alpha$}\n\n\n% this version shortened by A. Weiss, Dec 8.\n\n\\title*{\\bf Death of Stellar Baryonic Dark Matter}\n\n\n%\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\n\\author{Katherine Freese\\inst{1}\n\\and Brian Fields\\inst{2}\n\\and David Graff\\inst{3}}\n%\\footnote{\\tt [email protected]; [email protected]; [email protected]}\n%\\vskip 0.1in\n%\\centerline{talk presented by {\\bf Katherine Freese}}\n%\\centerline{at the MPA/ESO Workshop on}\n%\\centerline{The First Stars,}\n%\\centerline{Munich, Germany, August 1999}\n\\authorrunning{Katherine Freese et al.}\n\\institute{University of Michigan, Dept. of Physics, Ann Arbor, MI 48109-1120\n\\and Ohio State University, Astronomy Dept., Columbus, OH 43210\n\\and University of Illinois, Astronomy Dept., Urbana, IL 61801-3080}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\maketitle\n\\begin{abstract}\n\nThe nature of the dark matter in the haloes of galaxies is one of the\noutstanding questions in astrophysics. All stellar candidates, until\nrecently thought to be likely baryonic contributions to the Halo of\nour Galaxy, are shown to be ruled out. Faint stars and brown dwarfs\nare found to constitute only a few percent of the mass of the Galaxy.\nStellar remnants, including white dwarfs and neutron stars, are shown\nto be very constrained as well. High energy gamma-rays observed in\nHEGRA data place the strongest constraints, $\\Omega_{WD} < 3 \\times\n10^{-3} h^{-1}$, where $h$ is the Hubble constant in units of 100 km\ns$^{-1}$ Mpc$^{-1}$. Hence one is left with several unanswered\nquestions: 1) What are MACHOs seen in microlensing surveys? 2) What is\nthe dark matter in our Galaxy? Indeed a nonbaryonic component in the\nHalo seems to be required.\n\n\\end{abstract}\n\n\\section{Introduction}\n%\\setcounter{footnote}{0}\n%\\renewcommand{\\thefootnote}{\\arabic{footnote}}\n\nThe nature of the dark matter in the haloes of galaxies is an\noutstanding problem in astrophysics. Over the last several decades\nthere has been great debate about whether this matter\nis baryonic or must be exotic. Many astronomers believed\nthat a stellar or substellar solution to this problem might be\nthe most simple and therefore most plausible explanation.\nHowever, in the last few years, these candidates have been\nruled out as significant components of the Galactic Halo.\nI will discuss limits on these stellar candidates, and\nargue for my personal conviction that:\n{\\em Most of the dark matter in the Galactic Halo must be nonbaryonic.}\n\nUntil recently, stellar candidates for the dark matter, including\nfaint stars, brown dwarfs, white dwarfs, and neutron stars, were\nextremely popular. However, recent analysis of various data sets has\nshown that faint stars and brown dwarfs probably constitute no more\nthan a few percent of the mass of our Galaxy\n\\cite{kfrbfgk,kfrgf96a,kfrgf96b,kfrmcs,kfrfgb,kfrfreese}.\nSpecifically, using Hubble Space Telescope and \nparallax data, we showed\nthat faint stars and brown dwarfs contribute no more than 1\\% of the\nmass density of the Galaxy. Microlensing experiments\n(the MACHO \\cite{kfrmacho:1yr}, \\cite{kfrmacho:2yr} and EROS\n\\cite{kfransari}) experiments), which were\ndesigned to look for Massive Compact Halo Objects (MACHOs), also\nfailed to find these light stellar objects and ruled out\nsubstellar dark matter candidates in the $(10^{-7} - 10^{-2}) M_\\odot$ mass\nrange.\n\nRecently white dwarfs have received attention as possible dark matter\ncandidates. Interest in white dwarfs has been motivated by\nmicrolensing events interpreted as being in the Halo, with a best fit\nmass of $\\sim 0.5 M_\\odot $. \nHowever, I will show that stellar remnants including white dwarfs\nand neutron stars are extremely problematic as dark matter\ncandidates. A combination of excessive infrared radiation,\nmass budget issues and chemical abundances constrains the\nabundance of stellar remnants in the Halo quite severely,\nas shown below. \n%The most powerful (unavoidable) constraint on\n%stellar remnants arises as a consequence of TeV\n%gamma-rays seen in HEGRA data. The mere existence of these\n%$\\gamma$-rays places severe constraints; \n%in particular the $\\gamma$-rays constrain the amount of\n%infrared radiation that could have been produced by white dwarf\n%progenitors and hence limit the white dwarf abundance to $\\Omega_{WD}\n%< 3 \\times 10^{-3} h^{-1}$, where $h$ is the Hubble constant in units\n%of 100 km s$^{-1}$ Mpc$^{-1}$.\n%A significant fraction of the\n%baryons of the universe would have to be cycled through the white\n%dwarfs (or neutron stars) and their main sequence progenitors;\n%however, in the process, an overabundance of carbon and nitrogen is\n%produced, far in excess of what is observed both inside the Galaxy and\n%in the intergalactic medium. Agreement with measurements of these\n%elements in the Ly$\\alpha$ forest would require $\\Omega_{\\rm WD} h\n%\\leq 2 \\times 10^{-4}$. Some uncertainty in the yields\n%of C and N from low metallicity stars motivated us (Fields, Freese,\n%and Graff 1999) to look also at D and He$^4$, whose yields are far\n%better understood. The abundances of D and He$^4$ can be kept in\n%agreement with observations only for low mass white dwarf progenitors\n%$(m_{prog} \\sim 2 M_\\odot)$ and $\\Omega_{\\rm WD} < 0.003$. \nHence, white dwarfs, brown dwarfs, faint stars, and neutron stars are either ruled\nout or extremely problematic as dark matter candidates. Thus the\npuzzle remains, What are the 14 MACHO events that have been\ninterpreted as being in the Halo of the Galaxy? Are some of them\nactually located elsewhere, such as in the LMC itself? These questions\nare currently unanswered. As regards the dark matter in the Halo of\nour Galaxy, one is driven to nonbaryonic constituents as the bulk of\nthe matter. Possibilities include supersymmetric particles, axions,\nprimordial black holes, or other exotic candidates.\n\nIn this talk I will focus on the arguments against stellar remnants\nas candidates for a substantial fraction of the dark matter,\nas white dwarfs in particular have been the focus of attention\nas potential explanations of microlensing data. For a discussion\nof limits on faint stars and brown dwarfs, see earlier\nconference proceedings by Freese, Fields, and Graff (\\cite{kfrfreese} and\n\\cite{kfrconf1}).\n\n\\section{White Dwarfs}\n\nStellar remnants (white dwarfs and neutron stars) face\na number of problems and issues as dark matter candidates:\n1) infrared radiation;\n2) IMF (initial mass function);\n3) baryonic mass budget; \n4) element abundances. \n\nWe find that none of the expected signatures in the above\nlist of a significant white dwarf component in the Galactic\nHalo are seen to exist.\n\n\\subsection{Constraints from multi-TeV $\\gamma$-rays seen by HEGRA}\n\nThe mere existence of multi-TeV $\\gamma$-rays seen in\nthe HEGRA experiment places a powerful constraint on the\nallowed abundance of white dwarfs. This arises because\nthe progenitors of the white dwarfs would produce infrared\nradiation that would prevent the $\\gamma$-rays from getting here.\nThe $\\gamma$-rays and infrared photons would interact via\n$\\gamma \\gamma \\rightarrow e^+ e^-$. \n\nMulti-TeV $\\gamma$-rays from the blazar Mkn 501 at a redshift z=0.034\nare seen in the HEGRA detector. The\ncross section for (1-10)TeV $\\gamma$-rays peaks at infrared photon\nenergies of (0.03-3)eV. Photons in this energy range would be\nproduced in abundance by the progenitor stars to white dwarfs and\nneutron stars. \n%Hence the infrared flux from the remnant progenitors\n%would contribute to the opacity of multi-TeV $\\gamma$-rays (Konopelko\n%\\etal \\cite{kfrkonop}). \nBy requiring that the optical depth due to\n$\\gamma \\gamma \\rightarrow e^+ e^-$ be less than one for a source at\n$z=0.034$ we limit the cosmological density of stellar remnants\n\\cite{kfrgfwp} to\n\\(\\Omega_{\\rm WD} \\leq (1-3) \\times 10^{-3}\nh^{-1}\\).\nThis constraint is quite robust and model independent, as it applies\nto a variety of models for stellar physics, star formation rate and\nredshift, mass function, and clustering.\n\n\\subsection{Mass Budget Issues}\n%First, I discuss the mass budget issues\n%(based on work by Fields, Freese, and Graff \\cite{kfrffg})\n%general to all Halo Machos, regardless of the type of object.\n\n\\paragraph{Contribution of Machos to the Mass Density of the\nUniverse:}\n(based on work by Fields, Freese, and Graff \\cite{kfrffg})\nThere is a potential problem in that too many baryons are\ntied up in Machos and their progenitors (Fields, Freese, and Graff).\nWe begin by estimating the contribution of Machos to the mass density of the\nuniverse.\nMicrolensing results \\cite{kfrmacho:1yr} predict that the total mass\nof Machos in the Galactic Halo out to 50 kpc is\n$M_{\\rm Macho} = (1.3 - 3.2) \\times 10^{11} M_\\odot \\, .$\nNow one can obtain a ``Macho-to-light\" ratio for the Halo by\ndividing by the luminosity of the Milky Way (in the B-band),\n$L_{MW} \\sim (1.3-2.5) \\times 10^{10} L_\\odot,$\nto obtain\n$(M/L)_{\\rm Macho} = (5.2-25)M_\\odot /L_\\odot \\, .$\n>From the ESO Slice Project\nRedshift survey \\cite{kfrzuc},\nthe luminosity\ndensity of the Universe in the $B$ band is\n${\\cal L}_B = 1.9\\times 10^{8} h \\ L_\\odot \\ {\\rm Mpc}^{-3} \\, .$\nIf we assume that the $M/L$ which we defined for the Milky\nWay is typical of the Universe as a whole,\nthen the universal mass density of\nMachos is\n\\begin{equation}\n\\label{kfromega}\n\\Omega_{\\rm Macho} \\equiv \\rho_{\\rm Macho}/ \\rho_c = (0.0036-0.017) \\,\nh^{-1} \\, \n\\end{equation}\nwhere the critical density\n$\\rho_c \\equiv\n3H_0^2/8 \\pi G = 2.71 \\times 10^{11} \\, h^2 \\, M_\\odot \\ {\\rm Mpc}^{-3}$.\n\n\nWe will now proceed to compare our $\\omegam$\nderived in Eq.~\\ref{kfromega} with the baryonic density in the universe,\n$\\omegab$, as determined by primordial nucleosynthesis.\nTo conservatively allow for the full range of possibilities,\nwe will adopt\n$\\omegab= (0.005-0.022) \\ h^{-2} \\, .$\nThus, if the Galactic halo Macho\ninterpretation of the microlensing\nresults is correct,\nMachos make up an important fraction of the baryonic matter\nof the Universe.\nSpecifically, the central values give\n\\begin{equation}\n%\\label{kfrcentral}\n\\omegam/\\omegab \\sim 0.7\\, .\n\\end{equation}\nHowever, the lower limit on this fraction is\nconsiderably less restrictive,\n\\begin{equation}\n%\\label{kfrcomp}\n{\\omegam \\over \\omegab} \\geq {1 \\over 6} h \\geq \\frac{1}{12}\\, .\n\\end{equation}\n\n\\paragraph{Mass Budget constraints from\nMachos as Stellar Remnants: White Dwarfs or Neutron Stars}\n\nIn general, white dwarfs, neutron stars, or black holes all came from\nsignificantly heavier progenitors. Hence, the excess mass left over\nfrom the progenitors must be added to the calculation of $\\Omega_{\\rm\nMacho}$; the excess mass then leads to stronger constraints.\nTypically we find the contribution of Macho progenitors to the mass\ndensity of the universe to be\n\\( \\Omega_{{\\rm prog}} = 4 \\Omega_{{\\rm Macho}} = (0.016-0.08)h^{-1}\\).\nThe central values of all the numbers now imply\n$\\Omega_{\\rm prog} \\sim 3 \\Omega_B$, \nwhich is obviously unacceptable. One is driven to the lowest\nvalues of $\\Omega_{\\rm Macho}$ and highest value of $\\Omega_B$\nto avoid this problem.\n\n\\subsection{On Carbon and Nitrogen}\n%\\label{kfrsect:carbon}\n\nThe overproduction of carbon and/or nitrogen\nproduced by white dwarf progenitors is one of the\ngreatest difficulties faced by a white dwarf dark matter scenario,\nas first noted by Gibson and Mould \\cite{kfrgm}.\nStellar carbon yields for zero\nmetallicity stars are quite uncertain.\nStill, according to the yields by \\cite{kfrvdhg}, a star of mass\n2.5$M_\\odot $ will produce about twice the\nsolar enrichment of carbon.\nHowever, stars in our galactic halo have carbon\nabundance in the range $10^{-4}-10^{-2}$ solar.\nHence the ejecta of a\nlarge population of white dwarfs would have to be removed\nfrom the galaxy via a galactic wind.\n\nHowever, carbon abundances in intermediate redshift\n\\lya\\ forest lines have recently been measured to be\nquite low, at the\n$\\sim 10^{-2}$ solar level\n\\cite{kfrsc}, for \\lya\\ systems at $z \\sim 3$\nwith column densities $N \\ge 3 \\times 10^{15} \\, {\\rm cm}^{-2}$\n(for lower column densities, the mean C/H drops to $\\sim 10^{-3.5}$ solar\n\\cite{kfrlsbr}.\n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[scale=0.3,bb= 0 80 590 720]{freese_f1.ps}\n\\caption{{\\small (taken from Fields, Freese, and Graff 1999): {\\bf\n(a)} The D/H abundances and helium mass fraction $Y$ for models with\n$\\Omega_{\\rm WD} h = 6.1 \\times 10^{-4}$, $h=0.7$, and IMF peaked at\n$2M_\\odot $. \nThe short-dashed curve shows the initial abundances and the error bars\nthe range of D and He measurements. \nThe other three curves show the changes in primordial D and He as a\nresult of white dwarf production. The solid one is for the full\nchemical evolution model, the dotted one for instantaneous\nrecycling, and the long-dashed one for the burst model. \nThis is the absolute minimum\n$\\Omega_{\\rm WD}$ compatible with cosmic extrapolation of white dwarf\nMachos if Machos are contained only in spiral galaxies with luminosities\nsimilar to the Milky Way. {\\bf (b)} CNO abundances\nproduced in the same model as {\\bf a}, here plotted as a function of\n$\\Omega_B$. The CN abundances are\npresented relative to solar via the usual notation of the form\n$[{\\rm C/H}]= \\log_{10} \\frac{{\\rm C/H}}{({\\rm C/H})_\\odot} \\, .$\nThe C and N production in particular are greater than 1/10\nsolar.}}\n\\end{figure}\n\nIn order to maintain carbon abundances as low as $10^{-2}$ solar, only\nabout $10^{-2}$ of all baryons can have passed through the\nintermediate mass stars that were the predecessors of Machos\n\\cite{kfrffg}. Such a\nfraction can barely be accommodated for\nthe remnant density predicted from our extrapolation of the Macho\ngroup results, and would be in conflict with $\\Omega_{{\\rm prog}}$ in\nthe case of a single burst of star formation. Note that\nstars heavier than 4$M_\\odot $ may replace the carbon overproduction\nproblem with nitrogen overproduction\n\\cite{kfrvdhg,kfrlattbooth}.\n\nUsing the yields described above, we calculated the C and N that would\nresult from the stellar processing for a variety of initial mass\nfunctions for the white dwarf progenitors. We used a chemical\nevolution model based on a code described in Fields \\& Olive\n\\cite{kfrfo98} to obtain our numerical results. Our results are\npresented in the figure.\n\n\nIn the figure, we make the parameter choices that are in agreement with D\nand He$^4$ measurements (see the discussion below) and are the least\nrestrictive when comparing with the Ly$\\alpha$ measurements.\nWe take an initial mass function (IMF)\nsharply peaked at 2$M_\\odot $, so that there are very few progenitor\nstars heavier than 3$M_\\odot $ (this IMF is required by D and He$^4$\nmeasurements). In addition (see the figures in Fields,\nFreese, and Graff \\cite{kfrffg2}) we have considered a variety of other\nparameter choices. By comparing with the observations, we obtain the limit,\n\\(\\Omega_{\\rm WD} h \\leq 2 \\times 10^{-4}\\).\nAs a caveat, note that it is possible that carbon never leaves the\n(zero metallicity)\nwhite dwarf progenitors, so that carbon overproduction is not a\nproblem \\cite{kfrchabriernew}. \n\n\\subsection{Deuterium and Helium}\n\nBecause of the uncertainty in the C and N yields from low-metallicity\nstars, we have also calculated the D and He$^4$ abundances that would\nbe produced by white dwarf progenitors. These are far less uncertain\nas they are produced farther out from the center of the star and do\nnot have to be dredged up from the core. \nPanel a) in the figure displays our results. Also shown are the initial\nvalues from big bang nucleosynthesis and the (very generous) range of\nprimordial values of D and He$^4$ from observations.\n>From D and He alone, we can see that the white dwarf progenitor IMF\nmust be peaked at low masses, $\\sim 2M_\\odot $.\nWe obtain \\(\\Omega_{\\rm WD} \\leq 0.003\\).\n\n%\\section{Zero Macho Halo?}\n\n%The possibility exists that the 14 microlensing events that have been\n%$interpreted as being in the Halo of the Galaxy are in fact due to some\n%other lensing population. One of the most difficult aspects of\n%microlensing is the degeneracy of the interpretation of the data, so\n%that it is currently impossible to determine whether the lenses lie in\n%the Galactic Halo, or in the Disk of the Milky Way, or in the LMC. In\n%particular, it is possible that the LMC is thicker than previously\n%thought so that the observed events are due to self-lensing of the\n%LMC. All these possibilities are being investigated. More data\n%are required in order to identify where the\n%lenses are.\n\n\\section{Conclusions}\n\n\\paragraph{A Zero Macho Halo?}\nThe possibility exists that the 14 microlensing events that have been\ninterpreted as being in the Halo of the Galaxy are in fact due to some\nother lensing population. One of the most difficult aspects of\nmicrolensing is the degeneracy of the interpretation of the data, so\nthat it is currently impossible to determine whether the lenses lie in\nthe Galactic Halo, or in the Disk of the Milky Way, or in the LMC. In\nparticular, it is possible that the LMC is thicker than previously\nthought so that the observed events are due to self-lensing of the\nLMC. All these possibilities are being investigated. More data\nare required in order to identify where the\nlenses are.\n\nMicrolensing experiments have ruled out baryonic dark matter objects\nin the mass range $10^{-7}M_\\odot $ all the way up to $10^{-2}M_\\odot$.\nIn this talk\nI discussed the heavier possibilities in the range $10^{-2}M_\\odot $\nto a few $M_\\odot $. Brown dwarfs and faint stars\nare ruled out as significant dark matter components; they contribute\nno more than 1\\% of the Halo mass density. Stellar remnants\nare not able to explain the dark matter of the Galaxy either;\nnone of the expected\nsignatures of stellar remnants, i.e., infrared radiation,\nlarge baryonic mass budget, and C,N, and He$^4$ abundances,\nare found observationally.\n\nHence, in conclusion, \\hfill\\break 1) Nonbaryonic dark matter in our\nGalaxy seems to be required, and \\hfill\\break 2) The nature of the\nMachos seen in microlensing experiments and interpreted as the dark\nmatter in the Halo of our Galaxy remains a mystery. Are we driven to\nprimordial black holes \\cite{kfrcarr} \\cite{kfrjedam},\nnonbaryonic Machos (Machismos?), mirror matter Machos (\\cite{kfrmohap})\nor perhaps a no-Macho Halo?\n\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{kfrbfgk} Bahcall, J.N., Flynn,. C., Gould, A.,\n\\& Kirkahos, S., 1994, ApJ, 435, L51\n\\bibitem{kfrgf96a} Graff, D.S., \\& Freese, K. 1996a, ApJ, 456, L49\n\\bibitem{kfrgf96b} Graff, D.S., \\& Freese, K. 1996b, ApJ, 467, L65\n\\bibitem{kfrmcs} M\\'era, D., Chabrier, G., \\& Schaeffer, R.\n1996, Europhys.\\ Lett., 33, 327\n\\bibitem{kfrfgb} Flynn, C., Bahcall, J., \\& Gould, A. 1996,\nApJ, 466, L55\n\\bibitem{kfrfreese} Freese,K., Fields, B., \\& Graff, D.,\n``What are Machos? Limits on Stellar Objects as the Dark Matter\nof Our Halo,\" Conf. Proc. of the Int'l Workshop\non Aspects of Dark Matter in Astro and Particle Physics, Heidelberg,\nGermany, astro-ph/9901178\n\\bibitem{kfrconf1} Freese, K., Fields, B., \\& Graff, D., 1999,\nastro-ph/9904401\n\\bibitem{kfrmacho:1yr} Alcock, C., et al.\\ 1996, ApJ, 461, 84\n\\bibitem{kfrmacho:2yr} Alcock, C., et al.\\ 1997a, ApJ, 486, 697\n\\bibitem{kfransari} Ansari, R., et al. \\ 1996, A\\&A, 314, 94\n\\bibitem{kfraxelrod} Axelrod, T., MACHO experiment,\ntalk presented at Aspen, June 1997\n\\bibitem{kfrggt} Gates, E., Gyuk, G., \\& Turner, M.S. 1996, PRD,\n53, 4138\n\\bibitem{kfrkonop} Konopelko, A.K., Kirk, J.G., Stecker, F.W.,\n\\& Mastichiadis, A. 1999, astro-ph/9904057\n\\bibitem{kfrgfwp} Graff, D.S., Freese, K., Walker, T.P., \\& Pinsonneault,\nM.H. 1999, in press, ApJ Lett, astro-ph/9903181\n\\bibitem{kfrffg} Fields, B., Freese, K., \\& Graff, D.,\n1998, New Astron, 3, 347\n\\bibitem{kfrzuc} Zucca, E., et al.\\ 1997, A\\&A, 326, 477\n\\bibitem{kfrgm} Gibson, B.K., \\& Mould, J.R., 1997, ApJ, 482, 98\n\\bibitem{kfrsc} Songaila, A., \\& Cowie, L.L. 1996, AJ, 112, 335\n\\bibitem{kfrlsbr} Lu, L., Sargent, W.L.W., Barlow, T.A., \\& Rauch, M.\n1998, astro-ph/9802189\n\\bibitem{kfrffg2} Fields, B., Freese, K., \\& Graff, D., 1999,\nin press, ApJ\n\\bibitem{kfrvdhg} van den Hoek, L.B., \\& Groenewegen,\nM.A.T. 1997, A\\&AS, 123, 305\n\\bibitem{kfrlattbooth} Lattanzio, J.C. \\& Boothroyd, A.I., 1997\nastro-ph/9705186\n\\bibitem{kfrfo98} Fields, B.D., \\& Olive, K.A. 1998, ApJ, 506, 177\n\\bibitem{kfrchabriernew} Chabrier, G. 1999, ApJ Lett, in press;\nastro-ph/9901145\n\\bibitem{kfrcarr} Carr, B. 1994, ARAA, 32, 531\n\\bibitem{kfrjedam} Jedamzik, K. 1997, Phys. Rev. D, 55, 5871\n\\bibitem{kfrmohap} Mohapatra, R.N., \\& Teplitz, V.L. 1999,\nastro-ph/9902085\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002058.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{kfrbfgk} Bahcall, J.N., Flynn,. C., Gould, A.,\n\\& Kirkahos, S., 1994, ApJ, 435, L51\n\\bibitem{kfrgf96a} Graff, D.S., \\& Freese, K. 1996a, ApJ, 456, L49\n\\bibitem{kfrgf96b} Graff, D.S., \\& Freese, K. 1996b, ApJ, 467, L65\n\\bibitem{kfrmcs} M\\'era, D., Chabrier, G., \\& Schaeffer, R.\n1996, Europhys.\\ Lett., 33, 327\n\\bibitem{kfrfgb} Flynn, C., Bahcall, J., \\& Gould, A. 1996,\nApJ, 466, L55\n\\bibitem{kfrfreese} Freese,K., Fields, B., \\& Graff, D.,\n``What are Machos? Limits on Stellar Objects as the Dark Matter\nof Our Halo,\" Conf. Proc. of the Int'l Workshop\non Aspects of Dark Matter in Astro and Particle Physics, Heidelberg,\nGermany, astro-ph/9901178\n\\bibitem{kfrconf1} Freese, K., Fields, B., \\& Graff, D., 1999,\nastro-ph/9904401\n\\bibitem{kfrmacho:1yr} Alcock, C., et al.\\ 1996, ApJ, 461, 84\n\\bibitem{kfrmacho:2yr} Alcock, C., et al.\\ 1997a, ApJ, 486, 697\n\\bibitem{kfransari} Ansari, R., et al. \\ 1996, A\\&A, 314, 94\n\\bibitem{kfraxelrod} Axelrod, T., MACHO experiment,\ntalk presented at Aspen, June 1997\n\\bibitem{kfrggt} Gates, E., Gyuk, G., \\& Turner, M.S. 1996, PRD,\n53, 4138\n\\bibitem{kfrkonop} Konopelko, A.K., Kirk, J.G., Stecker, F.W.,\n\\& Mastichiadis, A. 1999, astro-ph/9904057\n\\bibitem{kfrgfwp} Graff, D.S., Freese, K., Walker, T.P., \\& Pinsonneault,\nM.H. 1999, in press, ApJ Lett, astro-ph/9903181\n\\bibitem{kfrffg} Fields, B., Freese, K., \\& Graff, D.,\n1998, New Astron, 3, 347\n\\bibitem{kfrzuc} Zucca, E., et al.\\ 1997, A\\&A, 326, 477\n\\bibitem{kfrgm} Gibson, B.K., \\& Mould, J.R., 1997, ApJ, 482, 98\n\\bibitem{kfrsc} Songaila, A., \\& Cowie, L.L. 1996, AJ, 112, 335\n\\bibitem{kfrlsbr} Lu, L., Sargent, W.L.W., Barlow, T.A., \\& Rauch, M.\n1998, astro-ph/9802189\n\\bibitem{kfrffg2} Fields, B., Freese, K., \\& Graff, D., 1999,\nin press, ApJ\n\\bibitem{kfrvdhg} van den Hoek, L.B., \\& Groenewegen,\nM.A.T. 1997, A\\&AS, 123, 305\n\\bibitem{kfrlattbooth} Lattanzio, J.C. \\& Boothroyd, A.I., 1997\nastro-ph/9705186\n\\bibitem{kfrfo98} Fields, B.D., \\& Olive, K.A. 1998, ApJ, 506, 177\n\\bibitem{kfrchabriernew} Chabrier, G. 1999, ApJ Lett, in press;\nastro-ph/9901145\n\\bibitem{kfrcarr} Carr, B. 1994, ARAA, 32, 531\n\\bibitem{kfrjedam} Jedamzik, K. 1997, Phys. Rev. D, 55, 5871\n\\bibitem{kfrmohap} Mohapatra, R.N., \\& Teplitz, V.L. 1999,\nastro-ph/9902085\n\\end{thebibliography}"
}
] |
astro-ph0002059
|
Kinematics of Molecular Hydrogen Emission from Planetary and Pre-planetary Nebulae
|
[
{
"author": "Joel H. Kastner"
},
{
"author": "Ian Gatley"
}
] |
We report results from a program of high-resolution spectral mapping of rotational H$_2$ emission from bipolar planetary and pre-planetary nebulae. Long-slit spectra obtained with the NOAO Phoenix near-infrared spectrometer allow us to probe the molecular kinematics of these nebulae at moderate spatial resolution. We find strong evidence of a component of rotation in the equatorial H$_2$ emission from the Egg nebula (RAFGL 2688). In this nebula and in the pre-planetary nebula RAFGL 618, the H$_2$ kinematics point to the recent emergence of high-velocity polar flows, which likely mark the fairly sudden terminations of the red giant phases of their central stars. The classical bipolar planetary NGC 2346 displays distinct kinematic components, which we interpret as arising in the morphologically distinct equatorial and polar regions of the nebula. The H$_2$ rings observed in the Phoenix position-velocity maps of this nebula support the hypothesis that ring-like planetaries that display H$_2$ emission possess bipolar structure.
|
[
{
"name": "kastner1.tex",
"string": "\\documentstyle[11pt,newpasp,epsf,twoside]{article}\n\\markboth{Kastner, Gatley, \\& Weintraub}{H$_2$ Kinematics of PNs and PPNs}\n\\pagestyle{myheadings}\n%\\nofiles\n\n% Some definitions I use in these instructions.\n\n%\\def\\emphasize#1{{\\sl#1\\/}}\n%\\def\\arg#1{{\\it#1\\/}}\n%\\let\\prog=\\arg\n\n%\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n%\\marginparwidth 1.25in\n%\\marginparsep .125in\n%\\marginparpush .25in\n%\\reversemarginpar\n\n%\\def\\plottwo#1#2{\\centering \\leavevmode\n%\\epsfxsize=.45\\textwidth \\epsfbox{#1} \\hfil\n%\\epsfxsize=.45\\textwidth \\epsfbox{#2}}\n\n\\begin{document}\n\n\\addcontentsline{toc}{section}{\nKinematics of Molecular Hydrogen Emission from \\\\ Planetary and\nPre-planetary Nebulae \\\\\n\\hspace{.25in} {\\it J.H. Kastner, I. Gatley, \\& D.A. Weintraub}}\n\n\\title{Kinematics of Molecular Hydrogen Emission from Planetary and\nPre-planetary Nebulae}\n\\author{Joel H. Kastner, Ian Gatley}\n\\affil{Chester F. Carlson Center for Imaging Science, Rochester Institute of\nTechnology, 54 Lomb Memorial Dr., Rochester, NY 14623}\n\\author{David A. Weintraub}\n\\affil{Dept.\\ of Physics \\& Astronomy, Vanderbilt University, Nashville, TN}\n\n\\begin{abstract}\n\nWe report results from a program of high-resolution\nspectral mapping of rotational H$_2$ emission\nfrom bipolar planetary and pre-planetary nebulae. Long-slit\nspectra obtained with the NOAO Phoenix near-infrared spectrometer\nallow us to probe the molecular kinematics of these nebulae\nat moderate spatial resolution. We find strong evidence of a\ncomponent of rotation in the equatorial H$_2$ emission from\nthe Egg nebula (RAFGL 2688). In this nebula and in the\npre-planetary nebula RAFGL 618, the H$_2$ kinematics point to\nthe recent emergence of high-velocity polar flows,\nwhich likely mark the fairly sudden terminations of the red giant\nphases of their central stars. The classical bipolar\nplanetary NGC 2346 displays distinct kinematic\ncomponents, which we interpret as arising in the\nmorphologically distinct equatorial and polar regions of the nebula. \nThe H$_2$ rings observed in the Phoenix position-velocity\nmaps of this nebula support the hypothesis that ring-like\nplanetaries that display H$_2$ emission possess bipolar structure.\n\n\\end{abstract}\n\n%\\keywords{ISM: molecules --- planetary nebulae: individual\n%(RAFGL 2688, RAFGL 618, NGC 2346) --- stars: AGB and post-AGB}\n\n\\section{Introduction}\n\nThe presence of molecular hydrogen\nemission is now recognized as a reliable indicator of\nbipolar structure in planetary nebulae (Zuckerman \\& Gatley\n1988; Kastner et al.\\ 1994, 1996). While the polar lobes\noften display H$_2$, the molecular emission is, with few\nexceptions, brightest toward the waists of bipolar\nplanetaries. These molecule-rich regions of planetary\nnebulae (PNs) appear to be the remnants of circumstellar\ndisks or tori formed during previous, asymptotic giant\nbranch (AGB) or post-AGB phases of the central\nstars. Furthermore, the available evidence suggests that the\nonset of H$_2$ emission postdates the AGB stage but precedes\nthe formation of the PN (Weintraub et al.\\ 1998). This onset\nlikely signals the beginning of a\nhigh-velocity, collimated, post-AGB wind, which shocks the\npreviously ejected, ``slow,'' AGB wind and thereby produces\nthe observed H$_2$ emission (Kastner et al.\\ 1999).\n\nThese observations make clear that further investigations of\nH$_2$ emission are important to our understanding of the\norigin of bipolarity in PNs. It is of particular interest to\nestablish whether the spatially distinct waist and lobe\nH$_2$ emission regions are kinematically distinct as well\nand, furthermore, whether the kinematics bear evidence of\nthe presence of circumstellar disks and/or high-velocity\npolar flows. To this end, we have undertaken a program of\nspectroscopic mapping of near-infrared H$_2$ emission from planetary and\npre-planetary nebulae at high spectral resolution. First\nresults from this program were presented in Weintraub et\nal.\\ (1998), in which H$_2$ emission was detected from a\npair of bipolar pre-planetary nebulae (PPNs), and in Kastner\net al.\\ (1999), where we described preliminary results for\nthe seminal PPN RAFGL 2688. Here we present further analysis\nand interpretation of H$_2$ velocity mapping of RAFGL 2688,\nas well as H$_2$ velocity mapping results for the PPN RAFGL\n618 and the bipolar planetary nebula NGC 2346 (see also Arias \\& Rosado,\nin this volume).\n\n\\section{Observations}\n\nData presented here were obtained with the\nNOAO\\footnote{National Optical Astronomy Observatories is\noperated by Associated Universities for Research in\nAstronomy, Inc., for the National Science Foundation.}\nPhoenix spectrometer on the 2.1 m telescope at\nKitt Peak, AZ, in 1997 June (RAFGL 2688) and 1997 December (RAFGL\n618, NGC 2346). Phoenix illuminates a $256\\times1024$ section of an Aladdin \nInSb detector array. The spectrograph slit was $\\sim60''\\times1.4''$\noriented approximately east-west. The velocity resolution was\n$\\sim4$ km s$^{-1}$ and the spatial resolution $\\sim1.5''$ \nat the time these spectra were obtained. \nA spectral image centered near the 2.121831 $\\mu$m $S(1)$, $v=1-0$\ntransition of H$_2$ was obtained at each of 12 spatial positions as the slit\nwas stepped from south to north across RAFGL 2688. The step size, $1.0''$,\nprovided coverage of the entire H$_2$ emitting region with spatial\nsampling approximating the slit height. For RAFGL 618, whose bright H$_2$\nemission regions are oriented almost perfectly east-west (Latter et al.\\\n1995), parallel to the Phoenix slit, we obtained a single spectral image\ncentered on the object. For NGC 2346 we obtained spectral images at selected \npositions near the waist of the nebula.\nSpectral images were reduced and wavelength calibrated as\ndescribed in Weintraub et al.\\ (1998). For the RAFGL 2688 data,\nthe reduced spectral images were stacked in declination according to the\ncommanded telescope offsets, to produce a (RA, dec, velocity) data cube of\nH$_2$ emission.\n\n\\section{Results and Discussion}\n\n\\begin{figure}[htbp]\n\n\\plotone{egg_vfield.eps}\n\n\\caption{Comparison of the model and observed \nH$_2$ velocity fields of RAFGL 2688. The velocity greyscale bar applies to\nthe center and right panels.\nThe HST/NICMOS H$_2$ image (Sahai et al.\\ 1998) is shown at left. \nThe observed velocity field (center) consists of velocity centroids\ncalculated from the Phoenix data cube. \nIn the model (right), we set the equatorial expansion velocity at $v_e=5$ km\ns$^{-1}$ and the equatorial rotation velocity at $v_r=10$ km s$^{-1}$.\nThe comparison indicates that there is reasonable qualitative and\nquantitative agreement between model and data for this\nchoice of parameters. }\n\n\\end{figure}\n\n\\subsection{RAFGL 2688}\n\nKastner et al.\\ (1999) presented selected velocity planes\nfrom the RAFGL 2688 Phoenix data cube. The four principal\n``lobes'' of H$_2$ emission seen in direct H$_2$ images\n(e.g., Sahai et al.\\ 1998) are also apparent in these Phoenix\ndata, with one pair oriented parallel to the polar axis\n(roughly N-S) and one perpendicular (roughly E-W). Each of\nthese H$_2$ lobe pairs displays a velocity gradient, with\nthe N and E lobes blueshifted by up to $\\sim30$ km s$^{-1}$\nand the S and W lobes similarly redshifted. However, the N-S\nand E-W H$_2$ lobe pairs differ in their detailed kinematic\nsignatures (Kastner et al.). \n\nThe H$_2$ kinematic data for RAFGL 2688, like velocity maps\nobtained from radio molecular line emission, can be\ndescribed in terms of a multipolar system of purely radially\ndirected jets (Cox et al.\\ 1997; Lucas et al., these\nproceedings). Given the constraints imposed by Phoenix and\n{\\it Hubble Space Telescope} data,\nhowever, this model would require that the ``equatorial''\ncomponents located east and west of the central star are in\nfact directed well above and below the equatorial plane,\nrespectively (Kastner et al.\\ 1999). If one postulates\ninstead that the E-W H$_2$ emission lobes are confined to\nthe equatorial plane of the system --- a hypothesis that\nappears to be dictated by certain details of the H$_2$\nsurface brightness distribution, as well as by simple\nsymmetry arguments --- then one must invoke a model\ncombining radial expansion with a component of azimuthal\n(rotational) velocity along the equatorial plane (Kastner et\nal.). In a forthcoming paper we will compare these two\nalternative models in more detail. Here, we describe a\nspecific formulation of the latter (expansion $+$ rotation)\nmodel that reproduces many of the salient features of the\nPhoenix data.\n\nTo construct this empirical model of the H$_2$ kinematics of RAFGL 2688, we are\nguided by the basic results described above. That is, the\npolar lobes are characterized by velocity gradients in which the fastest\nmoving material is found closest to the star, and the slowest moving\nmaterial is found at the tips of the H$_2$ emission regions. For simplicity,\nwe assume this behavior can be described by an inverse power law relationship \nbetween velocity and radius. For the\nequatorial plane H$_2$ emission, meanwhile, we assume a\ncombination of azimuthal (rotation) and radial (expansion) velocity\ncomponents, whose magnitudes we denote by $v_r$ and $v_e$, respectively. \n\nTo constrain these model parameters, we compared model velocity field images\nwith a velocity centroid image which we obtained\nfrom the Phoenix data cube. For the polar lobes, we find that \nthe exponent of the inverse power law velocity-distance relationship \nis roughly $\\sim0.7$ and that the outflow\nvelocities at the tips of the N and S lobes are $\\sim20$ km s$^{-1}$. \nFor the equatorial regions, good agreement between model and data is obtained\nfor values of $v_e$ and $v_r$\nthat lie in the range $5-10$ km s$^{-1}$, with the additional constraint $v_e\n+ v_r \\sim 15$ km s$^{-1}$. An example of the results for a representative\nmodel (with $v_e = 5$ km s$^{-1}$ and $v_r = 10$ km s$^{-1}$) \nis displayed in Fig.\\ 1. There is clear qualitative agreement\nbetween the model and observed velocity images for these parameter values,\nin the sense that the overall distribution of redshifted and blueshifted\nemission is captured by the model. Furthermore, this model reproduces \nspecific details of the observed H$_2$ velocity distribution, such as\nthe approximate magnitudes and positions of the velocity extrema in the \nfour H$_2$ lobes. While this model is by no means unique, the\ncomparison of calculated and observed velocity fields provides further\nsupport for a component of azimuthal velocity along the equatorial plane of\nRAFGL 2688, and offers an indication of the magnitude of this \n``rotational'' component relative to the components of radial expansion both \nparallel and perpendicular to the polar axis of the system.\n\n\\subsection{RAFGL 618}\n\n\\begin{figure}[ht]\n\n\\plotone{afgl618.eps}\n\\caption{Phoenix spectral image of RAFGL 618. The velocity scale of the\nimage is centered on the systemic velocity of RAFGL 618.\nEast is to the left. The image is displayed in a logarithmic\ngreyscale to bring out the line wing emission, which extends to at\nleast $\\sim \\pm 100$ km s$^{-1}$. The vertical band across\nthe image at RA offset $\\sim0''$ is produced by continuum\nemission from the vicinity of the central star.}\n\n\\end{figure}\n\nThe Phoenix spectral image obtained for RAFGL 618 is displayed in Fig.\\ 2. \nBright H$_2$ emission is detected along the entire polar axis of RAFGL 618. \nThese data demonstrate further that very high velocity H$_2$ emission \nis present in this bipolar outflow. \nThe highest velocity molecular material is found closest to the central star\nof RAFGL 618. We conclude that the velocity gradients along the polar axes \nof both RAFGL 2688 and RAFGL 618 trace rapid transitions from the ``slow,''\nspherically symmetric winds of their AGB progenitors to faster, collimated,\npost-AGB winds (Kastner et al.\\ 1999). \n\n\\subsection{NGC 2346}\n\n\\begin{figure}[ht]\n\n\\plotone{ngc2346cob.eps}\n\n\\caption{Left: Image of NGC 2346 in the 2.12 $\\mu$m line of H$_2$\nobtained with the NOAO Cryogenic Optical Bench (COB; Kastner\net al.\\ 1996). Right: Central region of the COB image,\nillustrating the slit positions used for Phoenix observations.}\n\n\\end{figure}\n\n\\begin{figure}[ht]\n\n\\plotone{ngc2346phx.eps}\n\n\\caption{Phoenix position-velocity images of NGC 2346 obtained\nat the slit positions illustrated in Fig.\\ 3. Top panels: images\nobtained as the slit was stepped northward. Bottom panels: images\nobtained as the slit was stepped southward.\nThe image in the leftmost panels in each series was obtained \nwith the slit centered\non the waist of the nebula. The vertical band across the\nimages at offsets of $0''$ and $2''$S is continuum emission\nfrom the binary companion to the central star (see Bond,\nthese proceedings).}\n\n\\end{figure}\n\nIn Fig.\\ 3 we display an H$_2$ image of NGC 2346 obtained with the NOAO\nCryogenic Optical Bench (Kastner et al.\\ 1996) and we illustrate\nthe slit positions used for Phoenix spectroscopic observations.\nPhoenix spectral images of NGC 2346 obtained at these positions\nare presented in Fig.\\ 4. These \nimages demonstrate that the H$_2$ emission from the bipolar NGC 2346 \nforms rings or ellipses in position-velocity space, an observation that \nreinforces our prior conclusion that ring-like planetaries which display \nH$_2$ are bipolar in structure (Kastner et al.\\ 1994, 1996).\n\nThe position-velocity\nellipse represented in the spectral image obtained with\nthe slit at $0''$ offset (leftmost panels) is noticably tilted, with the\nlargest redshifts found $\\sim15''$ to the east and the\nlargest blueshifts $\\sim15''$ to the west of the central\nstar. It is apparent from Fig.\\ 3 that this tilt is due to\nthe orientation of the Phoenix slit with respect to the object. That\nis, to the east of the star the slit takes in portions of\nthe rearward-facing (redshifted) south polar lobe of the\nnebula, whereas to the west the slit samples portions of the\nforward-facing (blueshifted) north polar lobe.\n\nFurthermore, the position-velocity ellipses in Fig.\\ 4\ncontain two distinct kinematic components: a central ring\nassociated with lower velocity material in the nebular waist \nand a pair of rings associated with higher velocity material \nin the bipolar outflow lobes.\nThe central ring is centered at the systemic velocity of the \nnebula and\ris most apparent in the spectral images obtained near the\nposition of the central star (i.e., in the four lefthand\npanels). The southern ring \nis primarily redshifted (righthand bottom panels) \nwhile the northern ring (righthand top panels) is primarily\nblueshifted. \nAll three rings are present in the images\nobtained nearest the position of the central star (lefthand\npanels), whereas the images obtained further from the\ncentral star display emission from only a portion of the central ring and\none of the outer rings. Hence\nFigs.\\ 3 and 4 indicate that the H$_2$ emission from the\nnebula's waist produces the inner position-velocity ring,\nwhile the outer rings arise from H$_2$ emission from the\npolar lobes. Because of the tilt of the slit with respect to\nthe waist of the nebula, a given slit position samples both\nthe waist region and one or both polar lobes, resulting in a\nsuperposition of these kinematic features in a given\nspectral image.\n\nIn summary, the Phoenix spectral images of NGC 2346 provide\nstrong evidence for distinct kinematic components in this\nnebula. These components consist of an equatorial ring or\ndisk which is expanding at relatively low velocity ($\\sim15$\nkm s$^{-1}$ projected along our line of sight; Fig.\\ 4,\nleftmost panels) and polar lobes that are expanding at\nlarger velocities (Fig.\\ 4, rightmost panels). Put differently, the\nequatorial confinement that is apparent in the morphology of\nthis classical bipolar PN has a direct kinematic\ncounterpart. It is tempting, therefore, to conclude that the\npinched waist of NGC 2346 has its roots in processes which\nwe are now beginning to explore in objects such as RAFGL\n2688.\n\n\\acknowledgments\nJ.H.K. acknowledges support from a JPL Infrared Space Observatory grant to\nRIT. LeeAnn Henn (MIT) reduced many of the Phoenix spectral images used in\nthis study. \n\n\\begin{references}\n\n\\reference Cox, P., et al. 1997, A\\&A, 321, 907\n\\reference Kastner, J.H., Gatley, I., Merrill, K.M., Probst, R.P., \\&\nWeintraub, D.A. 1994, ApJ, 421, 600\n\\reference Kastner, J.H., Weintraub, D.A., Gatley, I., Merrill, K.M., \\&\nProbst, R.P. 1996, ApJ, 462, 777\n\\reference Kastner, J.H., Henn, L., Weintraub, D.A., \\& Gatley, I. 1999, in\nIAU Symp.\\ 191, ``Asymptotic Giant Branch Stars,'' eds.\\ T. LeBertre,\nA. Lebre, \\& C. Waelkens, p.\\ 431\n\\reference Latter, W. B., Kelly, D. M., Hora, J. L., \\& Deutsch, L. K. 1995,\nApJS, 100, 159\n\\reference Sahai, R., Hines, D., Kastner, J.H., Weintraub, D.A., Trauger,\nJ.T., Rieke, M.J., Thompson, R.I., \\& Schneider, G. 1998, ApJ, 492, 163L \n\\reference Weintraub, D.A., Huard, T., Kastner, J.H., \\& Gatley, I. 1998,\nApJ, 509, 728\n\\reference Zuckerman, B., \\& Gatley, I. 1988, ApJ, 324, 501\n\n\\end{references}\n\n\\end{document}\n\n"
}
] |
[] |
astro-ph0002060
|
From Historical Perspectives to Some Modern Possibilities
|
[
{
"author": "Lawrence H. Aller"
}
] |
A historical perspective on the study of asymmetries in planetary nebulae (PNs) is presented. We also describe our ongoing work in high resolution spectroscopy of planetaries, and discuss some likely future directions for the study of asymmetrical PNs.
|
[
{
"name": "Aller.tex",
"string": "\\documentstyle[11pt,newpasp,twoside]{article}\n\\markboth{Aller}{Historical Perspectives}\n\\pagestyle{myheadings}\n%\\nofiles\n\n% Some definitions I use in these instructions.\n\n%\\def\\emphasize#1{{\\sl#1\\/}}\n%\\def\\arg#1{{\\it#1\\/}}\n%\\let\\prog=\\arg\n\n%\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n%\\marginparwidth 1.25in\n%\\marginparsep .125in\n%\\marginparpush .25in\n%\\reversemarginpar\n\n\\begin{document}\n\\setcounter{page}{3}\n\\addcontentsline{toc}{section}{From Historical Perspectives to Some\nModern Possibilities \\\\ \\hspace{.25in} {\\it L.H. Aller}}\n\n\\title{From Historical Perspectives to Some Modern Possibilities}\n\\author{Lawrence H. Aller}\n\\affil{Division of Astronomy \\& Astrophysics, Dept.\\ of Physics and\nAstronomy, University of California, Los Angeles, CA 90095--1562} \n\n\\begin{abstract}\nA historical perspective on the study of asymmetries in planetary nebulae\n(PNs) is presented. We also describe our ongoing work in high resolution\nspectroscopy of planetaries, and discuss some likely future directions for\nthe study of asymmetrical PNs.\n\\end{abstract}\n\n The first systematic study of planetary nebulae (PNs) was undertaken at\nLick Observatory from 1914 to 1917 and is reported in detail in Volume 13 of\ntheir publications. Of particular interest are the extensive papers of\nCurtis (1918) on the shapes and forms of planetaries and of Campbell \\&\nMoore (1918) on their internal motions.\n\n Curtis' discussion was based on plates taken with the Crossley\nReflector with a plate scale of 38.7$''$ mm$^{-1}$. Many PN are, of course,\nquite compact so the fine details are lost because of the limited resolution\nof the emulsion. Curtis obtained a series of graded exposures from which he\nmade drawings of each object, thus overcoming many of the limitations\nimposed by the non-linearity of photographic emulsions and the limited\nintensity range that can be accommodated by a single exposure. He recognized\nthat by going to a telescope of much longer focal length ``a wealth of\nminute structural detail would be shown in features that appeared on\nCrossley plates as diffuse areas and wisps.'' From direct photographs alone\n(even without monochromatic images that showed widely different structures\nin [O II], [O III], and He II, for example), Curtis noted: ``It is evident that\nwe have to do with structures of extraordinary complexities -- the aberrant\nwisps and striae and other minor formal irregularities in such structures as\nthe Ring Nebula in Lyra, NGC 7009, NGC 7026 and others would seem\nto defy all attempts to analyze the details, whatever hypothesis may be\nadopted regarding the general form of the structure as a whole.''\n\n Curtis (1918) noted that the ring hypothesis fails, as we should expect\na large number of elliptical or edge-on forms. The hypothesis of ellipsoidal\nshells of uniform thickness also fails, as it cannot explain very faint\ncentral regions or faintness at the ends of the major axis. He proposed some\ngeneral classes: ellipsoids or sphere-ring forms, ring shells, ellipsoidal\nshells, helical objects such as NGC 6543 and NGC 7293, and anomalous forms\nlike NGC 2440. He was unable to recognize such objects as NGC 7027 as shell\nstructures heavily obscured by dust and classified them as ``anomalous.''\n\n One of the earliest attempts to combine nebular direct photos with\nkinematical data was that made by Warren K. Green (1917). He compared direct\nimages and radial velocity studies of NGC 6543 and NGC 7009 and tried to\ninterpret them with a theoretical picture of rotating shells of gas. He told\nme that after he left Lick Observatory he wrote his thesis while he was in\nthe French Foreign Legion, and ``nevermore worked on planetary nebulae.''\n\n The idea that planetary nebulae had split and distorted spectral lines\nbecause they were in rotation seriously impaired progress in this field for\nmany years. Offhand, starting from the level of understanding of these\nobjects at the beginning of the 20th century, the hypothesis has a taint of\nplausibility. After all, from asteroids to galaxies, astronomical objects do\nrotate, so why not planetary nebulae? However expanding shells offer a\nsimpler, more rational explanation of the doubled lines, Perinne (1929)\nsuggested, while Zanstra (1931) soon conclusively demonstrated that only the\nexpansion hypothesis would work. The arguments are so elementary that there\nis no need to review them here; basically, were the PNs in rotation, the\nlines would be tilted when the slit was placed across the object\nperpendicular to the rotation axis. Further, in NGC 7662, the He II\n$\\lambda$4686 and 5007 [O III] lines were mirror images of one another,\nimplying shells rotating in opposite directions. Nevertheless, Campbell and\nMoore concluded that of the 23 PNs showing internal motions, 19 could be\ninterpretable as rotation!\n\n After this important initial effort, the next great leap forward came \nwith the application of atomic physics to spectroscopy, and especially to \nthe spectra of gaseous nebulae. The names of Zanstra, Bowen, Menzel, and \nAmbartzumian are particularly associated with this development, although \nmany others played important supporting roles. By the forties we had firm \nideas of how the spectra of gaseous nebulae could be interpreted and how \nmeasurement of the intensities of nebular lines could give important clues \nto their diagnostics, so important in understanding complex PNs.\n\nThe next important observational advances were made by Olin Wilson and\nRudolph Minkowski at the Mt. Wilson and Palomar Observatories. Wilson used\nthe coude spectrograph on the 100-inch telescope to observe the spectral\nlines of many ions. With the aid of a multislit spectrograph, in which a\nsingle slit was replaced of by a series of closely-spaced parallel slits, he\ncould observe the pattern of radial velocity motions over the entire\nimage. Thus the ``kinematical structure'' could be obtained across the whole\nPN and in several spectral lines. Wilson found a common kinematical pattern\nin many PNs in that the ions of highest excitation (e.g., [Ne V]) gave the\nsmallest expansion velocities, while those of low ionization (e.g.\\ [O II])\ngave the highest velocity of expansion (Wilson 1950). Possibly, radiation\npressure expelled the gases in the outermost part of the envelope outward\nwhile pushing the inner part of the nebular shell backwards towards the\nstar. Not all PNs conform to this rule (see Sabbadin \\& Hamazaoglu\n1981). In some planetaries of low excitation, [O I] and [S II] show\nsubstantial expansion velocities whilst other ions such as O$^+$, N$^+$ and\nO$^{++}$ seem to show no expansion at all (e.g., IC 418; Wilson 1950).\nWilson also secured monochromatic images of IC 418 in H$\\alpha$, [N II], and\n[O III] from which the spatial distributions of the relevant ions could be\ndeduced and compared with theoretical predictions of stratification.\n\n Direct photographs of a number of PNs were secured at the Mt.\\ Palomar\n200$''$ telescope by Minkowski in the 1940s and 1950s. Unfortunately, the\npublished record of these observations is only fragmentary; see e.g.\\\nMinkowski (1964) for some selected images. Isophotic contours of a number of\nimages were also published by Aller (1956). The original plan by Minkowski\nand Wilson to include both large scale images and kinematic data in what\nmight be considered an ``updated Lick Vol.\\ 13'' was never implemented,\nunfortunately.\n\n Minkowski obtained images in H$\\alpha$ + [N II], 4340, [O II], [0 III] and\nHe II in various PNs. These images bear out the intricacies hinted at by\nCurtis and show some remarkable differences between nebulae. Perhaps the\nmost dramatic comparison is between NGC 7293 (the faint Helix Nebula in\nAquarius), with its numerous famous ``cometary'' structures studied by many\nobservers, and the smooth NGC 3587 (Owl Nebula), which seemed to show no\nfine structure at all.\n\n Special mention must be made of Minkowski \\& Osterbrock's (1960)\nobservations of NGC 6720 and NGC 650-651, which appear to be cylinder or\nringlike forms seen in different projections on the sky (compare with Curtis\n1918). They estimate the electron densities inside the ring to be lower than\nin the rings from the [O II] $\\lambda$3729/$\\lambda$3726 line ratios. The\nphysical structures of the two PNs appear to be closely similar; the spatial\norientations differ.\n\n With the advent of the {\\it Hubble Space Telescope} (HST) and adaptive\noptics and the supplementing of direct images with high dispersion\nspectroscopic data, considerable progress seems possible. We have used the\nHamilton Echelle Spectrograph at the coude focus of the Lick Observatory 3m\ntelescope to observe lines from 3660 to 10,125 \\AA\\ with a spectral\nresolution generally of the order of 0.2\\AA\\ (full-width half maximum). The\nslit length is generally taken as 4.0$''$ to avoid overlapping echelle\norders. These data often are supplemented by observations with the\nInternational Ultraviolet Explorer (IUE).\n\n Note that the size of the slit generally used ($4.0'' \\times 1.2''$) is\nalmost invariably smaller than the size of the nebula under investigation.\nIn praxi, this means that we can reach faint, closely packed lines, like the\n[N I] $\\lambda\\lambda$5198, 5200 pair, at a particular point in the nebular\nimage but cannot explore the line variations from point to point. For this\npurpose, long slit data such as those employed by, e.g., Sabbadin \\&\nHamazaoglu (1982) must be\nused. While our setup is suitable for dredging up faint features,\nlarge-scale studies of spatial excitation variations require monochromatic\nimages or long-slit spectra.\n\nIn the 1940s it was recognized that the ratio of $\\lambda$4363 to the\n$\\lambda\\lambda$4959, 5007 [O III] lines could give a good clue to the\nelectron temperatures in gaseous nebulae (Menzel et al.\\ 1941) and that the\n$\\lambda$3726/$\\lambda$3729 [O II] line ratio would be valuable for getting\nelectron densities (Aller, Ufford, \\& van Vleck 1949). What was needed were\ngood cross-sections for collisional excitations of the relevant metastable\nlevels. These were provided by Seaton (1954a,b) and by Seaton \\& Osterbrock\n(1957). Improvements in the quantum mechanical treatment have been made over\nthe years, so that a greater variety of information can be extracted from\nthe forbidden line data, particularly for [O II] and other ions with three\nequivalent $p$ electrons.\n\nBy comparing lines of the nebular type transitions, e.g., $\\lambda\\lambda$6717\nand 6730 [S II], with those of the transauroral type transitions,\n$\\lambda\\lambda$4068, 4076 [S II] (or the auroral type transitions that in\nthis instance fall in the near-IR near 1 $\\mu$m), one can obtain both the\nelectron density and temperature for the same strata. Recall that in the\nearlier work on nebular diagnostics we obtained the electron temperature in\nthe [O III] (O$^{++}$) zone but the electron density in the [O II] (O$^{+}$)\nzone. Now it is possible to obtain the temperature and density in the same\nzone, e.g. O$^+$ (Keenan et al 1999). For the radiations of [N II], [O III],\n[Ne V], involving two equivalent $p$ electrons, we need to compare optical\nregion nebular-type transitions with IR transitions. This step involves\ncomparing data in very different spectral regions secured with radically\ndifferent detectors.\n\n Calculation of collision cross sections involving the auroral and\ntransauroral jumps in systems with 3 equivalent $p$ electrons are difficult\nand have been completed successfully only in recent years, but we can now\nuse lines of [O II], [Ne IV], [S II], and [Ar IV] to get diagnostics for nebular\nregions of very different excitation levels (Keenan et al.\\ 1996, 1997, 1998,\n1999). With the improvement of measurements of infrared lines, especially\nthose measurements obtained above the earth's atmosphere, we can greatly\nextend PN diagnostics. In spectra as well as images we are always dealing\nwith a two-dimensional projection of a three-dimensional image. The fine\nstructure of the nebula may be below the resolution of the imaging element\neven when seeing is eliminated, as in HST data. And we are always taking some\nkind of an average along the line of sight.\n\n That asymmetrical forms of PNs may be related to factors such as their \nchemical composition or mode of excitation is perhaps illustrated by \nobjects such as NGC 6537. Its isophotic contours as measured on a plate \nsecured by Minkowski are shown in Aller (1956; p.\\ 243). This PN appears to \nshow 4 arms with a strong increase in brightness towards the center. A \npossible interpretation by means of looped filaments is shown in the\ncartoon accompanying the plate.\n\n The spectrum is most remarkable (see, e.g., Feibelman et al.\\ 1985;\nAller et al.\\ 1999). Rowlands et al.\\ (1994) called attention to the\nunusually high electron temperatures found in this object and in NGC 6302\n($T_e\\sim$ 41,000 K and $T_e >$60,000 K, respectively, as\ndeduced from [Ne V]). The electron temperatures range\nfrom $\\sim$6500 K for [S II] and $\\sim$15,000 K for [O II] to $\\sim$30,000 K\nfor [Ne IV] and, as we have mentioned, even higher for [Ne V]! Many years\nago, Menzel \\& Aller (1941) showed that in a photoionized nebula of\napproximately solar composition, the electron temperature would not exceed\nabout 20,000 K, even though the central star temperature might be\n$\\ge$200,000 K. Clearly the high [Ne V] $T_e$ values found in NGC 6537 and\nNGC 6302 must be due to some cause other than the photoionization mechanism\nthat controls most planetaries.\n\n Is it any surprise that PNs in which shock excitation plays an \nimportant role may be asymmetrical? Another example, whose spectrum we\nare studying intensively, is NGC 6543 (the Cat's Eye Nebula).\n\n The importance of high resolution spatial resolution augmented by\nintensive spectroscopic data is obvious. It is important that additional\ndata for the infra-red and ultraviolet be secured. The significance of\nobservations from above Earth's atmosphere is clear. But it is also\nimportant that these efforts should be supported by concurrent theoretical\nstudies, involving crucial atomic parameters, as well as by\ntheoretical structural and hydrodynamical investigations.\n\n\n\n\\begin{references}\n\n\\reference Aller, L. H. 1956, ``Gaseous Nebulae'' (London: Chapman and Hall)\n\n\\reference Aller, L. H., Ufford, C. W. \\& Van Vleck, J. H. 1949, \\apj, 109, 42\n\n\\reference Aller, L. H., Hyung, S. \\& Feibelman, W. A. 1999, \nProc.\\ Nat.\\ Acad.\\ Sci., 96, 5371\n\n\\reference Campbell, W. A. \\& Moore, J. H. 1918, Lick Obs.\\ Publ., 13, 82.\n\n\\reference Curtis, H. D. 1918, Lick Obs.\\ Publ., 13, 57\n\n\\reference Feibelman, W. A., Aller, L. H., Keyes, C. D. \\& Czyzak, S. J. \n1985, Proc.\\ Nat.\\ Acad.\\ Sci., 84, 2292.\n\n\\reference Green, W. K. 1917, Lick Obs.\\ Bull., 9, 72\n\n\\reference Keenan, F. P., Aller, L. H., Bell, K. L. Hyung, S., McKenna, F., \n\\& Ramsbottom, C. 1996, MNRAS 287. 1073 \n\n\\reference Keenan, F. C., McKenna, F., Bell, K. L., Ramsbottom, C.,\nWickstead, A., Aller, L. H., \\& Hyung, S. 1997 \\apj, 487, 457 \n\n\\reference Keenan, F. C., Aller, L. H., Bell, K., Espey, Feibelman W. A.,\nHyung, S., McKenna, F., \\& Ramsbottom D. 1998, \\mnras, 295, 688 \n\n\\reference Keenan, D. C., Aller, L. H., Bell, K. L., Hyung, S., Crawford,\nF. L., Feibelman, W. A., McKenna, F., \\& McLaughlin, B. M. \n1999, \\mnras, 304, 27 \n\n\\reference Menzel, D. H., \\& Aller, L. H. 1941, \\apj, 93, 230\n\n\\reference Minkowski, R. 1964, \\pasp, 76. 197\n\n\\reference Minkowski, R., \\& Osterbrock, D. E. 1960, \\apj, 131, 547\n\n\\reference Perrine, C. D., 1929, Astr. Nach., 237, 89\n\n\\reference Pradhan, A. K. 1976, \\mnras, 177, 31 \n\n\\reference Rowlands, N. Houck, J. U., \\& Herter, E. 1994, \\apj, 427, 867\n\n\\reference Sabbadin, F., \\& Hamazaoglu, G., 1982, \\aap, 109, 134\n\n\\reference Seaton M. J. 1954a MNRAS 114, 154 \n\n\\reference Seaton M. J. 1954b, Annales d'Astrophysique, 17, 396\n\n\\reference Seaton, M. J., \\& Osterbrock, D.E. 1957, \\apj, 125, 66\n\n\\reference Wilson, O. C. 1950, \\apj, 111, 279\n\n\\reference Zanstra, H. 1931, \\zap, 2, 329\n\n\\end{references}\n\n\\end{document}\n"
}
] |
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astro-ph0002061
|
[] |
[
{
"name": "sbmitted.tex",
"string": "\n\\documentstyle[12pt, psfig, a4]{article}\n\\textwidth=6.0truein\n\\textheight=8.0truein\n\\hoffset=-0.32truein\n\\voffset=-0.40truein\n\\pagestyle{empty}\n\n\\newcommand{\\etal}{{\\em et al.}}\n\\newcommand{\\rsun}{R$_\\odot$}\n\n\\begin{document}\n\n\\begin{center}\n\n{\\large\\bf LASCO and EIT Observations of Coronal Mass Ejections}\n\n\\vspace{0.3cm}\nK. P. Dere\\\\\n\nNaval Research Laboratory, Code 7663, Washington DC 20375\\\\\n\n\\vspace{0.3cm}\n\nA. Vourlidas, P. Subramanian\\\\\n\nCenter for Earth Observing and Space Research, Institute for\nComputational Sciences, George Mason University, Fairfax, VA 22030\\\\\n\n\\end{center}\n\n\\begin{center}\n\nProceedings of the YOHKOH 8th Anniversary International Symposium,\n``Explosive Phenomena in Solar and Space Plasma'', Dec 6-8 1999, Sagamihara,\nJapan\n\n\\end{center}\n\nThe LASCO and EIT instruments on the SOHO spacecraft have provided an\nunprecedented set of observations for studying the physics of coronal\nmass ejections (CMEs). They provide the ability to view the pre-event\ncorona, the initiation of the CME and its evolution from the surface of\nthe Sun through 30 \\rsun. An example of the capability of these\ninstruments is provided in a description of a single event (Dere \\etal,\n1997). During the first 2 years of operation of LASCO and EIT on SOHO,\na substantial fraction, on the order of 25 to 50\\%, of the CMEs\nobserved exhibited structure consistent with the ejection of a helical\nmagnetic flux rope. An examples of these has been reported by Chen\n\\etal\\ (1997) and Dere \\etal\\ (1999). These events may be the coronal\ncounterpart of magnetic clouds discussed by Burlaga \\etal (1981) and\nKlein and Burlaga (1982). They analyzed observations of magnetic fields\nbehind interplanetary shocks and deduced that the field topology was\nthat of a helical flux rope.\n\nRecently, we have explored a number of the consequences of the helical\nflux rope description of these types of CMEs. Vourlidas et al. (1999)\nexamined the energetics of CMEs with data from the LASCO coronagraphs\non SOHO. The LASCO observations provide fairly direct measurements of\nthe mass, velocity and dimensions of CMEs. Using these basic\nmeasurements, we determined the potential and kinetic energies and\ntheir evolution for several CMEs that exhibited a flux-rope morphology.\nAssuming magnetic flux conservation ('frozen-in' fields), we used\nobservations of the magnetic flux in a variety of magnetic clouds near\nthe Earth to determine the magnetic flux and magnetic energy in CMEs\nnear the Sun. Figure 1 shows these quantities for a few representative\nflux rope CMEs. In general, we find that the potential and kinetic\nenergies increase at the expense of the magnetic energy as the CME\nmoves out, keeping the total energy roughly constant. This demonstrates\nthat flux rope CMEs are magnetically driven. Furthermore, since their\ntotal energy is constant, the flux rope parts of the CMEs can be\nconsidered to be a closed system above $\\sim$ 2 $R_{\\odot}$.\n\n\\begin{figure}\n\\psfig{file=energetics.ps,width=6.in}\n\\caption{On the left, the total (heavy line), potential (dashed line),\nkinetic (dot-dash line) and magnetic (full line) energies of three\nCMEs. On the right, their mass (diamonds) and velocity (asterisks).}\n\\end{figure}\n\n\nSubramanian et al. (1999) examined images from LASCO to study the\nrelationship of coronal mass ejections (CMEs) to coronal streamers. We\nwished to test the suggestion of Low (1996) that CMEs arise from flux\nropes embedded in streamers near their base. It is expected that the\nCME eruption would lead to the disruption of the streamer. To date,\nthis is the most extensive observational study of the relation between\nCMEs and streamers. The data span a period of 2 years near sunspot\nminimum through a period of increased activity as sunspot numbers\nincreased. We have used LASCO C2 coronagraph data which records\nThomson scattered white light from coronal electrons at heights between\n1.5 and 6$R_s$. Synoptic maps of the coronal streamers have been\nconstructed from C2 observations at a height of 2.5$R_s$ at the east\nand west limbs. We have superposed the corresponding positions of CMEs\nobserved with the C2 coronagraph onto the synoptic maps. We identified\nthe different kinds of signatures CMEs leave on the streamer structure\nat this height (2.5$R_s$). We find four categories of CMEs with respect\nto their effect on streamers:\n\\begin{enumerate}\n \\item CMEs that disrupt the streamer.\\\\[-0.8cm]\n \\item CMEs that have no effect on the streamer, even though they are\nrelated to it.\\\\[-0.8cm]\n \\item CMEs that create streamer-like structures.\\\\[-0.8cm]\n \\item CMEs that are latitudinally displaced from the streamer.\\\\[-0.8cm]\n\\end{enumerate}\n\nFigure 2 summarizes these results. CMEs in categories 3 and 4 are\nnot related to the streamer structure. We therefore conclude that\napproximately 35\\% of the observed CMEs bear no relation to the\npre-existing streamer, while 46\\% have no effect on the observed\nstreamer, even though they appear to be related to it.\n\nPrevious studies using SMM data (Hundhausen 1993) have made the general\nstatement that CMEs are mostly associated with streamers and that they\nfrequently disrupt it. Our conclusions thus significantly alters the\nprevalant paradigm about the relationship of CMEs to streamers.\n\n\\begin{figure}[htb]\n\\centerline{\\psfig{file=streamer_fig.ps,width=2.5in}} \n\\caption{The relationship of CMEs to streamers}\n\\end{figure}\n\nSubramanian and Dere (2000) have examined coronal transients observed\non the solar disk in EIT 195 \\AA\\ images that correspond to coronal mass\nejections observed by LASCO during the solar minimum phase of January\n1996 through May 1998. The objective of the study is to gain an\nunderstanding of the source regions from which the CMEs observed in\nLASCO images emanate. We compare the CME source regions as discerned\nfrom EIT 195 \\AA\\ images with photospheric magnetograms from the MDI on\nSOHO and from NSO Kitt Peak, and also with BBSO H$\\alpha$ images. The\noverall results of our study suggest that a majority of the CME related\ntransients observed in EIT 195 \\AA\\ images are associated with active\nregions. We have carried out detailed case studies of 5 especially\nwell observed events. These case studies suggest that active region\nCMEs are often associated with the emergence of parasitic polarities\ninto fairly rapidly evolving active regions. CMEs associated with\nprominence eruptions, on the other hand, are typically associated with\nlong lived active regions. Figure 3 summarizes these results.\n\n\\begin{figure}[htb]\n\\centerline{\n\\psfig{file=sourceregions.ps,angle=270,width=3.1in}}\n\\caption{Coronal sources of CMEs}\n\\end{figure}\n\n\n\n\\begin{description}\n\\item[]\\underline{References}\n\\item[]Chen, J., \\etal\\, 1997, ApJ, 338, L194\\\\[-0.8cm]\n\\item[]Dere, K. P., \\etal, 1997, Solar Phys., 175, 601.\\\\[-0.8cm]\n\\item[]Dere, K. P., Brueckner, G. E., Howard, R. A., Michels, D.J.,\nDelaboudiniere, J.P., 1999, ApJ, 516, 465.\\\\[-0.8cm]\n\\item[]Burlaga, L., Sittler, E., Mariani, F., Schwenn, R., 1981, JGR, 86, 6673\\\\[-0.8cm]\n\\item[]Klein, L. W., Burlaga, L. F., 1982, JGR, 87, 613\\\\[-0.8cm]\n\\item[]Subramanian, P. and Dere, K.P., 2000, ApJ, in preparation\\\\[-0.8cm]\n\\item[]Subramanian, P., Dere, K.P., Rich, N.B., Howard, R.A., 1999, JGR, 104, 22331\\\\[-0.8cm]\n\\item[]Vourlidas, A., Subramanian, P., Dere, K.P., Howard, R.A., 2000, ApJ, in press\\\\[-0.8cm]\n\\end{description}\n\n\\end{document}\n"
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astro-ph0002062
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Stellar Iron Abundances at the Galactic Center
|
[
{
"author": "Solange V. Ram\\'{\\i}rez\\altaffilmark{1,2}"
},
{
"author": "K. Sellgren\\altaffilmark{1,2}"
}
] |
We present measurements of [Fe/H] for six M supergiant stars and three giant stars within 0.5 pc of the Galactic Center (GC) and one M supergiant star within 30 pc of the GC. The results are based on high-resolution ($\lambda / \Delta \lambda =$ 40,000) $K-$band spectra, taken with CSHELL at the NASA Infrared Telescope Facility. We determine the iron abundance by detailed abundance analysis, performed with the spectral synthesis program MOOG. The mean [Fe/H] of the GC stars is determined to be near solar, [Fe/H] = +0.12 $\pm$ 0.22. Our analysis is a {differential} analysis, as we have observed and applied the same analysis technique to eleven cool, luminous stars in the solar neighborhood with similar temperatures and luminosities as the GC stars. The mean [Fe/H] of the solar neighborhood comparison stars, [Fe/H] = +0.03 $\pm$ 0.16, is similar to that of the GC stars. The width of the GC [Fe/H] distribution is found to be narrower than the width of the [Fe/H] distribution of Baade's Window in the bulge but consistent with the width of the [Fe/H] distribution of giant and supergiant stars in the solar neighborhood.
|
[
{
"name": "preprint.tex",
"string": "%This manuscript is prepared in AASTex 5.0 style\n\n\\documentclass[preprint,epsf]{aastex}\n\\input epsf\n\n\\newcommand{\\kms}{km~s$^{-1}$}\n\\newcommand{\\teff}{$T_{\\rm eff}$}\n\\newcommand{\\mbol}{$M_{\\rm bol}$}\n\\newcommand{\\aori}{$\\alpha$ Ori}\n\n\\received{Nov 12, 1999}\n\\revised{}\n\\accepted{}\n\\ccc{}\n\\cpright{}{}\n\n\\slugcomment{ApJ in press}\n\\shorttitle{Stellar [Fe/H] at the Galactic Center}\n\\shortauthors{Ram\\'{\\i}rez et al.}\n\n\\begin{document}\n\n\\title{Stellar Iron Abundances at the Galactic Center}\n\n\\vspace{10mm}\n\\author{Solange V. Ram\\'{\\i}rez\\altaffilmark{1,2}, \nK. Sellgren\\altaffilmark{1,2}}\n\\affil{Department of Astronomy, The Ohio State University}\n\n\\author{John S. Carr\\altaffilmark{2}}\n\\affil{Naval Research Laboratory}\n\n\\author{Suchitra C. Balachandran\\altaffilmark{2}}\n\\affil{Department of Astronomy, University of Maryland}\n\n\\author{Robert Blum\\altaffilmark{1,2}}\n\\affil{Cerro Tololo Inter-American Observatory}\n\n\\author{Donald M. Terndrup \\& Adam Steed}\n\\affil{Department of Astronomy, The Ohio State University}\n\n\\vspace{10mm}\n\\altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American Observatory.\nCTIO is operated by AURA, Inc.\\ under contract to the National Science\nFoundation.}\n\\altaffiltext{2}{Visiting Astronomer, Infrared Telescope Facility. \nIRTF is operated by the University of Hawaii under contract to the National\nAeronautics and Space Administration.}\n\n\\begin{abstract}\nWe present measurements of [Fe/H] for six M supergiant stars and three \ngiant stars within 0.5 pc of the Galactic Center (GC) and one M supergiant star\nwithin 30 pc of the GC. \nThe results are based on high-resolution ($\\lambda / \\Delta \\lambda =$ \n40,000) $K-$band spectra, taken with CSHELL at the NASA Infrared \nTelescope Facility. \nWe determine the iron abundance by detailed abundance analysis,\nperformed with the spectral synthesis program MOOG.\nThe mean [Fe/H] of the GC stars is determined to be near solar, \n[Fe/H] = +0.12 $\\pm$ 0.22. \nOur analysis is a {\\it differential} analysis, as we have observed and applied \nthe same analysis technique to eleven cool, luminous stars in the solar \nneighborhood with similar temperatures and luminosities as the GC stars.\nThe mean [Fe/H] of the solar neighborhood comparison stars, \n[Fe/H] = +0.03 $\\pm$ 0.16, is similar to that of the GC stars.\nThe width of the GC [Fe/H] distribution is found to be narrower than the \nwidth of the [Fe/H] distribution of Baade's Window in the bulge but \nconsistent with the width of the [Fe/H] distribution\nof giant and supergiant stars in the solar neighborhood. \n\\end{abstract}\n\n\\keywords{Galaxy: abundances, Galaxy: center, stars: abundances, \nstars: late-type}\n\n\n\\section{Introduction}\n\n\\citet{mor96} and \\citet{ser96} have summarized the relative importance of\nstar formation, gas inflow, and gas outflow in the Galactic Center (GC).\nGas from the inner disk flows into the nucleus, perhaps driven by a bar \npotential \\citep{sta91,mor96}, and some of the stellar mass-loss from the \nbulge may fall into the GC \\citep{bli93,jen94}.\n\\citet{ser96} have proposed that this inflow of disk gas results in\nsustained star formation in a ``central molecular zone\" (CMZ) within a\nradius from the GC of $R \\leq$ 200 pc.\nThe GC is observed to be currently forming stars in the CMZ\nat a rate of 0.3--0.6 M$_{\\odot}$ yr$^{-1}$ \\citep{gus89}. \nSome of the GC gas incorporated into stars, enriched by stellar nucleosynthesis,\nwill be returned to the GC interstellar medium by stellar mass-loss and \nsupernovae.\nX-ray observations of hot gas in the GC suggest that some gas could be driven\ntemporarily or permanently\nfrom the GC by a galactic fountain or wind \\citep{bli93,mor96}, however,\nmaking it unclear how much enriched material is incorporated into following\ngenerations of star formation.\nThe presence of strong magnetic fields in the GC also likely plays a role\nin whether enriched gas is driven from or is retained within the GC.\n\nContinued star formation in the central few hundred parsecs of the Galaxy may\nlead to higher metallicities within the CMZ. \nChemical abundances in the disks of spiral galaxies are observed to reach \ntheir highest values at the center \\citep[see ][]{pag81,shi90}. \nH II regions, planetary nebulae, and OB associations in the \nMilky Way also show a radial metallicity gradient \\citep{sha83,fic91,mac94,\nsim95,vil96,rud97,aff97,sma97,gum98}. Chemical evolution models strive to \nexplain these gradients by considering the relative star formation and gas \ninfall/outflow rates, and the metal abundance of the gas compared to the stars \n\\citep[see ][]{aud76,ran91}.\n\nThe metallicity of GC stars is needed in order to constrain models and \nunderstand the stellar processes in the central parsecs of our Galaxy.\nMeasurements of stellar metallicities in the center of the Milky Way\nGalaxy, which is obscured by approximately 30 mag of extinction at $V$, are\nonly now beginning to be feasible through infrared studies.\n\\citet{car00} found a solar Fe abundance in IRS 7, an M supergiant at\na distance of $R = $ 0.2 pc from the GC, from a detailed abundance analysis \nof CSHELL ($\\lambda / \\Delta \\lambda $ = 40,000) $K-$band spectra.\nOur work analyzes similar data for several M supergiant and giant stars \nlocated in the central cluster, within 0.5 pc of the GC, and also one M \nsupergiant star located in the Quintuplet cluster, 30 pc away from the GC.\n\n\\section{Observations}\n\n\\subsection{Sample Selection}\n\nThe GC stars were selected with three requirements. First, they have to \nbe brighter than $K$ = 9.5, a limit set by the sensitivity of the instrument.\nAn hour of integration time is required for high signal-to-noise (S/N) \nspectra for a $K$ = 9 \nstar when observing with CSHELL at the NASA Infrared Telescope Facility (IRTF). \nSecond, the stars should be cool luminous stars, to ensure we are observing\nphotospheric absorption lines rather than the stellar wind emission lines \ncharacteristic of hot luminous stars in the GC. Third, these cool luminous\nstars should have little or no water absorption.\nThis is because published line lists for water (wavelengths, excitation \npotentials, dissociation potentials, oscillator strengths, and damping \nconstants) are not yet adequate for detailed abundance analysis of \nhigh-resolution stellar spectra.\nThe amount of water absorption is determined from $H$ and $K-$band \nlow-resolution spectra ($\\lambda / \\Delta \\lambda \\sim$ 500) taken with the \nIRS at CTIO \\citep{ram99}. \nThe selected sample consists of nine stars located in the central cluster\n($R <$ 0.5 pc), and one star located in the Quintuplet cluster ($R$ = 30 pc). \nThe central cluster stars are IRS 7, IRS 11, IRS 19, IRS 22, BSD 72, BSD 114, \nBSD 124, BSD 129, and BSD 140 \n\\citep[names and positions are given by ][]{blu96a}.\nThe star located in the Quintuplet cluster is VR5-7 \\citep{mon94}.\nEleven cool, luminous stars in the solar neighborhood were selected from the \nliterature to be observed\nand analyzed the same way as the GC stars. These eleven stars have \nknown abundances from detailed analysis in the optical \\citep{luc82a,\nluc82b,lam84,smi85,smi86,luc89} and in the infrared \\citep{car00}. These \ncool, luminous stars in the solar neighborhood\nwere carefully selected to be in the same range of effective\ntemperature and surface gravity as the GC stars. This is very important \nin order to allow a differential analysis comparison, which will cancel \npossible systematic errors such as NLTE effects (see Sec. 4.2). \nThe selected cool, luminous stars in the solar neighborhood are listed\nin Table 1.\n\n\\subsection{Data Acquisition and Reduction}\n\nThe $K-$band high-resolution ($\\lambda / \\Delta \\lambda =$ 40,000)\nspectra used in the abundance analysis were taken with CSHELL\nat the IRTF.\nThe IRTF is a 3--m telescope located at Mauna Kea Observatory in Hawaii, \nand CSHELL is the facility cryogenic infrared echelle spectrograph \n\\citep{tok90}.\nThe observations were carried out in 1993 May, 1996 June, 1996 August,\n1997 July, 1998 May, 1998 July, and 1999 June.\nThe detector for the 1993 observations was a 256$\\times$256 NICMOS-3 HgCdTe \narray, which provided a spectral coverage of $\\approx$ 1000 \\kms ~or 73 \\AA. \nThe detector for the\nrest of the observations was a 256$\\times$256 SBRC InSb array, which gives a \nsmaller coverage of $\\approx$ 750 \\kms ~or 55 \\AA.\nThe slit used to achieve a resolution of $\\lambda / \\Delta \\lambda =$ 40,000\nis 0.5\\arcsec ~wide, 30\\arcsec ~long, with a pixel scale of 0.25\\arcsec ~per\npixel for 1993 data and 0.20\\arcsec ~per pixel for later data.\nOur highest quality data were taken in 1998 and in 1999 when new \norder-separating circular variable filters were installed, providing \nspectra free of fringes.\n\nEight iron lines were selected by inspecting the high resolution atlas of \ncool stars \\citep{wal96} and by analyzing synthetic spectra, which includes\natomic and molecular features (see details in Section 3.0 and in \\citet{car00}).\nThousands of lines of molecules like CN, CO and ${\\rm H_{2}O}$ are present \nthroughout the infrared spectrum of cool stars.\nThe selected iron lines are almost free of known molecular contamination and\nunidentified lines. The eight iron lines are observed using three grating \nsettings of CSHELL. Atomic parameters of the eight iron lines used in the abundance analysis are listed in Table 2. \n\nSpectra were acquired at two different positions along the slit and reduced\nseparately, to determine any systematic effects like \nfringes. Several individual spectrum pairs were observed per star, until\nthe desired signal to noise ratio was reached. \nStars of spectral type A or B were observed as close to the program star's\nairmass as possible to correct for telluric absorption features and to remove\nfringes. \nSuch stars have no significant spectral features in the observed \nwavelength regions.\n\nImage Reduction and Analysis Facility (IRAF\\altaffilmark{3}) and VISTA\nwere used for data reduction.\\altaffiltext{3}\n{The IRAF software is distributed by the National Optical\nAstronomy Observatories under contract with the National Science Foundation}\nThe reduction process began by flat fielding the individual spectra with \ncalibration lamp flats, which were taken for every grating setting. \nSky subtraction was performed by subtracting two consecutive spectra taken at \ndifferent positions along the slit. \nBad pixels were replaced by an interpolated value computed from neighboring\npixels in both the dispersion and perpendicular directions.\nIndividual spectra were extracted with a 5 pixel wide aperture using the \nAPSUM package in IRAF. \nExtracted spectra observed at the same position along the slit were averaged to \nproduce two spectra per star, one spectrum for each position along the slit. \nSpectra of the program stars were then divided by the appropriate A or B type\natmospheric standards, observed at the same position along the slit and \nreduced in the same way, to remove telluric absorption features and fringes. \nEach spectrum was then multiplied by a blackbody of the same temperature as\nthe A or B star to put the spectra on a relative flux density \n(${\\rm F_{\\lambda}}$) scale. \nThe temperature of the A or B star was determined from its spectral type.\nMore than five telluric absorption lines were used to obtain wavelength \nsolutions. The\nwavelength calibration was performed using the tasks of VISTA.\nSpectra were shifted in wavelength to correct for radial velocity differences,\nby comparing the observed and synthetic spectra. The spectra were normalized\nby a linear fit of continuum bands. These continuum bands were chosen by \ncomparing \nthe observed spectrum of \\aori ~from the high-resolution atlas \\citep\n{wal96} with the synthetic spectrum of \\aori. The bands selected are \nregions in the spectrum where the synthesis and the normalized observations \nof \\aori ~are coincident and equal to unity.\nWe estimated the error per pixel as the difference of observations taken \nat two positions along the slit. We computed the mean signal to noise ratio\n(S/N) per pixel by the average of the signal to noise ratio per pixel for all\nspectra observed for that star. The mean S/N \nper pixel for each star is listed in Tables 1 and 3.\n\n\\section{Abundance Analysis}\n\nThe abundance analysis was done using a current version of the LTE \nspectral synthesis program MOOG \\citep{sne73}. \nThe program requires a line list giving the wavelength, excitation\npotential, gf--values, and damping constants for all atomic and molecular\nlines that contribute to the spectrum. The method used to construct the line\nlist is described in Sec. 3.1.\nIn addition, an input model atmosphere for the effective temperature\nand surface gravity appropriate for each star and a value for the \nmicroturbulent velocity is also required.\nThe solar-abundance model atmospheres from Plez \\citep{ple92a,ple92b} were \nused in our analysis because they are the only ones that include gravities and \ntemperatures as low as those of the Galactic Center stars.\nThe Plez models also include sphericity, which is appropriate for supergiant\nstars \\citep{ple92b}. MOOG, however, does not account for sphericity in its\ncalculations. \\citet{car00}, who also used MOOG, compute the effective \ntemperature and\nmicroturbulent velocity of \\aori, VV Cep (HR8383), and $\\beta$ And using \ndifferent sets of model atmospheres, including the Plez models and two \nplane-parallel \natmospheres. When the stellar parameters derived from each model were used \nself-consistenly to derive [Fe/H], the result for [Fe/H] was the same. \nThe determination of the stellar parameters for our sample is discussed in\nSec. 3.2.\n\n\\subsection{Atomic and Molecular Parameters}\n\nThe line list was created the same way as \\citet{car00}, using two main\nsteps: 1. The solar spectrum was used to determine the gf--values\nand the damping constants. 2. Minor adjustments were made by comparison to the \nArcturus spectrum \\citep{wal96}. \nAn initial line list was compiled using Fe I line positions and \nenergy levels\nfrom \\citet{nav94} and the \\citet{kur93} line lists for CN and other atomic\nlines. The damping constants for all atomic lines were initially set to twice \nthat of the Uns\\\"{o}ld approximation for van der Waals broadening \\citep{hol91}.\nA synthetic spectrum \nwas generated for the Sun, using the \\citet{kur93} solar model. The gf--values\nand damping constants were adjusted to match the observed solar spectrum\n\\citep{liv91}, when needed, and unidentified lines were noted. Then, a \nsynthetic spectrum was generated for Arcturus, using the model atmosphere,\nstellar parameters, and abundances from \\citet{pet93}. \nThe solar line list provided a \ngood match to the Arcturus spectrum. \nThe gf--values of low excitation lines, not\nobservable in the Sun, had to be adjusted. The final Fe I atomic \nparameters are listed in Table 2. \nA synthetic spectrum of \\aori, generated using the final line list,\nis compared in Figure 1 to the observed spectrum from \\citet{wal96}\nin the region of each of our eight Fe I lines.\nA Plez model atmosphere with the stellar parameters listed in Table 3,\nand the CNO abundances from \\citet{lam84} were used.\n\nThe depth of line formation was examined using contribution functions, \nwhich provide an indication of spectral line formation coming \nfrom different layers of a stellar model atmosphere \\citep[see details in][] \n{edm69,sne73}. The determination of the depth of line formation \nis needed to make sure each line is formed in the range of opacity ($\\tau$)\ncovered by our model atmosphere. \nThe eight iron lines used in this abundance analysis are formed in the range of\n--2.0 $<$ log $\\tau < $ 0.3, where Plez model atmospheres cover a range of\n--5.6 $<$ log $\\tau < $ 2.6 .\nNote that the Sc I lines in supergiant stars, which neither we nor \\citet[][who\nincluded hyperfine splitting calculations for Sc I lines]{car00}\nare able to model correctly, are shown by the contribution function to be \npartially formed at optical depths outside the range of the Plez models.\nWe therefore approximately model Sc I lines by scaling the Fe I line profiles to\nthe correct depth and width to allow us to separate the one Fe I line at \n22399 \\AA ~which is blended with a \nSc I line at 22400 \\AA. In the case of IRS 7 this procedure was not successful.\n\n\\subsection{Stellar Parameters}\n\n\\subsubsection{Effective Temperature}\n\nThe effective temperature (\\teff) is a key parameter for any \nabundance analysis.\nFor the cool, luminous stars in the solar neighborhood, \nthe effective temperatures were taken from \nthe literature. Some effective temperatures come from \nspectroscopic measurements \\citep{luc82a,luc82b,luc89,car00}. \nOther effective temperatures come from the calibration of $(V-K)$ colors vs. \n\\teff, where \\teff ~comes from angular diameters measured by lunar occultation\n\\citep{smi85,smi86}. \n\\aori ~has an \\teff ~determination from its angular diameter \nmeasured by lunar occultation \\citep[\\teff ~= 3605 $\\pm$ 43 K,][]{dyc98},\nwhich is very good agreement with the spectroscopic value obtained by \n\\citet{car00} (\\teff ~= 3540 $\\pm$ 260, see Table 1).\n\nFor IRS 7, the brightest infrared source in the GC, \\citet{car00} determined\n\\teff ~spectroscopically by requiring the carbon abundance derived from CO \nlines to be independent of the lower excitation potential. \nWe adopt the stellar parameters for IRS 7 from \\citet{car00}, which were\nderived using the standard Plez grid of model atmospheres.\nTheir \\teff ~analysis relied largely on the second overtone CO lines\npresent in the $H-$band (1.5$\\mu$m - 1.8$\\mu$m), because most of the \nfirst overtone CO lines present in the $K-$band are saturated. \n\nFor the remaining nine stars in the GC the $H-$band spectra are too faint to be\nobserved with CSHELL at the IRTF, because of high extinction. \nTherefore CO cannot be used to compute the effective temperature.\nFor those nine GC stars, broad molecular bands present in $H$ and $K-$band low \nresolution spectra ($\\lambda / \\Delta \\lambda \\sim$ 500) are used to \nestimate \\teff ~\\citep{ram99}. \nThese features are CO (2.3 $\\mu$m) and ${\\rm H_{2}O}$ \n(1.9 $\\mu$m). The CO strength increases with decreasing \\teff ~and\ndecreasing surface gravity (log $g$). The ${\\rm H_{2}O}$ strength also \nincreases with decreasing \\teff, but increases\nwith increasing log $g$. These two features together, therefore, provide \ntwo-dimensional spectral classification \\citep{bal73,kle86,blu96b}.\nThe low resolution spectra of GC stars were taken with the IRS at CTIO, \nused in cross-dispersed mode to acquire the $H$ and $K-$band simultaneously \n\\citep{ram99}.\nNearby late-type stars with \\teff ~determinations based directly or indirectly\non the lunar occultation technique \n\\citep{smi85,smi86,smi90,fer90,mcw90,dyc98,ric98} \nwere observed to calibrate our \\teff ~determination. \nThe low resolution spectra of cool, luminous stars stars with known \\teff \n~were taken with the IRS at CTIO, and with TIFKAM at MDM Observatory \n\\citep{ram99}.\nThe distinction between giants and supergiants is determined \nby the presence or weakness of ${\\rm H_{2}O}$, respectively. \nThe CO index is computed in the same way as in \\citet{blu96b}. \nOnce the distinction between giants and \nsupergiants is established, \\teff ~is determined from the relations \nshown in Figure 2, which are the best unweighted linear fit to the data. \nVR 5-7, IRS 19, IRS 22, BSD 72, BSD 124, and BSD 129 were classified as \nsupergiant stars, and IRS 11, BSD 114 and BSD 140 were classified as giant \nstars. The luminosity class for GC stars is also listed in Table 3.\nOur values for \\teff ~for GC stars agree with the results from \\citet{blu96b},\nfor the stars that are common to both samples. Our value for \\teff ~from \nthe CO index of IRS 7, 3400 $\\pm$ 300 K, is also in good agreement with\nthe spectroscopic value of \\teff ~from \\citet{car00}, 3470 $\\pm$ 250 K.\nIRS 7 has a low carbon abundance (Carr et al. 2000, [C/H] = -0.8). The good\nagreement between the \\teff ~from CO index and the spectroscopic \\teff \n~suggests that our derived values of \\teff ~are not strongly affected by\nmoderate variations in the abundance of carbon.\nThe typical uncertainty in \\teff ~computed from the CO index is 300 K\nfor supergiants and 280 K for giants. \nThe \\teff ~for cool, luminous stars in the solar neighborhood is listed in \nTable 1 and for GC stars is listed in Table 3. \n\n\\subsubsection{Surface Gravity}\n\nFor the cool, luminous stars in the solar neighborhood, \nthe surface gravity, $g$, from the literature was used\n\\citep{luc82a,luc82b,smi85,smi86,luc89,car00}.\nFor the GC stars, the surface gravity is determined from the relation:\n\\begin{equation}\n{\\rm log}~g = {\\rm log}(M/M_{\\odot}) + 4~{\\rm log}\n(T_{\\rm eff}/T_{\\rm eff_{\\odot}}) - {\\rm log}(L/L_{\\odot}) - \n{\\rm log}~g_{\\odot}. \n\\end{equation}\n\\teff ~has been already determined. The luminosity, $L$, is computed from \n\\mbol, which is determined from $K$, $A_{K}$, the GC \ndistance, and the bolometric correction, B.C. A GC distance of 8 kpc is \nassumed \\citep{rei93}, $K$ and $A_{K}$ are from\n\\citet{blu96a}, and the B.C. is taken from \\citet{eli85}. The final \n\\mbol ~for the GC stars is listed in Table 3. The uncertainty in \\mbol\n~from the GC stars comes mainly from uncertainties in the extinction curve, \n$E(H-K)/A_{K}$\n, and it estimated to be $\\pm$0.4 \\citep{car00}. Once \\mbol ~and \n\\teff ~are determined, the stars are placed \nin the HR diagram, and masses, $M$, are obtained by over-plotting evolutionary \ntracks of varying initial masses. Solar metallicity evolutionary tracks \n\\citep{sch92} are used to determine masses for supergiant stars. \nFor the coolest stars, that fall outside the \\teff ~range of \\citet{sch92} \nevolutionary tracks, asymptotic giant branch (AGB) tracks from \\citet{mar96} \nwere used to estimate their masses.\nNote that the stellar evolution models assume mass loss for the more massive \nstars, and the current mass of the star at its present age is assumed.\nTwice solar metallicity evolutionary tracks \\citep{sch93} gave the same result\nfor the derived masses. \nThe value of log $g$ for GC stars is listed in Table 3. The uncertainty is\nestimated considering the uncertainties in mass, effective temperature and\nluminosity. \nFigure 3 shows the HR diagram of GC stars and also the cool, luminous stars \nin the solar neighborhood.\nIt is seen that the GC stars and the cool, luminous stars in the solar \nneighborhood occupy the same\nplace in the HR diagram, hence are very similar types of stars.\n\n\\subsubsection{Microturbulent Velocity}\n\nThe values for the microturbulent velocity ($\\xi$) for the cool, luminous stars \nfound in the literature show considerable variation among authors.\n\\citet{car00} found for VV Cep (HR 8383)\na much lower value ($\\xi$ = 3.7 $\\pm$ 0.2 \\kms) than the one from \n\\citet[][$\\xi$ = 5.0 $\\pm$ 0.5 \\kms]{luc82b}. \n\\citet{car00} used CO \nlines of the same excitation potential, for which the carbon abundance should \nbe independent of the equivalent widths of the lines when $\\xi$ is correct. \n\\citet{luc82b} used the same principle, but used Fe I lines instead of CO lines.\n\nSeven of our Fe I lines have similar excitation potential, and those lines \nwere used to derive the microturbulence for the cool, luminous stars in the \nsolar neighborhood. This was done in an iterative way.\nAn Fe abundance was derived from the synthetic model of cool, luminous stars in the solar neighborhood,\nwhich included lines of Fe, CN, and other lines.\nUsing the derived Fe abundance, a synthetic model was computed containing only \nFe lines, and an equivalent width was measured for the Fe lines.\nThis way the equivalent width is free from contributions from CN or other \nspecies.\nThen, the derived Fe abundances from the synthesis were plotted vs. the \nFe equivalent widths. This process was repeated with different\nmicroturbulent velocities until the Fe abundance was independent of the Fe\nequivalent width. The final equivalent widths of the Fe lines used in this\nprocess are listed in Table 4. \nThe obtained value of $\\xi$ for cool, luminous stars in the solar neighborhood\nis listed in Table 1. \nThe uncertainty in the obtained microturbulent velocity comes \nfrom the uncertainty in the slope in the graph of Fe abundance vs. equivalent\nwidth, based on the scatter of the data points. \nOur value of $\\xi$ for \\aori ~($\\xi$ = 2.8 $\\pm$ 0.2) is slightly different\nfrom the value of $\\xi$ from \\citet{car00} ($\\xi$ = 3.23 $\\pm$ 0.15).\nThere is good agreement between\nour values of $\\xi$ and the ones given by \\citet{smi85,smi86}, where\nthe mean difference is 0.15 \\kms. Our values of $\\xi$ are systematically \nlower than the values given by \\citet{luc82b} and \\citet{luc89} (HR 8383,\nHD 202380, HD 163428, BD+59 594, HD 232766), where\nthe mean difference is 2.4 \\kms. Our value of $\\xi$ for HR 8726 is in good\nagreement with the value given by \\citet{luc82a}.\n\nWe do not have sufficient S/N for the GC stars to apply this technique for \nfinding $\\xi$. Instead, to get the microturbulent velocity for the GC stars, \na relation between log $g$ and $\\xi$ is used.\n\\citet{mcw90} showed that log $g$ and $\\xi$ are related in G and K giants.\nThe values of $\\xi$ and log $g$ for cool, luminous stars in the solar \nneighborhood, including the values \nfrom \\citet{car00} and \\citet{smi85,smi86,smi90}, \nare plotted to get a relation to apply to the GC stars. Figure 4 shows\nthis relation for stars with \\teff ~and log $g$ similar to those of the\nGC stars. An unweighted linear fit to the data gives :\n\\begin{equation}\n\\xi = ( 2.78 - 0.82 \\times {\\rm log}~g )~{\\rm km~s^{-1}}.\n\\end{equation}\n\nThe uncertainty in the microturbulent velocity is estimated from the \nuncertainty of the\nfit ($\\pm$0.4 \\kms) and the uncertainty from the surface gravity.\nThe value of $\\xi$ for IRS 7 obtained by this fit, $\\xi$ = 3.3 $\\pm$ 0.4 \\kms,\nis in good agreement with \nthe value of $\\xi$ from \\citet{car00}, $\\xi$ = 3.30 $\\pm$ 0.34 \\kms, obtained \nusing CO lines.\n\n\\subsubsection{Macroturbulent Velocity}\n\nThe synthetic spectra have to be convolved with a macroturbulent broadening\nfunction \\citep{gra92}, and with instrumental broadening, to match the line\nwidths of the observed spectrum. The instrumental broadening is a gaussian of\nfull width half maximum given by\nthe spectral resolution of the instrument (7 \\kms). \nCN lines in two bands (21798 \\AA ~-- \n21804 \\AA; 22403 \\AA ~-- 22409 \\AA) were used to determine the macroturbulent \nvelocity ($\\zeta$) for the cool, luminous stars in the solar neighborhood. Several synthetic spectra \nwere generated by MOOG using different values of $\\zeta$ and N abundances. \nThen, \n$\\chi^{2}$ was computed for each synthetic spectrum, and the best set of\nN abundance and $\\zeta$ was chosen for the minimum $\\chi^{2}$. Note that \nthis procedure is not measuring $\\zeta$, but determining the best line\nbroadening that fits the data. Also, the N abundance obtained by this technique\nis not real, because the \nC and O abundances have not been measured independently. Figure 5\nshows the $\\chi^{2}$ contour maps, one for each band, for HR 8726.\nFigure 5 also shows the observed spectrum of HR 8726 and the synthetic\nspectrum for the values of $\\zeta$ and N abundance which give a minimum \n$\\chi^{2}$ for both bands. The macroturbulent velocity for\nthe cool, luminous stars in the solar neighborhood is given in Table 1. \nThe uncertainty in $\\zeta$\nis given by the standard deviation of the values of $\\zeta$ derived for each\nband. This uncertainty is more conservative than the uncertainty derived \nfrom $\\chi^{2}$ statistics.\n\nFor the GC stars, the same method was used for IRS 7, VR 5-7, IRS 19, \nIRS 22, and IRS 11. For the remaining stars, BSD 72, BSD 114, BSD 124, BSD 129,\nand BSD 140, only one band with CN lines was observed and the band did not \nhave enough S/N to carry out this method. \nThe values of $\\zeta$ in Table 1 were used to derive a relationship between\nlog $g$ and $\\zeta$ for supergiant stars. \\citet{gra79} established a \nrelationship between $\\xi$ and $\\zeta$ for giant stars. \n\\citet{mcw90} shows that $\\xi$ depends on log $g$, so by combining these two \ndependences we derive a relation between $\\zeta$ and log $g$.\nThe values of $\\zeta$ for supergiant stars measured by the \nbroadening of the CN lines are plotted vs. log $g$ to get a relation to apply \nto the fainter GC supergiant stars. \nFigure 6 shows this relation. An unweighted linear fit to the data gives :\n\\begin{equation}\n\\zeta = ( 14.5 - 4.40 \\times {\\rm log}~g )~{\\rm km~s^{-1}}.\n\\end{equation}\nThe uncertainty in the microturbulent velocity is estimated from the \nuncertainty of the\nfit ($\\pm$2.4 \\kms) and the uncertainty in the surface gravity.\nEquation (3) was applied to BSD 72, BSD 124, and BSD 129.\n\nFor giant stars, the range in log $g$ is too narrow to derive a relationship.\nA mean value of $\\zeta$ = 9.0 $\\pm$ 3.0 \\kms~is used for the GC giant stars.\nThis mean value is derived from values of $\\zeta$ for solar neighborhood\ngiant stars and IRS 11 measured by the broadening of the CN lines, as \ngiven in Tables 1 and 3.\nThis mean value was adopted for BSD 114 and BSD 140.\n\n\\subsection{Uncertainties}\n\nOur basic observable parameters, \\teff ~and \\mbol, have uncertainties that \ncome from the technique used to compute them (sections 3.2.1 \\& 3.2.2). \nThe surface gravity uncertainty includes both the uncertainty in \\teff ~and \nthe uncertainty in \\mbol ~(section 3.2.2). The microturbulent\nvelocity uncertainty includes both the uncertainties in log $g$ and the \nuncertainty of the fit used to calculate it (section 3.2.3). \nThe same is true for the macroturbulent velocity (section 3.2.4).\n\nIt is important to know what are the effects of each of these uncertainties in \nthe abundance determination. \nThe uncertainty in [Fe/H] for each stellar parameter\nhas been estimated by varying one of the stellar parameters and computing the\ndifference in iron abundance. \nA typical uncertainty in \\teff ~of $\\pm$300 K results in an uncertainty of \n$\\mp$ 0.08 dex in [Fe/H]. \nA typical uncertainty of $\\pm$0.35 in log $g$ implies an uncertainty of \n$\\pm$0.12 dex in [Fe/H]. \nA typical uncertainty of $\\pm$0.4 \\kms ~in $\\xi$ causes an uncertainty of \n$\\mp$ 0.09 dex in [Fe/H].\nA typical uncertainty of $\\pm$1.8 \\kms ~in $\\zeta$ translates to an uncertainty\nof $\\pm$0.13 dex in [Fe/H]. \nThe iron abundance is not very sensitive to uncertainties in \\teff ~and $\\xi$,\nbut it is more sensitive to uncertainties in log $g$ and $\\zeta$. \nIn addition to the uncertainty from the stellar parameters, \nthe standard error must also be considered for each star. \nThe standard error comes from the scatter in [Fe/H]\nas derived from individual Fe I lines. \nAll the uncertainties from stellar parameters and the\nstandard error for each star are listed in Table 7 and 8. \nThe total uncertainty is the quadratic addition of the uncertainties derived \nfrom the stellar parameters and the standard error in the value of [Fe/H]\nfrom individual Fe I lines.\nFor the solar neighborhood stars and IRS 7, the quadratic addition of the\nuncertainties is a good estimation of the total uncertainty, because all \nthe uncertainties come from independent measurements.\nIn the cases where $\\xi$ and $\\zeta$ are computed though their relationships\nwith log $g$, the uncertainties are not independent, and the quadratic addition\ncan be an overestimation of the total uncertainty. \nWe estimate that the total uncertainty will decrease by \nno more than 0.05 dex, if we consider the correlation of the uncertainties \nin log $g$, $\\xi$ and $\\zeta$.\n\nSystematic errors may be present as well. They may come from unidentified\nlines, which could make a contribution that is not included in our synthetic \nspectrum because of the lack\nof atomic and molecular parameters. They may also come from errors in the\ngf--values determination, or failure of the model atmospheres to correctly model\nthe stars we observe, because model atmospheres use solar abundance ratios, \nor NLTE effects. \n\n\\subsection{NLTE effects}\n\nThe iron abundance could be affected by departures from LTE. The main NLTE \neffect in late-type stars is caused by overionization of electron donor \nmetals by ultraviolet radiation \\citep{aum75}. \nUsing the Saha equation, we found that in our typical star 93 \\% of iron\nis neutral. Thus overionization should be smaller in our stars than in\nwarmer giants, where only a few percent of iron is neutral.\n\nIt is known from empirical studies that abundances derived from low excitation\nlines give systematically lower abundances ($\\sim$0.3 dex) than the ones \nderived from high excitation and ionized lines in late-type stars; high \nexcitation and ionized lines give very similar abundance results\n\\citep{rul80,ste85,tak91,tom83}. \nRecently, \\citet{the99} studied NLTE effects in Fe abundances in\nmetal-poor late-type stars. They found that ionized lines are not significantly\naffected by NLTE, and that NLTE corrections become less important as [Fe/H]\nincreases, being minimal for solar abundance stars.\nMostly high excitation lines are used in our analysis, so the NLTE effects that\nmight be present should be minimal.\n\n\\citet{tom83} found that NLTE \neffects cancel out when a differential analysis is carried out relative to a \nvery similar star in terms of effective temperature and luminosity.\nNearby stars of similar effective temperature and luminosity as\nthe GC stars (see Figure 2) have been analyzed similarly in this paper, \nproviding a differential abundance comparison that should \nremove any NLTE effects that might be present. \n\n\\section{Results}\n\nEach iron abundance value for a particular Fe I line and star was derived from \na comparison between the synthetic spectrum\ngenerated by MOOG and the observed spectrum. The [Fe/H] results for each line\nfor cool, luminous stars in the solar neighborhood and GC stars are listed in \nTable 5 and 6, respectively. The uncertainties per line are estimated from the\nability to distinguish models with different [Fe/H] considering the S/N of\nthe observed spectrum. \nFor cool, luminous stars in the solar neighborhood, the uncertainty per line \nis estimated to be $\\pm$0.05 dex, \nsince the S/N is very homogeneous among all lines and stars. For\nGC stars, the uncertainty is listed individually for each line in\nTable 6.\nFigures 1, 7 and 8 show the synthetic and observed spectra\nfor each line for \\aori, cool, luminous stars in the solar neighborhood, and GC\nstars, respectively.\n\nThe final [Fe/H] results for each star are listed in Table 9. These values\nare the mean [Fe/H] weighted by the individual uncertainties in [Fe/H] for\neach Fe I line, as listed in Tables 5 and 6.\nThe final uncertainty in Table 9 is the total uncertainty from Table 7 and 8.\n\nThe analyses of our paper and \\citet{car00} have five stars in common: IRS 7, \n\\aori, HR 6146 (30 Her), HR 6702, and HR 8383 (VV Cep).\nThere is agreement in the Fe abundances within 0.1 dex for four stars \n(IRS 7, \\aori, HR 6146, and HR 8383).\nOur Fe abundance for HR 6702 is 0.18 dex lower than that of \\citet{car00}.\nThe abundance technique used in both studies is very similar, \nbut \\citet{car00} included a different set of Fe I lines and slightly \ndifferent stellar parameters. \n\nIRS 7 is known to be a variable supergiant \\citep{blu96a}. \nThere is one Fe line common to the analysis of \\citet{car00} and of this\npaper, which was observed at different epochs by \\citet{car00} and by us.\nFor this line, our result is consistent within\nthe uncertainties with the results of \\citet{car00}. \nAnother spectrum of IRS 7, taken with NIRSPEC at the Keck Telescope one\nyear after our observationes was kindly made available to us \n(Figer, private communication). We have one Fe line in common with the\nNISPEC spectrum, and again the iron abundance\nresults from both data sets are also consistent within the uncertainties.\nWe conclude that the effect of variability on our IRS 7 results are negligible\nconsidering our uncertainties.\n\n\\subsection{Galactic Center Mean [Fe/H]}\n\nAn unweighted mean value of [Fe/H] = +0.09 is obtained for the GC stars. \nA mean weighted by the total uncertainties in [Fe/H] (Table 9) gives a value \nof [Fe/H] = +0.12 for the GC stars. The estimated dispersion or $\\sigma$ \nis 0.22 dex, which is not significantly different from the typical total \nuncertainty in [Fe/H] for each GC star of 0.28 dex.\nEven if the total uncertainties are overestimated by $\\sim$0.05 dex by the \nquadratic addition of the individual uncertainties,\nthe typical uncertainty per star does not get small enough to resolve\nthe [Fe/H] distribution (see Sec. 3.3).\nThis means that the dispersion of the GC [Fe/H]\ndistribution can be understood by the uncertainties present in the data.\n\nNote that the supergiant VR 5-7, at $R$ = 30 pc, has [Fe/H] = +0.09 $\\pm$ 0.22, \nwhich is similar to the supergiants at $R <$ 0.5 pc, which have a mean \n[Fe/H] = +0.21 $\\pm$ 0.15.\n\nAn unweighted mean of [Fe/H] = --0.05 and a mean weighted by the total \nuncertainties of [Fe/H] = +0.03 was obtained for the eleven \ncool, luminous stars in the solar neighborhood. \nThe estimated dispersion or $\\sigma$ is 0.16 dex, which again is not\nsignificantly different from the typical total uncertainty in [Fe/H] \nwhich is 0.20 dex for these stars.\n\nThe obtained mean [Fe/H] for the GC is close to solar, and furthermore, \nvery similar to the cool, luminous stars in the solar neighborhood that \nwere analyzed in the same way.\n\n\\section{Discussion}\n\nOur mean [Fe/H] for the GC stars, +0.12 $\\pm$ 0.22, is similar to that of \nsupergiants in the Galactic disk.\nFigure 9a compares the GC [Fe/H] distribution with the [Fe/H] distribution\nof 40 F, G, K, and M supergiants within 2 kpc of the Sun \\citep{luc89}.\nThe mean [Fe/H] of the solar neighborhood supergiant stars from \\citep{luc89}\nis +0.13 with a dispersion of 0.20 dex.\nThe width and mean of the two distributions agree closely.\nIn Figure 9b, we compare the GC [Fe/H] distribution with that of the 11\ncool supergiants and luminous giants we have analyzed in this paper.\nAgain, the mean and width of the [Fe/H] distribution for the GC stars and\nsolar neighborhood stars are consistent.\nUnlike the \\citet{luc89} sample of supergiants, our 11 nearby stars \nare restricted to the same range in stellar parameter space as the GC\nsample; in addition, we have used the same analysis method, Fe I lines,\nand stellar models for all the stars.\nIt is important to emphasize that this differential analysis makes the\nabundance comparison between our samples of GC and nearby stars robust\nagainst possible systematic errors that might effect the absolute values\nof [Fe/H].\nHence, we can conclude that the Fe abundances for the sample of GC stars\nin this paper are nearly identical to those of similar \\teff ~and luminosity\nstars in the solar neighborhood, with no evidence for a super-solar \nmetallicity.\n\nOur mean [Fe/H] for the GC stars of +0.12 $\\pm$ 0.22 appears to be in conflict\nwith the iron abundance of the Pistol star, at $R =$ 30 pc in the Quintuplet\ncluster. \\citet{naj99} derive [Fe/H] $\\sim$ 0.5 for the Pistol star.\nThey qualify their result as preliminary, since details of the\natmosphere modeling, such as the effects of charge exchange reactions,\nhave to be studied and included in future work.\nThe Pistol star abundance is derived from emission lines in the winds from\nthis hot star, so the atmospheric modeling techniques are fundamentally\ndifferent from those more established techniques we have used to study\nabundances from photospheric absorption lines in cool giant or supergiant stars.\n\n\\citet{ser96} have proposed that the central cluster was built up by \ncontinuous, perhaps episodic, star formation over the lifetime of the \nGalaxy. In this case, the central 100 pc would form a stellar population\ndistinct from the old population of the Bulge.\nIn Figure 9c, the GC [Fe/H] distribution is compared with the [Fe/H]\ndistribution for 262 stars in Baade's Window (BW) in the bulge\n\\citep[$l,b=1^{\\circ}, -4^{\\circ}$; ][]{sad96}.\n\\citet{sad96} have a typical uncertainty per star of $\\pm$0.2 dex, so their\nfinding that [Fe/H] ranges from --1.0 to +0.5 in BW shows the\nabundance spread of BW's distribution is well-resolved by\ntheir technique.\nThe distribution of [Fe/H] in the GC, however, has a similar width as the\nuncertainties in [Fe/H], 0.28 dex per star. \nStars as metal-rich or as metal-poor as observed in the Bulge are not found\nin our sample of GC stars. However, our GC stars are restricted to a \nyoung to intermediate age population, and hence an old stellar population,\nif it exists in the central 100 pc, is not sampled by the work of this \npaper.\nA larger abundance spread could be represented in such an older population,\nbut a spectroscopic abundance analysis will require the sensitivity to\nreach K and M giants. A more complete comparison must also include\nmeasurements of the abundance patterns in the central regions relative\nto the Bulge. For example, the Bulge K giants analyzed by \\citet{mcw94}\nshow a distinct enhancement in the $\\alpha-$elements, compared to Fe.\n\nAn IMF weighted toward more massive stars in the GC has been proposed by\n\\citet{mor96}. \nRecently, \\citet{fig99} have found an IMF slanted towards massive stars for\nthe Arches and Quintuplet clusters, both located within 30 pc of the GC.\nA history of chemical evolution dominated by massive stars is expected to\nresult in enhancements of oxygen and $\\alpha-$elements, such as Mg, Si, Ca, \nand Ti, relative to Fe \\citep{whe89}.\nThe next step of our GC project is to measure abundances of $\\alpha-$elements \nand study selective enrichment in the GC. \n\nChemical evolution models try to explain abundance patterns by \nconsidering the relative star formation rate, the gas infall and outflow rates,\nthe star formation history and the abundance of the gas compared to the stars \n\\citep[see ][]{aud76,ran91}. \nMost chemical evolution models that reproduce the radial gradients in galaxies\nare valid only for distances greater than 2 kpc from the Galactic Center \n\\citep{tin78,sam97,chi99,por99}. \nNow that the molecular gas in the GC (from which stars form) has been \nextensively studied \\citep{sta91,bli93,mor96}, and that the abundances of \nstars in the GC has been obtained \nfor the first time, we strongly urge theoreticians to put all these data \ntogether into a detailed chemical evolution model describing the central \nparsecs of our Galaxy.\n\n\\section{Conclusions.}\n\nWe present the first measurement of stellar [Fe/H] for ten stars in the \nGalactic Center (GC), at distances from the GC of $R <$ 30 pc. \nNine GC stars are located in the central cluster ($R <$ 0.5 pc) and one \nstar is located in the Quintuplet cluster ($R$ = 30 pc). \nThe abundance analysis is based on high-resolution \n($\\lambda / \\Delta \\lambda =$ 40,000) $K-$band spectra.\nThe mean [Fe/H] of the GC is determined to be near solar, [Fe/H] = +0.12 \n$\\pm$ 0.22, and also similar to the mean [Fe/H] for cool, luminous stars \nin the solar neighborhood, [Fe/H] = +0.03 $\\pm$ 0.16, observed and analyzed \nin the same way. \nThe width of the GC [Fe/H] distribution, which ranges from [Fe/H] = --0.3\nto +0.5, is found to be significantly narrower than the width of the [Fe/H]\ndistribution of Baade's Window, which ranges from [Fe/H] = --1.0 to +0.8.\nThe GC [Fe/H] distribution is consistent with the [Fe/H] distribution of \nsupergiant stars in the solar neighborhood.\nThis suggest that the most luminous stars in the GC are unlikely to be \ndominated by bulge-like stars, and that the evolutionary path of the GC, \nwhile unique, is closer to the disk's than to the bulge's.\nThe Quintuplet star at $R$ = 30 pc has a similar [Fe/H] to stars located in \nthe central cluster at $R <$ 0.5 pc.\nIn the future, abundance measurements of CNO and $\\alpha-$elements are planned\nto provide a complete view of the abundance patterns of the stars in the \ncentral regions of the Milky Way.\n\n%% thanks\n\\acknowledgments\nSupport for this work was generously provided by the National Science Foundation\nthrough NSF grant AST-9619230 to K.S. and R.D.B. S.V.R. also gratefully\nacknowledges support from a Gemini Fellowship (grant \\# GF-1003-97 from the \nAssociation of Universities for Research in Astronomy, Inc., under NSF \ncooperative agreement AST-8947990 and from Fundaci\\'on Andes under project \nC-12984), from an Ohio State Presidential Fellowship, and from an Ohio\nState Alumni Research Award.\nS.C.B. acknowledges support from NSF grants AST-9618335 and AST-9819870, and\nJ.S.C. from the Office of Naval Research.\nS.V.R. would like to thank E. Luck, R. Kraft, B. Plez, A. Pradhan, R. Pogge, \nA. Gould, A. Sills, and C. Sneden for useful suggestions and enlightening \ncomments. We thank D. Figer for his generosity in sharing his spectrum of\nIRS 7 in advance of publication. Electronic versions of our spectra are\navailable upon request to S.V.R.\n\\vspace{5mm}\n\\noindent\n\n%% tables\n\n\\clearpage\n\n\\begin{deluxetable}{llcccccc}\n\\tablewidth{0pt}\n\\tablecolumns{7}\n\\tablecaption{Stellar Parameters for Nearby Late Type Stars.\\label{tab01}}\n\\tablehead{\\colhead{Star} & \\colhead{Spectral} & \\colhead{S/N\\tablenotemark{a}}&\n\\colhead{\\teff\\tablenotemark{a}} & \\colhead{\\mbol\\tablenotemark{a}} & \n\\colhead{log $g$ \\tablenotemark{a}} & \\colhead{$\\xi$ \\tablenotemark{a}} & \n\\colhead{$\\zeta$ \\tablenotemark{a}} \\\\\n\\colhead{} & \\colhead{Type} & \\colhead{} &\n\\colhead{(K)} & \\colhead{} &\n\\colhead{} & \\colhead{(\\kms)} & \\colhead{(\\kms)} } \n\\startdata\nHR 6146 &M6 III\\tablenotemark{1} &45\\tablenotemark{2} \n&3250$\\pm$100\\tablenotemark{1}&\n-5.5\\tablenotemark{1} & 0.2$\\pm$0.3\\tablenotemark{1}&\n2.0$\\pm$0.5\\tablenotemark{2}& 9.6$\\pm$1.1\\tablenotemark{2}\\\\\nHR 6702 &M5 II-III\\tablenotemark{1} &36\\tablenotemark{2}\n&3300$\\pm$100\\tablenotemark{1}&\n-3.4\\tablenotemark{1} & 0.7$\\pm$0.3\\tablenotemark{1}&\n2.0$\\pm$0.5\\tablenotemark{2}& 7.8$\\pm$1.8\\tablenotemark{2}\\\\\nHR 7442 &M5 IIIas\\tablenotemark{3} &36\\tablenotemark{2}\n&3450$\\pm$100\\tablenotemark{3}&\n-4.0\\tablenotemark{3} & 0.5$\\pm$0.3\\tablenotemark{3}&\n2.4$\\pm$0.2\\tablenotemark{2}&10.5$\\pm$2.7\\tablenotemark{2}\\\\\nHR 8062 &M4 IIIas\\tablenotemark{3} &34\\tablenotemark{2}\n&3450$\\pm$100\\tablenotemark{3}&\n-3.5\\tablenotemark{3} & 0.7$\\pm$0.3\\tablenotemark{3}&\n1.7$\\pm$0.2\\tablenotemark{2}& 8.9$\\pm$0.5\\tablenotemark{2}\\\\\n\\aori &M1-2 Iab-a\\tablenotemark{4}&305\\tablenotemark{5}\n&3540$\\pm$260\\tablenotemark{4}&\n-7.4\\tablenotemark{6} & 0.0$\\pm$0.3\\tablenotemark{6}&\n2.8$\\pm$0.2\\tablenotemark{2}&14.7$\\pm$0.5\\tablenotemark{2}\\\\\nHR 8383 &M2 Iape+\\tablenotemark{7} &100\\tablenotemark{2}\n&3480$\\pm$250\\tablenotemark{4}&\n-6.8\\tablenotemark{7,8}& 0.0$\\pm$0.3\\tablenotemark{7}&\n2.7$\\pm$0.2\\tablenotemark{2}&14.4$\\pm$2.1\\tablenotemark{2}\\\\\nHD 202380&M3 Ib\\tablenotemark{7} &46\\tablenotemark{2}\n&3600$\\pm$200\\tablenotemark{7}&\n-5.7\\tablenotemark{7,8}& 0.6$\\pm$0.5\\tablenotemark{7}&\n2.5$\\pm$0.2\\tablenotemark{2}&16.2$\\pm$0.5\\tablenotemark{2}\\\\\nHD 163428&K5 II\\tablenotemark{7} &67\\tablenotemark{2}\n&3800$\\pm$200\\tablenotemark{7}&\n-5.5\\tablenotemark{7,8}& 0.6$\\pm$0.5\\tablenotemark{7}&\n2.3$\\pm$0.2\\tablenotemark{2}&11.5$\\pm$3.2\\tablenotemark{2}\\\\\nBD+59 594&M1 Ib\\tablenotemark{9} &49\\tablenotemark{2}\n&4000$\\pm$200\\tablenotemark{9}&\n-6.6\\tablenotemark{8} &-0.9$\\pm$0.3\\tablenotemark{9}&\n3.1$\\pm$0.2\\tablenotemark{2}&18.2$\\pm$1.0\\tablenotemark{2}\\\\\nHD 232766&M1 Iab\\tablenotemark{9} &38\\tablenotemark{2}\n&4000$\\pm$200\\tablenotemark{9}&\n-6.6\\tablenotemark{8} & 0.2$\\pm$0.3\\tablenotemark{9}&\n2.2$\\pm$0.2\\tablenotemark{2}&11.5$\\pm$3.7\\tablenotemark{2}\\\\\nHR 8726 &K5 Iab\\tablenotemark{10} &57\\tablenotemark{2}\n&4000$\\pm$200\\tablenotemark{10}&\n-5.2\\tablenotemark{10,8}& 0.5$\\pm$0.3\\tablenotemark{10}&\n2.4$\\pm$0.2\\tablenotemark{2}&11.4$\\pm$0.5\\tablenotemark{2} \n\\enddata\n\\tablenotetext{a}{S/N = mean signal to noise ratio per pixel ; \n\\teff~= effective temperature; \n\\mbol ~= bolometric magnitude; $g$ = surface gravity; \n$\\xi$ = microturbulent velocity; $\\zeta$ = macroturbulent velocity.}\n\\tablerefs{ (1) \\citet{smi85}; (2) this paper; (3) \\citet{smi86};\n(4) \\citet{car00}; (5) \\citet{wal96}; (6) \\citet{lam84}; \n(7) \\citet{luc82b}; (8) \\cite{lan91};\n(9) \\citet{luc89}; (10) \\citet{luc82a}.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{ccc}\n\\tablewidth{0pt}\n\\tablecaption{Fe Line Data.\\label{tab02}}\n\\tablehead{\\colhead{Wavelength (\\AA)} & \\colhead{$\\chi$ (eV) \\tablenotemark{a}} \n& \\colhead{log gf \\tablenotemark{a}}}\n\\startdata\n21781.82 & 3.415 & --4.485 \\\\\n22381.27 & 5.844 & --1.458 \\\\\n22386.90 & 5.033 & --0.481 \\\\\n22391.22 & 5.320 & --1.600 \\\\\n22398.98 & 5.099 & --1.249 \\\\\n22818.82 & 5.792 & --1.296 \\\\\n22838.60 & 5.099 & --1.325 \\\\\n22852.17 & 5.828 & --0.612\n\\enddata\n\\tablenotetext{a}{$\\chi$ = Excitation Potential; gf = gf--value determined in \nthis paper.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccccc}\n\\tablewidth{0pt}\n\\tablecolumns{7}\n\\tablecaption{Stellar Parameters for Galactic Center Stars.\\label{tab03}}\n\\tablehead{ \\colhead{Star} & \\colhead{Luminosity} & \n\\colhead{S/N\\tablenotemark{a}} &\n\\colhead{\\teff\\tablenotemark{a}} & \\colhead{\\mbol\\tablenotemark{a,b}} & \n\\colhead{$M$\\tablenotemark{a}} & \\colhead{log $g$ \\tablenotemark{a}} & \n\\colhead{$\\xi$ \\tablenotemark{a}} & \\colhead{$\\zeta$ \\tablenotemark{a}} \\\\\n\\colhead{} & \\colhead{Class} & \\colhead{} & \\colhead{(K)} & \\colhead{} \n& \\colhead{(${\\rm M_{\\odot}}$)} & \\colhead{} & \\colhead{(\\kms)} & \n\\colhead{(\\kms)} }\n\\startdata\nIRS 7\\tablenotemark{c}& I &52&3470$\\pm$250&--9.0&17$\\pm$3 &--0.6$\\pm$0.2&\n3.3$\\pm$0.4& 20.6$\\pm$2.7 \\\\\nVR 5-7 & I &30&3500$\\pm$300&--7.8&14$\\pm$2 &--0.2$\\pm$0.3&\n2.9$\\pm$0.5& 12.6$\\pm$1.6 \\\\\nIRS 19 & I &75&3650$\\pm$300&--7.2&14$\\pm$2 & 0.1$\\pm$0.3&\n2.7$\\pm$0.5& 13.4$\\pm$2.0 \\\\\nIRS 22 & I &25&3550$\\pm$300&--6.4&10$\\pm$2 & 0.3$\\pm$0.3&\n2.5$\\pm$0.5& 12.8$\\pm$1.6 \\\\\nBSD 124 & I &10&3600$\\pm$300&--5.5& 7$\\pm$3 & 0.4$\\pm$0.3&\n2.4$\\pm$0.5& 12.7$\\pm$2.7 \\\\\nBSD 129 & I &13&3650$\\pm$300&--5.3& 7$\\pm$3 & 0.5$\\pm$0.3&\n2.4$\\pm$0.5& 12.3$\\pm$2.7 \\\\\nBSD 72 & I &13&3750$\\pm$300&--4.5& 5$\\pm$2 & 0.8$\\pm$0.3&\n2.1$\\pm$0.5& 11.0$\\pm$2.7 \\\\\nBSD 114 &III&15&3100$\\pm$280&--5.8& 3$\\pm$1 &--0.2$\\pm$0.5&\n2.9$\\pm$0.6& 9.0$\\pm$3.0 \\\\\nIRS 11 &III&16&3100$\\pm$280&--5.3& 3$\\pm$1 & 0.0$\\pm$0.5&\n2.8$\\pm$0.6& 9.1$\\pm$2.2 \\\\\nBSD 140 &III&13&3100$\\pm$280&--4.8&2.5$\\pm$1&--0.1$\\pm$0.5&\n2.9$\\pm$0.6& 9.0$\\pm$3.0\n\\enddata\n\\tablenotetext{a}{S/N = mean signal to noise ratio per pixel; \n\\teff~= effective temperature; \n\\mbol ~= bolometric magnitude; $M$ = mass; $g$ = surface gravity; \n$\\xi$ = microturbulent velocity; $\\zeta$ = macroturbulent velocity.}\n\\tablenotetext{b}{Error in \\mbol ~is $\\pm$0.4 \\citep{car00}, \ndominated by the uncertainty in the extinction curve \n($ E(H-K) / A_{K}$ ).} \n\\tablenotetext{c}{Stellar parameters from \\citet{car00}.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lccccccc}\n\\tablewidth{0pt}\n\\tablecaption{Fe I Equivalent Widths for Nearby Late-Type Stars.\\label{tab04}}\n\\tablehead{\\colhead{} & \\multicolumn{7}{c}{Wavelength of Fe I lines (\\AA)} \\\\\n\\colhead{} & \\colhead{22381.3} & \\colhead{22386.9} & \\colhead{22391.2} & \n\\colhead{22399.0} & \\colhead{22818.8} & \\colhead{22838.6} & \\colhead{22852.2} \\\\\n\\cline{1-8}\n\\colhead{Star} & \\multicolumn{7}{c}{Equivalent Widths of Each Fe I line (m\\AA)}}\n\\startdata\nHR 6146 & 90$\\pm$ 6 & 355$\\pm$ 8 & 162$\\pm$ 7 &\n210$\\pm$ 7 & 130$\\pm$ 6 & 277$\\pm$ 7 & 211$\\pm$ 7 \\\\\nHR 6702 & 67$\\pm$ 5 & 332$\\pm$ 9 & 136$\\pm$ 7 &\n189$\\pm$ 7 & 119$\\pm$ 6 & 234$\\pm$ 7 & 220$\\pm$ 7 \\\\\nHR 7442 & 60$\\pm$ 5 & 339$\\pm$ 9 & 143$\\pm$ 8 &\n174$\\pm$ 8 & 141$\\pm$ 8 & 294$\\pm$ 8 & 246$\\pm$ 8 \\\\\nHR 8062 & 65$\\pm$ 5 & 351$\\pm$ 9 & 149$\\pm$ 7 &\n199$\\pm$ 6 & 110$\\pm$ 6 & 208$\\pm$ 7 & $-$ \\\\\n\\aori & 101$\\pm$ 8 & 520$\\pm$10 & 218$\\pm$10 &\n319$\\pm$10 & 178$\\pm$10 & 339$\\pm$10 & 271$\\pm$10 \\\\\nHD 202380 & 102$\\pm$ 8 & 476$\\pm$11 & 180$\\pm$ 9 &\n311$\\pm$ 9 & 137$\\pm$ 8 & 299$\\pm$ 9 & $-$ \\\\\nHR 8383 & 86$\\pm$ 7 & 466$\\pm$10 & 183$\\pm$ 9 &\n285$\\pm$ 9 & 112$\\pm$ 8 & 261$\\pm$ 9 & 233$\\pm$ 9 \\\\\nHD 163428 & 87$\\pm$ 7 & 430$\\pm$ 9 & 172$\\pm$ 9 &\n241$\\pm$ 9 & 113$\\pm$ 8 & 263$\\pm$ 8 & $-$ \\\\\nBD+59 594 & 107$\\pm$ 9 & 522$\\pm$11 & 171$\\pm$12 &\n329$\\pm$12 & 96$\\pm$ 9 & 289$\\pm$13 & 226$\\pm$12 \\\\\nHD 232766 & 66$\\pm$ 6 & 410$\\pm$ 8 & 159$\\pm$ 9 &\n228$\\pm$ 9 & 97$\\pm$ 8 & 216$\\pm$ 9 & 173$\\pm$ 9 \\\\\nHR 8726 & 71$\\pm$ 6 & 397$\\pm$ 8 & 158$\\pm$ 8 &\n234$\\pm$ 8 & 115$\\pm$ 8 & 239$\\pm$ 8 & 186$\\pm$ 8\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccccc}\n\\tablewidth{0pt}\n\\tablecaption{[Fe/H] for Nearby Late Type Stars. \\label{tab05}}\n\\tablehead{\\colhead{} & \\multicolumn{8}{c}{Wavelength of Fe I lines (\\AA)} \\\\\n\\colhead{} & \\colhead{21781.8} & \\colhead{22381.3} &\n\\colhead{22386.9} & \\colhead{22391.2} & \\colhead{22399.0} &\n\\colhead{22818.8} & \\colhead{22838.6} & \\colhead{22852.2} \\\\\n\\cline{1-9}\n\\colhead{Star} & \\multicolumn{8}{c}{[Fe/H] \\tablenotemark{a} \\ Determined from\nEach Fe I Line}}\n\\startdata\nHR 6146 & --0.05& +0.05& --0.20& 0.00& --0.30& +0.15& +0.25& +0.10 \\\\\nHR 6702 & --0.05& --0.05& --0.25& --0.05& --0.30& +0.20& +0.10& +0.30 \\\\\nHR 7442 & +0.10& +0.10& --0.25& +0.10& --0.60& +0.20& +0.20& +0.20 \\\\\nHR 8062 & +0.10& --0.10& --0.05& +0.05& --0.20& +0.10& --0.05& $-$ \\\\\n\\aori & +0.15& 0.00& +0.05& +0.05& --0.10& +0.20& +0.10& 0.00 \\\\\nHD 202380& +0.10& +0.10& +0.10& 0.00& +0.10& +0.10& +0.10& $-$ \\\\\nHR 8383 & --0.05& --0.10& --0.10& --0.10& --0.20& --0.15& --0.25& --0.10 \\\\\nHD 163428& +0.07& 0.00& 0.00& --0.02& --0.25& --0.05& --0.05& $-$ \\\\\nBD+59 594& --0.10& 0.00& --0.25& --0.25& --0.25& --0.30& --0.35& --0.35 \\\\\nHD 232766& --0.10& --0.20& --0.15& --0.15& --0.40& --0.20& --0.40& --0.40 \\\\\nHR 8726 & +0.15& --0.10& 0.00& --0.05& --0.20& 0.00& --0.10& --0.20 \\\\\n\\enddata\n\\tablenotetext{a}{Error in [Fe/H] for each line is $\\pm$ 0.05 dex.}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccccc}\n\\tablewidth{0pt}\n\\tablecaption{[Fe/H] for Galactic Center Stars.\\label{tab06}}\n\\tablehead{\\colhead{} & \\multicolumn{8}{c}{Wavelength of Fe I lines (\\AA)} \\\\\n\\colhead{} & \\colhead{21781.8} & \\colhead{22381.3} &\n\\colhead{22386.9} & \\colhead{22391.2} & \\colhead{22399.0} &\n\\colhead{22818.8} & \\colhead{22838.6} & \\colhead{22852.2} \\\\\n\\cline{1-9}\n\\colhead{Star} & \\multicolumn{8}{c}{[Fe/H] Determined from Each Fe I Line}}\n\\startdata\nIRS 7 & +0.35& +0.22&--0.15&--0.10& -- & +0.38&--0.30& -- \\\\\n &$\\pm$0.05&$\\pm$0.07&$\\pm$0.10&$\\pm$0.05& &$\\pm$0.05&$\\pm$0.05& \\\\\nVR 5-7 & +0.12& +0.20&--0.30& +0.15&--0.40& +0.10& +0.15& -- \\\\\n &$\\pm$0.03&$\\pm$0.07&$\\pm$0.10&$\\pm$0.05&$\\pm$0.10&$\\pm$0.05&$\\pm$0.07& \\\\\nIRS 19 & +0.30& +0.40&--0.30& +0.40&--0.05& +0.45&--0.05& -- \\\\\n &$\\pm$0.05&$\\pm$0.05&$\\pm$0.10&$\\pm$0.07&$\\pm$0.10&$\\pm$0.05&$\\pm$0.10& \\\\\nIRS 22 & +0.30&--0.05&--0.40& +0.15&--0.40& +0.20& +0.35& +0.30\\\\\n&$\\pm$0.05&$\\pm$0.05&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10\\\\\nBSD 124 & -- & +0.22& +0.20& +0.20&--0.10& +0.20& +0.20& -- \\\\\n & &$\\pm$0.07&$\\pm$0.10&$\\pm$0.20&$\\pm$0.10&$\\pm$0.05&$\\pm$0.10& \\\\\nBSD 129 & -- & +0.50& +0.50& +0.70& +0.20& +0.60& +0.60& -- \\\\\n & &$\\pm$0.20&$\\pm$0.10&$\\pm$0.20&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10& \\\\\nBSD 72 & -- & +0.10& +0.40& +0.35& +0.05& +0.35&--0.20& -- \\\\\n & &$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10& \\\\\nBSD 114 & -- &--0.20&--0.85&--0.10&--0.70&~~0.00&--0.30& -- \\\\\n & &$\\pm$0.10&$\\pm$0.20&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10& \\\\\nIRS 11 &--0.15& +0.25&--0.80&--0.20&--0.80&--0.15&--0.50& -- \\\\\n &$\\pm$0.05&$\\pm$0.05&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10&$\\pm$0.10& \\\\\nBSD 140 & -- &~~0.00&--0.40& +0.10&--0.40&~~0.00&~~0.00& -- \\\\ \n & &$\\pm$0.20&$\\pm$0.20&$\\pm$0.20&$\\pm$0.20&$\\pm$0.10&$\\pm$0.10& \n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccc}\n\\tablewidth{0pt}\n\\tablecolumns{7}\n\\tablecaption{Uncertainties in [Fe/H] for Solar Neighborhood Stars.\n\\label{tab07}}\n\\tablehead{\\colhead{Star} & \\colhead{$\\pm$ \\teff \\tablenotemark{a}} &\n\\colhead{$\\pm$log $g$ \\tablenotemark{a}} &\n\\colhead{$\\pm \\xi$ \\tablenotemark{a}} &\n\\colhead{$\\pm \\zeta$ \\tablenotemark{a}} &\n\\colhead{Std.\\tablenotemark{b}} & \n\\colhead{Total\\tablenotemark{c}} }\n\\startdata\nHR 6146 &$\\mp$0.03 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.08 &$\\pm$0.07 &$\\pm$0.19\\\\\nHR 6702 &$\\mp$0.03 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.13 &$\\pm$0.08 &$\\pm$0.22\\\\\nHR 7442 &$\\mp$0.03 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.19 &$\\pm$0.11 &$\\pm$0.25\\\\\nHR 8062 &$\\mp$0.03 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.04 &$\\pm$0.04 &$\\pm$0.13\\\\\n\\aori &$\\mp$0.07 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.04 &$\\pm$0.03 &$\\pm$0.14\\\\\nHD 202380 &$\\mp$0.05 &$\\pm$0.17 &$\\mp$0.04 &$\\pm$0.04 &$\\pm$0.02 &$\\pm$0.19\\\\\nHR 8383 &$\\mp$0.07 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.15 &$\\pm$0.03 &$\\pm$0.20\\\\\nHD 163428 &$\\mp$0.05 &$\\pm$0.17 &$\\mp$0.04 &$\\pm$0.22 &$\\pm$0.04 &$\\pm$0.29\\\\\nBD+59 594 &$\\mp$0.05 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.07 &$\\pm$0.05 &$\\pm$0.15\\\\\nHD 232766 &$\\mp$0.05 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.26 &$\\pm$0.05 &$\\pm$0.29\\\\\nHR 8726 &$\\mp$0.05 &$\\pm$0.10 &$\\mp$0.04 &$\\pm$0.04 &$\\pm$0.04 &$\\pm$0.13\\\\\n\\enddata\n\\tablenotetext{a}{\\teff~= effective temperature; $g$ = surface gravity;\n$\\xi$ = microturbulent velocity; $\\zeta$ = macroturbulent velocity.}\n\\tablenotetext{b}{standard error, determined from scatter among [Fe/H] values \nmeasured for different Fe I lines.}\n\\tablenotetext{c}{total uncertainty, derived from quadratic sum of \nuncertainties due to the standard error and the uncertainties from the \nstellar parameters (\\teff, log $g$, $\\xi$, $\\zeta$).}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccc}\n\\tablewidth{0pt}\n\\tablecolumns{7}\n\\tablecaption{Uncertainties in [Fe/H] for Galactic Center Stars.\n\\label{tab08}}\n\\tablehead{\\colhead{Star} & \\colhead{$\\pm$ \\teff \\tablenotemark{a}} &\n\\colhead{$\\pm$log $g$ \\tablenotemark{a}} &\n\\colhead{$\\pm \\xi$ \\tablenotemark{a}} &\n\\colhead{$\\pm \\zeta$ \\tablenotemark{a}} &\n\\colhead{Std.\\tablenotemark{b}} &\n\\colhead{Total\\tablenotemark{c}} }\n\\startdata\nIRS 7 &$\\mp$0.07 &$\\pm$0.07 &$\\mp$0.09 &$\\pm$0.19 &$\\pm$0.13 &$\\pm$0.27\\\\\nVR 5-7 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.11 &$\\pm$0.11 &$\\pm$0.23\\\\\nIRS 19 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.14 &$\\pm$0.13 &$\\pm$0.26\\\\\nIRS 22 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.11 &$\\pm$0.12 &$\\pm$0.24\\\\\nBSD 124 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.19 &$\\pm$0.06 &$\\pm$0.26\\\\\nBSD 129 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.19 &$\\pm$0.08 &$\\pm$0.27\\\\\nBSD 72 &$\\mp$0.08 &$\\pm$0.10 &$\\mp$0.11 &$\\pm$0.19 &$\\pm$0.10 &$\\pm$0.27\\\\\nBSD 114 &$\\mp$0.08 &$\\pm$0.17 &$\\mp$0.13 &$\\pm$0.21 &$\\pm$0.16 &$\\pm$0.35\\\\\nIRS 11 &$\\mp$0.08 &$\\pm$0.17 &$\\mp$0.13 &$\\pm$0.15 &$\\pm$0.18 &$\\pm$0.33\\\\\nBSD 140 &$\\mp$0.08 &$\\pm$0.17 &$\\mp$0.13 &$\\pm$0.21 &$\\pm$0.10 &$\\pm$0.32\n\\enddata\n\\tablenotetext{a}{\\teff~= effective temperature; $g$ = surface gravity;\n$\\xi$ = microturbulent velocity; $\\zeta$ = macroturbulent velocity.}\n\\tablenotetext{b}{standard error, determined from scatter among [Fe/H] values\nmeasured for different Fe I lines.}\n\\tablenotetext{c}{total uncertainty, derived from quadratic sum of\nuncertainties due to the standard error and the uncertainties from the\nstellar parameters (\\teff, log $g$, $\\xi$, $\\zeta$).}\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lccclcc}\n\\tablewidth{0pt}\n\\tablecolumns{5}\n\\tablecaption{Mean [Fe/H] for each star.\\label{tab09}}\n\\tablehead{\\multicolumn{3}{c}{Solar Neighborhood Stars} & \\colhead{} &\n\\multicolumn{3}{c}{Galactic Center Stars} \\\\\n\\cline{1-3} \\cline{5-7} \n\\colhead{Star} & \\colhead{N$_{\\rm lines}$} & \\colhead{[Fe/H]\\tablenotemark{a}} \n& \\colhead{} &\n\\colhead{Star} & \\colhead{N$_{\\rm lines}$} & \\colhead{[Fe/H]\\tablenotemark{a}} }\n\\startdata\nHR 6146 & 8 &--0.01$\\pm$0.19 & & IRS 7 & 6 & +0.09$\\pm$0.27 \\\\\nHR 6702 & 8 &--0.02$\\pm$0.22 & & VR 5-7\\tablenotemark{b}&7& +0.09$\\pm$0.23 \\\\\nHR 7442 & 8 & +0.01$\\pm$0.25 & & IRS 19 & 7 & +0.29$\\pm$0.26 \\\\\nHR 8062 & 7 &--0.03$\\pm$0.13 & & IRS 22 & 8 & +0.09$\\pm$0.24 \\\\\n\\aori & 8 & +0.05$\\pm$0.14 & & BSD 124 & 6 & +0.17$\\pm$0.26 \\\\\nHD 202380 & 7 & +0.07$\\pm$0.19 & & BSD 129 & 6 & +0.49$\\pm$0.27 \\\\\nHR 8383 & 8 &--0.14$\\pm$0.20 & & BSD 72 & 6 & +0.17$\\pm$0.27 \\\\\nHD 163428 & 7 &--0.05$\\pm$0.29 & & BSD 114 & 6 & --0.29$\\pm$0.35 \\\\\nBD+59 594 & 8 &--0.24$\\pm$0.15 & & IRS 11 & 7 & --0.16$\\pm$0.33 \\\\\nHD 232766 & 8 &--0.26$\\pm$0.29 & & BSD 140 & 6 & --0.06$\\pm$0.32 \\\\\nHR 8726 & 8 &--0.07$\\pm$0.13 & & & & \\\\\n\\enddata\n\\tablenotetext{a}{Error in [Fe/H] is the total uncertainty from Table 7 and 8.}\n\\tablenotetext{b}{M supergiant star in the Quintuplet cluster ($R$ = 30 pc).}\n\\end{deluxetable}\n\n\\clearpage\n\n% bibliography\n\n\\begin{thebibliography}{}\n\n\\bibitem[Afflerbach et al.(1997)]{aff97} Afflerbach, A., Churchwell, E.,\n\\& Werner, M. 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R., 1998, \\apj, 116, 981\n\n\\bibitem[Edmonds(1969)]{edm69} Edmonds, F. N., 1969, JQSRT, 9, 1427\n\n\\bibitem[Elias et al.(1985)]{eli85} Elias, J. H., Frogel, J. A., \\& Humphreys,\nR. M., 1985, \\apjs, 57, 91\n\n\\bibitem[Fern\\'{a}ndez-Villaca\\~{n}as et al.(1990)]{fer90} \nFern\\'{a}ndez-Villaca\\~{n}as, J. L., Rego, M., \\& Cornide, M., 1990, \\aj,\n99, 1961\n\n\\bibitem[Fich \\& Silkey(1991)]{fic91} Fich, M. \\& Silkey, M., 1991, \\apj, 366,\n107\n\n\\bibitem[Figer et al.(1999)]{fig99} Figer, D. F., Kim, S. S., Morris, M., \nSerabyn, E., Rich, R. M., \\& McLean, I. S., 1999, \\apj, in press\n\n\\bibitem[Gray \\& Martin(1979)]{gra79} Gray, D. F. \\& Martin, B. E., 1979,\n\\apj, 231, 139\n\n\\bibitem[Gray(1992)]{gra92} Gray, D. F., 1992, The Observation and Analysis of \nStellar Photospheres, 2nd ed. (Cambridge: Cambridge University Press), p. 405\n\n\\bibitem[Gummersbach et al.(1998)]{gum98} Gummersbach, C. A., Kaufer, A., \nSch\\\"afer, D. R., Szeifert, T., \\& Wolf, B., 1998, \\aap, 338, 881\n\n\\bibitem[G\\\"usten(1989)]{gus89} G\\\"usten, R. 1989, in The center of the Galaxy, \nIAU Symp. 136, ed. M. Morris, p. 89\n\n\\bibitem[Holweger et al.(1991)]{hol91} Holweger, H., Bard, A., Kock, A., \\& \nKock, M., 1991, \\aap, 249, 545\n\n\\bibitem[Jenkins \\& Binney(1994)]{jen94} Jenkins, A. \\& Binney, J., 1994,\n\\mnras, 270, 703\n\n\\bibitem[Kleinmann \\& Hall(1986)]{kle86} Kleinmann, S. G. \\& Hall, D.\nN. B. 1986, \\apjs, 62, 501\n\n\\bibitem[Kurucz(1993)]{kur93} Kurucz, R. L., 1993, Kurucz CD-ROM No. 13, \n``ATLAS9 Stellar Atmosphere Programs and the 2 km/s Grid'', (Cambridge: \nSmithsonian Astrophysical Observatory)\n\n\\bibitem[Lambert et al.(1984)]{lam84} Lambert, D. L., Brown, J. A., Hinkle,\nK. H., \\& Johnson, H. R., 1984, \\apj, 284, 223\n\n\\bibitem[Lang(1991)]{lan91} Lang, K. R., 1991, Astrophysical Data: Planets\nand Stars, (New York: Springer-Verlag), p. 142\n\n\\bibitem[Livingstone \\& Wallace(1991)]{liv91} Livingstone, W. \\& Wallace, L.,\n1991, An Atlas of the Solar Spectrum in the Infrared from 1850 to 9000 \n${\\rm cm^{-1}}$ (1.1 to 5.4 $\\mu$m), N.S.O. Technical Report \\#91-001,\n(Tucson: National Solar Observatory)\n\n\\bibitem[Luck(1982a)]{luc82a} Luck, R. E., 1982a, \\apj, 256, 177\n\n\\bibitem[Luck(1982b)]{luc82b} Luck, R. E., 1982b, \\apj, 263, 215\n\n\\bibitem[Luck \\& Bond(1989)]{luc89} Luck, R. E. \\& Bond, H. E., 1989, \\apjs,\n71, 559\n\n\\bibitem[Maciel \\& K\\\"oppen(1994)]{mac94} Maciel, W. J. \\& K\\\"oppen, J., 1994,\n\\aap, 282, 436\n\n\\bibitem[Marigo et al.(1996)]{mar96} Marigo, P., Bressan, A., \\& Chiosi, C., \n1996, \\aap, 313, 545\n\n\\bibitem[McWilliam(1990)]{mcw90} McWilliam, A., 1990, \\apjs, 74, 1075\n\n\\bibitem[McWilliam \\& Rich(1994)]{mcw94} McWilliam, A. \\& Rich, R. M., 1994,\n\\apjs, 91, 749\n\n\\bibitem[Moneti et al.(1994)]{mon94}Moneti, A., Glass, I. S., \\& Moorwood, \nA. F. M. 1994, \\mnras, 268, 194\n\n\\bibitem[Morris \\& Serabyn(1996)]{mor96} Morris, M. \\& Serabyn, E. 1996, \\araa,\n34, 645\n\n\\bibitem[Najarro et al.(1999)]{naj99} Najarro, F., Hillier, D. J., Figer, D. F.,\n\\& Geballe, T. R., 1999, in The Central Parsecs of the Galaxy, ASP Conf. \nSer. 186, p 340 \n\n\\bibitem[Nave et al.(1994)]{nav94} Nave, G., Johansson, S., Learner, R. C. M., \nThrone, A. P., \\& Brault, J. W., 1994, \\apjs, 94, 221\n\n\\bibitem[Pagel \\& Edmunds(1981)]{pag81} Pagel, B. E. J. \\& Edmunds, M. G. 1981,\n\\araa, 19, 77\n\n\\bibitem[Peterson et al.(1993)]{pet93} Peterson, R. C., Dalle Ore, C. M., \\&\nKurucz, R. L., 1993, \\apj, 404, 333\n \n\\bibitem[Plez(1992)]{ple92a} Plez, B., 1992, \\aaps, 94, 527\n\n\\bibitem[Plez et al.(1992)]{ple92b} Plez, B., Brett, J. M., \\& \nNordlund, A., 1992, \\aap, 256, 551\n\n\\bibitem[Portinari \\& Chiosi(1999)]{por99} Portinari, L. \\& Chiosi, C., 1999,\n\\aap, in press\n\n\\bibitem[Ram\\'{\\i}rez et al.(1999)]{ram99} Ram\\'{\\i}rez, S. V., Blum, R. D.,\nSellgren, K., 1999, in preparation\n\n\\bibitem[Rana(1991)]{ran91} Rana, N. C. 1991, \\araa, 29, 129\n\n\\bibitem[Reid(1993)]{rei93} Reid, M. J., 1993, \\araa, 31, 345\n\n\\bibitem[Richichi et al.(1998)]{ric98} Richichi, A., Ragland, S., Stecklum, B.,\n\\& Leinert, Ch., 1998, \\aap, 338, 527\n\n\\bibitem[Rudolph et al.(1997)]{rud97} Rudolph, A. L., Simpson, J. P., Haas, \nM. R., Erickson, E. F., \\& Fich, M., 1997, \\apj, 489, 94\n\n\\bibitem[Ruland et al.(1980)]{rul80} Ruland, F., Holweger, H., Griffin, R., \\& \nBiehl, D., 1980, \\aap, 92, 70\n\n\\bibitem[Sadler et al.(1996)]{sad96} Sadler, E. M., Rich, R. M., \\& Terndrup,\nD. M., 1996, \\aj, 112, 171\n\n\\bibitem[Samland et al.(1997)]{sam97} Samland, M., Hensler, G., \\& Theis, Ch.,\n1997, \\apj, 476, 544\n\n\\bibitem[Schaller et al.(1992)]{sch92} Schaller, G., Schaerer, D., Meynet, G., \n\\& Maeder, A., 1992, \\aaps, 96, 269\n\n\\bibitem[Schaerer et al.(1993)]{sch93} Schaerer, D., Charbonnel, C., Meynet, G.,\nMaeder, A., \\& Schaller, G., 1993, \\aaps, 102, 339\n\n\\bibitem[Serabyn \\& Morris(1996)]{ser96} Serabyn, E. \\& Morris, M. 1996, \n\\nat, 382, 602\n\n\\bibitem[Shaver et al.(1983)]{sha83} Shaver, P. A., McGee, R. X., Newton, L. M.,\nDanks, A. C., \\& Pottasch, S. R., 1983, \\mnras, 204, 53\n\n\\bibitem[Shields(1990)]{shi90} Shields, G. A., 1990, \\araa, 28, 525\n\n\\bibitem[Simpson et al.(1995)]{sim95} Simpson, J. P., Colgan, S. W. J., \nRubin, R. H., Erickson, E. F., \\& Haas, M. R., 1995, \\apj, 444, 721\n\n\\bibitem[Smartt \\& Rolleston(1997)]{sma97} Smartt, S. J. \\& Rolleston, W. R. J.,\n1997, \\apj, 481, L47\n\n\\bibitem[Smith \\& Lambert(1985)]{smi85} Smith, V. V. \\& Lambert, D. L., 1985,\n\\apj, 294, 326\n\n\\bibitem[Smith \\& Lambert(1986)]{smi86} Smith, V. V. \\& Lambert, D. L., 1986,\n\\apj, 311, 843\n\n\\bibitem[Smith \\& Lambert(1990)]{smi90} Smith, V. V. \\& Lambert, D. L., 1990,\n\\apjs, 72, 387\n\n\\bibitem[Sneden(1973)]{sne73} Sneden, C., 1973, Ph.D. thesis, Univ. of Texas\n\n\\bibitem[Stark et al.(1991)]{sta91} Stark, A. A., Bally, J., Gerhard, O. E., \n\\& Binney, J. 1991, \\mnras, 248, 14p\n\n\\bibitem[Steenbock(1985)]{ste85} Steenbock, W., 1985, in Cool Stars with Excess\nof Heavy Elements, eds. M. Jaschek \\& P. C. Keenan, (Dordrecht: Reidel), p 231\n\n\\bibitem[Takeda(1991)]{tak91} Takeda, Y., 1991, \\aap, 242, 455\n\n\\bibitem[Th\\'{e}venin \\& Idiart(1999)]{the99} Th\\'evenin, F. \\& Idiart, T. P.,\n1999, \\apj, 521, 753\n\n\\bibitem[Tinsley \\& Larson(1978)]{tin78} Tinsley, B. M. \\& Larson, R. B., 1978,\n\\apj, 221, 554\n\n\\bibitem[Tokunaga et al.(1990)]{tok90} Tokunaga, A. T., Toomey, D. W.,\nCarr, J. S., Hall, D. N. B., \\& Epps, H. W., 1990, SPIE, 1235, 131\n\n\\bibitem[Tomkin \\& Lambert(1983)]{tom83} Tomkin, J. \\& Lambert, D. L., 1983,\n\\apj, 273, 722\n\n\\bibitem[V\\'{\\i}lchez \\& Esteban(1996)]{vil96} V\\'{\\i}lchez, J. M. \\& Esteban,\nC., 1996, \\mnras, 280, 720\n\n\\bibitem[Wallace \\& Hinkle(1996)]{wal96} Wallace, L. \\& Hinkle, K. 1996,\n\\apjs, 107, 312\n\n\\bibitem[Wheeler et al.(1989)]{whe89} Wheeler, J. C., Sneden, C., \\& Truran, \nJ. W. 1989, \\araa, 27, 279\n\n\\end{thebibliography}\n\n% figcaptions\n\n\\clearpage\n\n\\figcaption[]{Observed spectrum ($filled~squares$) of \\aori ~from \\citet{wal96}\ncompared with synthetic spectra generated by MOOG, using CNO abundances from \n\\citet{lam84}, model atmosphere from \\citet{ple92a}, and stellar parameters \nlisted in Table 1.\nThe error bars come from the difference of observations taken in two epochs. \nWe overplot a synthetic spectrum ($thick~line$) derived using the Fe abundances\nlisted in Table 5 and synthetic spectra ($thin~lines$) computed with Fe \nabundances different by $\\pm$0.20 dex , which corresponds to the typical \nuncertainty in [Fe/H] for a solar neighborhood cool, luminous star.\nFe lines and their wavelengths in \\AA ~are marked ($bold~vertical~lines$) at \nthe top of each panel. \nCN, Sc, and unidentified lines ($question~marks$) are also marked \n($vertical~lines$). \nTickmarks along the x-axis are 1 \\AA ~apart.\nThe [Fe/H] value from Table 5 for each line is given in each panel.\n\\label{fig1}}\n\n\\figcaption[]{CO index vs effective temperature, \\teff, for supergiant and \ngiant stars. \nUpper panel: the calibration for supergiant stars, with\n\\teff ~from \\citet{dyc98} ($filled~squares$) and \\citet{ric98} ($open~circles$),\nboth measured from lunar occultations.\nLower panel: the calibration for giant stars.\nValues of \\teff ~from \\citet{mcw90} ($open~triangles$), \n\\citet{smi85,smi86,smi90} ($filled~circles$), and \\citet{fer90} ($open~stars$)\nare derived from a relationship between $V-K$ and \\teff ~measured by lunar \noccultation techniques.\n\\teff ~from \\citet{dyc98} ($open~circles$), are derived from lunar \noccultation measurements.\nIn both panels the uncertainties come from the literature.\nThe best unweighted linear fit to the data ($solid~lines$) is used to \ncompute the \\teff ~of the galactic center stars.\n\\label{fig2}}\n\n\\figcaption[]{HR diagram of galactic center (GC) stars ($filled~circles$) and \ncool, luminous stars in the solar neighborhood\n($open~squares$). Stellar parameters and their uncertainties are given in \nTables 1 and 3.\nSolar metallicity evolutionary tracks \\citep{sch92} are overplotted to \ndetermine masses for GC stars. \nThe GC stars and the cool, luminous stars in the solar neighborhood occupy \nthe same place in the HR diagram, hence are very similar types of stars.\n\\label{fig3}}\n\n\\figcaption[]{Relation between microturbulent velocity ($\\xi$) and surface\ngravity (log $g$). Values of $\\xi$ and log $g$ are from Table 1 of this paper\n($open~squares$), \\citet{car00} ($crosses$), and \\citet{smi85,smi86,smi90} \n($filled~triangles$).\nThe best unweighted linear fit to the data ($solid~line$) is used to compute \n$\\xi$ for the GC stars. \n\\label{fig4}}\n\n\\figcaption[]{Left panels: $\\chi^{2}$ contour maps for determining \nthe nitrogen abundance, log $\\epsilon$ (N), and macroturbulent \nvelocity ($\\zeta$) for HR 8726. \nThe minimum $\\chi^{2}$ gives the best set of log $\\epsilon$ (N) and $\\zeta$\nfor each set of CN lines (21798 \\AA ~-- 21804 \\AA ~at the top, and \n22403 \\AA ~-- 22409 \\AA ~at the bottom). \nRight panels: observed spectrum of HR 8726 ($filled~squares$) with\nerror bars from the difference of observations taken at two positions along the\nslit and the synthetic spectrum of HR 8726 ($solid~line$)\nusing the derived log $\\epsilon$ (N) and $\\zeta$ for each CN band\n(21798 \\AA ~-- 21804 \\AA ~at the top, and 22403 \\AA ~-- 22409 \\AA ~at \nthe bottom).\nThe synthetic spectrum is calculated by MOOG, using stellar parameters in\nTable 1 and a model atmosphere from \\citet{ple92a}.\nThe value of log $\\epsilon$ (N) derived by this technique is not a true \nnitrogen abundance, because a combination of C and N abundances are needed\nto derive a true value of log $\\epsilon$ (N) from CN lines.\n\\label{fig5}}\n\n\\figcaption[]{Relation between macroturbulent velocity ($\\zeta$) and surface\ngravity (log $g$) for supergiant stars ($filled~circles$). \nAll supergiant stars from Table 1 and IRS 7, VR 5-7, IRS 19, and IRS 22 from \nTable 3 are plotted. \nThe best unweighted linear fit to the data ($solid~line$) is used to compute \n$\\zeta$ for the GC supergiant stars BSD 72, BSD 124, and BSD 129.\n\\label{fig6}}\n\n\\figcaption[]{Observed ($filled~squares$) and synthetic spectra ($solid~line$)\nfor cool, luminous stars in the solar neighborhood.\nThe synthetic spectrum computed by MOOG, using the stellar\nparameters listed in Table 1 and model atmospheres from \\cite{ple92a}.\nThe error bars come from the difference of observations taken at two positions \nalong the slit.\nFe lines and their wavelengths in \\AA ~are marked ($bold~vertical~lines$) at\nthe top panels.\nCN, Sc, and unidentified lines ($question~marks$) are also marked\n($vertical~lines$).\nTickmarks along the x-axis are 1 \\AA ~apart.\nThe [Fe/H] value from Table 5 for each line is given in each panel.\n\\label{fig7}}\n\n\\figcaption[]{Similar to Fig. 7, except these are observed and synthetic \nspectra for galactic center stars, using stellar parameters given in Table 3. \nSymbols are the same as Fig. 7.\nThe [Fe/H] value from Table 6 for each line is given in each panel.\n\\label{fig8}}\n\n\\figcaption[]{\n(a) Fractional distribution of [Fe/H] for 10 GC stars (\n$solid~line$) compared to [Fe/H] for 40 solar neighborhood supergiant stars\n($dashed~line$) from \\citet{luc89}. \n(b) Fractional distribution of [Fe/H] for\n10 GC stars ($solid~line$) compared to [Fe/H] for 11 solar neighborhood stars\nobserved and analyzed in this paper ($dashed~line$).\n(c) Fractional distribution of [Fe/H] for 10 GC stars ($solid$ \n$line$) compared to [Fe/H] for 262 Baade's window stars ($dashed$ $line$) \nfrom \\citet{sad96}.\n\\label{fig9}}\n\n% figures\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig01.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig02.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig03.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig04.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig05.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig06.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig07a.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig07b.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig08a.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig08b.eps}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize \\hsize\n\\epsfbox{fig09.eps}\n\\end{figure}\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002062.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Afflerbach et al.(1997)]{aff97} Afflerbach, A., Churchwell, E.,\n\\& Werner, M. W., 1997, \\apj, 478, 190\n\n\\bibitem[Audouze \\& Tinsley(1976)]{aud76} Audouze, J. \\& Tinsley, B. M. 1976, \n\\araa, 14, 43\n\n\\bibitem[Auman \\& Woodrow(1975)]{aum75} Auman, J. R. \\& Woodrow, J. E. J., \n1975, \\apj, 197, 163\n\n\\bibitem[Baldwin et al.(1973)]{bal73} Baldwin, J. R., Frogel, J. A., \\&\nPersson, S. E., 1973, \\apj, 184, 427\n\n\\bibitem[Blitz et al.(1993)]{bli93} Blitz, L., Binney, J., Lo, K. Y., \nBally, J., \\& Ho, P. T. P. 1993, \\nat, 361, 417\n\n\\bibitem[Blum et al.(1996a)]{blu96a} Blum, R. D., Sellgren, K.,\nDePoy, D. D., 1996a, \\apj, 470, 864\n\n\\bibitem[Blum et al.(1996b)]{blu96b} Blum, R. D., Sellgren, K.,\nDePoy, D. D., 1996b, \\aj, 112, 1988 \n\n\\bibitem[Carr et al.(2000)]{car00} Carr, J. S., Sellgren, K., \nBalachandran, S. C., 2000, \\apj in press\n\n\\bibitem[Chiappini et al.(1999)]{chi99} Chiappini, C., Matteucci, F., \\& \nPadoan, P., 1999, \\apj, in press\n\n\\bibitem[Dyck et al.(1998)]{dyc98} Dyck, H. M., van Belle, G. T., \\& Thompson,\nR. R., 1998, \\apj, 116, 981\n\n\\bibitem[Edmonds(1969)]{edm69} Edmonds, F. N., 1969, JQSRT, 9, 1427\n\n\\bibitem[Elias et al.(1985)]{eli85} Elias, J. H., Frogel, J. A., \\& Humphreys,\nR. M., 1985, \\apjs, 57, 91\n\n\\bibitem[Fern\\'{a}ndez-Villaca\\~{n}as et al.(1990)]{fer90} \nFern\\'{a}ndez-Villaca\\~{n}as, J. L., Rego, M., \\& Cornide, M., 1990, \\aj,\n99, 1961\n\n\\bibitem[Fich \\& Silkey(1991)]{fic91} Fich, M. \\& Silkey, M., 1991, \\apj, 366,\n107\n\n\\bibitem[Figer et al.(1999)]{fig99} Figer, D. F., Kim, S. S., Morris, M., \nSerabyn, E., Rich, R. M., \\& McLean, I. S., 1999, \\apj, in press\n\n\\bibitem[Gray \\& Martin(1979)]{gra79} Gray, D. F. \\& Martin, B. E., 1979,\n\\apj, 231, 139\n\n\\bibitem[Gray(1992)]{gra92} Gray, D. F., 1992, The Observation and Analysis of \nStellar Photospheres, 2nd ed. (Cambridge: Cambridge University Press), p. 405\n\n\\bibitem[Gummersbach et al.(1998)]{gum98} Gummersbach, C. A., Kaufer, A., \nSch\\\"afer, D. R., Szeifert, T., \\& Wolf, B., 1998, \\aap, 338, 881\n\n\\bibitem[G\\\"usten(1989)]{gus89} G\\\"usten, R. 1989, in The center of the Galaxy, \nIAU Symp. 136, ed. M. Morris, p. 89\n\n\\bibitem[Holweger et al.(1991)]{hol91} Holweger, H., Bard, A., Kock, A., \\& \nKock, M., 1991, \\aap, 249, 545\n\n\\bibitem[Jenkins \\& Binney(1994)]{jen94} Jenkins, A. \\& Binney, J., 1994,\n\\mnras, 270, 703\n\n\\bibitem[Kleinmann \\& Hall(1986)]{kle86} Kleinmann, S. G. \\& Hall, D.\nN. B. 1986, \\apjs, 62, 501\n\n\\bibitem[Kurucz(1993)]{kur93} Kurucz, R. L., 1993, Kurucz CD-ROM No. 13, \n``ATLAS9 Stellar Atmosphere Programs and the 2 km/s Grid'', (Cambridge: \nSmithsonian Astrophysical Observatory)\n\n\\bibitem[Lambert et al.(1984)]{lam84} Lambert, D. L., Brown, J. A., Hinkle,\nK. H., \\& Johnson, H. R., 1984, \\apj, 284, 223\n\n\\bibitem[Lang(1991)]{lan91} Lang, K. R., 1991, Astrophysical Data: Planets\nand Stars, (New York: Springer-Verlag), p. 142\n\n\\bibitem[Livingstone \\& Wallace(1991)]{liv91} Livingstone, W. \\& Wallace, L.,\n1991, An Atlas of the Solar Spectrum in the Infrared from 1850 to 9000 \n${\\rm cm^{-1}}$ (1.1 to 5.4 $\\mu$m), N.S.O. Technical Report \\#91-001,\n(Tucson: National Solar Observatory)\n\n\\bibitem[Luck(1982a)]{luc82a} Luck, R. E., 1982a, \\apj, 256, 177\n\n\\bibitem[Luck(1982b)]{luc82b} Luck, R. E., 1982b, \\apj, 263, 215\n\n\\bibitem[Luck \\& Bond(1989)]{luc89} Luck, R. E. \\& Bond, H. E., 1989, \\apjs,\n71, 559\n\n\\bibitem[Maciel \\& K\\\"oppen(1994)]{mac94} Maciel, W. J. \\& K\\\"oppen, J., 1994,\n\\aap, 282, 436\n\n\\bibitem[Marigo et al.(1996)]{mar96} Marigo, P., Bressan, A., \\& Chiosi, C., \n1996, \\aap, 313, 545\n\n\\bibitem[McWilliam(1990)]{mcw90} McWilliam, A., 1990, \\apjs, 74, 1075\n\n\\bibitem[McWilliam \\& Rich(1994)]{mcw94} McWilliam, A. \\& Rich, R. M., 1994,\n\\apjs, 91, 749\n\n\\bibitem[Moneti et al.(1994)]{mon94}Moneti, A., Glass, I. S., \\& Moorwood, \nA. F. M. 1994, \\mnras, 268, 194\n\n\\bibitem[Morris \\& Serabyn(1996)]{mor96} Morris, M. \\& Serabyn, E. 1996, \\araa,\n34, 645\n\n\\bibitem[Najarro et al.(1999)]{naj99} Najarro, F., Hillier, D. J., Figer, D. F.,\n\\& Geballe, T. R., 1999, in The Central Parsecs of the Galaxy, ASP Conf. \nSer. 186, p 340 \n\n\\bibitem[Nave et al.(1994)]{nav94} Nave, G., Johansson, S., Learner, R. C. M., \nThrone, A. P., \\& Brault, J. W., 1994, \\apjs, 94, 221\n\n\\bibitem[Pagel \\& Edmunds(1981)]{pag81} Pagel, B. E. J. \\& Edmunds, M. G. 1981,\n\\araa, 19, 77\n\n\\bibitem[Peterson et al.(1993)]{pet93} Peterson, R. C., Dalle Ore, C. M., \\&\nKurucz, R. L., 1993, \\apj, 404, 333\n \n\\bibitem[Plez(1992)]{ple92a} Plez, B., 1992, \\aaps, 94, 527\n\n\\bibitem[Plez et al.(1992)]{ple92b} Plez, B., Brett, J. M., \\& \nNordlund, A., 1992, \\aap, 256, 551\n\n\\bibitem[Portinari \\& Chiosi(1999)]{por99} Portinari, L. \\& Chiosi, C., 1999,\n\\aap, in press\n\n\\bibitem[Ram\\'{\\i}rez et al.(1999)]{ram99} Ram\\'{\\i}rez, S. V., Blum, R. D.,\nSellgren, K., 1999, in preparation\n\n\\bibitem[Rana(1991)]{ran91} Rana, N. C. 1991, \\araa, 29, 129\n\n\\bibitem[Reid(1993)]{rei93} Reid, M. J., 1993, \\araa, 31, 345\n\n\\bibitem[Richichi et al.(1998)]{ric98} Richichi, A., Ragland, S., Stecklum, B.,\n\\& Leinert, Ch., 1998, \\aap, 338, 527\n\n\\bibitem[Rudolph et al.(1997)]{rud97} Rudolph, A. L., Simpson, J. P., Haas, \nM. R., Erickson, E. F., \\& Fich, M., 1997, \\apj, 489, 94\n\n\\bibitem[Ruland et al.(1980)]{rul80} Ruland, F., Holweger, H., Griffin, R., \\& \nBiehl, D., 1980, \\aap, 92, 70\n\n\\bibitem[Sadler et al.(1996)]{sad96} Sadler, E. M., Rich, R. M., \\& Terndrup,\nD. M., 1996, \\aj, 112, 171\n\n\\bibitem[Samland et al.(1997)]{sam97} Samland, M., Hensler, G., \\& Theis, Ch.,\n1997, \\apj, 476, 544\n\n\\bibitem[Schaller et al.(1992)]{sch92} Schaller, G., Schaerer, D., Meynet, G., \n\\& Maeder, A., 1992, \\aaps, 96, 269\n\n\\bibitem[Schaerer et al.(1993)]{sch93} Schaerer, D., Charbonnel, C., Meynet, G.,\nMaeder, A., \\& Schaller, G., 1993, \\aaps, 102, 339\n\n\\bibitem[Serabyn \\& Morris(1996)]{ser96} Serabyn, E. \\& Morris, M. 1996, \n\\nat, 382, 602\n\n\\bibitem[Shaver et al.(1983)]{sha83} Shaver, P. A., McGee, R. X., Newton, L. M.,\nDanks, A. C., \\& Pottasch, S. R., 1983, \\mnras, 204, 53\n\n\\bibitem[Shields(1990)]{shi90} Shields, G. A., 1990, \\araa, 28, 525\n\n\\bibitem[Simpson et al.(1995)]{sim95} Simpson, J. P., Colgan, S. W. J., \nRubin, R. H., Erickson, E. F., \\& Haas, M. R., 1995, \\apj, 444, 721\n\n\\bibitem[Smartt \\& Rolleston(1997)]{sma97} Smartt, S. J. \\& Rolleston, W. R. J.,\n1997, \\apj, 481, L47\n\n\\bibitem[Smith \\& Lambert(1985)]{smi85} Smith, V. V. \\& Lambert, D. L., 1985,\n\\apj, 294, 326\n\n\\bibitem[Smith \\& Lambert(1986)]{smi86} Smith, V. V. \\& Lambert, D. L., 1986,\n\\apj, 311, 843\n\n\\bibitem[Smith \\& Lambert(1990)]{smi90} Smith, V. V. \\& Lambert, D. L., 1990,\n\\apjs, 72, 387\n\n\\bibitem[Sneden(1973)]{sne73} Sneden, C., 1973, Ph.D. thesis, Univ. of Texas\n\n\\bibitem[Stark et al.(1991)]{sta91} Stark, A. A., Bally, J., Gerhard, O. E., \n\\& Binney, J. 1991, \\mnras, 248, 14p\n\n\\bibitem[Steenbock(1985)]{ste85} Steenbock, W., 1985, in Cool Stars with Excess\nof Heavy Elements, eds. M. Jaschek \\& P. C. Keenan, (Dordrecht: Reidel), p 231\n\n\\bibitem[Takeda(1991)]{tak91} Takeda, Y., 1991, \\aap, 242, 455\n\n\\bibitem[Th\\'{e}venin \\& Idiart(1999)]{the99} Th\\'evenin, F. \\& Idiart, T. P.,\n1999, \\apj, 521, 753\n\n\\bibitem[Tinsley \\& Larson(1978)]{tin78} Tinsley, B. M. \\& Larson, R. B., 1978,\n\\apj, 221, 554\n\n\\bibitem[Tokunaga et al.(1990)]{tok90} Tokunaga, A. T., Toomey, D. W.,\nCarr, J. S., Hall, D. N. B., \\& Epps, H. W., 1990, SPIE, 1235, 131\n\n\\bibitem[Tomkin \\& Lambert(1983)]{tom83} Tomkin, J. \\& Lambert, D. L., 1983,\n\\apj, 273, 722\n\n\\bibitem[V\\'{\\i}lchez \\& Esteban(1996)]{vil96} V\\'{\\i}lchez, J. M. \\& Esteban,\nC., 1996, \\mnras, 280, 720\n\n\\bibitem[Wallace \\& Hinkle(1996)]{wal96} Wallace, L. \\& Hinkle, K. 1996,\n\\apjs, 107, 312\n\n\\bibitem[Wheeler et al.(1989)]{whe89} Wheeler, J. C., Sneden, C., \\& Truran, \nJ. W. 1989, \\araa, 27, 279\n\n\\end{thebibliography}"
}
] |
astro-ph0002063
|
STRUCTURE OF THE CIRCUMNUCLEAR REGION OF SEYFERT 2 GALAXIES REVEALED BY RXTE HARD X--RAY OBSERVATIONS OF NGC 4945
|
[
{
"author": "G. Madejski$^{1,2}$"
},
{
"author": "P. \\.{Z}ycki$^{3}$"
},
{
"author": "C. Done$^{4}$"
},
{
"author": "A. Valinia$^{1,2}$"
},
{
"author": "P. Blanco$^{5}$"
},
{
"author": "R. Rothschild$^{5}$"
},
{
"author": "B. Turek$^{1,6}$"
}
] |
NGC~4945 is one of the brightest Seyfert galaxies on the sky at 100 keV, but is completely absorbed below 10 keV, implying an optical depth of the absorber to electron scattering of a few; its absorption column is probably the largest which still allows a direct view of the nucleus at hard X--ray energies. Our observations of it with the Rossi X--ray Timing Explorer (RXTE) satellite confirm the large absorption, which for a simple phenomenological fit using an absorber with Solar abundances implies a column of $4.5^{+0.4}_{-0.4} \times 10^{24}$ cm$^{-2}$. Using a a more realistic scenario (requiring Monte Carlo modeling of the scattering), we infer the optical depth to Thomson scattering of $\sim 2.4$. If such a scattering medium were to subtend a large solid angle from the nucleus, it should smear out any intrinsic hard X--ray variability on time scales shorter than the light travel time through it. The rapid (with a time scale of $\sim$ a day) hard X--ray variability of NGC~4945 we observed with the RXTE implies that the bulk of the extreme absorption in this object does {\sl not} originate in a parsec-size, geometrically thick molecular torus. Limits on the amount of scattered flux require that the optically thick material on parsec scales must be rather geometrically thin, subtending a half-angle $< 10^\circ$. This is only marginally consistent with the recent determinations of the obscuring column in hard X--rays, where only a quarter of Seyfert~2s have columns which are optically thick, and presents a problem in accounting for the Cosmic X--ray Background primarily with AGN possessing the geometry as that inferred by us. The small solid angle of the obscuring material, together with the black hole mass (of $\sim 1.4 \times 10^6$ $M_{\odot}$) from megamaser measurements, allows a robust determination of the source luminosity, which in turn implies that the source radiates at $\sim 10$\% of the Eddington limit.
|
[
{
"name": "4945_apJ_lanl.tex",
"string": "\\documentstyle[11pt,aaspp4]{article}\n\n\\newcommand {\\ie} {{\\it i.e.}}\n\\newcommand {\\cf} {{\\it cf.}}\n\n\\newcommand {\\eg} {{\\it e.g.}}\n\\newcommand {\\ea} {{\\it et~al.}}\n\n\\newcommand {\\be} {\\begin{equation}}\n\\newcommand {\\ee} {\\end{equation}}\n\n\\def\\refitem{\\par\\parskip 0pt\\noindent\\hangindent 20pt}\n\\input psfig.sty\n\n\\begin{document}\n\n\\title{STRUCTURE OF THE CIRCUMNUCLEAR REGION OF SEYFERT 2 \nGALAXIES REVEALED BY RXTE HARD X--RAY OBSERVATIONS OF NGC 4945}\n\n\\author{\nG. Madejski$^{1,2}$, P. \\.{Z}ycki$^{3}$, C. Done$^{4}$, \nA. Valinia$^{1,2}$, P. Blanco$^{5}$, R. Rothschild$^{5}$, B. Turek$^{1,6}$}\n\n\\affil{\n$^1$ Laboratory for High Energy Astrophysics, NASA/GSFC, Greenbelt, MD\n20771, USA\\\\\n$^2$ Dept. of Astronomy, University of Maryland, College Park \\\\\n$^3$ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716\nWarsaw, Poland \\\\\n$^4$ University of Durham, Physics Dept., Durham, DH1 3LE, UK \\\\\n$^5$ Center for Astrophysics and Space Sciences, Univ. of \nCalifornia / San Diego, LaJolla, CA\\\\\n$^6$Dept. of Physics, Stanford University, Palo Alto, CA}\n\n\\vskip 0.4 cm\n\n\\centerline {\\sl Submitted to the Astrophysical Journal (Letters)} \n\n\\begin{abstract}\n\nNGC~4945 is one of the brightest Seyfert galaxies on the sky at 100\nkeV, but is completely absorbed below 10 keV, implying an optical \ndepth of the absorber to electron scattering of a few; its absorption \ncolumn is probably the largest which still allows a direct view of the \nnucleus at hard X--ray energies. Our observations of it with the Rossi \nX--ray Timing Explorer (RXTE) satellite confirm the large absorption, \nwhich for a simple phenomenological fit using an absorber with Solar \nabundances implies a column of $4.5^{+0.4}_{-0.4} \\times 10^{24}$ cm$^{-2}$.\nUsing a a more realistic scenario (requiring Monte Carlo modeling of \nthe scattering), we infer the optical depth to Thomson scattering \nof $\\sim 2.4$. If such a scattering medium were to subtend a large\nsolid angle from the nucleus, it should smear out any intrinsic \nhard X--ray variability on time scales shorter than the light travel \ntime through it. The rapid (with a time scale of $\\sim$ a day) \nhard X--ray variability of NGC~4945 we observed with the RXTE \nimplies that the bulk of the extreme absorption in this object does {\\sl\nnot} originate in a parsec-size, geometrically thick molecular\ntorus. Limits on the amount of scattered flux require that the optically\nthick material on parsec scales must be rather geometrically thin,\nsubtending a half-angle $< 10^\\circ$. This is only marginally\nconsistent with the recent determinations of the obscuring column in \nhard X--rays, where only a quarter of Seyfert~2s have columns which \nare optically thick, and presents a problem in accounting for the \nCosmic X--ray Background primarily with AGN possessing the geometry as \nthat inferred by us. The small solid angle of the obscuring material, \ntogether with the black hole mass (of $\\sim 1.4 \\times \n10^6$ $M_{\\odot}$) from megamaser measurements, allows a robust\ndetermination of the source luminosity, which in turn implies that \nthe source radiates at $\\sim 10$\\% of the Eddington limit. \n\n\\end{abstract}\n\n\\keywords{galaxies: individual (NGC 4945) -- galaxies: Seyfert\nX--rays: galaxies}\n\n\\section{Introduction}\n\nOur current best picture of nuclei of Seyfert galaxies includes \nthe central source (i.e. black hole, accretion disk and broad line region)\nembedded within an optically thick molecular torus (cf. Antonucci \\&\nMiller 1985). The object is classified as a Seyfert~1 for\nviewing directions which lie within the opening angle of the torus, \nso that there is a direct view of the nucleus, and as a Seyfert~2 for \ndirections intersecting the obscuring material. The torus absorbs the \noptical, UV and soft X--ray nuclear light, so the nucleus\nin Seyfert~2s can only be seen at these energies through scattered\nradiation. One of the central questions still under debate in the\ncontext of the Unification Models of the two types of Seyferts is:\nhow optically thick is this putative torus? \n\nNGC~4945 is a nearby (3.7 Mpc; Mauersberger et al. 1996) edge--on \ngalaxy. It has strong starburst activity, producing intense IR \nemission concentrated in a compact nuclear region (Rice et al. \n1988; Brock et al. 1988), and a ``superwind'' outflowing along \nthe minor axis of the galaxy (Heckman, Armus, \\& Miley 1990). \nIt also has an active nucleus, first seen unambiguously in Ginga \nX--ray observations (Iwasawa et al. 1993), confirming the \nSeyfert~2-type classification. These data showed a heavily obscured, \nstrong hard X--ray source above 10 keV, confirmed by the \nCGRO OSSE observations \n(Done, Madejski, \\& Smith 1996) which in turn revealed that NGC~4945 \nis one of the brightest extragalactic sources in the sky at 100 keV! \nThe absorbing column, a few $\\times$ $10^{24}$ cm$^{-2}$, is among the \nlargest which still allows a direct view of the nucleus at hard X--ray \nenergies.\nIf such a scattering medium were to subtend a large solid angle from \nthe nucleus, it would smear out any intrinsic hard X--ray variability \non timescales shorter than the light travel time through it. \n\nThe presence of the Seyfert nucleus is further supported by the fact\nthat the object is a megamaser source (detected in the H$_2$O bands) \nimplying an edge--on geometry, but one of the key features which makes \nits study so important is that it is one of only four AGN where the \nblack hole mass can be constrained (at $\\sim 1.4 \\times 10^6$ $M_{\\odot}$) from\ndetailed mapping of the megamaser spots (Greenhill, Moran, \\&\nHerrnstein 1997). As such, it is one of a few unique sources \nwhere the luminosity in Eddington units can be reliably estimated. \n\nBelow we present the data from the RXTE, confirming the large\nabsorbing column, but also revealing large amplitude hard X--ray \nvariability on a time scale of days. A distant absorber with an\nappreciable optical depth, subtending a large solid angle as seen by\nthe nucleus, would smear out the rapid variability on time scales\nshorter than the light travel time through such an absorber. Given\nour data, we conclude that the optically thick absorber cannot be \nboth distant and geometrically thick. \n\n\\section{Observations: Spectrum and Variability}\n\nNGC~4945 was observed by the Rossi X--ray Timing Explorer (RXTE)\nsatellite for about a month, starting on October 8, 1997. \nThe observations included 38 pointings of $\\sim 2000$ s each, \ntaken about once per day. \nThe Proportional Counter Array (PCA) and \nHigh Energy X--ray Timing Experiment (HEXTE) data were reduced using \nstandard procedures. For the PCA data, this included an extraction\nin the {\\tt standard2} mode using the {\\tt ftool saextrct}; the \nestimation of the background was done via {\\tt ftool pcabackest}, using\nthe background model ``L7'' (model files {\\tt \npca\\_bkgd\\_faint240\\_e03v03.mdl} and {\\tt pca\\_bkgd\\_faintl7\\_e03v03.mdl}). \nFor consistency, we use data only from 3 PCA detectors, which were \nactive during all pointings. For HEXTE, the background is collected \nsimultaneously by switching two halves of the array on- and off-source \nevery 16 seconds; both source and background files were extracted \nusing the {\\tt ftool seextrct}, and dead-time corrected using {\\tt \nftool hxtdeadpha}. The total ``good data'' intervals were: 69,280 s for\nPCA, 18,364 s and 19,060 s for HEXTE clusters A and B. \n\nThe summed background-subtracted PCA and HEXTE files were fitted with \na phenomenological model including a hard power law with low-energy \nphotoelectric cutoff (using the cross-sections and abundances as \ngiven in Morrison \\& McCammon 1983) and a high-energy exponential cutoff\n(assumed to be at an energy $E_c$ of 100 keV, in agreement with the\nhigh energy Seyfert spectra; e.g., Zdziarski et al. 1995). Our model also \nincludes a Gaussian Fe K emission line, plus a soft component, which \nwe modeled as another power law. In our fits, we used the PCA data\ncorresponding to the energy range of 3 to 30 keV, and HEXTE data for\n20 to 100 keV. The resulting fit (cf. Fig.~1) was essentially consistent\nwith the Ginga / OSSE results of Done et al. (1996). The hard power\nlaw (with $E_c$ of 100 keV) showed an \nenergy index of $0.45 \\pm 0.1$, with absorption of $4.5 \\pm 0.4 \\times \n10^{24}$ cm$^{-2}$, and an observed 10 - 50 keV flux of $1 \\times \n10^{-10}$ erg cm$^{-2}$ s$^{-1}$, with resulting $\\chi^2 = 80.6 / 75$ \nd.o.f. The Fe K line energy was at $6.38 \\pm 0.05$ keV, with an \nintrinsic width $\\sigma$ of $ 0.37 \\pm 0.13$ keV, and a flux\nof $0.9 \\times 10^{-4}$ photons cm$^{-2}$ s$^{-1}$. Allowing the\ncutoff to be unconstrained yielded the best fit of $90^{+130}_{-30}$\nkeV. Regarding the soft component, its energy power law index of \nwas $0.57 \\pm 0.15$, with the 1 keV monochromatic flux of of 0.001 \nphotons cm$^{-2}$ s$^{-1}$ keV$^{-1}$. It is important to note that \nthe PCA field of view is about 1 deg$^{2}$, so at least a fraction \nof the Fe K line and soft component flux could have arisen from the \nmore extended (non-nuclear) region, a likely possibility given the \nstarburst nature of the galaxy. Furthermore, given its modest flux, \nwhich over the 2 -- 10 keV band is $6 \\times 10^{-12}$ erg cm$^{-2}$ \ns$^{-1}$ -- only three times that of the $1 \\sigma$ fluctuations of the \nCosmic X--ray Background on the angular scale of the PCA field of view \n-- we caution that any detailed spectral analysis of the PCA data for\nthis soft component is unreliable. Nonetheless, we can clearly reject\nthe hypothesis that the entire flux of this soft component is due to\nsome kind of a ``leaky absorber,'' as it does not appear to vary. \n\nThe spectral analysis above confirmed the results of Done et al. (1996)\nthat the source spectrum consists of the soft, relatively faint, \nunabsorbed component, a bright, heavily absorbed (hard) component, and a\nstrong Fe K line. With that, we studied the variability of each\ncomponent separately. The flux of the soft continuum component \n(below 8 keV) is consistent with being constant; this is also true \nof the Fe K line. The hard component (8 -- 30 keV), on the other\nhand, is highly variable, with a factor of 4 change in 10 days, and a\nfactor of 1.7 -- 2 in 1 day between the minimum and maximum flux. \nThis is plotted in Fig.~2. This light curve (collected with 3 PCUs,\nand binned on 1 day intervals) shows RMS variance ($1 \\sigma$) of 0.82 \ncts s$^{-1}$. Unfortunately, the source was too faint to study the \nvariability with HEXTE. \n\nWe investigated if the variability could be due to instrumental\neffects, and specifically, imprecise background subtraction. To\nassess this, we also analyzed in an analogous manner the hard \n(8 -- 30 keV) light curves binned in 1 day intervals of a cluster \nof galaxies Abell 754 (cf. Valinia et al. 1999) and a faint quasar \nPG1211+143, which shows very little flux in the PCA data above 8 keV \n(Netzer, Madejski, \\& Kaspi in prep.). Analysis of 9 data points \ncollected over 9 days for A754 (from which no source variability is \nexpected) yields $\\sigma = 0.018$ cts s$^{-1}$. For PG1211+143, we \nhad 32 pointings spread nearly uniformly over 6 months. These data, \nwhere some intrinsic source variability may be present, yield \n$\\sigma = 0.13$ cts s$^{-1}$; we consider this a conservative upper \nlimit to the instrumental effects, and thus deem the rapid hard X--ray\nvariability of NGC~4945 with $\\sigma$ of 0.82 cts s$^{-1}$ highly \nsignificant. \n\nCould this variability be due to varying absorption? We examined \nthis possibility by modeling separate spectra from high and low count\nrate observations. To improve statistics, we co-added the PCA spectra from \na number of individual observations with highest and lowest count rates.\nThe two resulting spectra were then modeled using the Monte Carlo \nabsorption model discussed below. We assumed first that the intrinsic \nsource spectrum (and normalization) is the same for both, but \nthe absorption is different and, secondly, that the normalization of the\nintrinsic source has changed while the absorption stayed constant.\nThe first hypothesis yielded $\\chi^{2} = 401/110$ dof, while the second one\nyielded $\\chi^{2} = 143/110$ d.o.f. This clearly shows \nthat the variability is intrinsic to the unabsorbed nucleus. \n\n\\section{Discussion}\n\nThe variability we see in NGC~4945 is then entirely compatible with \nthat expected from the {\\sl intrinsic} source, with no significant \nscattered delay by a distant material. If this absorber has an \nappreciable Compton thickness (as is the case here), and if it \nsubtends a large solid angle to the X--ray source, then it \nshould intercept and scatter a large fraction of the flux. If it is\nalso distant from the nucleus, the light travel time effects\nwill ``wash out'' any intrinsic variability on time scales shorter\nthan the light travel time through the absorber. Conversely, \na structure with much smaller scale height subtends a much smaller \nsolid angle, making scattering less important. This also \nprecludes the observed X--rays to be purely due to Compton \nreflection, as this would require a contrived geometry of the \nreflector with respect to the primary X--ray source: the reflector \nwould have to be located very close to a completely covered central \nsource. We note that by comparison, a well studied unabsorbed Seyfert~1 \nNGC~3516 showed X--ray variability with a similar fractional \namplitude on $\\sim 10 \\times$ longer time scales (Nandra \n\\& Edelson 1999) than seen in NGC~4945. While the black hole mass \nin NGC~3516 is not as well known, it is estimated to be \n$\\sim 10^7$ $M_{\\odot}$. The fact that the ratio of variability time\nscales is roughly the same as the ratio of nuclear masses -- as\nexpected for accreting black holes -- further supports our conclusion \nthat the hard X--ray variability we see in NGC~4945 is intrinsic. \n\nWith the optical depth to electron scattering of a few, the shape of \nthe absorption cutoff would be different than expected from pure \nphotoelectric absorption, and the detailed shape of the emergent \nspectrum depends on the geometry. We model this numerically with a \nMonte Carlo code as given in Krolik, Madau, \\& \\.Zycki (1994), \nassuming a torus with square cross-section where the half-angle \nsubtended by the torus, $\\theta_0$, its optical depth to electron \nscattering $\\tau_{\\rm e}$, and the power law index of the incident \nenergy spectrum $\\alpha$ are free parameters (the Comptonization \ncutoff is set to 100 keV as above). The results of our fits (using\nthe PCA data over the range of 3 -- 20 keV, and HEXTE data as above) \nare shown in Table 1, where the 90\\% confidence regions on $\\Gamma$ \nand $\\tau_{\\rm e}$ are typically 0.1. \n\nA small scale height absorber \n($\\theta_0 \\sim 10^\\circ$) gives $\\tau_{\\rm e} = 2.4$, compared\nto a large scale height ($\\theta_0 \\sim 80^\\circ$) which gives \n$\\tau_{\\rm e} = 2.1$. \nWith an iron abundance of twice Solar, these fits change to \n$\\tau_{\\rm e} = 1.7$, and \n$\\tau_{\\rm e} = 1.5$, respectively. (Since the photoelectric \ncutoff present in our data is mainly sensitive to the column density of Fe, \nlarger-than-Solar abundance of Fe would make us overestimate \nthe true absorbing column if we assumed Solar abundances, and vice-versa.) \nWhile statistically these might marginally favor \nthe large scale height absorber, we consider that all the fits are \nprobably equally likely given that modeling the spectrum with a fixed \ncutoff energy may introduce systematic uncertainties. Our \ncalculations include the Fe K emission line produced by the torus but \nwe also include an additional Fe line (such as may be expected to \narise in the photoionized scattering medium). Those calculations \nalso imply that large ($> 4 \\times$ Solar) Fe abundances can be\nexcluded: they would imply a stronger Fe K line than is seen in our\ndata. In reality, this limit is probably more stringent, given the fact that at\nleast a fraction of the Fe K line originates in a more extended\nregion. \n\nThese Monte Carlo results also give the distribution of the number of\nscatterings which the photons undergo before reaching the observer\npositioned in the equatorial plane. \nThis is key in determining the solid angle subtended by the optically\nthick absorber, and thus its vertical size scale. Fig.~3\nshows the fraction of the observed photons that underwent 0, 1, 2, 3, \netc. scatterings before reaching the observer for eight values of\n$\\theta_0$ as discussed above (cf. Table~1), \nwith the solid and dotted lines showing the results for Solar and\ntwice Solar abundance of iron, respectively. The fraction of \nphotons which arrive without being scattered is 19\\% and 63\\% \nrespectively for a ``thick'' ($\\theta_0 = 80^\\circ$) and ``skinny'' \n($\\theta_0 = 10^\\circ$) torus. For $2 \\times$ Solar abundance of \nFe these numbers are 32\\% and 75\\%. The data in Fig.~2 imply \nthat fewer than 40\\% of the observed photons are scattered over path \nlengths longer than 1 light day, so the half-angle subtended by the \noptically thick material is less than $\\sim 10^\\circ$. \nThis implies a rather small scale height, and perhaps \nis due to the same material which produces the H$_{2}$O maser emission \n(Greenhill et al. 1997). \n\nThe details of the geometry of Seyfert~2s are important in the\nassessment of their contribution to the Cosmic X--ray background, as\nthe heavily absorbed AGN were postulated to make up the bulk of it \n(cf. Krolik et al. 1994; Madau, Ghisellini, \\& Fabian 1994; Comastri \net al. 1995). The value of $\\theta_0$ of $10^\\circ$ is marginally \nconsistent with the torus geometry inferred from recent observations \nat hard X--ray energies. These observations show that Seyfert~2s \noutnumber Seyfert~1s by a factor of 4:1, while more than a quarter \nof Seyfert~2s have a column which is optically thick (see Giommi et \nal. 1998, and Gilli, Risaliti, \\& Salvati 1999 and references therein). \nAssuming a single geometry for the Seyfert nuclei where the torus \nhas a rectangular cross-section, we can attempt to reproduce these \nratios by assuming that if the central flux barely ``grazes'' the \ntorus, we classify the object as {\\sl any} Seyfert~2, while an object \nis an optically thick Seyfert~2 only if the line of sight encounters \nthe entire radial distance in the torus. In this context, requiring \nsuch 1:4:1 ratio would then imply that the torus is somewhat flattened, \nwith outer radius of 6.5 $\\times$ its inner radius and equatorial\nheight of 1.3 $\\times$ its inner radius. In this scenario, all \nSeyfert~2s are then seen at angles smaller than $\\sim 50^\\circ$ from \nthe plane, while the optically thick Seyfert~2s are confined to angles \nof $\\le 12^\\circ$. We repeated the Monte--Carlo calculations with\nthis rectangular geometry and find that the fraction of scattered\nphotons is $\\sim$ 50\\%, still too large to match the observed hard\nX--ray variability. A further problem arises if\nthis is indeed a universal geometry for all Seyferts as the\nThomson depth of the absorber is large, $\\sim 1.7$ in the \nmore restrictive $2 \\times$ Solar case. This absorber reduces the \nunabsorbed flux $\\sim$ five-fold or more, and this is not consistent with \nthe 1:4:1 ratio, by a large margin. We thus conclude that a\npopulation of AGN with \ngeometry very nearly that of NGC~4945 cannot make up the CXB. \nInstead, significantly larger fraction of the heavily obscured AGN \nis required (implying a large solid angle subtended by the absorber) \nthan implied from the rather small $\\theta_0$ inferred by us. One\nplausible scenario would have the local optically thick Seyfert~2s \nsurrounded by absorbers that already collapsed to an accretion \ndisk, while in the more distant objects -- in the earlier stages of \nevolution -- such absorbers had larger vertical extent. \n\nAlternately, the absorption could come from a structure which is\nmuch closer to the nucleus. The variability limits impose constraints\non the amount of scattered flux that is lagged on time scales of more\nthan 1 day, and thus they do not constrain the height of any structure which \nis $<< 1$ light day from the X--ray source (corresponding to a \ndistance of $<< 10^4$ Schwarzschild radii for the mass of the black \nhole of $\\sim 10^6$ $M_{\\odot}$). While a very geometrically thick \naccretion disk cannot be ruled out from our data, there are \nconsiderable theoretical difficulties in maintaining a structure \nwith a large height scale. It is far easier to envisage a structure \nwith a small height scale such an accretion disk with outer\nregions somewhat thickened by instabilities resulting from radiation\npressure warping (cf. Maloney, Begelman, \\& Pringle 1996). \n\nWith these arguments for the Thomson-thick absorber subtending a small \nsolid angle in NGC~4945, we can now estimate the true luminosity of \nthe source. The Monte Carlo simulations show that the intrinsic \nflux must be substantially larger than that observed (by a factor \nof $e^{\\tau_{\\rm e}}$, or $\\times 11$ for Solar abundances) because \nany scattered nuclear photons are lost from the line of sight. \nThe 1-500 keV flux, corrected for photoelectric absorption alone, \nis $\\sim 5 \\times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$, so correcting for \nthe Thomson opacity yields a 1-500 keV intrinsic X--ray \nluminosity of $10^{43}$ erg~s$^{-1}$. Assuming that the thermal (opt/UV/EUV) \nemission from the accretion disk is roughly equal to the hard X--ray emission\ngives a total bolometric luminosity of the nucleus of $\\sim 2 \\times \n10^{43}$ erg~s$^{-1}$. With this, and $M_{\\rm BH}$ of $1.4 \\times\n10^6$ $M_{\\odot}$, the source is radiating at $\\sim$ 10\\% of the \nEddington luminosity; even if the abundances are twice-Solar (which \nyields $\\tau_{\\rm e}$ of 1.7), $L/L_{\\rm Edd}$ is at least $\\sim$ 5\\%. \n(We note that similar $L/L_{\\rm Edd}$ was also inferred by \nGreenhill et al. (1997), but the discovery of the rapid hard X--ray \nvariability allows us to determine the source luminosity more\naccurately, as now we know that relatively few photons are scattered \n{\\sl back} to the line of sight.) NGC~4945 is one of the few AGN where this \nquantity can be calculated robustly, since the mass of the central object is\n{\\sl known}, although we are aware that the value of its central mass is not \nas accurate as for the famous megamaser NGC~4258; the resulting \nuncertainty in the estimate of $L/L_{\\rm Edd}$ may be a factor of 2, \ncomparable to the effects of the unknown Fe abundance or the ratio of \n$L_{\\rm Tot} /L_{\\rm X-ray}$. The resulting $L/L_{\\rm Edd}$ is comparable \nto that inferred for the well studied Seyfert~2 NGC~1068, although since the\nabsorber is completely opaque even to hard X--rays, the central luminosity can\nbe estimated only indirectly. These two AGN are at the opposite end of \nthe scale to NGC~4258, which radiates at $\\sim 10^{-4}$ $L_{\\rm Edd}$ \nor less (Lasota et al.\\ 1996). The mass accretion rates inferred \nfrom those values of $L/L_{\\rm Edd}$ put strong constraints on\npossible underlying radiation mechanisms. While the recently popular \nadvective disk models can produce X--ray hot flows up to about 10\\% \nof the Eddington limit, these collapse at higher $L/L_{\\rm Edd}$: \nour data show that NGC~4945 lies perilously close to this limits. \n\n\\bigskip\n\n{\\bf ACKNOWLEDGEMENTS:} We thank the\nRXTE satellite team for scheduling the observations allowing the daily\nsampling, Tess Jaffe for her help with the RXTE data reduction via\nher indispensable script {\\tt rex}, and Dr. Julian Krolik for his\nhelpful comments on the manuscript. This project was partially supported by \nITP/NSF grant PHY94-07194, NASA grants and contracts to University of\nMaryland and USRA, and the Polish KBN grant 2P03D01816.\n\n\\begin{references}\n\n\\refitem Antonucci, R., \\& Miller, J. 1985, ApJ, 297, 621\n\n\\refitem Brock, D., Joy, M., Lester, D. F., Harvey, P. M., \\& Ellis, \nH. B. Jr. 1988, ApJ, 329, 208 \n\n\\refitem Comastri, A., Setti, G., Zamorani, G., \\&\nHasinger, G. 1995, A\\&A, 296, 1\n\n\\refitem Done, C., Madejski, G., \\& Smith, D. 1996, ApJ, 463, L63\n\n\\refitem Gilli, R., Risaliti, G., \\& Salvati, M. 1999, preprint\n(astro-ph/9904422) \n\n\\refitem Giommi, P., Fiore, F., Ricci, D., Molendi, S., Maccarone,\nM. C., \\& Comastri, A. 1998, Nucl. Phys. B, 69/1-3, 591\n\n\\refitem Greenhill, L. J., Moran, J. M., \\& Herrnstein, J. R. 1997,\nApJ, 481, L23\n\n\\refitem Heckman, T., Armus, L., \\& Miley, G. 1990, ApJS, 74, 833\n\n\\refitem Iwasawa, K., et al. 1993, ApJ, 409, 155\n\n%\\refitem Johnson W. N., Zdziarski A. A., Madejski G. M., Paciesas W. S., \n%Steinle H., \\& Lin Y.-C. 1997, in The 4th Compton Symposium, eds. \n%C. D. Dermer, M. S. Strickman, \\& J. D. Kurfess (AIP: New York), 283\n\n\\refitem Krolik, J., Madau, P., \\& \\.{Z}ycki, P. 1994, ApJ, 420, L57 \n\n\\refitem Lasota, J.-P., Abramowicz, M., Chen, X., Krolik, J., \nNarayan, R., \\& Yi, I. 1996, ApJ, 462, 142\n\n\\refitem Madau, P., Ghisellini, G., \\& Fabian, A. C. 1994, MNRAS, 270, 17p\n\n\\refitem Maloney, P., Begelman, M., \\& Pringle, J. 1996, ApJ, 472, 582\n\n\\refitem Mauersberger, R., Henkel, C., Whiteoak, J., Chin,\nY.-N., \\& Tieftrunk, A. 1996, A\\&A, 309, 705\n\n\\refitem Morrison, R., \\& McCammon, D. 1983, ApJ, 270, 119\n\n\\refitem Nandra, K., \\& Edelson, R. 1999, ApJ, 514, 682 \n\n\\refitem Rice, W., et al. 1998, ApJS, 68, 91\n\n\\refitem Zdziarski, A., Johnson, W., Done, C., Smith, D., \\& \nMcNaron-Brown, K. 1995, ApJ, 438, L63\n\n\\end{references}\n\n\\setcounter{table}{0}\n\\begin{deluxetable}{ccccccccc}\n\\tablewidth{0pc}\n\\tablecolumns{9}\n\\tablecaption {Results of Monte Carlo Fits to the RXTE Data for NGC~4945 \nfor Assumed Solar and $2 \\times $ Solar Fe Abundances}\n\\tablehead{\n\\colhead {Assumed torus} & \\multicolumn {2} {c} {Fitted spectral} & \n\\multicolumn {2} {c} {Fitted optical} & \\multicolumn {2} {c} { $\\chi^2$} & \\multicolumn {2} {c} {Fraction of \ndetected} \\\\\n\\colhead {half-angle $\\theta_0$} & \n\\multicolumn {2} {c} {index $\\alpha$} & \n\\multicolumn {2} {c} {depth $\\tau_{\\rm e}$} & \\multicolumn {2} {c} {76 d.o.f.} & \n\\multicolumn {2} {c} {{\\sl unscattered} photons } \\\\\n\\colhead {(degrees)} & \n\\colhead {A$_{\\rm Fe} = 1$} & \\colhead {A$_{\\rm Fe} = 2$} & \n\\colhead {A$_{\\rm Fe} = 1$} & \\colhead {A$_{\\rm Fe} = 2$} & \n\\colhead {A$_{\\rm Fe} = 1$} & \\colhead {A$_{\\rm Fe} = 2$} & \n\\colhead {A$_{\\rm Fe} = 1$} & \\colhead {A$_{\\rm Fe} = 2$} \n}\n\\startdata\n 80 & 0.7 & 0.75 & 2.1 & 1.5 & 68.5 & 68.5 & 19\\% & 31\\% \\nl\n 70 & 0.7 & 0.75 & 2.1 & 1.5 & 69.8 & 68.3 & 22\\% & 35\\% \\nl\n 60 & 0.7 & 0.75 & 2.2 & 1.5 & 71.5 & 72.9 & 24\\% & 39\\% \\nl\n 50 & 0.8 & 0.75 & 2.2 & 1.6 & 70.9 & 69.6 & 28\\% & 42\\% \\nl\n 40 & 0.7 & 0.75 & 2.2 & 1.6 & 70.9 & 72.7 & 33\\% & 48\\% \\nl\n 30 & 0.8 & 0.75 & 2.3 & 1.6 & 76.6 & 74.6 & 38\\% & 55\\% \\nl\n 20 & 0.8 & 0.75 & 2.4 & 1.6 & 74.5 & 77.0 & 47\\% & 63\\% \\nl\n 10 & 0.8 & 0.8 & 2.4 & 1.7 & 75.4 & 79.4 & 63\\% & 76\\% \\nl\n\\enddata\n\\end{deluxetable}\n\n\\vskip 1 cm\n\n\\centerline {\\bf Figure Captions}\n\n\\refitem{\\bf Fig.~1:} \nBroad-band unfolded X--ray spectrum of NGC~4945 as measured with the \nRXTE PCA and HEXTE instruments. The data were fitted with a \nphenomenological model which includes a hard power law component\nphoto--electrically absorbed by neutral gas with Solar abundances at a\ncolumn of $4.5 \\pm 0.3 \\times 10^{24}$ cm$^{-2}$, \nwith photon spectral index $\\Gamma = 1.45^{+0.1}_{-0.1}$,\nexponentially cutting off at 100 keV, plus a non-variable \nsoft component (assumed to be a power law), \nand a Fe K line. The observed 8 -- 30 keV flux of the hard component\nis $5 \\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$. \n\n\\vskip 1 cm\n\n\\refitem{\\bf Fig.~2:} Hard X--ray light curve of the Seyfert~2 galaxy \nNGC~4945 measured with the RXTE PCA instrument, showing a rapid,\nlarge amplitude flux variability. Plotted are data from all three\nlayers of three PCA detectors that were turned on during all \npointings, over the energy channels nominally corresponding to the range \nof 8 -- 30 keV. \n\n\\vskip 1 cm\n\n\\refitem{\\bf Fig.~3:} Fraction of the observed photons reaching an\nobserver located in the equatorial plane of a torus plotted against \nthe number of scatterings that those photons encountered before \nreaching an observer. The angle given in each \npanel is the vertical half-angle $\\theta_{\\rm 0}$ subtended by the torus\nas seen from the central source. Iron abundance (relative to Solar)\nis assumed to be 1 (solid line) and 2 (dotted line), with \n$\\tau_{\\rm e}$ equal to the best fit value for a given Fe abundance\nand $\\theta_0$ (cf. Table 1).\nSince the fractional amplitude of variability on short time scales \n(cf. Fig.~2) is large ($>$ 60\\%), $\\theta_{\\rm 0}$ of the optically\nthick \nstructure must be small, so that majority of the photons reaching an observer\nare not scattered.\n\n\\vfill\\eject\n\\centerline{\\psfig{file=madejski_fig1.ps,height=5.3 in,angle=270}}\n\\vfill\\eject\n\\centerline{\\psfig{file=madejski_fig2.ps,height=5.3 in,angle=270}}\n\\vfill\\eject\n\\centerline{\\psfig{file=madejski_fig3.ps,height=8 in,angle=0}}\n\n\\enddocument\n"
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astro-ph0002064
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Correlation Statistics of Spectrally-Varying Quantized Noise
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[
{
"author": "Carl R. Gwinn"
}
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I calculate the noise in the measured correlation functions and spectra of digitized, noiselike signals. In the spectral domain, the signals are drawn from a Gaussian distribution with variance that depends on frequency. Nearly all astrophysical signals have noiselike statistics of this type, many with important spectral variations. Observation and analysis of such signals at millimeter and longer wavelengths typically involves sampling in the time domain, and digitizing the sampled signal. (Quantum-mechanical effects, not discussed here, are important at infrared and shorter wavelengths.) The digitized noise is then correlated to form a measured correlation function, which is then Fourier transformed to produce a measured spectrum. When averaged over many samples, the elements of the correlation function and of the spectrum, follow Gaussian distributions. For each element, the mean of that distribution is the deterministic part of the measurement. The standard deviation of the Gaussian is the noise. Here I calculate that noise, as a function of the parameters of digitization. The noise of the correlation function is related to the underlying spectrum, by constants that depend on the digitization parameters. Noise affects variances of elements of the correlation function and covariances between them. In the spectral domain, noise also produces variances and covariances. I show that noise is correlated between spectral channels, for digitized spectra, and calculate the correlation. These statistics of noise are important for understanding of signals sampled with very high signal-to-noise ratio, or signals with rapidly-changing levels such as pulsars.
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"name": "spect_57.tex",
"string": "% spect_54.tex\n% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n%\n\\documentclass[10pt,preprint]{aastex}\n%\n\\def\\re{{\\rm Re}}\n\\def\\im{{\\rm Im}}\n%\n\\def\\gtwid{\\mathrel{\\raise.3ex\\hbox{$>$\\kern-.75em\\lower1ex\\hbox{$\\sim$}}}}\n\\def\\ltwid{\\mathrel{\\raise.3ex\\hbox{$<$\\kern-.75em\\lower1ex\\hbox{$\\sim$}}}}\n%\n\\def\\haf{{\\textstyle{{1}\\over{2}}}}\n\\def\\qua{{\\textstyle{{1}\\over{4}}}}\n\\def\\eig{{\\textstyle{{1}\\over{8}}}}\n%\n%\n\\def\\hwh{{\\hat w^{\\phantom{*}}}}\n\\def\\hxh{{\\hat x^{\\phantom{*}}}}\n\\def\\hyh{{\\hat y^{\\phantom{*}}}}\n\\def\\hzh{{\\hat z^{\\phantom{*}}}}\n\\def\\hrh{{\\hat r^{\\phantom{*}}}}\n\\def\\hah{{\\hat a^{\\phantom{*}}}}\n\\def\\hwc{{\\hat w^* }}\n\\def\\hxc{{\\hat x^* }}\n\\def\\hyc{{\\hat y^* }}\n\\def\\hzc{{\\hat z^* }}\n\\def\\hrc{{\\hat r^* }}\n\\def\\hac{{\\hat a^* }}\n%\n\\def\\rwx{{\\rho_{WX}}}\n\\def\\rwy{{\\rho_{WY}}}\n\\def\\rwz{{\\rho_{WZ}}}\n\\def\\rxy{{\\rho_{XY}}}\n\\def\\rxz{{\\rho_{XZ}}}\n\\def\\ryz{{\\rho_{YZ}}}\n%\n\\def\\rWX{{\\rho_{WX}}}\n\\def\\rWY{{\\rho_{WY}}}\n\\def\\rWZ{{\\rho_{WZ}}}\n\\def\\rXY{{\\rho_{XY}}}\n\\def\\rXZ{{\\rho_{XZ}}}\n\\def\\rYZ{{\\rho_{YZ}}}\n%\n%\n\\def\\la{{\\langle}}\n\\def\\ra{{\\rangle}}\n%\n\\def\\alp{{\\alpha}}\n\\def\\ups{{\\upsilon}}\n\n\\def\\twr{{\\tilde r}}\n\\def\\twe{{\\tilde a}}\n\\def\\twp{{\\tilde\\rho}}\n\\def\\twa{{\\tilde \\alpha}}\n\n\\def\\ckr{{\\breve r}}\n\\def\\cke{{\\breve a}}\n%\n\\def\\pa{{\\phantom{^*}}}\n%\n% from /home/cgwinn/tex/greekbf.tex\n\\def\\pmb#1{\\setbox0=\\hbox{#1}%\n \\kern-.025em\\copy0\\kern-\\wd0\n \\kern.05em\\copy0\\kern-\\wd0\n \\kern-.025em\\raise.0433em\\box0 }\n\n% Examples of pre-defined greek letters:\n\n\\def\\balpha{\\pmb{$\\alpha$}}\n\\def\\bdelta{\\pmb{$\\delta$}}\n\\def\\bpsi{\\pmb{$\\psi$}}\n\\def\\bsigma{\\pmb{$\\sigma$}}\n%\n\\def\\blankline {\\vskip10truept}\n%\n%\n\\shortauthors{GWINN}\n\\shorttitle{}\n\\begin{document}\n\\input epsf\n\n\\title{Correlation Statistics of Spectrally-Varying Quantized Noise}\n\\author{Carl R. Gwinn}\n\\affil{Department of Physics, University of California, Santa Barbara, California 93106}\n\\email{[email protected]} \n%\n%\n\\vskip 1 truein\n\\begin{abstract}\n\nI calculate the noise in the measured correlation functions and spectra of \ndigitized, noiselike signals.\nIn the spectral domain,\nthe signals are drawn from a Gaussian distribution with variance that depends on frequency.\nNearly all astrophysical signals have noiselike statistics of this type, many with\nimportant spectral variations. \nObservation and analysis of such signals at millimeter and longer wavelengths\ntypically involves sampling in the time domain, and digitizing the sampled signal.\n(Quantum-mechanical effects,\nnot discussed here, are important at infrared and shorter wavelengths.)\nThe digitized noise is then correlated to form a measured correlation function,\nwhich is then Fourier transformed to produce a measured spectrum.\nWhen averaged over many samples, \nthe elements of the correlation function and of the spectrum, follow Gaussian distributions.\nFor each element, the mean of that distribution is the deterministic part of the measurement.\nThe standard deviation of the Gaussian is the noise.\nHere I calculate that noise, as a function of the parameters of digitization.\nThe noise of the correlation function is related to the underlying spectrum,\nby constants that depend on the digitization parameters. \nNoise affects variances\nof elements of the correlation function and covariances between them.\nIn the spectral domain, noise also produces variances and covariances.\nI show that noise is correlated between spectral channels, for digitized spectra, and calculate the\ncorrelation.\nThese statistics of noise are important for understanding of signals sampled with very\nhigh signal-to-noise ratio, or signals with rapidly-changing levels such as pulsars.\n\n\\end{abstract}\n\n\\keywords{methods: data analysis -- techniques}\n\n\\section{INTRODUCTION}\n\n\\subsection{Correlation Functions and Spectra}\n\nElectric fields from nearly all astrophysical sources are indistinguishable from\nGaussian noise.\nThus, nearly all of the information in such signals lies in variances of and covariances between\nelectric fields of different\npolarizations, spatial locations, or frequencies.\nSpectra and cross-power spectra are estimates of the variance or covariance \nof the electric field as a function of frequency.\nThese spectra are the Fourier transforms of auto- or cross-correlation functions.\nSuch correlation functions are the averaged products\nof pairs of elements drawn from the series, for a range of time offsets or ``lags''.\nThe elements are drawn from separate series for cross-correlation, and from the same for\nautocorrelation.\nThe resulting correlation, as a function of lag, is commonly\naveraged over enough realizations to provide the desired signal-to-noise ratio. The correlation\nfunction is then Fourier\ntransformed to form the desired cross-power or\nautocorrelation spectrum,\nas a function of frequency. In practice,\ncorrelation and averaging can take place before or after the Fourier transform;\nthis makes little difference to the result from the standpoint of this paper.\n\nOften, data are digitized before correlation. \nFor bandwidths that are within the capability of digital circuitry,\nprocessing is usually more accurate and economical\nfor digital signals than for analog signals.\nDigitization\ninvolves sampling, or averaging over time intervals; and quantization, or\ndescribing the signal amplitude in each interval as one of a discrete\nset of values, rather than as a continuous variable.\nQuantization is an intrinsically nonlinear operation that destroys \ninformation, unlike the linear operations of sampling and\nFourier transform.\nI find that quantization introduces effects similar to noise in the final result,\nas one might perhaps expect.\n\nUsually observers wish to minimize noise, while maintaining an invertible,\ndeterministic relationship between the mean correlation and the \nunderlying covariance.\nOptimal parameters for quantization, and errors from departures from those parameters,\nare topics of classic work in radio astronomy (see, for example, \\citet{coo70,hag73,kul80,dad84} and references\ntherein).\nCalculation of the actual noise level can be important when\nsignal strength varies rapidly, \nand quantizer settings cannot remain optimal,\nas is sometimes the case for pulsars \\citep{jen98};\nor when the distribution of the intensity of the signal must be measured accurately\n\\citep{gwi00}.\nAs sensitivities of radiotelescopes improve, and as demands on the observed data increase,\ncalculation of the noise level from quantizer parameters can be expected to become more important.\n\nBecause correlation functions and spectra are averaged over many\nrealizations, the Central Limit Theorem implies\nthat the resulting correlation function or spectrum has Gaussian\nstatistics. Thus, the statistics of the spectrum are fully described\nby each spectral channel's mean and \nvariance, and covariances between channels. \nThe mean of the spectrum is the deterministic part\nof the measurement; variances and covariances are\nthe random part, or noise. In principle, one\nseeks to minimize the noise, while preserving the relationship\nbetween the mean and the underlying spectrum.\nIn \\citet{gwi04} (hereafter Paper 1), I discussed this problem for ``white'' signals,\nwhich have zero correlation except for elements\nof the two series with zero lag.\nHere I consider the more general case, where signals have arbitrary\nspectral character, so that covariance can depend on lag.\nThe effect of quantization on the statistics of such ``colored'' spectra, \nparticularly their noise, is the subject of this paper.\n\nI calculate the noise in the quantized cross- and autocorrelation functions.\nThe noise differs from that for correlation of continuous data in \nadditional terms, some of them constant and others proportional\nto the autocorrelation function,\nand products of auto- and cross-correlation functions.\nI present this calculation through second order in correlation.\n\nI then \nFourier transform these expressions to determine the mean spectrum\nand its variance. \nThe mean spectrum is simply the Fourier transform of the mean correlation function,\nwhile\nthe noise in the spectrum is a double Fourier transform of the noise in the correlation function.\nI find that in the spectral domain, a gain factor, and white noise added in quadrature, approximately \nrepresent the effects of quantization in a single channel.\nThe added white noise is commonly known as ``quantization noise''.\nIndeed, the gain factor and the noise\nare identical to those previous workers found for the deterministic,\nmean spectrum \\citep{coo70,jen98}.\nHowever, I also show that noise is correlated across spectral channels. This covariance \ncan reduce, or increase,\nthe total noise in the spectrum, depending on the details of the quantization scheme and\nthe details of the spectrum. \nFor ``white'' signals without spectral variation, \nthe more general result of this paper\nreduces to that found in Paper 1. \nIn this case, the correlations \nor anti-correlations \nof noise between channels can represent an effect of the same order as\nquantization noise, when integrated over all channels of a spectrum.\n\n\\subsection{Organization of this Paper}\n\nI consider cross-correlation of two time series, $x$ and $y$, and autocorrelation\nof $x$.\nIn \\S\\ref{continuous} I introduce these \nunderlying complex time series \n$x_{\\ell}$ and $y_{\\ell}$ and describe their assumed statistical\nproperties.\nI calculate the mean and variance of their correlation\nfunction and its Fourier transform.\nI show that covariance of noise in different spectral channels is zero\nfor correlation of the continuous (un-digitized) series.\n\nI introduce information-destroying quantization in \n\\S\\ref{quantized}. \nUnder the assumption that the covariances are small (except for\nthe zero lag of the autocorrelation function, which must be 1),\nI calculate the mean and the variance\nof the quantized correlation function\nfor quantized data, and present analytic expressions for them.\nI compare the analytical results with computer simulations and find excellent agreement.\n\nIn \\S\\ref{section_quantspectrum} I find the statistics of the cross-power and power spectra.\nThe cross-power spectrum is the Fourier transform of the cross-correlation function;\nand the power spectrum (sometimes called the autocorrelation spectrum) is the Fourier\ntransform of the autocorrelation function.\nI calculate the noise in the spectra by a double Fourier transform of the noise in the correlation functions.\nI show that the noise in a single spectral channel\ncan be approximately represented by a gain factor and white ``digitization noise''\nadded in quadrature with the original signal.\nHowever, I also show that noise is correlated (or, more commonly, anti-correlated)\nacross spectral channels.\nI present analytical results for autocorrelation functions, and autocorrelation spectra,\nin \\S\\ref{acf_subsection} and\\ \\ref{acspect_subsection}.\nI summarize results in \\S\\ref{summary}, and show that correlations of noise between channels can\nrepresent an effect of the same order as quantization noise, when integrated over all spectral channels.\n\n\\section{CORRELATION FUNCTIONS AND SPECTRA OF CONTINUOUS SIGNALS}\\label{continuous}\n\n\\subsection{Time Series of Gaussian Noise}\n\nConsider time series $x_{\\ell}$ and $y_{\\ell}$.\nThese might be, for example, the electric fields recorded as analog signals \nat two antennas.\nAll elements of each are\ndrawn from Gaussian\ndistributions in the complex plane.\nThe distributions have zero mean.\nI further assume that the series are stationary,\nso that the properties of $x_{\\ell}$ and $y_{\\ell}$ are independent of\nthe time index $\\ell$.\nThus, the variance of each series is constant,\nand the covariances between elements can depend only\non their time separation and whether they belong to the same\nor different series.\nThe ensemble-average spectra, defined in \\S\\ref{meanspectrum} below,\ndepend only on these variances and covariances.\n\nFor this paper, I assume that the series are statistically identical,\nin the sense that the exchange of $x$ and $y$\nleaves the statistical properties of the spectra unchanged.\nInstrumental effects often violate this assumption in a mild fashion,\nas by variations in complex gain between two antennas.\nSometimes the assumption is violated in a more fundamental way,\nas in spatial variation of the spatial and spectral character\nof scintillating sources \\citep{des92, jau00, den02}.\nThis assumption can easily be relaxed, by defining separate autocorrelation\nfunctions for the two series in the results below.\n\nFor convenience, I scale variances of real and imaginary parts\nof the series $x_{\\ell}$ and $y_{\\ell}$ to 1.\n(This is in accord with \nmuch of the literature on quantization, which assumes real series with\nunit variance.)\nThe variances are then:\n\\begin{equation}\n\\haf \\la x_{\\ell}\\, x_{\\ell}^*\\ra =\\haf \\la y_{\\ell}\\, y_{\\ell}^*\\ra = 1 .\n\\label{xxc_yyc_equiv_1}\n\\end{equation}\nHere, the angular brackets $\\la ... \\ra$ indicate a statistical\naverage, over an ensemble of time series with identical statistics.\n\nI assume that the time series have no particular intrinsic\noverall phase,\nso that the transformation \n\\begin{equation}\nx_{\\ell}\\rightarrow x_{\\ell}e^{i\\phi},\n\\quad\ny_{\\ell}\\rightarrow y_{\\ell}e^{i\\phi}\n\\label{phase_invariance}\n\\end{equation}\nleaves the variances and covariances unchanged.\nConsequently, products of factors with the same conjugation average to zero:\n\\begin{equation}\n\\la x_{\\ell} y_{m} \\ra =\\la x_{\\ell} x_{m}\\ra =\\la y_{\\ell} y_{m}\\ra =0 ,\n\\label{no_intrinsic_phase}\n\\end{equation}\nfor any $\\ell$ and $m$.\n\n\\subsection{Mean Correlation Function and Spectrum: Continuous Data}\\label{continuous_avg}\n\n\\subsubsection{Mean Correlation Function}\n\nThe covariances between elements in the series $x$ and $y$\nare given by\nthe statistically-averaged cross-correlation $\\rho_{\\tau}$,\nand the statistically-averaged auto-correlation $\\alpha_{\\tau}$:\n\\begin{eqnarray}\n\\rho_\\tau &=& \\haf \\la x_{\\ell}\\, y_{\\ell+\\tau}^* \\ra\\label{rhotau_alptau_def}\\\\\n\\alp_{\\tau} &=& \\haf \\la x_{\\ell}\\, x_{\\ell+\\tau}^* \\ra\n=\\haf \\la y_{\\ell}\\, y_{\\ell+\\tau}^* \\ra . \\nonumber\n\\end{eqnarray}\nNote the conjugation symmetry of $\\alp_{\\tau}$:\n\\begin{equation}\n\\alp_{\\tau}=\\alp_{-\\tau}^* .\n\\end{equation}\nEq.\\ \\ref{xxc_yyc_equiv_1} gives\n$\\alp_0 = 1$.\n\nMeasurements seek to estimate the statistically-averaged correlation\nfunctions via the finite averages:\n\\begin{eqnarray}\nr_{\\tau}&=&{{1}\\over{2 N_o}} \\sum_{\\ell=1}^{N_o} x_{\\ell}\\, y_{\\ell+\\tau}^* \\label{rtau_atau_def} \\\\\na_{\\tau}&=&{{1}\\over{2 N_o}} \\sum_{\\ell=1}^{N_o} x_{\\ell}\\, x_{\\ell+\\tau}^* . \\nonumber\n\\end{eqnarray}\nHere, $N_o$ is the number of elements observed in each series.\n\nI assume that the correlation functions ``wrap,''\nin the sense that:\n\\begin{equation}\nx_{(\\ell)}=x_{(\\ell+N_o)},\ny_{(\\ell)}=y_{(\\ell+N_o)}\\quad {\\rm for\\ all\\ } \\ell .\n\\label{wrap_assumption} \n\\end{equation}\nThen, the sums in Eq.\\ \\ref{rtau_atau_def}\ncontain the same number of terms, for each $\\tau$.\nThis simplifies counting arguments below.\nAlso, of course, $r_{\\tau}=r_{\\tau+N_o}$;\nthis simplifies discussion of the Fourier transform to spectra.\nNote that in practice, many correlator do not ``wrap'' in this fashion.\nThey zero-pad the data so that $x_{\\ell}\\, y_{\\ell+\\tau}^*=0$,\nif either $\\ell$ or $\\ell+\\tau$ is greater than $N_o$ or less than zero.\nThe issue is moot if the number of lags correlated\nis smaller than the span of data $N_o$,\nor for ``FX'' correlators, which correlate in the frequency domain.\nOtherwise, it can affect the noise,\nthrough uneven sampling of \n$\\alpha$ in Eq.\\ \\ref{continuous_rtruc} below.\nI will discuss the effect heuristically in a separate paper,\nin comparison of theory with measurements.\n\nWith the definitions in Eq.\\ \\ref{rtau_atau_def},\n\\begin{eqnarray}\n\\la r_{\\tau}\\ra&=&\\rho_{\\tau} \\label{ra_relate_rhoalp}\\\\\n\\la a_{\\tau}\\ra&=&\\alp_{\\tau} . \\nonumber\n\\end{eqnarray}\nNote that Greek letters $\\rho$ and $\\alpha$\ndenote the statistically-averaged quantities,\nwhereas roman letters $r$ and $a$ denote the observed,\nfinite averages.\n\n\\subsubsection{Mean Spectrum}\\label{meanspectrum}\n\nThe statistically-averaged \ncross- and auto-correlation functions are related to the cross-power and autocorrelation spectra\nby Fourier transforms:\n\\begin{eqnarray}\n\\twp_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau}\\rho_{\\tau} \\label{define_statavg_spectra}\\\\\n\\twa_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau}\\alp_{\\tau} . \\nonumber \n\\end{eqnarray}\nHere, $2 N$ is the number of frequency channels.\nNote that $\\twa_k$ is real, because of the conjugation symmetry of $\\alp_{\\tau}$.\nOther conventions for the Fourier transform\nhave been used in the past.\nThe present convention has the advantage that\nthe spectrum $\\twa_k$ has values that \nare independent of numbers of samples $N_o$ or of spectral channels $2N$.\n\nSimilarly, \nI define the measured\ncross-power and autocorrelation spectra,\n\\begin{eqnarray}\n\\twr_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} r_{\\tau} \\\\\n\\twe_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} a_{\\tau} . \\nonumber \n\\end{eqnarray}\nSo, by Eqs.\\ \\ref{ra_relate_rhoalp} and \\ref{define_statavg_spectra},\n\\begin{eqnarray}\n\\la \\twr_k\\ra &=& \\twp_k \\label{twrk_twpk_twak_twak}\\\\\n\\la \\twe_k\\ra &=& \\twa_k . \\nonumber\n\\end{eqnarray}\n\nAs a simple example, a ``white'' spectrum\nwith a spectrally-uniform correlation $\\rho_w$ has\n$\\twa_k=1$ and\n$\\twp_k=\\rho_w$.\nThen, only the zero lags \nof the statistically-averaged correlation functions\nwill have nonzero values:\n$\\alp_0=1$\nand \n$\\rho_0=\\rho_w$.\nFor all other lags $\\tau$, $\\alp_{\\tau}=\\rho_{\\tau}=0$.\n\n\\subsection{Noise: Continuous Data}\n\n\\subsubsection{Noise for Correlation Function}\n\nThe variance of the observed correlation function\ndescribes the noise.\nWe therefore seek:\n\\begin{eqnarray}\n\\la r_{\\tau} r_{\\ups}^*\\ra &=&\n{{1}\\over{(2 N_o)^2}} \\sum_{\\ell=1}^{N_o}\\sum_{m=1}^{N_o} \\la x_{\\ell} y_{\\ell+\\tau}^* x_m^* y_{m+\\ups}\\ra .\n\\label{rtru_sum_expand}\n\\end{eqnarray}\nThe fourth moment of elements drawn from a Gaussian distribution \nis related to their second moments, \nso that:\n\\begin{equation}\n\\la x_{\\ell} y_{\\ell+\\tau}^* x_m^* y_{m+\\ups}\\ra \n=\\la x_{\\ell}y_{\\ell+\\tau}^*\\ra \\la x_{m}^* y_{m+\\ups}\\ra\n+\\la x_{\\ell}x_{m}^*\\ra \\la y_{\\ell+\\tau}^* y_{m+\\ups}\\ra .\n\\label{continuous_fourth_moment}\n\\end{equation}\nA third product of second moments,\n$\\la x_{\\ell}y_{m+\\ups}\\ra \\la y_{\\ell+\\tau}^* x_{m}^*\\ra$,\nwould ordinarily appear on the right-hand side of \nEq.\\ \\ref{continuous_fourth_moment},\nbut vanishes here\nbecause of the assumption that $x$ and $y$ have\nno intrinsic phase (Eq.\\ \\ref{no_intrinsic_phase}).\nEq.\\ \\ref{rtau_atau_def} gives the second moments,\n% in Eq.\\ \\ref{continuous_fourth_moment}, \nso that\nEq.\\ \\ref{rtru_sum_expand} becomes:\n\\begin{equation}\n\\la r_{\\tau} r_{\\ups}^*\\ra = \\rho_{\\tau}\\rho_{\\ups} + {{1}\\over{N_o}}\\sum_{n=1}^{N_o}\\alp_{n}\\alp_{-n+(\\tau-\\ups)} .\n\\label{continuous_rtruc}\n\\end{equation}\nHere, I have\nused the ``wrap'' assumption for the correlation function (Eq.\\ \\ref{wrap_assumption}).\nThe variance is thus:\n\\begin{equation}\n\\la r_{\\tau} r_{\\ups}^*\\ra -\\la r_{\\tau}\\ra\\la r_{\\ups}^*\\ra =\n{{1}\\over{N_o}}\\sum_{n=1}^{N_o}\\alp_{n}\\alp_{-n+(\\tau-\\ups)} .\n\\label{continuous_rtruc_stddev}\n\\end{equation}\n\nThree variances,\nor two principal axes and an angle,\nare required to fully describe the elliptical distribution of noise in the complex plane.\nBecause $r_{\\tau} r_{\\tau}^*$ is always real, we require two more.\nA convenient independent statistic is:\n% \\begin{equation}\n% \\la r_{\\tau} r_{\\ups}\\ra = \\rho_{\\tau}\\rho_{\\ups} + {{1}\\over{N_o}}\\sum_{n=1}^{N_o}\\rho_{n}\\rho_{-n+(\\tau-\\ups)} .\n% \\label{continuous_rtru}\n% \\end{equation}\n% From this, one sees that\n\\begin{equation}\n\\la r_{\\tau} r_{\\ups}\\ra -\\la r_{\\tau}\\ra\\la r_{\\ups}\\ra =\n{{1}\\over{N_o}}\\sum_{n=1}^{N_o}\\rho_{n}\\rho_{-n+(\\tau-\\ups)} .\n\\label{continuous_rtru_stddev}\n\\end{equation}\nThis expression is, in general, complex and thus provides the needed additional two statistics.\nAs an example, \none can easily recover the expressions given in Paper 1 for the noise of a\n``white'' spectrum, for continuous-valued data, from Eqs.\\ \\ref{continuous_rtruc_stddev} and \\ref{continuous_rtru_stddev}.\n\n\\subsubsection{Noise for Spectrum}\\label{continuous_spectrum_noise}\n\nThe variances of the spectral channels give the noise.\nOne can obtain the variance by Fourier transforming Eq.\\ \\ref{continuous_rtruc}:\n\\begin{eqnarray}\n\\la \\twr_k \\twr_k^*\\ra &=& \n\\sum_{\\tau=-N}^{N-1} \\sum_{\\ups=-N}^{N-1} e^{i{{2\\pi}\\over{2N}}k (\\tau-\\ups)}\n\\la r_{\\tau}r_{\\ups}^* \\ra \\\\\n&=& \\twp_k \\twp_k^* + {{2N}\\over{N_o}}\\twa_k \\twa_k . \\nonumber\n\\end{eqnarray}\nThis uses the fact that the Fourier transform of the autocorrelation function\nis the power spectrum\n(Eqs.\\ \\ref{convolution_fact},\\ref{convolution_fact_rho}).\nI assume here that all nonzero elements of the correlation functions\n$\\alp_{\\tau}$, $\\rho_{\\tau}$\nlie within the range that is transformed to a spectrum, $-N<\\tau<N-1$.\nIn other words, the spectral resolution is sufficient to \ncompletely resolve all features of the spectrum.\nAlso, I again use the wrap assumption, Eq.\\ \\ref{wrap_assumption}.\nThus,\n\\begin{equation}\n\\la \\twr_k \\twr_k^*\\ra - \\la \\twr_k \\ra\\la \\twr_k^*\\ra \n= {{2N}\\over{N_o}} \\twa_k \\twa_k^* . \n\\label{continuous_twrktwrkc}\n\\end{equation}\nAnalogously from Eq.\\ \\ref{continuous_rtru_stddev} one finds:\n\\begin{equation}\n\\la \\twr_k \\twr_k\\ra -\\la \\twr_k \\ra\\la \\twr_k\\ra = {{2N}\\over{N_o}} \\twp_k \\twp_k . \n\\label{continuous_twrktwrk}\n\\end{equation}\n\nTogether, Eq. \\ref{continuous_twrktwrkc} and \\ref{continuous_twrktwrk}\ndescribe the noise of the cross-power spectrum.\nNote that the noise, measured as the standard deviation,\nincreases proportionately with the square root of the number of spectral channels $\\sqrt{2N}$,\nand decreases as the inverse square root of number of measurements $\\sqrt{2 N_o}$.\nEach of the $N_o$ complex terms in the correlation function\ninvolves measurement of two quantities, \nso that for counting arguments the number of independent data is actually $2 N_o$.\n\nIf we suppose that a particular element $\\twp_k$ of the cross-power spectrum is real\n(or, equivalently, if we rotate the phase of $x$ until $\\twp_k$ is real!),\nthen Eqs.\\ \\ref{continuous_twrktwrkc} and\\ \\ref{continuous_twrktwrk}\nshow that:\n\\begin{eqnarray}\n\\la \\re[\\twr_k]\\ra &=& \\twp_k \\label{continuous_spectrum_facts} \\\\\n\\la \\im[\\twr_k]\\ra &=& 0 \\nonumber \\\\\n\\la \\re[\\twr_k]\\re[\\twr_k]\\ra - \\la \\re[\\twr_k]\\ra\\la\\re[\\twr_k]\\ra &=& {{2N}\\over{2N_o}}(|\\twa_k|^2 + \\twp_k^2) \\nonumber \\\\\n\\la \\im[\\twr_k]\\im[\\twr_k]\\ra \\phantom{- \\la \\re[\\twr_k]\\ra\\la\\re[\\twr_k]\\ra }\n&=& {{2N}\\over{2N_o}}(|\\twa_k|^2 - \\twp_k^2) \\nonumber \\\\\n\\la \\re[\\twr_k]\\im[\\twr_k]\\ra \\phantom{- \\la \\re[\\twr_k]\\ra\\la\\re[\\twr_k]\\ra }\n&=& 0 . \\nonumber\n\\end{eqnarray}\nThese equations describe the error ellipses in the complex plane\nfor spectral measurements.\nThey are consistent with the results of Paper 1 for a white spectrum ($\\alp_k=1$, $\\rho_k={\\rm const}$),\nand are closely related to ``self-noise'' (see Paper 1).\n\nThe noise in the measured autocorrelation spectrum $\\twe_k$ is identical to that in\nthe cross-power spectrum $\\twr_k$ (Eq.\\ \\ref{continuous_twrktwrk} or \n\\ref{continuous_spectrum_facts}), with substitution of $\\twa_k$ for $\\twp_k$.\n\n\\subsubsection{Noise is Uncorrelated Between Spectral Channels}\\label{noise_uncorr_continuous}\n\nThe correlation of noise between spectral channels \ncan be found from a generalization of Eq.\\ \\ref{continuous_twrktwrkc}:\n\\begin{eqnarray}\n\\la \\twr_k \\twr_{\\ell}^* \\ra &=& \\sum_{\\tau,\\ups=-N}^{N-1} e^{i(k\\tau -\\ell\\ups)} \\la r_{\\tau} r_{\\ups}^* \\ra \\\\\n% &=&{{1}\\over{N_o^2}}\\sum_{\\tau,\\ups=-N}^{N-1} \\sum_{m,n=1}^{N_o}e^{i(k\\tau-\\ell\\ups)} \n% \\left(\\la x_m y_{m+\\tau}^*\\ra\\la x_n^* y_{n+\\ups}\\ra\n% + \\la x_m x_n^* \\ra\\la y_{m+\\tau}^* y_{n+\\ups}\\ra \\right) \\\\\n&=&\n\\la \\twr_k\\ra\\la \\twr_{\\ell}^*\\ra +\n{{2 N}\\over{2 N_o}} \\sum_{\\ups,\\mu=-N}^{N-1} \\sum_{m,n=1}^{N_o} e^{i(k\\mu+(k-\\ell)\\ups)}\\la a_{n-m}\\ra\\la a_{-(n-m)+\\mu}\\ra \\nonumber \\\\\n&=& 0 , \\quad {\\rm unless}\\ \\ell=m .\n\\end{eqnarray}\nHere, I have introduced \n$\\mu=\\tau-\\ups$.\nThe summation over \n$\\ups$ \nyields zero unless \n$\\ell=m$ \n(in which case one recovers \nEq.\\ \\ref{continuous_twrktwrkc}).\nThus,\nnoise is uncorrelated between different channels, for the spectrum of a continuous signal.\n% \\begin{eqnarray}\n% \\la\\twr_k\\twr_{\\ell}^*\\ra-\\la\\twr_k\\ra\\la\\twr_{\\ell}^*\\ra &=&0,\\quad {\\rm and} \\\\\n% \\la\\twr_k\\twr_{\\ell}\\phantom{^*}\\ra-\\la\\twr_k\\ra\\la\\twr_{\\ell}\\phantom{^*}\\ra &=&0,\\quad {\\rm for\\ }\\ell\\neq m .\n% \\nonumber\n% \\end{eqnarray}\n\n\\section{CORRELATION FUNCTIONS OF QUANTIZED SIGNALS}\\label{quantized}\n\n\\subsection{Quantized Gaussian Noise}\n\nSuppose now that the time-series $x_{\\ell}$\nand $y_{\\ell}$ are quantized,\nto produce the time series $\\hat x_{\\ell}$\nand $\\hat y_{\\ell}$.\nQuantization involves converting value of the continuous\nvariables $x_{\\ell}$\nand $y_{\\ell}$ to one of a discrete set of values via a \ncharacteristic curve. Fig.\\ \\ref{4_level} shows an example,\nfor 4-level quantization.\nSuch curves can be parametrized by the locations of the steps, $\\{v_{xi}\\}$ and $\\{v_{yi}\\}$,\nand the weights of each step, $\\{n_{i}\\}$.\nI assume that the \nsame curve is used for the real and imaginary parts of \nboth $x_{\\ell}$ and $y_{\\ell}$,\nalthough the curve for $x_{\\ell}$ may differ from that for $y_{\\ell}$.\nI also assume that the characteristic curve is antisymmetric\nfor both real and imaginary parts:\n$\\hat X (X) = -\\hat X(-X)$,\nwhere $X$ is the real or imaginary part of $x$;\nand analogously for $y$.\nPaper 1 discusses additional details of quantization, with references.\nQuantization will preserve some properties of \nthe continuous signals and their correlation functions and spectra,\nand change others, as this section investigates.\n\n\\subsection{Correlation Function for Quantized Data}\n\nFrom the quantized time series $x_{\\ell}$ and $y_{\\ell}$,\none can form the\ncross-correlation function $\\hat r_{\\tau}$, \n\\begin{equation}\n\\hat r_{\\tau}={{1}\\over{2 N_o}}\\sum_{\\ell=1}^{N_o}\\hat x_{\\ell}\\, \\hat y_{\\ell+\\tau}^* , \\label{rtau_def} \\\\\n\\end{equation}\nand the autocorrelation function of $\\hat x$:\n\\begin{equation}\n\\hat a_{\\tau}={{1}\\over{2 N_o}}\\sum_{\\ell=1}^{N_o}\\hat x_{\\ell}\\, \\hat x_{\\ell+\\tau}^* .\n\\label{atau_def}\n\\end{equation}\nAgain I use the ``wrap'' assumption, Eq.\\ \\ref{wrap_assumption}.\nNote that $\\hat a$ may differ for the series $x$ and $y$ because of differences in characteristic curves,\nas well as for reasons noted above.\nOne seeks to relate $\\hat r_{\\tau}$ and $\\hat a_{\\tau}$ as closely as possible to \nthe ensemble averages for continuous data, \n$\\rho_{\\tau}$ and $\\alp_{\\tau}$, \nvia a simple deterministic relationship\nand with as little noise as possible.\n\nAmong the classic treatments of correlation of quantized signals\nare the works of \\citet{coo70} and \\citet{jen98}.\nIn the notation of Paper 1 and the following sections,\nCooper found that $\\hat r(\\rho)$ is proportional to $\\rho$, for small $\\rho$,\nand determined the constant of proportionality.\n\\citet{jen98} pointed out that this proportionality is \nquite accurate until $\\rho$ approaches 1 closely, where the departure becomes significant.\nMost cross-correlations of astrophysical data yield small $\\rho$,\njustifying the linear approximation.\nHowever, for autocorrelation, the\n``zero lag'' must yield unit correlation: $\\alp_0=1$ \n(see \\S\\ref{continuous_avg} above),\nfor which the linear approximation is poor.\nJenet \\& Anderson concluded \n that the autocorrelation function for quantized data is nearly proportional\nto the desired result $\\alp_{\\tau}$, with an additional spike\nat zero lag.\n\n\\subsection{Simulations of Cross-Correlation}\\label{simulations}\n\nFor comparison with analytical results, I simulated correlation \nof Gaussian noise.\nFigure\\ \\ref{dxcf_avgplot}\nshows the average spectra and correlation functions for one simulation,\nwith $2N=8$ lags, used as an example in the rest of the paper.\nThe autocorrelation function is \n``white'' with $\\alpha_{\\tau}=1$ for $\\tau = 0$, and $\\alpha_{\\tau}=0$ for $\\tau\\neq 0$.\nThe cross-correlation function has \nonly 2 nonzero lags, $\\tau=1,2$: $\\rho_1=\\rho_2=0.4$.\nNote that this is somewhat different from typical radioastronomical\ndata, which typically contain a white background noise\nspectrum (which appears as a spike in the autocorrelation function\nat $\\tau=0$),\nwith an admixture of spectrally-varying noise,\nperhaps with varying correlation.\n\nI formed the original noiselike data for Figure\\ \\ref{dxcf_avgplot} by \ndrawing elements from Gaussian distributions for each spectral channel.\nThis method reflects the underlying assumption that the\nspectrum consists of a number of independent spectral components\nwith different frequencies.\nFor each spectral channel, the Gaussian distribution had unit variance\n(as indicated by the flat autocorrelation spectrum $\\alpha_k = 1$ in the \nupper panel of Figure\\ \\ref{dxcf_avgplot}).\nHowever, correlations between the conjugates of $x_k$ and $y_k$ varied with\nspectral channel $k$, to yield the spectral variation of $\\rho_k$ seen in the figure.\nPaper 1 (\\S\\ 4) describes formation of such a distribution. \nFor this work, the phase of one series was rotated, in each channel, to produce the \nphase desired for $\\rho_k$.\nI then Fourier transformed these frequency-domain data to the time domain,\nto produce the series \n$x_{\\ell}$ and $y_{\\ell}$.\nThis yielded Gaussian noise with the desired correlations.\nI then quantized these series using a characteristic curve as in Figure\\ \\ref{4_level}\nwith $v_0=1.5$, $n=3$ to form the series $\\hat x_{\\ell}$, $\\hat y_{\\ell}$.\nAfter quantization,\nI correlated the \ntime series to produce the correlation function\n$\\hat r_{\\tau}$. \nI discuss Fourier transform of $\\hat r_{\\tau}$ to form the quantized spectrum in \n\\S\\ref{section_quantspectrum} below.\n\nThe predictions of \\citet{coo70} and \\citet{jen98} for the average correlation function,\nre-derived in the following section, agree with the simulation to much better than the\nsize of the points in the figure.\nIn the following sections, I calculate the expected noise in the \ncorrelation function, \nand compare \nresults with simulations of this spectrum.\n\n\\subsection{Mean Cross-Correlation Function for Quantized Data}\n\nTo introduce the analytical technique used \nto find the noise below,\nI re-derive the results of \\citet{coo70} and \\citet{jen98}.\nEq.\\ \\ref{rtau_def} gives the ensemble-average autocorrelation function:\n\\begin{equation}\n\\la \\hat r_{\\tau} \\ra = {{1}\\over{2 N_o}}\\sum_{\\ell} \\la \\hxh_{\\ell} \\hyh_{\\ell+\\tau}\\ra .\n\\label{digital_rt_expand}\n\\end{equation}\nThe quantity $\\la \\hat x_{\\ell} \\hat y_{\\ell+\\tau}^*\\ra$\nis of the form $\\la \\hat w \\hat x^*\\ra$, where $\\hat w$ and $\\hat x$ are quantized random variables. \nThis average can be expanded into products of\npairs of real and imaginary parts of $\\hat w$ and $\\hat x$:\n\\begin{equation}\n\\la \\hat w \\hat x^*\\ra = \\big(\\la\\re[\\hat w]\\re[\\hat x]\\ra + \\la\\im[\\hat w]\\im[\\hat x]\\ra\\big) \n+ i\\big(\\la\\im[\\hat w]\\re[\\hat x]\\ra - \\la\\re[\\hat w]\\im[\\hat x]\\ra\\big) .\n\\label{reimparts_wxc}\n\\end{equation}\nThe various averages of the \n{\\it real} quantized Gaussian variables on the right-hand side of this\nequation are given in Table\\ \\ref{table_real_avgs};\nin this case, by the first line:\n$\\la\\hat W \\hat X\\ra = B_W B_X \\rho_{WX}$.\nHere, $W$ and $X$ are real (or imaginary) variables drawn from the bivariate\nGaussian distribution with covariance $\\rho_{WX}$,\nand $\\hat W$ and $\\hat X$ are their quantized counterparts.\nThe statistical average $\\la ...\\ra$ is an integral over the probability\ndistribution for $W$ and $X$, times the characteristic curves for $\\hat W(W)$ and $\\hat X(X)$.\nIn \\S\\ 3.2.1 of Paper 1, this expression was expanded in powers of $\\rho_{XY}$ to yield\nthe term in the second column of Table\\ \\ref{table_real_avgs},\ntimes one-dimensional Gaussian distributions of $W$\nand $X$ and their \ncharacteristic curves.\nIntegration over $X$ and $Y$ \nyields the term in the third column in Table\\ \\ref{table_real_avgs}.\n\nAs Eq.\\ \\ref{reimparts_wxc} shows,\nseveral expressions of the form $\\la \\hat W(W)\\hat X(X)\\ra$ must be combined\nto find the complex average $\\la \\hat w \\hat x^*\\ra$.\nThe covariances of the various real and imaginary parts\ncan be combined to form a complex covariance, $\\rho_{WX}$:\n\\begin{eqnarray}\n\\la\\re[w]\\re[x]\\ra &=& \\phantom{-}\\la\\im[w]\\im[x]\\ra = \\re[\\rho_{WX}] \\\\\n\\la\\im[w]\\re[x]\\ra &=& -\\la\\re[w]\\im[x]\\ra = \\im[\\rho_{WX}] . \\nonumber\n\\end{eqnarray}\nOne thus obtains the expression for $\\la \\hat w \\hat x^*\\ra$ given in the first\nline of Table\\ \\ref{table_complex_avgs}, in the third column:\n\\begin{equation}\n\\la \\hat w \\hat x^*\\ra = 2 [B_X B_Y] \\rho_{WX} .\n\\label{wxc}\n\\end{equation}\nNote that this result is accurate through second order;\nas discussed in Paper 1, the next correction is third-order.\nSubstitution into Eq.\\ \\ref{digital_rt_expand} recovers the result of \\citet{coo70}, here with complex correlations:\n\\begin{equation}\n\\la \\hat r_{\\tau} \\ra = B_X B_Y \\rho_{\\tau} . \\label{avg_rtau_rhotau_prop}\n\\end{equation}\n\n\\subsection{Mean Autocorrelation Function for Quantized Data}\n\nAs \\citet{jen98} point out, the mean autocorrelation function must be\ntreated differently from cross-correlation.\nEq.\\ \\ref{atau_def} gives the ensemble-average autocorrelation function:\n\\begin{equation}\n\\la \\hat a_{\\tau} \\ra = {{1}\\over{2 N_o}}\\sum_{\\ell} \\la \\hxh_{\\ell} \\hxh_{\\ell+\\tau}\\ra .\n\\end{equation}\nThis involves products of different elements for $\\tau\\neq 0$,\nand square moduli of elements for $\\tau=0$.\nThus, it involves terms of both the form $\\la \\hat w \\hat x^*\\ra$,\nand of the form $\\la \\hat w \\hat w^*\\ra$.\nThe first is the same as for cross-correlation;\nthe second requires a different, though analogous, calculation.\nThe results in the first 2 lines in Table\\ \\ref{table_complex_avgs},\nyield the expression of \\citet{jen98} for the \nstatistically-averaged cross-power spectrum:\n\\begin{eqnarray}\n\\la \\hat a_{\\tau}\\ra &=&\\cases { A_{X2},& if $\\tau=0$; \\cr\nB_X^2 \\alp_{\\tau}, & if $\\tau\\neq 0$. \\cr}\n\\label{avg_hat_a}\n\\end{eqnarray}\nAgain, the constants $A_{X2}$ and $B_X$ depend on the characteristic curve;\nPaper 1 presents expressions for them.\nThe result holds through second order in $\\alp_{\\tau}$.\nFigure \\ref{dxcf_avgplot} illustrates the resulting spike at zero lag, for autocorrelation.\n\n\\subsection{Noise of Cross-Correlation Functions for Quantized Signals}\n\nThe variance of the correlation function measures the noise.\nThe noise\nthus involves the fourth moment of the quantized signals $\\hat x_{\\ell}$ and $\\hat y_{\\ell}$.\nBecause the correlation function is complex,\nit is drawn from an elliptical Gaussian distribution in the complex plane, \nand one must determine both $\\la \\hat r\\hat r^*\\ra$\nand $\\la \\hat r\\hat r\\ra$ to characterize its noise.\nBoth of these expressions are sums of terms\nof the general form $\\la \\hat w \\hat x^* \\hat y^* \\hat z\\ra$, or $\\la \\hat w \\hat x^* \\hat y \\hat z^*\\ra$.\nUp to 2 of the 4 quantities $\\hat w \\hat x \\hat y \\hat z$ can be\nidentical \nfor the cross-power spectrum,\nand all of them can be identical for the autocorrelation spectrum.\nThe identical quantities result in special cases, for quantized data,\nas Jenet \\& Anderson found. \n\nPrecisely along the lines of the discussion of the second moments\nin the preceding section,\nexpansion of the fourth moments into real and imaginary parts \nyields statistical averages of the form $\\la \\hat W \\hat X \\hat Y \\hat Z\\ra$,\nwhere $W$ $X$ $Y$ and $Z$ are real quantities drawn from \na multivariate Gaussian distribution.\nThe first column of Table\\ \\ref{table_real_avgs} lists the terms\nimportant for the correlation functions.\nI expand the multivariate Gaussian distribution\nfor $W$ $X$ $Y$ and $Z$ through second order in covariances\n$\\rho_{WX}$, $\\rho_{WY}$, and so on;\nthis yields the terms in the second column of Table\\ \\ref{table_real_avgs},\ntimes 1D Gaussian distributions for each variable.\nMultiplication by the quantizing functions\n$\\hat W(W)$ $\\hat X(X)$ $\\hat Y(Y)$ and $\\hat Z(Z)$ and integration over the distributions\nyields the averages in the third column of Table\\ \\ref{table_real_avgs}.\nThese averages of quantized real (or imaginary) quantities \ncombine to yield the averages of quantized complex quantities\ngiven in Table\\ \\ref{table_complex_avgs}.\nI then combine these averages, using the schemes summarized in Table\\ \\ref{table_terms_in_Xsums}\nto find expressions for the variance of the cross-correlation function $\\hat r$.\n\n\\subsubsection{$\\la\\hat r\\hat r^*\\ra - \\la\\hat r\\ra\\la\\hat r^*\\ra$}\\label{rtrtc}\n\nThe noise in the modulus of the correlation function,\n$\\la\\hat r\\hat r^*\\ra - \\la\\hat r\\ra\\la\\hat r^*\\ra$,\ngives the average diameter of the error ellipse for $\\hat r$.\nTo find this,\none must calculate\n\\begin{equation}\n\\la\\hat r_\\tau\\hat r_\\ups^*\\ra = {{1}\\over{(2 N_o)^2}} \n\\sum_{\\ell, m =1}^{N_o}\n\\la x_{\\ell}y^*_{\\ell+\\tau}x^*_{m}y_{m+\\ups} \\ra .\n\\label{quant_rtruc}\n\\end{equation}\nAgain,\nI assume that covariances between terms are small,\nso that expansion through second order is sufficient.\n\nThe calculation \nis straightforward when\nall 4 of the averaged elements are different: \nin other words, when\n$\\ell\\neq m$ and $\\ell+\\tau\\neq m+\\ups$.\nIn this case,\nthe average is proportional to\nthat expected for continuous correlation, Eq.\\ \\ref{continuous_fourth_moment}:\n\\begin{equation}\n\\la \\hat x_\\ell \\hat y_{\\ell+\\tau}^* \\hat x_m^* \\hat y_{m+\\ups} \\ra = \n\\big[4 B_X^2 B_Y^2\\big] \\rho_\\tau \\rho_\\ups^* + \\big[4 B_X^2 B_Y^2\\big] \\left( \\alp_{m-\\ell}\\alp_{-(m-\\ell)+(\\tau-\\ups)}\\right) .\n\\label{WXcYZc}\n\\end{equation}\nThis is the average given by the term\n$\\la \\hat w \\hxc \\hyc \\hat z \\ra$ in Table\\ \\ref{table_complex_avgs},\nwhere it appears as ``class'' $1111+$.\nThe 1's indicate that one term of each variable appears once;\nthe ``$+$'' indicate the symmetry of average under \nmultiplication of $x$ by $e^{i\\pi/2}$, or equivalently\nrotation by $\\pi/2$ in the complex plane.\n% xxx better way to express this\nThis term also appears in Table\\ \\ref{table_terms_in_Xsums},\nwith ID ``Xcn.0''. \nIn this identifier,\nthe ``X'' indicates cross-correlation,\nthe ``c'' indicates the product of $\\hat r$ with its conjugate: $\\hat r\\hat r^*$,\nthe ``n'' indicates that $\\tau\\neq\\ups$,\nand the ``0'' indicates that the indices $\\ell$, $m$, $\\ell+\\tau$, and $m+\\ups$ are distinct.\nAs the table indicates under ``Multiplicity,'' \nthis form of term appears $N_o^2-2 N_o$ times in the sum.\n\nIf \n$\\tau\\neq\\ups$, but $\\ell=m$, then one encounters the average\n\\begin{equation}\n\\la \\hat x_\\ell \\hat y_{\\ell+\\tau}^* \\hat x_\\ell^* \\hat y_{\\ell+\\ups} \\ra = \n\\big[2 (C_{X2}-A_{X2})B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups}^* \n+\\big[4 A_{X2}B_Y^2\\big]\\alp_{(\\tau-\\ups)}.\n\\label{WXcWcY}\n\\end{equation}\nThis term has\nthe form $\\la \\hat w \\hxc \\hwc \\hat y \\ra$, and ``Class'' $211+$ in\nTable\\ \\ref{table_complex_avgs}.\nIt appears as ``Xcn.1'' in Table\\ \\ref{table_terms_in_Xsums},\nand appears $N_o$ times in the sum.\n\nIf $\\tau\\neq\\ups$, but $\\ell+\\tau=m+\\ups$, one then encounters\n\\begin{equation}\n\\la \\hat x_\\ell \\hat y_{\\ell+\\tau}^* \\hat x_{\\ell+\\tau-\\ups}^* \\hat y_{\\ell+\\tau} \\ra = \n\\big[2 B_X^2(C_{Y2}-A_{Y2})\\big]\\rho_{\\tau}\\rho_{\\ups}^* +\\big[4 B_X^2A_{Y2}\\big]\\alp_{(\\tau-\\ups)}\\; .\n\\label{WXcYcX}\n\\end{equation}\nThis term also has\nthe form $\\la \\hat w \\hxc \\hwc \\hat y \\ra$, and Class $211+$ in\nTable\\ \\ref{table_complex_avgs}.\n(Note however that the roles of $\\hat x$ and $\\hat y$ \nare interchanged from those in Table\\ \\ref{table_complex_avgs}).\nIt appears as ``Xcn.2'' in Table\\ \\ref{table_terms_in_Xsums},\nand appears $N_o$ times in the sum.\n\nFrom Eqs.\\ \\ref{WXcYZc} through\\ \\ref{WXcYcX}, I evaluate the sum, Eq.\\ \\ref{quant_rtruc} (for $\\tau\\neq\\ups$):\n\\begin{eqnarray}\n\\la \\hat r_{\\tau} \\hat r_{\\ups}^*\\ra &=& \n{{1}\\over{(2 N_o)^2}}\\biggl\\{\nN_o^2 \\big[4 B_x^2 B_y^2\\big]\\rho_\\tau\\rho_\\ups^* \n+N_o \\sum_{n=1}^{N_o}\\big[4 B_x^2 B_y^2\\big]\\alp_{-n} \\alp_{n+(\\tau-\\ups)} \\label{prolix_digital_rtruc} \\\\\n&&\\phantom{{{1}\\over{(2 N_o)^2}}}\n-2\\times N_o \\Bigl\\{\\big[ 4B_x^2 B_y^2\\big]\\rho_\\tau \\rho_\\ups^* + \\big[ 4B_x^2 B_y^2\\big]\\alp_0 \\alp_{(\\tau-\\ups)} \\Bigr\\} \\nonumber \\\\\n&&\\phantom{{{1}\\over{(2 N_o)^2}}}\n+N_o \\left(\\big[2(C_{X2}-A_{X2})B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups}^* \n+\\big[4 A_{X2}B_Y^2\\big]\\alp_{(\\tau-\\ups)}\\right) \\nonumber \\\\\n&&\\phantom{{{1}\\over{(2 N_o)^2}}}\n+N_o \\left(\\big[2B_X^2(C_{Y2}-A_{Y2})\\big]\\rho_{\\tau}\\rho_{\\ups}^* +\\big[ 4B_X^2A_{Y2}\\big]\\alp_{(\\tau-\\ups)}\\right) \\biggr\\} . \\nonumber\n\\end{eqnarray}\nNote that the first 2 terms on the right side of this equation \ngive the contribution for all unlike $w x y z$, Eq.\\ \\ref{WXcYZc},\nwith multiplicity $2 N_o$ greater than correct.\nThe second 2 terms subtract off the extras for the special cases $\\ell=m$ and $\\ell+\\tau=m+\\ups$,\nwith multiplicity of $N_o$ each;\nand the last 4 terms add back in the correct contributions for these 2 special cases\n(Eqs.\\ \\ref{WXcWcY} and\\ \\ref{WXcYcX}),\nwith multiplicity $N_o$ each.\nEq.\\ \\ref{prolix_digital_rtruc} simplifies to:\n% refer: /home/egret/cgwinn/tex/noise/spect/FT.spect_35.8.nb \n\\begin{eqnarray}\n\\la\\hat r_{\\tau}\\hat r_{\\ups}^*\\ra \n% &=& \\big[B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups} +\n&-& \\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\ups}^*\\ra =\n{{1}\\over{2 N_o}}\\sum_{n=1}^{N_o}\\big[2B_X^2 B_Y^2\\big]\\alp_{n+(\\tau-\\ups)}\\alp_{-n} \\label{digital_rtruc} \\\\\n&&+{{1}\\over{2 N_o}}\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups}^* \\nonumber \\\\\n&&+{{1}\\over{2 N_o}}\\big[2A_{X2}B_Y^2+2B_X^2A_{Y2}-4B_X^2 B_Y^2\\big]\\alp_{(\\tau-\\ups)} . \\nonumber\n\\end{eqnarray}\n\nSimilarly, when $\\tau=\\ups$, the contributing terms are given under Xce in \nTable\\ \\ref{table_terms_in_Xsums}.\nThe case $\\ell=m$ again presents a special situation;\nfor $\\tau=\\ups$ this case is identical to $\\ell+\\tau = m+\\ups$.\nWith this special case $\\ell=m$ again included incorrectly,\nsubtracted back off, and then added in correctly, one finds:\n\\begin{eqnarray}\n\\la \\hat r_{\\tau} \\hat r_{\\tau}^*\\ra\n% &=& \\big[B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups} +\n &-& \\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\tau}^*\\ra =\n{{1}\\over{2 N_o}}\\sum_{n=1}^{N_o}\\big[2 B_X^2 B_Y^2\\big]\\alp_n\\alp_{-n} \\label{digital_rtrtc} \\\\\n&&+{{1}\\over{2 N_o}}\\big[\\haf(C_{X2}-A_{X2})(C_{Y2}-A_{Y2})-2B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\tau}^* \\nonumber \\\\\n&&+{{1}\\over{2 N_o}}\\big[2A_{X2}A_{Y2}-2B_X^2 B_Y^2\\big] \\nonumber\n\\end{eqnarray}\n\n\\subsubsection{$\\la\\hat r\\hat r\\ra - \\la\\hat r\\ra\\la\\hat r\\ra$}\\label{rtrt}\n\nThe variance of the correlation function,\ngiven by $\\la\\hat r \\hat r\\ra - \\la\\hat r\\ra\\la\\hat r\\ra$,\nmeasures the departure of the error ellipse for $\\hat r$ from circularity.\nAs in the previous section, \nthe averages for which 2 or more of the elements of the sum are identical\nmust be calculated separately.\nFor $\\tau\\neq\\ups$, the terms appear under Xrn in Table\\ \\ref{table_terms_in_Xsums}.\nThis yields:\n\\begin{eqnarray}\n\\la\\hat r_{\\tau}\\hat r_{\\ups}\\ra \n% &=& \\big[2B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups} +\n&-& \\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\ups}\\ra =\n{{1}\\over{2 N_o}}\\sum_{n=1}^{N_o} \\big[2B_X^2 B_Y^2\\big]\\rho_{n+(\\tau+\\nu)}\\rho_{-n} \\label{digital_rtru} \\\\\n&&+{{1}\\over{2 N_o}}\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\ups} \\; . \\nonumber\n\\end{eqnarray}\nSimilarly for $\\tau=\\ups$,\nfor which the terms appear under Xre in Table\\ \\ref{table_terms_in_Xsums}:\n\\begin{eqnarray}\n\\la\\hat r_{\\tau}\\hat r_{\\tau}\\ra \n% &=& \\big[B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\tau}\n&-& \\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\tau}\\ra = \n{{1}\\over{2 N_o}}\\sum_{n=1}^{N_o} \\big[2B_X^2 B_Y^2\\big]\\rho_{n+(2\\tau)}\\rho_{-n} \\label{digital_rtrt} \\\\\n&&+{{1}\\over{2 N_o}}\\big[(\\haf(C_{X2}-A_{X2})+B_X^2)(\\haf(C_{Y2}-A_{Y2})+B_Y^2)-4B_X^2 B_Y^2\\big]\\rho_{\\tau}\\rho_{\\tau} \\nonumber\\\\\n&&+{{1}\\over{2 N_o}}\\big[(\\haf(C_{X2}-A_{X2})-B_X^2)(\\haf(C_{Y2}-A_{Y2})-B_Y^2)\\big]\\rho_{\\tau}^*\\rho_{\\tau}^* . \\nonumber\n\\end{eqnarray}\n% Note that the autocorrelation of the cross-correlation function appears in both cases $\\tau\\neq\\ups$\n% and $\\tau=\\ups$.\n\n\\subsubsection{Simulation of Cross-Correlation Function}\\label{xcf_simulate}\n\nFigure\\ \\ref{dxcf_noiseplot}\nshows statistics,\nin the lag domain,\nfor\nthe simple correlation function shown in\nFigure\\ \\ref{dxcf_avgplot}.\nPlots on the left show\n$\\la\\hat r_{\\tau}\\hat r_{\\ups}^*\\ra\n-\\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\ups}^*\\ra$,\nand on the right \n$\\la\\hat r_{\\tau}\\hat r_{\\ups}\\ra\n-\\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\ups}\\ra$ .\nThe upper plot shows\nthe arrangement of nonzero terms,\nand the lower plot gives their values.\n\nThe diagonal terms are the \nsquared standard deviations\nof the amplitude\nof $\\hat r_{\\tau}$,\nas given by Eq.\\ \\ref{digital_rtrtc}.\nThe off-diagonal terms give the covariances\nof the noise between lags,\nas given by Eq.\\ \\ref{digital_rtruc}.\n\nThe right panels show the moments\n$\\la\\hat r_{\\tau}\\hat r_{\\tau}\\ra\n-\\la\\hat r_{\\tau}\\ra\\la\\hat r_{\\tau}\\ra$.\nFor a real cross-correlation function\n(like that used here),\nthe diagonal terms are the {\\it differences}\nof the standard deviations of real and imaginary\nparts of $\\hat r_{\\tau}$,\nas given by\nEq.\\ \\ref{digital_rtrt}.\nThey thus measure the departure\nof the noise from isotropy in phase.\nThese terms are proportional to squares or products of the cross-correlation function $\\rho$.\nFor this test data, $\\rho^2=0.16$, and so these terms are smaller than the largest terms in the left panels.\nThis indicates that the error ellipses for the correlation function are approximately circular.\n\n\\subsection{Autocorrelation Functions}\\label{acf_subsection}\n\nAutocorrelation correlation functions and spectra present many special cases.\nOn the other hand,\nfor the autocorrelations \nthe ``zero lags'' $\\tau=0$ and $\\ups=0$\nyield unit correlation, and thus play a special role;\nthis is unlike the cross-correlations,\nwhere the quantities being correlated\nare distinct at any lag.\nFortunately, one needs only one of $\\la\\hah_{\\tau}\\hac_{\\ups}\\ra$\nand $\\la\\hah_{\\tau}\\hah_{\\ups}\\ra$\nbecause \n$\\la\\hah_{\\tau}\\hah_{\\ups}\\ra =\\la\\hah_{\\tau}\\hac_{-\\ups}\\ra$.\nFurthermore, $X$ and $Y$ are the same,\nso I simplify the notation by dropping the subscripts from the integrals $A$, $B$, $C$.\n\nFor the case\n$\\tau\\neq\\ups$, \nwe have the the general case where neither $\\tau$ nor $\\ups$ is $0$, as well as the special sub-cases $\\tau=0$ and $\\ups=0$.\nTable\\ \\ref{table_terms_in_Asums} summarizes these various\ncases,\nwith identifiers Antu, An0u and Ant0.\nIn these identifiers,\n``A'' indicates autocorrelation,\n``n'' indicates $\\tau\\neq\\ups$,\nand ``0u'' indicates $\\tau=0$ whereas ``t0'' indicates $\\ups=0$.\nWithin these cases we have the same special\ncases as for the cross-correlation function\n$\\ell=m$ and $\\ell+\\tau=m+\\ups$,\nplus the special cases $\\ell+\\tau=m$\nand $\\ell=m+\\ups$, which are special cases for autocorrelation\n(although not for cross-correlation).\nThese are listed as Antu.1, Antu.2, etc.\nSome of these special cases become degenerate when\n$\\tau=0$ or $\\ups=0$.\n\nI adopt the previous strategy of \nsubtracting off, and then adding back in, contributions for the special cases.\nFor autocorrelations with $\\tau\\neq\\ups$, \nand both $\\tau\\neq 0$ and $\\ups\\neq 0$,\nthis requires \nthe ``Antu'' terms in Table\\ \\ref{table_terms_in_Asums}.\n% Added together with the correct multiplicity, they are:\n% \\begin{eqnarray}\n% \\la\\hah_{\\tau}\\hac_{\\ups}\\ra&=&{{1}\\over{(2 N_o)^2}}\\biggl\\{ N_o^2 \\big[4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups} + N_o \\sum_n \\big[4B^4\\big]\\alp_{n} \\alp_{-n+(\\tau-\\ups)} \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% -2\\times N_o \\Bigl\\{\\big[4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups} + \\big[4B^4\\big]\\alp_{0} \\alp_{(\\tau-\\ups)}\\Bigr\\} \\nonumber \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% +N_o\\left(\\big[2(C-A)B^2\\big]\\alp_{\\tau}\\alp_{-\\ups}+\\big[4AB^2\\big]\\alp_{\\tau-\\ups}\\right) \\nonumber \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% +N_o\\left(\\big[2(C-A)B^2\\big]\\alp_{\\tau}\\alp_{-\\ups}+\\big[4AB^2\\big]\\alp_{\\tau-\\ups}\\right) \\nonumber \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% -2\\times N_o \\Bigl\\{\\big[4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups} + \\big[4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups}\\Bigr\\} % \\nonumber \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% +N_o\\left(\\big[2(C-A)B^2+4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups}\\right) \\nonumber \\\\\n% &&\\phantom{{{1}\\over{(2 N_o)^2}}}\n% +N_o\\left(\\big[2(C-A)B^2+4B^4\\big]\\alp_{\\tau}\\alp_{-\\ups}\\right) \n% \\biggr\\} \\nonumber\n% \\end{eqnarray}\n% Here I have defined $n=\\ell-m$. Note that $\\ell-m$ takes on different values in the sub-cases\n% Antu.3 or Antu.4, as compared with Antu.1 or Antu.2, so that the correction terms are different.\n% This simplifies to:\nThe sum simplifies to:\n\\begin{eqnarray}\n\\la\\hah_{\\tau}\\hac_{\\ups}\\ra &-& \\la\\hah_{\\tau}\\ra\\la\\hac_{\\ups}\\ra =\n{{1}\\over{2N_o}} [2B^4]\\sum_{n=1}^{N_o} \\alp_n \\alp_{-n+(\\tau-\\ups)} \\label{A1_sum} \\\\ \\label{auto_1}\n&&+{{1}\\over{2N_o}}[4(C-A)B^2-8 B^4]\\alp_{\\tau}\\alp_{-\\ups} \\label{auto_2}\n+{{1}\\over{2N_o}}[4 A B^2 -4 B^4]\\alp_{\\tau-\\ups} . \\nonumber \\label{auto_3}\n\\end{eqnarray}\nHere I have defined $n=\\ell-m$. Note that $\\ell-m$ takes on different values in the sub-cases\nAntu.3 or Antu.4, as compared with Antu.1 or Antu.2, so that the correction terms are different.\nThis equation is analogous to, but different from, Eq.\\ \\ref{digital_rtruc}, with which it should be compared.\n\nIn the case $\\ups=0$, $\\tau\\neq\\ups$ (Ant0 in Table\\ \\ref{table_terms_in_Asums}), one obtains:\n\\begin{eqnarray}\n\\la \\hah_{\\tau} \\hah_0\\ra & - & \\la\\hah_{\\tau}\\ra\\la\\hah_{0}\\ra =\n{{1}\\over{2N_o}} [(C-A)B^2]\\sum_{n=1}^{N_o} (\\alp_{(n+\\tau)} \\alp_{-n}) \\label{ata0c} \\\\ \\label{auto_4A}\n&&+{{1}\\over{2 N_o}}[2 B_3 B - 2 C B^2]\\alp_{\\tau} . \\nonumber \\label{auto_5A}\n\\end{eqnarray}\nNote here that $B=\\int dX\\, X e^{-{{1}\\over{2}}X^2} \\hat X(X)$, whereas \n$B_3=\\int dX\\, X e^{-{{1}\\over{2}}X^2} (\\hat X(X))^3$. (See Paper 1.)\n\nOne obtains the analogous expression in the case $\\tau=0$, $\\tau\\neq\\ups$ (An0u in Table\\ \\ref{table_terms_in_Asums}).\n\nIn the case $\\tau=\\ups$, $\\tau\\neq 0$ (Aet in Table\\ \\ref{table_terms_in_Asums}), one obtains:\n\\begin{eqnarray}\n\\la \\hah_{\\tau} \\hac_{\\tau}\\ra &-& \\la\\hah_{\\tau}\\ra\\la\\hac_{\\tau}\\ra = \n{{1}\\over{2 N_o}} [2 B^4] \\sum_n (\\alp_n \\alp_{-n}) \\\\ \\label{auto_6}\n&& + {{1}\\over {2 N_o}} [2 A^2 - 2 B^4] \\label{auto_7}\n+ {{1}\\over {2 N_o}}[ (\\haf)((C-A)+2 B^2)^2\\,-\\,8 B^4 ] (\\alp_{\\tau}\\alp_{\\tau}^*) . \\nonumber \\label{auto_8}\n\\end{eqnarray}\nThis equation is analogous to Eq.\\ \\ref{digital_rtrtc}.\nFinally, in the case $\\tau=\\ups=0$ (Ae0 in Table\\ \\ref{table_terms_in_Asums}), one obtains:\n\\begin{eqnarray}\n\\la \\hah_0 \\hac_0\\ra &-& \\la \\hah_0\\ra\\la \\hac_0\\ra = \n{{1}\\over{2 N_o}}[\\haf (C-A)^2]\\sum_n (\\alp_n \\alp_{-n}) \\label{a0a0c} \\\\ \\label{auto_9}\n&& +{{1}\\over{2 N_o}}[ A_4 - 2 A^2 - \\haf(C-A)^2] . \\nonumber \\label{auto_10}\n\\end{eqnarray}\nNote here that $A=\\int dX\\, X e^{-{{1}\\over{2}}X^2} (\\hat X(X))^2$,\nwhereas $A_4=\\int dX\\, X e^{-{{1}\\over{2}}X^2} (\\hat X(X))^4$.\n\n\\section{SPECTRA OF QUANTIZED SIGNALS}\\label{section_quantspectrum}\n\nThe measured spectrum \nis the Fourier transform of the measured correlation function.\nThus, for quantized data, the cross-power spectrum $\\ckr$ and the autocorrelation spectrum $\\cke$ are:\n\\begin{eqnarray}\n\\ckr_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} \\hat r_{\\tau} . \\\\\n\\cke_k &=& \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} \\hat a_{\\tau} . \\nonumber\n\\end{eqnarray}\n\\citet{jen98} show that the proportionality factor found by \\citet{coo70} relates \nthe average of the quantized cross-power spectrum $\\la \\ckr \\ra$ \nto the true cross-power spectrum $\\twp$;\nand the same factor, \nwith an offset resulting from the spike at zero lag, relates $\\la \\cke \\ra$ to $\\twa$.\n\nNoise in the spectrum is related to noise in the autocorrelation function by a double Fourier transform.\nI use this fact to find the noise in the spectrum, through second order in $\\alp$ and $\\rho$, in\nthis section. I find that many of the terms for noise in the correlation functions are diluted over the channels of the spectrum. They can be neglected, in many cases, for spectra containing many\nchannels. I find that the dominant terms for noise in individual channels of the spectra are\nanalogous to results for continuous spectra,\ngiven by Eqs.\\ \\ref{continuous_twrktwrkc} and \\ref{continuous_twrktwrk}.\nI also find that the noise is correlated between channels.\nThis is opposite the conclusion for continuous data (\\S\\ref{noise_uncorr_continuous}).\n\n\\subsection{Mean Spectra for Quantized Signals}\\label{spectra_mean}\n\nThe Fourier transform of the proportionality \nEq.\\ \\ref{avg_rtau_rhotau_prop}\nyields the ensemble-averaged spectrum:\n\\begin{equation}\n\\la \\ckr_k \\ra = B_X B_Y \\twp_k ,\n\\label{avg_hat_rk}\n\\end{equation}\nwhere both sides of the expression are complex.\n\nThe ensemble average of the Fourier transform of the quantized autocorrelation function is:\n\\begin{equation}\n\\la \\twe_k\\ra = \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} \\hat a_{\\tau} .\n\\end{equation}\nThis sum contains $2N-1$ terms involving $\\hat a_{\\tau} = B_X^2 \\alp_{\\tau}$, \nand one involving $\\hat a_{0} = A_{X2}$.\nI adopt the approach, as in calculations of noise,\nof including an incorrect zero-lag term will all others in the sum,\nsubtracting that incorrect term, \nand then adding the correct term:\n\\begin{eqnarray}\n\\la \\twe_k\\ra &=& \\bigg( \\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}k\\tau} B_X^2 \\alp_{\\tau} \\bigg)\n\\; - \\bigg( B_X^2 \\alp_0 \\bigg) \n\\; + \\bigg( A_{X2} \\bigg) . \\label{avg_hat_ak} \\\\\n&=& B_X^2\\left(\\twa_k + \\left({{A_{X2}}\\over{B_X^2}}-1\\right)\\right) . \\nonumber\n\\end{eqnarray}\nThis recovers the results of \\citet{jen98}, who showed that the mean spectrum \nfor quantized data is equal to the statistically-averaged spectrum for continuous data,\nplus an offset, times the gain factor $B_{X}^2$.\n\n\\subsection{Spectral Noise for Quantized Signals}\\label{spectral_noise}\n\n\\subsubsection{Variances: $\\la\\ckr_k\\ckr^*_k\\ra$}\n\nCalculation of the noise in the spectrum involves the Fourier transform of the variance-covariance matrix.\nThe Appendix summarizes facts useful for this transform.\nThe approach is analogous to that taken in \\S\\ref{continuous_spectrum_noise},\nvia a double Fourier transform.\nI use the facts in the Appendix,\ntogether with Eqs.\\ \\ref{digital_rtruc} and\\ \\ref{digital_rtrtc}\nto find:\n\\begin{eqnarray}\n\\la \\ckr_k \\ckr_k^*\\ra &-&\n\\la \\ckr_k\\ra\\la\\ckr_k^*\\ra =\n{{(2N)}\\over{2 N_o}} \n\\big[2(A_{X2}+B_X^2(\\twa_k-1))(A_{Y2}+B_Y^2(\\twa_k-1))\\big] \\label{digital_ckrkckrkc} \\\\\n&&+{{1}\\over{2 N_o}} \n\\big[\\haf(C_{X2}-A_{X2})B_Y^2+B_X^2\\haf(C_{Y2}-A_{Y2})-2B_X^2 B_Y^2\\big] \n\\twp_k\\twp_k^* \\nonumber \\\\\n&&\\,-\\,{{1}\\over{2 N_o}}\n\\big[2(\\haf(C_{X2}-A_{X2})-\\haf B_X^2)(\\haf(C_{Y2}-A_{Y2})-\\haf B_Y^2)-\\haf B_X^2 B_Y^2\\big]\n\\sum_{\\ell=-N}^{N-1} {{1}\\over{(2N)}} \\twp_\\ell\\twp_\\ell^* . \\nonumber\n\\end{eqnarray}\nNote that the first term on the right-hand side is of order $2N$;\nthe second is of order $1$;\nand the third is of order $1/2N$.\n\n\\subsubsection{Variances: $\\la\\ckr_k\\ckr_k\\ra$}\n\nUsing the expressions in the Appendix\ntogether with Eqs.\\ \\ref{digital_rtru} and\\ \\ref{digital_rtrt},\nI find:\n\\begin{eqnarray}\n\\la \\ckr_k \\ckr_k\\ra &-& \\la\\ckr_k\\ra\\la\\ckr_k\\ra = \n+{{(2N)}\\over{(2N_o)}}\\big[2B_X^2 B_Y^2\\big]\\twp_k\\twp_k \\label{digital_ckrkckrk} \\\\\n&&+{{1}\\over{(2N_o)}}\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2B_Y^2\\big]\n\\twp_k\\twp_k \\nonumber \\\\\n&&+{{1}\\over{(2N_o)}}\\big[(\\haf(C_{X2}-A_{X2})-B_X^2)(\\haf(C_{Y2}-A_{Y2})-B_Y^2)\\big] \n{{1}\\over{(2N)}} \\left( \\tilde C_{\\rho}(k) + \\tilde C_{\\rho}^*(-k) \\right) . \\nonumber \n\\end{eqnarray}\nAgain, the first term on the right-hand side is of order $2N$,\nthe second of order $1$, and the third of order $1/2N$.\n\n\\subsection{Correlation of Noise Across Spectral Channels}\n\nFor quantized data, noise in different spectral channels can be correlated.\nThe correlation of noise between channels involves $\\la \\ckr_k \\ckr_{\\ell}^* \\ra$, with $k\\neq\\ell$.\nThese covariances can be\ncalculated by the double Fourier transform of Eqs.\\ \\ref{digital_rtruc} and\\ \\ref{digital_rtrtc}.\n% \\begin{equation}\n% \\la\\ckr_k\\ckr_{\\ell}^*\\ra = \\sum_{\\tau=-N}^{N-1}\\sum_{\\ups=-N}^{N-1}\n% e^{i{{2\\pi}\\over{2N}}(k\\tau-\\ell\\ups)}\\la\\hat r_{\\tau}\\hat r_{\\ups}^*\\ra ,\n% \\label{ckrkckrlc_def}\n% \\end{equation}\n% with $k\\neq\\ell$;\n% and the analogous fact for $\\la\\ckr_k\\ckr_{\\ell}\\ra$\n\n\\subsubsection{Covariances: $\\la\\ckr_k\\ckr_{\\ell}^*\\ra$}\\label{covar_ckrckrc}\n\nFor calculation of covariances between channels, \nclassification of the terms in Eq.\\ \\ref{digital_rtruc} and\\ \\ref{digital_rtrtc}\nis helpful.\nIn Eq.\\ \\ref{digital_rtruc}, the first term on the right-hand\nside is proportional to the autocorrelation function $\\alpha$ convolved with itself,\nthe second is proportional to the square of the cross-correlation function $\\rho$,\nand the third is proportional to $\\alpha$.\nOf these, only the second will contribute to \nthe covariance between channels.\n% % Eq.\\ \\ref{ckrkckrlc_def}.\n% In particular,\n% consider the double Fourier transform of the third term, and note that:\n% \\begin{eqnarray}\n% \\sum_{\\tau=-N}^{N-1}\\sum_{\\ups=-N}^{N-1}\n% e^{i{{2\\pi}\\over{2N}}(k\\tau-\\ell\\ups)}\\alp_{(\\tau-\\ups)} \n% &=&\\sum_{\\tau=-N}^{N-1}\\sum_{\\lambda=-N}^{N-1} \n% e^{i{{2\\pi}\\over{2N}}(k\\tau-\\ell(\\tau-\\lambda))}\\alp_{\\lambda} ,\n% \\quad {\\rm where}\\ \\lambda=\\tau-\\ups\n% \\label{contributes_nothing_to_covar}\n% \\\\\n% &=&\\sum_{\\tau=-N/2}^{N/2-1}\\sum_{\\lambda=-N/2}^{N/2-1}\n% e^{i{{2\\pi}\\over{2N}}((k-\\ell)\\tau +\\ell\\lambda)}\\alp_{\\lambda}\n% =0 ,\\quad {\\rm for}\\ k\\neq \\ell \\; ,\n% \\nonumber \n% \\end{eqnarray}\n% where the sum over $\\tau$ yields 0 unless $k=\\ell$.\n% The same construction serves to show that the contribution\n% of the first term, the convolution of $\\alpha$ with itself, is also 0. \nNone of the 3 terms on the right-hand side of Eq.\\ \\ref{digital_rtrtc} contribute either,\nfor $k\\neq\\ell$.\nThus, only the second term on the right-hand side of Eq.\\ \\ref{digital_rtruc}\ncontributes, and it contributes in a simple way:\n\\begin{equation}\n\\sum_{\\tau=-N}^{N-1}\\sum_{\\ups=-N}^{N-1}\ne^{i{{2\\pi}\\over{2N}}(k\\tau-\\ell\\ups)}\\rho_{\\tau}\\rho_{\\ups}^* =\n\\twp_k\\twp_{\\ell}^* ,\n\\end{equation}\nso that\n\\begin{equation}\n\\la\\ckr_k\\ckr_{\\ell}^*\\ra -\\la\\ckr_k\\ra\\la\\ckr_{\\ell}^*\\ra \n= \n{{1}\\over{2 N_o}}\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2 B_Y^2\\big]\n\\twp_k\\twp_{\\ell}^* ,\\quad {\\rm for}\\ k\\neq\\ell .\n\\label{covar_pkplc}\n\\end{equation}\n% mean SHOULD be subtracted off here -- added this 1 May 2005 xxx\nThe combination of constants \n$\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2 B_Y^2\\big]$\nis always less than 0\nfor $n=3$ (although it can be positive for other values of\n$n$), so the covariance is negative in that case.\nIn other words, when noise increases the height of one\nspectral peak, noise will tend to reduce the heights of\nother spectral peaks.\nNote that the contribution of $\\twp_k\\twp_k^*$ to the variance\nappears in the covariance as well:\nthis contribution to the noise is perfectly correlated between spectral channels.\n\n\\subsubsection{Covariances: $\\la\\ckr_k\\ckr_{\\ell}\\ra$}\\label{covar_ckrckr}\n\nThe covariances $\\la\\ckr_k\\ckr_{\\ell}\\ra$ can be found from \nEqs.\\ \\ref{digital_rtru} and\\ \\ref{digital_rtrt}.\n% and\n% \\begin{equation}\n% \\la\\ckr_k\\ckr_{\\ell}\\ra = \\sum_{\\tau=-N}^{N-1}\\sum_{\\ups=-N}^{N-1}\n% e^{i{{2\\pi}\\over{2N}}(k\\tau+\\ell\\ups)}\\la\\hat r_{\\tau}\\hat r_{\\ups}\\ra .\n% \\label{ckrkckrl_def}\n% \\end{equation}\nAs in the preceding section, % \\S\\ref{covar_ckrckrc},\nclassification of the terms in\nEqs.\\ \\ref{digital_rtru} and\\ \\ref{digital_rtrt} is helpful.\nIn both expressions,\nthe first term is proportional to the convolution of the \ncross-power spectrum with itself;\nit does not contribute to the covariance.\n% by an argument parallel to Eq.\\ \\ref{contributes_nothing_to_covar}.\nThe other terms in Eq.\\ \\ref{digital_rtrt} also contribute nothing.\nWe thus obtain:\n\\begin{equation}\n\\la\\ckr_k\\ckr_{\\ell}\\ra -\\la\\ckr_k\\ra\\la\\ckr_{\\ell}\\ra = \n{{1}\\over{2 N_o}}\\big[(C_{X2}-A_{X2})B_Y^2+B_X^2(C_{Y2}-A_{Y2})-4B_X^2 B_Y^2\\big]\n\\twp_k\\twp_{\\ell} ,\\quad k\\neq\\ell .\n\\label{covar_pkpl}\n\\end{equation}\n% means SHOULD be subtracted off -- 1 May 2005\nThe covariances have the same coefficient for variances $\\la\\ckr_k\\ckr^*_{\\ell}\\ra$ \nand $\\la\\ckr_k\\ckr_{\\ell}\\ra$ .\n\n\\subsubsection{Simulation of Cross-Power Spectrum}\\label{xps_simulate}\n\nI Fourier transformed each of the simulated correlation\nfunctions from the simulation and form spectra.\nThe statistical properties of these spectra are in\ngood agreement with the results of \\S\\ref{spectral_noise}.\nFigure\\ \\ref{phasor_plot} shows an example spectrum as\na phasor plot.\nThis is the spectrum\ncorresponding to the correlation function\nof Figures\\ \\ref{dxcf_avgplot} and\\ \\ref{dxcf_noiseplot},\nplotted in phasor form.\nThe prediction is plotted as a solid line,\nusing Fourier interpolation.\n% :\n% \\begin{equation}\n% \\la\\ckr_k\\ra = B_X B_Y\\; 0.4 \n% \\big\\{ e^{i{2\\pi}\\over{8} k}+e^{i{2\\pi}\\over{8} 2 k} \\big\\}.\n% \\end{equation}\nThe mean measurements in the discrete channels are plotted as points,\nand surrounded by error ellipses that give the spread.\nThe error ellipses for each point have major axes that point toward\nthe origin of the complex plane;\nthis is a consequence of the fact that,\nfor this choice of parameters,\nthe first term on the right-hand side of Eq.\\ \\ref{digital_ckrkckrk}\ndominates the other 2,\nand it is proportional to $\\rho_k^2$.\nThis term defines the major axis.\n\nFigure\\ \\ref{noisecompare}\nshows a spectrum and the standard deviations plotted in more traditional\nform.\nAgain, I use Fourier interpolation to show\nthe model as a continuous function of the channel index, $k$.\n\n\\subsubsection{Spectrally-Correlated Noise: Simulation}\n\nFigure\\ \\ref{correl} shows an example of correlated noise in\ntwo spectral channels.\nFor this simulation I used a different initial spectrum and correlator parameters,\nmore suited to showing the covariance.\nBoth channels have strong signals, with zero phase, \nas the spectrum in the upper panel shows.\nThe lower panel shows results of simulations of correlation of quantized data.\nThe mean values $\\re[\\la\\ckr_k]$ and $\\re[\\ckr_{\\ell}\\ra]$\nlocate the centroid of the ellipse.\nNoise gives the ellipse extension.\nThe covariance of noise tilts the ellipse:\nwhen $\\ckr_k$ is smaller than its mean,\n$\\ckr_{\\ell}$ tends to be larger; and vice versa.\nThis demonstrates the correlation of noise between two channels.\n\nComparison of Eqs.\\ \\ref{covar_pkplc} and\\ \\ref{covar_pkpl}\nshows that the correlated noise is in phase with the underlying signals:\nin other words, if both $\\ckr_k$ and $\\ckr_{\\ell}$ are real,\nthen the noise between real parts is correlated,\nbut the imaginary parts are uncorrelated. Thus, the figure corresponding\nto\\ \\ref{correl} for imaginary parts would show an ellipse\ncentered at the origin, with principal axes aligned with the coordinate axes.\n\n\\subsection{Autocorrelation Spectra}\\label{acspect_subsection}\n\nFor the autocorrelation function, the\nspecial cases of $\\tau=0$, or $\\ups=0$, or both,\ndescribed by Eqs.\\ \\ref{ata0c} and\\ \\ref{a0a0c},\nlead to additional correction terms that must be included in the sums.\n\nIt is useful to classify the terms in Eqs.\\ \\ref{ata0c} and\\ \\ref{a0a0c}.\nSome involve a factor of the autocorrelation of the\nautocorrelation function $\\alp_{\\tau}$,\n$\\sum_{n=1}^{N_o} \\alp_{n+\\tau} \\alp_{-n}\\pa$.\nOthers involve a simple factor of $\\alp_{\\tau}$,\nor the product $\\alp_{\\tau} \\alp_{-\\ups}$.\nFinally, some terms in the special case\n$\\tau=\\ups=0$ do not involve $\\alp$ at all: they are constants.\nThese 3 types of terms Fourier transform in different ways.\n% The Fourier transform of the autocorrelation of the\n% autocorrelation function is the square modulus of the spectrum,\n% as given by Eq.\\ \\ref{convolution_fact}.\n% The Fourier transform of $\\alp_{\\tau}$ is, of course, $\\twa$,\n% and that of $\\alp_{\\tau}\\alp_{-\\ups}$\n% is, in this case, $\\twa_k \\twa_k^*$.\n% The Fourier transforms of a constant at \n% $\\tau=\\ups=0$ is a constant present in all channels.\nThe additional correction terms also have terms\nof the first and second sort.\nThe Appendix gives expressions helpful for the three sorts of Fourier transforms.\n\nThe Fourier transform of Eqs.\\ \\ref{A1_sum} through\\ \\ref{a0a0c}\nyields:\n\\begin{eqnarray}\n\\la \\twa_k \\twa_k^*\\ra &-& \\la \\twa_k\\ra\\la\\twa_k^*\\ra = \n{{(2 N)}\\over{(2 N_o)}} \\Big[2\\big(A+B^2(\\twa_k-1)\\big)^2 \\Big] \\label{digital_akakc} \\label{FT_auto_1n3n7+}\n% \\\\\n% &&+{{1}\\over{2 N_o}} \\big[6(C-A)B^2 - 12 B^4\\big] \\twa_k\\twa_k^* \\\\ \\label{FT_auto_2}\n% &&+{{1}\\over{2 N_o}} 2 \\big[2 B_3 B - 6 C B^2 + 12 B^4\\big] \\twa_k \\\\ \\label{FT_auto_2x5p}\n% &&+{{1}\\over{2 N_o}} \\big[A_4-4 A^2 + 9 B^4 -((C-A)+B^2)^2\\big] \\\\ \\label{FT_auto_10p}\n% &&+{{1}\\over{2 N_o}} \\big[ ({1}\\over{2}}) ((C-A)^2+4(C-A)B^2-4 B^4) \\big] \\\\\n% {{1}\\over{2 N}} \\sum_{k=-N}^{N-1} \\twa_k \\twa_k^* \\\\ \\label{FT_auto_8p}\n% &&+{{1}\\over{2 N_o}} \\big[({1}\\over{2}})((C-A)^2-2B^4\\big]\n% {{1}\\over{2 N}}\\sum_{k=-N}^{N-1} \\twa_k \\twa_k^* \\\\ \\label{FT_auto_9p}\n% \\label{nb_auto_6_is_auto_1}\n\\end{eqnarray}\nwhere for simplicity I have omitted terms smaller by a factor of $1/(2 N)$ or more.\nThe complete expression includes additional terms of these orders,\nbut they are small for spectra containing more than a few channels.\nNote that, again, the noise in the spectral domain can be represented by\nthe ``digitization noise,'' a spectrally-constant noise $(A-B)/B$ added in quadrature with \nthe signal $\\twa_k$.\n\n\\subsection{Correlation of Noise Across Spectral Channels}\n\nJust as in the case of the cross-power spectrum,\nthe variation of noise on the correlation (explored in Paper 1) leads to correlations\nin the spectral domain for the autocorrelation spectrum.\nAn argument precisely analogous to that for the cross-power spectrum,\nin \\S\\ref{covar_ckrckrc} above, shows that only the second of the 3 terms in\nEq.\\ \\ref{A1_sum} contributes to the covariance. \nThat covariance is given by:\n\\begin{equation}\n\\la \\twa_k \\twa_{\\ell}^*\\ra - \\la \\twa_k\\ra \\la\\twa_{\\ell}^*\\ra\n= {{1}\\over{2 N_o}} \\big[4(C-A)B^2 - 8 B^4\\big] \\twa_k \\twa_{\\ell}^* .\n\\label{covar_akal}\n\\end{equation}\nThis expression should be compared with Eq.\\ \\ref{covar_pkpl}.\nThe covariance is twice as great for the autocorrelation function.\n\n\\section{DISCUSSION}\\label{discussion}\n\n\\subsection{Quantization Noise: One of Many Channels}\n\nIn the limit of spectra with many channels, $2N>>1$,\nthe noise in one particular channel is given by\nterms in Eqs\\ \\ref{digital_ckrkckrk} and\\ \\ref{digital_ckrkckrkc}\nwith coefficient $2N$ for cross-power spectra.\nIn this approximation,\n\\begin{eqnarray}\n\\la \\ckr_k \\ckr_k^*\\ra &\\approx & \\la \\ckr_k\\ra \\la\\ckr_k^*\\ra\n+{{2N}\\over{2N_o}} \\big[ 2 B_X^2 B_Y^2 \\big]\n\\left(\\twa_k+\\left({{A_{X2}}\\over{B_X^2}}-1\\right)\\right)\n\\left(\\twa_k+\\left({{A_{Y2}}\\over{B_Y^2}}-1\\right)\\right)\\\\\n\\la \\ckr_k \\ckr_k\\ra &\\approx & \\la \\ckr_k\\ra \\la\\ckr_k\\ra\n+{{2N}\\over{2N_o}}\n\\big[ 2 B_X^2 B_Y^2 \\big]\\twp_k\\twp_k\n\\end{eqnarray}\nThese equations closely resemble the expressions for noise for continuous\ncorrelation, Eqs.\\ \\ref{continuous_spectrum_facts} and\\ \\ref{continuous_spectrum_facts},\nexcept that everything has been multiplied\nby the gain factor $B_X^2 B_Y^2$, and a white noise component\nwith variance $({{A_{X2}}\\over{B_X^2}}-1)$ (or the corresponding quantity for $Y$)\nhas been added to the autocorrelation spectrum $\\twa_k$.\nThese factors are those represented in the gain of the quantized cross-power spectrum (see Eq.\\ \\ref{avg_hat_rk}),\nand in the gain and offset of the autocorrelation spectrum (see Eq.\\ \\ref{avg_hat_rk}).\nNote that $A_{X2}>B_X^2$ for all $(v_0,\\;n)$, so that the added noise component\nis always positive.\nThis component is conveniently interpreted as quantization noise.\nIn this particular approximation,\ntreatment of the effects of quantization as white noise added in quadrature\nis accurate.\n\n\\subsubsection{Correlation of Noise and Noise Reduction}\n\nBecause the noise in different spectral channels is covariant (often with negative covariance),\nthe integrated noise across a spectral channel is different from the summed, squared values of the noise in\neach channel (often less).\nEqs.\\ \\ref{covar_pkplc},\\ \\ref{covar_pkpl}, and\\ \\ref{covar_akal} give the covariances.\nAlthough the covariances\nare smaller than the variances of the spectral channels given above by factors of $2 N$, they sum coherently\nacross the channel, whereas the variances do not. Thus, in principle they yield comparable contributions\nwhen summed over all channels. \nIn practice, of course,\nthe results of such a sum are given by Eqs.\\ \\ref{digital_rtrtc}\nand\\ \\ref{digital_rtrt} with $\\tau=0$, \nor Eq.\\ \\ref{a0a0c} for autocorrelation,\nbecause the sum over all spectral channels yields the zeroth lag.\nThe interested reader can verify that the results for this lag are identical to those of Paper 1, for a white spectrum.\n\nIn principle, the reduction of noise by the covariances offers the possibility of reducing quantization noise in a \nspectrally-narrow signal. For example, one could introduce additional correlated signals, with known \n$\\tilde \\alpha_k$ and $\\tilde \\rho_k$, and measure the variation of those from theoretically-expected results.\nUsing Eqs.\\ \\ref{covar_pkplc},\\ \\ref{covar_pkpl}, and\\ \\ref{covar_akal} one can calculate what weighted sum of\nthose variations should be applied to the unknown signal, to reduce the noise as much as possible. \nThis potential application is closely related to ``dithering'' in quantization\n(see, for example, \\citet{bal05} and references therein).\n\n\\subsection{Symmetries}\n\nNote that the noise in the cross-correlation function depends on\nboth $\\alpha$ and $\\rho$.\nThe variance\n$\\la\\ckr_k\\ckr_k^*\\ra-\\la\\ckr_k\\ra\\la\\ckr_k^*\\ra$\nmeasures the summed squares of the principal axes of the elliptical Gaussian distribution\nof noise, or its overall size. \nAs one might expect from Eq.\\ \\ref{continuous_twrktwrkc}, that size depends primarily on the \nautocorrelation spectrum in that channel $\\twa_k$.\nThe error ellipse must maintain the same size under the transformation\n$\\rho\\rightarrow e^{i\\phi}\\rho$, so the noise can depend only on even powers of $\\twa$, as it does.\n\nSimilarly, the variance\n$\\la\\ckr_k\\ckr_k\\ra-\\la\\ckr_k\\ra\\la\\ckr_k\\ra$\nmeasures the difference of the squares of the principal axes of the elliptical Gaussian distribution\nof noise, or its shape. This shape must be circular for $\\twp=0$, \nso that the variance must vanish there,\nand so one expects that it cannot depend on $\\twa$ independently of $\\twp$.\nEq.\\ \\ref{continuous_twrktwrk} confirms this.\nThe difference must remain the same under the transformation $\\twp\\rightarrow-\\twp$,\nfor example, so dependence on $\\twp$ must be second order.\n\n\\subsection{Limits of Validity}\n\nNumerical experiments suggest that Eqs.\\ \\ref{digital_ckrkckrkc} \nand\\ \\ref{digital_ckrkckrk} reach their limits most commonly for\nspectra encountered in radio astronomy when the autocorrelation function\nbecomes large at lags other than the zero lag.\nFor example, for a single narrow line,\nwhen the integrated power in the line becomes comparable to the\nintegrated continuum (including system noise),\nthen the autocorrelation function will reach about 0.5\nin nonzero lags.\nThis usually leads to noise larger than that expected from the second-order analytical expressions,\nespecially in channels containing the line, but also throughout the spectrum.\n\nFor particular spectra, \nthe additional noise can be modeled accurately by expressions that involve\nhigher-order terms allowed by the preceding discussion, such as $\\twa_k\\twp_k^2$\nor $\\twa_k^3$. \n\n\\section{SUMMARY}\\label{summary}\n\nThis paper investigates signal and noise for correlation of digitized data.\nI assume that the received data are noiselike, in the sense that \namplitudes and phases are drawn from complex Gaussian distributions in the spectral domain.\nThe variance varies with frequency. For cross-correlation of two data streams,\ncovariance between the data streams may also depend on frequency.\nAlmost all astrophysical signals have this character.\nThe variances and covariances contain all the information in the signal.\nThe observed time series are the Fourier transforms of these spectral components.\nAt millimeter and longer wavelengths, these time series are commonly digitized,\nand then correlated to obtain estimates of the underlying variances and covariances.\nThe correlation functions are finally Fourier transformed to yield the \nestimated autocorrelation or cross-power spectrum.\nAveraged over a number of realizations, the elements of the correlation function will approach\na Gaussian distribution.\nThe mean correlation\nrepresents the deterministic part of a measurement, or \nthe signal. The standard deviation of the measurement represents the random part, or noise.\n\nDigitization of the signals involves quantization, which represents the \ncontinuous signal with a finite set of levels, and thus destroys information.\nThis affects both the signal and the noise.\nI summarize results for continuous data in \\S\\ref{continuous},\nand present new results, for noise for quantized data, in \\S\\ref{quantized} \nand \\S\\ref{section_quantspectrum}.\n\nIn \\S\\ref{quantized} I investigate statistics of correlation functions.\nUnder the assumption that the correlation is smaller than 1\n(except equal to 1 for the zero-lag of the autocorrelation function), I find expressions for the mean\ncross- and autocorrelation functions.\nResults agree with earlier work \\citep{coo70,jen98}.\nI then find analytical expressions for the noise in the correlation functions.\nThis noise takes the form of variances of the measured elements, as a function of lag;\nand of covariances between the measured elements.\n\nIn \\S\\ref{section_quantspectrum} I investigate statistics of \nspectra.\nThe mean spectra are related to the mean correlation functions by Fourier transform;\nthe noise in the spectra is related to that in the correlation functions by a double Fourier transform.\nI find that \nthe mean cross-power spectrum for quantized data equals that for\ncontinuous data, times a gain factor. The mean autocorrelation spectrum \nequals that for continuous data times the same gain factor, plus white noise added in\nquadrature with the original data:\n``quantization noise''.\nThis accords with previous results \\citep{coo70,jen98}.\nI then find analytical expressions for the noise in the spectra.\nFor both cross-power and autocorrelation spectra,\nI find that noise in one channel of a spectrum \nis equal to a gain factor times that for continuous data, plus\nthe same quantization noise found for the autocorrelation spectrum.\nHowever, I also find that noise is correlated (most commonly anticorrelated) across spectral channels.\nThus, when noise increases the value measured in one channel above the mean,\nnoise will tend to decrease the value measured in another channel.\nThis correlation can produce a contribution comparable to, or even greater than,\nthe quantization noise when summed over all spectral channels.\n\n\\acknowledgments\n\nI am grateful \nto the DRAO for supporting this work with extensive\ncorrelator time.\nI gratefully acknowledge the VSOP Project, which is led by the Japanese \nInstitute of Space and Astronautical Science in cooperation with many \norganizations and radio telescopes around the world.\nThe U.S. National Science Foundation provided partial financial support for this work.\n\n\\appendix\n\n\\section{Useful Facts for Spectra}\\label{useful_spectral_facts}\n\nParseval's theorem states:\n\\begin{equation}\n\\sum_{\\tau=-N}^{N-1} \\rho_{\\tau}\\rho_{\\tau}^* \n= {{1}\\over{2N}} \\sum_{k=-N}^{N-1}\\twp_k\\twp_k^* .\n\\label{parseval}\n\\end{equation}\n\nTherefore,\n\\begin{equation}\n\\sum_{\\tau\\neq\\ups}\ne^{i{{2\\pi}\\over{2N}}k(\\tau-\\ups)}\\rho_{\\tau}\\rho_{\\ups}^*=\n\\twp_k \\twp_k^*\n-\n{{1}\\over{(2N)}}\\sum_{k=-N}^{N-1}\\twp_k\\twp_k^* .\n\\end{equation}\nAlso note that\n\\begin{equation}\n\\sum_{\\tau\\neq\\ups}\ne^{i{{2\\pi}\\over{2N}}k(\\tau-\\ups)} \\alp_{(\\tau-\\ups)} \n= \n(2N) \\twa_k - (2N)\n\\end{equation}\n\n\\begin{equation}\n\\sum_{\\nu=-N}^{N-1} e^{i{{2\\pi}\\over{2 N}}\\nu k} \\sum_{n=1}^{N_o}\\alp_{n}\\alp_{-n+\\nu}\n=(2N) \\twa_k^2.\n\\label{convolution_fact}\n\\end{equation}\n\nFor convolutions, recall that\n\\begin{equation}\n\\sum_{\\tau=-N}^{N-1}\\sum_{\\ups=-N}^{N-1}\ne^{i{{2\\pi}\\over{2N}}k(\\tau-\\ups)}\n\\sum_{n=1}^{N_o} \\rho_{n}\\rho_{-n+(\\tau-\\ups)}\n= (2N) \\twp_k \\twp_k .\n\\label{convolution_fact_rho}\n\\end{equation}\nwhere I assume that the correlation function wraps,\nand that the correlation function includes all lags\nwith nonzero signal.\n\nI define the quantity:\n\\begin{equation}\n\\tilde C_{\\rho}(k)=\\sum_{\\tau=-N}^{N-1} e^{i{{2\\pi}\\over{2N}} 2 k \\tau} \\rho_{\\tau} \\rho_{\\tau} .\n\\end{equation}\n\n\\clearpage\n\n\\begin{thebibliography}{99}\n% \\bibitem[Anantharamaiah et al.(1991)]{ana91}Anantharamaiah, K. R., Deshpande, A. A., Radhakrishnan, V., Ekers, R. D., Cornwell, T. J., \\& Goss, W. M. 1991, ASP Conf. Ser. 19: IAU Colloq. 131: Radio Interferometry. Theory, Techniques, and Applications, San Francisco: Astronomical Society of the Pacific, p. 6\n\\bibitem[Balestrieri et al.(2005)]{bal05}Balestrieri, E., Daponte, P., \\& Rapuano, S. 2005, IEEE Trans. Inst. Meas., 54, 1388\n\\bibitem[Cooper(1970)]{coo70}Cooper, B.F.C. 1970, AustJPhys, 23, 521 % -527 Correlators with 2-bit quantization\n\\bibitem[D'Addario et al.(1984)]{dad84}D'Addario, L.R., Thompson, A.R., Schwab, F.R., \\& Granlund, J. 1984, Radio Sci., 19, 931\n\\bibitem[Dennett-Thorpe \\& de Bruyn(2002)]{den02}Dennett-Thorpe, J., \\& de Bruyn, A. G. 2002, Nature, 415, 57.\n\\bibitem[Desai et al.(1992)]{des92}Desai, K.M., Gwinn, C.R., Reynolds, J.R., King, E.A., Jauncey, D., Flanagan, C., Nicolson, G., Preston, R.A., \\& Jones, D.L. 1992, ApJ, 393, L75\n% \\bibitem[Gwinn(2001)]{gwi01}Gwinn, C.R. 2001, ApJ, 554, 1197 % Interferometric Visibility of a Scintillating Source\n\\bibitem[Gwinn et al.(2000)]{gwi00}Gwinn, C.R., Britton, M.C., Reynolds, J.E., Jauncey, D.L., King, E.A., McCulloch, P.M., Lovell, J.E.J., Flanagan, C.S., Preston, R.A. 2000, ApJ, 531, 902 % size of the Vela pulsar's emission region at 13 cm wavelength\n\\bibitem[Gwinn(2004)]{gwi04}Gwinn, C.R. 2004, PASP, 116, 84 (Paper 1)% statistics of correlation of quantized gaussian noise\n\\bibitem[Hagen \\& Farley(1973)]{hag73}Hagen, J.B., \\& Farley, D.T. 1973, Radio Sci, 8, 775 % Digital-correlation techniques in radio science\n\\bibitem[Jauncey et al.(2000)]{jau00}Jauncey, D.L., Kedziora-Chudczer, L.L., Lovell, J.E.J., Nicolson, G.D., Perley, R.A., Reynolds, J.E., Tzoumis, A.K., Wieringa, M.H. 2000, Astrophysical Phenomena Revealed by Space VLBI, eds. H. Hirabayashi, P.G. Edwards, D.W. Murphy, ISAS: Sagamihara, p. 147\n\\bibitem[Jenet \\& Anderson(1998)]{jen98}Jenet, F.A., \\& Anderson, S.B. 1998, PASP, 110, 1467 % - 1478 The effects of digitization on nonstationary stochastic signals with application to pulsar signal baseband recording\n% \\bibitem[Jenet, Anderson, \\& Prince(2001)]{jen01}Jenet, F.A., Anderson, S.B., \\& Prince T.A. 2001, ApJ, 558, 302\n% \\bibitem[Kokkeler, Fridman, \\& van Ardenne(2001)]{kok01}Kokkeler, A. B. J., Fridman, P., \\& van Ardenne, A. 2001, Experimental Astronomy, 11, 33 % degradation due to quantization noise in radio astronomy phased arrays\n\\bibitem[Kulkarni \\& Heiles(1980)]{kul80}Kulkarni, S.R., \\& Heiles, C. 1980, AJ, 85, 1413 %How to obtain the true correlation from a 3-level digital correlator\n% \\bibitem[Kulkarni(1989)]{kul89}Kulkarni, S.R. 1989, AJ, 98, 1112 % -1130 Self-Noise in Interferometers: Radio and Infrared\n% \\bibitem[Meyer(1975)]{mey75}Meyer, S.L. 1975, Data Analysis for Scientists and Engineers (Wiley: New York)\n% \\bibitem[Press et al.(1989)]{pre89}Press, W.H., Flannery, B.P., Teukolsky, S.A., \\& Vetterling, W.T. 1989, Numerical Recipes, Cambridge UK: Cambridge Univ. Press\n% \\bibitem[Rickett(1975)]{ric75}Rickett, B.J. 1975, ApJ, 197, 185 % -191 Amplitude-modulated noise - An empirical model for the radio radiation received from pulsars\n% \\bibitem[Thompson, Moran, \\& Swenson(1986)]{tms86}Thompson, A.R., Moran, J.M., \\& Swenson, G.W. Jr. 1986, Interferometry and Synthesis in Radio Astronomy, (New York: Wiley)\n% \\bibitem[Van Vleck \\& Middleton(1966)]{van66}Van Vleck, J.H., \\& Middleton, D. 1966, Proc. IEEE, 54, 2% -19 The Spectrum of Clipped Noise\n\\end{thebibliography}\n\n\\newpage\n\\figurenum{1}\n\\begin{figure}[t]\n\\epsscale{.50}\n% fig 1:\n% \\plotone{/home/egret/cgwinn/tex/noise/figures/4_level_characteristic_curve.ps}\n\\plotone{f1.ps} % \\plotone{4_level_characteristic_curve_crop.pdf}\n\\figcaption[]{\nCharacteristic curve for 4-level quantization.\n\\label{4_level}}\n\\end{figure}\n\n\\newpage\n\\figurenum{2}\n\\begin{figure}[t]\n\\epsscale{.60}\n% fig 2:\n% \\plotone{/home/egret/cgwinn/vsop/calc/noise/rwalk_45.spect.ps}\n\\plotone{f2.ps} % \\plotone{rwalk_45_spect_crop.pdf}\n\\figcaption[]{\nModel spectra and correlation functions for simulations of correlation.\nUpper panel: Cross-power spectrum $\\twr_k$ (circles) \nand autocorrelation spectrum $\\twa_k$ (crosses).\nCurves show interpolated spectrum.\nMiddle panel: Cross-correlation function $r_{\\tau}$ and autocorrelation function $a_{\\tau}$\nfor continuous data.\nLower panel: Cross-correlation function $\\hat r_{\\tau}$ and autocorrelation function $\\hat a_{\\tau}$\nfor quantized data. Note the gain for \ncross-correlation of $\\hat r_{\\tau} =B_x B_y 0.4 = 0.693$ for $\\tau=1,2$,\nand offset to $a_0 = 2.07$ for the zero-lag autocorrelation.\nData were quantized with \n$v_0=1.5$ and \n$n=3$. Correlation includes $2N=8$ lags.\nWhen\naveraged over $N_o =2\\times 10^6$ simulated correlation functions,\nthe simulated spectra and correlation functions are indistinguishable from theoretical values.\n\\label{dxcf_avgplot}}\n\\end{figure}\n\n\\newpage\n\\figurenum{3}\n\\begin{figure}[t]\n\\epsscale{.90}\n% fig 3:\n\\plotone{f3.ps} % \\plotone{rwalk_45_2_crop.pdf}\n% \\plotone{/home/egret/cgwinn/vsop/calc/noise/rwalk_45.2.ps}\n% see /home/egret/cgwinn/tex/noise/spect/rwalk_45.for & outputs fort.??\n% /home/egret/cgwinn/tex/noise/spect/rwalk_45.nb\n% /home/egret/cgwinn/tex/noise/spect/rwalk_45.calc.spect.nb\n% /home/egret/cgwinn/tex/noise/spect/rwalk_45.2.mac\n\\figcaption[]{\nNoise for cross-correlation function shown in Figure\\ \\ref{dxcf_avgplot}.\nUpper panels: Schematic depiction of the correlation matrices\n$\\la r_{\\tau} r_{\\ups}^*\\ra - \\la r_{\\tau}\\ra\\la r_{\\ups}^*\\ra$\n(left panel: Equations\\ \\ref{digital_rtruc} and\\ \\ref{digital_rtrtc});\nand \n$\\la r_{\\tau} r_{\\ups}\\ra - \\la r_{\\tau}\\ra\\la r_{\\ups}\\ra$\n(right panel: Equations\\ \\ref{digital_rtru} and\\ \\ref{digital_rtrt}).\nLetters indicate positions with expected nonzero standard deviation,\naccording to those equations,\nwith the same standard deviation expected\nfor identical letters. \nLower panels: corresponding noise, as found\nfor a 4-level correlator for the spectrum of\nFigure\\ \\ref{dxcf_avgplot}.\nStandard deviations are for $N_o=16$ measurements with $2N=8$ lags,\ncalculated over $10^6$ simulated correlation functions.\nCircles show statistics of the simulations,\nand horizontal bars show predictions of \nEqs.\\ \\ref{digital_rtruc},\\ \\ref{digital_rtrtc},\n\\ \\ref{digital_rtru}, and\\ \\ref{digital_rtrt}.\n\\label{dxcf_noiseplot}}\n\\end{figure}\n\n\n\\newpage\n\\figurenum{4}\n\\begin{figure}[t]\n\\epsscale{.90}\n% fig 4:\n\\plotone{f4.ps} % \\plotone{ellipse_rwalk_48_crop.pdf}\n% \\plotone{/home/egret/cgwinn/vsop/calc/noise/ellipse.rwalk_48.ps}\n%\n% xxxx Use: /home/egret/cgwinn/vsop/calc/noise/rwalk_45_sim.ps xxxxx\n%\n% macro ``phasor_plot''\n%\n\\figcaption[]{\nSpectrum for model correlation function\nof Figures \\ref{dxcf_avgplot} and \\ref{dxcf_noiseplot},\nin phasor form.\nSolid line shows expected form,\nusing Fourier interpolation.\nEllipses show measured averages and standard deviations.\nSimulations used a 4-level correlator with\n$v_0=1.5$, $n=3$ with $N_o=16$, $2N=8$.\nThe displayed statistics were calculated from $10^7$ simulated spectra.\nThe value of $v_0$ was chosen to emphasize the eccentricity of the error \nellipses;\nin other words, of the size of the term $\\la \\ckr_k \\ckr_k^*\\ra$.\nNote that major axes point toward the origin.\n\\label{phasor_plot}}\n\\end{figure}\n\n\\newpage\n\\figurenum{5}\n\\begin{figure}[t]\n\\epsscale{.80}\n% fig 5:\n% from /home/egret/cgwinn/vsop/calc/noise/noisecompare.rwalk_47.3.mac -- use smooth_mod\n% this uses rwalk_47.04.fort.24\n% for v0=0.4, n=3 see /home/egret/cgwinn/vsop/calc/noise/rwalk_48.calc.spect.nb\n% \\plotone{/home/egret/cgwinn/vsop/calc/noise/noisecompare.rwalk_47.ps}\n\\plotone{f5.ps} % \\plotone{noisecompare_rwalk_47_crop.pdf}\n\\figcaption[]{\nModel spectrum and noise, shown for simulations (circles: real parts,\nstars: imaginary parts), and for theory (solid line: real part, dotted\nline: imaginary part). Simulations used a 4-level correlator with\n$v_0=0.4$, $n=3$ with $N_o=16$, $2N=8$, and $10^7$ simulations. \nThe\nlevel $v_0$ was chosen to emphasize the $\\rho$-dependent term in \nEq.\\ \\ref{digital_ckrkckrkc},\nwhich appears as the variation from a constant value in the middle panel.\n\\label{noisecompare}}\n\\end{figure}\n\n\\newpage\n\\figurenum{6}\n\\begin{figure}[t]\n\\epsscale{.70}\n% fig 6:\n% \\plotone{/home/egret/cgwinn/vsop/calc/noise/correl.rwalk_55.3.ps}\n\\plotone{f6.ps} % \\plotone{correl_rwalk_55_3_crop.pdf}\n\\figcaption[]{\nCovariance of noise \nin two spectral channels, for simulated correlation of quantized noise.\nUpper panel: Model spectrum, showing autocorrelation spectrum $\\alpha$ \nand cross-power spectrum $\\rho$.\nAll of the cross-power, and 80\\% of the autocorrelation spectrum,\nis concentrated into channels $-3$ and $+1$.\nLower panel: Distribution of noise in channels 1 and -3, \nrealized from the model spectrum after quantization.\nQuantizer parameters were $v_0=0.1$, $n=3$.\nSimulations used $N_o=800$ measurements, $2N=8$ spectral channels.\nPoints show $10^4$ realizations.\nEllipses show 1- and 2-standard deviation contours.\nThe tilt of the ellipse shows the \nnegative covariance of the noise in the two channels.\n\\label{correl}}\n\\end{figure}\n\n\\clearpage\n\n\\begin{deluxetable}{clll}\n\\tablenum{1}\n\\tablecolumns{4}\n\\tablewidth{0pc}\n\\tablecaption{Second and Fourth Moments of Quantized Real Gaussian Variables}\n% \n% /home/egret/cgwinn/tex/noise/spect/2-variate_distribution_expansion.nb \n% /home/egret/cgwinn/tex/noise/spect/3-variate_distribution_expansion.nb \n% /home/egret/cgwinn/tex/noise/spect/4-variate_distribution_expansion.nb \n% \n\\tablehead{\n& \\colhead{Terms of 2nd or Lower Order} & \\colhead{Moments of} \\\\ \n\\colhead{Average} &\\colhead{that Contribute to Expansion}& \\colhead{Quantized Variables} & \\\\ \n}\n\\startdata\n$\\la \\hat W \\hat X \\ra $&$ [W X] (\\rWX) $&$ [B_{W} B_{X}] \\rWX $\\\\\n$\\la \\hat W^2 \\ra $&$ [1] $&$ [A_{W2}] $\\\\\n$ $&$ $&$ $\\\\\n$\\la \\hat W \\hat X \\hat Y \\hat Z \\ra $&$ [W X Y Z] (\\rWX\\rYZ+\\rWY\\rXZ+\\rWZ\\rXY) $&$ [B_{W} B_{X} B_{Y} B_{Z}] (\\rWX\\rYZ+\\rWY\\rXZ+\\rWZ\\rXY) $\\\\\n$\\la \\hat W^2 \\hat X \\hat Y \\ra $&$ [X Y] (\\rXY)+ [(W^2-1) X Y] (\\rWX\\rWY) $&$ [A_{W2}B_{X} B_{Y}] (\\rXY)+[(C_{W2}-A_{W2})B_{X}B_{Y}](\\rWX\\rWY)$\\\\\n$\\la \\hat W^2 \\hat X^2 \\ra $&$ [1] + [\\haf (1-W^2)(1-X^2)] (\\rWX^2) $&$ [A_{W2}A_{X2}]+[\\haf(C_{W2}-A_{W2})(C_{X2}-A_{X2})]\\rWX^2 $\\\\\n$\\la \\hat W^3 \\hat X \\ra^{a}$&$ [W X] (\\rWX) $&$ [B_{W3}B_{X}] \\rWX $\\\\\n$\\la \\hat W^4 \\ra^{a}$&$ [1] $&$ [A_{W4}] $\\\\\n\\enddata\n\\tablenotetext{a} {Important only for autocorrelations.}\n\\label{table_real_avgs}\n\\end{deluxetable}\n\\clearpage\n\n\\begin{deluxetable}{lll}\n\\tablenum{2}\n\\tablecolumns{3}\n\\tablewidth{0pc}\n\\tablecaption{Fourth Moments of Quantized Complex Gaussian Variables:\n$\\hat w$ $\\hat x$ $\\hat y$ and $\\hat z$ }\n% /home/egret/cgwinn/tex/noise/autospect/reim.exp.5.nb\n\\tablehead{\n\\colhead{Class} & \\colhead{Form} & \\colhead{Result: Quantized} \\\\ \n}\n\\startdata\n{\\scriptsize $11$} &$\\la \\hwh \\hxc \\ra $&$ [2 B_W B_X] \\rwx $\\\\\n &$ $&$ $\\\\\n{\\scriptsize $2$} &$\\la \\hwh \\hwc \\ra ^{a} $&$ [2 A_{W2}] $\\\\\n &$ $&$ $\\\\\n{\\scriptsize $1111+$}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra $&$ [4 B_W B_X B_Y B_Z] (\\rwx\\ryz^*+\\rwy\\rxz^*) $\\\\\n{\\scriptsize $1111-$}&$\\la \\hwh \\hxc \\hyh \\hzc \\ra $&$ [4 B_W B_X B_Y B_Z] (\\rwx\\ryz +\\rwz\\rxy^*) $\\\\\n &$ $&$ $\\\\\n{\\scriptsize $211+$} &$\\la \\hwh \\hxc \\hwc \\hyh \\ra $&$ [2 (C_{W2}-A_{W2})B_X B_Y](\\rwx\\rwy^*)+[4 A_{W2}B_X B_Y](\\rxy^*)$\\\\\n{\\scriptsize $211-$} &$\\la \\hwh \\hxc \\hwh \\hyc \\ra $&$ [2 (C_{W2}-A_{W2})B_X B_Y + 4 B_W^2 B_X B_Y ](\\rwx\\rwy)$\\\\\n \n &$ $&$ $\\\\\n{\\scriptsize $22+$} &$\\la \\hwh \\hxc \\hwc \\hxh \\ra $&$ [(C_{W2}-A_{W2})(C_{X2}-A_{X2})](\\rwx \\rwx^*) + [4 A_{W2} A_{X2}] $\\\\\n{\\scriptsize $22-$} &$\\la \\hwh \\hxc \\hwh \\hxc \\ra $&$\\phantom{+}[\\haf ((C_{W2}-A_{W2})+2 B_W^2)((C_{X2}-A_{X2})+2 B_X^2)] (\\rwx \\rwx ) $\\\\\n &$ $&$ + [\\haf ((C_{W2}-A_{W2})-2 B_W^2)((C_{X2}-A_{X2})-2 B_X^2)] (\\rwx^* \\rwx^*) $\\\\\n \n &$ $&$ $\\\\\n{\\scriptsize $31+$} &$\\la \\hwh \\hwc \\hwc \\hxh \\ra^{a}$&$ [ 2 B_{W3} B_X + 2 A_{W2} B_W B_X ] \\rwx^* $\\\\\n{\\scriptsize $31-$} &$\\la \\hwh \\hwc \\hwh \\hxc \\ra^{a}$&$ [ 2 B_{W3} B_X + 2 A_{W2} B_W B_X ] \\rwx $\\\\\n \n &$ $&$ $\\\\\n{\\scriptsize $4$} &$\\la \\hwh \\hwc \\hwc \\hwh \\ra^{a}$&$ [ 2 A_{W4} + 2 A_{W2}^2] $\\\\ \n &$ $&$ $\\\\\n\\enddata\n\\tablenotetext{a} {Important only for autocorrelations.}\n\\label{table_complex_avgs}\n\\end{deluxetable}\n\\clearpage\n\n\\begin{deluxetable}{llllllllcl}\n% \\tabletypesize{\\scriptsize}\n\\tablenum{3}\n\\tablecolumns{10}\n\\tablewidth{0pc}\n\\tablecaption{Terms in XCF Sums: $\\hat r\\hat r^*$ and $\\hat r\\hat r$}\n%\n\\tablehead{\n\\colhead{ID} &\n\\colhead{Conditions} & \\multicolumn{4}{c}{Subscript} &\n\\colhead{Class} & \\colhead{Form} & \\colhead{Multiplicity} & \\colhead{Notes} \\\\\n\\cline{3-6}\\\\\n\\colhead{} &\n\\colhead{} & \\colhead{$a$} & \\colhead{$b$} & \\colhead{$c$} & \\colhead{$d$} &\n\\colhead{} & \\colhead{} & \\colhead{} & \\colhead{}\n}\n\\startdata\n\\cutinhead{Xc: $\\la\\hrh_{\\tau}\\hrc_{\\ups} \\ra=\\la\\hxh_{\\ell} \\hyc_{\\ell+\\tau} \\hxc_{m} \\hyh_{m+\\ups}\\ra=\\la\\hxh_a\\hyc_b\\hxc_c\\hyh_d\\ra$ }\n\\sidehead{Xcn: $\\tau\\neq\\ups$:}\nXcn.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$\\ell $&$\\ell+\\ups $&\\scriptsize{$211+ $}&$\\la \\hwh \\hxc \\hwc \\hyh \\ra$&$ N_o $& Eq.\\ 41 \\\\\nXcn.2 &$ \\ell+\\tau= m+\\ups $&$ \\ell $&$ \\ell+\\tau $&$\\ell+(\\tau-\\ups)$&$\\ell+\\tau $&\\scriptsize{$211+ $}&$\\la \\hwh \\hxc \\hwc \\hyh \\ra$&$ N_o $&Eq.\\ 42,a \\\\\nXcn.3 &$ \\ell+\\tau= m $& & & & &\\scriptsize{$1111+$}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ - $& b \\\\\nXcn.4 &$ \\ell= m+\\ups $& & & & &\\scriptsize{$1111+$}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ - $& b \\\\\nXcn.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\ups $&\\scriptsize{$1111+$}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ N_o^2-2N_o $&Eq.\\ 40 \\\\\n\n\\sidehead{Xce: $\\tau =\\ups $}\nXce.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell $&$\\ell+\\tau $&\\scriptsize{$22+ $}&$\\la \\hwh \\hxc \\hwc \\hxh \\ra$&$ N_o $& \\\\\nXce.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\tau $&\\scriptsize{$1111+$}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ N_o^2-N_o $& \\\\\n \n\\cutinhead{Xr: $\\la\\hrh_{\\tau}\\hrh_{\\ups}\\ra=\\la\\hxh_{\\ell}\\hyc_{\\ell+\\tau}\\hxh_{m}\\hyc_{m+\\ups}\\ra=\\la\\hxh_a\\hyc_b\\hxh_c\\hyc_d\\ra$}\n\\sidehead{Xrn: $\\tau\\neq\\ups$:} \nXrn.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$\\ell $&$\\ell+\\ups $&\\scriptsize{$211- $}&$\\la \\hwh \\hxc \\hwh \\hyc \\ra$&$ N_o $& \\\\\nXrn.2 &$ \\ell+\\tau= m+\\ups $&$ \\ell $&$ \\ell+\\tau $&$\\ell+(\\tau-\\ups)$&$\\ell+\\tau $&\\scriptsize{$211- $}&$\\la \\hwh \\hxc \\hyh \\hwc \\ra$&$ N_o $& a\\\\\nXrn.3 &$ \\ell+\\tau= m $& & & & &\\scriptsize{$1111-$}&$\\la \\hwh \\hxc \\hyh \\hzc \\ra$&$ - $& b\\\\\nXrn.4 &$ \\ell= m+\\ups $& & & & &\\scriptsize{$1111-$}&$\\la \\hwh \\hxc \\hyh \\hzc \\ra$&$ - $& b\\\\\nXrn.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\ups $&\\scriptsize{$1111-$}&$\\la \\hwh \\hxc \\hyh \\hzc \\ra$&$ N_o^2-2N_o $& \\\\\n \n\\sidehead{Xre: $\\tau =\\ups$} \nXre.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell $&$\\ell+\\tau $&\\scriptsize{$22- $}&$\\la \\hwh \\hxc \\hwh \\hxc \\ra$&$ N_o $& \\\\\nXre.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\tau $&\\scriptsize{$1111-$}&$\\la \\hwh \\hxc \\hyh \\hzc \\ra$&$ N_o^2-N_o $& \\\\\n\n\\enddata\n\\tablenotetext{a} {Roles of $\\hat x$ and $\\hat y$ reversed from Table\\ \\ref{table_complex_avgs}. \nUse complex conjugate. }\n\\tablenotetext{b} {Important only for autocorrelations. Yields standard form for cross-correlation.}\n\\label{table_terms_in_Xsums}\n\\end{deluxetable}\n\\clearpage\n\n\\begin{deluxetable}{llllllllcl}\n% \\tabletypesize{\\scriptsize}\n\\tablenum{4}\n\\tablecolumns{10}\n\\tablewidth{0pc}\n\\tablecaption{Terms in ACF Sums: $\\hat a\\hat a^*$ }\n%\n%\n\\tablehead{\n\\colhead{ID} &\n\\colhead{Conditions} & \\multicolumn{4}{c}{Subscript} &\n\\colhead{Class} & \\colhead{Form} & \\colhead{Multiplicity} & \\colhead{Notes} \\\\\n\\cline{3-6}\\\\\n\\colhead{} &\n\\colhead{} & \\colhead{$a$} & \\colhead{$b$} & \\colhead{$c$} & \\colhead{$d$} &\n\\colhead{} & \\colhead{} & \\colhead{} & \\colhead{}\n}\n\\startdata\n\\cutinhead{ACF: $\\la\\hah_{\\tau}\\hac_{\\ups}\\ra=\\la\\hxh_{\\ell} \\hxc_{\\ell+\\tau} \\hxc_{m} \\hxh_{m+\\ups}\\ra=\\la\\hxh_a\\hxc_b\\hxc_c\\hxh_d\\ra$}\n\\sidehead{Antu: $\\tau\\neq\\ups$, $\\tau\\neq 0$, $\\ups\\neq 0$}\nAntu.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$\\ell $&$\\ell+\\ups $&\\scriptsize{$ 211+ $}&$\\la \\hwh \\hxc \\hwc \\hyh \\ra$&$ N_o $& \\\\\nAntu.2 &$ \\ell+\\tau= m+\\ups $&$ \\ell $&$ \\ell+\\tau $&$\\ell+(\\tau-\\ups)$&$\\ell+\\tau $&\\scriptsize{$(211+)^*$}&$\\la \\hxh \\hwc \\hyc \\hwh \\ra$&$ N_o $& a\\\\\nAntu.3 &$ \\ell+\\tau= m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell+\\tau $&$\\ell+\\tau+\\ups$&\\scriptsize{$(211-)^*$}&$\\la \\hxh \\hwc \\hwc \\hyh \\ra$&$ N_o $& a\\\\ \nAntu.4 &$ \\ell= m+\\ups $&$ \\ell $&$ \\ell+\\tau $&$ \\ell-\\ups $&$\\ell $&\\scriptsize{$ 211- $}&$\\la \\hwh \\hxc \\hyc \\hwh \\ra$&$ N_o $& \\\\\nAntu.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\ups $&\\scriptsize{$ 1111+ $}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ N_o^2-4N_o $& \\\\\n \n\\sidehead{An0u: $\\tau\\neq\\ups$, $\\tau=0$:} \nAn0u.1&$ \\ell=m $&$ \\ell $&$ \\ell $&$ \\ell $&$\\ell+\\ups $&\\scriptsize{$ 31+ $}&$\\la \\hwh \\hwc \\hwc \\hxh \\ra$&$ N_o $ \\\\\nAn0u.2&$ \\ell=m+\\ups $&$ \\ell $&$ \\ell $&$ \\ell-\\ups $&$ \\ell $&\\scriptsize{$ 31- $}&$\\la \\hwh \\hwc \\hxc \\hwh \\ra$&$ N_o $ \\\\\nAn0u.0&3 distinct &$ \\ell $&$ \\ell $&$ m $&$ m +\\ups $&\\scriptsize{$ 211+ $}&$\\la \\hwh \\hwc \\hxc \\hyh \\ra$&$ N_o^2-2N_o $ \\\\\n\t\t\t\t\t\t\t\t\t\t\t \t\t\t \n\\sidehead{Ant0: $\\tau\\neq\\ups$, $\\ups=0$:}\t\t\t\t\t\t \t\t\t \nAnt0.1&$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell $&$\\ell $&\\scriptsize{$ 31- $}&$\\la \\hwh \\hxc \\hwc \\hwh \\ra$&$ N_o $& \\\\\nAnt0.2&$ \\ell+\\tau= m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell+\\tau $&$ \\ell+\\tau $&\\scriptsize{$ 31+ $}&$\\la \\hxh \\hwc \\hwc \\hwh \\ra$&$ N_o $& \\\\\nAnt0.0&3 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m $&\\scriptsize{$ 211+ $}&$\\la \\hxh \\hyc \\hwc \\hwh \\ra$&$ N_o^2-2N_o $& \\\\\n\t\t\t\t\t\t\t\t\t\t\t \t\t\t \n\\sidehead{Aet: $\\tau =\\ups$, $\\tau\\neq 0$:}\t\t\t\t\t\t \t\t\t \nAet.1 &$ \\ell=m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell $&$\\ell+\\tau $&\\scriptsize{$ 22+ $}&$\\la \\hwh \\hxc \\hwc \\hxh \\ra$&$ N_o $& \\\\\nAet.2 &$ \\ell=m+\\tau $&$ \\ell $&$ \\ell+\\tau $&$ \\ell-\\tau $&$\\ell $&\\scriptsize{$ 211- $}&$\\la \\hwh \\hxc \\hyc \\hwh \\ra$&$ N_o $& a\\\\\nAet.3 &$ \\ell+\\tau=m $&$ \\ell $&$ \\ell+\\tau $&$ \\ell+\\tau $&$\\ell+2\\tau $&\\scriptsize{$(211-)^*$}&$\\la \\hxh \\hwc \\hwc \\hyh \\ra$&$ N_o $& a\\\\\nAet.0 &4 distinct &$ \\ell $&$ \\ell+\\tau $&$ m $&$ m +\\tau $&\\scriptsize{$ 1111+ $}&$\\la \\hwh \\hxc \\hyc \\hzh \\ra$&$ N_o^2-3N_o $& \\\\\n\t\t\t\t\t\t\t\t\t\t\t \t\t\t \n\\sidehead{Ae0: $\\tau =\\ups$, $\\tau=0$:}\t\t\t\t\t\t\t \t\t\t \nAe0.1&$ \\ell=m $&$ \\ell $&$ \\ell $&$ \\ell $&$\\ell $&\\scriptsize{$ 4 $}&$\\la \\hwh \\hwc \\hwc \\hwh \\ra$&$ N_o $& \\\\\nAe0.0&2 distinct &$ \\ell $&$ \\ell $&$ m $&$ m $&\\scriptsize{$ 22+ $}&$\\la \\hwh \\hwc \\hxc \\hxh \\ra$&$ N_o^2-N_o $& \\\\\n\\enddata\n\\tablenotetext{a} {Complex conjugate of element in Table\\ \\ref{table_complex_avgs}.}\n\\label{table_terms_in_Asums}\n\\end{deluxetable}\n\\clearpage\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002064.extracted_bib",
"string": "\\begin{thebibliography}{99}\n% \\bibitem[Anantharamaiah et al.(1991)]{ana91}Anantharamaiah, K. R., Deshpande, A. A., Radhakrishnan, V., Ekers, R. D., Cornwell, T. J., \\& Goss, W. M. 1991, ASP Conf. Ser. 19: IAU Colloq. 131: Radio Interferometry. Theory, Techniques, and Applications, San Francisco: Astronomical Society of the Pacific, p. 6\n\\bibitem[Balestrieri et al.(2005)]{bal05}Balestrieri, E., Daponte, P., \\& Rapuano, S. 2005, IEEE Trans. Inst. Meas., 54, 1388\n\\bibitem[Cooper(1970)]{coo70}Cooper, B.F.C. 1970, AustJPhys, 23, 521 % -527 Correlators with 2-bit quantization\n\\bibitem[D'Addario et al.(1984)]{dad84}D'Addario, L.R., Thompson, A.R., Schwab, F.R., \\& Granlund, J. 1984, Radio Sci., 19, 931\n\\bibitem[Dennett-Thorpe \\& de Bruyn(2002)]{den02}Dennett-Thorpe, J., \\& de Bruyn, A. G. 2002, Nature, 415, 57.\n\\bibitem[Desai et al.(1992)]{des92}Desai, K.M., Gwinn, C.R., Reynolds, J.R., King, E.A., Jauncey, D., Flanagan, C., Nicolson, G., Preston, R.A., \\& Jones, D.L. 1992, ApJ, 393, L75\n% \\bibitem[Gwinn(2001)]{gwi01}Gwinn, C.R. 2001, ApJ, 554, 1197 % Interferometric Visibility of a Scintillating Source\n\\bibitem[Gwinn et al.(2000)]{gwi00}Gwinn, C.R., Britton, M.C., Reynolds, J.E., Jauncey, D.L., King, E.A., McCulloch, P.M., Lovell, J.E.J., Flanagan, C.S., Preston, R.A. 2000, ApJ, 531, 902 % size of the Vela pulsar's emission region at 13 cm wavelength\n\\bibitem[Gwinn(2004)]{gwi04}Gwinn, C.R. 2004, PASP, 116, 84 (Paper 1)% statistics of correlation of quantized gaussian noise\n\\bibitem[Hagen \\& Farley(1973)]{hag73}Hagen, J.B., \\& Farley, D.T. 1973, Radio Sci, 8, 775 % Digital-correlation techniques in radio science\n\\bibitem[Jauncey et al.(2000)]{jau00}Jauncey, D.L., Kedziora-Chudczer, L.L., Lovell, J.E.J., Nicolson, G.D., Perley, R.A., Reynolds, J.E., Tzoumis, A.K., Wieringa, M.H. 2000, Astrophysical Phenomena Revealed by Space VLBI, eds. H. Hirabayashi, P.G. Edwards, D.W. Murphy, ISAS: Sagamihara, p. 147\n\\bibitem[Jenet \\& Anderson(1998)]{jen98}Jenet, F.A., \\& Anderson, S.B. 1998, PASP, 110, 1467 % - 1478 The effects of digitization on nonstationary stochastic signals with application to pulsar signal baseband recording\n% \\bibitem[Jenet, Anderson, \\& Prince(2001)]{jen01}Jenet, F.A., Anderson, S.B., \\& Prince T.A. 2001, ApJ, 558, 302\n% \\bibitem[Kokkeler, Fridman, \\& van Ardenne(2001)]{kok01}Kokkeler, A. B. J., Fridman, P., \\& van Ardenne, A. 2001, Experimental Astronomy, 11, 33 % degradation due to quantization noise in radio astronomy phased arrays\n\\bibitem[Kulkarni \\& Heiles(1980)]{kul80}Kulkarni, S.R., \\& Heiles, C. 1980, AJ, 85, 1413 %How to obtain the true correlation from a 3-level digital correlator\n% \\bibitem[Kulkarni(1989)]{kul89}Kulkarni, S.R. 1989, AJ, 98, 1112 % -1130 Self-Noise in Interferometers: Radio and Infrared\n% \\bibitem[Meyer(1975)]{mey75}Meyer, S.L. 1975, Data Analysis for Scientists and Engineers (Wiley: New York)\n% \\bibitem[Press et al.(1989)]{pre89}Press, W.H., Flannery, B.P., Teukolsky, S.A., \\& Vetterling, W.T. 1989, Numerical Recipes, Cambridge UK: Cambridge Univ. Press\n% \\bibitem[Rickett(1975)]{ric75}Rickett, B.J. 1975, ApJ, 197, 185 % -191 Amplitude-modulated noise - An empirical model for the radio radiation received from pulsars\n% \\bibitem[Thompson, Moran, \\& Swenson(1986)]{tms86}Thompson, A.R., Moran, J.M., \\& Swenson, G.W. Jr. 1986, Interferometry and Synthesis in Radio Astronomy, (New York: Wiley)\n% \\bibitem[Van Vleck \\& Middleton(1966)]{van66}Van Vleck, J.H., \\& Middleton, D. 1966, Proc. IEEE, 54, 2% -19 The Spectrum of Clipped Noise\n\\end{thebibliography}"
}
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astro-ph0002065
|
An X-ray Flare Detected on the M8 dwarf VB 10
|
[
{
"author": "Thomas A. Fleming"
}
] |
We have detected an X-ray flare on the very low mass star VB 10 (GL 752 B; M8 V) using the ROSAT High Resolution Imager. VB 10 is the latest type (lowest mass) main sequence star known to exhibit coronal activity. X-rays were detected from the star during a single 1.1-ksec segment of an observation which lasted 22 ksec in total. The energy released by this flare is on the order of $10^{27}$ ergs s$^{-1}$. This is at least two orders of magnitude greater than the quiescent X-ray luminosity of VB 10, which has yet to be measured. This X-ray flare is very similar in nature to the far ultraviolet flare which was observed by Linsky et al. (1995) using the Goddard High Resolution Spectrograph onboard the Hubble Space Telescope. We discuss reasons for the extreme difference between the flare and quiescent X-ray luminosities, including the possibility that VB 10 has no quiescent ($10^6$ K) coronal plasma at all.
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[
{
"name": "ms.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n%\\received{ }\n%\\accepted{ }\n%\\journalid{ }{ }\n%\\articleid{ }{ }\n\\begin{document}\n\\title{ An X-ray Flare Detected on the M8 dwarf VB 10 }\n\n\\author{ Thomas A. Fleming }\n\\affil{ Steward Observatory \\\\ \nUniversity of Arizona \\\\ \nTucson, AZ 85721 \\\\\[email protected] }\n\\author{ Mark S. Giampapa }\n\\affil{ National Solar Observatory \\\\\nNational Optical Astronomy Observatories\\altaffilmark{1} \\\\\nTucson, AZ 85726 \\\\\[email protected] }\n\\author{ J\\\"urgen H.M.M. Schmitt }\n\\affil{ Hamburg Sternwarte \\\\ \nGojensbergsweg 112 \\\\\n21029 Hamburg, Germany \\\\\[email protected] }\n\n\\altaffiltext{1}{The National Optical Astronomy Observatories are operated for\nthe National Science Foundation by the Association of Universities for \nResearch in Astronomy.}\n\\begin{abstract}\n We have detected an X-ray flare on the very low mass star VB 10 (GL 752 B;\nM8 V) using the ROSAT High Resolution Imager. VB 10 is the latest type \n(lowest mass) main sequence star known to exhibit coronal activity. \nX-rays were detected from the\nstar during a single 1.1-ksec segment of an observation which lasted 22 ksec in\ntotal. The energy released by this flare is on the order of $10^{27}$ \nergs s$^{-1}$. This is at least two orders of magnitude greater than the \nquiescent X-ray luminosity of VB 10, which has yet to be measured. This X-ray\nflare is very similar in nature to the far ultraviolet flare which was \nobserved by Linsky et al. (1995) using the Goddard High Resolution Spectrograph\nonboard the Hubble Space Telescope. We discuss reasons for the extreme\ndifference between the flare and quiescent X-ray luminosities, including the \npossibility that VB 10 has no quiescent ($10^6$ K) coronal plasma at all.\n\\end{abstract}\n\\keywords{stars: X-rays, coronae, low mass }\n\\section{Introduction }\nStars at the very bottom of the main sequence have been a very popular \ntopic of research during the last few years, including in studies of stellar\nactivity.\nFleming, Schmitt, \\& Giampapa (1995) demonstrated that fully-convective M \ndwarfs, i.e. those with masses less than 0.3 M$_\\odot$, exhibit high levels\nof coronal activity, although at that time, virtually no X-ray detections \nhad been made of stars less massive than VB 8 and LHS 3003 (both type M7.) \nThe star VB 10 (a.k.a. GL 752 B, LHS 474; type M8)\nappeared to have been marginally detected once by the Einstein High Resolution \nImager and was catalogued by Barbera et al. (1993). Then Linsky et al. (1995) \nreported the detection of a large amplitude \nflare on VB 10 in the far UV using the Goddard High Resolution Spectrograph.\nMore recently, Neuhauser \\& Com\\`oron (1998) have detected X-ray emission from\na very young brown dwarf in Chameleon. This confirms that activity does exist \nfor the very lowest mass stellar (or substellar) configurations.\n\nWe have used the ROSAT High Resolution Imager (HRI) to reobserve VB 10, which\nwas not detected by the ROSAT Position Sensitive Proportional Counter (PSPC)\nduring either the All-Sky Survey or a 7.3-ksec pointed observation (Fleming et \nal. 1993). By obtaining a deeper exposure, we hoped to discover the nature\nof the VB 10 corona, detect its quiescent X-ray luminosity, and compare its\nlevel of coronal activity to that of the more massive M dwarfs. We have \nsucceded in detecting X-ray emission from VB 10, but only during a brief flare\nsimilar to the one observed by Linsky et al. (1995) at ultraviolet wavelengths.\n\nIn this paper, we present the latest ROSAT data on VB 10. Section 2\ncontains a description of the observations and data analysis. In Section 3,\nwe discuss a hypothesis to account for the stark contrast between \nthe flare and non-flare X-ray flux values, including the possibility of a \ntotal lack of $10^6$ K coronal plasma about VB 10.\n\n\n\\section{Observation}\n\nThe star VB 10 was observed during the period of 1997 October 27-31 for a total\nof 21,992 sec with the ROSAT HRI (Zombeck et al. 1990). \nThe total image is shown in\nFig. 1a. The one obvious X-ray source seen in Fig. 1 is positionally \ncoincident with the star Wolf 1055 (type M3.5 Ve),\nwhich has a common proper motion with VB 10. At the position of VB 10, which\nis marked in Fig. 1a, there is only a marginal detection. However, when\nthe data are separated into their individual Observation Intervals (OBIs),\nwe find that all of the photons in the VB 10 detection are contained within\none single OBI (Figs. 1b and 1c).\n\n\\begin{figure}\n%\\plotfiddle{f1a.ps}{3.0in}{-90}{50}{50}{-210}{320}\n\\caption{ROSAT HRI image of the field around VB 10: a) the entire 22-ksec\nexposure; b) a single 1.1-ksec OBI from UT 1997 October 29 3:05:24 to 3:25:43;\nc) the remaining 20.9-ksec exposure. The bright source seen in all three\nimages is Wolf 1055. All X-ray photons from VB 10 arrive in the single OBI in\nFig. 1b \\label{fig1} }\n%\\plotfiddle{f1b.ps}{3.0in}{-90}{50}{50}{-210}{270}\n%\\plotfiddle{f1c.ps}{3.0in}{-90}{50}{50}{-210}{220}\n\\plotfiddle{f2.ps}{3.0in}{-90}{50}{50}{-210}{270}\n\\caption{Histogram of arrival times for the X-ray source photons from VB 10\n\\label{fig2} }\n\\end{figure}\nThis particular OBI, which began on UT 1997 October 29 at 3:05:24 and ended \nat 3:25:43, had an effective total exposure time of 1,138 sec. Within an \nextraction radius of $12\\arcsec$ around the optical position of VB 10,\n11 photons were detected. By examining the rest of the image, we determined \nthat the density of background photons for this OBI was 0.0024 cts arcs$^{-2}$.\nThe solid angle of our extraction circle about VB 10 was 452.4 arcs$^2$,\nwhich means that we would expect one photon in the extraction circle to \nbe from the background. Therefore, with 10 source photons, the mean count \nrate over the entire OBI is $8.9 (\\pm 2.8) \\times 10^{-3}$ cts s$^{-1}$ \n(this includes a deadtime and vignetting correction factor of 1.017.)\n\nOf course, to get a better idea of the flare duration and flux, one needs\nto look at the temporal distribution of the source photons throughout the \nobservation. In Fig 2, we show a histogram in arrival time for the 11 \nphotons contained within the source extraction radius. Remember, we do not \nknow which one is the background photon. The histogram is binned in 3-minute\n(180 sec) intervals over the nearly 20-minute observation. One can see that\n5 photons arrived in the first 3 minutes of the observation, 5 photons \narrived during the last 8 minutes, with the remaining photon arriving in \nbetween.\nThe data are consistent with there being \nonly one flare which is tailing off during our observation. In this case, the\nflare duration is at least 20 minutes and $2.8 \\times 10^{-2}$ cts s$^{-1}$\n(5 photons in 3 minutes) represents a lower limit to the peak count rate.\n\n%Should this be the one background photon, then we could be seeing two distinct\n%flares. In this case, the count rate for the first flare would be at least\n%$2.8 \\times 10^{-2}$ cts s$^{-1}$. We can only give a lower limit since the \n%flare occurs right at the very beginning of the OBI, so the duration could\n%be longer than 3 minutes. However, \n\nIn order to get the X-ray luminosity, we adopt a conversion factor of \n$2.4 \\times 10^{-11}$ ergs cm$^{-2}$ cnt$^{-1}$. This comes from Table 10\nof David et al. (1999), the ROSAT HRI Calibration Report (Cambridge: \nSAO)\\footnote{$http://hea-www.harvard.edu/rosat/rsdc_www/hricalrep.html$}, \nfor a Raymond-Smith spectrum of 0.5 keV\nand negligible interstellar absorption. This yields an apparent energy flux,\n$f_X = 2.14 (\\pm 0.68) \\times 10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ for \nthe mean count rate. At a distance of 5.74 pc,\nthis gives us a luminosity, $L_X = 8.4 (\\pm 2.7) \\times\n10^{26}$ ergs s$^{-1}$. Again, this is just a mean luminosity for the \nobservation. The peak flare luminosity would be at least $2.65 \\times 10^{27}$\nergs s$^{-1}$.\n\nWe have also analyzed the remaining 20,854 sec of our HRI observation, in\nwhich no X-ray source was detected at the position of VB 10. Using the \nnon-detection analysis software in MIDAS/EXSAS, we have calculated a $3\\sigma$\n(i.e. 99.7\\% confidence) upper limit of $1.8 \\times 10^{-4}$ cts s$^{-1}$.\nThis translates into $3\\sigma$ upper limits on the apparent X-ray flux and\nX-ray luminosity of $4.21 \\times 10^{-15}$ ergs cm$^{-2}$ s$^{-1}$ and \n$1.7 \\times 10^{25}$ ergs s$^{-1}$, respectively, for VB 10 outside of flare.\nThese are upper limits on any quiescent emission, if it exists.\n\nAll of the numbers presented in this section have been tabulated in Table 1.\n\n\\begin{deluxetable}{lclllr}\n\\footnotesize\n\\tablecaption{ X-ray Parameters for ROSAT HRI Observation of VB 10 \n\\label{tbl-1}}\n\\tablewidth{0pt}\n\\tablehead{\n& \\colhead{Exp Time} & \\colhead{Count Rate} & \\colhead{ f$_X$ } &\n\\colhead{ L$_X$ } & \\colhead{ log (L$_X$/L$_{bol}$) } \\\\\n& \\colhead{ ks } & \\colhead{ cts s$^{-1}$ } & \\colhead{ $10^{-13}$ erg cm$^{-2}$ s$^{-1}$} \n& \\colhead{ $10^{26}$ erg s$^{-1}$ } & }\n\n\\startdata\n\nFlare (mean) & 1.14 & $0.0089 \\pm 0.0028 $ & $2.1 \\pm 0.7$ &\n$8.4 \\pm 2.7$ & $-3.3$ \\nl\nFlare (peak) & 0.18 & $> 0.028 $ & $> 6.7 $ &\n$> 27 $ & $> -2.8$ \\nl\nNon-flare & 20.85 & $< 0.00018 $ & $< 0.042 $ &\n$< 0.17 $ & $< -5.0$ \\nl\n\n\\enddata\n\\end{deluxetable}\n\n\\section{Discussion}\n\nThis X-ray flare on VB 10 is reminiscent of the far-UV flare which was \ndetected on VB 10 by Linsky et al. (1995). These authors observed C II,IV\nand Si IV emission lines only during the last five minutes of an hour-long\nexposure taken with the GHRS onboard HST. They concluded that the flare\nwhich they had observed indicated increased magnetic heating rates for \nlow-mass stars near the hydrogen-burning mass limit. \n \nIn both the UV and ROSAT X-ray observations, quiescent (i.e. non-flare) \nemission \nwas never detected from VB 10. For the UV flare, the emission line fluxes \nwere an order of magnitude greater than the upper limits placed on the \nnon-flare emission by Linsky et al. (1995). For this most recent X-ray flare,\nthe contrast is even greater. The peak flare luminosity is {\\it at least} \nmore than two orders of magnitude greater than the non-flare value.\n\nFor ease of comparison to more massive M dwarfs, we will normalize L$_X$ \nby L$_{bol}$, which for VB 10 is $1.74 \\times 10^{30}$ ergs s$^{-1}$ \nbased on the absolute K magnitude measured by Leggett (1992) and the \nbolometric correction of Veeder (1974).\nThis gives us log (L$_X$/L$_{bol}) > -2.8$ for the peak of the flare and\nlog (L$_X$/L$_{bol}) < -5.0$ outside of flare. Using the data of Fleming \net al. (1995) for the late (later than M5), presumably fully-convective M\ndwarfs within 7 pc of the Sun, we find that these star have values of \nlog (L$_X$/L$_{bol}$) which are typically $-3.5$. But during flares \n(e.g. AZ Cnc; Fleming et al. 1993), these stars can reach values of \n(L$_X$/L$_{bol}) = -3.0$ to $-2.5$. Therefore, the magnitude of the flare on\nVB 10 is completely consistent with that of flares on more massive M dwarfs.\n\nIn Fig. 3 we display a plot of normalized X-ray luminosity versus \nabsolute visual magnitude for all known M dwarfs within 7 pc that are later \nthan M5, based on data from a volume-limited survey by Fleming et al. 1995.\nInspection of Fig. 3 reveals the sharp contrast between the upper limit\nto the non-flare X-ray emission in VB 10 and the X-ray emission levels of\nother late dMe stars. In particular, the upper limit for VB 10 is\n1-2 orders of magnitude less than that detected in the late dMe stars. \nIt is comparable to the upper limit for GJ1002 in Fig. 3, a quiescent dM5.5 \nstar that does not exhibit H$\\alpha$ emission nor any reported flare activity.\nBy contrast, VB 10 is a known flare star with (variable) H$\\alpha$ line\nemission in its spectrum.\nWhile one cannot build\na theory based on one observation, we cannot help but speculate that our \nresult for VB 10 does indeed reflect a decline \nin coronal heating\nefficency near the H-burning mass limit. But somehow these stars are still \nable to flare.\n\n We do not understand in detail the mechanisms that give rise\nto energetic, transient outbursts identified as ``flares'' in the Sun and\nlate-type stars. However, flares do appear to be the result of \ninstabilities that return stressed systems toward configurations that\nare characterized by lower potential energy (Rosner \\& Vaiana 1978).\nSince we do not have an X-ray spectrum, we cannot verify through \nmodeling that the observed emission in VB 10 is consistent with \nthe presence of loop-like magnetic structures. However, the \nenergetics of the event suggest the possible occurrence of a large \nvolume of flare plasma, implying the presence of large-scale magnetic\nstructures in the atmosphere. In particular, we can crudely estimate the \nplausible range of spatial scales that characterize the flare event in \nthe following manner.\n\n In the absence of an actual energy spectrum (such as the pulse-height \nspectra that were produced by the now-defunct ROSAT PSPC), we \nassume some plausible flare plasma parameters. Based on X-ray observations\nof other flare events on M dwarfs, we adopt a flaring temperature of \n$T~\\sim~$ 10$^{7}$ K. We note that a large flare event recorded by \nthe ROSAT PSPC on a late M dwarf star was well-described by a thermal\nplasma model fit characterized by a temperature of 2 -- 4 $\\times$ 10$^{7}$ K\n(Sun et al. 1999). Utilizing the XSPEC analysis package combined with \nthe observed flux from the HRI and the adopted temperature yields a\ndifferential emission measure at the flare maximum of EM $> 1.8 \\times\n10^{29}$ cm$^{-5}$. The corresponding volume emission measure is\n$$\nVEM = 4 \\pi R_{*}^2 EM > 1.1 \\times 10^{50}~~cm^{-3}\\,,\n\\eqno(1)\n$$\nwhere R$_{*}$ = 0.102 R$_{\\odot}$ (Linsky et al. 1995). Given this estimate\nof volume emission measure along with electron densities in the range of\n$n_e~\\sim$ 10$^{10}$ cm$^{-3}$ to 10$^{11}$ cm$^{-3}$, we find \ncharacteristic linear \ndimensions for the flare in the range of 0.003 R$_{*}$ to 0.30 R$_{*}$.\nThus, the flaring plasma covers a large fraction of the stellar surface if\n$n_e~\\sim$ 10$^{10}$ cm$^{-3}$, but only a small fraction if \n$n_e~>$ 10$^{11}$ cm$^{-3}$. We note that the distance traveled by a \nsound wave in a 10$^{7}$ K plasma in the 3 minute duration of the flare\nmaximum is about 0.7 R$_{*}$. These estimates, while not conclusive,\nare consistent with the likely occurrence of large-scale magnetic structures\nassociated with the flare event on VB 10.\n \n\n The enormous contrast between the X-ray flare luminosity and \nthe upper limit to quiescent emission invites further consideration,\nespecially in view of the likely existence of significant surface magnetic \nflux and large magnetic structures in VB 10. \n%Addition to text follows (7/21/99):\nWe note that if VB10 is characterized by quiescent X-ray emission at a level\nwhich is typical for the Sun at the maximum in its activity cycle, i.e.,\nlog($L_x/L_{bol})~\\approx$ -6.3 (following Schmitt 1997), then we would still\nnot have had sufficient sensitivity to detect it. The upper limit for \nnon-flare X-ray emission in VB 10 is more comparable to the levels of emission\nseen in earlier, more massive M dwarfs (non-dMe flare stars) which are \nthemselves characterized by X-ray emission levels that are in excess of\nsolar, or log($L_x/L_{bol})~\\sim$ -6 to -5 (following Fleming, Schmitt\n\\& Giampapa 1995).\n\n We thus cannot exclude the possibility that VB 10 does indeed have \nundetected, quiescent X-ray emission at the level of the Sun or that\nof earlier,\nquiescent dwarf M stars. However, inspection of Fig. 3 suggests that the low\nlevel of non-flare X-ray emission in VB 10 is unusual with respect to \nother late-type, active dMe flare stars. \n%End insert (7/21/99)\nWe will therefore briefly \nconsider a hypothesis that may account for \nthe extremely low, or even the possible absence of, steady, quiescent \nheating in this very cool dwarf. \n\n\\begin{figure}\n\\plotfiddle{f3.ps}{2.0in}{-90}{70}{60}{-250}{350}\n\\caption{The normalized X-ray luminosity, log$(L_{x}/L_{bol})$, vs $M_{V}$\nfor M dwarfs later than M5. Filled circles denote dMe stars. Upper limits\nare indicated by arrows. Flare and non-flare values for certain objects\nare shown. Data are taken from Fleming et al. (1993) and Giampapa et al. \n(1996). Solar values are from Peres et al. (1999). \\label{fig3} }\n\n\\end{figure}\n\n While there is no comprehensive theory for coronal \nheating---even in the case of the Sun---a common feature of current \ntheories is that the origin of the nonradiative heating \nof the corona involves the interaction \nbetween turbulent convective motions in the photosphere and the \nfootpoints of magnetic loops (Parker 1972, 1983a,b, 1986; van Ballegooijen\n1986 and references therein). \n%In brief (and highly simplified) summary,\n%convective turbulence causes a random alteration of the structure of the \n%magnetic field lines that penetrate the photosphere, leading to the\n%topological interweaving of fields within closed loops that, in turn, \n%causes the build up of magnetic stresses. The twisted magnetic field\n%in closed loop configurations returns to equilibrium by the dissipation\n%of energy through the associated electric currents that heat the corona.\nIn this context, our observations of VB 10 may imply that at the \nphotosphere there is simply\nnot enough in the way of random motions at the loop footpoints to jostle\nthe magnetic fields and, in turn, provide sufficient dynamical stresses \nto lead to detectable plasma heating to coronal ($T~\\sim$ 10$^{6}$ K) \ntemperatures. For example, a high magnetic field strength may suppress \nconvective motions, analogous to the situation in sunspots which are \nalso X-ray quiet. We further note that the very cool and dense \nphotosphere of VB 10 is dominated\nin content by molecular hydrogen combined with neutral metals bound in \nmolecules. Thus, there are few ions to couple the magnetic field with the \nphotospheric gas. We estimate by extrapolation from \nM dwarf model photospheres (Mould 1976) to \nthe effective temperature of VB 10 (T$_{eff}$ = 2600 K; Linsky et al. \n1995) that \nthe ionization fraction, $\\zeta$, in the dense, \nupper photosphere of VB 10 is $\\zeta~\\sim~$ 10$^{-7}$. By contrast,\n$\\zeta~\\sim~$ 10$^{-4}$ in the upper photosphere of the quiet Sun \n(Vernazza, Avrett, \\& Loeser 1976). In early M dwarfs we have \nthat $\\zeta~\\sim~$ 10$^{-5}$ (following Mould 1976). \nHence, for stars in the temperature-density regime of VB 10, the upper \nphotospheres are characterized by ionization fractions that are \n2 orders of magnitude less than that of earlier M dwarfs and \n3 orders of magnitude below that of the Sun.\nConsequently, the interaction between the field and the \nambient gas occurs deeper in the photosphere where the ionization fraction \nis higher but where sufficient energy to produce significant coronal \nheating is unable to propagate outward.\n\n The consequences for coronal heating of the occurrence of magnetic \nstructures in very cool dwarfs such as VB 10 is summarized in the following\nargument due to F. Meyer (1999, private communication; see also \nMeyer \\& Meyer-Hofmeister 1999). Given that the \ngas pressure in the corona is typically negligible compared \nto the magnetic stresses, we must have that the magnetic field configuration,\nor ``loop'', is force-free, or $\\bf F = (J \\times B)/{\\rm c}$ = \n0. Thus, the electric currents must flow along the magnetic \nfield lines. Since for steady magnetic phenomena the current density \nis divergence-free ($\\bf \\nabla \\cdot J$ = 0), currents must also \nflow through the magnetic footpoints \nin the photosphere. In the cool and dense photosphere of stars such as\nVB 10, the electrical conductivity is so low that any current system \nrapidly decays. From this it follows that the magnetic equilibrium must\nbe current-free everywhere. \nThat is, $\\bf J$ = 0 so that $\\bf \\nabla \\times B$ = 0, and \n${\\bf B = -\\nabla}{\\rm \\Phi}$. Given that the potential field is a minimum\nenergy configuration, any further build-up and storage of magnetic field\nenergy is excluded, implying no (or only a relatively low degree) of \nmagnetic field-related heating of the atmosphere. At the very least, the\ndecay rate of energy at the footpoints must be faster than any energy input \nderived from the interaction between motions in the upper photosphere\nand the magnetic loops, effectively quenching any non-radiative heating\nthat might otherwise have occurred.\n\n Clearly, the above picture as outlined cannot explain flare events.\nInstead, the transient or flare outbursts observed in these very cool \nstars must arise from more complex magnetic topologies where the storage of \nmagnetic field energy occurs, but which do not have footpoints in the \ncool, dense underlying photosphere.\n\nIn summary, we have confirmed that the M8 dwarf VB 10 (Gl 752 B) does indeed \nemit X-rays. It is the lowest mass star on the main sequence which is known\nto do so. This emission, however, appears to be only transient in nature.\nThe contrast between the flare X-ray flux and any possible non-flare \n(i.e., quiescent) X-ray emission is at least two orders of magnitude. \nWe note that X-ray emission in VB 10 at solar levels or even at the \nlevels seen in earlier dwarf M (non-dMe) stars would not be detected at \nour sensitivity limits. In comparison to dMe stars later than M5, the \nupper limit to the non-flare X-ray emission in VB 10 is unusually low.\n\nWe have\nconsidered a hypothesis that the low ionization fraction and, hence, low\nconductivity, in the photosphere of VB 10 inhibits coronal \nheating to the point where quiescent, $10^6$ K coronal plasma may \nnot even exist. In this scenario, the transient, presumably $10^7$ K coronal \nplasma which\ngives rise to the observed X-ray flare would then be associated with \ntopologically complex\nmagnetic field structures that do not have footpoints in \nthe cool photosphere which is, in turn, dominated by neutral atomic\nand molecular species. Should this scenario prove to be correct,\nthen there may indeed be a drop in coronal activity at the bottom of the \nmain sequence: not at the mass where stars become fully convective, as was\nonce suggested, but at the hydrogen-burning mass limit itself.\n\n\\acknowledgements\n We acknowledge insightful discussions with F. Meyer, B. Durney and\nA. van Ballegooijen whose ideas materially contributed to this work.\nTAF acknowledges support from NASA grant NAGW-3160. MSG also acknowledges\nsupport from NASA under the ROSAT Guest Observer program. The ROSAT project is \nsupported by the German Bundesministerium f\\\"ur Forschung und Technologie \n(BMFT/DARA) and the Max Planck Gesellschaft.\n\\clearpage\n\\begin{references}\n\\reference{} Barbera, M., Micela, G., Sciortino, S., Harnden, F.R., Jr.,\n\\& Rosner, R. 1993, \\apj, 414, 846\n\\reference{} Fleming, T.A., Schmitt, J.H.M.M., \\& Giampapa, M.S. 1995,\n\\apj, 450, 401\n\\reference{} Fleming, T.A., Giampapa, M.S., Schmitt, J.H.M.M., \\& Bookbinder, \nJ.A. 1993, \\apj, 410, 387\n\\reference{} Giampapa, M.S., Rosner, R., Kashyap, V., Fleming, T.A., \nSchmitt, J.H.M.M., \\& Bookbinder, J.A. 1996, \\apj, 463, 707\n\\reference{} Leggett, S.K. 1992, \\apjs, 82, 351\n\\reference{} Linsky, J.L., Wood, B.E., Brown, A., Giampapa, M.S., \\& \nAmbruster, C. 1995, \\apj, 455, 670\n\\reference{} Meyer, E. \\& Meyer-Hofmeister, E. 1999, \\aap, 341, L23\n\\reference{} Mould, J. R. 1976, \\aap, 48, 443\n\\reference{} Neuhauser, R. \\& Comeron, F. 1998, Science, 282, 83\n\\reference{} Parker, E. N. 1972, \\apj, 174, 499\n\\reference{} Parker, E. N. 1983a, \\apj, 264, 635\n\\reference{} Parker, E. N. 1983b, \\apj, 264, 642\n\\reference{} Parker, E. N. 1986, in Proc. Trieste Workshop Series, Relations\nbetween Chromospheric-Coronal Heating and Mass Loss in Stars, ed. \nJ. B. Zirker and R. Stalio (Sunspot: Sacramento Peak Observatory), p. 199.\n\\reference{} Peres, G., Orlando, S., Reale, F., Rosner, R., \\& Hudson, H. 1999,\n\\apj, in press\n\\reference{} Rosner, R. \\& Vaiana, G. S. 1978, \\apj, 222, 1104\n\\reference{} Sun, X., Fenimore, E. E., Li, H., Wei, J., Hu, J., Zhao, Y. 1999,\n\\apj, submitted\n\\reference{} van Ballegooijen, A. A. 1986, \\apj, 311, 1001\n\\reference{} Veeder, G.J. 1974, \\aj, 79, 1056\n\\reference{} Vernazza, J. E., Avrett, E. H. \\& Loeser, R. 1976, \\apjs, 30, 1\n\\reference{} Zombeck, M.V., Conroy, M., Harnden, F.R., Roy, A., Br\\\"auninger,\nH., Burkert, W., Hasinger, G., \\& Predehl, P. 1990, \\procspie, 1344, 267\n\n\\end{references}\n\n\\end{document}\n\n\n"
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astro-ph0002066
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\hst\/ Images of Stephan's Quintet: Star Cluster Candidates in a Compact Group Environment
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"author": "S. C. Gallagher"
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We present \hst\/ WFPC2 images of Stephan's Quintet which encompass three interacting galaxies and their associated tidal features. These deep, three-color ($B,V,I$) images indicate recent, massive stellar system formation in various regions within the compact group environment. We have identified star cluster candidates (SCC) both within the interacting galaxies and in the tidal debris. We compare the SCC colors with stellar population synthesis models in order to constrain cluster ages, and compare the pattern of formation of SCC in different regions to the inferred dynamical history of the group.
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"name": "gallaghers.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Gallagher, Hunsberger, Charlton, \\& Zaritsky}{Star Cluster Candidates In Stephan's Quintet}\n\\pagestyle{myheadings}\n\\nofiles\n\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\\def\\hst{{\\it HST}}\n\\def\\todo{{\\Huge $\\bullet$}}\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\def\\simgt{\\lower 2pt \\hbox{$\\, \\buildrel {\\scriptstyle >}\\over {\\scriptstyle\\sim}\\,$}}\n\\def\\simlt{\\lower 2pt \\hbox{$\\, \\buildrel {\\scriptstyle <}\\over {\\scriptstyle\\sim}\\,$}}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n%For clarity in the footnotes, I will use the symbols rather than the numbers.\n%My second footnote is for a mathematical symbol, and if a number is used it\n%is unclear.\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\n\\begin{document}\n\\title{\\hst\\/ Images of Stephan's Quintet: Star Cluster Candidates in a \nCompact Group Environment}\n \\author{S. C. Gallagher}\n\\affil{Dept. of Astronomy \\& Astrophysics, Penn State, \n525 Davey Lab, University Park, PA 16802, USA}\n\\author{S. D. Hunsberger}\n\\affil{Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, USA}\n\\author{J. C. Charlton}\n\\affil{Dept. of Astronomy \\& Astrophysics, Penn State}\n\\author{D. Zaritsky}\n\\affil{University of Arizona/Steward Observatory, 933 N. Cherry St., Tucson,\nAZ 85721, USA}\n%\n%-----------------------------------------------------------------------------------------\n\\begin{abstract}\nWe present \\hst\\/ WFPC2 images of Stephan's Quintet which encompass three interacting\ngalaxies and their associated tidal features. These deep, three-color\n($B,V,I$) images indicate recent, massive stellar system formation in\nvarious regions within the compact group environment. We have identified\nstar cluster candidates (SCC) both within the interacting galaxies and\nin the tidal debris. We compare the SCC colors with stellar population\nsynthesis models in order to constrain cluster ages, and compare the pattern\nof formation of SCC in different regions to the inferred dynamical history \nof the group.\n\\end{abstract}\n%\n\\keywords{stars -- clusters; galaxies -- compact groups}\n%\n%-----------------------------------------------------------------------------------------\n\\section{Introduction}\nThe Hickson Compact Groups (HCG; Hickson 1982) are among the densest concentrations of\ngalaxies in the local universe. These high densities combined with relatively low velocity \ndispersions, $\\sigma\\sim(2-3)\\times10^2$~km~s$^{-1}$ (Hickson et al. 1992),\nmake them active sites of strong galaxy interactions. \nInteractions are believed to initiate bursts of star cluster formation on many\nscales from dwarf galaxies along tidal tails\nto massive star clusters, the progenitors of today's globular clusters. \nOne group in particular, Stephan's Quintet (SQ; also known as HCG~92), is notable for \nevidence of multiple interactions.\n%-----------------------------------------------------------------------------------------\n\\begin{figure}[t]\n\\plotfiddle{gallaghers1.eps}{3in}{-90}{50}{50}{-165}{220}\n\\caption{This $V-$band image is produced from two overlapping pointings of\nWFPC2. The field-of-view is approximately $3\\farcm7 \\times 2\\farcm5$, and the regions of interest\nhave been labeled. The fifth member of the group, NGC~7317, is out of the frame to the west.\nNote that NGC~7320 is a foreground galaxy not relevant to the current\ndiscussion.}\n\\end{figure}\n%-----------------------------------------------------------------------------------------\n\nSQ is comprised of five galaxies: NGC~7317, NGC~7318A and B, NGC~7319 and NGC~7320\n(see Fig.~1 for galaxy identifications).\nBased on multiwavelength observations of the group, NGC~7317 and NGC~7320 \nshow no evidence for recent interactions, unlike the other three galaxies \n(NGC~7320 is a foreground galaxy).\nIn particular, NGC~7318B shows morphological disruption of spiral structure,\nand a long tidal tail extends from NGC~7319.\nThe interactions have resulted in recent and ongoing star formation\nas evident from $B-V$ (Schombert et al. 1990), H$\\alpha$\n(V\\'{\\i}lchez \\& Iglesias-P\\'aramo 1998) and far-infrared (Xu, Sulentic \\& Tuffs 1999) \nimaging. \nFurthermore, in the photometric dwarf galaxy study of Hunsberger, \nCharlton, \\& Zaritsky (1996), SQ was identified as hosting the richest known system \nof tidal dwarf galaxy candidates. From these studies, only the largest star-forming \nregions were resolved; many of the young stars appeared to be distributed in the \ndiffuse light in the tidal features between the galaxies. High spatial resolution is \nrequired to identify star cluster candidates (SCC)\nwhich at the distance of SQ ($z=0.02$; $d\\sim66h^{-1}$~Mpc) are faint point sources on the \nWide Field and Planetary Camera 2 (WFPC2). {\\it Hubble Space Telescope} (\\hst)\nimaging was the obvious next step for investigating the full range in \nscale of massive star formation structure. Furthermore, with these images \nwe could investigate whether \nstar clusters form in diverse environments from the inner regions of \ngalaxies to tidal debris tens of kiloparsecs from a galaxy center.\n%\n%-----------------------------------------------------------------------------------------\n\\section{Observations and Data Analysis}\nSQ was observed with the \\hst\\ WFPC2 in \ntwo pointings. The first on 30 Dec 1998, encompassed\nNGC~7318A/B and NGC~7319. The second, on 17 Jun 1999, covered the extended \ntidal tail of NGC~7319.\nOn both occasions, the images were once dithered{\\footnote[1]{Dithering entails \noffsetting the image position\nby a half-integer pixel amount in both the $x$ and $y$ directions in order to increase \nthe effective resolution of the combined image by better sampling the PSF. In this case,\nwe obtained two images in each field and filter.}} \nand taken through three wide-band filters: F450W ($B$), F569W ($V$) and F814W ($I$). \nThe exposure times in each field were $4\\times 1700$~s, $4\\times800$~s and $4\\times500$~s for\n$B$, $V$ and $I$, respectively. The data were first processed through the \nstandard \\hst\\ pipeline. \nSubsequently, they were cleaned of cosmic\nrays using the STSDAS task GCOMBINE, followed by the IRAF task COSMICRAYS to remove hot\npixels. Fig.~1 shows the $V$ band image of both fields combined with the\nregions of interest labeled.\n\nThe initial detection of point sources was undertaken using the DAOFIND routine in \nDAOPHOT (Stetson 1987)\nwith a very low detection threshold. This produced thousands of sources per chip, and \nwe then performed aperture photometry on all sources. Those sources with $S/N>3.0$ that \nappeared in the images at both dither positions were retained. Sources with ${\\rm FWHM}>2.5$ \nor $\\Delta_V>2.4${\\footnote[2]{$\\Delta_V$ is the difference between the $V$ magnitudes \ncalculated with two photometric apertures: one with radius 0.5~pix and the other \nwith radius 3.0~pix.}} \nwere rejected as extended (Miller et al. 1997).\nThose point sources with $V-I>2.0$ are likely foreground stars, \nand the remaining sources are considered star cluster candidates (SCC). \nThis sample will clearly contain some foreground stars and background galaxies, \nbut the spatial coincidence of \nmost of the sources with the galaxy bulges and tidal features is evidence that\nmany candidates are legitimate SCC. Approximately 150 sources were found in all \nthree filters; they are plotted in the $B-V$ versus $V-I$ color-color plot in Fig.~2. \nIn Fig.~3, zoom images\nof the tidal tail in NGC~7319 and the northern starburst region (NSR) have the \nSCC marked with circles. For a discussion of the extended sources in the field, see \nHunsberger et al. (this proceedings).\n%--------------------------------------------------------------------------------------------\n\\begin{figure}[t!]\n\\plotfiddle{gallaghers2.eps}{3.0in}{0}{45}{45}{-130}{-15}\n\\caption{$B-V$ versus $V-I$ color-color plot of star cluster candidates (SCC). \nThe solid line represents the \nevolutionary tracks for a Bruzual \\& Charlot (1993) stellar population \nsynthesis instantaneous-burst model\n(with a Salpeter IMF and solar metallicity). Numbers along the \ntracks are years. The SCC photometry has not been corrected for Galactic \nreddening; the models have been reddened with $A_{B}=0.49$\n(value from the Large Extragalactic Database for Astronomy; Paturel et al. 1997).}\n\\end{figure}\n%--------------------------------------------------------------------------------------------\n\\section{Discussion}\n\\subsection{Dynamical History of Stephan's Quintet}\nThe diversity of tidal features in SQ is indicative of the complex interaction\nhistory in the group. In the dynamical history proposed by Moles, Sulentic, \\& M\\'arquez \n(1997; hereafter MSM97), NGC~7320C (out of the frame of Fig.~1 to the northeast) passed through \nthe group a few hundred million years ago stripping NGC~7319 of much of its HI \n(Shostak et al. 1984)\nand inducing the extension of the tidal tail. \nIn addition, gas was deposited in the area that is currently the NSR. \nThis first event would have induced star formation\nin the environs of NGC~7319 and perhaps triggered the observed Seyfert~2 \nactivity in the nucleus.\n\nTwo of the four galaxies in Fig.~1, NGC~7319 and NGC~7318A,\nhave radial velocities within 50~km~s$^{-1}$ of 6600~km~s$^{-1}$. A third,\nNGC~7318B, while apparently interacting with NGC~7318A, has a discordant velocity, \n$v=5700$~km~s$^{-1}$ (Hickson et al. 1992). This discrepancy is \ninconsistent with the interpretation of NGC~7318B as a foreground galaxy because\nof the obvious morphological distortion seen in Fig. 1.\nInstead, in the most recent and ongoing interaction event NGC~7318B is \nfalling into the group for the first time.\nHI maps of the group show that NGC~7318B still retains the bulk of its gas \n(Shostak et al. 1984; MSM97) unlike all of the galaxies with concordant\nvelocities. As NGC~7318B approaches SQ, its ISM is shocking the gas of the intragroup medium \n(IGM) in the NSR and along its eastern spiral arm. An extended arc of both \nradio continuum (van der Hulst \\& Rots 1981)\nand X-ray (Pietsch et al. 1997) emission supports the \nshocked gas scenario, and H$\\alpha$ emission in the same region at the \nradial velocity of NGC~7318B indicates that the collision-compressed gas is being converted\ninto stars (MSM97). Hunsberger et al. (1996) also found tidal dwarf \ngalaxy candidates along part of the same structure.\n%--------------------------------------------------------------------------------------------\n\\begin{figure}[t!]\n%\\plotone{tail.eps}\n\\plotfiddle{gallaghers3.eps}{4.2in}{0}{55}{55}{-150}{0}\n\\caption{$B-$band zoom images of tidal features with star cluster candidates circled; \nnot to the same scale. {\\sc top}: Tidal tail of \nNGC~7319. {\\sc bottom}: Northern starburst region.}\n\\end{figure}\n%--------------------------------------------------------------------------------------------\n%\n\\subsection{Star Formation History from SCC Colors}\nIn all regions with tidal features or galaxies, we identified SCC.\nFrom the simulations of Ashman \\& Zepf (1992) of merger remnants, we expected to find\nmassive young star clusters in the bulges of NGC~7318A and B, but there \nwe only detected point sources with colors consistent with old globular clusters. \nThis result can be \nunderstood if the interaction between NGC~7318A and B is relatively recent, and \nstar formation is just beginning in the outer regions of the galaxies. This picture\nis consistent with the observations of NGC~7252 (Miller et al. 1997) and \nthe Antennae (Whitmore et al. 1999) which suggest that cluster formation is initiated\nat large galactic radii and propagates inward over time. In NGC~7319, we do find young\nSCC in the disk and bulge, supporting the older interaction scenario for the event which\nstripped it of its gas and pulled out the tidal tail.\n\nFrom our images, it is also clear that star clusters can form {\\it outside} of galaxies. \nIn the NSR, the star formation is occurring $\\simgt20$~kpc from the bulge of \nthe nearest galaxy. In addition, we discovered several young star clusters in the \ntidal tail of NGC~7319. In the color-color plot (Fig.~2), there is a clear distinction\nbetween the sources associated with NGC~7318B and those in NGC~7319 and its tidal tail. \nThe most recent star formation is occurring in the NSR and the spiral arms of NGC~7318B;\nages of some SCC in those regions are at least as young as 5~Myr. Any intrinsic dust \nextinction would only cause an overestimate of the ages as the reddening vector is \napproximately parallel to the evolutionary tracks at that point.\n%\nIn addition to the youngest SCC in each region, we also observe a spread of ages from \nold globular cluster candidates (GCC) with ages $\\tau\\sim~10^{10}$~yr to more \nintermediate-aged SCC, $\\tau\\sim~10^{8}$~yr. This spread is most apparent in the \nNSR and along the tidal tail, both regions where extended periods of \ninteraction-induced star formation are reasonable. Furthermore, the \npresence of the old GCC in the tidal features \nsuggests they were pulled out of their birth galaxies as a result of the interactions. \n%-----------------------------------------------------------------------------------------\n%\n\\section{Conclusions}\nFrom \\hst\\ WFPC2 images, we find $\\sim150$ SCC in the environs of SQ. SCC are \nfound both within the bulges of each of the galaxies NGC~7318A/B and NGC~7319,\nand also in tidal features. \nThe ages deduced from $B-V$ versus $V-I$ colors of SCC\nare consistent with the complex interaction scenario outlined by \nMSM97. Since only old GCC are found in the\ncenters of NGC~7318A/B, this suggests that recent star formation has not yet occurred there. Very\nyoung SCC are found along the interaction shock front between the ISM of NGC~7318B \nand the IGM of SQ supporting the hypothesis that this is a recent event. The spread\nof ages in SCC found throughout the field is indicative of recurring episodes of \ninteraction-induced star formation. \n\n\\acknowledgements \nWe are grateful to A. Kundu and B. Whitmore for sharing \ntheir expertise in identifying and analyzing point sources in WFPC2 images. \nThis work was supported by Space Telescope Science Institute under Grant GO--06596.01.\n%\n\\begin{references}\n\\reference Ashman, K. M. \\& Zepf, S. E. 1992, \\apj, 384, 50\n\\reference Bruzual, G. A. \\& Charlot, S. 1993, \\apj, 405, 538\n\\reference Hickson, P. 1982, \\apj, 255, 382\n\\reference Hickson, P., Mendes De Oliveira, C., Huchra, J. P. \\& Palumbo, G. G. 1992, \\apj, 399, 353\n\\reference Hunsberger, S. D., Charlton, J. C. \\& Zaritsky, D. 1996, \\apj, 462, 50 \n\\reference Miller, B. W., Whitmore, B. C., Schweizer, F. \\& Fall, S. M. 1997, \\aj, 114, 2381\n\\reference Moles, M., Sulentic, J. W., \\& M\\'arquez, I. 1997, \\apj, 485, L69 (MSM97)\n\\reference Moles, M., M\\'arquez, I., \\& Sulentic, J. W. 1998, \\aap, 334, 473\n\\reference Paturel, G., et al. 1997, \\aaps, 124, 109 \n\\reference Pietsch, W., Trinchieri, G., Arp, H., \\& Sulentic, J. W. 1997, \\aap, 322, 89\n\n\\reference Schombert, J. M., Wallin, J. F. \\& Struck-Marcell, C. 1990, \\aj, 99, 497 \n\\reference Shostak, G. S., Allen, R. J., \\& Sullivan, W. T. 1984, \\aap,139, 15\n\\reference Stetson, P.B. 1987, \\pasp, 99, 191\n\\reference van der Hulst, J. M. \\& Rots, A. H. 1981, \\aj, 86, 12\n\\reference V{\\'{\\i}}lchez, J. M. \\& Iglesias-P\\'aramo, J. 1998, \\apjs, 117, 1\n\\reference Whitmore, B. C., Zhang, Q. , Leitherer, C. , Fall, S. M. , Schweizer, F. \\& Miller, B. W. 1999, \\aj, 118, 1551 \n\\reference Xu, C. , Sulentic, J. W. \\& Tuffs, R. 1999, \\apj, 512, 178\n\\end{references}\n\n\\section*{Discussion}\n\n{\\it J. Gallagher:\\/} What is the spatial distribution of the cluster colors as\ncompared to colors of the more diffuse debris? This might help in investigating \ndifferences between cluster formation versus cluster evolution.\n\n\\noindent{\\it S. G.:\\/} In general, the diffuse emission between the galaxies has $B-V$ colors\nsimilar to those of the outer regions of spiral disks. More\nspecifically, in the NSR and along the eastern spiral arm of NGC~7318B, the diffuse light\nhas $B-V$ colors between 0.3 and 0.5 (Schombert et al. 1990), as do some regions \nin the tidal tail. \nWe find young cluster candidates in those regions with similar colors as well \nas some with $B-V<0.3$.\n\n\\noindent{\\it T. B\\\"oker:\\/} In your color-color diagram, there are a handful of ``clusters'' that \nare not explained by reddening. Do you have any idea what they are?\n\n\\noindent{\\it S. G.:\\/} There does appear to be a group of point sources clumped below the\nevolutionary tracks on the red end of the $V-I$ axis. I have investigated each of them, and\nthey do not appear to be part of a distinct population. A few of these sources\nare quite faint in $B$ which could cause some scatter, and there is certainly\nsome contamination from background galaxies and stars. \n\n\\noindent{\\it U. Fritze-von Alvensleben:\\/} Where is HI located? Is there any correlation \nbetween the absence of HI and the absence of young star clusters?\n\n\\noindent{\\it S. G.:\\/} The HI distribution is unusual as most of the gas in the group \nis {\\it outside} of the galaxies. There is as much HI as is typically found in an \nentire spiral galaxy to the south of NGC~7319, including the tidal tail, \nand a fair amount in the NSB as well\n(Shostak et al. 1984). \nWe find young SCC in both of those regions. The disk of NGC~7319 is almost entirely \nlacking in gas, but we find some young SCC candidates in that galaxy, though they are\nstrung along the spiral arms. The bulge of NGC~7318B still has its HI, and does not\nappear to contain any young SCC.\n\n\\noindent{\\it G. Meurer:\\/} Are any of the centers of the galaxies blue? I suspect the \nreason that you don't see any nuclear clusters is because the galaxies are too far away hence \ncrowding makes them difficult to distinguish.\n\n\\noindent{\\it S. G.:\\/} NGC~7318A and B have similar central colors: $B-V\\sim1.0$ and \n$V-I\\sim1.2$ that are not particularly blue (though there may be a significant amount\nof intrinsic reddening).\nNGC~7319 is bluer with $B-V\\sim0.5$ and $V-I\\sim1.2$; those colors are consistent with\nthe Seyfert~2 activity in the nucleus. The complex structure in the center of \neach of these galaxies would certainly make detecting a nuclear cluster very difficult. \nHowever, we find no young SCC within the inner 2--3~kpc even where the light distribution \nis smooth. In NGC~7319 we do find young SCC within the bulge of the galaxy.\n\n\\end{document}\n"
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astro-ph0002067
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Fast Reconnection of Magnetic Fields in Turbulent Fluids
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Reconnection is the process by which magnetic fields in a conducting fluid change their topology. This process is essential for understanding a wide variety of astrophysical processes, including stellar and galactic dynamos and astrophysical turbulence. To account for solar flares, solar cycles and the structure of the galactic magnetic field reconnection must be fast, propagating with a speed close to the Alfv\'en speed. Earlier attempts to deal with magnetic reconnection assumed that magnetized fluids are laminar and as a result obtained slow reconnection rates. We show that the presence of a random magnetic field component substantially enhances the reconnection rate and enables {fast reconnection}, i.e. reconnection that does not depend on fluid resistivity. The enhancement of the reconnection rate is achieved via a combination of two effects. First of all, only small segments of magnetic field lines are subject to direct Ohmic annihilation. Thus the fraction of magnetic energy that goes directly into fluid heating goes to zero as fluid resistivity vanishes. However, the most important enhancement comes from the fact that unlike the laminar fluid case where reconnection is constrained to proceed line by line, the presence of turbulence enables many magnetic field lines to enter the reconnection zone simultaneously. A significant fraction of magnetic energy goes into MHD turbulence and this enhances reconnection rates through an increase in the field stochasticity. In this way magnetic reconnection becomes fast when field stochasticity is accounted for. As a consequence solar and galactic dynamos are also fast, i.e. do not depend on fluid resistivity.
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"string": "\\documentclass[proceedings]{rmaa}\n\n%% Miscellaneous definitions\n\\newcommand{\\ibid}{\\rule[-0.03cm]{4.7em}{.01cm}.\\ }\n\\newcommand{\\taulyc}{\\mbox{$\\tau_{LyC}$}}\n\\newcommand{\\alphaalpha}{\\mbox{$\\alpha^{eff}_{H\\alpha}$}}\n\\newcommand{\\alphaB}{\\mbox{$\\alpha_{B}$}}\n\\newcommand{\\kms}{\\mbox{$\\,$km s$^{-1}$}}\n\\newcommand{\\thC}{$\\theta^1\\,$C~Ori}\n\\newcommand{\\thA}{$\\theta^2\\,$A~Ori}\n\\newcommand{\\subsun}{M$_{\\hbox{$\\odot$}}$}\n\\newcommand{\\peryr}{yr$^{-1}$}\n\\newcommand{\\HST}{{\\em HST\\/}}\n\\newcommand{\\Av}{A_V}\n\\newcommand{\\tevap}{t_{\\rm e}} \n\\newcommand{\\tdyn}{t_{\\rm d}}\n\\newcommand{\\rcrit}{r_{\\rm cr}}\n\\newcommand{\\smy}{\\mbox{M}_\\odot \\, \\mbox{yr}^{-1}}\n\\newcommand{\\XXXX}[1]{{\\bfseries ****{\\sffamily #1}}}\n\\newcommand{\\FigBox}[2][\\columnwidth]{\\framebox[#1]{\\rule{0pt}{#2}}}\n\\newcommand{\\rmaacls}{{\\LARGE\\texttt{rmaa.cls}}}\n%% The spectral lines\n\\newcommand{\\Ha}{H$\\alpha$}\n\\newcommand{\\Hb}{H$\\beta$}\n\\newcommand{\\SII}{[\\ion{S}{2}]\\ 6731\\AA}\n\\newcommand{\\NII}{[\\ion{N}{2}]\\ 6583\\AA}\n\\newcommand{\\OI}{[\\ion{O}{1}]\\ 6300\\AA}\n\\newcommand{\\HeI}{\\ion{He}{1}\\ 5676\\AA}\n\\newcommand{\\OIII}{[\\ion{O}{3}]\\ 4959\\AA}\n\\newcommand{\\SIII}{[\\ion{S}{3}]\\ 6312\\AA}\n%% short versions\n\\newcommand{\\SIIshort}{[\\ion{S}{2}]}\n\\newcommand{\\NIIshort}{[\\ion{N}{2}]}\n\\newcommand{\\OIshort}{[\\ion{O}{1}]}\n\\newcommand{\\HeIshort}{\\ion{He}{1}}\n\\newcommand{\\OIIIshort}{[\\ion{O}{3}]}\n\\newcommand{\\SIIIshort}{[\\ion{S}{3}]}\n\n\\def\\plotBTD#1#2{%\n \\expandafter\\ifx\\csname epsfbox\\endcsname\\relax\n \\immediate\\write16{%\n You need to input epsf; I'll do it for you\n }%\n \\input epsf\n \\fi\n \\epsfysize=#2\n \\openin 1 #1 \\ifeof 1\n \\immediate\\write16{Can't open #1}%\n \\vskip \\the\\epsfysize\n \\else\n \\closein 1\n \\centerline{\\epsfbox{#1}}%\n \\fi\n}\n\n\n\n\\title{Fast Reconnection of Magnetic Fields in Turbulent Fluids}\n\n\\author{A. Lazarian \\affil{Department of Astronomy, University of\n Wisconsin-Madison, USA} \\and\n E. Vishniac \\affil{Department of Physics and Astronomy, Johns\n Hopkins University, Baltimore, USA}}\n\n\\fulladdresses{ \\item A. Lazarian: Dept. of Astronomy, University of Wisconsin,\n5534 Sterling Hall, 475 N. Charter St., Madison, WI 53706, USA\n([email protected]) \n\\item E. Vishniac: Dept. of Physics and Astronomy, Johns Hopkins University,\n3400 N. Charles St., Baltimore, MD 21218, USA ([email protected])}\n\n\n\n\\shortauthor{Lazarian \\& Vishniac}\n\\shorttitle{Fast Turbulent Reconnection}\n\n%\\resumen{La reconecci\\'on es el proceso mediante el cual los campos\n%magn\\'eticos cambian de topolog\\'{\\i}a en un medio conductor. Este evento\n%es fundamental para entender diferentes procesos astrof\\'{\\i}sicos, incluyendo\n%la turbulencia y los dinamos estelares y gal\\'acticos. La reconecci\\'on debe\n%ser r\\'apida, propag\\'andose a una velocidad ceracana a la de Alfv\\'en, para\n%explicar las estructura del campo gal\\'actico y las r\\'afagas y el ciclo\n%solar. Los trabajos anteriores sobre la reconecci\\'on consideraban fluidos\n%laminares magnetizados y obten\\'{\\i}an tasas de reconecci\\'on peque\\~nas.\n%Mostramos que la presencia de una componente aleatoria del campo magn\\'tico\n%aumenta la tasa de reconecci\\'on y permite una {\\it reconnecci\\'on r\\'apida},\n%que no depende de la resistencia del fluido. Este aumento se debe a dos\n%efectos. Primero, s\\'olo segmentos peque\\~nos de las l\\'{\\i}neas de campo\n%participan en forma directa en la disipaci\\'on Ohmica. De manera que la\n%fracci\\'on de energ\\'{\\i}a magn\\'etica que se transforma directamente en \n%calor se va a cero cuando la resistencia del fluido desaparece. El aumento\n%m\\'as importante viene del hecho de que, a diferencia de un fluido laminar\n%donde el proceso avanza l\\'{\\i}nea por l\\'{\\i}nea, en el caso turbulento\n%participan muchas l\\'{\\i}neas simult\\'aneamente en la zona de reconecci\\'on.\n%Un fracci\\'on importante de la energ\\'{\\i}a magn\\'etica se va a la\n%turbulencia MHD, lo cual aumenta la tasa de reconecci\\'on al aumentar la\n%parte aleatoria del campo. De manera que la reconecci\\'on se vuelve r\\'apida\n%cuando se incluyen efectos estoc\\'asticos. Como consecuencia, los dinamos\n%solares y gal\\'acticos tambi\\'en se vuelven r\\'apidos.}\n\n\\resumen{La reconecci\\'on es el proceso mediante el cual los campos\n magn\\'eticos cambian de topolog\\'{\\i}a en un medio conductor y es\n fundamental para entender diferentes procesos, incluyendo la\n turbulencia interestelar y los dinamos estelares y gal\\'acticos.\n Para explicar el campo gal\\'actico y las r\\'afagas y el ciclo solar,\n la reconecci\\'on debe ser r\\'apida y propagarse a la velocidad de\n Alfv\\'en. Trabajos anteriores consideraban fluidos laminares y\n obten\\'{\\i}an tasas de reconecci\\'on peque\\~nas. Mostramos que la\n presencia de una componente aleatoria del campo magn\\'tico permite\n una {\\it reconnecci\\'on r\\'apida} ya que, a diferencia del caso\n laminar donde el proceso avanza l\\'{\\i}nea por l\\'{\\i}nea, en el\n caso turbulento participan muchas l\\'{\\i}neas simult\\'aneamente. Una\n fracci\\'on importante de la energ\\'{\\i}a magn\\'etica se va a la\n turbulencia MHD, lo cual aumenta la tasa de reconecci\\'on al\n aumentar la parte aleatoria del campo. Como consecuencia, los\n dinamos solares y gal\\'acticos tambi\\'en se vuelven r\\'apidos.}\n\n\\abstract{Reconnection is the process by which magnetic fields in a\n conducting fluid change their topology. This process is essential\n for understanding a wide variety of astrophysical processes,\n including stellar and galactic dynamos and astrophysical turbulence.\n To account for solar flares, solar cycles and the structure of the\n galactic magnetic field reconnection must be fast, propagating with\n a speed close to the Alfv\\'en speed. Earlier attempts to deal with\n magnetic reconnection assumed that magnetized fluids are laminar and\n as a result obtained slow reconnection rates. We show that the\n presence of a random magnetic field component substantially enhances\n the reconnection rate and enables {\\it fast reconnection}, i.e.\n reconnection that does not depend on fluid resistivity. The\n enhancement of the reconnection rate is achieved via a combination\n of two effects. First of all, only small segments of magnetic field\n lines are subject to direct Ohmic annihilation. Thus the fraction of\n magnetic energy that goes directly into fluid heating goes to zero\n as fluid resistivity vanishes. However, the most important\n enhancement comes from the fact that unlike the laminar fluid case\n where reconnection is constrained to proceed line by line, the\n presence of turbulence enables many magnetic field lines to enter\n the reconnection zone simultaneously. A significant fraction of\n magnetic energy goes into MHD turbulence and this enhances\n reconnection rates through an increase in the field stochasticity.\n In this way magnetic reconnection becomes fast when field\n stochasticity is accounted for. As a consequence solar and galactic\n dynamos are also fast, i.e. do not depend on fluid resistivity.}\n\n\\keywords{galaxies: magnetic fields --- ISM: magnetic fields\n ---Magnetic fields --- MHD --- Sun: magnetic fields} \n\n\\begin{document}\n\n\\maketitle\n\\vspace*{-4ex}\n\\section{Flux Freezing \\& Reconnection}\n\nPlasma conductivity is high for most astrophysical circumstances.\nThis suggests that ``flux freezing'', where magnetic field lines move\nwith the local fluid elements, is usually a good approximation within\nastrophysical magnetohydrodynamics (MHD). The coefficient of magnetic\nfield diffusivity in a fully ionized plasma is $\\eta=c^2/(4\\pi\n\\sigma)=10^{13}T^{3/2}$~s$^{-1}$ cm$^2$ s$^{-1}$, where $\\sigma=10^7\nT^{3/2}$ s$^{-1}$ is the plasma conductivity and $T$ is the electron\ntemperature. The characteristic time for field diffusion through a\nplasma slab of size $y$ is $y^2/\\eta$, which is large for any\n``astrophysical'' $y$.\n\nWhat happens when magnetic field lines intersect? Do they deform each\nother and bounce back or they do change their topology? This is the\ncentral question of the theory of magnetic reconnection. In fact, the\nwhole dynamics of magnetized fluids and the back-reaction of the\nmagnetic field depends on the answer.\n\nMagnetic reconnection is a long standing problem in theoretical MHD.\nThis problem is closely related to the hotly debated issue of the\nmagnetic dynamo (see Parker 1979; Moffatt 1978; Krause \\& Radler\n1980). Indeed, it is impossible to understand the amplification of\nlarge scale magnetic fields without a knowledge of the mobility and\nreconnection of magnetic fields. Dynamo action invokes a constantly\nchanging magnetic field topology\\footnote{Merely winding up a\n magnetic field can increase the magnetic field energy, but cannot\n increase the magnetic field flux. We understand dynamos in the\n latter sense. The Zel'dovich ``fast'' dynamo (Vainshtein \\&\n Zel'dovich 1972) also invokes reconnection for continuous dynamo\n action (Vainshtein 1970).} and this requires efficient reconnection\ndespite very slow Ohmic diffusion rates.\n\n\\section{The Sweet-Parker Scheme and its Modifications}\n\nThe literature on magnetic reconnection is rich and vast (see e.g.,\nBiskamp 1993 and references therein). We start by discussing a robust\nscheme proposed by Sweet and Parker (Parker 1957; Sweet 1958). In\nthis scheme oppositely directed magnetic fields are brought into\ncontact over a region of $L_x$ size (see Fig.~1). The diffusion of\nmagnetic field takes place over the vertical scale $\\Delta$ which is\nrelated to the Ohmic diffusivity by $\\eta\\approx V_r \\Delta$, where\n$V_r$ is the velocity at which magnetic field lines can get into\ncontact with each other and reconnect. Given some fixed $\\eta$ one may\nnaively hope to obtain fast reconnection by decreasing $\\Delta$.\nHowever, this is not possible. An additional constraint posed by mass\nconservation must be satisfied. The plasma initially entrained on the\nmagnetic field lines must be removed from the reconnection zone. In\nthe Sweet-Parker scheme this means a bulk outflow through a layer with\na thickness of $\\Delta$. In other words, the entrained mass must be\nejected, i.e., $\\rho V_r L_x = \\rho' V_A \\Delta$, where it is assumed\nthat the outflow occurs at the Alfv\\'en velocity. Ignoring the\neffects of compressibility, then $\\rho=\\rho'$ and the resulting reconnection\nvelocity allowed by Ohmic diffusivity and the mass constraint is\n$V_r\\approx V_A {\\cal R}_L^{-1/2}$, where ${\\cal R}_L^{-1/2}=(\\eta/V_A\nL_x)^{1/2}$ is the Lundquist number. This is a very large number in\nastrophysical contexts (as large as $10^{20}$ for the\nGalaxy) so that the Sweet-Parker reconnection rate is negligible.\n\\enlargethispage{2ex}\n%\\begin{figure}[h]\n%\\begin{center}\n%\\leavevmode\n%\\includegraphics[height=8cm]{vishniacfig1.ps}\n% \\caption{({\\it Top}) Sweet-Parker scheme of reconnection. ({\\it\n% Middle}) The new scheme of reconnection that accounts for field\n% stochasticity. ({\\it Bottom}) A blow up of the contact region. \n%Thick arrows depict outflows of plasma.\n%}\n%\\end{center}\n%\\end{figure}\n\nIt is well known that using the Sweet-Parker reconnection rate it is\nimpossible to explain solar flares and it is impossible to reconcile\ndynamo predictions with observations. Are there any ways to increase\nthe reconnection rate? In general, we can divide schemes for fast\nreconnection into those which alter the microscopic resistivity,\nbroadening the current sheet, and those which change the global\ngeometry, thereby reducing $L_x$. An example of the latter is the\nsuggestion by Petschek (1964) that reconnecting magnetic fields would\ntend to form structures whose typical size in all directions is\ndetermined by the resistivity (`X-point' reconnection). This results\nin a reconnection speed of order $V_A/\\ln {\\cal R}_L$. However,\nattempts to produce such structures in simulations of reconnection\nhave been disappointing (Biskamp 1984, 1986). In numerical\nsimulations the X-point region tends to collapse towards the\nSweet-Parker geometry as the Lundquist number becomes large (Biskamp\n1996; Wang, Ma, \\& Bhattacharjee 1996). One way to understand this\ncollapse is to consider perturbations of the original X-point\ngeometry. In order to maintain this geometry reconnection has to be\nfast, which requires shocks in the original (Petschek) version of this\nmodel. These shocks are, in turn, supported by the flows driven by\nfast reconnection, and fade if $L_x$ increases. Naturally, the\ndynamical range for which the existence of such shocks is possible\ndepends on the Lundquist number and shrinks when fluid conductivity\nincreases. The apparent conclusion is that at least in the\ncollisional regime reconnection occurs through narrow current sheets.\n\nIn the collisionless regime the width of the current sheets may be\ndetermined by the ion cyclotron (or Larmor) radius $r_c$ (Parker 1979)\nor by the ion skin depth (Ma \\& Bhattacharjee 1996; Biskamp, Schwarz,\n\\& Drake 1997; Shay et al.\\ 1998) which differs from the former by the\nratio of $V_A$ to ion thermal velocity. In laboratory conditions this\noften leads to a current sheet thickness which is much larger than\nexpected (`anomalous resistivity'). However, this effect is not likely\nto be important in the interstellar medium. The thickness of the\ncurrent sheet $\\Delta$ scales in the Sweet-Parker scheme as\n$L_x^{1/2}$. Therefore, for a sufficiently large $L_x$ the natural\nSweet-Parker sheet thickness becomes larger than the thickness\nentailed by anomalous effects. Note that the ion Larmor radius $r_c$\nin an interstellar magnetic field is about a hundred kilometers. One\ncannot really hope to squeeze quickly the matter from many parsecs\nthrough a slot of this size!\n\\begin{figure}[t]\n\\parbox{0.5\\textwidth}{\\hspace*{3em}\\includegraphics[height=7cm]{ethan.ps}}\\hfill%\n\\begin{minipage}{0.45\\textwidth}\n \\caption{({\\it Top}) Sweet-Parker scheme of reconnection. ({\\it\n Middle}) The new scheme of reconnection that accounts for field\n stochasticity. ({\\it Bottom}) A blow up of the contact region. \nThick arrows depict outflows of plasma.\n}\n\\end{minipage}\n\\end{figure}\n\nOne may invoke anomalous resistivity to stabilize the X-point\nreconnection for collisionless plasma. For instance, Shay et al.\\\n(1998) found that the reconnection speed in their simulations was\nindependent of $L_x$, which would suggest that something like Petschek\nreconnection emerges in the collisionless regime. However, their\ndynamic range was small and the ion ejection velocity increased with\n$L_x$, with maximum speeds approaching $V_A$ for their largest values\nof $L_x$. Assuming that $V_A$ is an upper limit on ion ejection\nspeeds we may expect a qualitative change in the scaling behavior of\ntheir simulations at slightly larger values of $L_x$. One may expect\nthe generic problems intrinsic to X-point reconnection to persist for\nlarge ${\\cal R}_L$.\n\\enlargethispage{2ex}\n\nIf neither anomalous resistivity or/and X-point reconnection work, are\nthere any other ways to account for fast reconnection? Can\nreconnection speeds be substantially enhanced if the plasma coupling\nwith magnetic field is imperfect? This is the case in the presence of\nBohm diffusion, which is a process that is observed in laboratory\nplasma but lacks a good theoretical explanation. Its characteristic\nfeature is that ions appear to scatter about once per Larmor\nprecession period. The resulting particle diffusion destroys the\n`frozen-in' condition and allows significant larger magnetic field\nline diffusion. The effective diffusivity of magnetic field lines is\n$\\eta_{\\rm Bohm}\\sim V_A r_c$ (see Lazarian \\& Vishniac 1999,\nhenceforth LV99) which is a large increase over Ohmic resistivity. The\nmajor shortcoming of this idea is that it is unclear at all whether\nthe concept of Bohm diffusion is applicable to astrophysical\ncircumstances. Moreover, we note that even if we make this\nsubstitution, it can produce fast reconnection, of order $V_A$, only\nif $r_c\\sim L_x$. It therefore fails as an explanation for fast\nreconnection for the same reason that anomalous resistivity does.\n\nMatter may also diffuse perpendicular to magnetic field lines if the\nplasma is partially ionized. Since neutrals are not directly affected\nby magnetic field lines the neutral outflow layer may be much broader\nthan the $\\Delta$ determined by Ohmic diffusivity. The trouble with\nambipolar diffusion is that ions and electrons are left in the\nreconnection zone. As a result, the reconnection speed is determined\nby a slow recombination process. Calculations in Vishniac \\& Lazarian\n(1999) show that the ambipolar reconnection rates are slow unless the\nionization ratio is extremely low.\n\nCan plasma instabilities increase the reconnection rate? The narrow\ncurrent sheet formed during Sweet-Parker reconnection is unstable to\ntearing modes. A study of tearing modes in LV99 showed that an\nincrease over the Sweet-Parker rates is possible and the resulting\nreconnection rates may be as high as $V_A {\\cal R}_L^{3/10}$. However,\nthese speeds are still exceedingly small in view of the enormous\nvalues of ${\\cal R}_L$ encountered in astrophysical plasmas.\nBelow we discuss a different approach to the problem of rapid\nreconnection i.e., we consider magnetic reconnection\\footnote{The mode\n of reconnection discussed here is sometimes is called {\\it free}\n reconnection as opposed to {\\it forced} reconnection. Wang et al.\\ \n (1992) define {\\it free} reconnection as a process caused by a\n nonideal instability driven by the free energy stored in an\n equilibrium. If the equilibrium is stable, reconnection can be\n forced if a perturbation is applied externally.} in the presence of\na weak random field component.\n\n\\section{Turbulent Reconnection}\n\\enlargethispage{2ex}\n\n\\subsection{Reconnection in Two and Three Dimensions}\n\nTwo idealizations were used in the preceding discussion. First, we\nconsidered the process in only two dimensions. Second, we assumed\nthat the magnetized plasma is laminar. The Sweet-Parker scheme can\neasily be extended into three dimensions. Indeed, one can always take\na cross-section of the reconnection region such that the shared\ncomponent of the two magnetic fields is perpendicular to the\ncross-section. In terms of the mathematics nothing changes, but the\noutflow velocity becomes a fraction of the total $V_A$ and the shared\ncomponent of the magnetic field will have to be ejected together with\nthe plasma. This result has motivated researchers to do most of their\ncalculations in 2D, which has obvious advantages for both analytical\nand numerical investigations.\n\nHowever, physics in two and three dimensions is very different. For\ninstance, in two dimensions the properties of turbulence are very\ndifferent. In LV99 we considered three dimensional reconnection in a\nturbulent magnetized fluid and showed that reconnection is fast. This\nresult cannot be obtained by considering two dimensional turbulent\nreconnection (cf.\\ Matthaeus \\& Lamkin 1986). Below we briefly discuss\nthe idea of turbulent reconnection, while the full treatment of the\nproblem is given in LV99.\n\n\\subsection{A Model of Turbulent Reconnection}\n\nMHD turbulence guarantees the presence of a stochastic field component,\nalthough its amplitude and structure clearly depends on the model we adopt\nfor MHD turbulence, as well as the specific environment of the field. \nWe consider the case in which there exists a large scale,\nwell-ordered magnetic field, of the kind that is normally used as\na starting point for discussions of reconnection. This field may,\nor may not, be ordered on the largest conceivable scales. However,\nwe will consider scales smaller than the typical radius of curvature\nof the magnetic field lines, or alternatively, scales below the peak\nin the power spectrum of the magnetic field, so that the direction\nof the unperturbed magnetic field is a reasonably well defined concept.\nIn addition, we expect that the field has some small scale `wandering' of\nthe field lines. On any given scale the typical angle by which field\nlines differ from their neighbors is $\\phi\\ll1$, and this angle persists\nfor a distance along the field lines $\\lambda_{\\|}$ with\na correlation distance $\\lambda_{\\perp}$ across field lines (see Fig.~1).\n\nThe modification of the mass conservation constraint in the presence\nof a stochastic magnetic field component is self-evident. Instead of\nbeing squeezed from a layer whose width is determined by Ohmic\ndiffusion, the plasma may diffuse through a much broader layer,\n$L_y\\sim \\langle y^2\\rangle^{1/2}$ (see Fig.~1), determined by the\ndiffusion of magnetic field lines. This suggests an upper limit on\nthe reconnection speed of $\\sim V_A (\\langle y^2\\rangle^{1/2}/L_x)$.\nThis will be the actual speed of reconnection; the progress of\nreconnection in the current sheet itself does not impose a smaller\nlimit. The value of $\\langle y^2\\rangle^{1/2}$ can be determined once\na particular model of turbulence is adopted, but it is obvious from\nthe very beginning that this value is determined by field wandering\nrather than Ohmic diffusion as in the Sweet-Parker case.\n\nWhat about limits on the speed of reconnection that arise from\nconsidering the structure of the current sheet? In the presence of a\nstochastic field component, magnetic reconnection dissipates field\nlines not over their entire length $\\sim L_x$ but only over a scale\n$\\lambda_{\\|}\\ll L_x$ (see Fig.~1), which is the scale over which a\nmagnetic field line deviates from its original direction by the\nthickness of the Ohmic diffusion layer $\\lambda_{\\perp}^{-1} \\approx\n\\eta/V_{rec, local}$. If the angle $\\phi$ of field deviation does not\ndepend on the scale, the local reconnection velocity would be $\\sim\nV_A \\phi$ and would not depend on resistivity. In LV99 we claimed that\n$\\phi$ does depend on scale. Therefore, the {\\it local} reconnection\nrate $V_{rec, local}$ is given by the usual Sweet-Parker formula but\nwith $\\lambda_{\\|}$ instead of $L_x$, i.e. $V_{rec, local}\\approx V_A\n(V_A\\lambda_{\\|}/\\eta)^{-1/2}$. It is obvious from Figure~1 that $\\sim\nL_x/\\lambda_{\\|}$ magnetic field lines will undergo reconnection\nsimultaneously (compared to a one by one line reconnection process for\nthe Sweet-Parker scheme). Thus, the overall reconnection rate may\nbe as large as $V_{rec, global}\\approx V_A\n(L_x/\\lambda_{\\|})(V_A\\lambda_{\\|}/\\eta)^{-1/2}$. Whether or not this\nlimit is important depends on the value of $\\lambda_{\\|}$.\n\nThe relevant values of $\\lambda_{\\|}$ and $\\langle y^2\\rangle^{1/2}$\ndepend on the magnetic field statistics. This calculation was\nperformed in LV99 using the Goldreich-Sridhar (1995) model of MHD\nturbulence, the Kraichnan model (Iroshnikov 1963; Kraichnan 1965) and\nfor MHD turbulence with an arbitrary spectrum. In all the cases the\nupper limit on $V_{rec,global}$ was greater than $V_A$, so that the\ndiffusive wandering of field lines imposed the relevant limit on\nreconnection speeds. For instance, for the Goldreich-Sridhar (1995)\nspectrum the upper limit on the reconnection speed was\n\\begin{equation}\nV_{r, up}=V_A \\min\\left[\\left({L_x\\over l}\\right)^{\\frac{1}{2}} , \n\\left({l\\over L_x}\\right)^{\\frac{1}{2}}\\right]\n\\left({v_l\\over V_A}\\right)^{2},\n\\label{main}\n\\end{equation}\nwhere $l$ and $v_l$ are the energy injection scale and turbulent\nvelocity at this scale respectively. In LV99 we also considered other\nprocesses that can impede reconnection and find that they are less\nrestrictive. For instance, the tangle of reconnection field lines\ncrossing the current sheet will need to reconnect repeatedly before\nindividual flux elements can leave the current sheet behind. The rate\nat which this occurs can be estimated by assuming that it constitutes\nthe real bottleneck in reconnection events, and then analyzing each\nflux element reconnection as part of a self-similar system of such\nevents. This turns out to limit reconnection to speeds less than\n$V_A$, which is obviously true regardless. As a result, we showed in\nLV99 that equation~(\\ref{main}) is not only an upper limit, but is the best\nestimate of the speed of reconnection.\n\nNaturally, when turbulence is negligible, i.e. $v_l\\rightarrow 0$, the\nfield line wandering is limited to the Sweet-Parker current sheet and\nthe Sweet-Parker reconnection scheme takes over. However, in practical\nterms this means an artificially low level of turbulence that should\nnot be expected in realistic astrophysical environments. Moreover,\nthe release of energy due to reconnection, at any speed, will\ncontribute to the turbulent cascade of energy and help drive the\nreconnection speed upward.\n\nWe stress that the enhanced reconnection efficiency in turbulent\nfluids is only present if 3D reconnection is considered. In this case\nohmic diffusivity fails to constrain the reconnection process as many\nfield lines simultaneously enter the reconnection region. The number\nof lines that can do this increases with the decrease of resistivity\nand this increase overcomes the slow rates of reconnection of\nindividual field lines. It is impossible to achieve a similar\nenhancement in 2D (see Zweibel 1998) since field lines can not cross\neach other.\n\n\\subsection{Energy Dissipation and its Consequences}\n\\enlargethispage{2ex}\n\nIt is usually believed that rapid reconnection in the limit of\nvanishing resistivity implies a current singularity (Park, Monticello,\n\\& White 1984). Our model does not require such singularities.\nIndeed, they show that while the amount of Ohmic dissipation tends to\n0 as $\\eta \\rightarrow 0$, the smallest scale of the magnetic field's\nstochastic component decreases so that the rate of the flux\nreconnection does not decrease.\n\nThe turbulent reconnection process assumes that only small segments of\nmagnetic field lines enter the reconnection zone and are subjected to\nohmic annihilation. Thus, only a small fraction of the magnetic energy,\nproportional to ${\\cal R}_L^{-2/5}$ (LV99), is released in the form of\nohmic heat. The rest of the energy is released in the form of\nnon-linear Alfv\\'en waves that are generated as reconnected magnetic\nfield lines straighten up.\n\nNaturally, the low efficiency of electron heating is of little\ninterest when ion and electron temperatures are tightly coupled. When\nthis is not the case the LV99 model for reconnection has some\ninteresting consequences. As an example, we may consider advective\naccretion flows (ADAFs), following the general description given in\nNarayan and Yi (1995) in which advective flows can be geometrically\nthick and optically thin with a small fraction of the dissipation\ngoing into electron heating. If, as expected, the magnetic pressure\nis comparable to the gas pressure in these systems, then a large\nfraction of the orbital energy dissipation occurs through reconnection\nevents. If a large fraction of this energy goes into electron heating\n(cf.\\ Bisnovatyi-Kogan \\& Lovelace 1997) then the observational\narguments in favor of ADAFs are largely invalidated. The results in\nLV99 suggest that reconnection, by itself, will not result in\nchanneling more than a small fraction of the energy into electron\nheating. Of course, the fate of energy dumped into a turbulent\ncascade in a collisionless magnetized plasma then becomes a critical\nissue.\n\nWe also note that observations of solar flaring seem to show that\nreconnection events start from some limited volume and spread as\nthough a chain reaction from the initial reconnection region initiated\na dramatic change in the magnetic field properties. Indeed, solar\nflaring happens as if the resistivity of plasma were increasing\ndramatically as plasma turbulence grows (see Dere 1996 and references\ntherein). In our picture this is a consequence of the increased\nstochasticity of the field lines rather than any change in the local\nresistivity. The change in magnetic field topology that follows\nlocalized reconnection provides the energy necessary to feed a\nturbulent cascade in neighboring regions. This kind of nonlinear\nfeedback is also seen in the geomagnetic tail, where it has prompted\nthe suggestion that reconnection is mediated by some kind of nonlinear\ninstability built around modes with very small $k_{\\|}$ (cf.\\ Chang\n1998 and references therein). The most detailed exploration of\nnonlinear feedback can be found in the work of Matthaeus and Lamkin\n(1986), who showed that instabilities in narrow current sheets can\nsustain broadband turbulence in two dimensional simulations. Although\nour model is quite different, and relies on the three dimensional\nwandering of field lines to sustain fast reconnection, we note that\nthe concept of a self-excited disturbance does carry over and may\ndescribe the evolution of reconnection between volumes with initially\nsmooth magnetic fields.\n\n\\section{Implications}\n\n\\subsection{Turbulent Reconnection and Turbulent Diffusivity}\n\nWe would like to stress that in introducing turbulent reconnection we\ndo not intend to revive the concept of ``turbulent diffusivity'' as\nused in dynamo theories (Parker 1979). In order to explain why\nastrophysical magnetic fields do not reverse on very small scales,\nresearchers have usually appealed to an {\\it ad hoc} diffusivity which\nis many orders of magnitude greater than the ohmic diffusivity. This\ndiffusivity is assumed to be roughly equal to the local turbulent\ndiffusion coefficient. While superficially reasonable, this choice\nimplies that a dynamically significant magnetic field diffuses through\na highly conducting plasma in much the same way as a passive tracer.\n This is referred to as turbulent diffusivity and\ndenoted $\\eta_t$, as opposed to the Ohmic diffusivity $\\eta$. Its name\nsuggests that turbulent motions subject the field to kinematic\nswirling and mixing. As the field becomes intermittent and intermixed\nit can be assumed to undergo dissipation at arbitrarily high speeds.\n\nParker (1992) showed convincingly that the concept of turbulent\ndiffusion is ill-founded. He pointed out that turbulent motions are\nstrongly constrained by magnetic tension and large scale magnetic\nfields prevent hydrodynamic motions from mixing magnetic field regions\nof opposing polarity unless they are precisely anti-parallel.\nHowever, results in LV99 show that the mobility of a magnetic field in\na turbulent fluid is indeed enhanced. For instance, due to fast\nreconnection the magnetic field will not form long lasting knots.\nMoreover, the magnetic field can be expected to straighten itself and\nremove small scale reversals as required, in a qualitative sense, by\ndynamo theory. Nevertheless, the underlying physics of this process is\nvery different from what is usually meant by ``turbulent\ndiffusivity''. Within the turbulent diffusivity paradigm, magnetic\nfields of different polarity were believed to filament and intermix on\nvery small scales while reconnection proceeded slowly. On the\ncontrary, we have shown in LV99 that the global speed of reconnection\nis fast if a moderate degree of magnetic field line wandering is\nallowed. The latter, unlike the former, corresponds to a realistic\npicture of MHD turbulence and does not entail prohibitively high\nmagnetic field energies at small scales.\n\nOn the other hand, the diffusion of particles through a magnetized\nplasma is greatly enhanced when the field is mildly stochastic. There\nis an analogy between the reconnection problem and the diffusion of\ncosmic rays (Barghouty \\& Jokipii 1996). In both cases charged\nparticles follow magnetic field lines and in both cases the wandering\nof the magnetic field lines leads to efficient diffusion.\n\n\\subsection{Dynamos}\n\nThere is a general belief that magnetic dynamos operate in stars,\ngalaxies (Parker 1979) and accretion disks (Balbus \\& Hawley\n1998). In stars, and in many accretion disks, the plasma has a high\n$\\beta$, that is the average plasma pressure is higher than the\naverage magnetic pressure. In such situations the high diffusivity of the\nmagnetic field can be explained by concentrating flux in\ntubes\\footnote{Note that flux tube formation requires initially\n high reconnection rates. Therefore, the flux tubes by themselves\n provide only a partial solution to the problem.} (Vishniac 1995a,b).\nThis trick does not work in the disks of galaxies, where the magnetic\nfield is mostly diffuse (compare Subramanian 1998) and ambipolar\ndiffusion impedes the formation of flux tubes (Lazarian \\& Vishniac\n1996). This is the situation where our current treatment of magnetic\nreconnection is most relevant. However, our results suggest that\nmagnetic reconnection proceeds regardless and that the concentration\nof magnetic flux in flux tubes via turbulent pumping is not a\nnecessary requirement for successful dynamos in stars and accretion\ndiscs.\n\nTo enable sustainable dynamo action and, for example, generate a\ngalactic magnetic field, it is necessary to reconnect and rearrange\nmagnetic flux on a scale similar to a galactic disc thickness within\nroughly a galactic turnover time ($\\sim 10^8$~years). This implies\nthat reconnection must occur at a substantial fraction of the Alfv\\'en\nvelocity. The preceding arguments indicate that such reconnection\nvelocities should be attainable if we allow for a realistic magnetic\nfield structure, one that includes both random and regular fields.\n\nOne of the arguments against traditional mean-field dynamo theory is\nthat the rapid generation of small scale magnetic fields suppresses\nfurther dynamo action (e.g., Kulsrud \\& Anderson 1992). Our results\nthus far show that a random magnetic field enhances reconnection by\nenabling more efficient diffusion of matter from the reconnection\nlayer. This suggests that the existence of small scale magnetic\nturbulence is a prerequisite for a successful large scale dynamo. In\nother words, we are arguing for the existence of a kind of negative\nfeed-back. If the magnetic field is too smooth, reconnection speeds\ndecrease and the field becomes more tangled. If the field is\nextremely chaotic, reconnection speeds increase, making the field\nsmoother. We note that it is common knowledge that magnetic\nreconnection can sometimes be quick and sometimes be slow. For\ninstance, the existence of bundles of flux tubes of opposite polarity\nin the solar convection zone indicates that reconnection can be very\nslow. At the same time, solar flaring suggests very rapid reconnection\nrates.\n\n%We do not address here the controversial issue of the turbulent dynamo\n%in clusters of galaxies. This was first suggested by (Jaffe 1980) and\n%was elaborated in great detail by Ruzmaikin, Sokoloff \\& Shukurov\n%(1989), who claimed an excellent match between observations and\n%predictions based on the Kazantsev (1968) theory of the turbulent\n%dynamo. However, Goldshmidt \\& Rephaeli (1993) found a large ($\\sim\n%10^{20}$) numerical error in the value of Ohmic diffusivity used by\n%Ruzmaikin et al. (1989), which formally invalidated their result.\n%However, if it were possible to use the effective diffusivity\n%determined by the reconnection rate instead of Ohmic diffusivity, then\n%the theory of turbulent dynamo can be revived for clusters of\n%galaxies.\n\nOur results show that in the presence of MHD turbulence magnetic\nreconnection is fast, and this in turn allows the possibility\nof `fast' dynamos in astrophysics (see the discussion of the {\\it fast\ndynamo} in Parker 1992). \n\nFinally, we have assumed that we are dealing with a strong magnetic\nfield, where motions that tend to mix field lines of different\norientations are largely suppressed. The galactic magnetic field is\nusually taken to have grown via dynamo action from some extremely weak\nseed field (cf.\\ Zel'dovich, Ruzmaikin, \\& Sokoloff 1983; Lazarian 1992\nand references contained therein). When the field is weak it can be\nmoved as a passive scalar and its spectrum will mimic that of\nKolmogorov turbulence. The difference between $\\lambda_{\\bot}$ and\n$\\lambda_{\\|}$ vanishes, the field becomes tangled on small scales,\nand $V_{rec, local}$ becomes of the order of $V_A$. Of course, in\nthis stage of evolution $V_A$ may be very small. However, on such small\nscales $V_A$ will grow to equipartition with the turbulent velocities\non the turn over time of the small eddies. The enhancement of\nreconnection as $V_A$ increases accelerates the inverse cascade as\nsmall magnetic loops merge to form larger ones.\n\n\\section{Discussion}\n\nIt is not possible to understand the dynamics of magnetized\nastrophysical plasmas without understanding how magnetic fields\nreconnect. Here we have compared traditional approaches to the problem\nof magnetic reconnection and a new approach that includes the presence\nof turbulence in the magnetized plasma.\n\nOne of the more striking aspects of our result is that the global\nreconnection speed is relatively insensitive to the actual physics of\nreconnection. Equation (\\ref{main}) only depends on the nature of the\nturbulent cascade. Although this conclusion was reached by invoking a\nparticular model for the strong turbulent cascade, we showed in LV99\nthat any sensible model gives qualitatively similar results.\nOne may say that the conclusion that reconnection is fast, even when\nthe local reconnection speed is slow, represents a triumph of global\ngeometry over the slow pace of ohmic diffusion. In the end,\nreconnection can be fast because if we consider any particular flux\nelement inside the contact volume, assumed to be of order $L_x^3$, the\nfraction of the flux element that actually undergoes microscopic\nreconnection vanishes as the resistivity goes to zero.\n\nThe new model of fast turbulent reconnection changes our understanding\nof many astrophysical processes. Firstly, it explains why\ndynamos do not suppress themselves through the excessive generation of\nmagnetic noise, as some authors suggest (Kulsrud \\& Anderson 1992).\nThe model also explains why reconnection may be sometimes fast and\nsometimes slow, as solar activity demonstrates. ADAFs and the\nacceleration of cosmic rays at reconnection sites are other examples\nof processes where a new model of reconnection should be applied.\n\nOur results on turbulent reconnection assume that the turbulent\ncascade is limited by plasma resistivity. If gas is partially ionized\ncollisions with neutrals may play an important role in damping\nturbulence. A study in Lazarian \\& Vishniac (2000) shows that for gas\nwith low levels of ionization turbulent reconnection may be impeded as\nmagnetic field wandering is suppressed on small scales. However, the\nlevel of suppression depends on the details of the energy injection\ninto the turbulent cascade (see a discussion in Lazarian \\& Pogosyan\n2000), which are far from being clear. Moreover, for very low\nionization levels there will be an enhancement of the reconnection\nprocess as neutrals diffuse perpendicular to magnetic field lines.\nThus, reconnection may still be an important process in the evolution\nof molecular clouds and in star formation. \n\n\\acknowledgments\nAL acknowledges valuable discussions with Chris McKee.\n\n\\begin{thebibliography}\n\\bibitem{BH98}Balbus, S. A., \\& Hawley, J. F. 1998, Rev. Mod. Phys., 1, 1 \n\\bibitem{BJ96} \nBarghouty, A. F., \\& Jokipii, J. 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Press), 123\n\\bibitem{S98} Subramanian, K. 1998, MNRAS, 294, 718 \n\\bibitem{V70}Vainshtein, S. I.\\ 1970, Sov. Phys. - JETP Lett., 31, 87\n\\bibitem{VZ72}Vainshtein, S. I. \\& Zel'dovich, Ya. B.\\ 1972,\nSov. Phys. - Uspekhi, 15, 159\n\\bibitem{V95a} Vishniac, E. T.\\ 1995a, \\apj, 446, 724\n\\bibitem{V95b}\\ibid 1995b, \\apj, 451, 816\n\\bibitem{VL98a} Vishniac, E. T., \\& Lazarian, A.\\ 1999, \\apj, 511, 193\n\\bibitem{WMB92} Wang, X., Ma, Z. W., \\& Bhattacharjee, A. 1992,\nPhys. Fluids B, 4, 1795\n\\bibitem{WMB96} \n\\ibid 1996, Phys. Plasmas, 3(5), 2129\n\\bibitem{ZRS83}\nZel'dovich, Ya. B., Ruzmaikin, A. A., \\& Sokoloff, D. D.\\ 1983,\nMagnetic Fields in Astrophysics (New York: Gordon and Breach)\n\\bibitem{Z98} Zweibel, E. 1998, Phys. Plasmas, 5, 247 \n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002067.extracted_bib",
"string": "\\begin{thebibliography}\n\\bibitem{BH98}Balbus, S. A., \\& Hawley, J. F. 1998, Rev. Mod. Phys., 1, 1 \n\\bibitem{BJ96} \nBarghouty, A. F., \\& Jokipii, J. R. 1996, \\apj, 470, 858\n\\bibitem{B84}Biskamp, D.\\ 1984, Phys. Lett. A, 105, 124\n\\bibitem{B86}\\ibid 1986, Phys. Fluids, 29, 1520\n\\bibitem{B93} \\ibid 1993, \nNonlinear Magnetohydrodynamics, (Cambridge: Cambridge University Press)\n\\bibitem{B96}\\ibid 1996, ApSS, 242,165\n\\bibitem{BSD97}Biskamp, D., Schwarz, E., \\& Drake, \nJ. F.\\ 1997, Phys. Plasmas, 4, 1002\n\\bibitem{BL97}\nBisnovatyi-Kogan, G. S., \\& Lovelace, R. V. E.\\ 1997,\n\\apjl, 486, L43\n\\bibitem{C98} Chang, T.\\ 1998, in AGU Monographs Vol.\\ 104,\nGeospace Mass and Energy Flow, ed. J. L. Horwitz, D. L. Gallagher,\n\\& W. K. Peterson (Washington DC: American Geophysical Union) p. 193 \n\\bibitem{D96} Dere, K. P. 1996, ApJ, 472, 864\n\\bibitem{GS95} Goldreich, P., \\& Sridhar, S.\\ 1995,\n\\apj, 438, 763\n%\\bibitem{GR93}Goldshmidt, O., \\& Rephaeli, Y. 1993, ApJ, 411, 518 \n\\bibitem{I63} Iroshnikov, P. S. 1963, AZh, 40, 742\n%\\bibitem{J80}Jaffe, W. 1980, ApJ, 241, 925 \n%\\bibitem{KA68}Kazantsev, A. P. 1968, Soviet Phys.-JETP Lett., 26, 1031\n\\bibitem{K65} Kraichnan, R. H. 1965, Phys. Fluids, 8, 1385\n\\bibitem{KR80} Krause, F., \\& Radler, K. H. 1980, Mean-Field\n Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon) \n\\bibitem{KA92} \nKulsrud, R. M., \\& Anderson, S. W. \\ 1992, \\apj, 396, 606\n\\bibitem{L92} Lazarian, A. 1992, A\\&A, 264, 326\n\\bibitem{} Lazarian, A., \\& Pogosyan, D. 2000, \\apj, in press\n\\bibitem{LV96} \nLazarian, A., \\& Vishniac, E. T. 1996, in ASP Conf.\\ Ser.\\ Vol.\\ 97,\nPolarimetry of the Interstellar Medium, ed. W. G. Roberge \\&\nD. C. B. Whittet (San Francisco: Astronomical Society of the Pacific), 537\n\\bibitem{LV99}\\ibid 1999, \\apj, 517, 700\n\\bibitem{} \\ibid 2000\n\\apj, in preparation \n\\bibitem{MB96} Ma, Z. W., \\& Bhattacharjee, A. \n1996, Geophys.\\ Res.\\ Lett., 23(21), 2955\n\\bibitem{ML85} \nMatthaeus, W. H., \\& Lamkin, S. L. 1986, Phys. Fluids, 29(8), 2513\n\\bibitem{M78} Moffatt, H. K. 1978, Magnetic Field Generation in Electrically\nConducting Fluids (Cambridge: Cambridge University Press)\n\\bibitem{NY95} Narayan, R., \\& Yi, I.\\ 1995, \\apj, 452, 710\n\\bibitem{PMW84}Park, W., Monticello, D. A., \\& White, R. B. \n\\ 1984, Phys. Fluids, 27, 137\n\\bibitem{P57}Parker, E. N.\\ 1957, J. Geophys. Res., 62, 509\n\\bibitem{P79}\\ibid 1979, Cosmical \nMagnetic Fields (Oxford: Clarendon Press)\n\\bibitem{P92}\\ibid 1992, \\apj, 401, 137\n\\bibitem{P64} Petschek, H. E. 1964, The Physics of Solar Flares, AAS-NASA Symposium (NASA SP-50), ed. W. H. Hess (Greenbelt, MD: NASA), 425\n%\\bibitem{RS89}Ruzmaikin A. A., Shukurov A. M., \\& Sokoloff D. D. 1989, MNRAS, 241, 1\n\\bibitem{SDDB98}Shay, M. A., Drake, J. F.,\nDenton, R. E., \\& Biskamp, D.\\ 1998, J. Geophys. Res., 103, 9165\n\\bibitem{S58} Sweet, P. A.\\ 1958, in IAU Symp.\\ 6, Electromagnetic \nPhenomena in \nCosmical Plasma, ed. B. Lehnert (New York: Cambridge Univ. Press), 123\n\\bibitem{S98} Subramanian, K. 1998, MNRAS, 294, 718 \n\\bibitem{V70}Vainshtein, S. I.\\ 1970, Sov. Phys. - JETP Lett., 31, 87\n\\bibitem{VZ72}Vainshtein, S. I. \\& Zel'dovich, Ya. B.\\ 1972,\nSov. Phys. - Uspekhi, 15, 159\n\\bibitem{V95a} Vishniac, E. T.\\ 1995a, \\apj, 446, 724\n\\bibitem{V95b}\\ibid 1995b, \\apj, 451, 816\n\\bibitem{VL98a} Vishniac, E. T., \\& Lazarian, A.\\ 1999, \\apj, 511, 193\n\\bibitem{WMB92} Wang, X., Ma, Z. W., \\& Bhattacharjee, A. 1992,\nPhys. Fluids B, 4, 1795\n\\bibitem{WMB96} \n\\ibid 1996, Phys. Plasmas, 3(5), 2129\n\\bibitem{ZRS83}\nZel'dovich, Ya. B., Ruzmaikin, A. A., \\& Sokoloff, D. D.\\ 1983,\nMagnetic Fields in Astrophysics (New York: Gordon and Breach)\n\\bibitem{Z98} Zweibel, E. 1998, Phys. Plasmas, 5, 247 \n\\end{thebibliography}"
}
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astro-ph0002068
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The role of the outer boundary condition in accretion disk models: theory and application
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[
{
"author": "Feng Yuan"
}
] |
In a previous paper (Yuan 1999, hereafter Paper I), we find that the outer boundary conditions(OBCs) of an optically thin accretion flow play an important role in determining the structure of the flow. Here in this paper, we further investigate the influence of OBC on the dynamics and radiation of the accretion flow on a more detailed level. Bremsstrahlung and synchrotron radiations amplified by Comptonization are taken into account and two-temperature plasma assumption is adopted. The three OBCs we adopted are the temperatures of the electrons and ions and the specific angular momentum of the accretion flow at a certain outer boundary. We investigate the individual role of each of the three OBCs on the dynamical structure and the emergent spectrum. We find that when the general parameters such as the mass accretion rate $\dot{M}$ and the viscous parameter $\alpha$ are fixed, the peak flux at various bands such as radio, IR and X-ray, can differ by as large as several orders of magnitude under different OBCs in our example. Our results indicate that OBC is both dynamically and radiatively important therefore should be regarded as a new ``parameter'' in accretion disk models. As an illustrative example, we further apply the above results to the compact radio source Sgr A$^*$ located at the center of our Galaxy. Advection-dominated accretion flow (ADAF) model has been turned out to be a great success to explain its luminosity and spectrum. However, there exists a discrepancy between the mass accretion rate favored by ADAF models in the literature and that favored by the three dimensional hydrodynamical simulation, with the former being 10-20 times smaller than the latter. By seriously considering the outer boundary condition of the accretion flow, we find that due to the low specific angular momentum of the accretion gas, the accretion in Sgr A$^*$ should belong to a new accretion pattern, which is characterized by possessing a very large sonic radius. This accretion pattern can significantly reduce the discrepancy between the mass accretion rate. We argue that the accretion occurred in some detached binary systems, the core of nearby elliptical galaxies and active galactic nuclei(AGNs) very possibly belongs to this accretion pattern.
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[
{
"name": "fyuan.tex",
"string": "\\documentstyle[11pt,aaspp4,flushrt]{article} % this is for submittal (double-s\n%\\documentstyle[emulateapj]{article}\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\mdot{\\dot{m}}\n\\def\\ergs{{\\rm\\,erg\\,s^{-1}}}\n\\def\\msun{M_{\\odot}}\n\\def\\ergscc{\\rm \\ \\ erg \\ cm^{-3} \\ s^{-1}}\n\\def\\Ti{T_{{\\rm out},i}}\n\\def\\Te{T_{{\\rm out},e}}\n\\def\\gs{\\rm \\,g\\,s^{-1}}\n\\def\\ergscc{\\rm \\,erg\\,cm^{-3}\\,s^{-1}}\n\\def\\ergs{\\rm \\,erg\\,s^{-1}}\n\\input psfig.tex\n\\begin{document}\n\\date{}\n\\title{The role of the outer boundary condition in accretion disk models:\ntheory and application}\n\n\\author{Feng Yuan}\n\\affil{Department of Astronomy, Nanjing University, Nanjing 210093,\\\\\nand Beijing Astrophysics Center, Beijing 100080, China\n\\\\ Email: [email protected]}\n \n\\author{Qiuhe Peng}\n\\affil{Department of Astronomy, Nanjing University, Nanjing 210093, China}\n\n\\author{Ju-fu Lu}\n\\affil{Center for Astrophysics, University of Science \\& Technology of China, \nHefei, 230026, China,\\\\ and\nNational Astronomical Observatories, Chinese Academy of Sciences}\n\n\\author{Jianmin Wang}\n\\affil{Laboratory of Cosmic Ray and High Energy Astrophysics,\\\\\nInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039,\n China}\n\n\\begin{abstract}\nIn a previous paper (Yuan 1999, hereafter Paper I), \nwe find that the outer boundary conditions(OBCs) of an \noptically thin accretion flow\nplay an important role in determining\nthe structure of the flow. Here in this paper, we further\ninvestigate the influence of OBC\non the dynamics and radiation of the accretion flow on a \nmore detailed level. Bremsstrahlung and synchrotron\nradiations amplified by Comptonization are \ntaken into account and two-temperature\nplasma assumption is adopted. The three OBCs we adopted are the \ntemperatures of the electrons and ions and the specific angular\nmomentum of the accretion flow at a certain outer boundary.\nWe investigate the individual \nrole of each of the three OBCs\non the dynamical structure and the emergent spectrum. \nWe find that when the general \nparameters such as the mass accretion rate $\\dot{M}$ \nand the viscous parameter $\\alpha$ are fixed,\nthe peak flux at various bands such as radio, IR and X-ray,\ncan differ by as large as \nseveral orders of magnitude under different OBCs in our \nexample. Our results indicate\nthat OBC is both dynamically and radiatively important\ntherefore should be regarded as a new ``parameter'' in accretion disk models.\n\nAs an illustrative example, we further apply the above \nresults to the compact radio source Sgr A$^*$ \nlocated at the center of our Galaxy. \nAdvection-dominated accretion flow (ADAF) model has been turned out to\nbe a great success to explain its luminosity and spectrum. However,\nthere exists a discrepancy between the mass accretion rate \nfavored by ADAF models in the literature \nand that favored by the three dimensional hydrodynamical simulation,\nwith the former being \n10-20 times smaller than the latter. \nBy seriously considering the\nouter boundary condition of the accretion flow, we find that\ndue to the low specific angular momentum of the accretion gas, the\naccretion in Sgr A$^*$ should belong to a new accretion pattern,\nwhich is characterized by possessing a very large sonic radius.\nThis accretion pattern can significantly reduce the discrepancy between \nthe mass accretion rate. We argue that\nthe accretion occurred in some detached binary systems,\nthe core of nearby elliptical galaxies and active galactic nuclei(AGNs)\nvery possibly belongs to this accretion pattern.\n\n\\end{abstract}\n\n\\keywords{accretion, accretion disks -- black hole physics -- \ngalaxies: active -- Galaxy: center -- hydrodynamics\n -- radiation mechanisms: thermal}\n \n\\section{INTRODUCTION}\nThe dynamics of an accretion flow around \na black hole is described by a set\nof non-linear differential equations. \nSo this is intrinsically an initial value problem, and generally\nthe outer boundary condition(OBC) \nhas a significant influence on the global solution.\nIn the standard thin disk model (Shakura \\& Sunyaev 1973), all the differential\nterms are neglected therefore the equations are reduced to \na set of algebraic equations which don't entail any boundary condition \nat all. However, in many cases it has been shown that \nthe differential terms, such as the inertial and the horizontal pressure\ngradient terms in\nthe radial momentum equation and the advection term in the \nenergy equation, play an important role and can not \nbe neglected (Begelman 1978; Begelman \\&\nMeier 1982; Abramowicz et al. 1988). This is especially the case for an\noptically thin advection dominated \naccretion flow (ADAF) (Ichimaru 1977; Rees et al. 1982; Narayan \\&\n Yi 1994; Abramowicz et al. 1995; Narayan, Kato \\& Honma\n 1997; Chen, Abramowicz \\& Lasota 1997). It is the existence\nof the differential terms that will make OBC an important\nfactor to determine the behavior of an accretion flow.\n\nThis expectation has been initially confirmed in our Paper I.\nIn that paper, taking optically thin one- and two-temperature\nplasma as examples, we investigated the influence of OBC \non the dynamics of an accretion flow. We adopted \nthe temperature and\nthe ratio of the radial velocity to the local sound speed\n(or, equivalently, the angular velocity $\\Omega_{\\rm out}$) at a certain outer \nboundary $r_{\\rm out}$ as the outer boundary conditions \nand found that in \nboth cases, the topological structure and the profiles of angular momentum \nand surface density of the flow differ greatly under \ndifferent OBCs. In terms of the topological structure and the profile \nof the angular momentum, three types of solutions are found. \nWhen $T_{\\rm out}$ is relatively low,\nthe solution is of type I. When $T_{\\rm out}$ is relatively high and \nthe angular velocity $\\Omega_{\\rm out}$ is high,\nthe solution is of type II. Both types I and II possess small sonic radii,\nbut their topological structures and angular momentum profiles \nare different. When $T_{\\rm out}$ is relatively high and the \nangular velocity is lower than a critical value, the solution is of type III,\ncharacterized by possessing a much larger sonic radius. \nFor a one-temperature plasma\nor ions in a two-temperature plasma, the discrepancy of the temperature\nin the solutions with different OBCs lessen rapidly away from the outer\nboundary, but the discrepancy of the electron temperature at $r_{\\rm out}$\npersists throughout the disk. This is because when the \naccretion rate is low, the electrons are basically adiabatic,\ni.e., both the local radiative cooling and the energy transfer from\nthe ions to the electrons can be neglected compared with \nthe energy advection of the electrons. While for a one-temperature plasma\nor ions, the local viscous dissipation in the energy\nbalance plays an important role, thus their temperature \nis more {\\em locally} determined. \n\nIn the present paper we will focus on the two-temperature\naccretion flows. Our first aim is to extend our study in Paper I by including \nsynchrotron radiation as well. This is a \nvery strong local radiative cooling mechanism \nin the inner region of a disk when a magnetic field is present. We \nwill check whether our conclusion of Paper I still holds or not \nin this case.\n\nThe main aim of this paper is to calculate the emergent spectrum\nunder different OBCs and to investigate the applications. We want to\nprobe whether and how the spectrum is \ndependent upon the OBCs (Sections 2 \\& 3). We find that each of the three OBCs \nhas a significant influence on the emergent spectrum.\nThis result indicates the importance of\nconsidering the initial physical state of the accretion flow.\nIn Section 4 we apply our theory of OBC to Sgr A$^*$. We find that the \ndiscrepancy between the mass accretion rate favored by\nthe numerical simulation and that required in all ADAF models in the literature\nis naturally solved by seriously considering the OBCs of accretion flows.\nThe last section is devoted to summary and discussion, where \nthe promising applications in nearby elliptical galaxies and \nActive Galactic Nuclei (AGNs) are shortly discussed.\n\n\\section{MODEL}\n\nWe consider a steady axisymmetric accretion flow around a Schwarzschild black\nhole of mass $M$.\nPaczy\\'nski \\& Wiita (1980) potential $\\phi=-GM/(r-r_g)$ is used to mimic the\ngeometry of the hole, where $r_g=2GM/c^2$ is the Schwarzschild radius. \nThe standard $\\alpha$-viscosity prescription is adopted. We assume that\nall the viscous dissipated energy is transfered to ions and the energy\ntransfer from ions to electrons is provided solely by Coulomb collisions.\nSo the plasma has a two-temperature structure \nin the present optically thin case. \nA randomly oriented magnetic field is assumed to exist in \nthe accretion flow. The total pressure is then taken to be\n\\be\np=p_{\\rm gas}+p_{\\rm mag},\n\\ee\nwhere $p_{\\rm gas}$ is the gas pressure and $p_{\\rm mag}$ is the magnetic\npressure. For simplicity, we assume the ratio of gas pressure\nto the total pressure $\\beta$ to be a global parameter independent of radius\n$r$. Under the optically thin assumption, the equation of state\ncan be written as:\n\\be\np_{\\rm gas}=\\beta p=p_i+p_e=\\frac{\\rho}{\\mu_i}\\frac{k}{m_\n\\mu}T_i+\\frac{\\rho}{\\mu_e}\\frac{k}{m_\\mu}T_e,\n\\ee\nand\n\\be\np_{\\rm mag}=(1-\\beta)p=\\frac{B^2}{8\\pi}.\n\\ee\nHere and hereafter subscripts $i$ and $e$ indicate the quantities for ions and\nelectrons, respectively. The mean molecular weight for ions and\nelectrons are:\n\\be\n\\mu_i=1.23 \\hspace{1cm} \\mu_e=1.13,\n\\ee\nrespectively. We take the shear stress to be simply \nproportional to the pressure, i.e.,\nshear stress=-$\\alpha p$. The hydrostatic balance in the vertical direction\nis also assumed.\n\nUnder the above assumptions, the set of height-integrated equations describing \nthe behavior of accretion flows read as follows.\n\\be\n-4\\pi r H\\rho v=\\dot{M},\\hspace{4mm}{\\rm with} \\hspace{3mm} \n H=c_s/\\Omega_{\\rm k} \n\\equiv \\sqrt{p/\\rho}/\\Omega_{\\rm k},\n\\ee\n\\be\nv \\frac{dv}{dr}=-\\Omega_{\\rm k}^2 r+\\Omega^2 r-\\frac{1}{\\rho}\\frac\n{dp}{dr},\n\\ee\n\\be\nv(\\Omega r^2-j)=\\alpha r \\frac{p}{\\rho},\n\\ee\n\\be\n\\rho v \\left(\\frac{d \\varepsilon_i}{dr}+p_i \\frac{d}{dr}\n \\left( \\frac{1}{\\rho}\\right)\n\\right)=q^+-q_{ie}=-\\alpha p r \\frac{d\\Omega}{dr}-q_{ie},\n\\ee\n\\be\n\\rho v \\left(\\frac{d \\varepsilon_e}{dr}+p_e \\frac{d}{dr}\n \\left( \\frac{1}{\\rho}\\right) \\right)=q_{ie}-q^-.\n\\ee\nAll above quantities have their popular meanings. \nThe difference between eq. (7) above and eq. (2.11) in Narayan, \nKato, \\& Honma (1997) or eq. (2.13) in Narayan, Mahadevan, \\& Quataert (1998)\nis due to the difference of the adopted viscosity prescription\n(see, e.g., Abramowicz et al. 1988; Nakamura et al. 1997; Manmoto,\nMineshige, \\& Kusunose 1997). We adopt this kind of viscosity prescription\nbecause in this case the no-torque condition at the hole horizon \nis automatically satisfied therefore the calculation can be simplified\n(Abramowicz et al. 1988; Narayan, Kato, \\& Honma 1997).\n$q_{ie}$ denotes the energy transfer rate from ions to electrons by \nCoulomb collisions which takes the form\n(Dermer, Liang \\& Canfield 1991):\n\\be\nq_{ie}=\\frac{3}{2}\\frac{m_e}{m_i}n_en_i \\sigma_T c {\\rm ln} \\Lambda\n\\left(kT_i-kT_e\\right)\\frac{\\left(\\frac{2}{\\pi}\\right)^{1/2}+\\left(\\theta_e+\n\\theta_i\\right)^{1/2}}{\\left(\\theta_e+\\theta_i \\right)^{3/2}},\n\\ee\nwhere ${\\rm ln} \\Lambda=20$ is the Coulomb logarithm, and $\\theta_i \\equiv\nkT_i/m_i c^2$ and $\\theta_e \\equiv kT_e/m_e c^2$ is the dimensionless \nions and electrons temperatures, respectively. This formula is accurate enough\nfor our purpose because $q_{ie}$ is only a small\nfraction in the energy balance of both ions (eq. 8) and\nelectrons (eq. 9) (Nakamura et al. 1997). \n$\\varepsilon_i$ and $\\varepsilon_e$ denote the internal energies for ions\nand electrons per unit mass of the gas, respectively. \nSince in ADAFs the ions never\nbecome relativistic while the electrons are transrelativistic, \nfollowing Esin et al. (1997b),\nwe adopt the following forms\\footnote{\nbased upon the argument of Esin et al.(1997a), \nthe adiabatic index $\\gamma_{i(e)}$ in Esin et al.(1997b) \ninclude the contribution of the magnetic density as well. But \nQuataert \\& Narayan (1999a) found that this is incorrect if MHD\nadequately describes the accretion flow. So we exclude it in the present \npaper. See Quataert \\& Narayan (1999b).}:\n\\be\n\\varepsilon_i=\\frac{1}{\\gamma_i-1}\\frac{kT_i}{\\mu_i m_{\\mu}}= \n\\frac{3}{2}\\frac{kT_i}{\\mu_i m_{\\mu}},\n\\ee\n\\be\n\\varepsilon_e=\\frac{1}{\\gamma_e-1}\\frac{kT_e}{\\mu_e m_{\\mu}}\n = a(T_e)\\frac{kT_e}{\\mu_e m_{\\mu}}.\n\\ee\nThe expression for \ncoefficient $a(T_e)$ is (Chandrasekhar 1939):\n\\be\na(\\theta_e)=\\frac{1}{\\theta_e}\\left[\\frac{3K_3(1/\\theta_e)+K_1(1/\\theta_e)}\n{4K_2(1/\\theta_e)}-1\\right],\n\\ee\nwhere $K_1, K_2,$ and $K_3$ are modified Bessel \nfunctions of the second kind of order 1,\n2, and 3, respectively.\n\nAs for the calculation of the radiative cooling $q^-$, we \nfollow the procedure in Manmoto, Mineshige \\& Kusunose (1997). \n%Their procedure deal with the free-free absorption and\n%synchrotron self-absorption at low frequency quite well. \nThe considered radiative mechanisms include\nbremsstrahlung, synchrotron radiation and Comptonization of \nsoft photons. Assuming the disk is isothermal \nin the vertical direction, the spectrum of unscattered photons at a given\nradius is calculated by solving the radiative\ntransfer equation in the vertical direction of the disk basing upon the\ntwo-stream approximation (Rybicki \\& Lightman 1979).\nThe result is (Manmoto, Mineshige \\& Kusunose 1997):\n\\be\n F_{\\nu}=\\frac{2 \\pi}{\\sqrt{3}}B_{\\nu}[1-{\\rm exp}(-2\\sqrt{3} \\tau^*_{\\nu}],\n\\ee\nwhere $\\tau^*_{\\nu} \\equiv (\\pi^{1/2}/2) \\kappa_{\\nu}H$ is the optical\ndepth for absorption of the accretion flow in the vertical direction with\n$\\kappa_{\\nu}=\\chi_{\\nu}/(4\\pi B_{\\nu})$ being the absorption coefficient,\nwhere $\\chi_{\\nu}=\\chi_{\\nu, {\\rm brems}}+\\chi_{\\nu,{\\rm synch}}$\nis the emissivity, and $\\chi_{\\nu, {\\rm brems}}$ and \n$\\chi_{\\nu,{\\rm synch}}$ are the bremsstrahlung and synchrotron \nemissivities, respectively. Then the local radiative \ncooling rate $q^-$ reads as follows:\n\\be\nq^-=\\frac{1}{2H}\\int d \\nu \\eta(\\nu)2F_{\\nu},\n\\ee\nwhere $\\eta$ is the energy enhancement factor first introduced by Dermer,\nLiang \\& Canfield (1991) and modified by Esin et al. (1996)\n(See Manmoto, Mineshige \\& Kusunose 1997 for the exact formula).\n\nGiven the values of parameters $M, \\dot{M}, \\alpha$ and $\\beta$, \nwe numerically solve the above set of equations describing the radiation\nhydrodynamics of a two-temperature \n accretion flow around a black hole. The equations are\nreduced to a set of differential equations with three variables $v$,\n$T_i$ and $T_e$. The global\nsolutions must satisfy simultaneously the no-torque condition at the horizon,\nthe sonic point condition at a sonic radius $r_{\\rm s}$ \nand three outer boundary conditions given at a certain outer boundary \n$r_{\\rm out}$. The numerical method we adopted is the same as in\nNakamura et al.(1997).\n\nWe adopt the same procedure as in Manmoto et al. (1997) to calculate \nthe emergent spectrum. The spectrum of unscattered photons \nis calculated from equation (14)\nand the Compton scattered spectrum is calculated by using the formula \ngiven by Coppi \\& Blandford (1990). Since the Comptonization\nis mainly occurred in the inner region of the disk $r \\la 10 r_{\\rm g}$,\nwhere $H/r \\la 0.4$, our ``local'' instead of ``global'' \ntreatment of Comptonization\nwill not cause a serious error. \n At last, the redshift due to gravity and \ngas motion are also considered in the following simple way\n(Manmoto, Mineshige \\& Kusunose 1997).\nThe effect of gravitational redshift is included by taking the ratio\nof the the observed energy of a photon to its energy emitted\nat radius $r$ to be $(1-r_g/r)^{1/2}$. As for the redshift due to \nthe relativistic radial motion, we concentrate \non the face-on case and take the\nrate of energy change to be $1/[1-(v/c)^2]$.\n\n\\section{RESULTS}\n\nThroughout this paper, we set $M=10^9 \\msun$ and \n$\\dot{m}=\\dot{M}/\\dot{M}_{\\rm Edd}=10^{-4}$, where $\\dot{M}_{\\rm Edd}\n=10L_{\\rm Edd}/c^2=2.2 \\times 10^{-8} M {\\rm yr}^{-1}$\nis defined as the Eddington accretion rate. Other parameters are\n$\\alpha=0.1, \\beta=0.9$ and $r_{\\rm out}=10^3 r_{\\rm g}$. \nAt $r_{\\rm out}$, the three outer boundary conditions \nwe imposed are $T_i=T_{{\\rm out},i}, T_e=T_{{\\rm out},e}$ and \n$\\lambda(\\equiv v/c_s \\equiv v/\\sqrt{p/\\rho}\n)=\\lambda_{\\rm out}$(see Paper I). \nThis set of boundary conditions are equivalent to $(T_{{\\rm out},i}, \nT_{{\\rm out},e}, \\Omega_{\\rm out})$ according to eq. (7) \nbecause $j$ is the eigenvalue of the problem rather \nthan a free parameter. We assign\n($T_{{\\rm out},i}, T_{{\\rm out},e}, \\lambda_{\\rm out}$)\n to different sets of values \nand investigate their effects on the \nstructure of the accretion flow and the\n emergent spectrum. The results are as follows.\n\nWe find that the results are qualitatively the same as in Paper I \nalthough the synchrotron radiation, a strong {\\it local} cooling term, \nis included in the electron energy equation. This is because\nthe differential terms, which \nstand for the {\\it global} character of the equations, still play a\ndominated role. We find that only when OBCs are \nwithin a certain range do the global solutions exist.\nIn terms of the ion temperature, the range is \n$T_{{\\rm out},i} \\sim (0.01-1) T_{\\rm virial}$ ( \nhere $T_{\\rm virial} \\equiv 2GM m_{\\mu}\n/3kr$ denotes the virial temperature). The electrons temperature is \nslightly lower than $T_{{\\rm out},i}$. As for the range of $\\Omega_{\\rm out}$,\nit must satisfy $\\Omega_{\\rm out} \\la 0.8 \\Omega_{\\rm K}(r_{\\rm out})$,\notherwise the viscous heating term takes a negative value under our\nviscous description. This result was first pointed out by \nManmoto, Mineshige \\& Kusunose (1997).\nThe range of OBCs slightly varies under different parameters \n$\\dot{m}, \\alpha$ and $\\beta$, and it is also the function of the value\nof $r_{\\rm out}$, as we describe in the subsequent section of this paper. \nThe structures of the solutions with different OBCs are greatly different.\nThree types of solutions \nare also found in terms of their topological structures and\nangular momentum profiles (cf. Paper I). \nGenerally, when $T_{\\rm out}$ is relatively low,\nthe solution is of type I. When $T_{\\rm out}$ is high and \n$\\lambda_{\\rm out}$ is small (or equivalently $\\Omega_{\\rm out}$ is large), \nthe solution is of type II. Types I and II \nboth have small values of sonic \nradii $r_{\\rm s} \\la 10 r_{\\rm g}$, but their angular momentum profiles \nare different (see Figure 1 of Paper I and Figure 1 in the present paper). \nWhen $T_{\\rm out}$ is high and $\\lambda_{\\rm out}$ is large\n(or equivalently $\\Omega_{\\rm out}$ is\nsmall), the solution becomes type III, which\n has much larger $r_{\\rm s}$. \n\nFigure 1 shows the effect of different $\\Ti$ on the solution structures. \nThe values of $\\Te$ and $\\lambda_{\\rm out}$ are the same, with $\\Te=1.2 \n\\times 10^8K$ and $\\lambda_{\\rm out}=0.2$. The solid line \n(belonging to type I solution) \nis for $\\Ti=2 \\times 10^8K$,\nthe dotted line (type I) for $\\Ti=6 \\times 10^8K$,\nthe short-dashed line (type II) for $\\Ti=2 \\times 10^9K$ and\nthe long-dashed line (type III) for $\\Ti=3.2 \\times 10^9K$.\nSix plots in the figure show the radial \nvariations of the Mach number (defined as\n$v/\\sqrt{((3 \\gamma_i-1)+2(\\gamma_i-1)\\alpha^2)/(\\gamma_i+1)}/c_s$ so that \nthe Mach number equals 1 at the sonic point), the electrons and \nions temperatures, profiles of the specific angular momentum and \nsurface density $\\Sigma$ ($\\equiv 2\\rho H$), and the ratio of the vertical \nscale height of the disk $H(r)$ to the radius, respectively. \nFrom the figure, we find that the discrepancy \nin the ion temperature is rapidly reduced as the \nradius decreases and $T_i$ converges to\nthe virial temperature. This is because the local viscous\ndissipation in the ions energy equation plays an important\nrole therefore the temperature of ions is mainly ``locally'' \ndetermined, like the case of a one-temperature plasma (Paper I).\n However, the discrepancy \nin the surface density of the disk\npersists throughout the disk.\n\nSuch discrepancy in the solution structures results in the discrepancy\nin the emission spectrum, as Figure 2 shows.\nThe discrepancy in the luminosity at certain \nindividual wave band can be\nunderstood by referring to Figure 1. In the radio-submillimeter band,\nthe power is principally due to synchrotron\nemission for which we approximately have \n$L_{\\nu} \\propto \\rho^{4/5} T_e^{21/5}$ for the ``general''\nfrequency and $\\nu_p L_{\\nu_p} \\propto \n\\rho^{3/2}T_e^7$ for the peak frequency (Mahadevan 1997). Synchrotron radiation\nmainly comes from the inner region of the disk, $\\la 10r_g$.\nSo the long-dashed line in the figure possesses the lowest\nradio power is mainly due to its lowest surface density, since $T_e$\nis almost the same for different solutions. \nFor such a low mass accretion rate\nsystem as considered in this paper, the low frequency part of the\nsubmillimeter to hard X-ray spectrum is mainly contributed by\nthe Comptonization of synchrotron photons, and it is bremsstrahlung emission\nthat is responsible for the high frequency part.\nThe long-dashed line still possesses the lowest power in the low frequency band \n because its corresponding\namount of synchrotron soft photons is the least and \nits corresponding Compton y-parameter $y \\equiv \\tau_{\\rm es}kT_e/m_ec^2$\nis the smallest.\nIn the X-ray band, the solid line has the highest\npower. This is because for bremsstrahlung emission we\napproximately have $L_{\\rm brems} \\propto T_e^{-1/2}e^{-h\\nu/kT_e} \\rho^2$,\ni.e., the density instead of $T_e$ is the dominated factor, and the solid\nline possesses the highest density among the four solutions.\n\nThe effect of $\\Te$ on the structures of the global solutions \nis shown in Figure 3. All the three lines in the figure have\n$\\Ti=2 \\times 10^9K$ and $\\lambda_{\\rm out}=0.2$. \nThe solid line is for $\\Te=1.2 \\times 10^8K$, the dotted line for\n$\\Te=8 \\times 10^8K$ and the dashed line for $\\Te=1.2 \\times 10^9$.\nDifferent with $T_i$, the discrepancy in $T_e$ persists \nthroughout the disk rather than converges as the radius decreases. \nThis is because the electrons are essentially adiabatic for the\npresent low accretion rate case, i.e., both $q_{ie}$ and $q^-$ are very small \ncompared with the advection term on the left-hand side of equation (8),\nso the electron temperature is globally determined. While for the ion,\nthe {\\em local} viscous dissipation in the energy \nequation plays an important role;\nthus, the temperature of ion is determined more locally than the electron.\nSuch discrepancy in the electron temperature produces significant \ndiscrepancy in the emission spectrum especially \nin the radio, submillimeter and IR bands,\nas Figure 4 shows.\n\nThe effect of modifying $\\lambda_{\\rm out}$ (i.e., modifying $\\Omega_{\\rm out}$)\non the structure of the accretion flows is shown in Figure 5. \nEach of the three lines in the figure corresponds \nto $T_{{\\rm out},i}=2 \\times 10^9 {\\rm K}$\nand $T_{{\\rm out},e}=1.2 \\times 10^9 {\\rm K}$. \nThe values of $\\lambda_{\\rm out}$ are\n$0.18$ (solid line, type II), $0.22$ \n(dotted line, type II) and $0.26$ (dashed line, type III), \nand their corresponding angular velocities are \n$0.45 \\Omega_{\\rm k}, 0.37 \\Omega_{\\rm k}$ and $0.29 \\Omega_{\\rm k}$,\nrespectively. \n\nWhen $\\Omega_{\\rm out}$ decreases across a certain critical\nvalue, $\\sim 0.36 \\Omega_{\\rm k}(r_{\\rm out})$ in the present case, \nan accretion pattern characterized by possessing \na much larger sonic radius appears (referred to as type III solution). \nAs we argue later in this paper, this accretion pattern is\nof particular interest to us.\nIn all previous works on viscous accretion flows, only the \nsolutions with small sonic radii $\\sim $ several $r_{\\rm g}$ have been \nfound (Muchotreb \\& Paczy\\'nski 1982; \nMatsumoto et al. 1984; Abramowicz et al. 1988; Chen \\& Taam 1993;\nNarayan, Kato \\& Honma 1997; Chen, Abramowicz \\& Lasota 1997; \nNakamura et al. 1997); therefore, this pattern is new. \nThe reason why previous authors did not find this pattern \nis that they generally set the\nstandard thin disk solutions as the OBCs \n(Muchotreb \\& Paczy\\'nski 1982; Matsumoto et al. 1984;\nAbramowicz et al. 1988; Chen \\& Taam 1993; \nNarayan, Kato \\& Honma 1997; Chen, Abramowicz \\& Lasota 1997),\nwhere the specific angular momentum of the flow is Keplerian;\nor, a specific angular momentum with a value near the \nKeplerian one is set as the OBC (Nakamura et al. 1997; \nManmoto, Mineshige \\& Kusunose 1997).\n\nSuch transition between the sonic radii happened when \n$\\Omega_{\\rm out}$ passes across a critical value is clearly shown in \nFigure 6. The value of the critical $\\Omega_{\\rm out}$\nvaries with the parameters such as $\\alpha$ and $\\beta$, and it is \nalso the functions of $\\Ti, \\Te$ and $r_{\\rm out}$. \nGenerally, it decreases with the decreasing $\\alpha$ and/or the \nincreasing $r_{\\rm out}$. \nSimilar transition has been found previously in the context \nof adiabatic (inviscid) accretion \nflow by Abramowicz \\& Zurek (1981). In that case,\nthey found that when the specific angular momentum of the flow $l$, \na constant of motion, decreased across a critical value $l_c(E)$\n(here the specific energy $E$ of the flow is another constant of motion),\na transition from a disk-like accretion pattern to \na Bondi-like one would happen (Abramowicz \\& Zurek 1981;\nLu \\& Abramowicz 1988). Here in this paper we find that this \ntransition still exist when the flow becomes viscous, confirming \nthe prediction of Abramowicz \\& Zurek (1981). \n\nThe physical reason of the transition between the two patterns is obvious.\nWhen the specific angular momentum of the gas \nis low, the centrifugal force can be neglected and the gravitational force\nplays a dominated role in the radial momentum equation (eq. 6),\ntherefore the gas becomes supersonic far before the horizon like\nin Bondi accretion. When the specific angular momentum is high, \nhowever, since the centrifugal force becomes stronger, \nthe gas becomes transonic only after passing through a sonic \npoint near the horizon with the help of the general relativistic \neffect (Abramowicz \\& Zurek 1981; Shapiro \\& Teukolsky 1984).\n\nFigure 7 shows the corresponding spectra of the solutions \npresented in Figure 5. The accretion flow belonging to the \nnew accretion pattern, which is denoted by the\ndashed line, emits the lowest X-ray luminosity. This is because\nthis accretion pattern possesses the largest \nsonic radius therefore the corresponding density \nof the accretion flow is the lowest.\n\nAll above results are obtained for a fixed outer boundary $r_{\\rm out}=\n10^3 r_{\\rm g}$. We also investigate the influence of increasing the\nvalue of $r_{\\rm out}$ on the global solutions. We find \nthat the general feature are quantitatively the same. \nOne remarkable difference is that the ranges of $\\Ti$ and $\\Te$ \nwithin which we can obtain a global solution lessen with the increasing radii.\nFor example, if we increase $r_{\\rm out}$ from $10^3r_{\\rm g}$ to\n$10^4r_{\\rm g}$, the temperature\nrange will lessen from $\\sim (0.01-1) T_{\\rm virial}$ \nto $\\sim (0.1-1) T_{\\rm virial}$. If $r_{\\rm out}$ is taken to be large enough,\n$\\Ti (\\approx \\Te)$ almost be unique.\n%This is the case of Sgr A$^*$, a compact radio source which we will discuss in \n%the next section of this paper. \nHowever, the feasible range of $\\Omega_{\\rm out}$\nis almost constant, no matter how large $r_{\\rm out}$ is. \nMoreover, when the value of $r_{\\rm out}$ becomes larger,\nthe transition between the accretion patterns, happened \nwhen $\\Omega_{\\rm out}$ pass across the critical value, becomes more ``obvious''\nin the sense that the small sonic radius becomes \nsmaller and the large sonic radius becomes \nlarger. Consequently, the discrepancy between the surface density \nof the accretion disk of the two accretion patterns becomes \nlarger compared with the case of small $r_{\\rm out}$, and this will further \nresult in the increase of the discrepancy of the X-ray \nluminosity emitted by the accretion flow. This is the crucial factor\nto solve the puzzle of the mass accretion rate of Sgr A$^*$.\n\n\\section{APPLICATION TO Sgr A$^*$}\n\nKinematic measurements suggest that the energetic radio source\nSgr A$^*$ located at the center our Galaxy\n is a supermassive compact object with a mass\n$\\sim 2-3 \\times 10^6 \\msun$.\n This is widely believed to be a black hole (Mezger, Duschl \\& Zylka 1996).\nOn the other hand, observations of gas outflows\nnear Sgr A$^*$ indicate the existence of\na hypersonic stellar wind coming from\nthe cluster of stars within several arc-seconds from Sgr A$^*$.\nThe wind should be accreting onto the black hole (Melia 1992).\nIf the flow past Sgr A$^*$ is uniform, then\nthe mass accretion rate can be simply obtained by\nthe classical Bondi-Hoyle scenario (Bondi \\& Hoyle 1944) as follows.\nSince the wind is significantly hypersonic, as such, a standing bow-shock\nis inevitable. This shock is located roughly where flow elements'\npotential energy equals kinetic energy (Shapiro 1973; Melia 1992),\n$R_{\\rm A}=2GM_{\\rm BH}/v^2_w$,\nwhere $M_{\\rm BH}$ is the mass of the black hole and $v_w$ is\nthe wind velocity. From here the shocked gas is assumed to\naccret into the hole. Since the mass flux in the gas at large radii is\n$m_p n_w v_w$, where $m_p$ is proton mass and $n_w$ is the number density\nof the gas, the mass accretion rate is\n$\\dot{M}_{\\rm BH}=\\pi R_{\\rm A}^2 m_p n_w v_w$.\n\nThis result is only valid for an uniform source.\nIn reality the flow past Sgr A$^*$ comes from multiple sources.\nIn this case, the wind-wind shocks dissipate some of\nthe bulk kinetic energy and lead to a higher capture rate for\nthe gas (Coker \\& Melia 1997).\nThe exact value of accretion rate $\\dot{M}$ depends on the stellar spatial\ndistribution and can only be obtained by numerical simulation.\nThe three-dimensional hydrodynamical simulation of\nCoker \\& Melia (1997) gives the average value $\\dot{M}=1.6 \\dot{M}_{\\rm BH}$\nfor two extreme spatial distributions, spherical and planar ones.\nWith the available data at that time,\nthe accretion rate obtained in Coker \\& Melia (1997)\nis $\\dot{M} \\sim 10^{22} \\gs$.\nConsidering that recent work suggests\nthe Galactic Centre wind is dominated by a few hot stars with\nhigher wind velocities of $\\sim 1000 {\\rm \\,km}\\,s^{-1}$(Najarro et al. 1997)\nrather than $700 {\\rm \\,km \\,s}^{-1}$ taken by Coker \\& Melia (1997),\nthe more reliable accretion rate should be\n$\\dot{M} \\sim (700/1000)^3 \\times 10^{22} \\gs \\sim\n9 \\times 10^{-4} \\dot{M}_{\\rm Edd}$.\n\nAssuming the accretion is via a standard thin disk,\nthe accretion rate required to model the luminosity\nis more than three orders of magnitude\nlower than this value. \nADAF model has been turned out to be\na significant success to model its low luminosity \n(Narayan, Yi \\& Mahadevan 1995; Manmoto, Mineshige \\&\nKusunose 1997; Narayan et al. 1998).\nHowever, there exists a discrepancy between the accretion rate favored \nby all ADAF models\nin the literature and that favored by the simulation mentioned above, \nwith the former being 10-20 times smaller than that favored by the \nlatter (Coker \\& Melia 1997; Quataert \\& Narayan 1999b).\nThe most up-to-date calculation\ngives $\\dot{M}=6.8 \\times 10^{-5} \n\\dot{M}_{\\rm Edd}$ (Quataert \\& Narayan 1999b) and this value \napproaches the lower limit considered plausible \nfrom Bondi capture (Quataert, Narayan, \\& Reid 1999). \nIn an ADAF model, the mass accretion\nrate is determined by fitting the theoretical\nX-ray flux to the observation.\nIf a larger accretion rate\nwere adopted, then bremsstrahlung radiation\nwould yield an X-ray flux well\nabove the observational limits. Even though we assume that significant\naccretion mass may be lost to a wind, detailed calculation shows\nthat since the bremsstrahlung radiation comes from large radii in the\naccretion flow, the discrepancy can not be\nalleviated no matter how strong the winds are (Quataert \\& Narayan 1999b).\n%This poses a serious problem.\n\nThe present research on the role of OBC tells us that we should \nseriously consider the physical state of accretion flows\nat the outer boundary. However, we note that\nin all present ADAF models of Sgr A$^*$,\n the outer boundary condition\nis roughly treated. In our view, this might be an origin of the discrepancy\nbetween the mass accretion rate.\n% required by ADAF models\n%and that favored by hydrodynamical simulations.\n\nBasing upon the above consideration,\nwe recalculate the spectrum of Sgr A$^*$.\nWe set the outer boundary at the\n``accretion radius'' $R_A=2GM/v_w^2 \\sim 1.5 \\times\n10^5r_{\\rm g}$. In the present case of Sgr A$^*$, \nthe temperatures of ions and electrons\nin the flow just after the bow-shock should equal the virial temperature\n$\\sim 10^{12}/(r/r_{\\rm g})K$.\nBut the value of the specific angular momentum at the outer boundary\nis not certain. We set it as various values and find that,\nwhen it pass across a critical value $\\sim 0.16 \\Omega_{\\rm K}$,\nthe transition of the accretion pattern\noccurs. Figure 8 shows the Mach number and the surface density of\nthe two accretion patterns.\nThe parameters of both the solid and the dashed lines\nin the figure are: \n$M_{\\rm BH}=2.5 \\times 10^6 \\msun$,\n$\\dot{M}=4 \\times 10^{-4} \\dot{M}_{\\rm Edd}$,\n$\\alpha=0.1$ and $\\beta=0.9$. \nAt the outer boundary $R_{\\rm A}$, the two lines possess identical\ntemperature of $8 \\times 10^6{\\rm K}$, but their specific angular momenta\nare different. The solid line, which stands for our new accretion\npattern, corresponds to relatively\nlow angular velocity, $\\sim 0.15 \\Omega_{\\rm K}$, while \nthe angular velocity possessed by the dashed \nline, which we draw for comparison,\nis much higher, $\\sim 0.46 \\Omega_{\\rm K}$.\nTheir sonic radii are $\\sim 4 r_{\\rm g}$ (dashed line),\nand $\\sim 6000 r_{\\rm g}$ (solid line), respectively.\nThe difference\nof the sonic radius results in the discrepancy in the surface density,\nwhich further results in the difference of the X-ray luminosity, \nas shown by Figure 9. \n\nFigure 9 shows our calculated X-ray spectra\ntogether with the observation of Sgr A$^*$. Here we assume that the\nbremsstrahlung radiation is the only contributor to this waveband.\nThis assumption requires that the synchrotron radiation\ncan not be too strong, otherwise the contribution from the\nComptonization of the synchrotron photons\nwill exceed that from bremsstrahlung radiation.\nThis requirement can be satisfied according to \nthe radio observation of Sgr A$^*$.\nWe will discuss this question in the following part.\nFrom the figure, we find that accretion rate as high as\n$4 \\times 10^{-4} \\dot{M}_{\\rm Edd}$ is\nacceptable, if only the angular momentum\nat the outer boundary is relatively low. Compared with\nthe value of $6.8 \\times 10^{-5} \\dot{M}_{\\rm Edd}$\nin Quataert \\& Narayan (1999b), this value is much\ncloser to that favored by the numerical\nsimulation. If the angular momentum of the flow at $R_{\\rm A}$\nis relatively high, however, as shown by the dashed line, the X-ray\nflux is well above the observation.\n\nNow the crucial moment is whether the value\nof the angular velocity at $R_{\\rm A}$ is really low.\nIn this context, we note that the three-dimensional\nnumerical simulation by Coker \\& Melia (1997) indicates that\nthe accreted angular velocity\nin Sgr A$^*$ is very low, $\\Omega_{\\rm out} \\approx\n0.1 \\Omega_{\\rm K}(r_{\\rm out})$ for their run 1 and\n$\\approx 0.2 \\Omega_{\\rm K}(r_{\\rm out})$ for their run 2.\nThe consistency with our result is satisfactory.\n\n\\section{SUMMARY AND DISCUSSION}\n\nIn this paper, we numerically solve the radiation hydrodynamic\nequations describing an optically thin advection dominated accretion flow\nand calculate its emergent spectrum.\nWe fix all the parameters such as $\\alpha, \\beta, M$ and\n$\\dot{M}$, and set the outer boundary condition as $\\Ti, \\Te$\nand $\\lambda_{\\rm out}(\\equiv v/c_s)$\nat certain outer boundary $r_{\\rm out}$.\nOur primary focus is to investigate the effects of the outer boundary\nconditions on the structure of the global\nsolution and, especially, on the emergent spectrum.\n\nWe find that OBCs must lie in a certain range,\notherwise we can't find the corresponding global solutions.\nHowever, this range is large enough in the sense that both the structure\nof the solution and its corresponding spectrum differ greatly\nfrom each other under different OBCs. \nThree types of solutions\nare also found under various OBCs,\nqualitatively agree with the result of Paper I, where magnetic\nfield is neglected and the description to radiation is crude.\nThe value of the sonic radius in type III solution\nis much larger than types I and II. We examine the\nindividual influence of $\\Ti, \\Te$ and $\\lambda_{\\rm out}$ on\nthe structures and spectrum and find that each factor especially\nthe temperature, plays a significant role. The peak flux in\nthe radio, IR and X-ray bands can differ by nearly two \norders of magnitude or more in our example, \nalthough all the other parameters are exactly the same.\n\nWe also investigate the effect of modifying the value of $r_{\\rm out}$.\nWe find that the feasible ranges of $\\Ti$ and $\\Te$ lessen with the\nincreasing radii. If the value of $r_{\\rm out}$ is too large, the values of\n$\\Ti$ and $\\Te$ are almost unique. \nThis result seems to mean the reduction of the effect of OBC on the solution.\nHowever, on the one hand we expect that \nin some cases, such as some binary system\nor the system where a thin disk-ADAF transition is \nexpected to occur (e.g., X-ray binaries A0620-00 \nand V404 Cyg, and low luminosity AGN NGC 4258; see Narayan, Mahadevan, \\&\nQuataert 1998 and references therein), \n the value of $r_{\\rm out}$\nmight be small. On the other hand, the feasible range of \n$\\Omega_{\\rm out}$ is almost constant no matter how large \n$r_{\\rm out}$ is. \n\nThe reason why previous works on ADAF global solution\n(e.g., Narayan, Kato, \\& Honma 1997; Chen,\nAbramowicz, \\& Lasota 1997)\ndid not find the obvious effect of OBC on the global solution \nis that, both Narayan, Kato \\&\nHonma (1997) and Chen, Abramowicz \\& Lasota (1997) concentrated\non the dynamics of a {\\em one-temperature plasma}, \nwhere the {\\em local} viscous dissipation \nin the energy equation plays an important role. \nDue to this reason, their global solutions are in principle \n``locally'' rather than ``globally'' \ndetermined, the effect of OBC weakens rapidly \nwith the decreasing radii and the solutions converged rapidly over\na small radial extent away from the outer boundary. \nWe also obtained similar results with theirs\nfor the one-temperature plasma in our Paper I. \nHowever, according to our result, the variation of $\\Omega_{\\rm out}$ \nacross a certain critical value\nwill produce obvious OBC-dependent behavior such as the \ntransition of the sonic radius,\nno matter what type the plasma is, one- or two-temperature. \nThey did not find this result might be due to the \nfact that $\\Omega_{\\rm out}$ adopted by them, \n$\\Omega_{\\rm K}(r_{\\rm out})$ for Keplerian disk \nouter boundary condition or\n$\\sim 0.34 \\Omega_{\\rm K}(r_{\\rm out})$ \nfor self-similar solution outer boundary condition, is \nalways larger than the critical value, so the effect of OBC\nis very small hence is hard to find. \n \nThe present study concentrates on the low-$\\dot{M}$ case where\nthe differential terms in the equation such as the energy advection\nplay an important role therefore the effect of OBC are most obvious.\nWhen $\\dot{M}$ becomes higher, the role of \nthe local radiation loss terms in the energy balance\nwill become more important. In this case, we expect that the discrepancy \ndue to OBC in the profile of the \ntemperature will lessen. However, from our calculation to\nthe one-temperature accretion flow whose temperature\nis also principally determined locally (Paper I), and Figure 5 in \nthe present paper, we expect\nthat the flow should still present OBC-dependent\nbehavior in, e.g., the angular momentum and the Mach number\nprofiles. \n\nWe do not include winds in the present study. Since the Bernoulli parameter\nof ADAF is positive therefore the gas can in principle \nescape to infinity with positive energy (Narayan \\& Yi 1994, 1995).\nBlandford \\& Begelman (1999) recently suggested that mass loss\nthrough winds might be dynamically important. The effect of winds on the\nspectrum of ADAF has been investigated by Quataert \\& Narayan (1999b).\nIt is interesting to investigate the effect \nof OBC on ADAF with winds. We expect the result is probably similar\nwith the present results since in that case the differential terms in \nthe equation still play an important role.\n\nIt is a meaningful problem whether a standing shock occurs\nin an accretion flow. Although some authors have set up\nthe shock-included global solutions (e.g. Chakrabarti 1996),\nthe result is generally thought not to be so\nconvincing because in their numerical procedure\n$r_{\\rm s}$ and $j$ are treated as two\nfree parameters instead of\nthe eigenvalues of the problem.\nA necessary condition for the shock\nformation is the existence of the global solution\nwith a large sonic radius outside the centrifugal \nbarrier. This is the key of the problem.\nAccording to our result, this kind of large-sonic-radius \nsolution, belonging to our type III, can only be \nrealized when the specific angular momentum of the accretion flow\nis low. We note that this requirement to the angular momentum\nis exactly what Narayan, Kato \\& Honma(1997)\nanticipated, and it has recently been\nconfirmed by the numerical simulation by Igumenshchev, Illarionov \\&\nAbramowicz (1999).\n\nThe large-sonic radius solution (type III) is a new accretion pattern since \nin all previous studies on viscous accretion onto black holes \nthe sonic radii are small. We find that the discrepancy in the mass\naccretion rate of Sgr A$^*$ between the value favored by the previous \nADAF models in the literature and that favored by the \nhydrodynamical numerical simulation is significantly reduced if the accretion\nis via this pattern. This result hints us that\nsuch low angular momentum accretion may be\nvery common in the universe. One example is the detached binary system,\nwhere the accretion material is the stellar wind from the companion\ntherefore the angular momentum of the accreting gas is\nvery low (Illarionov \\& Sunyaev 1975). \nAnother example is\nthe cores of nearby giant elliptical galaxies, where the angular momentum\nof the hot (accretion) gas is again assumed to be \nvery small.\n\n\\acknowledgements\n\nWe are grateful to the referee for \nmany helpful comments and suggestions which enabled us \nto improve the presentation. \nThis work is supported in part by the National Natural Science\nFoundation of China under grant 19873007. F.Y. also\nthanks the financial support\nfrom China Postdoctoral Science Foundation.\n\n%\\vfill\\eject\n\\references\n\\def\\refpar{\\hangindent=3em\\hangafter=1}\n\\def\\reference{\\refpar\\noindent}\n\\def\\apj{ApJ}\n\\def\\apjs{ApJS}\n\\def\\mnras{MNRAS}\n\\def\\aa{A\\&A}\n\\def\\aas{A\\&A Suppl. Ser.}\n\\def\\aj{AJ}\n\\def\\araa{ARA\\&A}\n\\def\\nat{Nature}\n\\def\\pasj{PASJ}\n\n\\reference Abramowicz, M.A., Chen, X., Kato, S., Lasota, J.-P., \\&\nRegev, O. 1995, \\apj, 438, L37\n\n\\reference Abramowicz, M.A., Czerny, B., Lasota, J.P., \\& Szuszkiewicz, E.,\n1988, \\apj, 332, 646\n\n\\reference Abramowicz, M., A., Zurek, W.H., 1981, ApJ, 246, 31\n\n\\reference Begelman, M.C., 1978, \\mnras, 243, 610\n\n\\reference Begelman, M.C., \\& Meier, D.L., 1982, \\apj, 253, 873\n\n\\reference Blandford, R.D., \\& Begelman, M.C. 1999, MNRAS, 303, L1\n\n\\reference Bondi, H. \\& Hoyle, E. 1944, \\mnras, 104, 273\n\n\\reference Chakrabarti, S.K. 1996, \\apj, 464, 664\n\n\\reference Chandrasekhar, S. 1939, Introduction to the Study of\nStellar Structure(New York: Dover)\n\n\\reference Chen, X., Abramowicz, M. A., \\& Lasota, J.-P. 1997, \\apj, 476, 61\n\n\\reference Chen, X. \\& Taam, R. 1993, \\apj, 412, 254\n \n\\reference Coker, R., \\& Melia, F., 1997, \\apj, 488, L149\n\n\\reference Coppi, P.S., \\& Blandford, R.D. 1990, \\mnras, 245, 453\n\n\\reference Dermer, C.D., Liang, E.P., \\& Canfield, E. 1991, \\apj, 369, 410\n\n\\reference Esin, A.A., Narayan, R., Ostriker, E., \\& Yi, I. 1996, \\apj, 465, 312\n\n\\reference Esin, A.A., 1997a, \\apj, 482, 400\n\n\\reference Esin, A.A., McClintock, J. E., \\& Narayan, R. 1997b, \\apj, 489, 865\n\n\\reference Ichimaru, S., 1977, \\apj, 214, 840\n\n\\reference Igumenshchev, I.V., Illarionov, A.F. \\& Abramowicz, M.A. 1999, \n\\apj, 517, L55\n\n\\reference Illarionov, A.F., \\& Sunyaev, R.A., 1975, \\aa, 39, 185\n\n\\reference Lu, J.F., \\& Abramowicz, M.A. 1988, Acta Ap. Sin., 8, 1\n \n\\reference Mahadevan, R. 1997, \\apj, 477, 585\n\n\\reference Manmoto, T., Mineshige, S., Kusunose, M. 1997, \\apj, 489, 791\n\n\\reference Matsumoto, R., Kato, S., Fukue, J., \\& Okazaki, A.T. 1984, \\pasj, 36,\n71\n\n\\reference Melia, F 1992, \\apj, 1992, 387, L25\n\n\\reference Mezger, P.G., Duschl, W.J., \\& Zylka, R. 1996, A\\&AR, 7, 289\n\n\\reference Muchotreb, B., \\& Paczy\\'nski, B. 1982, Acta Astron. 32, 1\n\n\\reference Najarro, E., et al. 1997, \\aa, 325, 700\n\n\\reference Nakamura, K. E., Kusunose, M., Matsumoto, R., \\& Kato, S. 1997,\n\\pasj, 49, 503\n\n\\reference Narayan, R., Kato, S. \\& Honma, F. 1997, \\apj, 476, 49\n\n\\reference Narayan, R., Mahadevan, R., Grindlay, J.E., Popham, R. \\&\n Gammie, C., 1998, \\apj, 492, 554\n\n\\reference Narayan, R., Mahadevan, R., \\& Quataert, E. 1998, in ``The Theory\nof Black Hole Accretion Discs'', eds. M.A. Abramowicz, G. Bjornsson,\nand J.E. Pringle, (Cambridge University Press)\n\n\\reference Narayan, R. \\& Yi, I. 1994, \\apj, 428, L13\n\n\\reference Narayan, R. \\& Yi, I. 1995, \\apj, 444, 231\n\n\\reference Narayan, R., Yi, I., Mahadevan, R. 1995, \\nat, 374, 623\n\n\\reference Paczy\\'nski, B., \\& Wiita, P. J. 1980, \\aa, 88, 23\n\n\\reference Quataert, E., \\& Narayan, R., 1999a, \\apj, 516, 399\n\n\\reference Quataert, E., \\& Narayan, R., 1999b, \\apj, 520, 298 \n\n\\reference Quataert, E., Narayan, R., \\& Reid, M.J. 1999, \\apj, 517, L101\n\n\\reference Rybicki, G., \\& Lightman, A.P. 1979, Radiative Processes \nin Astrophysics (New York: Wiley)\n\n\\reference Rees, M.J., Begelman, M.C., Blandford, R.D., \\& Phinney, E.S., \n1982, \\nat, 295, 17\n\n\\reference Shakura, N.I., \\& Sunyaev, R.A., 1973, \\aa, 24, 337\n\n\\reference Shapiro, S.L. 1973, \\apj, 180, 531\n\n\\reference Shapiro, S.L., \\& Teukolsky, S.A. 1984, \n{\\em Black Holes, White Dwarfs,\nand Neutron Stars} (New York: Wiley)\n\n\\reference Yuan, F. 1999, \\apj, 521, L55 (Paper I)\n\n\\newpage\n\n\\begin{figure}\n\\psfig{file=fig1.ps,width=1.\\textwidth,angle=270}\n\\caption{The structures of the accretion flow with\ndifferent $\\Ti$. The solid line (type I solution)\nis for $\\Ti=2 \\times 10^8K$,\nthe dotted line (type I) for $\\Ti=6 \\times 10^8K$,\nthe dashed line (type II) for $\\Ti=\n2 \\times 10^9K$ and the long-dashed line (type III)\nfor $\\Ti=3.2 \\times 10^9K$.\nOther OBCs are $\\Te=1.2 \\times 10^8K$ and $\\lambda_{\\rm out}=0.2$.\nThe outer boundary is set at $r_{\\rm out}=10^3r_{\\rm g}$.\nOther parameters are\n$\\alpha=0.1, \\beta=0.9, M=10^9 \\msun$ and $\\dot{M}=10^{-4} \\dot{M}_{\\rm Edd}$.\nThe units of $\\Sigma$ and $T$ are ${\\rm g \\ cm^{-2}}$ and K}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig2.ps,width=1.\\textwidth,angle=270}\n\\caption{The corresponding spectra of the solutions shown in Figure 1.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig3.ps,width=1.\\textwidth,angle=270}\n\\caption{The structures of the accretion flows with different $\\Te$.\nThe solid, dotted and the dashed lines are for $\\Te=1.2 \\times 10^8K,\n8 \\times 10^8 K$ and $1.2 \\times 10^9K$, respectively.\nOther OBCs are $\\Ti=2 \\times 10^9K$ and $\\lambda_{\\rm out}=0.2$.\nThe outer boundary is set at $r_{\\rm out}=10^3r_{\\rm g}$.\nOther parameters and the units are the same as those in Figure 1.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig4.ps,width=1.\\textwidth,angle=270}\n\\caption{The corresponding spectra of the solutions shown in Figure 3.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig5.ps,width=1.\\textwidth,angle=270}\n\\caption{The structures of the accretion flows with\ndifferent $\\lambda_{\\rm out}$.\nThe solid, dotted and the dashed lines are for\n$\\lambda_{\\rm out}=0.18,\n0.22$ and $0.26$, respectively. The corresponding angular velocities are\n$0.447 \\Omega_{\\rm K}, 0.37 \\Omega_{\\rm K}$ and\n$0.289 \\Omega_{\\rm K}$.\nOther OBCs are $\\Ti=2 \\times 10^9K$ and $\\Te=1.2 \\times 10^9K$.\nThe outer boundary is set at $r_{\\rm out}=10^3r_{\\rm g}$.\nOther parameters and the units are the same as those in Figure 1.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig6.ps,width=1.\\textwidth,angle=270}\n\\caption{The variation of the value of the sonic radii with\nthe angular velocity at the outer boundary. A transition is clearly shown.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig7.ps,width=1.\\textwidth,angle=270}\n\\caption{The corresponding spectra of the solutions shown in Figure 5.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig8.ps,width=1.\\textwidth,angle=270}\n\\caption{The radial variations of the\nsurface density and the Mach\nnumber of the accretion flows with different\nspecific angular momenta at the outer\nboundary $R_{\\rm A}$. The solid line, which\nstands for our new accretion pattern, is for\n$\\Omega_{\\rm out}=0.15 \\Omega_{\\rm K}$ while the dashed line\nis for $\\Omega_{\\rm out}=0.46 \\Omega_{rm K}$. }\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig9.ps,width=1.\\textwidth,angle=270}\n\\caption{The X-ray spectrum of Sgr A$^*$.\nThe measured fluxes were converted to luminosity assuming\na distance of 8.5 kpc to the Galactic Centre. The observational\ndata are compiled by Narayan et al. (1998).\nThe spectra represented by the solid\nand the dashed lines are produced by the accretion flows denoted\nby the same style of lines as in Figure 8.\nDue to the difference of the angular momentum of the flow at the outer\nboundary, the X-ray flux differs by a factor $\\sim$ 8.}\n\\end{figure}\n\n\n\\end{document}\n"
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astro-ph0002069
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"author": "Feng Yuan"
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Taking optically thin accretion flows as an example, we investigate the dynamics and the emergent spectra of accretion flows with different outer boundary conditions (OBCs) and find that OBC plays an important role in accretion disk model. This is because the accretion equations describing the behavior of accretion flows are a set of {\em differential} equations, therefore, accretion is intrinsically an initial-value problem. We argue that optically thick accretion flow should also show OBC-dependent behavior. The result means that we should seriously consider the initial physical state of the accretion flow such as its angular momentum and its temperature. An application example to Sgr A$^*$ is presented.
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"name": "fyuan.tex",
"string": "\\documentclass{edbk} % Computer Modern font calls\n\\usepackage[dvips]{epsfig}\n\\usepackage{edbkps}% PostScript font calls\n\n\\setcounter{secnumdepth}{3}\n\\setcounter{tocdepth}{1}\n\\kluwerbib\n\n\\def\\be{\\begin{equation}}\n\\def\\ee{\\end{equation}}\n\\def\\mdot{\\dot{m}}\n\\def\\ergs{{\\rm\\,erg\\,s^{-1}}}\n\\def\\msun{M_{\\odot}}\n\\def\\ergscc{\\rm \\ \\ erg \\ cm^{-3} \\ s^{-1}}\n\\def\\Ti{T_{{\\rm out},i}}\n\\def\\Te{T_{{\\rm out},e}}\n\\def\\gs{\\rm \\,g\\,s^{-1}}\n\\def\\ergscc{\\rm \\,erg\\,cm^{-3}\\,s^{-1}}\n\\def\\ergs{\\rm \\,erg\\,s^{-1}}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{document}\n\n\\articletitle[Accretion Disk]{A New Parameter In Accretion Disk Model}\n\n\\author{Feng Yuan}\n\n\\affil{Department of Astronomy, Nanjing University, Nanjing 210093, China}\n\\email{[email protected]}\n\n\\begin{abstract}\nTaking optically thin accretion flows as an example, we investigate the \ndynamics and the emergent spectra of accretion flows with different outer \nboundary conditions (OBCs) and \nfind that OBC plays an important role in\naccretion disk model. This is because the accretion equations describing the\nbehavior of accretion flows are a set of {\\em differential} equations,\ntherefore, accretion is intrinsically an initial-value \nproblem. We argue that optically thick accretion flow should also \nshow OBC-dependent behavior. \nThe result means that we should seriously consider \nthe initial physical state of the accretion flow such as its angular \nmomentum and its temperature. An application example to Sgr A$^*$ is presented. \n\\end{abstract}\n\n\\section{Introduction}\nIt has long been assuming that the parameters describing the accretion flow\ninclude the accretion rate, the mass of the central black hole,\nthe viscosity parameter, and the parameter \ndescribing the strength of the magnetic\nfield in the accretion flow. Once these parameters \nare given, we can obtain almost all the \ninformation of the accretion flow including the dynamics and the emergent\nspectrum. However, the set of equations describing the accretion flow\nare nonlinear differential equations, therefore it is intrinsically \nan initial-value problem. Thus the outer boundary condition (OBC)\npossibly plays an important role. \n\nOn the other hand, the complicated astrophysical environments\nmake the physical states of the accreting gas at \nthe outer boundary $r_{\\rm out}$,\nsuch as its temperature and angular momentum, various.\nFor example, in semi-detached binary system, where the critical \nRoche lobe is filled up and the accretion of matter takes \nplace through the inner Lagrangian point, the angular momentum of the accreted\ngas should be high; while in detached binary system the accretion \nmatter is stellar winds therefore their angular momenta are much lower\n(Illarionov \\& Sunyaev 1975). \nIn the nuclei of galaxies, where the supply of the accretion matter \nis unclear, the initial physical states of the accretion flows \nshould be more complicated.\nThe complexity of astrophysical environments makes it important \nto investigate the role of OBC in accretion disk model.\n\n\\section{The role of OBC in optically thin accretion flows}\n\n\\begin{figure}\n\\vskip -0.4cm\n\\epsfig{file=fig1.eps, width=7.5cm, height=12.cm,angle=270}\n\\vskip -0.4cm\n\\caption{\nSolutions for one temperature global solutions with different OBCs for\n$ M=10 \\msun$, $\\dot{M}=\n10^{-3} \\dot{M}_{\\rm E}$ and $\\alpha=10^{-2}$. The solid, dot-dashed and\ndashed lines represent $(T_{\\rm out}, \\lambda_{\\rm out}(\\equiv \nv/c_s \\equiv v/\\sqrt{p/\\rho}))$=($2 \\times\n10^8 {\\rm K}, 0.4), (3.6 \\times 10^9 {\\rm K}, 0.08)$ and\n$(3.6 \\times 10^9 {\\rm K}, 0.107$) respectively. The units of $\\Sigma, T$\nare ${\\rm g \\ cm^{-2}}$ and K, $r$, $Be$ and $l$ are in $c=G=M=1$ units.\nMach number is simply defined as $v/c_s$. The upper-left\nplot represents the ratio of the advected energy to the viscous\ndissipated energy. Adopted from Yuan (1999).\n}\\label{fig1}\\end{figure}\n\n\\begin{figure}\n\\vskip -0.4cm\n\\epsfig{file=fig2.eps, width=7.5cm, height=12.cm,angle=270}\n\\vskip -0.4cm\n\\caption{\nSolutions for two temperature global solutions with different $\\Ti$.\nThe solid line (type I solution) is for $\\Ti=2 \\times 10^8K$,\nthe dotted line (type I) for $\\Ti=6 \\times 10^8K$,\nthe dashed line (type II) for $\\Ti=\n2 \\times 10^9K$ and the long-dashed line (type III) for $\\Ti=3.2 \\times 10^9K$.\nOther OBCs are $\\Te=1.2 \\times 10^8K$ and $\\lambda_{\\rm out}=0.2$.\nThe outer boundary is set at $r_{\\rm out}=10^3r_{\\rm g}$. Other parameters are\n$\\alpha=0.1, \\beta=0.9, M=10^9 \\msun$ and $\\dot{M}=10^{-4} \\dot{M}_{\\rm Edd}$.\nThe units of $\\Sigma$ and $T$ are ${\\rm g \\ cm^{-2}}$ and K. Adopted\nfrom Yuan et al. (2000).\n}\\label{fig2}\\end{figure}\n\nIn previous papers (Yuan 1999; Yuan et al. 2000), taking optically \nthin accretion onto a black hole as an \nexample, we calculated the dynamics and the \nemergent spectrum of one- and two-temperature accretion plasma \nby self-consistently solving the radiation hydrodynamical \nequations. For the one temperature case, only bremsstrahlung emission\nand its Comptonization are considered, while for the two temperature case,\nsynchrotron emission and its Comptonization are also included.\nWe concentrated on the role of OBC by setting the same \n``general parameters'' such as accretion rate, viscosity\nparameter and black hole mass while adopting different OBCs.\nWe adopted the temperature $T_{\\rm out}$ and\nthe ratio of the radial velocity to the local sound speed \n$\\lambda_{\\rm out}$\n(or, equivalently, the angular velocity $\\Omega_{\\rm out}$) at a certain outer\nboundary $r_{\\rm out}$ as the outer boundary conditions\nand found that in\nboth cases, the topological structure and the profiles of angular momentum\nand surface density of the flow differ greatly under\ndifferent OBCs, as shown by Figures 1 (for a one-temperature plasma) \nand 2 (for a two-temperature plasma; only the ions temperature $\\Ti$ varies: \nfor other cases, see Yuan et al. 2000). \nIn terms of the topological structure and the profile\nof the angular momentum, three types of solutions are found.\nWhen $T_{\\rm out}$ is relatively low,\nthe solution is of type I. When $T_{\\rm out}$ is relatively high and\nthe angular velocity $\\Omega_{\\rm out}$ is higher than a critical \nvalue $\\Omega_{\\rm crit}$,\nthe solution is of type II. Both types I and II possess small sonic radii,\nbut their topological structures and angular momentum profiles\nare different. When $T_{\\rm out}$ is high but the\nangular velocity is lower than $\\Omega_{\\rm crit}$, the \nsolution becomes of type III,\ncharacterized by a much larger sonic radius.\nSimilar transition has been found previously in the context\nof adiabatic (inviscid) accretion\nflow by Abramowicz \\& Zurek (1981). In that case,\nthey found that when the specific angular momentum of the flow\ndecreased across a critical value,\na transition from a disk-like accretion pattern (with small sonic radii) to\na Bondi-like one (with large sonic radii) \nwould happen (Abramowicz \\& Zurek 1981;\nLu \\& Abramowicz 1988). Here in this paper we find that this\ntransition still exist when the flow becomes viscous, confirming\nthe prediction of Abramowicz \\& Zurek (1981).\nFigure 3 shows the emergent spectrum of the solutions presented in \nFigure 2. Considering that they possess the same ``general'' parameters\nthe discrepancy among the spectra completely caused by \nthe difference of OBC is impressive. At last, we should emphasize that \nsuch ``OBC-dependent'' effect on the spectrum \nhas relation with the value of $r_{\\rm out}$: \nthe smaller $r_{\\rm out}$ is, the more significant the effect becomes. Thus, \nthis effect should be very obvious in the accretion flow \nwhere standard thin disk-ADAF transition occurs. As a result, \nsome confusing problems can \nbe promisingly solved (Yuan \\& Yi, in preparation).\n\n\\begin{figure}\n\\vskip -0.cm\n\\epsfig{file=fig3.eps, width=8cm, height=11.cm,angle=270}\n\\vskip -0.4cm\n\\caption{\nThe corresponding spectra of the solutions shown in Figure 2. Adopted\nfrom Yuan et al. (2000).}\n\\label{fig3}\\end{figure}\n\n\\section{An illustrative application to Sgr A$^*$}\n\nAs an illustrative example, we apply the above\nresults to the compact radio source Sgr A$^*$\nlocated at the center of our Galaxy.\nAdvection-dominated accretion flow (ADAF) model has been turned out to\nbe of great success to explain its low luminosity and spectrum (Narayan, Yi \\&\nMahadevan 1995; Narayan et al. 1998). However,\nthere exists a discrepancy between the mass accretion rate\nfavored by ADAF models in the literature\nand that favored by the three dimensional hydrodynamical simulation,\nwith the former ($\\sim 6.8 \\times 10^{-5}\\dot{M}_{\\rm Edd}$,\nsee Quataert \\& Narayan 1999) being\n10-20 times smaller than the latter ($\\sim 9\\times 10^{-4} \n\\dot{M}_{\\rm Edd}$, see Coker \\& Melia 1997). \nBy seriously considering the\nouter boundary condition of the accretion flow, we find that\ndue to the low specific angular momentum of the \naccretion gas (Coker \\& Melia 1997), the\naccretion in Sgr A$^*$ should belong to type III\nwhich possesses a very large sonic radius.\nThis accretion pattern can significantly reduce the discrepancy between\nthe mass accretion rate, as Figure 4 shows (see Yuan et al. 2000 for details).\n\n\\begin{figure}\n\\vskip -0.4cm\n\\epsfig{file=fig4.eps, width=7.5cm, height=10.cm,angle=270}\n\\vskip -0.4cm\n\\caption{\nThe X-ray spectrum of Sgr A$^*$.\nThe observational\ndata are compiled by Narayan et al. (1998).\nThe spectra represented by the solid\nand the dashed lines are produced by the accretion flows \nwith the same accretion rate $\\dot{M}=4 \\times 10^{-4} \\dot{M}_{\\rm Edd}$\nbut different angular momentum at $r_{\\rm out}$, \n$\\Omega_{\\rm out}=0.15 \\Omega_{\\rm K}$ \nfor the solid line and\n$\\Omega_{\\rm out}=0.46 \\Omega_{rm K}$ for the dashed line.\nDue to the difference of the angular momentum of the flow at the outer\nboundary, the X-ray flux differs by a factor $\\sim$ 8. \nAdopted from Yuan et al. (2000).}\n\\label{fig4}\\end{figure}\n\n\\section{Discussion}\n\nThe present study is concentrated on the low-$\\dot{M}$ case where\nthe differential terms in the equation such as the energy advection\nplay an important role therefore the effect of OBC are most obvious.\nHow about the role of OBC when \nthe flows become optically thick? \nIn this case, the electron and the ion possess\nthe identical temperature due to the strong couple between them and\nthe local viscous dissipation and radiation loss terms in the energy balance\nplay an important role. As a result, the temperature profile \nis mainly determined {\\em locally} rather than \n{\\em globally} as in the case of optically thin flows.\nThus, the discrepancy of the\ntemperature caused by OBC will\nlessen rapidly with the decreasing radii from the outer boundary.\nThis is also the reason why the temperature profiles\nof one-temperature plasma and ions in Figures 1 and 2 converge\nrapidly with decreasing radii. \nHowever, from our calculation to\nthe one-temperature accretion flow whose temperature\nis also principally determined locally (Yuan 1999),\n we predict that the optically thick accretion \nflow should still present OBC-dependent\nbehavior in, e.g., the angular momentum and the Mach number\nprofiles which are in principle determined by the {\\em momentum} \nrather than the {\\em energy} equations. \nWhen the angular momentum of the accretion flow \nis less than a certain critical value, the accretion pattern should \nbecome of ``type III'' (Bondi-like). \nAlthough these conjectures need the confirmation\nof detailed calculation, we note that the angular momentum profile\nof slim disk model (see Figure 3 of Abramowicz et al. 1988),\nand a recent numerical simulation (Igumenshchev, Illarionov \\&\nAbramowicz 1999) seems to support this point.\n\nWhy the role of OBC in accretion disk models has been long neglected?\nIn the standard thin disk model, \nall the differential terms in the equations are neglected and the\ndifferential equations are reduced into an algebraic one which \ndon't entail any boundary conditions at all. \nIn the later works on the global solutions \nfor slim disks (Matsumoto et al. 1984; Abramowicz et al. 1988;\nChen \\& Taam 1993) and optically thin advection-dominated\naccretion flows \n(Narayan, Kato \\& Honma 1997; Chen, Abramowicz \\& Lasota 1997),\nsome authors did investigate the role of OBC, but failed to find\nits importance. The main reason is that for optically\nthick accretion flows (slim disk) or {\\it one-temperature}\noptically thin accretion flow, the local viscous dissipation \nplays an important role in the energy equation, so the effect of \nOBC lessen rapidly away from the outer boundary. In addition, the \nangular momentum in their outer boundary condition was always \nsomewhat large. This might be the reason why they \ndidn't find the solutions with\nvery large sonic radii. \n\n\\begin{chapthebibliography}{1}\n\n\\bibitem{}\nAbramowicz, M.A., et al. 1988, ApJ, 332, 646 \n\n\\bibitem{}\nAbramowicz, M., A., Zurek, W.H., 1981, ApJ, 246, 31\n\n\\bibitem{}\nChen, X., Abramowicz, M. A., \\& Lasota, J.-P. 1997, ApJ, 476, 61\n\n\\bibitem{}\nChen, X. \\& Taam, R. 1993, ApJ, 412, 254\n\n\\bibitem{}\nCoker, R., \\& Melia, F., 1997, ApJ, 488, L149\n\n\\bibitem{}\nIgumenshchev, I.V., Illarionov, A.F. \\& Abramowicz, M.A. 1999,\nApJ, 517, L55\n\n\\bibitem{}\nIllarionov, A.F., \\& Sunyaev, R.A. 1975, A\\&A, 39, 185\n\n\\bibitem{}\nLu, J.F., \\& Abramowicz, M.A. 1988, Acta Ap. Sin., 8, 1\n\n\\bibitem{}\nMatsumoto, R., et al. 1984, PASJ, 36, 71\n\n\\bibitem{}\nNarayan, R., Kato, S., \\& Honma, F. 1997, ApJ, 476, 49\n\n\\bibitem{}\nNarayan, R., et al. 1998, ApJ, 492, 554\n\n\\bibitem{}\nNarayan, R., Yi, I., Mahadevan, R. 1995, Nature, 374, 623\n\n\\bibitem{}\nQuataert, E., \\& Narayan, R., 1999, ApJ, 520, 298\n\n\\bibitem{}\nYuan, F. 1999, ApJ, 521, L55\n\n\\bibitem{}\nYuan, F., et al. 2000, ApJ, in press (astro-ph/0002068)\n\n\\end{chapthebibliography}\n\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002069.extracted_bib",
"string": "\\bibitem{}\nAbramowicz, M.A., et al. 1988, ApJ, 332, 646 \n\n\n\\bibitem{}\nAbramowicz, M., A., Zurek, W.H., 1981, ApJ, 246, 31\n\n\n\\bibitem{}\nChen, X., Abramowicz, M. A., \\& Lasota, J.-P. 1997, ApJ, 476, 61\n\n\n\\bibitem{}\nChen, X. \\& Taam, R. 1993, ApJ, 412, 254\n\n\n\\bibitem{}\nCoker, R., \\& Melia, F., 1997, ApJ, 488, L149\n\n\n\\bibitem{}\nIgumenshchev, I.V., Illarionov, A.F. \\& Abramowicz, M.A. 1999,\nApJ, 517, L55\n\n\n\\bibitem{}\nIllarionov, A.F., \\& Sunyaev, R.A. 1975, A\\&A, 39, 185\n\n\n\\bibitem{}\nLu, J.F., \\& Abramowicz, M.A. 1988, Acta Ap. Sin., 8, 1\n\n\n\\bibitem{}\nMatsumoto, R., et al. 1984, PASJ, 36, 71\n\n\n\\bibitem{}\nNarayan, R., Kato, S., \\& Honma, F. 1997, ApJ, 476, 49\n\n\n\\bibitem{}\nNarayan, R., et al. 1998, ApJ, 492, 554\n\n\n\\bibitem{}\nNarayan, R., Yi, I., Mahadevan, R. 1995, Nature, 374, 623\n\n\n\\bibitem{}\nQuataert, E., \\& Narayan, R., 1999, ApJ, 520, 298\n\n\n\\bibitem{}\nYuan, F. 1999, ApJ, 521, L55\n\n\n\\bibitem{}\nYuan, F., et al. 2000, ApJ, in press (astro-ph/0002068)\n\n"
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\noindent{We present an overview of observational progress in the study of extragalactic globular cluster systems. Globular clusters turn out to be excellent tracers not only for the star-formation histories in galaxies, but also for kinematics at large galactocentric radii. Their properties can be used to efficiently constrain galaxy formation and evolution. After a brief introduction of the current methods and futures perspectives, we summarize the knowledge gained in various areas of galaxy research through the study of globular clusters. In particular, we address the star-formation histories of early-type galaxies; globular cluster population in late-type galaxies and their link to early-type galaxies; star and cluster formation during mergers and violent interactions; and the kinematics at large radii in early-type galaxies. The different points are reviewed within the context of galaxy formation and evolution. Finally, we revisit the globular cluster luminosity function as a distance indicator. Despite its low popularity in the literature, we demonstrate that it ranks among one of the most precise distance indicators to early-type galaxies, provided that it is applied properly. }
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"name": "gcs_rev.tex",
"string": "% after proof corrections\n\\NeedsTeXFormat{LaTeX2e}\n\\documentclass[twoside]{article}\n\\usepackage[latin1]{inputenc}\n\\usepackage{t1enc}\n\\usepackage{a4}\n\\usepackage{tabularx}\n\\usepackage{epsf}\n\\usepackage{psfig}\n\\usepackage{rotate}\n\n\\textheight=194mm\n\\textwidth=118mm\n\\oddsidemargin=-7mm\n\\evensidemargin=-7mm\n\\topmargin=-16mm\n\\headheight=2mm\n\\headsep=6mm\n\\topskip=3.5mm\n\n\\def\\ref{\\vspace{4pt}\\noindent\\hangindent=10mm}\n\\def\\arcsec{$^{''}$}\n\\def\\arcmin{$^{'}$}\n\n\\begin{document}\n\n\\setcounter{figure}{0}\n\\setcounter{section}{0}\n\\setcounter{equation}{0}\n\n\\begin{center}\n{\\Large\\bf\nExtragalactic Globular Cluster Systems}\\\\[0.2cm]\n{\\large\\bf A new Perspective on Galaxy Formation and Evolution}\\\\[0.7cm]\n\nMarkus Kissler-Patig \\\\[0.17cm]\nEuropean Southern Observatory \\\\\nKarl-Schwarzschild-Str.~2, 85748 Garching, Germany \\\\\[email protected], http://www.eso.org/$\\sim$mkissler\n\\end{center}\n\n\\vspace{0.5cm}\n\n\\begin{abstract}\n\\noindent{\\it\nWe present an overview of observational progress in the study of\nextragalactic globular cluster systems. Globular clusters turn out to be \nexcellent tracers not only for the star-formation histories in galaxies, but \nalso for kinematics at large galactocentric radii. Their properties can be used\nto efficiently constrain galaxy formation and evolution. After a brief \nintroduction of the current methods and futures perspectives, we\nsummarize the knowledge gained in various areas of galaxy research through\nthe study of globular clusters. \nIn particular, we address the star-formation histories of early-type\ngalaxies; globular cluster population in late-type galaxies and their\nlink to early-type galaxies; star and cluster formation during mergers and \nviolent interactions; and the kinematics at large radii in early-type\ngalaxies. The different points are reviewed within the \ncontext of galaxy formation and evolution.\n\nFinally, we revisit the globular cluster luminosity function\nas a distance indicator. Despite its low popularity in the literature, we\ndemonstrate that it ranks among one of the most precise distance indicators \nto early-type galaxies, provided that it is applied properly.\n}\n\\end{abstract}\n\n\\section{Preamble}\n\nThis brief review on extragalactic globular cluster systems is derived\nfrom a lecture given for the award of the Ludwig-Bierman-Preis of the\nAstronomische Gesellschaft in G\\\"ottingen during September 1999. \nThe Oral version aimed at introducing, mostly from an observer's point of view, \nthis field of research and at emphasizing its tight links to galaxy formation \nand evolution. \n\nThe scope of this written follow-up is {\\it not} to give a complete review on \nglobular cluster systems but to present recent discoveries, including\nexamples, and to set them into the context of galaxy formation and\nevolution. The choice of examples and the emphasis of certain ideas will\nnecessarily be subjective, and we apologize at this point for any missing\nreferences.\n\nExcellent recent reviews can be found in the form of two books: ``Globular\nCluster Systems'' by Ashman \\& Zepf (1998), as well as ``Globular Cluster\nSystems'' by Harris (2000). These include a full description of the\nglobular clusters in the Local group (not discussed here), as well as an \nextensive list of references, including to older reviews.\n\nThe plan of the article is the following. In section 2, we give an introduction\nand the motivation for studying globular cluster systems with the aim of \nunderstanding galaxies.\nSection 3 presents current and future methods of observations, and the\nrational behind them. This section reviews recent progress in optical and \nnear-infrared photometry and multi-object, low-resolution spectroscopy. \nIt can be skipped by readers interested in results rather than methods.\nIn Section 4 we present in turn the status of our knowledge on\nglobular cluster systems in ellipticals, spirals and mergers.\nWhat are the properties of the systems? How are the galaxy\ntypes linked? And do mergers produce real `globular' clusters?\nIn section 5, we discuss sub-populations of globular clusters and their\npossible origin. The most popular scenarios to explain the presence of\nglobular cluster sub-populations around galaxies are listed. The pros\nand cons, as well as the expectations of each scenario are discussed.\nWe present, in section 6, some results from the study of globular cluster\nsystem kinematics. \nFinally, in section 7, we revisit the globular cluster luminosity\nfunction as a distance indicator. Under which conditions can it be used,\nand how should it be applied to minimize any systematic errors? It is\ncompared to other distance indicators and shown to do very well.\nSome conclusions and an outlook are given in section 8.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Motivation}\n\nAs a reminder, globular clusters are tyically composed of $10^4$ to\n$10^6$ stars clustered within a few parsecs. They are old, although\nyoung globular-cluster-like objects are seen in mergers, and their\nmetallicity can vary between [Fe/H]$\\simeq -2.5$ dex and [Fe/H]$>0.5$ dex.\nWe refer to a globular cluster system as the totallity of globular\nclusters surrounding a galaxy.\n\n\\subsection{Why study globular cluster systems?}\n\n\\begin{figure}[t]\n\\psfig{figure=GCS_montage.ps,height=8cm,width=12cm\n ,bbllx=5mm,bblly=5mm,bburx=205mm,bbury=285mm,angle=-90}\n\\caption{The figures shows a montage of what we are observing. The\ngalaxy NGC 1399 of the Fornax galaxy cluster is shown on the left. It is\nlocated at a distance of $\\sim 18$ Mpc from the Milky Way. Many of the\npoint source surrounding it are globular clusters. If we could resolve\nthese clusters into stars (which we cannot), we would see clusters\nsimilar to the Galactic clusters M~15, shown on the right.}\n\\end{figure}\n\nThe two fundamental questions in galaxy formation and evolution are: {\\it\n1)} When and how did the galaxies assemble? and {\\it 2)} When and how\ndid the galaxies form their stars? A third question could be whether,\nand to what extend, the two first points are linked.\n\nGenerally speaking, in order to answer these questions from an\nobservational point of view, one can follow two paths. The first would\nbe to observe the galaxies at high redshift, right at the epoch of\ntheir assembly and/or star formation. We will consider this to be the\n``hard way''. These observations are extremely challenging for many\nreasons (shifted restframe wavelength, faint magnitudes, small angular\nscales, etc...). Nevertheless, they are pursued by a number of\ngroups through the observations of absorption line systems along the line of \nsights of quasars, or the detection of high-redshift (e.g.~Lyman break) \ngalaxies, etc... (see e.g.~Combes, Mamon, \\& Charmandaris 1999, Bunker \\&\nvan Breugel 1999, Mazure, Le Fevre, \\& Le Brun 1999 for\nrecent proceedings on the rapidly evolving subject).\n\n\nThe second path is to wait until a galaxy reaches very low redshift and\ntry to extract information about its past. This would be the ``lazy\nway''. This is partly done by the\nstudy of the diffuse stellar populations at 0 redshift and the\ncomparison of its properties at low redshift. Such studies on\nfundamental relations (fundamental plane, Mg-$\\sigma$, Dn-$\\sigma$) tend\nto be consistent with the stellar populations evolving purely passively \nand having formed at high redshifts ($z>2$). \nAlternatively, one can study merging events among galaxies at\nlow- to intermediate-redshift (e.g.~van Dokkum et al.~1999) in order to\nunderstand the assembly of galaxies.\n\nHow do globular clusters fit into these picture? Globular cluster\nstudies could be classified as the ``very lazy way'', since they reach\nout to at most redshifts of $z=0.03$. However, globular clusters are\namong the oldest objects in the universe, i.e.~they witnessed most,\nif not all, of the history of their host galaxy. The goal of the\nglobular cluster system studies is therefore to extract the memory of\nthe system. Photometry and spectroscopy are used to derive their ages\nand chemical abundances which are used to understand the epoch(s) of\nstar formation in the galaxy. Kinematic information obtained from the\nglobular clusters (especially at large galactocentric radii) can be used to \nhelp understanding the assembly mechanism of the galaxies. \n\n\\subsection{Advantages of using globular clusters}\n\nFigure 1 illustrates extragalactic globular cluster studies. We show the\ngalaxy NGC 1399 surrounded by a number of point sources. If these point\nsources could be resolved, they would look like one of the Galactic\nglobular clusters (here shown as M~15). However, even with diffraction limited\nimaging from space, we cannot resolve clusters at distances of 10 to 100\nMpc into single stars, and have to study their integrated properties.\nThe study of a globular cluster system is therefore equivalent to studying the\nintegrated properties of a large number of globular clusters surrounding a \ngalaxy, in order to derive their individual properties and compare them,\nas well as the properties of the system as a whole, with the properties of \nthe host galaxy.\n\nThe purely practical advantages of observing objects at $z=0$ \nis the possibility to study the objects in great\ndetail. Very low $z$ observations are justified if the gain in\ndetails outbalances the fact that at high $z$ one is seeing events closer\nto the time at which they actually happened. One example that\ndemonstrates that the gain is significant in the case of extragalactic globular\nclusters, is the discovery of several sub-populations of clusters around a \nlarge number of early-type galaxies. The presence of two or more distinct star-formation\nepochs/mechanisms in at least a large number if not all giant galaxies\nwas not discovered by any other type of observations.\n\nThe old age of globular clusters is often advanced as argument for their study, \nsince they witnessed the entire past of the galaxy including\nthe earliest epochs. If this would be the whole truth, globular clusters\nwould not be suited to study the recent star formation epochs. Nor would\nthey present a real advantage over stars, which can be old too.\nWhat are the advantages of observing globular clusters as tracers of the\nstar-formation / stellar populations instead of studying directly the diffuse \nstellar population of the host galaxies?\n\n\\vskip 3mm\n\\noindent {\\it Globular clusters trace star formation}\n\nA number of arguments support the fact that globular clusters indeed \ntrace the star formation in galaxies. However, we know that some star formation\ncan occur without forming globular clusters. One example is the Large\nMagellanic Cloud which, at some epochs, produced stars but no clusters\n(e.g.~Geha et al.~1998). On the other hand, we know that major star formation\nepisodes induce the formation of a large number of star clusters. For\nexample, the violent star formation in interacting galaxies is accompanied by\nthe formation of massive young star clusters (e.g.~Schweizer 1997).\nAlso, the final number of globular clusters in a galaxy is roughly\nproportional to the galaxy luminosity, i.e.~number of stars (see Harris\n1991). This hints at a close link between star and cluster\nformation. Additional support for such a link comes from the close relation\nbetween the number of young star clusters in spirals and their current star \nformation rate (Larsen \\& Richtler 1999).\n\nIn summary, globular clusters are not perfect tracers for star\nformation, as they will not form during every single little (i.e. low\nrate) star formation event. But they will trace the major (violent)\nepochs of star formation, which is our goal.\n\n\\vskip 3mm\n\\noindent {\\it From a practical point of view}\n\nGlobular clusters exist around all luminous ($M_V>17$) \ngalaxies observed to date. Their number, that scales with the mass of the\ngalaxy, typically lies around a few hundreds to a few thousands.\n\nFurthermore, globular clusters can be observed out to $\\sim$\n100 Mpc. This is not as far as the diffuse light can be observed, but\nfar enough to include many thousands of galaxies of all types and in all\nvarieties of environments.\n\nThe study of globular clusters is therefore not restricted to a specific\ntype or environment of galaxies: unbiased samples can be constructed.\nFrom this point of view, diffuse stellar light and globular clusters are \nequally appropriate.\n\n\\vskip 3mm\n\\noindent {\\it The advantages of globular clusters over the diffuse stellar\npopulation}\n\nGlobular clusters present a significant advantage\nwhen trying to determine the star formation history of a galaxy: they are far\nsimpler structures. A globular cluster can be characterized by a single age \nand single\nmetallicity, while the diffuse stellar population of a galaxy needs to be\nmodeled by an unknown mix of ages and of metallicities. Studying a\nglobular cluster system returns a large number of discrete age/metallicity \ndata points. These can be grouped to determine the mean ages and chemical\nabundances of the main sub-populations present in the galaxy.\n\nAlong the same line, and as shown above, globular clusters form\nproportionally to the number of stars. That is, the number of globular\nclusters in a given population reflects the importance of the star\nformation episode at its origin. Counting globular cluster in different\nsub-populations indicates right away the relative importance of the\ndifferent star formation events. In contrast, the different populations\nin the diffuse stellar light appear luminosity weighted: a small (in\nterms of mass) but recent star formation event can outshine a much more\nimportant but older event that has faded. \n\n\\vskip 3mm\n\\noindent {\\it The bonus}\n\nAs for stellar populations, kinematical informations can be derived from\nthe spectra originally aimed at determining ages and metallicities. Globular\nclusters have the advantage that they can be traced out to\ngalactocentric distances unreachable with the diffuse stellar light.\nThe dynamical information of the clusters can be used to study the\nassembly of the host galaxy. In Section 6, we will come back to this\npoint. \n\n\\vskip 1cm\n\nThe bottom line is that globular clusters are good tracers for the star\nformation history of their host galaxies, and eventually allow some\ninsight into their assembly too. They present a number of advantages\nover the study of stellar populations, and complement observations at\nhigh redshift. Their study allows new insight into galaxy formation and\nevolution.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Current and future observational methods}\n\nThis section is intended to give a feeling for the observational methods\nused to study globular cluster systems. It addresses the problems still\nencountered in imaging and spectroscopy, as well as the improvements to\nbe expected with future instruments. \n\nTo set the stage: we are trying to analyze the light of objects with\ntypical half-light radii of 1 to 5 pc, at distances of 10 to 100 Mpc\n(i.e.~half-light radii of 0.01\\arcsec\\ to 0.1\\arcsec\\ ), and absolute\nmagnitudes ranging from $M_V\\sim -10$ to $-4$ (i.e.~$V>20$). The\ngalaxies in the nearest galaxy clusters (Virgo, Fornax) have globular\ncluster luminosity functions that peak in magnitude around $V\\sim 24$,\nand globular clusters have typical half-light radii of $\\sim$ 0.05\\arcsec\\ .\n\nWe intend to study both the properties of the individual clusters, as\nwell as the ones of the whole cluster system. For the individual\nglobular clusters, our goal is to derive their ages, chemical\nabundances, sizes and eventually masses. This requires spectral\ninformation (the crudest being just a color) and high angular resolution.\nFor the whole system, our goal is to determine the total numbers, the\nglobular cluster luminosity function, the spatial\ndistributions (extent or density profile, ellipticity), and any radial \ndependencies\nof the cluster properties (e.g.~metallicity gradients). These properties\nshould also be measured for individual sub-populations, if they are present.\nThe requirements for the systems are therefore deep, wide-field imaging, and\nthe ability to distinguish potential sub-populations from each other.\n\n\\subsection{Optical photometry}\n\nGlobular clusters outside the Local Group were, for a long time, exclusively \nstudied with optical photometry. Optical, ground-based photometry\n(reaching $V>24$ in a field $>$ 5\\arcmin $\\times$ 5\\arcmin\\ ) turns out to be\nsufficient to determine most morphological properties of the systems\n(see Sect.~4).\nThe depth allows to reasonably sample the luminosity function, and a\nfield of several arcminutes a side usually covers the vast majority of the \nsystem.\n\nProblems with optical photometry arise when trying to determine ages and\nmetallicities. It is well known that broad-band optical colors are\ndegenerate in age and metallicity (e.g.~Worthey 1994). A younger age is \ncompensated by a higher metallicity in most broad-band, optical colors.\nTo some extent the problem is solved by the fact that most globular\nclusters are older than several Gyr, and colors do not depend\nsignificantly on age in that range. This, of course, means that deriving\nages from optical colors is hopeless, except for young clusters as\nseen e.g.~in mergers.\n\nFor old clusters, the goal is to find a color that is as sensitive\nto metallicity as possible. The widely used $V-I$ color is the least\nsensitive color to metallicity. $B-V$ and $B-I$ do better in the\nJohnson-Cousins system (e.g.~Couture et al.~1991 for one of the first \ncomparisons), but the mini break-through came with the use of Washington \nfilters (e.g.~Geisler \\& Forte 1990). These allowed the discovery of the\nfirst multi-modal globular cluster color distributions around galaxies\n(Zepf \\& Ashman 1993). However, the common use of the Johnson system,\ncombined with large errors in the photometry at faint magnitudes, do\nstill not allow a clean separation of individual globular clusters\ninto sub-populations around most galaxies.\n\nAnother problem with ground-based imaging is that its resolution is\nby far insufficient to resolve globular clusters. This prohibits the\nunambiguous identification of globular clusters from foreground stars\nand background galaxies. In most cases the over-density of globular\nclusters around the host galaxy is sufficient to derive the general\nproperties of the system. Control fields should be used (although often\nleft out because of the lack of observing time), and statistical background\nsubtraction performed. The individual identification of globular\nclusters became possible with WFPC2 on HST. Globular clusters appear barely\nextended in WFPC2 images, which allows on the one hand to reliably\nseparate them from foreground stars and background galaxies, and on the\nother hand to systematically study for the first time globular cluster sizes\noutside the Local group (Kundu \\& Whitmore 1998, Puzia et al.~1999,\nKundu et al.~1999). The disadvantage of\nWFPC2 observations is that the vast majority was carried out in $V-I$,\nthe least performant system in terms of metallicity sensitivity.\nFurthermore, the WFPC2 has a\nsmall field of view which biases all the analysis towards the center of the\ngalaxies, making it very hard to derive the global properties of a\nsystem without large extrapolations or multiple pointings.\n\nIn summary, ground-based photometry returns the general properties of\nthe systems, and eventually of the sub-systems when high quality\nphotometry is obtained. It suffers from confusion when identifying individual\nclusters, and is limited in age/metallicity determinations. Space photometry \nis currently as bad in deriving ages/metallicities, but allows to\ndetermine sizes of individual clusters. The current small fields,\nhowever, restrict the studies of whole systems.\n\nFuture progress is expected with the many wide-field imagers coming\nonline, provided that deep enough photometry is obtained (errors $<0.05$\nmag at $V=24$). These will provide a large number of targets for\nspectroscopic follow-up. In space, the ACS to be mounted on HST will\nsuperseed the WFPC2. The field of view remains modest, but the slightly\nhigher resolution will support further size determinations, and the\nhigher throughput will allow a more clever choice of filters, including\n$U$ and $B$.\n\n\\begin{figure}[t]\n\\psfig{figure=hst_isaac_bw.ps,height=10cm,width=8cm}\n% ,bbllx=30mm,bblly=30mm,bburx=270mm,bbury=210mm}\n\\caption{NGC 4365 observed in the V band with the WFPC2 on HST, and in\nthe K band with ISAAC on the VLT. The field of views are similar; the\nresolution is $\\sim 0.1\"$ in the HST images, $\\sim 0.4\"$ in the K\nimages; the depths are comparable. This illustrates that optical and\nnear-infrared imaging are becoming more and more similar for purposes of\nstudying globular cluster systems (images provided by T.H.~Puzia).}\n\\end{figure}\n\n\\subsection{Near-infrared photometry}\n\n\\begin{figure}[h]\n\\centerline{\\psfig{figure=matrix350.best.ps,height=8cm,width=8cm\n,bbllx=8mm,bblly=63mm,bburx=205mm,bbury=245mm}}\n\\caption{Globular cluster colors shown in the (V$-$I)--(V$-$K) plane. \nFor this plot, data for NGC 3115 from ISAAC on the VLT and WFPC2 onboard HST\nwere combined to allow a better separation of the two sub-populations\n(taken from Puzia et al.~2000, in preparation). Density contours show\nthe color peaks for two main sub-populations.}\n\\end{figure}\n\nSince the introduction of 1024$\\times$1024 pixel arrays in the near\ninfrared a couple of years ago, imaging at wavelength from 1.2$\\mu$m to \n2.5$\\mu$m became competitive in terms of depths and field size with\noptical imaging (see Figure 2).\n\nHistorically, the first near-infrared measurements of extragalactic globular\nclusters were carried out in M31 (Frogel, Persson \\& Cohen 1980) and the\nLarge Magellanic Cloud (Persson et al.~1983). \nWhy extend the wavelength range to the near infrared? For old globular\nclusters, $V-K$ is a measure of the temperature of the red giant branch \nthat is directly dependent on metallicity but hardly on age. $V-K$ is even \nmore sensitive to metallicity than the Washington $C-T_1$ index. The\ncombination of optical and near-infrared colors is therefore superior to\noptical imaging alone, both for deriving metallicities, and for\na clean separation of cluster sub-populations (see Figure 3). \nIt is also used to detect potential sub-populations were optical colors \nfailed to reveal any.\n\nIn young populations, $V-K$ is most sensitive to the asymptotic giant\nbranch which dominates the light of populations that are 0.2 to 1 Gyr old.\nThe combination of optical and near infrared colors can be used to\nderive ages (and metallicities) of these populations (e.g.~Maraston, \nKissler-Patig, \\& Brodie 2000). \n\nThe disadvantages of complementing optical with near-infrared colors is \nthe need for a second instrument (usually a second observing run) in addition \nto the optical one. Near-infrared observations will continue fighting\nagainst the high sky background in addition to the background light of\nthe galaxy which requires blank sky observations. Overall, obtaining \nnear-infrared data is still very time consuming when compared to optical\nstudies. For example, a deep $K$ image of a galaxy will require a full\nnight of observations. Currently both depth and field size do not allow the near\ninfrared to fully replace optical colors for the study of morphological\nproperties or the globular cluster luminosity function. But this might\nhappen in the future whth the NGST.\n\nThe immediate future looks bright, with a number of ``wide-field''\nimagers being available, such as ISAAC on the VLT, SOFI on the 3.5m NTT,\nthe Omega systems on the 3.5m Calar Alto, etc.. and 2k $\\times$ 2k \ninfrared arrays coming soon. The ideal future\ninstrument would have a dichroic which would allow to observe\nsimultaneously in the near-infrared and the optical.\n\n\\begin{figure}[t]\n\\psfig{figure=n1399_spec.ps,height=10cm,width=10cm\n,bbllx=8mm,bblly=57mm,bburx=185mm,bbury=245mm}\n\\caption{Three representative spectra of globular clusters are shown, \nranging from blue, \nover red, to very red color. While the H$\\beta$ gets slightly weaker from the\nblue to the red object, the metal lines (Mg, Fe, Na) become much\nstronger (taken from Kissler-Patig et al.~1998a).\n}\n\\end {figure}\n\n\\subsection{Multi-object spectroscopy}\n\nSpectroscopy is the only way to unambiguously associate a globular cluster\nwith its host galaxy by matching their radial velocities. Also, it is\nthe most precise way to determine the metallicity of single objects, and\nthe only way to determine individual ages. Obviously, it\nis also the only way to get radial velocities.\nIdeally, one would like a spectrum of each globular cluster identified\nfrom imaging.\n\nIn practice, good spectra are still hard to obtain. Early attempts\nwith 4m-class telescopes succeeded in obtaining radial velocities, but mostly\nfailed to determine reliable chemical abundances (see Sect.~6).\nWith the arrival of 10m-class telescopes, it became feasible to obtain\nspectra with high enough signal-to-noise to derive chemical abundances\n(Kissler-Patig et al.~1998a, Cohen, Blakeslee \\& Ryzhov 1998).\nSuch studies are still limited to relatively bright objects ($V<23$) and\nremain time consuming ($\\sim$ 3h integration time for low-resolution\nspectroscopy). Figure 4 shows a few examples of globular clusters in NGC\n1399. High-resolution spectroscopy in order to measure internal\nvelocity dispersions of individual clusters is still out of reach for\nold clusters, and was only carried out for two nearby super star\nclusters (Ho \\& Fillipenko 1996a,b), in addition to several clusters\nwithin the Local Group. Even low-resolution spectroscopy\nis currently still limited to follow-ups on photometric studies,\ntargeting a number of selected, representative clusters, rather than\nbuilding up own spectroscopic samples.\n\nCurrent problems are the low signal-to-noise, even with 10m-telescopes,\nthat prohibit very accurate age or metallicity determinations for\nindividual clusters. The multiplexity of the existing instruments \n(FORS1 \\& 2 on the VLT, LRIS on Keck) is low and only allows to spectroscopy \na limited number of selected targets. \nFinally, the absorption indices that\nare being measured on the spectra in order to determine the various\nelement abundances are not optimally defined. These indices lie in\nthe region 3800\\AA\\ to 6000\\AA\\ and were designed for spectra with 8\\AA\\\nto 9\\AA\\ resolution. They often include a number of absorption lines in the\nbandpass (or pseudo-continuum) other than the element to be measured. This\nintroduces an additional dependence e.g.~of the Balmer indices on metallicity,\netc... Using a slightly higher resolution might help defining better\nindices. \n\nThe immediate future of spectroscopy are instruments such as VIMOS on\nthe VLT or DEIMOS on Keck that will allow a multiplexity of 100 to 150.\nThese will allow to increase the exposure times and slightly the spectral \nresolution to solve a number of the problems mentioned above. These\nwill also allow to obtain several hundred radial velocities of globular\nclusters around a given galaxy in a single night, improving\nsignificantly the potential of kinematical studies (see Sect.~6).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Globular clusters in various galaxy types, and what we learned from\nthem}\n\nIn this section, we present some properties of globular cluster systems and \nof young clusters in ellipticals, spirals and mergers. In the last\nsection we mentioned what are the properties measured in globular cluster\nsystems: The metallicity distribution can be obtained from photometry\n(colors) or spectroscopy (absorption line indices). The luminosity\nfunction of the clusters is computed from the measured magnitudes folded\nwith any incompleteness or contamination function. The total number of\nclusters (and eventually number of metal-poor and metal-rich clusters) is\nobtained by extrapolating the observed counts over the luminosity\nfunction and eventually applying any geometrical completeness for the\nregions that are not covered. For the latter, one uses also knowledge\nabout the spatial distribution (position angle, ellipticity) and radial \ndensity profile of the globular cluster system. For young star clusters,\nthe color distribution no longer reflects the metallicity distribution,\nbut a mix of ages and metallicities. More complex comparisons with\npopulation synthesis models and/or spectroscopy are needed to\ndisentangle the two quantities. Of interest for young clusters are also\nthe mass distribution (derived from the luminosity function) that helps\nto understand how many of the newly formed clusters will indeed evolve\ninto massive ``globular'' clusters.\n\n\\subsection{Globular clusters in early-type galaxies}\n\nEarly-type galaxies have the best studied globular cluster systems.\nSpirals have the two systems studied in most details (i.e.~the\nMilky Way and M31) due to our biased location in space, but a far larger sample\nnow exists for early-type galaxies.\n\nDespite looking remarkably similar in many respects (e.g.~globular cluster\nluminosity function), globular cluster\nsystems in early-type galaxies also show a large scatter in a number\nof properties. For example, the number of globular clusters normalized\nto the galaxy light (specific frequency, see Harris \\& van den Bergh\n1981) appears to scatter by a factor of several, mainly driven by the very \nhigh specific frequencies of central giant ellipticals (and recently\nalso observed in faint dwarf galaxies, see Durrel et al.~1996, Miller et \nal.~1998). \nFurthermore, the radial density profiles are very extended for large galaxies,\nwhile following the galaxy light in the case of intermediate ellipticals\n(e.g.~Kissler-Patig 1997a).\n\nIn the early 90's, Zepf \\& Ashman (1993) discovered the presence of\nglobular cluster sub-populations in several early-type galaxies. We will\ncome back to the origin of the sub-populations in Sect.~5. Here, we will\ndiscuss the implications of sub-populations on our understanding of the \nglobular cluster system properties.\n\n\\begin{figure}[h]\n\\centerline{\n\\psfig{figure=hbteta.ps,height=6cm,width=6cm\n,bbllx=8mm,bblly=63mm,bburx=205mm,bbury=245mm}\n\\psfig{figure=hbprof.ps,height=6cm,width=6cm\n,bbllx=8mm,bblly=57mm,bburx=205mm,bbury=245mm}\n}\n\\caption{\nLeft panel: The angular distribution of halo and bulge globular clusters\naround NGC 1380 in 30 degree sectors, after a point symmetry around the center\nof the galaxy. Note that the blue objects are spherically distributed,\nwhile the red objects have an elliptical distribution that peaks at the\nposition angle of the diffuse stellar light.\nRight panel: Surface density profiles of red and blue globular clusters\naround NGC 1380, plotted once against the radius in arcseconds (upper panel)\nand once against the semi-major axis (lower panel). Note how the blue\nobjects have a much flatter density profile than the red ones, which are\nconcentrated towards the center and follow a similar density profile as\nthe stellar light. Both plots are taken from Kissler-Patig et al.~(1997).\n}\n\\end{figure}\n\nUntil the early 90's, properties were derived for the whole globular\ncluster system. Since then, it became clear that many\nproperties need to take into account the existence of (at least two) different\nsub-populations, in order to be explained. Probably the first work to\nshow this most clearly was the presentation of the properties of blue\nand red clusters in NGC 4472 by Geisler et al.~(1996). Taking into\naccount the existence and different spatial distribution of blue and red\nclusters, they explained two properties of whole systems at once. First, the\ncolor gradient observed in several systems could be explained by a\nvarying ratio of blue to red clusters with radius (without any gradient\nin the individual sub-populations). Second, the mean color of the\nsystems was previously thought to be systematically bluer than the diffuse\ngalaxy light. It turns out that the color of the red sub-population\nmatches the color of the galaxy, while it is the presence of the blue\n``halo'' population that makes the color of the whole globular cluster\nsystem appear bluish. \n\nIt has not yet been demonstrated that the scatter in the specific\nfrequency and in the slopes of the radial density profiles also\noriginate from different mixes of blue to red sub-populations, but this\ncould be the case. The few studies that investigated separately\nthe morphological properties of blue and red clusters (Geisler et\nal.~1996, Kissler-Patig et al.~1997, Lee et al.~1998, Kundu \\& Whitmore\n1998) found the metal-poor (blue) population to be more spherically\ndistributed and extended than the metal-rich population that\nhas a steeper density profile, tends to be more flattened and appears to\nfollow the diffuse stellar light of the galaxy in ellipticity and\nposition angle (cf.~Fig.~5). Thus, a larger fraction of blue clusters\nin a galaxy would mimic a flatter density profile of the whole globular\ncluster system. \n\nFurthermore, the specific frequency of the blue clusters (when related\nto the blue light) appears to be very high ($>30$ see Harris 2000).\nThis, by the way, could be explained if the latter came from small fragments\nsimilar to the dwarf ellipticals observed today, that also show high\nspecific frequency values (although not as high, but in the range 10 to 20). \nThus, an overabundance of blue clusters would\nimply a high specific frequency. Incidentally, the shallow density\nprofiles are found in the galaxies with the highest specific frequencies\n(see Kissler-Patig 1997a). We can therefore speculate that the properties\nof the entire globular cluster systems of these massive (often central)\ngiant ellipticals can be explained by a large overabundance of\nmetal-poor globular clusters originating from small fragments. The\nscatter in the globular cluster system properties among ellipticals\ncould then (at least partly) be explained by a varying fraction of\nmetal-poor ``halo'' and metal-rich ``bulge'' globular\nclusters.\n\nObservationally, this could be verified by determining the number ratios\nof metal-rich and metal-poor globular clusters in a sample of galaxies\nshowing different globular cluster radial density profiles and specific\nfrequencies. The number of studies investigating the\nproperties of metal-poor and metal-rich populations needs to increase in\norder to confirm the general properties of these two groups.\nWe end with a word of caution: the existence of such sub-populations has\nbeen observed in only $\\sim 50$\\% of all early-type galaxies studied\n(e.g.~Gebhardt \\& Kissler-Patig 1999), and still remains to be\ndemonstrated in all cases. Furthermore, the exact formation process of\nthese sub-populations is still unclear (see Sect.~5).\n\n\\subsection{Globular clusters in late-type galaxies}\n\nThe study of globular cluster systems of late-type spirals started with\nthe work of Shapley (1918) on the Milky Way system. Despite a head-start\nof nearly 40 years compared to studies in early-type galaxies, the\nnumber of studied systems in spirals lags far behind the one in\nellipticals. This is mainly due to the observational difficulties:\nglobular clusters in spirals are difficult to identify on the\ninhomogeneous background of disks. Furthermore, internal extinction in\nthe spiral galaxies make detection and completeness estimations\ndifficult, and photometry further suffers from confusion by reddened H{\\tt\nII} regions, open clusters or star forming regions.\n\nThe best studied cases (Milky Way and M31) show sub-populations\n(e.g.~Morgan 1959, Kinman 1959, Zinn 1985; Ashman \\& Bird 1993,\nBarmby et al.~1999) associated in our Galaxy with the\nhalo and the bulge/thick disk (Minniti 1995, C\\^ot\\'e 1999). Beyond the\nlocal group, spectroscopy is needed to separate potential\nsub-populations. Both abundances and kinematics are needed, while colors\nsuffer too much from reddening to serve as useful metallicity\ntracers. Spectroscopic studies have been rare in the past, but are now\nbecoming feasible (see Sect.~3.3 and 4.1). For example, a recent study\nof M81 allowed to identify a potential thick disk population beside\nhalo and bulge populations (see Schroder et al.~2000 and references therein).\n\nSome of the open questions are whether all spirals host halo and bulge\nclusters, and whether one or both populations are related to the\nmetal-poor and metal-rich populations in early-type galaxies. \nThe number of globular clusters as traced by the specific frequency appears\nroughly constant in spirals of all types independently of the presence\nof a bulge and/or thick disk (e.g.~Kissler-Patig et al.~1999a). This\nwould mean that spirals are dominated by metal-poor populations, with\ntheir globular cluster systems only marginally affected by the presence\nof a bulge/thick disk. If metal-poor globular clusters indeed formed in\npre-galactic fragments, then one would expect the metal-poor populations\nin spirals and ellipticals to be the same. We know that the globular\ncluster luminosity functions are extremely similar, but the metallicity\ndistributions and other properties remain to be derived and compared\n(see Burgarella et al.~2000 for a first attempt).\nFinally, a good understanding of the globular cluster systems in spirals\nwill also help predicting the resulting globular cluster system of a\nspiral--spiral merger. Predictions can then be compared to the\nproperties of systems of elliptical galaxies in order to constrain this\nmode of galaxy formation. \n\n\\subsection{Star clusters in mergers and violent interactions}\n\nAfter some speculations and predictions that massive star clusters\ncould/should form in mergers (Harris 1981, Schweizer 1987), these were finally\ndiscovered in the early 90's (Lutz 1991, Holtzman et al.~1992). Since\nthen a number of studies focussed on the detection and properties of\nthese massive young star clusters (see Schweizer 1997, and reviews cited in\nSect.~1 for an overview).\n\nThe most intense debate around these young clusters focussed on whether or not\ntheir properties were compatible with a formation of early-type galaxies\nthrough spiral--spiral mergers. It was noticed early on (Harris 1981,\nvan den Bergh 1982) that ellipticals appeared to host more clusters than\nspirals, and thus that mergers would have to produce a large number of\nglobular clusters. Moreover, the specific frequency of ellipticals\nappeared higher than in spirals, i.e.~mergers were supposed to form\nglobular clusters extremely efficiently. \nIn a second stage, a number of studies investigated whether or not these\nnewly formed clusters would resemble globular clusters, and/or would survive\nas bound clusters at all. \n\nThe above questions are still open, except maybe for the last one. The\nyoung clusters studied to date show luminosities, sizes, and masses\n(when they can be measured) that are compatible with them being bound\nstellar clusters and able to survive the next several Gyr (see Schweizer 1997 \nfor a summary of the studies and extensive references).\nWhether they will have the exact same properties as old globular\nclusters in our Milky Way is still controversial. First spectroscopic\nmeasurements found the young clusters in NGC 7252 compatible with a\nnormal initial mass function (IMF) (Schweizer \\& Seitzer 1998), while in\nNGC 1275 the young clusters show anomalies and potentially have a\nflatter IMF (Brodie et al.~1998) which would compromise their evolution\ninto old globular clusters, as we know them from the Galaxy.\n\nThe mass distribution of these young cluster was first found to be a\npower-law (e.g.~Meurer 1995), as opposed to a log-normal distribution\nfor old globular clusters. This result is likely to suffer from\nuncertainties in the conversion of luminosities into masses, when neglecting \nthe significant age spread among the young clusters (see Fritze-von \nAlvensleben 1999). However, deeper data seem to rule out the possibility\nthat the initial mass distribution has already the same shape as the one observed\nfor old clusters (see Whitmore et al.~1999, Zepf et al.~1999).\nBut the slope of the mass distributions could be affected during the\nevolution of the system by dynamical destruction at the low-mass end.\nFinally, Whitmore et al.~(1999) recently found a break in the mass\nfunction of the young clusters of the Antennae galaxies, similar to the\ncharacteristic mass of the old clusters further supporting similar mass\nfunctions for young and old cluster populations (see also Sect.~7).\nOverall, the young clusters might or might not resemble old Galactic\nglobular clusters, but some will survive as massive star clusters and\ncould mimic a population of metal-rich globular clusters.\n\nThe most interesting point remains the number of clusters produced in\nmergers. Obviously, this will depend on the gas content (`fuel') that is\nprovided by the merger (e.g.~Kissler-Patig, et al.~1998b).\nMost gas-rich mergers form a large number of star clusters, but few of\nthe latter have masses that would actually allow them to evolve into massive\nglobular clusters as we observe them in distant ellipticals. Harris\n(2000) reviews comprehensively this issue and other problems related\nwith a scenario in which all metal-rich globular clusters of ellipticals\nwould have formed in mergers. The main problem with such a scenario is that\nthe high specific frequency of ellipticals should be due to metal-rich\nclusters, which is usually not the case. Potential other problems,\ndepending on the exact enrichment history, are that large ellipticals would be\nbuild up by a series of mergers that should probably produce an even broader\nmetallicity distribution than observed; and that radial metallicity gradients\nmight be expected to be steeper in high specific frequency ellipticals. \n\nIn summary, mergers are the best laboratories to study younger stellar\npopulations and the formation of young stellar cluster, but how\nimportant they are in the building of globular cluster systems (and\ngalaxies) remains\nuncertain. However, a good understanding of these clusters is crucial\nfor the understanding of globular cluster systems in early-type\ngalaxies, since merger events must have played a role at some stage.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Globular cluster sub-populations and their origin}\n\nIn this section we come back to the presence of multiple sub-population\nof globular clusters around a number of giant galaxies. We will briefly\nreview the different scenarios present in the literature that could\nexplain the properties of such composite systems and discuss their pros\nand cons.\n\nSub-populations of globular clusters were first identified in the Milky\nWay (Morgan 1959, Kinman 1959, Zinn 1985), and associated with \nthe halo (in the case of the\nmetal-poor population) and the ``disk'' (in the case of the metal-rich\npopulation. The ``disk'' clusters are now better associated with the\nbulge (e.g.~Minniti 1995, C\\^ot\\'e 1999). The presence of multiple\ncomponent populations in other giant galaxies was \nfirst detected by Zepf \\& Ashman (1993).\nObviously the multiple sub-populations get associated with several\ndistinct epochs or mechanisms of star/cluster formation.\n\nThe simple scenario of a disk--disk merger explaining the presence of\ntwo populations of globular clusters (Ashman \\& Zepf 1992) found a\nstrong support in the community for 5-6 years, partly because of a lack\nof alternatives. It was backed up by the \ndiscovery of newly formed, young star clusters in interacting galaxies\n(Lutz et al.~1991, Holtzman et al.~1992). Only recently, other scenarios\nexplaining the presence of at least two distinct populations were\npresented and discussed.\n\n\\subsection{The different scenarios for sub-populations}\n\nWe will make a (somewhat artificial) separation in four scenarios and\nbriefly outline them and their predictions. \n\n\\vskip 3mm\n{\\it The merger scenario}\n\nThe fact that mergers could produce new globular clusters was mentioned\nin the literature early after Toomre (1977) proposed that ellipticals\ncould form out of the merging of two spirals (see Harris 1981 and Schweizer \n1987).\nBut the first crude predictions of the spiral-spiral merger scenario go back to\nAshman \\& Zepf (1992). They predicted two populations of globular\nclusters in the resulting galaxy: one old, metal-poor population from the\nprogenitor spirals and one newly formed, young, metal-rich population.\nThe metal-poor population would be more extended and would have been\ntransfered some of the orbital angular momentum by the merger. The\nmetal-rich globular clusters would be more concentrated towards the\ncenter and probably on more radial orbits.\n\n\\vskip 3mm\n{\\it In situ scenarios}\n\nIn situ scenarios see all globular clusters forming within the entity\nthat will become the final galaxy. In this scenario, globular clusters\nform in the collapse of the galaxy, which happens in two distinct phases\n(see Forbes et al.~1997, Harris et al.~1998, Harris et al.~1999). The\nfirst burst produces metal-poor globular clusters and stars (similar to\nSearle \\& Zinn 1978) and provokes\nits own end e.g.~by ionizing the gas or expelling it (e.g.~Harris et\nal.~1998). The second collapse happens shortly later (1-2 Gyr) and is at\nthe origin of the metal-rich component. Both populations are linked with the\ninitial galaxy.\n\n\\vskip 3mm\n{\\it Accretion scenarios}\n\nAccretion scenarios were reconsidered in detail to explain the presence\nof the large populations of metal-poor globular clusters around\nearly-type galaxies. In these scenarios, the metal-rich clusters belong\nto the seed galaxy, while the metal-poor clusters are accreted from or\nwith dwarf galaxies (e.g.~Richtler 1994). \nC\\^ot\\'e et al.~(1998) showed in extensive\nsimulations that the color distributions could be reproduced. Hilker (1998) \nand Hilker et al.~(1999) proposed the accretion of stellar as well as\ngas-rich dwarfs that would form new globular when accreted.\nIn such scenarios, the metal-poor clusters\nwould not be related to the final galaxies but rather have properties\ncompatible with that of globular clusters in dwarf galaxies. \nFurthermore, this scenario is the\nonly one that could easily explain metal-poor cluster that are younger than \nmetal-rich ones.\nIn a slightly differently scenario, Kissler-Patig et al.~(1999b) mentioned the\npossibility that central giant ellipticals could have accreted both metal-poor\nand metal-rich clusters from surrounding medium-sized galaxies. \n\n\\vskip 3mm\n{\\it Pre-galactic scenarios}\n\nPre-galactic scenarios were proposed long ago by Peebles \\& Dicke (1968),\nwhen the Jeans mass in the early universe was similar to globular\ncluster masses. Meanwhile, it was reconsidered in the frame of globular\ncluster systems (Kissler-Patig 1997b, Kissler-Patig et al.~1998b,\nBurgarella et al.~2000). The metal-poor globular clusters would have\nformed in fragments before the assembly of the galaxy, later-on building\nup the galaxy halos and feeding with gas the formation of the bulge. In\nthat scenario too, the metal-poor globular clusters do not have\nproperties dependent from the final galaxy, while the metal-rich clusters do.\nAlso, metal-poor clusters are older than metal-rich clusters.\n\n\\vskip 3mm\nOverall, the scenarios are discussed in the literature as different but\ndo not differ by much. The first scenario explains the presence of the \nmetal-rich population, as opposed to the last two that deal with the \nmetal-poor population. These three scenarios are mutually not exclusive.\nOnly in situ models connect the metal-rich and metal-poor components.\nFor the metal-rich clusters, the question resumes to whether they formed \nduring the collapse of the bulge/spheroid, or whether they formed in a\nviolent interaction. Although an early, gas-rich merger event at the\norigin of the bulge/spheroid would qualify for both scenarios.\nIn the case of metal-poor clusters, \nthe difference between the last three scenarios is mostly semantics.\nThey differ slightly on when the clusters formed, and models two and four might\nexpect differences in whether or not the properties of the clusters are\nrelated to the final galaxy.\nBut the bottom line is that the boarder-line between the\nscenarios is not very clear. \nExplaining the building up of globular cluster systems is probably\na matter of finding the right mix of the above mechanisms, and this for\nevery given galaxy.\n\n\\subsection{Pros and cons of the scenarios}\n\nThe predictions of the different scenarios are fairly fuzzy, and no scenario \nmakes clear, unique predictions. Nevertheless, we can present the pros and cons\nto outline potential problems with any of them. \n\n\\vskip 3mm\n{\\it The merger scenario}\n\nPros: we know that new star cluster form in mergers (e.g.~above\nmentioned reviews, and see Schweizer 1997), and will populate the\nmetal-rich sub-population of the resulting galaxy. Note also, that the\nmerger scenario is the only one that predicted bimodal color\ndistributions rather then explaining them after fact.\n\nCons: we do not know {\\it i)} if all early-type galaxies formed in\nmergers, {\\it ii)} if the star clusters formed in mergers will indeed \nevolve into globular clusters (e.g.~Brodie et al.~1998), {\\it iii)} if\nall mergers produce a large number of clusters (which depends on the gas\ncontent). Furthermore, we would then expect the metal-rich populations\nto be significantly younger in many galaxies (according e.g.~to the\nmerger histories predicted by hierarchical clustering models). There are\nstill problems in explaining the specific frequencies and the right mix\nof blue and red clusters in early-type galaxies in the frame of the\nmerger scenario (e.g.~Forbes et al.~1997).\n\n\\vskip 3mm\n{\\it In situ scenarios}\n\nPros: Searle \\& Zinn (1978) list the evidences for our Milky Way halo\nglobular clusters to have formed in fragments building up the halo. The\nmassive stars in such a population would quickly create a hold of the \nstar/cluster formation for a Gyr or two.\n\nCons: if a correlation between metal-poor clusters and galaxy is\nexpected, the scenario would be ruled out. A clear age sequence from\nmetal-poor to metal-rich clusters is predicted but not yet verified.\nThis scenarios is not in line with hierarchical clustering models\nfor the formation of galaxies (Kauffmann et al.~1993, Cole et al.~1994), \nshould the latter turn out to be the right model for galaxy formation.\n\n\\vskip 3mm\n{\\it Accretion scenarios}\n\nPros: dwarf galaxies are seen in great numbers around giant galaxies,\nand hierarchical clustering scenarios predict even more at\nearly epochs. Dwarf galaxies do get accreted (e.g.~Sagittarius in our\nGalaxy). We observe ``free-floating'' populations around central cluster\ngalaxies (e.g.~Hilker et al.~1999) and the color distributions of\nglobular cluster systems can be reproduced (C\\^ot\\'e et al.~1998).\n\nCons: we are missing detailed dynamical simulations of galaxy groups\nand clusters to test whether the predicted large number of dwarf\ngalaxies gets indeed accreted (and when). We do not know whether the\n(dwarf) galaxy luminosity function was indeed as steep as required at\nearly times to explain the large accretion rates needed. \nAlso, the model does not provide a physical explanation for\nthe metal-rich populations.\n\n\\vskip 3mm\n{\\it Pre-galactic scenarios}\n\nPros: similar to the above, we observe a ``free-floating'', spatially\nextended populations of globular clusters around central galaxies. The\nproperties of the metal-poor populations do not seem to correlate with\nthe properties of their host galaxies (Burgarella et al.~2000). \nThe metal-poor globular cluster are observed to be very old\n(e.g.~Ortolani et al.~1995 for our Galaxy; Kissler-Patig et al.~1998a, \nCohen et al.~1998, Puzia et al.~1999 for analogies in extragalactic\nsystems).\n\nCons: galaxies and galaxy halos might not have formed by the agglomeration of \nindependent fragments. No physical model exists, except a broad\ncompatibility with hierarchical clustering models (see also \nBurgarella et al.~2000).\n\n\\vskip 3mm\n\nSome pros and cons are listed only under one scenario but apply\nobviously to others. It should be noted that these pros and cons apply to\n``normal'' globular cluster systems. It has been noted that several\ngalaxies host very curious mixes of metal-poor and metal-rich clusters\n(Gebhardt \\& Kissler-Patig 1999, Harris et al.~2000) that pose\nchallenges to all scenarios. Fine difference will require a much more\ndetailed abundance analysis of the individual clusters in\nsub-populations, as well as their dynamical properties and (at least\nrelative) ages for the different globular cluster populations. These\nmight allow to identify a unique prediction supporting the one or the\nother formation mode, or constrain the importance of each formation mechanism.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Kinematics of globular clusters}\n\n\\begin{figure}[h]\n\\hskip 1cm \\psfig{figure=dynamic1.ps,height=8cm,width=8cm\n,bbllx=8mm,bblly=57mm,bburx=205mm,bbury=245mm}\n\\caption{Velocity dispersion as a function of radius for various\ncomponents\naround NGC 1399, see Kissler-Patig et al.~(1998a) for details. The two\nsolid lines are fits to the velocity data of the globular clusters and\nof the Fornax galaxies. The dashed line shows the X--ray temperature\nconverted to a velocity dispersion, the triangles are stellar\nmeasurements.}\n\\end{figure}\n\n\\begin{figure}[h]\n\\hskip 2cm \\psfig{figure=dynamic2.ps,height=8cm,width=14cm\n,bbllx=8mm,bblly=57mm,bburx=205mm,bbury=245mm}\n\\caption{Kinematics of red (thin line) and blue (thick line) globular clusters\nin M87. Projected velocity dispersion, and projected rotational velocity\nas functions of radius for a fixed position angle of 120$^{\\circ}$.\nDotted lines mark the 68\\% confidence bands. Taken from Kissler-Patig\n\\& Gebhardt 1998.\n}\n\\end{figure}\n\nIn this section, we briefly discuss recent results from kinematical\nstudies of extragalactic globular clusters. The required measurements\nwere discussed in Sect.~3. Kinematics can be used both to understand the\nformation of the globular cluster systems, as well as to derive dynamics\nof galaxies at large radii.\n\n\\subsection{Globular cluster system formation}\n\nGlobular cluster system kinematics are used since a long time to\nconstrain their formation. In the Milky Way, kinematics support the\nassociation of the various clusters with the halo and the bulge (see\nHarris 2000 and references therein). In M31, similar results were\nderived (Huchra et al.~1991, Barmby et al.~1999). In M81, the\nsituation appears very similar again (Schroder et al.~2000). \nBeyond the Local group, radial velocities for globular clusters are somewhat\nharder to obtain. Nevertheless, studies of globular cluster kinematics in\nelliptical galaxies started over a decade ago (Mould et al.~1987, 1990,\nHuchra \\& Brodie 1987, Harris 1988, Grillmair et al.~1994).\n\nFigure 6 illustrates one example where the kinematics of globular\nclusters allowed to gain some insight into the globular cluster\nsystem formation (from Kissler-Patig et al.~1999b). The figure\nshows the velocity dispersion as a function of radius around NGC 1399, the \ncentral giant elliptical in Fornax. \nThe velocity dispersion of the globular clusters increases with\nradius, rising from a value not unlike that for the outermost stellar\nmeasurements at 100\\arcsec , to values almost twice as high at\n$\\sim$ 300\\arcsec . The outer velocity dispersion measurements are in\ngood agreement with the temperature of the X-ray gas and the velocity\ndispersion of galaxies in the Fornax cluster. Thus, a large fraction of the\nglobular clusters which we associate with NGC 1399 could rather be\nattributed to the whole of the Fornax cluster. By association, this\nwould be true for the stars in the cD envelope too.\nThis picture strongly favors the accretion or pre-galactic scenarios for\nthe formation of the metal-poor clusters in this galaxy. \n\nAs another example, Fig.~7 shows the velocity dispersion and rotational\nvelocity for the metal-poor and metal-rich globular clusters around\nM87, the central giant elliptical in Virgo. There is some evidence that the \nrotation is confined to the metal--poor globular clusters. If, as assumed, the\nlast merger was mainly dissipationless (and did not form a significant\namount of metal-rich clusters), this kinematic difference\nbetween the two sub--populations could reflect the situation \nin the {\\it progenitor} galaxies of M87. These would then\nbe compatible (see Hernquist \\& Bolte 1992) with a formation in a gas-rich\nmerger event (see Ashman \\& Zepf 1992).\n\nGenerally, the data seem to support the view that the metal-poor\nglobular clusters form a hot system with some rotation, or tangentially\nbiased orbits. The metal-rich globular clusters have a lower velocity\ndispersion in comparison, and exhibit only weak rotation, if at all\n(Cohen \\& Ryzhov 1997, Kissler-Patig et al.~1999b, Sharples et al.~1999,\nKissler-Patig \\& Gebhardt 1999, Cohen 2000). The interpretation of these\nresults in the frame of the different formation scenarios presented in\nSect.~5 is unclear, since no scenario makes clear and unique predictions\nfor the kinematics of the clusters. Furthermore, some events unrelated\nto the formation of the globular clusters can alter the dynamics:\ne.g.~a late dissipationless mergers of two ellipticals could convey\nangular momentum to both metal-rich and metal-poor clusters, bluring\nkinematical signatures present in the past. Detailed dynamical\nsimulations of globular cluster accretion and galaxy mergers are\nnecessary in order to compare the data with scenario predictions. But\nclearly, kinematics can help understanding differences in the metal-poor\nand metal-rich components, exploring intra-cluster globular clusters,\nand studying the formation of globular cluster systems as a whole.\n\n\\subsection{Galaxy dynamics}\n\nKinematical studies of globular clusters can also be used to study\ngalaxy dynamics. The globular clusters do only represent discrete probes in the\ngravitational potential of the galaxy, as opposed to the diffuse stellar\nlight that can be used as a continuous probe with radius, but globular\nclusters have the advantage (such as planetary nebulae) to extend\nfurther out. Globular clusters can be measured out to several effective\nradii, probing the dark halo and dynamics at large radii.\n\nThe velocity dispersion around NGC 1399, presented above, is one\nexample. Another example was presented by Cohen \\& Ryzhov (1997) who derived \nfrom the velocity dispersion of\nthe globular clusters in M87 a mass of $3\\times10^{12}M_\\odot$ at 44kpc and \na mass-to-light ratio $>30$, strongly supporting the presence of a massive\ndark halo around this galaxy. With the same data, Kissler-Patig \\&\nGebhardt (1998) derived a spin for M87 of $\\lambda \\sim 0.2$, at the\nvery high end of what is predicted by cosmological N-body simulations.\nThe authors suggested as most likely explanation for the data a major \n(dissipationless) merger as the last major event in the building of M87.\n\nThese examples illustrate what can be learned about the galaxy formation\nhistory from kinematical studies of globular cluster system. In the\nfuture, instruments such as VIMOS and DEIMOS will allow to get many\nhundreds velocities in a single night for a given galaxy. These data\nwill allow to constrain even more strongly galaxy dynamics at large\nradii.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Globular clusters as distance indicators}\n\nIn this section, we will review the globular cluster luminosity function\n(GCLF) as a distance indicator. The method is currently ``unfashionable'' in \nthe literature mainly because some previous results seem to be in\ncontradiction with other distance indicators (e.g.~Ferrarese et al.~1999).\nWe will try to shade some light on the discrepancies, and show that, if\nthe proper corrections are applied, the GCLF competes well with other\nextragalactic distance indicators. \n\n\\subsection{The globular cluster luminosity function}\n\nA nice overview of the method is given in Harris (2000), including some\nhistorical remarks and a detailed description of the method. A further\nreview on the GCLF method was written by Whitmore (1997), who\naddressed in particular the errors accompanying the method.\nWe will only briefly summarize the method here.\n\nThe basics of the method are to measure in a given filter (most often\n$V$) the apparent magnitudes of a large number of globular clusters in\nthe system. The so constructed magnitude distribution, or luminosity\nfunction, peaks at a characteristic (turn-over) magnitude. The absolute value\nfor this characteristic magnitude is derived from local or secondary\ndistance calibrators, allowing to derive a distance modulus from the observed\nturn-over magnitude. Figure 8 shows a typical globular cluster luminosity\nfunction with its clear peak (taken from Della Valle et al.~1998).\n\n\\begin{figure}[t]\n\\psfig{figure=vgclf.ps,height=10cm,width=10cm\n,bbllx=8mm,bblly=57mm,bburx=205mm,bbury=245mm}\n\\caption{Typical GCLF, observed in the $V$ band in the galaxy NGC 1380\n(Della Valle et al.~1998). Over-plotted are two fits (a Gaussian\nand a student t$_5$ function). The dotted lines show the 50\\%\ncompleteness limit in the $V$ filter and in the filter combination\n($B,V,R$) that was used to select the globular clusters. The apparent peak\nmagnitude can be derived and the distance computed using the\nabsolute magnitude obtained from local or secondary calibrators.}\n\\end{figure}\n\nThe justification of the method is mainly empirical. \nApparent turn-overs for galaxies at the same distance (e.g.~in the same\ngalaxy cluster) can be compared and a scatter around 0.15 mag is then\nobtained, without\ncorrecting for any external error. Similarly, a number of well observed\napparent turn-over magnitudes can be transformed into absolute ones using \ndistances from other distance indicators (Cepheids where possible, or a mean of\nCepheids, surface brightness fluctuations, planetary luminosity\nfunction, ...) and a similar small scatter is found (see Harris 2000 for a\nrecent compilation). Taking into account the errors in the\nphotometry, the fitting of the GCLF, the assumed distances, etc... this hints\nat an internal dispersion of the turn-over magnitude of $<0.1$, making it a\ngood standard candle. From a theoretical point of view, this constancy\nof the turn-over magnitude translates into a ``universal''\ncharacteristic mass in the globular cluster mass distributions in all\ngalaxies. Whether this is a relict of a characteristic mass in the mass\nfunction of the molecular clouds at the origin of the globular clusters,\nor whether it was implemented during the formation process of the\nglobular clusters is still unclear.\n\nThe absolute turn-over magnitude lies around $V_{TO}\\sim-7.5$, and the \ndetermination of the visual turn-over is only accurate if the peak of\nthe GCLF is reached by the observations. From an observational point of\nview, this means that the data must reach e.g.~$V\\sim 25$ to determine\ndistances in the Fornax or Virgo galaxy clusters (D$\\sim 20$ Mpc), and\nthat with HST or 10m-class telescopes reaching typically $V\\sim 28$, the\nmethod could be applied as far out as 120 Mpc (including the Coma galaxy\ncluster).\n\nThe observational advantages of this method over others are that \nglobular clusters are brighter than other standard candles (except for \nsupernovae), and do not vary, i.e.~no repeated observations are\nnecessary. Further, they are usually measured at large radii or in the\nhalo of (mostly elliptical) galaxies where reddening is not a concern.\n\n\\subsection{General problems}\n\nA large number of distance determinations from the GCLF were only\nby-products of globular cluster system studies, and often suffered from\npurely practical problems of data taken for different purposes.\n\nFirst, a good estimation of the background contamination is necessary to\nclean the globular cluster luminosity function from the luminosity\nfunction of background galaxies which tends to mimic a fainter turn-over\nmagnitude. Next, the finding incompleteness for the globular clusters\nneeds to be determined, in \nparticular as a function of radius since the photon noise is changing \ndramatically with galactocentric radius. Proper reddening corrections\nneed to be applied and might differ whether one uses the ``classical''\nreddening maps of Burstein \\& Heiles (1984) or the newer maps from\nSchlegel et al.~(1998). When necessary, proper aperture correction for\nslightly extended clusters on WFPC2/HST images has to be made (e.g.~Puzia et \nal.~1999). Finally, several different ways of fitting the GCLF are used:\nfrom fitting a histogram, over more sophisticated maximum-likelihood\nfits taking into account background contamination and incompleteness.\nThe functions fitted vary from Gaussians to Student (t$_5$) functions,\nwith or without their dispersion as a free parameter in addition to the\npeak value.\n\nIn addition to these, errors in the absolute calibration will be added\n(see below). Furthermore,\ndependences on galaxy type and environment were claimed, although the\nformer is probably due to the mean metallicity of globular clusters\ndiffering in early- and late-type galaxies, while the latter was never \ndemonstrated with a reliable set of data.\n\nAll the above details can introduce errors in the analysis that might sum up\nto several tenths of a magnitude. The fact that distance determinations using\nthe GCLF are often a by-product of studies aiming at understanding globular\ncluster or galaxy formation and evolution, did not help in constructing\na very homogeneous sample in the past. The result is a very\ninhomogeneous database (e.g.~Ferrarese et al.~1999) dominated by large\nrandom scatter introduced in the analysis, as well as systematic errors\nintroduced by the choice of calibration and the complex nature of\nglobular cluster systems (see below).\nNevertheless, most of these problems were recognized and are overcome by\nbetter methods and data in the recent GCLF distance determinations. \n\n\\subsection{The classical way: using all globular clusters of a system}\n\nHarris (2000, see also Kavelaars et al.~2000) outline what we will call\nthe classical way of measuring distances with the GCLF. This method\nimplies that the GCLF is measured from all globular clusters in a\nsystem. In addition, it uses the GCLF as a ``secondary''\ndistance indicator, basing its calibration on distances derived by\nCepheids an other distance indicators. The method compares the peak of the \nobserved GCLF with the peak of a compilation of GCLFs from mostly Virgo and\nFornax ellipticals, adopting from the literature a distance to these \ncalibrators.\nThis allowed, among others, Harris' group to determine a distance to Coma\nellipticals and to construct the first Hubble diagram from GCLFs in\norder to derive a value for H$_0$ (Harris 2000, Kavelaars et al.~2000).\n\nIn practice, an accurate GCLF turn-over is determined (see above) and calibrated\nwithout any further corrections using M$_V(TO) = -7.33\\pm0.04$ (Harris\n2000) or M$_V(TO) = -7.26\\pm0.06$ using Virgo alone (Kavelaars et al.~2000).\n\nThe advantages of this approach are the following. Using all globular clusters\n(instead of a limited sub-population) often avoids problems with small number\nstatistics. This is also the idea behind using Virgo GCLFs instead of\nthe spars Milky Way GCLF as calibrators. The Virgo GCLFs, derived from giant \nelliptical galaxies rich in globular clusters, are well sampled and do not \nsuffer from small number statistics. Further, since most newly derived\nGCLFs come from cluster ellipticals, one might be more confident\nto calibrate these using Virgo (i.e.~cluster) ellipticals, in order to avoid \nany potential dependence on galaxy type and/or environment. \n\nHowever, the method has a number of caveats. The main one is that giant\nellipticals are known to have globular cluster sub-populations with\ndifferent ages and metallicities. This automatically implies that the\ndifferent sub-populations around a given galaxy will have different\nturn-over magnitudes. By using the whole globular cluster systems, one\nis using {\\it a mix} of turn-over magnitudes. One could in principal try\nto correct e.g.~for a mean metallicity (as proposed by Ashman, Conti \\&\nZepf 1995), but this correction depends on the population synthesis\nmodel adopted (see Puzia et al.~1999) and implies that the mix of\nmetal-poor to metal-rich globular clusters is known. This mix does not only vary\nfrom galaxy to galaxy (e.g.~Gebhardt \\& Kissler-Patig 1999), but also\nvaries with galactocentric radius (e.g.~Geisler et al.~1996, Kissler-Patig \net al.~1997). It results in a displacement of the turn-over peak and the\nbroadening of the observed GCLF of the whole system.\nThe Virgo ellipticals are therefore only valid calibrators for other\ngiant ellipticals with a similar ratio of metal-poor to metal-rich\nglobular clusters {\\it and} for which the observations cover similar\nradii. This is potentially a problem when comparing ground-based\n(wide-field) studies with HST studies focusing on the inner regions of\na galaxy. Or when comparing nearby galaxies where the center is well\nsampled to very distant galaxies for which mostly halo globulars are\nobserved. In the worse case, ignoring the presence of different\nsub-populations and comparing very different galaxies in this respect,\ncan introduce errors a several tenths of magnitudes.\n\nAnother caveat of the classical way, is that relative distances to Virgo\ncan be derived, but absolute magnitudes (and e.g.~values of H$_0$) will\nstill dependent on other methods such as Cepheids, surface brightness\nfluctuations (SBF), Planetary Nebulae luminosity functions (PNLF), and\ntip of red-giant branches (TRGB), i.e.~the method will never overcome\nthese other methods in accuracy and carry along any of their potential \nsystematic errors.\n\n\\subsection{The alternative way: using metal-poor globular clusters only}\n\nAs an alternative to the classical way, one can focus on the metal-poor\nclusters only. The idea is to isolate the metal-poor globular clusters\nof a system and to determine their GCLF. As a calibrator, one can use\nthe GCLF of the metal-poor globular clusters in the Milky Way, which\navoids any assumption on the distance of the LMC and will be independent\nof any other extragalactic distance indicator. For the Milky Way GCLF,\nthe idea is to re-derive an absolute distance to each individual cluster,\nresulting in individual absolute magnitudes and allowing to derive an absolute\nluminosity function. Individual distances to the clusters are derived using the\nknown apparent magnitudes of their horizontal branches and a relation\nbetween the absolute magnitude of the horizontal branch and the\nmetallicity (e.g.~Gratton et al.~1997). The latter is based on {\\tt\nHIPPARCOS} distances to sub-dwarfs fitted to the lower main sequence of\nchosen clusters. This methods follows a completely different path\nthan methods based at some stage on Cepheids. In particular, the method\nis completely independently from the distance to the LMC.\n\nIn practice, an accurate GCLF turn-over (see above) for the metal-poor clusters\nin the target galaxy\nis derived and calibrated, without any further corrections, using M$_V(TO)=\n-7.62\\pm0.06$ derived from the metal-poor clusters of the Milky Way (see\nDella Valle et al.~1998, Drenkhahn \\& Richtler 1999; note that the error\nis statistical only and does not include any potential systematic error\nassociated with the distance to Galatic globular clusters, currently\nunder debate).\n\nThe advantages of this method are the following. This method takes into\naccount the known sub-structures of globular cluster systems. Using the\nmetal-poor globular clusters is motivated by several facts. First, they\nappear to have a true universal origin (see Burgarella et al.~2000), and\ntheir properties seem to be relatively independent of galaxy type,\nenvironment, size and metallicity. Thus, to first order they can be used\nin all galaxies without applying any corrections. In addition, the Milky Way is\njustified as calibrator even for GCLFs derived from elliptical galaxies.\nFurther, they appear to be ``halo'' objects, i.e.~little affected by\ndestruction processes that might have shaped the GCLF in the inner few\nkpc of large galaxies, or that affect objects on radial orbits. They\nwill certainly form a much more homogeneous populations than the total\nglobular cluster system (see previous sections).\nUsing the Milky Way as calibrator allows this method to be completely\nindependent on other distance indicators and to check independently\nderived distances and value of H$_0$.\n\nThe method is not free from disadvantages. First, selecting metal-poor\nglobular clusters requires better data than are currently used in most\nGCLF studies, implying more complicated and time-consuming observations. \nSecond, even with excellent data a perfect separation of metal-poor and\nmetal-rich clusters will not be\npossible and the sample will be somewhat contaminated by metal-rich\nclusters. Worse, the sample size will be roughly halved (for a typical\nratio of blue to red clusters around one). This\nmight mean that in some galaxies less than hundred clusters will be\navailable to construct the luminosity function, inducing error $>0.1$ on\nthe peak determination due to sample size alone.\nFinally, the same concerns applies as for the whole sample: how\nuniversal is the GCLF peak of metal-poor globular clusters? This remains\nto be checked, but since variations of the order of $<0.1$ seem to be\nthe rule for whole samples, there is no reason to expect a much larger\nscatter for metal-poor clusters alone.\n\n\\subsection{A few examples, comparisons, and the value of H$_0$ from the\nGCLF method}\n\nTwo examples of distance determinations from metal-poor clusters were\ngiven in Della Valle et al.~(1998), and Puzia et al.~(1999).\n\nThe first study derived a distance modulus for NGC 1380 in the Fornax\ncluster of $(m-M)=31.35\\pm0.09$ (not including a potential systematic error of\nup to 0.2). In this case, the GCLF of the metal-poor and the metal-rich\nclusters peaked at the same value, i.e.~the higher metallicity was\ncompensated by a younger age (few Gyr) of the red globular cluster\npopulation, so that it would not make a difference whether one uses the\nmetal-poor clusters alone or the whole system. As a comparison, values\nderived from Cepheids and a mean of Cepheids/SBF/PNLF to Fornax are\n$(m-M)=31.54\\pm0.14$ (Ferrarese et al.~1999) and $(m-M)=31.30\\pm0.04$\n(from Kavelaars et al.~2000).\n\nIn the case of NGC 4472 in the Virgo galaxy cluster, \nPuzia et al.~(1999) derived turn-overs from the\nmetal-poor and metal-rich clusters of $23.67\\pm0.09$ and $24.13\\pm0.11$\nrespectively. Using the metal-poor clusters alone, their derived\ndistance is then $(m-M)=30.99\\pm0.11$. This compares with the Cepheid\ndistance to Virgo from 6 galaxies of $(m-M)=31.01\\pm0.07$ and to the\nmean of Cepheids/SBF/TRGB/PNLF of $(m-M)=30.99\\pm0.04$ (from Kavelaars\net al.~2000). Both cases show clearly the excellent agreement of the\nGCLF method with other popular methods, {\\it despite the completely\ndifferent and independent calibrators used}. The accuracy of the GCLF method\nwill always be limited by the sample size and lies around $\\sim 0.1$.\n\nA nice example of the ``classical way'' is the recent determination of\nthe distance to Coma. At the distance of $\\sim 100$ Mpc the separation\nof metal-poor and metal-rich globular clusters is barely feasible\nanymore, and using the full globular cluster systems is necessary.\nKavelaars et al.~(2000) derived turn-over values of\nM$_V(TO)=27.82\\pm0.13$ and M$_V(TO)=27.72\\pm0.20$ for the two galaxies\nNGC 4874 and IC 4051 in Coma, respectively. Using Virgo ellipticals as\ncalibrators and assuming a distance to Virgo of $(m-M)=30.99\\pm0.04$,\nthey derive a distance to Coma of $102\\pm6$ Mpc. Adding several\nturn-over values for distant galaxies (taken from Lauer et al.~1998),\nthey construct a Hubble diagram for the GCLF technique and derive a\nHubble constant of H$_0=69\\pm9$ km s$^{-1}$ Mpc$^{-1}$. This example\ndemonstrates the reach in distance of the method.\n\n\\subsection{The Future of the method}\n\nIn summary, we think that the method is mature now and that most errors\nin the analysis can be avoided, as well as good choices for the\ncalibration made. In the future, with HST and 10m-class telescope data, a\nnumber of determinations in the 100 Mpc range will emerge, and\neventually, using metal-poor globular clusters only, this will give us a\ngrasp on the distance scale completely independent from distances based\nat some stage on the LMC distance or Cepheids.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Conclusions}\n\nAll the previous section should have made clear that globular clusters\ncan be used for a very wide variety of studies. They can constrain the\nstar formation history of galaxies, in particular on the two or more\ndistinct epochs of star formation in early-type galaxies. They can help\nexplaining the building up of spiral galaxies, and the star formation in\nviolent interactions. They can be useful to study galaxy dynamics at\nlarge galactocentric radii. And finally, they provide an accurate\ndistance indicator, independent of Cepheids and the distance to the LMC.\nThis makes the study of globular cluster systems one of the most\nversatile fields in astronomy.\n\nExtragalactic globular cluster research experienced a boom in the early\n90s with the first generation of reliable CCDs, and the first imaging\nfrom space. We can expect a continuation of the improvement of optical\nimaging, but more important, the field will benefit from the advancement\nin near-infrared imaging, and most of all, of the upcoming multi-object\nspectrographs on 10m telescopes. The next little revolution in this\nsubject will come with the determination of hundreds of globular\ncluster abundances around a large number of galaxies. The next 5 years\nwill be an exiting time.\n\n\\vspace{0.7cm}\n\\noindent\n{\\large{\\bf Acknowledgments}}\n\nFirst of all, I would like to thank the Astronomische Gesellschaft for awarding\nme the Ludwig-Bierman Price. I feel extremely honored and proud. For his\nconstant support, I would like to thank Tom Richtler,\nwho introduced me to the fascinating subject of globular clusters. For\nthe most recent years, I would like to thank Jean Brodie for her collaboration\nand for giving me the first\nopportunity to use a 10m telescope to satisfy my curiosity. I am grateful\nto my current collaborators Thomas Puzia, Claudia Maraston, Daniel\nThomas, Denis Burgarella, Veronique Buat, Sandra Chapelon, Michael\nHilker, Dante Minniti, Paul Goudfrooij, Linda Schroder and many\nothers, for helping me to keep up the flame. As usual, I would be lost without\nKarl Gebhardt's codes and sharp ideas. I am grateful to Klaas de Boer\nand Simona Zaggia for comments on various points. 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astro-ph0002071
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Alternative Solutions to Big Bang Nucleosynthesis
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"author": "Hannu Kurki-Suonio"
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Standard big bang nucleosynthesis (SBBN) has been remarkably successful, and it may well be the correct and sufficient account of what happened. However, interest in variations from the standard picture come from two sources: First, big bang nucleosynthesis can be used to constrain physics of the early universe. Second, there may be some discrepancy between predictions of SBBN and observations of abundances. Various alternatives to SBBN include inhomogeneous nucleosynthesis, nucleosynthesis with antimatter, and nonstandard neutrino physics.
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"name": "kurkisuonio.tex",
"string": "\\documentstyle[11pt,newpasp,twoside, epsf]{article}\n\\markboth{Kurki-Suonio}{Alternative Solutions to BBN}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Alternative Solutions to Big Bang Nucleosynthesis}\n\\author{Hannu Kurki-Suonio}\n\\affil{Helsinki Institute of Physics, P.O. Box 9, FIN-00014 University of\nHelsinki, Finland}\n\n\\begin{abstract}\nStandard big bang nucleosynthesis (SBBN) has been\nremarkably successful, and it may well be the correct and sufficient\naccount of what happened. However, interest in variations\nfrom the standard picture come from two sources:\nFirst, big bang nucleosynthesis can be used to constrain physics of the\nearly universe. Second, there may be some discrepancy between\npredictions of SBBN and observations of abundances.\nVarious alternatives to SBBN include inhomogeneous nucleosynthesis,\nnucleosynthesis with antimatter, and nonstandard neutrino physics.\n\\end{abstract}\n\n\\section{Introduction}\n\nThe success of standard big bang nucleosynthesis (SBBN) in predicting\nthe observed abundances of the light elements has led to the\nwidespread view that SBBN must be correct. According to this view,\nany remaining disagreements must be due to systematic errors in\nobservations or incorrect, or too crude, chemical evolution models. While\nthis view may well be the right one,\nwe should not be blind to other possibilities.\n\nI will stay within the context of the Hot Big Bang (for an alternative,\nsee Burbidge \\& Hoyle 1998), and discuss some models of nonstandard\nbig bang nucleosynthesis (NSBBN). NSBBN scenarios range\nfrom small modifications to SBBN to a complete change in the\ndecisive physical phenomena, like in the late-decaying massive\nparticle scheme of Dimopoulos et al. (1988).\n\n Motivations for studying NSBBN go in two\ndirections. First, the remarkable success of SBBN allows one to severely\nconstrain the physics of the early universe. If one tries to change\nthe conditions from the standard assumptions the resulting abundances\nof the light elements\ndiffer from the observed ones. For many modifications, BBN provides the\nstrongest constraints. BBN gives also the strongest constraint on \nthe single parameter of SBBN, the baryon density, usually given as the\nbaryon-to-photon ratio,\n\\begin{equation}\n \\eta \\equiv \\frac{n_b}{n_\\gamma}, \\qquad \\eta_{10}\\equiv10^{10}\\eta.\n\\end{equation}\nSecond, one may try to improve on SBBN. From time\nto time it has seemed that there might be some discrepancy\nbetween observations and SBBN, which could then be explained by NSBBN.\nIn particular, there has been tension between D/H and $Y_p$\n(see, e.g., Hata et al. 1995). To relieve this tension, \neither a lower D or a lower \n${}^4$He yield has been looked for.\nAlso one may want to relax the SBBN bounds to $\\eta$.\nOther astronomical considerations have given motivation\nfor trying to raise the upper limit to $\\eta$.\nIf one believes that the energy density of the universe is dominated\nby vacuum energy (the cosmological constant) and accepts the newer\nobservations on D/H and $Y_p$ favoring somewhat larger $\\eta$ within\nSBBN,\nthis motivation largely disappears.\n\nThere is a very large body of work on NSBBN.\nExtensive reviews are given by Malaney \\& Mathews\n(1993) and Sarkar (1996), which contain, respectively, over 500 and over\n700 references. Here I will be able to mention only a random few.\n\nMost of the work on NSBBN can be divided into four broad classes:\n\\begin{enumerate}\n\\item Inhomogeneous BBN. Usually this means inhomogeneity in the\nbaryon-to-photon ratio, $\\eta$, but there are also other\npossibilities, like \ninhomogeneity in the neutrino chemical potentials.\n\\item Nonstandard neutrino physics, e.g., additional (``sterile'')\nneutrino flavors, neutrino degeneracy (asymmetry),\nmassive $\\nu_{\\tau}$, or neutrino oscillations.\n\\item Late-decaying ($\\tau$ = 1--$10^8$ s) massive particles,\nblack holes, cosmic strings, etc.\n\\item Time-varying fundamental constants.\n\\end{enumerate}\nIn the interest of time and space, I will discuss the\nfirst two classes only. \n\n\\section{Inhomogeneous Big Bang Nucleosynthesis}\n\nThe single parameter of SBBN is the baryon-to-photon ratio $\\eta$,\nor the density of baryonic matter. In inhomogeneous big-bang \nnucleosynthesis (IBBN) one assumes that $\\eta$ is inhomogeneous.\nTo get a significant effect on BBN this inhomogeneity has to be large,\n$\\delta\\eta/\\eta \\ga 1$. Since the baryons make an insignificant\ncontribution to the energy density at nucleosynthesis time, the total\nenergy density may still be essentially homogeneous.\nThe inhomogeneity could be caused by, e.g., first-order\nphase transitions. The distance scale of this inhomogeneity is\nof crucial importance for IBBN. Without inflation, causal physics\ncan only produce significant inhomogeneity at subhorizon scales\n(see Table 1).\n\n\\begin{table}\n\\centering\n\\caption{The approximate temperature and horizon scale (in comoving\nunits) for various events in the early universe.}\n\\vspace{2mm}\n\\begin{tabular}{lcc}\n\\tableline\nevent & T & horizon \\\\\n\\tableline\nEW phase transition & 100 GeV & $10^{-3}$ pc \\\\\nQCD phase transition & 150 MeV & 1 pc \\\\\n${}^4$He synthesis & 70 keV & 1 kpc \\\\ \n\\tableline\n\\tableline\n\\end{tabular}\n\\end{table}\n\nMechanisms connected with inflation can produce inhomogeneity\nat any scale. The isotropy of the cosmic microwave background (CMB)\nrules out significant inhomogeneity at $\\ga 10$ Mpc scales,\nand it is difficult to construct an acceptable IBBN\nscenario which would explain inhomogeneity in observations. \nIn the usual IBBN models one considers a significantly smaller\ndistance scale, so that while $\\eta$ is inhomogeneous during\nBBN, resulting in inhomogeneous abundances at first, everything\ngets mixed and becomes chemically homogeneous before or during\ngalaxy formation. Thus the observable primordial abundances\nare homogeneous, while different from the SBBN predictions.\n\nThe simplest version of IBBN is one where SBBN occurs with different\n$\\eta$ in different parts of the universe, and the yields get\nmixed afterwards, so that one obtains the IBBN results by\naveraging SBBN results over the $\\eta$ distribution, whose\naverage we denote by $\\bar{\\eta}$. This kind\nof IBBN has a long history. Typically $Y_p$ goes up, \n${}^7$Li goes up (down for small $\\bar{\\eta}$), and\nD goes up for large $\\bar{\\eta}$, and down for small $\\bar{\\eta}$,\ncompared to SBBN with $\\eta = \\bar{\\eta}$. Leonard \\& Scherrer (1996) \nconcluded that this way one can reduce the lower bound to $\\eta$\nfrom observations (in fact remove it, if arbitrary $\\eta$ \ndistributions are allowed), but the upper bound is essentially\nunchanged from SBBN, as ${}^7$Li and ${}^4$He are overproduced for larger\n$\\bar{\\eta}$. The tension between D an ${}^4$He is worsened at the\nlarge end of the SBBN acceptable range. Thus this kind of \nmodification to BBN appears undesirable.\n\n\\subsection{Small Scale Inhomogeneity and Neutron Diffusion}\n\nThe above applies to inhomogeneity\nwith distance scales significantly larger than the neutron diffusion\nscale ($\\sim 0.1$ pc).\nIf there is inhomogeneity at smaller scales, neutrons will\ndiffuse out of the high density regions resulting in an inhomogeneous\n$n/p$ ratio. Especially if this results in \n$n/p > 1$ in some regions, the consequencies for BBN may be dramatic.\nThis scenario (Applegate, Hogan, \\& Scherrer 1987)\nlooked very exciting about ten years ago when it\nwas noted that the QCD (quark-hadron) transition seemed likely to produce\nstrong inhomogeneity at just the right distance scale, and\nearly IBBN calculations indicated a large reduction in $Y_p$\nand increase in D/H allowing very large $\\eta$, even a critical\ndensity in baryons only. More detailed calculations showed\nthat the effects were less dramatic, and the upper limit to $\\eta$\ngiven by D/H and $Y_p$ is raised at most by a factor of 2 or 3\nas compared to SBBN, and this only if the inhomogeneity was\nat near the optimal distance scale ($10^{-3}\\ldots10^{-2}$ pc),\nand most of the baryon number was in the high density regions.\nThe most severe problem for this kind of IBBN is ${}^7$Li\noverproduction. Some ${}^7$Li depletion (by a factor of 2 or 3)\nin Pop II stars is needed to allow for larger $\\eta$ than in SBBN.\nFigure 1 is from a recent review of this scenario\nby Kainulainen, Kurki-Suonio, \\& Sihvola (1999).\n\nRecent lattice QCD calculations favor a much smaller\ndistance scale, although uncertainties are big enough\nso that the optimal distance scale cannot be ruled out.\nThe distance scale from the electroweak (EW) phase transition\nmust be so small that the effects on BBN cannot be large; \nin the best case they could be comparable to other small \neffects that have recently been included in accurate BBN codes.\n\n\\begin{figure}\n\\plottwo{kurkisuonio1a.ps}{kurkisuonio1b.ps}\n\\plotfiddle{kurkisuonio1c.ps}{6cm}{0}{40}{40}{-32}{-66}\n\\caption{The ${}^4$He, D, and ${}^7$Li yields\nfrom small-scale inhomogeneous nucleosynthesis\nruns with a centrally condensed geometry,\nwith density contrast $R = 800$ and high-density\nvolume fraction $f_v = 0.125$.\nThe contours of (a) $Y_p$, (b) $\\log_{10}$D/H,\nand (c) $\\log_{10}{}^7$Li are plotted as\na function of the average baryon-to-photon ratio $\\eta$ and the distance scale\n$r$ of the inhomogeneity. The two horizontal dashed lines denote the horizon\nscale $\\ell_H$ at the QCD (upper) and EW (lower) phase transitions.\nFrom Kainulainen et al. (1999).}\n\\end{figure}\n\n\\subsection{Regions of Antimatter}\n\nA less-studied variant of IBBN is one where $\\eta$ is allowed to have\nnegative values, i.e., there are antimatter regions. \nThis is possible in some baryogenesis scenarios (Dolgov 1996).\nAntimatter in cosmology has been reviewed by Steigman (1976).\nIf the distance scale of antimatter regions is small, antimatter\nand matter will mix and annihilate in the early universe, and the\npresence of matter today implies that there was initially more \nmatter than antimatter. If the distance scale is large, so that\nantimatter regions will survive till present, observational constraints\nrequire either the amount of antimatter to be very small, or \nthe distance scale to be very large, comparable to the present\nhorizon or larger (Cohen, De R\\'{u}jula, \\& Glashow 1998),\nso that the case of large regions is not of interest for BBN. \n\nThe smaller the antimatter regions are, the earlier they annihilate.\nRehm \\& Jedamzik (1998) considered annihilation immediately before\nnucleosynthesis. Kurki-Suonio \\& Sihvola (1999) extended these results\nto larger distance scales where annihilation occurs during or after\nnucleosynthesis (see Figure 2). So far the focus has been on\nobtaining upper limits to the amount of antimatter at various scales in\nthe early universe, but clearly there is also potential for obtaining\nacceptable abundances with nonstandard values of $\\eta$, although\nprobably only with fine-tuned model parameters.\n\n\\begin{figure}\n\\plottwo{kurkisuonio2a.ps}{kurkisuonio2b.ps}\n\\caption{The (a) ${}^4$He and (b) ${}^3$He yields as a function of\nthe antimatter/matter ratio $R$\nand the antimatter domain radius $r$. The distance\nscales are given both at $T = 1$ keV (in meters)\nand today (in parsecs).\nWe plot contours of $Y_p$ and (the logarithm of) the\nnumber ratio ${}^3$He/H. The dotted lines show contours of the\n``median annihilation temperature'', i.e., the temperature of the\nuniverse when 50\\% of the antimatter has annihilated. Typically the\nannihilation is complete at a temperature lower\nthan this by about a factor of 3.\nThe dot-dashed line gives the upper limit to $R$ from CMB spectrum\ndistortion. This plot is for $\\eta_{10} = 6$.\nFrom Kurki-Suonio \\& Sihvola (1999).}\n\\end{figure}\n\n\n\\section{Neutrinos and Big Bang Nucleosynthesis}\n\nNeutrinos affect BBN in two ways, through the energy density effect\nand the $\\nu_e$ effect. The most significant effect is on $Y_p$ in\nboth cases.\n\nThe energy density in neutrinos affects the expansion rate of the\nuniverse. The simplest way to increase the energy density\nof the early universe from the standard model is to have\nadditional particle species (sterile neutrinos or other hypothetical\nparticles). The custom is to parametrize this by an ``effective\nnumber of neutrino species''. The standard case is $N_\\nu = 3$.\nWe now know that there are only three ``active'' neutrino \nspecies, so any additional species must be ``sterile'' neutrinos or\nother very weakly interacting particles.\nA higher energy density means faster expansion.\nThis leads to $n/p$ freezeout at a higher temperature, leaving more\nneutrons, and resulting in a higher\n${}^4$He yield. The D yield is also increased, so an increased\nenergy density is disfavored by BBN, and one gets an upper limit,\ne.g., $N_\\nu < 3.2$ (Burles et al. 1999) or\n$N_\\nu \\la 4$ (Lisi, Sarkar, \\& Villante 1999),\ndepending on what observational\nconstraints one uses.\n\nElectron neutrinos affect the weak $n \\leftrightarrow p$ reactions\ndirectly. More $\\nu_e$ leads to fewer neutrons and thus to less\n${}^4$He (and everything else), whereas more $\\bar{\\nu}_e$ leads\nto more neutrons and more ${}^4$He.\n\n\\subsection{Neutrino Degeneracy}\n\nIn SBBN one assumes that the neutrino asymmetry (difference \nbetween the number of neutrinos and antineutrinos), \n\\begin{equation}\n L_\\nu \\equiv \\frac{n_\\nu - n_{\\bar{\\nu}}}{n_\\gamma}\n = 0.069\\biggl(\\frac{T_\\nu}{T}\\biggr)^3\\bigl(\\pi^2\\xi + \\xi^3),\n\\end{equation}\nwhich is related to the\nneutrino chemical potential $\\mu_\\nu$, or the degeneracy parameter\n$\\xi \\equiv \\mu_\\nu/T$, is small, $\\ll 1$. This seems natural,\nsince the comparable baryon asymmetry $\\eta$ is small. \nHowever, the neutrino background is unobservable, so we cannot\nrule out a large neutrino asymmetry. A larger asymmetry always \nmeans a larger neutrino energy density, raising $N_\\nu$.\nTo have a significant effect on BBN, we must have $|\\xi|$,\n$|L_\\nu| \\ga 0.1$.\nThere is a separate contribution from each neutrino flavor.\nThus there are three indepedent\ndegeneracy parameters, \n$\\xi_e$, $\\xi_\\mu$, and $\\xi_\\tau$. The energy density effect\nis the same for all three flavors, and depends only on $|\\xi|$.\nThe electron neutrino effect depends only on $\\xi_e$, but is much stronger,\nand the direction of the effect depends on the sign. \n\nThere are two possible scenarios for affecting BBN. If\n$\\xi_e$ is comparable in magnitude to $\\xi_\\mu$ and $\\xi_\\tau$,\nor larger, one can forget the other\ntwo in first approximation. One can then adjust $\\xi_e$ to dial in the\ndesired value of $Y_p$. The other elements are hardly affected.\nA less natural scenario is one where the asymmetries in the other\ntwo neutrino flavors are much larger,\nand the energy density and $\\nu_e$ effects\nare balanced against each other to keep $Y_p$ in the acceptable\nrange. This way one can have a significant effect on the other \nabundances and raise the acceptable range for $\\eta$. This\nsecond scenario is constrained by structure formation, since the\nlarge neutrino energy density means that the matter/radiation equality\nand thus the beginning of structure formation occurs later.\nKang \\& Steigman (1992) used a generous lower limit\nfor matter/radiation equality, $z_{\\rm eq} > 10^3$ to widen\nthe SBBN acceptable range from $\\eta_{10}$ = 2.8--4.7 to\n$\\eta_{10}$ = 2.8--19.\n\n\n\\subsection{Inhomogeneous Neutrino Degeneracy}\n\nThe different results from high-$z$ D/H measurements\n(Tytler, Fan, \\& Burles 1996; Webb et al. 1997) raised the\nquestion whether there might be a large-scale inhomogeneity\nin primordial abundances. This is very difficult to achieve, since\nthe extreme isotropy of the CMB rules out any significant large-scale\ninhomogeneity in $\\eta$ or the energy density.\nDolgov \\& Pagel (1999) have come up with a way of getting around \nthis constraint. In their model\nthe asymmetries of the different neutrino flavors are inhomogeneous\nbut balanced with each other so that they add up to a homogeneous \ntotal energy density. The inhomogeneous $\\xi_e$ is then responsible\nfor the inhomogeneous primordial abundances through the $\\nu_e$ \neffect. They suggest that an Afflect-Dine type scenario of\ngeneration of leptonic charge asymmetry, respecting the symmetry\nbetween different lepton families, could be responsible for\ncreating a domain structure, where the neutrino asymmetries would\nhave the same three values but interchanged with respect to $e$, $\\mu$\nand $\\tau$.\nTo achieve a significant D/H inhomogeneity,\na huge $Y_p$ inhomogeneity has to be allowed.\nBut since there are no high-$z$ $Y_p$ determinations,\nthis cannot be used to rule out their model. Table 2 shows\nan example of\nwhat kind of abundances we could have in such a domain structure.\nThe first line would correspond to our local domain; from the\nother domains we would have only D/H observations.\n\n\\begin{table}\n\\centering\n\\caption{Abundances of light elements for $\\eta_{10} = 5$ and nonzero\nvalues of all three chemical potentials. One example from\nDolgov \\& Pagel (1999).}\n\\vspace{2mm}\n\\begin{tabular}{rrrccc}\n\\tableline\n$\\xi_e$ & $\\xi_\\mu$ & $\\xi_\\tau$ & D/H & $Y_p$ & ${}^7$Li/H \\\\\n\\tableline\n0.1 & $-1$ & 1 & $3.8\\times10^{-5}$ & 0.23 & $2.5\\times10^{-10}$ \\\\\n$-1$ & 0.1 & 1 & $9.2\\times10^{-5}$ & 0.55 & $4.5\\times10^{-10}$ \\\\\n1 & $-1$ & 0.1 & $2.8\\times10^{-5}$ & 0.08 & $1.1\\times10^{-10}$ \\\\\n\\tableline\n\\tableline\n\\end{tabular}\n\\end{table}\n\n\\subsection{Decay of a Massive Tau Neutrino}\n\nIf the rest mass of a neutrino species is much larger than 100 MeV,\nthen it is becoming nonrelativistic before nucleosynthesis and its\ncontribution to the energy density is different from the\nstandard zero-mass case. The laboratory limits for the neutrino \nmasses leave this as a possibility for $\\nu_\\tau$. Above\nthe neutrino decoupling temperature, $T \\sim 3$ MeV, a massive neutrino\nspecies contributes less energy density, because of\nneutrino-antineutrino annihilation, but after neutrino\ndecoupling the annihilation ceases and the rest mass then contributes\nextra energy density.\nNeutrinos this heavy must decay to avoid contributing\ntoo much to the present energy density.\nThe decay time and mode\nare of crucial importance to BBN. If the decay time is\nvery short, then the contribution to $N_\\nu$ will be less than one.\nThe most interesting\ncase is the one where $\\nu_\\tau$ decays into $\\nu_e$ (and a\nscalar particle), since then the $\\nu_e$ effect could cause a\nsignificant reduction in $Y_p$.\n \nThese calculations are difficult since the decisive effects occur\nnear the neutrino decoupling temperature, so thermal equilibrium is\nnot maintained and the neutrino spectra are distorted.\nThe recent results by Hannestad (1998) and Dolgov et al. (1999) are\nin disagreement with each other. Hannestad gets the maximum reduction\nof $Y_p$, from the SBBN result $Y_p = 0.239$ to $Y_p < 0.20$, for\n$\\nu_\\tau$ mass $m_\\nu$ = 0.2--0.5 MeV and lifetime \n$\\tau < 100$ s. According to Dolgov et al., the maximum reduction is\nless, to $Y_p \\sim 0.21$, and occurs for larger masses,\n$m_\\nu$ = 2--3 MeV, and requires a shorter lifetime\n$\\tau < 1$ s.\n\nThe most natural explanation of the SuperKamiokande (1998) result\non atmospheric neutrinos is $\\nu_\\mu \\rightarrow \\nu_\\tau$\noscillation. Then $\\nu_\\tau$ cannot be heavy and its mass\nwill not affect BBN significantly. To allow the above \nscenario, the atmospheric neutrino oscillations would have to\nbe into a sterile neutrino species, $\\nu_\\mu \\rightarrow \\nu_s$,\ninstead (Kainulainen et al. 1999).\n\n\\subsection{Neutrino Oscillations}\n\nObservations of solar neutrinos and atmospheric neutrinos\n(SuperKamiokande 1998) as\nwell as the LSND (1998) accelerator experiment see different amounts\nof the different neutrino flavors than predicted by the Standard Model.\nThis can be explained by neutrino oscillations. This is a\nquantum-mechanical phenomenon where the flavor \n$(\\nu_e,\\nu_\\mu,\\nu_\\tau)$ content of the neutrino varies periodically.\nThis requires nonzero neutrino masses and the effect is determined\nby the difference in mass-squared, $\\Delta m^2$, and the ``mixing\nangle''.\n\nAll three (solar, atmospheric, and LSND)\n``neutrino problems'' cannot be simultaneously explained \nby oscillations among three flavors, but require at least a fourth \nflavor, $\\nu_s$, which must be ``sterile'', i.e., much more weakly\ninteracting than the three known ``active'' flavors, in order\nnot to violate the limit $N_\\nu \\sim 3$ from $Z^0$ decay width\n(Particle Data Group 1998). A sterile\nneutrino would also be useful for supernova nucleosynthesis \n(Peltoniemi 1996; Caldwell, Fuller, \\& Qian 1999).\n\nThe LSND results are controversial, so the other viewpoint is\nto ignore them until they are confirmed by independent experiments,\nin which case the solar and atmospheric neutrino problems can be \nexplained just with the three active neutrinos.\n\nOscillations among (light, non-degenerate, i.e., $\\xi = 0$) active\nneutrinos do not affect BBN,\nsince they all have equal abundances. If the sterile neutrino exists,\nit would have thermally decoupled from the other neutrinos very early,\nmuch before BBN, so that its contribution to $N_\\nu$ would be $\\ll 1$.\nActive-sterile neutrino oscillations before BBN would\nthen lead to production of $\\nu_s$, increasing $N_\\nu$ \n(Enqvist, Kainulainen, \\& Thomson 1992), which from the BBN point\nof view is undesirable. The situation is more complicated, however.\nThe oscillation depends on the background temperature, and at a\ncertain temperature there is a resonance. This resonance temperature\ndepends on the neutrino energy, so as the temperature falls, the\nresonance sweeps through the neutrino spectrum. If there is a \nsmall pre-existing asymmetry (this will be the case, since\nthermal fluctuations suffice), the rates of neutrino \nand antineutrino oscillation will be different. \nResonant active--sterile neutrino oscillations will\nthen lead to a growth of the neutrino asymmetry by a\nlarge factor\n(Barbieri \\& Dolgov 1991; Foot \\& Volkas 1995; Shi 1996;\nEnqvist, Kainulainen, \\& Sorri 1999; Di Bari \\& Foot 2000).\nThis may generate a large enough electron neutrino asymmetry\nto affect BBN (Bell, Foot, \\& Volkas 1998; Kirilova \\& Chizhov 1998;\nShi, Fuller, \\& Abazajian 1999). \n\nDepending on the oscillation parameters, the asymmetry may\neither just grow or\noscillate between positive and negative values, so that the final\nsign of the asymmetry becomes unpredictable.\nTo calculate the effect\non BBN is complicated, since the resulting\ndistortion of the $\\nu_e$ spectrum\nis also important for BBN, and the process happens near the neutrino\ndecoupling temperature. There are two schemes to generate\na large $\\nu_e$ asymmetry, either directly via $\\nu_e \\leftrightarrow\n\\nu_s$ oscillations or indirectly via $\\nu_{\\mu(\\tau)} \\leftrightarrow\n\\nu_s$ and $\\nu_{\\mu(\\tau)} \\leftrightarrow \\nu_e$ oscillations.\n\nThis scenario is under active study and there is much\ncontroversy among the different research groups.\nIn Fig.~3 we show results obtained by Shi et al.\n(1999). The maximal effect on $Y_p$ seems to be\nat the $\\pm 0.01$ level.\n\n\\begin{figure}\n\\plottwo{kurkisuonio3a.ps}{kurkisuonio3b.ps}\n\\caption{The impact on the primordial $^4$He abundance $Y$\nif an asymmetry in $\\nu_e\\bar\\nu_e$ is generated by a resonant\n$\\nu_e\\leftrightarrow\\nu_s$ mixing (left) or\nby the indirect neutrino mixing scheme (right), as a function\nof $\\Delta m^2$.\nThe baryon-to-photon ratio is set\nto $\\eta=5.1\\times 10^{-10}$.\nFrom Shi et al. (1999).\n}\n\\end{figure}\n\n\\section{Conclusions}\n\nAt present, no NSBBN scenario appears as\nconvincing as SBBN, which is the simplest of all.\nOften the real world has turned out to be more complicated in the\nend than first assumed, but for the early universe a simple\npicture has been very successful. However, it is healthy to keep\nin mind the possibility that SBBN might not be the full story, \nand that any discrepancies between observations and SBBN might\nactually be telling us something important about the\nearly universe or particle physics.\n\n\\acknowledgements\nI thank K. Kainulainen, A. Kalliom\\\"{a}ki, J. Peltoniemi, and A. Sorri\nfor advice on neutrino physics. \n\n\\begin{references}\n\\reference Applegate, J. H., Hogan, C. J., \\& Scherrer, R. J. 1987,\n \\prd\\ 35, 1151\n\\reference Barbieri, R. \\& Dolgov, A. 1991, Nucl.Phys.B 237, 742 \n\\reference Bell, N. F., Foot, R., \\& Volkas, R. R. 1998, \\prd\\ 58, 105010 \n\\reference Burbidge, G., \\& Hoyle, F. 1998, \\apj\\ 509, L1\n\\reference Burles, S., Nollett, K. M., Truran, J. W., \\& Turner, M. S.\n 1999, \\prl\\ 82, 4176 \n\\reference Caldwell, D. O., Fuller, G. M., \\& Qian, Y.-Z. 1999,\n astro-ph/9910175\n\\reference Cohen, A. G., De R\\'{u}jula, A., \\& Glashow, S. L. 1998,\n \\apj\\ 495, 539\n\\reference Di Bari, P. \\& Foot, R. 2000, \\prd, to be published,\n hep-ph/9912215\n\\reference Dimopoulos, S., Esmailzadeh, R., Hall, L. J., \\& \n Starkman, G. D. 1988, \\apj\\ 330, 545\n\\reference Dolgov, A. D. 1996, in Proceedings of the\n International Workshop on Baryon Instability, Oak Ridge, March 1996,\n hep-ph/9605280\n\\reference Dolgov, A. D., Hansen, S. H., Pastor, S., \\& Semikoz, D. V.\n 1999, Nucl.Phys.B 548, 385\n\\reference Dolgov, A. D., \\& Pagel, B. E. J. 1999, New Astron 4, 223\n\\reference Enqvist, K., Kainulainen, K., \\& Thomson, M. 1992,\n Nucl.Phys.B 373, 498\n\\reference Enqvist, K., Kainulainen, K., \\& Sorri. A. 1999, \n Phys.Lett.B 464, 199\n\\reference Foot, R. \\& Volkas, R. R. 1995, \\prl\\ 75, 4350\n\\reference Hannestad, S. 1998, \\prd\\ 57, 2213\n\\reference Hata, N., Scherrer, R. J., Steigman, G., Thomas, D., \n Walker, T. P., Bludman, S., \\& Langacker, P. 1995, \\prl\\ 75, 3977\n\\reference Kainulainen, K., Kurki-Suonio, H., \\& Sihvola, E. 1999,\n \\prd\\ 59, 083505\n\\reference Kang, H.-S., \\& Steigman, G. 1992, Nucl.Phys.B 372, 494\n\\reference Kirilova, D. P. \\& Chizhov, M. V. 1998, \\prd\\ 58, 073004\n\\reference Kurki-Suonio, H., \\& Sihvola, E. 1999, astro-ph/9912473\n\\reference Leonard, R. E., \\& Scherrer, R. J. 1996, \\apj\\ 463, 420\n\\reference Lisi, E., Sarkar, S., \\& Villante, F. L 1999,\n \\prd\\ 59, 123520\n\\reference LSND Collaboration (Athanassopoulos, C., et al.) 1998,\n \\prl\\ 81, 1774; \\prc\\ 58, 2489\n\\reference Malaney, R. A., \\& Mathews, G. J. 1993, Phys.Rep 229, 145\n\\reference Particle Data Group (Caso, C., et al.) 1998,\n Eur.J.Phys.C 3, 1\n\\reference Peltoniemi, J. 1996, in Proceedings of the 3rd Tallinn Symposium\n on Neutrino Physics, ed. I. Ots, J. L\\~{o}hmus, P. Helde \\& L. Palgi,\n% (Institute of Physics of the Estonian Academy of Sciences, Tartu), 103,\n hep-ph/9511323\n\\reference Rehm, J. B., \\& Jedamzik, K. 1998, \\prl\\ 81, 3307\n\\reference Sarkar, S. 1996, Rep.Prog.Phys 59, 1493\n\\reference Shi, X. 1996, \\prd\\ 54, 2753\n\\reference Shi, X., Fuller, G. M., \\& Abazajian, K. 1999, \\prd\\ 60, 063002\n\\reference Steigman, G. 1976, \\araa\\ 14, 339\n\\reference Super-Kamiokande Collaboration (Fukuda, Y., et al.) 1998,\n \\prl\\ 81, 1562\n\\reference Tytler, D., Fan, X. M., \\& Burles, S. 1996, \n Nature 381, 207\n\\reference Webb, J. K., Carswell, R. F., Lanzetta, K. M., Ferlet, R., \n Lemoine, M., Vidal-Madjar, A., \\& Bowen, D. V. 1997, Nature 388, 250\n\\end{references}\n\n\\end{document}\n"
}
] |
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astro-ph0002072
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VLBI differential astrometry at 43\,GHz
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[
{
"author": "J.C.~Guirado\\inst{1}"
},
{
"author": "J.M.~Marcaide\\inst{1}"
},
{
"author": "M.A.~P\\'erez-Torres\\inst{1}"
},
{
"author": "E.~Ros\\inst{2}"
}
] |
From 43\,GHz VLBA observations of the pair of radio sources \1928+738 and \2007+777 we have demonstrated the feasibility of precision phase-delay differential astrometric techniques at millimeter wavelengths. For a pair of sources with 5\degr\, separation and high antenna elevations, we have shown that present astrometric models and millimeter arrays are advanced enough to model the differential phase-delay to within 2 picoseconds, less than one tenth of a phase-cycle at 43\,GHz. The root-mean-square of the differential phase-delay residuals is dominated by the fluctuations of the atmospheric water vapor. We have determined the relative position of the observed sources with a precision twofold better than previous determinations at lower frequencies and, more importantly, largely free from ambiguous definitions of the reference point on the structure of the radio sources. Our result makes 43\,GHz VLBI phase-delay differential astrometry an ideal tool to study the absolute kinematics of the highly variable structures of regions near the core of extragalactic radio sources. \keywords{astrometry -- techniques: interferometric -- quasars: individual: \1928+738 -- BL Lacertae object: individual: \2007+777}
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[
{
"name": "guirado.tex",
"string": "%\\documentclass[referee]{aa}\n\\documentclass{aa}\n\\def\\et{et al.\\ } \n\\def\\1928+738{QSO\\,1928+738} \n\\def\\2007+777{BL\\,2007+777} \n\\addtolength{\\topmargin}{1 cm} \n\\begin{document}\n\n\\thesaurus{11(05.01.1; 03.20.2; 11.17.4 \\1928+738; 11.02.2 \\2007+777)}\n\n\\title {VLBI differential astrometry at 43\\,GHz}\n\n\\author{J.C.~Guirado\\inst{1}\n\\and J.M.~Marcaide\\inst{1}\n\\and M.A.~P\\'erez-Torres\\inst{1} \n\\and E.~Ros\\inst{2} }\n\n\\offprints{J.C.~Guirado}\n\n\\institute{\n Departamento de Astronom\\'{\\i}a, Universitat de\nVal\\`{e}ncia, E-46100 Burjassot, Valencia, Spain\n\\and\n Max-Planck-Institut f\\\"ur Radioastronomie, Auf dem H\\\"ugel 69, D-53121, Bonn, Germany }\n\n\\date{A\\&A, 353, L37-L40 (2000) } \n\\maketitle\n\n\\begin{abstract}\n\nFrom 43\\,GHz VLBA observations of the pair of radio sources \\1928+738 and \n\\2007+777 we have demonstrated the feasibility of precision phase-delay differential \nastrometric techniques at millimeter wavelengths. \nFor a pair of sources with 5\\degr\\, separation and high \nantenna elevations, we have shown that present astrometric models and millimeter \narrays are advanced enough\nto model the differential phase-delay to within 2 picoseconds, less than one tenth \nof a phase-cycle at 43\\,GHz. The root-mean-square of the \ndifferential phase-delay residuals is dominated by the \nfluctuations of the atmospheric water vapor. \nWe have determined the relative position of the observed sources with a precision \ntwofold better than previous determinations at lower frequencies and, more \nimportantly, largely free from ambiguous definitions of the reference point on the structure of \nthe radio sources. Our result makes 43\\,GHz VLBI phase-delay differential astrometry an ideal tool \nto study the absolute kinematics of the highly variable structures of \nregions near the core of extragalactic radio sources. \n\n\\keywords{astrometry -- techniques: interferometric -- quasars: individual:\n\\1928+738 -- BL Lacertae object: individual: \\2007+777}\n\n\\end{abstract}\n\n\\markboth{J.C. Guirado et al: VLBI Differential Astrometry at 43\\,GHz}{}\n\n\\section{Introduction}\n\nOne of the trends in Very-Long-Baseline Interferometry (VLBI) is to augment the angular\nresolution of the observations in search for a more detailed \nview of the inner structure of extragalactic radio sources.\nThis is effectively carried out by either observing at millimeter wavelengths \n(mm-VLBI) or, at cm-wavelengths, by combining ground telescopes with antennas \nin space. The correct interpretation of these high-resolution observations is \nof much relevance\nsince they map the morphology of highly variable regions close to the \ncentral engine of AGNs. However, multi-epoch analyses directed \nto understand the dynamical behavior of these inner \nregions critically depend on the alignment of the images: no solid \nconclusions can be extracted without an accurate source component (i.e. core) \nidentification. In particular, VLBI reveals that cm-wavelength components \nbreak up in complex structures with multiple features at mm-wavelengths. \nThese compact mm-features \nshow a strong variability, which may be the result of phenomena only seen so far in \nnumerical simulations (G\\'omez et al. 1995). \nFor a meaningful physical understanding of those compact features, a detailed \nknowledge of the (absolute) kinematics \nof the region is crucial. It is therefore highly desirable to extend \nprecision differential phase-delay \nastrometry to mm-wavelengths.\\\\\nIn this Letter we demonstrate the feasibility of using phase-delay differential \nastrometry at 43\\,GHz. We have selected the pair of sources \\1928+738 and \n\\2007+777, $\\sim$5\\degr\\, apart, with flat spectra, high flux densities, and \nrich structures at 43\\,GHz. The astrometry analysis of these data show \nthe advantages and possibilities of mm-wavelength differential astrometry. \n\n\\section{Observations and Maps}\n\n\\begin{figure}[t]\n\\vspace*{313pt}\n\\special{psfile=guirado_f1.eps hoffset=0 voffset=0 hscale=60 vscale=60}\n\\caption[]{43\\,GHz hybrid maps of \\1928+738 (left) and \\2007+777 (right) at\nepoch 1999.01. Contours are -0.5,0.5,1,2,4,8,16,32,64, and 90\\% of\nthe peak of brightness, 0.56 Jy/beam, for \\1928+738, and\n-1,1,2,4,8,16,32,64, and 90\\% of\nthe peak of brightness, 0.22 Jy/beam, for \\2007+777.\nThe restoring beam (shown\nat the bottom left corner of each map) is an elliptical Gaussian of\n0.24$\\times$0.14\\,mas (P.A. 21\\degr) for \\1928+738, and\n0.23$\\times$0.14\\,mas (P.A. 29\\degr) for \\2007+777.\nThe astrometric reference points are labeled as\nQ1, and correspond to the peak of brightness of each map. See text.}\n\\end{figure}\n\nWe observed the radio sources \\1928+738 and \\2007+777 at 43\\,GHz on 1999 \nJanuary 3 from 15:00 to 23:30 UT. We used the complete Very Long Baseline \nArray (VLBA) recording in mode 256-8-2 in left circular polarization to \nachieve a recording bandwidth of 64\\,MHz. \nWe interleaved \nobservations of \\1928+738 and \\2007+777 using integration times between \n40 and 130 seconds on each source to make total cycle time durations \nbetween 110 and 300 seconds (antenna slew time was 15 seconds). \nThe data were correlated at the National Radio Astronomy Observatory \n(NRAO, Socorro, NM, USA). Detections were found on both sources to all \nstations but Hancock, presumably due to severe weather conditions at this site. \nWe made manual phase calibration, visibility amplitude\ncalibration (using system temperatures and gain curves from each antenna),\nand fringe fitting at\nthe correlation position with the NRAO Astronomical Image Processing\nSystem (AIPS). \nFor astrometric purposes, we further processed the data in AIPS\n(tasks {\\sc mbdly} and {\\sc cl2hf}) to obtain, for \neach baseline and epoch, estimates of the group delay, phase-delay rate, and \nfringe phase at a reference frequency of 43,185\\,MHz. \nWe discarded data from Saint Croix and\nPie Town stations, which showed unacceptable scatter in the observables, for the \nastrometric analysis presented in Sect. 3.\nFor mapping purposes, we transferred the data into the Caltech imaging \nprogram {\\sc difmap} (Shepherd \\et 1995). We performed several iterations of \nself-calibration in phase and gain. We present the resulting hybrid maps in Fig. 1.\\\\\nThe 43\\,GHz map of \\1928+738 displays several \njet components extending southwards. All these features appear blended together \nas only one or two components in previous maps at cm-wavelengths (Guirado \\et 1995, \nhereafter G95; Ros \\et 1999, hereafter R99), and those obtained with space VLBI \n(Murphy \\et 1999). \nThe brightest knot, labeled as Q1, is probably a jet component, unless the \nsource is two-sided, but it is compact and well defined. Thus, it constitutes\nan appropriate reference point for relative astrometry at a \nsingle epoch. However, this component would not be a suitable reference point \nfor a multi-epoch comparison of the relative separation between the two \nsources as it is likely to move and evolve in brightness and shape \nover time.\\\\ \n%we notice tnoticeNote however necessarily \n%located closer to the core than the brightest feature at lower frequencies. Thus, Q1 \n%is an appropriate and well defined reference point for \n%astrometry.\\\\ \nThe 43\\,GHz map of \\2007+777 represents a significant improvement in the \nknowledge of the inner structure \nof this source (see Fig. 1). The brightest knot seen earlier at cm-wavelengths \n(Guirado \\et 1998, hereafter G98; R99) breaks-up in at least three new features. \nThe kinematic nature of component Q2, almost \nas bright as the easternmost component Q1,\nis of much interest. The brightest feature of \\2007+777 at cm-wavelengths, \na blending of all components seen within 1\\,mas from the origin in our 43\\,GHz map,\nhas been taken as a reference point for astrometry (G95; G98; R99); even more, \nthis feature has been considered stationary for \nmulti-epoch astrometry analyses. Accordingly, should component Q2 be a \ntravelling knot, the selected reference point at cm-wavelengths is likely\nto be not stable over time and part of previous astrometry results must \nbe revised. \n\n\\section{Astrometry Analysis}\n\nA goal of this research has been to calibrate the limitations of our standard astrometry \nprocedure for 43\\,GHz, as well as to study the potential precision of the astrometric data \nat this frequency. Therefore, the data-reduction procedure for the 43\\,GHz observation \ndeliberately followed the same steps as those used for the 5\\,GHz (G95) or \n8.4\\,GHz observations (G98; R99). We briefly go again over \neach step of this analysis: For our 43\\,GHz data, (i) we predicted,\nvia a precise theoretical model of the geometry of the array and the propagation \nmedium, the number of cycles of phase between\nconsecutive observations of the same source to permit us to ``connect\" the phase delay\n(e.g. Shapiro \\et 1979; G95; R99);\n(ii) we defined as reference points in the 43\\,GHz images of the two radio sources\nthe maximum of the brightness distribution (components Q1 in the maps of \\1928+738 and \n\\2007+777; see Fig. 1) and subtract the contribution of the structure of the \nradiosources, with respect to the reference points selected, from the phase \ndelays; (iii) we formed the differenced\nphase delays by subtracting the residual (observed minus theoretical values)\nphase delay of \\2007+777 from the previous observation of \\1928+738; and\n(iv) we estimated the relative position of the reference points \nfrom a weighted-least-squares analysis of the differenced residual\nphase delays. For this analysis we used an improved version of the \nprogram VLBI3 (Robertson 1975).\n\n\\noindent\nIn step (i), the geometry of our theoretical model (set of antenna coordinates, \nEarth-orientation parameters, and source coordinates) was consistently taken \nfrom IERS (IERS 1998 Annual Report, 1999). The theoretical model also accounted for the \neffect of the propagation medium in the astrometric observables. We modeled the \nionospheric delay by using total electron contect (TEC) data from GPS-based global ionospheric maps \ngenerated at the epoch of our observations by the Center for Orbit\nDetermination in Europe (Schaer \\et 1998). We followed the geometric corrections described \nin Klobuchar (1975) and Ros \\et (2000). \nWe modeled the tropospheric zenith delay at each station as a\npiecewise-linear function characterized by values specified at epochs\none hour apart. We calculated a priori values at these nodes from\nlocal surface temperature, pressure, and humidity, based on the model\nof Saastamoinen (1973). The antenna elevations were always higher than \n20\\degr\\, at all stations; this allowed us to use the dry\nand wet Chao mapping functions (Chao 1974) to determine the\ntropospheric delay at non-zenith elevations for each observation at each site. \nWe estimated the tropospheric zenith delay at the nodes of each \nstation, along with the relative position of the sources, \nfrom a weighted-least-squares analysis. \n\n\\section{Results and Discussion}\n\n\\begin{table}[t]\n\\caption[]{Contributions to the standard errors of the\nestimates of the coordinates of \\1928+738 minus those of \\2007+777\n( $\\delta\\Delta\\alpha$, $\\delta\\Delta\\delta$) from the\nsensitivity study. }\n\\begin{flushleft}\n\\begin{footnotesize}\n\\begin{tabular}{llccc}\n\\hline\n Effect & & Standard & $\\delta\\Delta\\alpha^b$ & $\\delta\\Delta\\delta$ \\\\\n & & Deviation$^a$ & ($\\mu$s) & ($\\mu$as) \\\\\n\\hline\nStatistical errors$^c$ & & -- & 4 & 25 \\\\\nRef. point identification & & -- & 0.6 & 1 \\\\\nStation coordinates & & 2\\,cm & 6 & 25 \\\\\nCoordinates & $\\alpha$ & 100\\,$\\mu$s & 23 & 41 \\\\\nof \\2007+777: & $\\delta$ & 300\\,$\\mu$as & 9 & 9 \\\\\nEarth's pole: & $x$ & 150\\,$\\mu$as & 2 & 9 \\\\\n & $y$ & 250\\,$\\mu$as & 2 & 4 \\\\\nUT1-UTC & & 15\\,$\\mu$s & 3 & 5 \\\\\nEarth's nutation: & $d\\psi$ & 170\\,$\\mu$as & 0.3 & 1 \\\\\n & $d\\epsilon$ & 80\\,$\\mu$as & 1 & 2 \\\\\nIonosphere$^d$ & & 1 TECU & 1 & 2 \\\\\n\\hline\nrss$^e$ & & & 26 & 56 \\\\\n\\hline\n\\end{tabular}\n\\end{footnotesize}\n\n\\begin{scriptsize}\n\\noindent\n$^a$ The standard deviation of the fixed geometrical parameters of our astrometric model \n(all entries but ionosphere) \nwere taken from IERS Annual Report 1998 (1999). The 2\\,cm standard deviation of the site coordinates \ncorresponds to each of the three coordinates for each antenna site.\\\\ \n$^b$ Notice that the values of $\\delta\\Delta\\alpha$ are in $\\mu$s. To convert $\\mu$s to $\\mu$as, the factor \n15$\\cdot\\cos\\delta_{\\rm{QSO}\\,1928+738}$ ($\\sim$4.2 ) must be used.\\\\\n$^c$ The statistical errors include the uncertainties of the tropospheric zenith delays at the nodes of \nthe piecewise linear function used in the troposphere model (see Sect. 2).\\\\ \n$^d$ Standard deviation provided by the global ionospheric maps at each site. 1 TECU = 1$\\times$10$^{16}$ el\\,m$^{-2}$.\\\\\n$^e$ Root-sum-square of the tabulated values. \n\\end{scriptsize}\n\\end{flushleft}\n\\end{table}\n\n\n\\noindent\nFrom the astrometric analysis described in Sect. 3, we obtain the following \nJ2000.0 coordinates of \\1928+738 minus those of \\2007+777 at 43\\,GHz:\\\\\n\n\\noindent\n\\begin{tabular}{lll}\n$\\Delta\\alpha=$ & $-0^{h}\\,37^{m}\\,42\\rlap{.}^{s}503443$ & \\, $\\pm\\,0\\rlap{.}^{s}000026$\\\\ \n$\\Delta\\delta=$ & $-3^{\\circ}\\,54'\\,41\\rlap{.}''677208$ & \\, $\\pm\\,0\\rlap{.}''000056$\\\\\n\\end{tabular}\n\n\\vspace*{0.2cm}\n\\noindent\nwhere the quoted uncertainties are overall standard errors (see Table 1), nearly twofold \nsmaller than the standard errors corresponding to previous determinations at \n5 and 8.4\\,GHz. \nFrom the comparison of the results of the sensitivity analysis \ndisplayed in Table 1 with similar sensitivity analyses at lower\nfrequencies (G95; R99), \nwe see that the improvement in precision comes from\n(i) the small contribution to the standard errors \nof the reference point identification in the map (dominated by image noise), as \na consequence of the improvement of resolution of the maps and of the \nlack of ambiguity in selecting the components acting as reference, and \n(ii) the negligible contribution of the ionosphere, that \nscales down by a factor of 25 with respect to its contribution at 8.4\\,GHz. \nAs occurs at cm-wavelengths, the quoted standard errors of the relative position are dominated by the \nuncertainties of the fixed parameters of the astrometric model (entries 3 to 10 of Table 1), \nand, in particular, by the uncertainties of the coordinates of the reference source, \nas expected \nfor objects with a large angular separation (notice that this error is not frequency \ndependent). The comparison and interpretation of the relative \nposition estimate at 43\\,GHz with previously reported\nestimates at lower frequencies will be postponed to a later \npublication where the comparison will be made in great detail.\n\n\\noindent\nThe postfit residuals of the differenced phase delays corresponding \nto all baselines included in our analysis are shown in Fig. 2. Note the scale \nof the plots, $\\pm$23\\,ps, corresponding to $\\pm$1 phase cycle. The average \nroot-mean-square (rms) of the postfit residuals is 2\\,ps, less than one tenth of \nthe phase cycle at 43\\,GHz. At this level of \nprecision, the absence of systematic effects validates both the\nastrometric model, based on IERS \nstandards, and the propagation medium procedures for mm-wavelength VLBI astrometry \n(at least for cycle times, source \nseparations, weather conditions, and antenna elevations similar to those presented \nin this paper). To calibrate \nthe quality of our procedure, we compared the residual \nof the differenced phase delay with similar \nresiduals corresponding to observations at 8.4\\,GHz and 5\\,GHz\nmade in the past (G95, G98). The rms of \nthe residuals are about 15, 9, and 2\\,ps for the data sets at 5, 8.4, and 43\\,GHz, \nrespectively, which expressed in equivalent-phase yield \npostfit residuals of roughly 30 degrees at each of the three frequencies. \nThis similarity of the rms expressed in phase at all the observed frequencies \ndemonstrates not only that the phase connection process is feasible at 43\\,GHz, \nbut which is also of no less quality than at lower frequencies.\\\\\nLikely, the most important contributors to the scatter of the phases at 43\\,GHz \nare the unmodeled variations of the refractivity of the neutral atmosphere.\nFrom the average rms of 2\\,ps of the phase residuals of Fig. 2, and assuming \nuncorrelated contributions from the antennas forming each interferometric \npair, the average uncertainty for the single-site phase delay \nis $\\sqrt{2}$\\,ps. This uncertainty is in good agreement with \nthe predictions of water vapor fluctuations on time scales of \n100 seconds ($\\sim$2\\,ps) based on refractivity patterns \ndescribed by Kolmogorov turbulences (Treuhaft \\& Lanyi 1987).\\\\ \n%We notice that, given the observing scheme, with cycle times larger \n%than 100 seconds, the long-term ($>$\\,100 seconds) fluctuations \n%are, at least partially, canceled in the difference phases.\\\\ \nThe importance of our result translates to VLBI phase-referencing mapping. \nThis technique (see e.g. Lestrade \\et 1990) relies completely on the behavior \nof the phase of the reference source (usually a strong radio emitter) to \npredict the phase of the target source (usually a weak radio emitter). \nBeasley \\& Conway (1995) provide useful expressions for the maximum cycle time \nfor phase-referencing with the VLBA. Under good weather conditions, average \nantenna elevation of 40\\degr, and with the requirement that the rms phase between scans is\n$<$90\\degr, the maximum cycle time at 43\\,GHz is $\\sim$100s. This estimate \nshould be shortened if atmospheric spatial variations from different lines of \nsight are considered. Actually, the facts are more favorable. \nFor sources separated 5\\degr\\, on the sky, high antenna elevations, and good \nweather conditions, our results show that \n(i) the rms of the phases is below 90\\degr\\, throughout the experiment and \ndoes not seem to be substantially \ndependent of the cycle times used during our observation (100-300s); and \n(ii) the expected average uncertainty in interpolating the phases of one source to \nthe epoch of the other is $\\sim$30\\degr\\,in the differenced phase. This value \nis not larger than usual \nphase errors in phase-reference mapping at cm-wavelengths (e.g. Lestrade \\et 1990).\nTherefore, with the proper cycle times and nearby calibrator sources, diffraction \nlimited VLBI phase-reference images at 43\\,GHz should be possible.\n\n\\begin{figure}[t]\n\\vspace*{9cm}\n\\special{psfile=guirado_f2.ps hoffset=-40 voffset=-54 hscale=50 vscale=50}\n\\caption[]{Postfit residuals of the difference phase delays at 43\\,GHz for all baselines.\nFull vertical scale is $\\pm$one phase cycle ($\\pm$2$\\pi$ equivalent), i.e., \n$\\pm$23\\,ps. The average rms is 2 ps, less than one tenth of a phase cycle at 43\\,GHz. \nThe symbols correspond to the following VLBA antennas: B, Brewster; \nF, Fort Davis; K, Kitt Peak; L, Los Alamos; M, Mauna Kea; N, North Liberty; \nO, Owens Valley} \n\\end{figure}\n\n\\noindent\nOur observations have shown that VLBI differential astrometry at \n43\\,GHz provides high-precision relative positions. At this frequency, \nthe astrometric precision is nearly equivalent to the resolution of the \nmaps, and the reference point selected in the \nsource structure might be associated with \nthe core. This makes 43\\,GHz differential astrometry an ideal technique \nto trace unambiguously the kinematics of the inner regions of the \nextragalactic radiosources. \n\n\\acknowledgements{We thank Patrick Charlot for a constructive \nrefereeing of the paper and Walter Alef for his valuable comments. \nWe thank Jon Romney for his efforts during the \ncorrelation. This work has been supported by\nthe Spanish DGICYT grant PB96-0782. The National Radio Astronomy Observatory is \noperated by Associated Universities Inc., under a cooperative agreement with the \nNational Science Fundation.}\n\n\\begin{thebibliography}{}\n\n\\bibitem[]{}\nBeasley A.J., Conway J.E., 1995, In: Zensus J.A., Diamond P.J., Napier P.J. (eds.), \nVery Long Baseline Interferometry and the VLBA, ASP Conference Series 82, \nSan Francisco, CA, USA, p.\\ 327\n\n\\bibitem[]{}\nChao C.C., 1974, JPL/NASA Tech.\\ Rep.\\ No.\\ 32-1587, 61\n\n\\bibitem[]{}\nG\\'omez J.L., Mart\\'{\\i} J.M., Marscher, A.P., et al., 1995, ApJ 449, L19\n\n\\bibitem[]{}\nGuirado J.C., Marcaide J.M., El\\'osegui P., et al., 1995, A\\&A 293, 613 [G95]\n\n\\bibitem[]{}\nGuirado J.C., Marcaide J.M., Ros E., et al., 1998, A\\&A 336, 385 [G98]\n\n\\bibitem[]{}\nInternational Earth Rotation Service (IERS), 1999, Annual Report for 1998, \nGambis, D. (ed.), Observatoire de Paris, France\n\n\\bibitem[]{}\nKlobuchar J.A., 1975, Air Force Cambridge Research Laboratories Report \nNo.\\ AFCRL-TR-75-0502 (NTIS ADA 018862)\n\n\\bibitem[]{}\nLestrade J.F., Rogers, A.E.E., Whitney, A.R., et al., 1990, AJ 99, 1663\n\n\\bibitem[]{}\nMurphy, D.W., Tingay S.J., Preston R.A., et al., 1999, New Astronomy Reviews \n43, 727\n\n\\bibitem[]{}\nRobertson D.S., 1975, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, \nUSA\n\n\\bibitem[]{}\nRos E., Marcaide J.M., Guirado J.C., et al., 1999, A\\&A 348, 381 [R99]\n\n\\bibitem[]{}\nRos E., Marcaide J.M., Guirado J.C., et al., 2000, A\\&A submitted \n\n\\bibitem[]{}\nSaastamoinen J., 1973, Bull. G\\'{e}od\\'{e}sique 105, 279\n\n\\bibitem[]{}\nSchaer S., Gurtner W., Feltens J., 1998, In: Proceedings of the IGS AC Workshop, \nDarmstadt, Germany: http://www.cx.unibe.ch/aiub/ionosphere.html\n\n\\bibitem[]{}\nShapiro I.I., Wittels J.J., Counselman C.C., et al., 1979, AJ 84, 1459\n\n\\bibitem[]{}\nShepherd M.C., Pearson T.J., Taylor G.B., 1995, BAAS 26, 987\n\n\\bibitem[]{}\nTreuhaft R.N., Lanyi G.E., 1987, Radio Science 22, 251\n\n\\end{thebibliography}\n\\end{document}\n\n\n"
}
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[
{
"name": "astro-ph0002072.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{}\nBeasley A.J., Conway J.E., 1995, In: Zensus J.A., Diamond P.J., Napier P.J. (eds.), \nVery Long Baseline Interferometry and the VLBA, ASP Conference Series 82, \nSan Francisco, CA, USA, p.\\ 327\n\n\\bibitem[]{}\nChao C.C., 1974, JPL/NASA Tech.\\ Rep.\\ No.\\ 32-1587, 61\n\n\\bibitem[]{}\nG\\'omez J.L., Mart\\'{\\i} J.M., Marscher, A.P., et al., 1995, ApJ 449, L19\n\n\\bibitem[]{}\nGuirado J.C., Marcaide J.M., El\\'osegui P., et al., 1995, A\\&A 293, 613 [G95]\n\n\\bibitem[]{}\nGuirado J.C., Marcaide J.M., Ros E., et al., 1998, A\\&A 336, 385 [G98]\n\n\\bibitem[]{}\nInternational Earth Rotation Service (IERS), 1999, Annual Report for 1998, \nGambis, D. (ed.), Observatoire de Paris, France\n\n\\bibitem[]{}\nKlobuchar J.A., 1975, Air Force Cambridge Research Laboratories Report \nNo.\\ AFCRL-TR-75-0502 (NTIS ADA 018862)\n\n\\bibitem[]{}\nLestrade J.F., Rogers, A.E.E., Whitney, A.R., et al., 1990, AJ 99, 1663\n\n\\bibitem[]{}\nMurphy, D.W., Tingay S.J., Preston R.A., et al., 1999, New Astronomy Reviews \n43, 727\n\n\\bibitem[]{}\nRobertson D.S., 1975, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, \nUSA\n\n\\bibitem[]{}\nRos E., Marcaide J.M., Guirado J.C., et al., 1999, A\\&A 348, 381 [R99]\n\n\\bibitem[]{}\nRos E., Marcaide J.M., Guirado J.C., et al., 2000, A\\&A submitted \n\n\\bibitem[]{}\nSaastamoinen J., 1973, Bull. G\\'{e}od\\'{e}sique 105, 279\n\n\\bibitem[]{}\nSchaer S., Gurtner W., Feltens J., 1998, In: Proceedings of the IGS AC Workshop, \nDarmstadt, Germany: http://www.cx.unibe.ch/aiub/ionosphere.html\n\n\\bibitem[]{}\nShapiro I.I., Wittels J.J., Counselman C.C., et al., 1979, AJ 84, 1459\n\n\\bibitem[]{}\nShepherd M.C., Pearson T.J., Taylor G.B., 1995, BAAS 26, 987\n\n\\bibitem[]{}\nTreuhaft R.N., Lanyi G.E., 1987, Radio Science 22, 251\n\n\\end{thebibliography}"
}
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astro-ph0002073
|
The Morphological and Structural Classification of Planetary Nebulae
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[
{
"author": "Arturo Manchado"
}
] |
We present a statistical analysis of a complete sample (255) of northern planetary nebulae (PNe). Our analysis is based on morphology as a main parameter. The major morphological classes are: round (26\% of the sample), elliptical (61 \%), and bipolar (13 \%) PNe. About a half of the round and 30 \% of the elliptical PNe present multiple shells. Round PNe have higher galactic latitude ($|{b}| =$12) and galactic height ($<{z}>=$753 pc), than the elliptical ($|{b}| = {7},~<{z}>=$308 pc) and bipolar ($|{b}| = {3},~<{z}>=$179 pc). This possibly implies a different progenitor mass range across morphology, as a different stellar population would suggest.
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"name": "paperII.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Manchado et al.}{The Morphological and Structural\nClassification of PNe}\n%\\author{Arturo Manchado}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n \\def\\emphasize#1{{\\sl#1\\/}}\n \\def\\arg#1{{\\it#1\\/}}\n \\let\\prog=\\arg\n\\def\\etal{{\\it et al.~}}\n \\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n \\marginparwidth 1.25in\n \\marginparsep .125in\n \\marginparpush .25in\n \\reversemarginpar\n\n \\begin{document}\n \\title{The Morphological and Structural Classification of Planetary \nNebulae}\n \\author{Arturo Manchado, Eva Villaver}\n \\affil{Instituto de Astrof\\'{\\i}sica de Canarias, C/V\\'{\\i}a L\\'actea,\n 38200\n La Laguna, Tenerife, Spain}\n \\author{Letizia Stanghellini}\n \\affil{Space Telescope Science Institute, 3700 San Martin Drive,\n Baltimore, MD 21218, USA}\n \\author{Mart\\'{\\i}n A. Guerrero}\n \\affil{Department of Astronomy, University of Illinois, 1002 W. Green\n St., Urbana, IL 61801, USA}\n\n \\begin{abstract}\n We present a statistical analysis\n of a complete sample (255) of northern planetary nebulae (PNe).\nOur analysis is based on morphology as a main parameter.\n The major morphological classes are: round (26\\% of the sample), \nelliptical (61 \\%), and bipolar (13 \\%) PNe.\n About a half of the round and\n30 \\% of the elliptical PNe\n present multiple shells.\n Round PNe have higher galactic latitude ($|{\\rm b}| =$12) and\n galactic height\n ($<{\\rm z}>=$753 pc), than the elliptical ($|{\\rm b}| = {\\rm 7},~<{\\rm\n z}>=$308 pc)\n and bipolar ($|{\\rm b}| = {\\rm 3},~<{\\rm z}>=$179 pc). This possibly \nimplies a\n different progenitor mass range across morphology,\nas a different stellar population would suggest.\n\n\n \\end{abstract}\n\n \\section{Introduction}\n\nFor decades now, it has been well established that\nPNe are the result of the evolution of low and intermediate mass \nstars (M$<$ 10 M$_{\\odot}$). \nThe actual nebular formation process has been well understood since\nKwok, Purton \\& Fitzgerald (1978) explained the formation of PN as the\nresult of the interaction of a low density fast wind with a high\ndensity slow wind. \nThe only drawback of this {\\it two wind} model is that\nit can not explain well the formation of asymmetric PNe. \nSince it has been long observed\nthat most PNe do not have a round, regular shape, some other \nmechanism has to be invoked to produce asymmetry.\n \nMellema \\& Frank (1995) implemented an interacting wind model with an\nequatorial \ndensity enhancement. The fast low density wind interacts with an \nazimuthal dependent wind forming an asymmetrical PN.\nRotation as a way to produce asymmetric PNe has been proposed by different \nauthors (e.g. Calvet \\& Peimbert\n 1983; Ignace, Cassinelli \\& Bjorkman 1996; Garc\\'{\\i}a-Segura \\etal 1999).\n The presence of a magnetic field is also able to\nconvey an asymmetrical nebular evolution\n(e.g. Pascoli 1992; Chevalier \\&\n Luo 1994; Soker 1998; Garc\\'{\\i}a-Segura \\etal 1999). \n The common envelope evolutionary phase, typical of a close binary\nstar, also produces the appropriate equatorial density enhancement\nto make the PN ejecta asymmetric; a similar effect can be obtained by\nthe presence of a substellar object in the system (e.g.\n Soker 1997).\n\n By correlating the\n morphological class with the different nebular and stellar\n parameters, it may be possible to disclose\n the predominant mechanism responsible for the observed\n morphology. \n\n Morphological studies of PNe have lacked a univocal\n classification scheme. Since the pioneer work by Curtis (1918),\n who discovered large structured \"haloes\" around some PNe, there have been\nseveral studies all aimed at the same goal: a better understanding on the\nphysical meaning of nebular shapes. \n Greig (1971) classified PNe into 15 morphological classes, ultimately \ngrouped in two main classes: binebulous and circular;\nhe found that binebulous PNe\n have lower galactic height distribution than circular PNe (Greig 1972).\n Zuckerman \\& Aller (1986) studied a sample of 108 PNe,\n classifying them into 16 morphological types, then regrouped the\nmany classes into bipolar, elliptical, round, irregular, and other shapes;\n 50 \\% of their PN sample was bipolar, 30 \\% elliptical, 15 \\% round, and the\n rest\n irregular or other shapes. \nZuckermann \\& Aller (1986) could not find any correlation between the\n morphological class and the C/O abundance.\n Balick (1987) divided the morphological classes in round, elliptical,\n and butterfly. He proposed an evolutionary sequence within each \nmorphological type.\nChu, Jacoby \\& Arendt (1987), studied a sample of 126 extended\n PNe. They found that the frequence of multiple-shell planetary nebulae\n(MSPN) was 50 \\%.\n Schwarz, Corradi \\& Stanghellini (1993) classified\n the Schwarz, Corradi \\& Melnick (1992) sample of southern Galactic PNe\n into elliptical, bipolar, pointsymmetric, irregular, and\n stellar shapes. \nOn a subsample of the same catalog of PNe, \n Stanghellini, Corradi \\& Schwarz (1993) found that the central star\n distribution was different for bipolar and elliptical PNe.\n Corradi \\& Schwarz (1995), using a large PN sample ($\\sim$ 400 PNe), found\n a different galactic height distribution for\n elliptical (z=320 pc) and for bipolar (z=130 pc) PNe.\n\nMost of these classification schemes are based on incomplete or inhomogeneous\nsamples. On this basis, Manchado \\etal (1996) presented a complete set of\nnorthern Galactic PNe, to be analyzed for their morphological properties.\nIn $\\S$2 we will illustrate this sample; we also discuss the completeness and\nthe morphological classification based on the sample.\n$\\S$ 3 presents some of the relations found between the morphology and\nother nebular and stellar parameters, and includes a discussion on the \npossible evolutionary scheme for the different types of pointsymmetric PNe.\nConclusions are in $\\S$ 4.\n \n \\begin{figure}\n \\plotone{fig1d.ps}{}\n \\caption{From left to right, top to bottom: narrow band images of the\nPNe A 39, NGC 2438, IC 1295, He 2-429, He 2-437 and M 2-46\n }\n \\label{fone}\n \\end{figure}\n\n \\section{The PN sample and its completeness}\n\nThe selection criteria for our homogeneous sample of northern \nGalactic PNe includes:\n(1) all northern PNe with declination larger than --11 in the Acker \\etal\n(1992) catalog;\n(2) all the PNe larger than 4 arc-second;\n(3) images must be obtained in the narrow band filters (e.g. H$\\alpha$,\n[N II] or \\hbox{[O III]}).\n \nThere are 255 PNe that fulfill these selection criteria, 205 from the\n survey by Manchado \\etal (1996), 28 from Balick (1987) and 22 from\n Schwarz, Corradi \\& Melnick (1992). In Figure 1 we show a selection of\nthese images,\nrepresentative of the various morphologies. \n\n After a thorough analysis of the whole sample we decided to revise the\nmorphological classification by Manchado \\etal (1996). In fact, to make the\nindividual morphological classes statistically meaningful,\nwe decided to make only three major morphological classes: round (63 cases),\n elliptical\n (149 cases), and\n bipolar (43 cases) PNe. The quadrupolar PNe (7 cases) were included in the\n bipolar class, because the formation mechanisms could be very similar\n(Manchado, Stanghellini \\& Guerrero 1996).\n Pointsymmetry\n can be defined as a sub-class of elliptical and bipolar PNe: in fact, most \npointsymmetric PNe have either bipolar or elliptical main shapes. A typical\ncase of an elliptical pointsymmetric PNe is a PN with FLIERS (e.g.\nBalick \\etal 1993). \nFigure 2 shows a diagram with the new morphological scheme.\n \n\\begin{figure}\n\\plotone{figure2.ps}\n\\caption{Classification scheme\n }\n\\label{fone}\n\\end{figure}\n\n\\begin{figure}\n\\plotfiddle{figure3.ps}{5cm}{-90}{50}{50}{-210}{240}\n\\caption{Galactic distribution of elliptical (triangles), round (open circles) \n, and bipolar (filled circles) PNe.\n}\n\\label{fone}\n\\end{figure}\n\n\n Although the sample is complete as far as known PNe are concerned,\n there\n may be observational biases due to a different surface brightness limit\nfor each\n morphological class. In order to investigate this possible bias we\n compare the statistical distribution of each morphological class\n taking\n into account the distance (Cahn, Kaler \\& Stanghellini\n 1992)\n and the extinction (Cahn, Kaler \\& Stanghellini\n 1992; Tylenda \\etal 1992).\nThe overall distribution of morphology in our PN sample is\n 58 \\% elliptical, 25 \\% round and 17 \\% bipolar. However, we realized \nthat the sample is only\n complete up to a distance of 7 Kpc for all the morphological classes. \nIf we were to\n limit the statistical studies to those PNe within a distance of 7 Kpc, the \nmorphological distribution \n would be like 61 \\% elliptical, 26 \\% round and 13 \\% bipolar. \n\nIt can be argued that the statistical distances are not correct, so we used the\n extinction to infer completeness. \nIf the sample is confined to the galactic plane, we can\n assume an extinction distance relationship of c = 0.2 per Kpc.\n Therefore, if we limit the sample to PNe with $| b| <$ 4$^{\\circ}$ , \nc must be $<$ 1. In this newly defined space volume,\nwe find 59 \\% elliptical, 28 \\% round, and 13 \\% bipolar PNe.\nTherefore, the results\n obtained using the statistical distance and the extinction rule are very\n similar, which means that the completeness within this space volume is sound.\n\n \\section{Relations across morphological types}\n\n Each morphological class was correlated with a set of nebular and stellar\n parameters from the literature (for a complete reference list, see\nManchado \\etal 2000).\n \n It was found that electronic density has different values for each\n morphological class; the median value is 1500 cm$^{-3}$ for\n elliptical, 400 cm$^{-3}$ for round, and 1000 cm$^{-3}$ for bipolar.\n\n Dust temperatures were derived using the IRAS 25 and 60 $\\mu m$\n fluxes and dust emissivities taken from Draine \\& Lee\n (1984). Both\n elliptical and round PNe have a median dust temperature of 82 K, while\n bipolar temperature is 69 K.\n\n The [N II]/H$\\alpha$ ratio is higher for bipolar than for elliptical\n and round PNe.\n The N/O and He abundances of bipolar PNe are consistent with type I PNe\n (as defined by Peimbert \\& Torres-Peimbert 1983) and in\n MSPN they are consistent with type II PNe.\n\n The galactic latitude distribution is different for each morphological\n class. The median of the galactic latitude is $|{\\rm b}| = {\\rm 7}$\n for\n elliptical, $|{\\rm b}| =$12 for round and $|{\\rm b}| = {\\rm 3}$ for\n bipolar PNe. Figure 3 shows the galactic distribution of these three\nmorphological classes. \nThe median values of the Galactic height are $<{\\rm z}>=$308 pc for\n elliptical,\n $<{\\rm z}>=$753 pc for round, and $<{\\rm z}>=$179 pc for bipolar. \n\nBy studying the pointsymmetric PNe, we find that \nfor elliptical pointsymmetric the scale height is \n$<{\\rm z}>=$310 pc, while the elliptical PNe without pointsymmetry have\n a $<{\\rm z}>=$ 308 pc. Bipolar with pointsymmetric structure have $<{\\rm\n z}>=$248 pc, while bipolar without pointsymmetry $<{\\rm z}>=$110 pc.\n\n The different galactic height for the various morphological classes\nmay imply a different stellar population. According to Miller \\& Scalo\n (1979) $<{\\rm z}>=$300 pc implies that the progenitor star\n has mass $<$ 1.0 M$_{\\odot}$. For $<{\\rm z}>=$150 pc, the mass is \n $>$ 1.5 M$_{\\odot}$, while for $<{\\rm z}>=$230 pc and $<{\\rm z}>=$ 110 pc\n masses will be $>$ 1.2 M$_{\\odot}$ and $>$ 1.9 M$_{\\odot}$.\n Therefore elliptical and bipolar PNe might have\n different distribution masses for their progenitor stars ($<$ 1.0\n M$_{\\odot}$ and $>$ 1.5 M$_{\\odot}$). In the bipolar\n class there is also a mass segregation. In fact, according to to their\nscale height on the Galactic plane, PNe with pointsymmetric\n structure evolve from stellar masses $>$ 1.2 M$_{\\odot}$, while those without\n the\n pointsymmetric structure evolve from stellar masses $>$ 1.5 M$_{\\odot}$.\n These results are consistent with the other results from our \n statistical analysis, as bipolar PNe have higher N/O\n and helium abundances.\n\n The fact that two different mass distributions can be inferred for bipolar\nPNe, depending on the presence of pointsymmetry, can be explained with\n two evolutionary schemes for the two types:\na single, high mass star would form a bipolar PNe, due possibly to\nrotation and magnetic field (e.g. Garc\\'{\\i}a-Segura \\etal 1999),\nwhile a bipolar pointsymmetric PN could be\ndue to magnetic collimation\naround a precessing star (e.g. Garc\\'{\\i}a-Segura 1997).\n\n \\section{Conclusions}\n A proper statistical analysis of a complete sample of PNe has allowed\n us\n to classify them into elliptical, round, and bipolar, with the\n sub-classes of\n multiple-shell and pointsymmetric PNe. It was found that 60 \\% of our\nPN sample present an elliptical shape, while\n 26 \\% are round, and 13 \\% bipolar.\n\nWe use statistical distances that appear to be sound for the task. If\nthey are indeed correct, the different scale heights that\ncharacterize each morphological class hint of different progenitor mass \ndistribution for each class.\nTwo evolutionary schemes are proposed for bipolar PNe and\nbipolar PNe with pointsymmetric structure. \n\n\n\n\n \\section*{Acknowledgment}\n The work of EV and AM is supported by a grant of the Spanish DGES\n PB97-1435-C02-01. MAG is supported by the Spanish Ministerio de\nEducaci\\'on y Cultura.\n\n \\begin{references}\n \\reference Acker, A., Ochsenbein, F., Stenholm, B., Tylenda, R., Marcout, J.,\nSchohn, C.: 1992, Strasbourg--ESO catalogue of Galactic planetary nebulae, ESO\n\\reference Balick, B. 1987, AJ 94, 671\n \\reference Balick, B., Rugers, M., Terzian, Y., Chengalur, J.N. 1993,\nApJ 411, 778\n \\reference Cahn, J.H., Kaler, J., \\& Stanghellini, L. 1992, A\\&AS 94,\n 399\n \\reference Calvet, N., \\& Peimbert, M. 1983, Rev. Mex. Astron.\n Astrofis. 5, 319\n \\reference Chevalier, R. A. \\& Luo, D. 1994, ApJ, 421, 225\n \\reference Chu, Y.-H., Jacoby, G., \\& Arendt, R. 1987, ApJSS, 64, 529\n \\reference Corradi, R. L. M., \\& Schwarz H. E. 1995, A\\&A 293, 871\n \\reference Curtis, H.D. 1918, Pub. 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U.S.S.R. 33, 315\n \\reference Soker, N. 1997, ApJS 112, 487 \n \\reference Soker, N. 1998, MNRAS, 299, 1242\n \\reference Stanghellini, L. Corradi R. L. M. \\& Schwarz, H. E., 1993, A\\&A\n 279, 521\n \\reference Tylenda, R., Acker, A., Stenholm, B., Koeppen, J. 1992,\nA\\&AS 95, 337\n \\reference Zuckerman, B., \\& Aller, L. H. 1986, ApJ, 301, 772\n \\end{references}\n\n \\end{document}\n\n\n\n\n\n\n\n\n\n\n"
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astro-ph0002074
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Simultaneous Measurements of X-Ray Luminosity and Kilohertz Quasi-Periodic Oscillations in Low-Mass X-Ray Binaries
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[
{
"author": "Eric C. Ford\\altaffilmark{1}"
},
{
"author": "Michiel van der Klis\\altaffilmark{1}"
},
{
"author": "Mariano \\mm\\altaffilmark{1,2}"
},
{
"author": "Rudy Wijnands\\altaffilmark{1,3}"
},
{
"author": "Jeroen Homan\\altaffilmark{1}"
},
{
"author": "Peter G. Jonker\\altaffilmark{1}"
},
{
"author": "Jan van Paradijs\\altaffilmark{1,4}"
}
] |
We measure simultaneously the properties of the energy spectra and the frequencies of the kilohertz quasi-periodic oscillations (QPOs) in fifteen low mass X-ray binaries covering a wide range of X-ray luminosities. In each source the QPO frequencies cover the same range of approximately $300$ Hz to $1300$ Hz, though the sources differ by two orders of magnitude in their X-ray luminosities (as measured from the unabsorbed 2--50 keV flux). So the X-ray luminosity does not uniquely determine the QPO frequency. This is difficult to understand since the evidence from individual sources indicates that the frequency and luminosity are very well correlated at least over short timescales. Perhaps beaming effects or bolometric corrections change the observed luminosities, or perhaps part of the energy in mass accretion is used to power outflows reducing the energy emitted in X-rays. It is also possible that the parameters of a QPO model are tuned in such a way that the same range of frequencies appears in all sources. Different modes of accretion may be involved for example (disk and radial) or multiple parameters may conspire to yield the same frequencies.
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[
{
"name": "fordqpos.tex",
"string": "% Summary paper of QPOs - spectral fits + frequencies for all sources\n% Ford et al., accepted by ApJ 2 February 2000\n% uses AAS preprint style sheets version 5.01\n% draft1: 20 August 1999\n\n% note this file uses BibTeX, citations defined in refs.bib\n\n\\documentclass[preprint2,11pt]{aastex}\n%\\documentclass{aastex}\n\n% Put a space after macro unless followed by punctuation\n%\n\\newcommand\\puncspace{\\ifmmode\\,\\else{\\ifcat.\\C{\\if.\\C\\else\\if,\\C\\else\\if?\\C\\else%\n\\if:\\C\\else\\if;\\C\\else\\if-\\C\\else\\if)\\C\\else\\if/\\C\\else\\if]\\C\\else\\if'\\C%\n\\else\\space\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi\\fi}%\n\\else\\if\\empty\\C\\else\\if\\space\\C\\else\\space\\fi\\fi\\fi}\\fi}\n\\newcommand\\SP{\\let\\\\=\\empty\\futurelet\\C\\puncspace}\n\n% commands for this article\n\\newcommand{\\Msun}{{\\rm M}_\\sun\\SP}\n\\newcommand{\\mdot}{$\\dot{M}$\\SP}\n\\newcommand{\\lx}{$L_x$\\SP}\n\\newcommand{\\freq}{$\\nu_{kHz}$\\SP}\n\\newcommand{\\mm}{M\\'endez }\n\n\\citestyle{aa} % make citations look right\n\n%\\slugcomment{Submitted to ApJ, 14 December 1999}\n\\slugcomment{Accepted by ApJ, 2 Februrary 2000}\n\n\\shorttitle{QPOs and Spectra}\n\\shortauthors{Ford et al.}\n\n\\begin{document}\n\n\\title{Simultaneous Measurements of X-Ray Luminosity and Kilohertz\nQuasi-Periodic Oscillations in Low-Mass X-Ray Binaries}\n\n\\author{Eric C. Ford\\altaffilmark{1}, Michiel van der\nKlis\\altaffilmark{1}, Mariano \\mm\\altaffilmark{1,2}, Rudy\nWijnands\\altaffilmark{1,3}, Jeroen Homan\\altaffilmark{1}, Peter G.\nJonker\\altaffilmark{1}, Jan van Paradijs\\altaffilmark{1,4}}\n\n\\email{[email protected]}\n\n\\altaffiltext{1}{Astronomical Institute, ``Anton Pannekoek'',\nUniversity of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam,\nThe Netherlands}\n\\altaffiltext{2}{Facultad de Ciencias Astron\\'omicas y Geof\\'{\\i}sicas,\nUniversidad Nacional de La Plata, Paseo del Bosque S/N, 1900 La Plata,\nArgentina.}\n\\altaffiltext{3}{MIT, Center for Space Research, Cambridge, MA 02139}\n\\altaffiltext{4}{University of Alabama in Huntsville, Department\nof Physics, Huntsville, AL 35899}\n\n\\begin{abstract}\n\nWe measure simultaneously the properties of the energy spectra and the\nfrequencies of the kilohertz quasi-periodic oscillations (QPOs) in\nfifteen low mass X-ray binaries covering a wide range of X-ray\nluminosities. In each source the QPO frequencies cover the same range\nof approximately $300$ Hz to $1300$ Hz, though the sources differ by\ntwo orders of magnitude in their X-ray luminosities (as measured from\nthe unabsorbed 2--50 keV flux). So the X-ray luminosity does not\nuniquely determine the QPO frequency. This is difficult to understand\nsince the evidence from individual sources indicates that the\nfrequency and luminosity are very well correlated at least over short\ntimescales. Perhaps beaming effects or bolometric corrections change\nthe observed luminosities, or perhaps part of the energy in mass\naccretion is used to power outflows reducing the energy emitted in\nX-rays. It is also possible that the parameters of a QPO model are\ntuned in such a way that the same range of frequencies appears in all\nsources. Different modes of accretion may be involved for example\n(disk and radial) or multiple parameters may conspire to yield the\nsame frequencies.\n\n\\end{abstract}\n\n\\keywords{accretion, accretion disks --- black holes -- stars:\nneutron --- X--rays: stars}\n\n\\section{Introduction}\n\nMany low mass X-ray binaries exhibit quasi-periodic oscillations\n(QPOs) in their persistent X-ray flux in the kilohertz range as\nrevealed by the Rossi X-ray Timing Explorer (RXTE). There are\ncurrently 18 such sources with published results. Generally two\nkilohertz QPOs are observed simultaneously from a given system. In all\ncases, the QPOs are separated in frequency by about 250 to 350 Hz. The\nQPOs vary over a wide range in frequency. In 4U~0614+09, for example,\nthe higher frequency QPO has been measured at frequencies between\n$449\\pm20$ Hz and $1329\\pm4$ Hz \\citep{vanstraaten00}. For reviews and\nreferences see \\citet{vanderklis_rev98b} and\nhttp://www.astro.uva.nl/$^{\\sim}$ecford/qpos.html.\n\nThe low mass X-ray binaries (LMXBs) which exhibit QPOs come in a wide\nvariety. Most are persistent sources, but some transients are known\nwith kilohertz QPOs: 4U~1608-52 \\citep{berger96,mendez98a}, Aql~X-1\n\\citep{zhang98a}, and XTE~J2123-058 \\citep{homan99,tomsick99}. The\ntwo traditional classes of LMXBs, Z and atoll sources \\citep{hk89},\nhave very similar QPOs, though the QPOs in Z-sources tend to have\nlarger widths and smaller rms fractions. The X-ray dipper 4U~1915-05\n\\citep{boirin00} also has shown kilohertz QPOs. In all these systems,\nthe kilohertz QPO frequencies are very similar, even though the\ninferred mass accretion rates differ by orders of magnitude\n\\citep{vdk_rev97a,vdk_rev97b}.\n\nHere we quantify these comparisons by considering the ensemble of\nsources. The main tool is a measurement of the X-ray luminosity in\neach system simultaneous with a determination of its kilohertz QPO\nfrequencies. This approach is inspired by the strong correlation of\nQPO frequency and count rate in individual sources. This correlation\nis very strict on short time scales\n\\citep[e.g. 4U~1728-34;][]{strohmayer96}, though on longer timescales\nof days to weeks in some sources a single correlation no longer holds\n\\citep[e.g. 4U~0614+09,][4U~1608-52,]{ford97a,mendez99a}. The same\ncorrelations are present if one considers X-ray flux instead of count\nrate \\citep{ford97b, zhang98a}. The QPO frequencies are clearly\ninfluenced to some extent by the X-ray luminosity.\n\nCorrelations of luminosity and kilohertz QPO frequency provide a\nrather direct connection to QPO models. In most current models, the\nfrequency of one of the QPOs is set by the orbital frequency of matter\nin the inner disk \\citep{mlp98a,lai98,sv99,ot99b}. Higher QPO\nfrequencies are the result of faster orbital frequencies which are in\nturn coupled to higher mass accretion rates.\n\nIn the following we present simultaneous measurements of kilohertz\nQPOs and energy spectra in LMXBs. Section~2 details the analysis\nprocedure and results with special notes on each source. Section~3\ndiscusses these results in context with current QPO models.\n\n\\section{Analysis \\& Results}\n\nIn this analysis we use data from the RXTE Proportional Counter Array\n(PCA), \\citep{zhang93}. We consider fifteen sources with kilohertz\nQPOs, which includes all sources reported to date except\nXTE~J2123-058, 4U~1915-05 and GX~349+2. These latter three sources\nhave relatively few observations with kilohertz QPOs. For timing\nanalysis, we construct Fourier power spectra from the high-time\nresolution modes of the PCA with Nyquist frequencies of typically 4096\nHz. We fit these power spectra for QPO features in roughly the\n200--2000 Hz range. For intervals where a QPO is detected, we perform\nspectral fitting using the 16 sec resolution `Standard 2' mode PCA\ndata.\n\n% We have included 15 sources\n% NOTE on sources excluded:\n% XTE J2123-058 - about same Lx as X1728, doesn't add much (see Tomsick)\n% 4U 1915-05 - about same Lx as X1728, doesn't add much (see Boirin)\n% GX349+2 - just another Z-source, with one small interval, ignore it\n% EXO 0748 has a QPO, not yet published (Homan et al.) - don't include\n% Gal. Center (MXB1743-29?) - this only had burst QPOs\n\nIn the sources where the QPOs are strong (e.g. 4U 1608-52), the QPO\nfeatures are significantly detected in a time interval of 64 sec or\nless. In these cases we have chosen representative intervals and\nperformed the spectral fitting on the identical time interval where\nthe QPOs are detected. In other sources (e.g. 4U 1705-44) many power\nspectra from short time windows must be added before the signal to\nnoise improves to the level where the QPOs are detected. In such cases\nthe spectra are well measured on much shorter time scales and we\nselect an interval (typically 64 sec duration) in the middle of the\ninterval where the QPOs are detected. There are no large count rate or\ncolor variations within these intervals so this procedure is accurate.\nIn the case of Z sources, the QPO frequencies have been measured as a\nfunction of $S_z$, the position along a track in the X-ray\ncolor--color diagram or hardness--intensity diagram\n\\citep[e.g. GX~17+2,][]{wijnands98a}. In these cases we perform\nspectral fitting on matching intervals of $S_z$, using the same\nobservations where the timing analysis was performed.\n\nIn spectral fitting we use only the top of the three xenon/methane\nlayers of the proportional counter units (PCUs) to reduce systematic\neffects. We also do not include events in the uppermost\nanticoincidence propane layer. We use all of the five PCUs when\navailable, though in a few cases one or more PCUs were off, and we\nperformed spectral fitting on the subset of detectors that was on. We\nuse the background estimation tool pcabackest v2.1b, response matrix\ngenerator pcarsp v2.38 and the standard XSPEC v10.0 fitting\nroutines. Since the response is not well calibrated at low energy we\nignore standard mode 2 PCA channels 1--3 ($<2.4$ keV for gain epoch\nthree: 15 April 1996 to 22 March 1999). We also ignore channels above\n55 ($>22.4$ keV, gain epoch three) since the background dominates\nthere even in the brighter sources. We have ignored the HEXTE data,\nsince this provides no constraints on the spectral fit for the short\nintervals we consider here.\n\nWe have chosen to describe the continuum spectra in terms of the\nfollowing model components: a power law, a blackbody, and a Gaussian\nline at roughly 6.4 keV, all absorbed with an equivalent hydrogen\ncolumn density. This model, which is purely phenomenological, is often\nused in the literature \\citep[e.g.][]{cs97,wsp88} but is not intended\nas a physically self-consistent representation of the physical\nprocesses at work. All the parameters of the models are allowed to\nfloat (though in some cases the width of the Gaussian line is\nfixed). The reduced $\\chi^{2}$ values are close to one in all\ncases. There is no evidence for a roll-over at high energies,\nindicating that a power law is a sufficient description at least up to\nour cutoff energy of $\\sim22$ keV.\n\nFrom the model fits we calculate several parameters, the most\nimportant here being the total flux from 2 to 50 keV. We report the\nunabsorbed flux, which is corrected for the effect of absorption at\nlow energies by the interstellar medium and represents the actual flux\nemitted by the source. We take the unabsorbed 2--50 keV flux as\nsome indication of the bolometric flux of the source, though it is an\nobviously flawed indicator since the spectra are unmeasured below 2\nkeV and above $\\sim22$ keV. Observations with the Beppo-SAX\ninstruments, however, have good statistics over a much wider energy\nrange (0.1 to 200 keV). Beppo-SAX observations of 4U 0614+09\n\\citep{piraino99} and X1724-308 \\citep{guainazzi98} indicate that the\nmodel we employ here provides an accurate description of the\nspectra. In the 4U~0614+09 observations, \\citet{piraino99} find an\naccurate fit to the spectrum with a blackbody at $kT=1.45$ keV, a\npowerlaw with photon index 2.33 and a line at 0.71 keV that carries\n1\\% of the total flux, all absorbed by an equivalent neutral hydrogen\ncolumn of $3.3\\times10^{21}$ cm$^{-2}$. This spectral description is\nsimilar to the one used here.\n\nIn reporting here the unabsorbed 2-50 keV flux we tend to\nunderestimate the actual flux because of the truncation in energy. By\ntruncating at 2 keV we underestimate the flux that would have been in\nthe blackbody by roughly 2\\% to 20\\% in these spectra. By stopping\nthe integration at 50 keV we also underestimate the flux at high\nenergy, which in principle can be a large amount because of the hard\ntails in some sources \\citep[c.f.][]{barret94}. The observations\nconsidered here, however, did not find any source in an extremely hard\nstate. We estimate that we typically loose about 2\\% of the flux in\nthe power law by stopping the integration at 50 keV. In the hardest\nspectra (4U~0614+09 at low flux) we miss about 15\\% of the flux.\nThere is likely a break in the power law at high energy (not included\nhere) which makes the missing flux somewhat less than that. In the\nBeppo-SAX spectrum mentioned above, the flux from 0.1 keV to 2 keV is\n25\\% of the total flux and that above 50 keV is 7\\% of the\ntotal. Finally, the bolometric flux may be larger than our estimate if\nthe power law extends to very low energies (though this is physically\nnot so likely) or if different components are present in the extreme\nultraviolet or soft X-ray band.\n\nTo calculate a luminosity, \\lx, from the total unabsorbed 2--50 keV\nflux, we need to know the source distances. The distances we use here\nare quoted in Table~\\ref{tbl:dist} along with references. Distances\ncan be determined in a variety of ways \\citep[see][for a\ndescription]{vpm94}. In the sources showing type-I X-ray bursts, the\ndistance can be determined from radius expansion bursts where the\nluminosity is thought to reach the Eddington limit \\citep{lewin93}.\nIn some bursters, no radius expansion bursts have been observed, and\none derives only an upper limit by assuming the flux is less than the\nEddington limit. We use the upper limits as the actual distances (see\nTable~\\ref{tbl:dist}) , so that the derived \\lx are upper limits in\nthese cases. One source, 4U~1820-30, is in the globular cluster\nNGC~6624 and therefore has a relatively well determined distance. The\ndistances to the Z-sources, most of which do not show bursts, are more\nuncertain. Most of these sources are likely near the galactic center\n\\citep{penninx89}. A VLBA parallax measurement of Sco X-1 puts it at\n$2.8\\pm0.3$ kpc \\citep{bradshaw99}. A radius expansion burst was\nrecently observed from Cyg~X-2, yielding a distance of $11.6\\pm0.3$\nkpc \\citep{smale98}, though results from optical lightcurves put it\nsubstantially closer \\citep[see][]{ok99}. The Cyg X-2 fluxes we\nmeasure are consistent with the data from the Einstein Observatory\n\\citep{cs97} and EXOSAT \\citep{schulz99}.\n\n\nThe spectral analysis of Sco X-1 requires a special treatment which\ndeserves note. In this source, detector deadtime effects are important\nsince its count rate exceeds 25000 c s$^{-1}$ PCU$^{-1}$. We apply a\ncorrection for nonparalyzable deadtime, which amounts to simply\nmultiplying the effective exposure time by a factor of about 0.7\n\\citep{zhang95}. We calculate this factor from the measured rates, a\n10 $\\mu$sec deadtime appropriate for `Good Xe Events', and a 150\n$\\mu$sec deadtime appropriate for events registered as `Very Large\nEvents' in the instrument modes used. This deadtime treatment is\napproximate and does not take into account for example gain shifts due\nto the high count rates. We compare the flux we derive for Sco X-1 to\nthat from Einstein observations \\citep{cs97}. Relative to GX~17+2,\nthese fluxes are the the same.\n\nGiven the distance, $d$, and the flux, $F_x$, we calculate the the\nluminosity as $L_x = 4\\pi d^2 F_x$. Note that this assumes the\nemission is isotropic. In quoting luminosities we normalize to an\nEddington luminosity of $2.5\\times10^{38}$~erg~s$^{-1}$. Misestimates\nof distance, like the misestimates of flux discussed above, contribute\nto a spread in \\lx among sources. However, the observed range of \\lx\ncovers over two orders of magnitude and this large of a range cannot\nbe explained by these effects alone.\n\n%%% Table 1 - distances\n\n\\begin{deluxetable}{lll}\n\\tablenum{1}\n\\tablewidth{40pc}\n\\tablecaption{Distances}\n \n\\tablehead{ \\colhead{Source} & \\colhead{$D$} & \\colhead{Ref.} \\\\\n\\colhead{} & \\colhead{(kpc)} & \\colhead{} }\n\n\\startdata\n~~~ {\\em Atoll sources} & & \\\\\n4U 0614+09 & 3.0 $^{\\rm{a}}$ & \\citet{brandt92} \\\\\nAql X-1 & 3.4 & \\citet{thorstensen78}; [1] \\\\\n4U 1702-42 & 6.7 $^{\\rm{a}}$ & \\citet{oosterbroek91} \\\\\n4U 1608-52 & 3.6 & \\citet{nakamura89, ebisuzaki87} \\\\\n4U 1728-34 & 4.3 & \\citet{foster86} \\\\\n4U 1636-53 & 5.5 & \\citet{vanparadijs86}; [1] \\\\\n4U 1735-44 & 7.1 $^{\\rm{a}}$ & \\citet{ehs84} \\\\\nKS 1731-260 & 8.5 & \\citet{sunyaev90} \\\\\n4U 1820-30 & 7.5 & NGC~6624; \\citet{rich93} \\\\\n4U 1705-44 & 11.0 $^{\\rm{a}}$ & \\citet{ehs84,cs97} \\\\\n~~~ {\\em Z sources} & & \\\\\nCyg X-2 & 11.6 & \\citet{smale98} \\\\\nGX 17+2 & 7.5 & \\citet{ehs84,cs97} \\\\\nGX 340+0 & 9.5 & [1] \\\\\nGX 5-1 & 7.4 & [1] \\\\\nSco X-1 & 2.8 & \\citet{bradshaw99} \\\\\n\n\\tablecomments{ The sources and their distances used in this\npaper. References for the distances are shown. [1] is \\citep{vpw95}.}\n\n\\tablenotetext{a}{This is an upper limit based on burst fluxes. We use\nit as the distance in calculating \\lx.}\n\n\\enddata\n\\label{tbl:dist}\n\\end{deluxetable}\n\n\n% NOTES on distances\n% X1820-30 - Vacca et al. (1986) has a careful discussion of the\n% distance, conclude d=6.4 (see also Christian \\& Swank 97)\n% metalicity corrections are important, otherwise could be 8.3 kpc\n% Bildsten, 1995, ApJ, 438, 852 uses 7.3 kpc based on \n% Rich et al. 1993, ApJ, 406, 489 IUE measurements of distance\n% modulus, really Rich et al. is \n% m-M=14.35 to 14.40, i.e. 7.4 to 7.6 kpc --> I use 7.5 kpc\n\nThe results of the simultaneous spectral and timing measurements are\nshown in Figure~\\ref{fig:freqlx} as a function of \\lx. Both of the\ndouble kilohertz QPOs are shown; circled symbols are used to indicate\nthe higher frequency QPO. The lines connect points in time order, or\nin the case of Z-sources, in order along the Z track.\n\nIn each case we must identify which of the double QPOs is observed. In\nsome observations only one QPO is detected. As reported in the current\nliterature, all sources (except Aql~X-1) are known to have two\nQPOs. Both QPOs, however, are not always present in a given\nobservation. In 4U 1608-52 the lower frequency QPO peak is generally\nthe stronger and narrower of the two \\citep[see][]{mendez98a}\nproviding the identification. In 4U~0614+09 there is a robust\ncorrelation between the position in the X-ray color diagram and the\nfrequency which allows us to determine which QPO is present\n\\citep{vanstraaten00}. Similarly in other sources the relative\nproperties of the energy spectra or rms values generally allow a firm\nidentification of the peak.\n\nThe correlation of QPO frequency, \\freq, with \\lx can be parameterized\nas $\\nu_{kHz} = A L_x^{\\alpha}$. Taking the data of the upper\nfrequency QPO in Figure~\\ref{fig:freqlx} for 4U~1735-44 and\n4U~1702-42, we find $\\alpha=0.2$ and 0.5 respectively. We note however\nthat these data on the upper frequency QPO come from observations\nwidely separated in time. Over long timescales the \\freq--\\lx\ncorrelations shifts around and parallel lines are observed (see\nbelow). This data may therefore include several tracks of the parallel\nline correlations. In the data of 4U~1608-52 we can separate out the\nparallel lines \\citep{mendez99a} and measure $\\alpha$ within each\nstretch of correlated data. We find values of $\\alpha$ between 0.5 and\n1.6 with typical errors of 0.2, using the absorbed 2--10 keV flux\ninstead of \\lx. Note that though these correlations are measured over\na relatively small range in flux, this measurement does not mix up\ndifferent tracks. \n\nOf special note in Figure~\\ref{fig:freqlx} are the LMXBs which do not\nappear because they do not exhibit kilohertz QPOs: the atoll-type\nsources GX3+1, GX9+9, GX9+1 and GX13+1. The upper limits to the rms\nfractions of QPOs in these sources are 1 to 3\\%\n\\citep{strohmayer98a,wkp98,homan98}. The luminosities of these sources\nlie between the Z sources and other atoll sources \\citep{cs97} and\nthey are an important intermediate class of sources in some models\n\\citep[see][]{mlp98a}.\n\nWe note that only observations in which the LMXBs exhibit QPOs are\nreported here. The total range of \\lx that a source covers is\ngenerally larger than that in Figure~\\ref{fig:freqlx} since kilohertz\nQPOs are present preferentially at intermediate fluxes\n\\citep{mendez99a,mendez99c}. The only known exceptions to this so far\nare 4U~0614+09 \\citep{vanstraaten00} and 4U~1728-34 \\citep{disalvo99}.\n\nSome selected parameters from the spectral fitting are shown in\nFigure~\\ref{fig:paramlx}. These parameters are similar to those\npreviously measured for such sources and show that the Z-sources can\nbe fit by roughly the same spectral model as the atoll sources\n\\citep[see][]{schulz99,cs97,wsp88}. The ratio of powerlaw to blackbody\nflux is 2 to 3 in most cases, i.e. the blackbody is roughly 25\\% to\n35\\% of the total flux \\citep[c.f.][]{wsp88}. There is an overall\ntrend towards harder spectra at lower luminosities, reflected in our\nfits. This same trend is seen in previous studies of atoll sources\n\\citep[e.g.][]{vv94,bg95} and occurs in the emission even up to 100\nkeV \\citep{ford96}. It is also manifest in the patterns in X-ray color\ndiagrams. The softening at higher fluxes is often attributed to the\neffects of thermal Comptonization.\n\n\\section{Discussion}\n\nWithin a given low-mass X-ray binary the frequency of the kilohertz\nQPOs, \\freq, is well correlated with the X-ray flux \\citep{ford97b,\nzhang98a} or count rate\n\\citep{strohmayer96,wijnands98d,mendez99a,mendez99b,mendez99c}, at\nleast on the timescale of about a day. Considering all the binaries as\na group, however, such a correlation does not hold. This is a very\nclear feature of Figure~\\ref{fig:freqlx}, where \\freq covers roughly\nthe same range of frequencies for sources of widely different X-ray\nluminosities, \\lx. All sources have maximum frequencies at roughly\n1000 to 1300 Hz, a fact that \\citet{zss97} have used to argue that the\nmaximum \\freq is set by the orbital frequency at the marginally stable\norbit. In addition to the similar maximum \\freq, all the sources have\nroughly the same minimum \\freq and slope of their \\freq--\\lx\nrelation. This is the central mystery presented here. How is it that\n\\lx and \\freq are decoupled in the ensemble of systems?\n\nThis decoupling has an apparent analog within individual sources. In\na given system, \\freq and \\lx (or flux, or count rate) are uniquely\ncorrelated within single observations spanning less than roughly a\nday. Between observations more widely separated in time, however, the\ncorrelation shifts and parallel lines appear in the \\freq vs \\lx\ndiagram similar to those in Figure~\\ref{fig:freqlx}. Note, though,\nthat these parallel lines in individual sources covers a much narrower\nrange; flux shifts are a factor of a few at most in individual\nsources. 4U~0614+09 was first seen to have such parallel lines\n\\citep{ford97a,ford97b}, and the same effect is observed in Aql~X-1\n\\citep{zhang98a}, 4U~1608-52 \\citep{mendez99a}, 4U 1728-34\n\\citep{mendez99b}, and 4U~1636-53 \\citep{mendez99c}. There is a\nsimilar effect in Z-sources, where \\freq is correlated to the position\non the instantaneous Z-track in the X-ray color diagram\n\\citep[e.g.][]{wijnands98d, jonker00} while the tracks themselves\nshift around in intensity.\n\nOne possible solution to the mystery of decoupled \\lx and \\freq is\nthat the parameters of the mechanism producing the QPOs are tuned in\nsuch a way that \\freq is the same in all systems. As an example\nconsider the magnetospheric beat-frequency model. A simple version of\nthe theory predicts that the QPO frequency is set by $\\dot{M}/B^2$,\nwhere \\mdot is the mass accretion rate and $B$ is the surface magnetic\nfield strength \\citep{as85}. The frequencies could then be the same if\n$B$ scaled in such a way that $\\dot{M}/B^2$ is constant in all systems\n\\citep{wz97}. Such a connection between \\mdot and $B$ was suggested\npreviously on other grounds \\citep{hk89,pl97}. Other parameters, such\nas the neutron star spin, mass or temperature, might be involved as\nwell, though it is not clear how these would fit into a detailed\nmodel.\n\n% reference for explaining \\mdot-B correlation: Battacharya??\n\nThe observational data do suggest that \\mdot has a role in setting the\nQPO frequency. The correlations of \\freq and \\lx suggest this, in as\nmuch as \\lx and \\mdot are related (see below). The timing properties\npoint to a similar conclusion as well. The Fourier power spectra often\nshow a noise component, whose power decreases with frequency above a\nbreak frequency of roughly 10 Hz. The break frequency is strongly\ncorrelated with $\\nu_{kHz}$\n\\citep{fk98,vanstraaten00,reig00,disalvo00}. The fact that the break\nfrequency is thought to be a good indicator of $\\dot{M}$\n\\citep{vanderklis94}, suggests that the frequency of the kilohertz QPO\nis also correlated with \\mdot. Another timing signal is the QPO at\n10--50 Hz \\citep[e.g.][]{vanderklis96,fk98,pbk99} which also\ncorrelates with \\freq. Thus there are several timing features, all\ncorrelated with one another \\citep[see also][]{wk99,pbk99}. In\naddition \\freq also depends strongly on the energy spectra, sometimes\nparameterized as the distance along a track in the X-ray color diagram\n\\citep[e.g.][]{\nvanderklis96,wijnands98a,zhang98c,mendez99a,mendez99c,kaaret99b}. The\nimplication is that a single parameter underlies these correlations,\nand that parameter is likely \\mdot.\n\nIf there is a connection between \\freq and \\mdot, one might also\nexpect a correlation of \\freq and \\lx, since \\lx is some measure of\n\\mdot. Why then is the range of \\freq similar for very different \\lx\nin Figure~\\ref{fig:freqlx}? In the following we consider one logical\npossibility: that \\lx and \\mdot do {\\em not} track one another.\n\nPerhaps \\lx is simply not a good indicator of the bolometric\nluminosity and in fact the bolometric luminosity is similar in all\nsystems. In principle \\lx could misrepresent the bolometric\nluminosity just due to the limited 2--25 keV energy range of the\nRXTE/PCA. It is unlikely however that this is a large effect, since\nBeppo-SAX measurements from 0.1--200 keV indicate that not much energy\nis radiated outside the PCA band for these sources and our spectral\nmodels are applicable \\citep{piraino99}. Of course there could also be\nstrong emission in the unobserved extreme ultraviolet band.\n\nIf the emission is not isotropic, the measured \\lx will also be an\ninaccurate indicator of the total emission. Inclination effects are\none possibility: the lower \\lx sources may be viewed at a higher (more\nedge-on) inclination making \\lx smaller. This effect is well known in\nthe dipping X-ray systems where the inclination is extremely edge-on\nand \\lx is low \\citep{parmar86}. An added attraction of this scenario\nis that it may explain the fact that Z-sources are strong radio\nemitters while the atoll-sources are not \\citep{fender00}. In this\nscenario, the less inclined, higher \\lx, Z-sources show strong radio\nemission because the radio jet is beamed into the line of sight, while\natoll-sources at higher inclination and lower \\lx, are usually not\ndetected in the radio because the radio jet is more in the plane of\nthe sky. This may not be the full story, however, since the beaming\nwould have to be narrow and a search for effects of inclination in the\nX-ray spectra with EXOSAT uncovered no evidence that inclination is\nimportant \\citep{wsp88}.\n\nA general problem with preserving the same \\mdot in all the systems\nwhile changing the observed \\lx through anisotropy or bolometric\ncorrections is that, if all the sources had the same \\mdot, they\nshould all show the same X-ray burst properties. They do not; the\nZ-sources, for example, hardly burst at all \\citep{lewin93}. In the\nlow-\\lx sources, \\mdot is also likely low because the persistent\nemission is at least 10 times weaker than in the bursts, some of which\nare at the Eddington limit. Assuming the anisotropy is about the same\nin the burst and persistent emission, \\mdot in these sources is then\nlikely lower than in the sources near the Eddington limit, such as the\nZ sources.\n\nOutflows are another way to decouple \\lx and \\mdot, and are a\nwell-known feature of X-ray binaries, as seen for example in the\ncollimated radio jets \\citep{hjellming95,fender99b}. One might expect\nthat the outflows in the low-\\lx systems are stronger than those in\nthe high-\\lx systems to preserve a similar accreted rate in the\nvarious systems. Radio observations, however, suggest that the\nopposite is true; the atoll sources are less luminous in radio than\nthe Z-sources \\citep{fender00}.\n\nAnother alternative is that part of the \\mdot may be ineffective in\ndetermining \\freq while not being lost from the system. This could\nhappen if the mass accretion rate occurs in a two component flow,\nradially and through a disk \\citep[e.g.][]{gl79,flm89,wijnands96}. The\naccretion rate through the disk is primarily responsible for setting\n\\freq, while the radial flow does not affect \\freq but does change\n$L_x$ \\citep[see][]{kaaret98}. \\citet{mlp98a} suggest that the disk\naccretion rate is similar in all sources. Matter is `scooped off' into\na radial flow at the magnetospheric radius, and this process is more\nefficient in the higher \\lx sources because the fields are\nstronger. Under this scenario, the QPOs at higher \\lx should have a\nmuch smaller rms fraction due to the addition of unmodulated\nflux. This represents a problem for this scenario since the rms\nfraction apparently does not decrease enough with $L_x$\n\\citep{ford00}.\n\nAll of the above effects may act to decouple \\lx and \\mdot. As\noutlined above, though, no single effect can account for the\ndecoupling and each has problems. If \\lx and \\mdot are unrelated,\n\\mdot can set the frequency of the QPOs while \\lx assumes any value,\nas observed.\n\n\\acknowledgments\n\nThis work was supported by NWO Spinoza grant 08-0 to E.P.J.van den\nHeuvel, by the Netherlands Organization for Scientific Research (NWO)\nunder contract number 614-51-002, and by the Netherlands\nResearchschool for Astronomy (NOVA). 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H.~G. 1996,\n \\apjl, 469, L5\n\n\\bibitem[{{Zhang} {et~al.}(1998{\\natexlab{a}}){Zhang}, {Jahoda}, {Kelley},\n {Strohmayer}, {Swank}, \\& {Zhang}}]{zhang98a}\n{Zhang}, W., {Jahoda}, K., {Kelley}, R.~L., {Strohmayer}, T.~E., {Swank},\n J.~H., \\& {Zhang}, S.~N. 1998{\\natexlab{a}}, \\apjl, 495, L9\n\n\\bibitem[{{Zhang} {et~al.}(1995){Zhang}, {Jahoda}, {Swank}, {Morgan}, \\&\n {Giles}}]{zhang95}\n{Zhang}, W., {Jahoda}, K., {Swank}, J.~H., {Morgan}, E.~H., \\& {Giles}, A.~B.\n 1995, \\apj, 449, 930+\n\n\\bibitem[{{Zhang} {et~al.}(1998{\\natexlab{b}}){Zhang}, {Smale}, {Strohmayer},\n \\& {Swank}}]{zhang98c}\n{Zhang}, W., {Smale}, A.~P., {Strohmayer}, T.~E., \\& {Swank}, J.~H.\n 1998{\\natexlab{b}}, \\apjl, 500, L171\n\n\\bibitem[{{Zhang} {et~al.}(1997){Zhang}, {Strohmayer}, \\& {Swank}}]{zss97}\n{Zhang}, W., {Strohmayer}, T.~E., \\& {Swank}, J.~H. 1997, \\apjl, 482, L167\n\n\\bibitem[{Zhang {et~al.}(1993)}]{zhang93}\nZhang, W. {et~al.} 1993, SPIE, 2006, 324\n\n\\end{thebibliography}\n\n%\\bibliographystyle{apj}\n%\\bibliography{apj-jour,refs} %apj-hour.bib is an astronat distrib. file\n\n\\clearpage\n\\onecolumn\n\n%% FIG 1: Freq/Luminosity\n%%% NOTE: THIS IS A COLOR FIGURE !\n\\begin{figure*}\n\\begin{center}\n% need rescaling in preprint mode\n\\epsscale{1.0}\n\\plotone{f1.ps} %only works in AASTeX v 5.0.1 or higher\n\\caption{QPO frequency vs. luminosity, $L_x$, in the 2--50 keV\nband. $L_x$ is calculated from the distance (Table 1) and the flux in\nthe model fit for each observation corrected for absorption and\nnormalized to an Eddington luminosity of $2.5\\times10^{38}$ erg\ns$^{-1}$. Circled bullets are QPOs identified as the higher frequency\nof the two QPOs; uncircled bullets are the lower frequency QPO. \n~~~~~~~~~ ~~~~~ {\\bf NOTE: this figure is in color.}}\n\\label{fig:freqlx}\n\\end{center}\n\\end{figure*}\n\n\\clearpage\n\n%%% FIG 2: Spectral parameters/Luminosity\n\\begin{figure*}\n% need rescaling in preprint mode\n\\epsscale{1.0}\n\\plotone{f2.ps} \n\\caption{Spectral parameters vs. luminosity. Luminosity is calculated\nas in Figure~1. The panels show the index of the power law component\n({\\em top}), the temperature of the blackbody component ({\\em middle})\nand the ratio of the absorbed 2--20 keV flux in these two components\n({\\em bottom}).}\n\\label{fig:paramlx}\n\\end{figure*}\n\n\n\\end{document}\n% LocalWords: QPOs QPO luminosities unabsorbed keV colors RXTE vanstraaten mlp\n% LocalWords: vanderklis LMXBs mendez homan strohmayer timescales PCA zhang fk\n% LocalWords: sec color Sco PCUs wsp bolometric Beppo piraino powerlaw center\n% LocalWords: Eddington normalize wk vs lewin bursters magnetospheric XTE hk\n% LocalWords: tomsick rms boirin vdk rev lai sv ot GRS GX Nyquist pcabackest\n% LocalWords: pcarsp XSPEC HEXTE barret cs guainazzi vpm penninx VLBA kpc erg\n% LocalWords: bradshaw deadtime PCU nonparalyzable Cyg EXOSAT schulz Aql wkp\n% LocalWords: bg vv Comptonization zss analog jonker kuulkers wz reig disalvo\n% LocalWords: pbk parmar hjellming gl flm kaaret Misestimates misestimates Lx\n% LocalWords: parameterized timescale wijnands accreted unmodulated NGC smale\n% LocalWords: lightcurves ok Xe\n"
}
] |
[
{
"name": "astro-ph0002074.extracted_bib",
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H.~G. 1996,\n \\apjl, 469, L5\n\n\\bibitem[{{Zhang} {et~al.}(1998{\\natexlab{a}}){Zhang}, {Jahoda}, {Kelley},\n {Strohmayer}, {Swank}, \\& {Zhang}}]{zhang98a}\n{Zhang}, W., {Jahoda}, K., {Kelley}, R.~L., {Strohmayer}, T.~E., {Swank},\n J.~H., \\& {Zhang}, S.~N. 1998{\\natexlab{a}}, \\apjl, 495, L9\n\n\\bibitem[{{Zhang} {et~al.}(1995){Zhang}, {Jahoda}, {Swank}, {Morgan}, \\&\n {Giles}}]{zhang95}\n{Zhang}, W., {Jahoda}, K., {Swank}, J.~H., {Morgan}, E.~H., \\& {Giles}, A.~B.\n 1995, \\apj, 449, 930+\n\n\\bibitem[{{Zhang} {et~al.}(1998{\\natexlab{b}}){Zhang}, {Smale}, {Strohmayer},\n \\& {Swank}}]{zhang98c}\n{Zhang}, W., {Smale}, A.~P., {Strohmayer}, T.~E., \\& {Swank}, J.~H.\n 1998{\\natexlab{b}}, \\apjl, 500, L171\n\n\\bibitem[{{Zhang} {et~al.}(1997){Zhang}, {Strohmayer}, \\& {Swank}}]{zss97}\n{Zhang}, W., {Strohmayer}, T.~E., \\& {Swank}, J.~H. 1997, \\apjl, 482, L167\n\n\\bibitem[{Zhang {et~al.}(1993)}]{zhang93}\nZhang, W. {et~al.} 1993, SPIE, 2006, 324\n\n\\end{thebibliography}"
}
] |
astro-ph0002075
|
On energy spectra of UHE cosmic rays accelerated in supergalactic accretion flows
|
[
{
"author": "G. Siemieniec-Ozi\\c{e}b{\\l}o"
},
{
"author": "M. Ostrowski"
}
] |
Some ultra-high energy (UHE) cosmic ray (CR) events may be correlated with the Local Supercluster plane. We consider acceleration of such particles at the large-scale accretion flows of matter towards such plane and/or accretion flows onto galaxy clusters. The formed shocks and the general compression flow are expected to allow for CR diffusive acceleration of UHE particles. For a simplified flow geometry we consider a stationary acceleration of such CRs and we discuss influence of model parameters on a particle spectral index. We show that the general convergent flow pattern leads naturally to very flat proton spectra with the phase-space spectral indices $\sigma \approx 3.0$, as compared to the `canonical' shock value of $4.0$~. \keywords{cosmic rays -- acceleration of particles -- shock waves -- accretion}
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[
{
"name": "ms8663.tex",
"string": "\\input{epsfig.sty}\n\\documentstyle{l-aa} \n%\\documentstyle[12pt]{article}\n%\\documentstyle[referee]{l-aa}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\n\\begin{document}\n \n\\thesaurus{02.01.1, 02.01.2, 02.19.1}\n \n\\title{On energy spectra of UHE cosmic rays accelerated in\nsupergalactic accretion flows}\n\n\n\\author{G. Siemieniec-Ozi\\c{e}b{\\l}o, M. Ostrowski}\n\n\\institute{Obserwatorium Astronomiczne, Uniwersytet Jagiello\\'nski,\nul. Orla 171, 30-244 Krak\\'ow, Poland}\n\n\\offprints{G. Siemieniec-Ozi\\c{e}b{\\l}o, E-mail: grazyna\\@@oa.uj.edu.pl)}\n\n\\date{Received ...; accepted .. ; } \n \n\\maketitle \n \n\\markboth{G. Siemieniec-Ozi\\c{e}b{\\l}o \\& M. Ostrowski}{On energy\nspectra of UHE cosmic rays ...}\n \n\\begin{abstract} \nSome ultra-high energy (UHE) cosmic ray (CR) events may be correlated\nwith the Local Supercluster plane. We\nconsider acceleration of such particles at the large-scale accretion flows\n of matter towards such plane and/or accretion flows onto galaxy clusters.\n\nThe formed shocks and the general compression flow are expected to allow for CR\ndiffusive acceleration of UHE particles. For a simplified flow geometry \nwe consider a stationary\nacceleration of such CRs and we discuss influence of model parameters\non a particle spectral index. We show\nthat the general convergent flow pattern leads naturally to very flat\nproton spectra with the phase-space spectral indices $\\sigma \\approx\n3.0$, as compared to the `canonical' shock value of $4.0$~. \n\n\n\\keywords{cosmic rays -- acceleration of particles -- shock waves --\naccretion}\n \n\\end{abstract} \n\n\\section{Introduction}\n\nRecent studies of the ultra high energy (UHE) cosmic rays' (CRs)\ngeneration in large supergalactic structures are supported by\npresumable detection of extragalactic magnetic fields (Kim et al.\n1991) and theoretical modelling of large scale accretion flows (Ryu et\nal. 1993, Bertschinger 1985). Typical energies of UHE particles $E \\geq\n10^{18}$eV and the remarkable change in the observed spectrum in this\nenergy range indicate their extragalactic origin. Additionally, the\ngalactic magnetic fields in the range of a few $\\mu$G, with a typical\nLarmor radius of an UHE particle $>1$kpc, essentially exclude the\nacceleration sites located in our Galaxy. On the other hand the sources\nof particles with $E \\sim 10^{20}$ eV cannot be more distant than $50 -\n100$ Mpc due to particle interactions with the microwave background\nradiation.\n\nSeveral authors indicate the Local Supercluster (LSC) as a main\ncandidate to provide the sources of UHE CRs (Stanev et al. 1995; Sigl et al. 1999).\nThis idea is clearly motivated by two facts. First, this is a natural site \nof all potential UHE sources. Second, there are indications (Cen et al. 1994) that the \nlarge-scale accretion shocks can be a generic feature of gravitational structure \nformation.\n\n\nBelow, after a short discussion of physical parameters typical for LSC, \n we analyze some aspects of the\nacceleration process of energetic protons at a simplified supergalactic \nand/or galaxy cluster \nstructure, with the use of the diffusive acceleration model. We show\nthat the general convergent flow pattern leads naturally to very flat\nproton spectra with the phase-space spectral indices $\\sigma \\approx\n3.0$, as compared to the `canonical' shock value of $4.0$~. The actual\nvalue of the index depends on a number of parameters including the\ninvolved spatial scales of the flow, the involved velocity of accreting\nflow and diffusive properties of the medium, depending\non the magnetic field structure.\n\n\\section{Physical conditions in supergalactic accretion flows}\n\n\nIn analytic and numerical studies of the evolution of the mass distribution \none can see the hierarchy going from galaxy clusters up to two-dimensional \nstructures called {\\it walls} or {\\it sheets} and {\\it filaments} being at \nthe intersections of such walls.\n The same picture is revealed by observations of \nthe distribution of luminous matter (e.g. Lapparent et al. 1991). \n \n\nBelow we would like to recall the present status of the diffusion acceleration \nin large-scale shocks accompanying a structure formation in the universe. Thus, \nin the following we briefly review the constraints for the main parameters -- \nthe strength of extragalactic magnetic field, and the accretion flow velocity -- \nwhich are required to accelerate protons to energies beyond the EeV scale. \n Cosmic magnetic fields beyond the Galactic disk are poorly known. \n There \nare however some observational indications for its existence in galaxy \ncluster cores as well as in their outer regions (Kronberg 1994; \nKim et al.1991; Ensslin et al.\n1998a; Valee 1990, 1997). The observation of diffuse radio emission from\n galaxy clusters provides \nevidence that magnetic fields and relativistic electrons are distributed there \non megaparsec scales. Typical $\\mu$G fields and the 100 kpc scales were \ndetected by Faraday rotation measurements, but magnetic fields are still undetectable for \nlarger structures. Nevertheless, recently, existence\n of large-scale magnetic field correlated with large-scale structure of\nthe universe is often hypothesized \n(Ryu et al. 1998; Kulsrud et al. 1997; Medina Tanco 1998).\n There \nare X-rays from the hot gas detected outside clusters\n(Soltan et al. 1996), which allow \nto assume that the significant magnetic field \n occur there on scales typical for galaxy superclusters. Unfortunately, unless \nwe directly see the magnetic fields at radio or $\\gamma$-ray secondaries to \nUHE CRs (which spectral shape is sensitive to cosmological magnetic fields; \nsee discussion Lee et al. 1995),\nthey must serve \nonly as a postulate.\n\n\nThe nonuniform extragalactic magnetic field associated with the large-scale \nfilaments and sheets is supposed to be responsible for the Faraday rotation of \nextragalactic sources (Ryu et al. 1998). In contrast to the upper limit \n$B_{ext} \\leq 10^{-9}$G derived from RM of quasars based on the assumption \nof magnetic field uniformity, in the case of non-uniform fields, the field strength \n is expected to be in the range $10^{-9} - 10^{-6}$G. This high \nstrength inside the cosmological walls ($\\sim 0.1 \\mu $G) substantially \ndecreases in the surrounding voids. According to the simulations \nthe field can be well ordered along the structure for several megaparsecs. The \nrelatively high strength of magnetic field in the walls could be due to \nturbulent amplification associated with the \nof large-scale structure formation (Kulsrud et al. 1997).\n\n\n On the other hand, both numerical simulations\n (Ryu et al. 1993) and\ntheoretical modelling (Bertschinger 1985) of structure formation points\nout that large scale accretion shocks must occur, when the diffuse matter\nfalls down to generated deep potential wells. These shocks amplify\n and order the magnetic field. The increase \nof the strength and the field coherence length is suggested to be limited\n by the energy equipartition \nstate, which in the case of large scale sheets should be smaller than the value\n quoted by Ryu et al. for filaments. Thus the typical upper value of B$_{sheet}$ \nis expected to be $\\sim 0.1 \\mu$G at 10 Mpc coherence length scale.\n Although one cannot yet\nconfirm the existence of large-scale flows with direct observations it\nhas been suggested (Ensslin et al. 1998b) that the shocks coupled with\n galaxy clusters may be \nresponsible for acceleration of electrons which we observe in the \n so-called `cluster radio relics'. The regions of cluster relics which show diffuse radio\nemission and do not coincide with any host-galaxy are treated as tracers\nof accretion shock waves developing at large-scale plasma inflows onto \ngalaxy clusters (Ensslin et al. 1998a). \n\nIn spite of lack of evidence of shocks associated with sheets and filaments, \none believes, according to hydrodynamical simulation and theoretical investigations, \nthat they are formed on the border of the largest scale structure. \n\n\nThe properties of the considered shocks like the shock position and its velocity, $u$, \ncan also be derived through numerical simulations. In particular, shocks around \nclusters are typically described by $u \\sim 1000$ km/s (Kang et al. 1996). \nIn the case of larger structure, one only assumes that the accretion velocity \nonto a galaxy wall should be consistent with galaxy streaming velocity. Thus, for \n equipartition $\\sim 0.1 \\mu$G magnetic field the \n accreting matter velocity $u\n\\sim 400$ km/s is comparable to the characteristic turbulent velocity (Kulsrud et al.\n1997). This value is consistent with the bulk flow motion of field spiral galaxies\n(Giovanelli et al. 1998; Dekel 1994). Determined simultaneously by observations,\nthe gravitational instability theory and the numerical simulations, the coherent estimate \nof streaming motion velocities give values of $250 \\pm 40 $km/s at a distance \nof 10 Mpc from LSC plane. The simulations and analytic approach suggest their increase at the \nsmaller scales of order of a few Mpc (R. Juszkiewicz, private comm.). Thus the value \nof 400 km/s at the shock location seems to be reasonable. \nBelow, for the discussed accretion flow/shock structures we will derive spectra \nof accelerated high energy protons with the use of a simplified one dimensional \nmodel.\n\n\n\n\\section{A model of stationary acceleration}\n\n Let us consider a 1D\nsteady-state symmetric model for UHE CRs acceleration (Fig.~1). \nWe assume that seed particles are provided for the cosmic rays acceleration\nmechanism by the galaxies concentrated\nnear the central plane of a flattened supergalactic structure. On\nboth sides this structure is accompanied by planar shock waves (Fig.~1).\nFor numerical estimates we locate the shocks at the distance $x_0 \\sim 3$ Mpc\n from the supergalactic\nplane and for the accreting matter velocity we assume \n $u\n\\sim 400$ km/s.\n Then, for an order of $0.1$ $\\mu$G supergalactic \nmagnetic field,\n the diffusive description can be still valid for\nparticles with energies reaching $10^{20}$ eV (Blasi et al. 1999; Sigl et al. 1999).\nFor a finite extent of an acceleration region, in order to obtain the power-law \nparticles' distributions,\n one can assume \n a particle\nspatial diffusion coefficient $\\kappa$ to be a constant. As one cannot\nexpect this simplification to hold in real objects, the obtained\nsolutions should be treated as approximations valid in a limited energy\nrange.\n% (In reality, as disscused later, the turbulent magnetic field energy\n% density attains its \n%maximum at the shock location, leading to reduced value for the diffusion \n%coefficient.)\n\n The considered diffusive transport equation for cosmic ray phase space \n distribution function, $f(x,p)$, \ncan be written in the form\n\n\\be\n{u(x) {\\partial f \\over \\partial x} - \\kappa {\\partial^2 f \\over\n\\partial x^2} - {1 \\over 3} {\\partial u(x) \\over \\partial x} p {\\partial\nf \\over \\partial p} = Q(x,p)} \\quad ,\n\\ee\n\n\\noindent\nwhere\n\\begin{itemize}\n\n\\item a monoenergetic source is given in the central plane $x = 0$ by\n$Q(x,p)=Q_0\\delta(x) \\delta(p-p_0)$,\n\n\\item the velocity $u(x) = u_1(x) = - u_1 sgn(x)$ of accreting matter in both regions\nupstream of the shock ($\\mid x \\mid > x_0$) is assumed to be constant,\n\n\\item the velocity $u(x) = u_2(x)$ in the internal region of the\nstructure -- downstream of both shocks ($\\mid x \\mid < x_0$) -- is\nLinearly decreasing towards the central plane to model the plasma\ncompression process accompanying the structure formation inside the\nsupercluster. With the normalization constant $C$ defined by the shock\ncompression ratio $r$ -- $\\mid u_2(x_0) \\mid \\equiv C x_0 = u_1 / r$ -- it can be\nwritten as\n\n$$ u_2(x) = - C \\, x \\quad , $$\n\n\\item $\\kappa$ is the CR diffusion coefficient. It is taken constant in\nthe whole space to enable an analytic solution of Eq.~1~, which is the\npower-law in particle momentum.\n\n\\end{itemize}\n\n\\noindent\nThe free-escape boundaries are given at $x = \\pm L$ :\n\n\\be\nf(-L,p) = 0 = f(L,p) \\quad .\n\\ee\n\n\\noindent\nOne requires continuity of both, the proton distribution $f(x,p)$ and the\ndifferential particle flux\n\n\\be\nS(x,p) \\equiv -4\\pi p^2 \\left\\{ {u_i \\over 3} p {\\partial f \\over\n\\partial p} + \\kappa {\\partial f \\over \\partial x} \\right\\}\n\\ee\n\n\\begin{figure} % Fig. 1 \n\\vspace{5.5cm}\n\\special{psfile=ms8663.f1 hscale=45.0 vscale=45.0 hoffset=-45\nvoffset=-95}\n\\caption[ ]{A simplified symmetric supergalactic accretion flow model\nconsidered in the present paper. The involved spatial positions of\naccretion shocks at $\\pm x_0$ and of particle escape boundaries at $\\pm\nL$ are indicated with dashed lines. An inflow velocity plot is superposed on\nthis spatial structure.} \\end{figure}\n\n\\noindent\nat the shocks ($x = \\pm x_0$) and continuity of $f(x, p)$ in the central\nplane:\n\n\\be\n[f]_{x=\\pm x_0} = 0 = [f]_{x=0} \\quad ,\n\\ee\n\n\\be\n[S]_{x=\\pm x_0} = 0 \\quad .\n\\ee\n\n\\noindent\nAt the central plane a flux discontinuity occurs due to the source\nterm\n\n\\be\n[S]_{x=0} = -4\\pi p_0^2Q_0 \\delta (p-p_0) \\quad .\n\\ee\n\nFor positive $x$ a solution of Eq.~1 can be found in a separable form\n$f(x,p) = G_i(x) A(p)$, where we put $i = 1$ ($2$) for $x > x_0$ ($x < x_0$), \nthrough the succesive application of the above conditions. For negative\n$x$ the solution is provided by the symmetry $f(-x,p) = f(x,p)$ (cf.\nFig.~1). In the upstream region, $x_0 < x < L$, we obtain\n\n\\be\nG_1(x) = \\exp \\left [ {u_1 \\over \\kappa} (L-x) \\right ] -1 \\quad .\n\\ee\n\n\\noindent\nIn the downstream region ($0<x<x_0$) the solution is expressed by the\nhypergeometric confluent function (Abramovitz \\& Stegun 1965)\n\n\\be\nG_2(x) = {}_1F_1 \\left[ -{\\sigma \\over 6}, {1 \\over 2}, {C x^2 \\over 2\\kappa}\n\\right] \\quad .\n\\ee\n\n\\noindent\nThe resulting particle momentum spectrum for $p>p_0$ has the power-law\nform\n\n\\be\nA(p) \\propto \\left( {p \\over p_0} \\right)^\\sigma \\quad .\n\\ee\n\n\\noindent\nIn order to derive the spectral index $\\sigma$, one has to match (Eq-s~4 and 5)\nthe above solutions at the shock. After introducing the new\ndimensionless variables $\\rho$ and $\\psi$,\n\n$$\\rho = {Cx_0^2 \\over 2\\kappa} \\quad , \\quad \\psi = {L \\over x_0} \\quad\n, $$\n\n\\noindent\none gets a non-algebraic equation for $\\sigma$,\n\n\\bea\n{\\sigma \\over 3} \\, & + & \\left[ {r \\over (1+r)} {\\exp[2r\\rho(\\psi-1)]\n\\over \\exp[2r\\rho(\\psi-1)] -1} \\right. \\nonumber \\\\\n& - & \\left. {{\\sigma \\over 3} \\over (1+r)} {_1F_1[1-{\\sigma \\over 6},\n{3\\over2}, \\rho] \\over _1F_1[-{\\sigma \\over 6}, {1\\over2}, \\rho]}\n\\right] = 0 \\quad ,\n\\eea\n\n\\noindent\nto be solved numerically. Apart from the compression $r$ ($\\equiv u_1/C\nx_0$) the solution $\\sigma(\\rho, \\psi, r)$ is parametrized by the two\nadditional parameters. The quantity $\\rho = C x_0 {x_0 \\over 2 \\kappa} =\n{u_2(x=x_0) \\over u_{diff}(x_0)}$ may be regarded as the ratio of the\nflow velocity to the CR `diffusion' velocity at the shock spatial scale. The\n$\\psi$ variable gives the confinement volume `size' measured in the shock\ndistance units.\n\nIn order to visualize the resulting spectrum inclination we have\nplotted the spectral index as a function of $\\psi$ for a few values\nof the compression ratio $r$ and the parameter $\\rho$ (Fig.~2). For the \n size of the particle confinement volume of order\nof a few shock distances $x_0$, the spectral changes are\ninsignificant, provided the diffusive approach is valid $\\rho \\psi \\sim u_1 L / \\kappa \\gg 1$.\n The\nmain observed feature is a rapid spectral index flattening to its\nlimiting value $\\sigma = -3.0$ due to inefficient particle escape from\nthe `acceleration volume'. \nThe shock compression is less significant in determining $\\sigma$ (!).\nOn the other hand one\nhas to note its essential dependence on $\\rho$, in particular for\nsmall values of $\\rho$ ($< 1$) admitting for noticeable spectral\nchanges. \n \n\n\\begin{figure} % Fig. 2\n\\vspace{11.5cm}\n\\special{psfile=ms8663.f2 hscale=50.0 vscale=50.0 hoffset=0\nvoffset=-30}\n\\caption[ ]{The spectral index $\\sigma$ versus the spatial scale\n$L/x_0$. The results are presented for various $\\rho = C x_0 {x_0 \\over\n2 \\kappa}$ and two compressions, $r = 4$ (solid lines) and $r = 2$\n(dashed lines), as indicated in the figure.}\n\\end{figure}\n\nIn the asymptotic regime $\\rho \\gg 1$, i.e. when the particle advection\nterm dominates over the diffusive one at $\\mid x \\mid < x_0$~, Eq.~10\nreduces to\n\n\\be\n\\sigma \\approx -3 \\left[ {r \\over r+1} \\; {\\exp \\left( {u_1 \\over\n\\kappa} (L-x_0) \\right) \\over \\exp \\left( {u_1 \\over \\kappa} (L-x_0)\n\\right) -1} + {1 \\over 1+r} \\right] \\quad .\n\\ee\n\n\\noindent\nIn this limit, with diffusive particle\nescape against the flow substantially reduced,\n the resulting index value is close to -3.0, as the\nacceleration results both due to the shock compression and the plasma\nconvergent flow toward the supergalactic plane. On the other hand, if\n$\\rho \\ll 1$, Eq.~10 leads to\n\n\\be\n\\sigma \\approx\n-3 \\, {\\exp[2r\\rho(\\psi-1)] \\over \\exp[2r\\rho(\\psi-1)] -1} \\approx\n-3 \\, {\\kappa \\over u_1 (L-x_0)} \\quad , \\quad\n\\ee\n\n\\noindent\nprovided that $2 r \\rho (\\psi-1) \\equiv u_1(L-x_0)/\\kappa \\ll 1$.\n\n\nRequirement of the diffusive description validity yields the\nlower limit for the considered $\\rho$. Since the mean free path for \nproton, $l < x_0$, \nthe inequality holds $\\kappa < {1 \\over 3} c x_0 $. Thus\n$\\rho > {u_1 \\over c \\, r} \\sim {1 \\over 3} 10^{-3}$, where $c$ is the\nlight velocity. \n\n\n\\section{Discussion}\n\nThe spectrum of accelerated CR protons may either become very flat or steepen \naccording to the value of $\\rho$ parameter. As it was seen in Fig.~2 which \nrepresents the solution of Eq.~10 or directly, through its asymptotic solutions, \nEq.~11 and Eq.~12; $\\rho$ controls the spectrum inclination. On the other hand \nit depends on the diffusion coefficient. The critical value of $\\rho = 1$ separates \ntwo distinct spectra regimes. For $\\rho \\geq 1$ the spectral index saturates \nrapidly at the \nvalue of -3 (see Fig.~2) due to the compressive accretion flow predominance. \nBelow the critical value, i.e. in the case of \"diffusion \nvelocity\" greater than the inflow motions, the spectral changes can be attributed \nmainly to diffusion coefficient value. For the above considered parameters \n of $ u_1 = 400$ km/s, $x_0\n\\approx 3$ Mpc, $r = 2$, the critical value of the diffusion coefficient \ncorresponding to $\\rho_{cr}$ is $\\kappa^* = 10^{32}$ cm$^2$/s. \nFor $\\kappa < \\kappa^*$, we get the hard spectrum with $\\sigma = -3$, while for \n$\\kappa > \\kappa^*$ the spectrum steepens.\n\nTo estimate the maximum energy possible to achieve, let us first remind the \nrough dimensional restriction demanding the particle orbit should be smaller than \nthe acceleration size $L$. In fact the realistic spectrum requires the diffusion \nlength $\\kappa \\over u$, is smaller than $L$. For Bohm diffusion it gives the \nlimitation for Larmor radius $r_g \\leq 3 L (u / c) $, equivalent to $r_g \\leq 50 $ kpc \nwhich implies $E \\leq$ few $10^{18}$ eV. \nHere, we considered the\ntotaly chaotic magnetic field, where the Bohm diffusion gives the appropriate \ndescription and took for turbulent magnetic field strength $B \\approx 0.1$ $\\mu$G \nand $L = 10 $ Mpc.\nThis random magnetic field component is associated with turbulent motion which occurs \nsimultaneously with streaming accretion motion at the shock vicinity, which in \nturn generates its ordered component.\n\nThe planar \nsymmetry of the model, with correlated magnetic field inside the large scale \ncosmic structure, can make the diffusion \nhighly anisotropic. Therefore for $B$ aligned with supercluster plane, as \nrequired by Ryu at al. (1998), the cross-field \n diffusion for a quasi-perpendicular shock should be considered. \nThe minimum diffusion coefficient in the perpendicular shocks, derived by\nJokipii (1987), is \n $\\kappa_{J} = \n3 \\,{u_1 \\over c}\\, \\kappa _B$. \n Without \nentering into the topological characteristics of magnetic fields near the cosmic \nstructure we only put here the value of critical diffusion coefficient referring \nseparately to both magnetic field components and then compare the respective\n maximum energy. Above, it was clear that for entirely turbulent field, the UH \nenergies can be hardly achieved.\nContrary to that, for $B$ strongly aligned \nwith the structure, the diffusion can be reduced up to $({u_1 \\over c})^{-1} \\sim 10^3$ \ntimes with respect to the Bohm diffusion. Thus, for critical diffusion with $\\kappa_{J} = \\kappa ^*$ \none obtains for the Larmor radius $r_g \\sim 10^{25}$ cm, which corresponds to \n$E_{max} \\sim 10^{21}$ eV. The latter case gives also the flatter spectrum.\n\n\n\nThe application of this model to galaxy cluster inflow is even more suitable, \n since its spherical accretion symmetry will cause the \nacceleration process to be more efficient than in the planar case.\nAdopting the same argument as used above for supercluster case, let us consider \n the typical physical parameters\nfor a galaxy cluster: accretion velocity \n $u_1 = 2 \\cdot 10^3$ km/s, an upper limit for magnetic field \n $B \\approx 1$ $\\mu$G and $x_0\n\\approx 3$ Mpc. Thus, for the Bohm diffusion one obtains for \nparticle gyroradius $r_g \\leq 1.8 \\cdot 10^{23}$ cm. The maximum energy can reach \nthe value of $10^{20}$ eV \n and even larger for the Jokipii diffusion model.\n\n\nFinally, to make sure that such scenario may serve as a viable acceleration \nprocess, let us confront the resulted maximum proton energy with that, when \nthe energy losses are included. For UHE protons, \n acceleration in the astrophysical shock is governed \nby the equation $dE/dt = E/\\tau_{acc}$. The losses above $10^{19}$ eV \n are mainly due to pair (e$^{\\pm}$) \nand photomeson production. Both, the mean acceleration time and \nthe timescale for losses, $\\tau_{loss}$, has been considered in many papers. \nTheir equality gives the maximum energy up to which the particles can be accelerated. \nHere, \nwe use the results \ncalculated and plotted by Kang et al. (1997). In their Fig.~2 the intersection point of the\n curves \ndetermines the maximum energy achievable in acceleration process. Taking into \nconsideration the diffusion in a quasi-perpendicular case, the acceleration time \n$\\tau_{acc}$ scales like (Kang et al. 1997) $\\tau_{acc} \\propto u^{-1} B^{-1} $, \n to yield the maximum energy of $10^{19.6}$ eV. \n\nWe have to note \n that in our model the acceleration time will be smaller than the one estimated\n by \nKang et al. (1997) and the\nthe maximum energy can be greater. This is due to the presence of two \nshocks associated with the compression inflow structure \nmaking the particle escape more difficult. \nIn fact, we should consider the acceleration time estimated as \n$\\tau ^{-1}_{acc} = {\\tau_{s}}^{-1} \\, + \\, {\\tau_{c}}^{-1}$ , where \n$\\tau_{c} = {p \\over {{1 \\over 3} p {\\partial u(x) \\over \\partial x}}} \n={ 3 \\, x_0 \\over u_2} \\,$ is the acceleration time scale due to adiabatic \nacceleration in the compressive flow and $\\tau_s$ is the scale for the shock \nacceleration. Here, with the numerical parameters given above, we ignored \nthe second term since it is comparable to the age of universe. However, it must be \nincluded when both $\\tau_{s}$ and $\\tau_{c}$ are of the same order. \n\n\n\n\n\\section{Conclusions}\n\nWe demonstrated that the diffusive acceleration in the accretion flow onto the\ngalaxy supercluster can provide an extremely hard spectrum of\naccelerated UHE protons. It is a consequence of particle confinement in the\nconverging flows, involving the plasma inflow towards the structure\ncentral plane with embedded shocks. One should note that in such\nconvergent flows the particle acceleration process can proceed even\nwithout shocks. Thus a possibility of a significant deviation of the UHE\nCR spectral index from the often considered shock index, $\\sigma_0 =\n3r/(r-1)$, arises in a natural way. \nThis fact should be included in modelling -- based on acceleration in\nsupergalactic accretion flows -- of the most energetic cosmic rays'\ncomponent observed at Earth.\n\nOf course, the considered above a symmetric planar model is a substantial\nsimplification. A divergence of the spectrum from the derived $\\sigma\n\\approx -3.0$ may arise if particles easily escape from the structure,\n$u_1 L < \\kappa$, or additional particle sinks appear. The latter \nmay be a result of particle escape from the accretion flow along\nthe supergalactic structure, extending to the sides at distances larger\nor comparable to its vertical scale $L$. In both cases, the generated\nspectral index -- the one in the acceleration site -- is expected\nto grow with particle energy and efficiency of the acceleration process\ndecreases. \n\n\\begin{acknowledgements} \nWe are grateful to Dr. Z. Golda for his assistance in \"Mathematica\"\napplication and to the anonymous referee for his valuable \ncomments and suggestions. This work was supported from the `Komitet Bada\\'n\nNaukowych' through the grants No. 2 P03D02210 (GS-O) and PB 179/P03/96/11\n(MO) and its latest version through 2 P03B 112 17.\n\\end{acknowledgements}\n\n\n\\section*{References} \n\n\\parskip=0pt \n\\parindent=7mm\n\\noindent\nAbramovitz M., Stegun I., 1965, Handbook of \\par Mathematical Functions;\n Dover, New York \\\\\nBlasi P., Olinto A., 1999, Phys. Rev.D 59, 023001 \\\\\nBertschinger E., 1985, ApJS, 58, 39 \\\\\nCen R., Ostriker J., 1994, ApJ, 429,4 \\\\\nDekel A., 1994, ARA\\&A, 32, 371 \\\\\nEnsslin T., Biermann P., Klein U., Kohle S., 1998a, A\\&A, \\par 332, 395 \\\\\nEnsslin T., Biermann P., Klein U., Kohle S., 1998b, in \\par Proc. VII Int.\n Conf. and Lindau Workshop on Plasma \\par Astrophys. and Space Phys.,\n in press (astro-ph \\par /9805367) \\\\\nGiovanelli R. et al., 1998, ApJ Lett., 505, L91 \\\\\nJokipii J., 1987, ApJ, 313, 842 \\\\\nKang H., Rachen J., Biermann P., 1997, MNRAS, 286, \\par 257 \\\\\nKang H., Ryu D., Jones T., 1996, ApJ, 456, 422 \\\\\nKim K., Tribble P., Kronberg P., 1991, ApJ, 355, 29 \\\\\nKronberg P.,1994, Rep. Prog. Phys., 57, 325 \\\\\nKulsrud R., Cen R., Ostriker J., Ryu D., 1997, ApJ, 480, \\par 481 \\\\\nLapparent V., Geller M., Huchra J., 1991, ApJ, 369, 273 \\\\\nLee S., Olinto A., Sigl G., 1995, ApJ, 455, L21 \\\\\nMedina Tanco G., 1998, ApJ Lett., 505, L79 \\\\\nRyu D., Kang H., Biermann P., 1998, A\\&A, 335, 19 \\\\\nRyu D., Ostriker J., Kang H., Cen D., 1993, ApJ, 414, 1 \\\\ \nSigl G., Lemoine M., Biermann P., 1999, Astropart. Phys., \\par 10, 141 \\\\\nSoltan A., Hasinger G., Egger R., Snowden S., \\par Tr\\\"{u}mper J., 1996, A\\&A, 305, 17 \\\\\nStanev T., Biermann P., Lloyd-Evans J., Rachen J., Wat- \\par son A., 1995,\nPhys. Lett., 75, 3056 \\\\\nValee J., 1990, Astron. J., 99, 459 \\\\\nValee J., 1997, Fund. Cosm. Phys., 19, 1 \\\\\n\n\\end{document}\n\n\n"
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"name": "gsum.tex",
"string": "\\begin{table}[h]\n\\def\\arraystretch{1.2}\n\\centering\n\\begin{tabular}{ll}\n \n\\hline\n$I(10^5<N_e<1.15\\cdot10^6)$ & $(8.95\\pm 0.18)\\cdot10^{-11}(N_e/10^5)^{\\gamma_1}$\\\\\n$I(N_e>2.56\\cdot10^6)$ & $(3.23\\pm 0.40)\\cdot10^{-13}(N_e/10^6)^{\\gamma_2}$\\\\\n$\\gamma_1$ & $-2.54\\pm 0.012 $\\\\\n$\\gamma_2$ & $-2.94\\pm 0.042$ \\\\\n$\\Delta (N_{e_k})$ & ($1.15\\pm 0.034)\\cdot10^6$ \\ - \\ $(2.56\\pm 0.063)\\cdot10^6$ \\\\\n$N_{e_k}$ & $(1.75\\pm 0.05) \\cdot 10^6$\\\\\n$I(N_{e_k})$ & $(5.83\\pm 0.14)\\cdot 10^{-14}$\\\\\n\\hline\n\\end{tabular}\n\\caption{\\it Flux $[m^{-2}s^{-1}sr^{-1}]$ and knee region parameters \nof the size spectra measured with the MAKET ANI array.} \n\\label{gsum1}\n\\end{table} \n \n"
},
{
"name": "gtab.tex",
"string": " \n\\begin{table}[h]\n%\\vspace{-0.25cm}\n\\centering\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n Min.depth & \\multicolumn{2}{c|}{MAKET ANI} & \n\\multicolumn{2}{c|}{ANI+KASCADE}& \\multicolumn{2}{c|}{KASCADE} \\\\\n\\hline\n$X_0,g\\cdot cm^{-2}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ & $ \\Lambda_{int}$ & \n$ \\Lambda_{dif}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ \\\\\n\\hline\n$ 700$ & $248\\pm27$ & $247\\pm42$ & $203\\pm10$ & $203\\pm13$ & $ - $ & $ - $\\\\ \n\\hline\n$ 758$ & $236\\pm32$ & $237\\pm51$ & $195\\pm8$ & $196\\pm12$ & $ - $ & $ - $\\\\ \n\\hline\n$ 816$ & $211\\pm43$ & $218\\pm70$ & $186\\pm9$ & $188\\pm13$ & $ - $ & $ - $\\\\ \n\\hline\n$1020$ & $ - $ & $ - $ & $ - $ & $ - $ & $181\\pm14$ & $182\\pm23$\\\\ \n\\hline\n\\end{tabular}\n\\caption{\\it Attenuation lengths for the data from the \nMAKET ANI and KASCADE installations estimated\n by the CIC method from differential and integral size spectra}\n \\label{gtab1}\n\\end{table} \n%\n\\begin{table}[h]\n\\vspace{-0.15cm}\n\\centering\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n Min.depth & \\multicolumn{2}{c|}{MAKET ANI} & \n\\multicolumn{2}{c|}{ANI+KASCADE}& \\multicolumn{2}{c|}{KASCADE} \\\\\n \\hline\n$X_0,g\\cdot cm^{-2}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ & $ \\Lambda_{int}$ &\n$\\Lambda_{dif}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ \\cr\n\\hline\n$ 700$ & $239\\pm14$ & $240\\pm15$ & $191\\pm11$ & $193\\pm13$ & $ - $ & $ - $\\\\ \n\\hline\n$ 758$ & $232\\pm13$ & $228\\pm19$ & $186\\pm10$ & $184\\pm17$ & $ - $ & $ - $\\\\ \n\\hline\n$ 816$ & $213\\pm14$ & $219\\pm27$ & $179\\pm11$ & $181\\pm24$ & $ - $ & $ - $\\\\ \n\\hline\n$1020$ & $ - $ & $ - $ & $ - $ & $ - $ & $181\\pm7$ & $183\\pm11$\\\\ \n\\hline\n\\end{tabular}\n\\caption{\\it Attenuation lengths for the data from the \nMAKET ANI and KASCADE installations estimated\n by the recalculation from the absorption length for differential and \n integral size spectra}\n\\label{gtab3}\n\\end{table}\n%\n\\begin{table}[h]\n\\vspace{-0.15cm}\n\\centering\n\\begin{tabular}{|c|c|c|c|c|c|c|} \n\\hline\n Min.depth & \\multicolumn{2}{c|}{MAKET ANI} & \n\\multicolumn{2}{c|}{ANI+KASCADE}& \\multicolumn{2}{c|}{KASCADE} \\\\\n\\hline\n$X_0,g\\cdot cm^{-2}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ & $ \\Lambda_{int}$ &\n$\\Lambda_{dif}$ & $\\Lambda_{int}$ & $\\Lambda_{dif}$ \\cr\n\\hline\n$ 700$ & $302\\pm71$ & $295\\pm83$ & $241\\pm17$ & $237\\pm15$ & $ - $ & $ - $\\\\ \n\\hline\n$ 758$ & $272\\pm51$ & $263\\pm42$ & $242\\pm20$ & $221\\pm17$ & $ - $ & $ - $\\\\ \n\\hline\n$ 816$ & $ - $ & $ - $ & $225\\pm21$ & $225\\pm19$ & $ - $ & $ - $\\\\ \n\\hline\n$1020$ & $ - $ & $ - $ & $ - $ & $ - $ & $232\\pm26$ & $222\\pm28$\\\\ \n\\hline\n\\end{tabular}\n\\caption{\\it Attenuation lengths for the data from the MAKET ANI and\nKASCADE installations, estimated\n by the \"attenuation of knee position\" method from differential and integral size spectra}\n\\label{gtab2}\n\\end{table}\n"
},
{
"name": "paper.tex",
"string": "%*********************************************** ANI99 STYLE\n\\documentclass[11pt,dvips]{article}\n\\usepackage{epsfig}\n\\usepackage{wrapfig}\n% Setting various length parameters (DO NOT ALTER):\n\\setlength{\\textheight}{9in}\n\\setlength{\\textwidth}{6.63in}\n\\setlength{\\hoffset}{-0.2in}\n\\setlength{\\voffset}{0.37in}\n\\setlength{\\topmargin}{-15pt}\n\\setlength{\\headheight}{12pt}\n\\setlength{\\headsep}{10pt}\n\\setlength{\\oddsidemargin}{0in}\n\\setlength{\\evensidemargin}{0in}\n\\setlength{\\parindent}{3ex}\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\\renewcommand{\\bottomfraction}{0.999}\n\\renewcommand{\\topfraction}{0.999}\n\\renewcommand{\\textfraction}{0.001}\n\\setcounter{secnumdepth}{4} \n\\pagestyle{empty}\n\n\\begin{document}\n\\begin{center}\n \n \n%*********************************************\n\n{\\LARGE \\bf Determination of the EAS Attenuation Length from Data \nof the ANI Experiment} \n\\end{center}\n\n\\begin {center}\n{\n\\bf A.A. Chilingarian, G.V. Gharagyozyan, S.S. Ghazaryan, \nG.G. Hovsepyan, \\\\ E.A. Mamidjanyan,\nL.G. Melkumyan, S.H. Sokhoyan\\footnote{corresponding \nauthor: e-mail: [email protected]}\\\\\n}\n{\\it{Yerevan Physics Institute, Cosmic Ray Division, Armenia.}}\n\\end{center}\n\n\\vspace{1ex}\n\\begin{center}\n\\begin{minipage}[c]{5.5in}\n%\nUsing the EAS size spectra measured with the MAKET ANI \narray on Mt. Aragats, Armenia ($3200m$ a.s.l.- $700 g\\cdot cm^{-2}$) \nin the range of $N_e = 10^5 - 10^7$ for different \nangles-of-incidence, the EAS attenuation length has been \ndetermined applying different analysis methods. \nThe analysis is based on a data sample of $2.5 \\cdot 10^6$ events \ncollected in the period of June, 97 - April, 99. \nThe results are compared with results deduced from data of the \nEAS TOP and KASCADE experiments.\n\\end{minipage}\n\\end{center}\n\\vspace{1ex}\n\n\\section {Introduction}\nThe intensity of Extensive Air Showers (EAS) with fixed shower \nsizes $N_e$ is assumed to decrease exponentially with increasing \natmospheric depth of the observation level. This is considered to \nbe due to the absorption of the particles of the EAS \ncascade following an exponential law \n\\begin{equation}\\label{cascade} \nN_e(X)=N_e(X_0)exp{\\left(-\\frac{X-X_0}{\\Lambda}\\right)}, \n\\,\\,\\,\\, {\\rm with}\\,\\, X \\geq X_0 .\n\\end{equation}\n$X_0$ is a definite initial atmospheric depth after the maximum \nof the longitudinal development where the number of (charged) \nparticles is $N_e(X_0)$ and further decreasing exponentially, \n$N_e(X)$ is the number of particles of the EAS at the slant \ndepth $X[g \\cdot cm^{-2}]$. \\\\\nThe quantity $\\Lambda$ controls the attenuation of particles of the individual cascade \n\\cite{hayakawa} {\\it (size attenuation \nlength)}. It is related to the inelastic cross sections (to the \nmean free path length $\\lambda_A$) of the interaction of the \nprimary cosmic ray particles with air nuclei. The attenuation of \nthe flux intensity of Extensive Air Showers is characterized by \na related quantity $\\lambda_N$ {\\it (intensity attenuation length, absorption)}, \nwhich can be directly measured by cosmic rays detector arrays. \nThus measurements of the attenuation of the EAS intensity in the \natmosphere are considered to be an interesting source of \ninformation about hadronic interactions, especially if extended \nto the ultrahigh energy region expected \nfrom the forthcoming LHC and TESLA accelerators. In addition due \nto the sensitivity of the cross sections to the mass of the \nprimary, alterations of the attenuation length with the energy \nmay be indicative for the variations of the mass composition. \nMeasured results imply tests of the energy dependence of the \nextrapolated cross sections used for Monte Carlo simulations. \\\\\nThe investigations of the present paper are based on an EAS \nsample measured 1997-1999 with the MAKET ANI array\n\\cite{avak,hovsep98} on Mt. Aragats station (Armenia) and \nregistered for different angles-of-incidence in the zenith angle \ninterval $\\Theta = 0 - 45^\\circ$. The data basis of the analysis \ncan be enlarged by published data from KASCADE $(1046\\, g \\cdot cm^{-2})$ \n\\cite{kascade} and EAS TOP $(810\\, g \\cdot cm^{-2})$ \\cite{top1} \nexperiments. Spectra measured by EAS TOP are given in Ref. \n\\cite{top2}. Data and zenith angle dependence for KASCADE results \nare obtained by scanning the spectrum plots communicated by \nthe KASCADE collaboration \\cite{ralf1}. \\\\\nWe apply different procedures to deduce the attenuation. \nFirst we consider the degradation of the EAS flux with fixed \nshower size $N_e$ with increasing zenith angle i.e. increasing \natmospheric thickness of the shower development (characterized \nby the intensity attenuation length ($\\lambda_N$) \\cite{khris}). \nDifferently the technique of the constant intensity cut (CIC) \n\\cite{nagano} considers the intensity spectrum of EAS events \nand relates equal intensities observed at different atmospheric \ndepths. \n\nThere is the tacit assumption that the shower size \nreflects the energy of the primary. The procedure can be \nrefined by using the knee position in the $N_e$ spectrum as a \nbench mark for a well defined energy, so far we may associate \nthe knee phenomenon to a feature of the primary energy \nspectrum of cosmic radiation.\n\n\\section{Experimental spectra} \nThe experimental basis of the present investigations are \nmeasurements of shower size spectra in the knee region and their \nzenith-angle dependence performed with the MAKET ANI array of the \nMt. Aragats Cosmic Ray Station (3200 m a.s.l.) in Armenia. \nDetails of the measurements and the experimental procedures \ntaking into account the detector response are given elsewhere \n\\cite{gagik,hovsep99}. For a detailed description of the knee \nregion the traditional approximation with two different spectral \nindices below and above the knee, defining the knee position as \nintersection of two lines in a logarithmic presentation, \nappears to be insufficient. Hence a more sophisticated method \nhas been applied with parameterization of the slope of the spectra \n(see Ref.\\cite{serg1}). \\\\ \nTab.1 compiles the characteristics of the size spectra measured \nwith the MAKET ANI installation, the changes of the slopes in the \nknee region ($\\Delta N_{e_k}$), expressed by different spectral \nindices below ($\\gamma_ 1$) and above ($\\gamma_ 2$) the knee \nposition $N_{e_k}$ for the zenith-angle range of $\\Theta = 0 -\n45^\\circ$. For the display and the analysis of the zenith-angle \ndependence, the size spectra are determined in 5 angular bins \nof equal $\\Delta\\sec\\Theta$ widths. The accuracy of the zenith \nangle determination is estimated to be about $1.5^\\circ$ \n\\cite{gagik}. A correction due to barometric pressure changes, \nwhich lead to small fluctuations of the atmospheric absorption, \nhas not been made. Figure \\ref{makasdif} displays the spectra \nof mean values of each atmospheric depth bin and compares with \nthe results from EAS-TOP \\cite{top2} and KASCADE \\cite{ralf1} \nexperiments. \\\\\n\\input gsum\n%\n\\begin{figure}\n\\begin{minipage}[t]{0.48\\linewidth}\n\\epsfig{file=spcdifall.epsi,width=8.cm,height=8.cm} \n\\vspace{-.5cm}\n\\caption{\\label{makasdif} \\it{Differential size spectra for \ndifferent zenith angles ranges observed with MAKET ANI array, \ncompared with spectra reported by the KASCADE \\cite{ralf1} and \nthe EAS TOP \\cite{top2} collaborations.}}\n\\end{minipage} \n\\hspace*{0.4cm}\n\\begin{minipage}[t]{0.48\\linewidth}\n\\epsfig{file=lincas8.epsi,width=8.cm,height=8.cm}\n\\vspace{-.3cm}\n\\caption{\\label{lincas8} \\it{$N_e$ cascade in the \nobserved range of the atmospheric slant depth.}}\n\\vspace{.5cm}\n\\end{minipage}\n\\end{figure}\n%\nFollowing fixed intensities of the experimental spectra \n(see sect.3.2) the average $N_e$ cascade development can be \nimmediately reconstructed as shown in Figure \\ref{lincas8}. \nNote that the results in the range of the slant depth observed \nwith the ANI array deviate from the exponential decrease \n(eq.\\ref{cascade}). That is an interesting feature which can be \nrevealed more clearly when combining spectra accurately measured \non different altitudes. In the present paper we base the \nformulation of the procedures estimating the attenuation on the \nexponential decrease (eq.\\ref{cascade}). It is our interest to \nexplore, if this assumption applied to the ANI and KASCADE data \nlead to consistent results.\n \n\\section{Procedures for inference of the attenuation length \\\\\nfrom size spectra}\nWe consider the differential and integral size spectra \n$I(N_e,X)$ and $I(>N_e,X)$, respectively. \nIn addition to the basic assumption of exponential attenuation \nof $N_e$ (eq.\\ref{cascade}) a power-law dependence of the size \nspectrum\n\\begin{equation}\nI(N_e,X)\\propto{N_e}^{-\\gamma},\n\\end{equation}\nwith the spectral index $\\gamma$ is adopted.\n\n\\subsection{\\boldmath Attenuation of the intensity of fixed $N_e$: \nabsorption length}\nFor different fixed values of shower size $N_e$, on different \ndepths in the atmosphere or/and different zenith angles of \nincidence, from measured spectra (see vertical dotted lines on \nFigure \\ref{spintgcic}) we obtain several values of corresponding \nintensities from the equivalent depths from 700 till 1280\n$g\\cdot cm^{-2}$. \nFitting the depth dependence of the intensities by the straight \nline (in logarithmic scale) according to equation:\n\\begin{equation}\nI(N_e,X)= I(N_e,X_0)exp\\left(-\\frac{X-X_{0}}{\\lambda_N}\\right) \n\\label{eq-abs} \n\\end{equation}\nwe obtain the estimate of the absorption length $\\lambda_N$. \nThe absorption length can be estimated both by integral and\ndifferential spectra.\n%\n\\begin{figure}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\vspace{.2cm}\n\\epsfig{file=spintgmakas.epsi,width=8.cm,height=8.cm}\n\\vspace{-.2cm}\n\\caption{\\label{spintgcic} \\it{Integral size spectra for different \nzenith angles ranges observed with MAKET ANI array, compared with \nspectra reported by the KASCADE \\cite{ralf1}: illustration of\nthe procedures for absorption and attenuation length estimates.}}\n\\end{minipage}\n\\hspace*{0.4cm}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\epsfig{file=xkndifintg.epsi,width=8.cm,height=8.cm}\n\\vspace{-.2cm}\n\\caption{\\label{xkn} \\it{The variation of the knee position \nwith the atmospheric depth.}}\n\\vspace{1.5cm}\n\\end{minipage}\n\\end{figure}\n%\n\\subsection{Constant intensity cut}\nThe basic idea of this procedure is to compare the average size of \nshowers which have the same rate (showers per $m^2 \\cdot s \\cdot sr$)\nin the different bins of the zenith angle of shower incidence and \ndifferent slant depth, respectively \\cite{nagano}. \\\\\nConsidering two different depths in atmosphere \n$X_{1}$,$X_{2} > X_{0}$ the expressions of differential\nintensities $I(N_e,X)$ has the form\n%\n\\begin{equation}\\label {eq-cic}\nN_e(X_1)^{-\\gamma}exp\\left[-\\left(\\gamma-1\\right)\\frac{X_1-X_{0}}{\\Lambda}\n\\right]=N_e(X_2)^{-\\gamma}exp\\left[-\\left(\\gamma-1\\right)\\frac{X_2-X_{0}}{\\Lambda}\\right]\n\\end{equation}\nWith simple transformations we obtain:\n\\begin{equation}\\label {cicdif}\n\\Lambda_{diff}(I)=\\frac{\\gamma-1}{\\gamma}\\frac{X_2-X_1}\n{ln\\left(\\frac{N_e(X_1)}{N_e(X_2)}\\right)}\n\\end{equation}\n%\nThe attenuation lengths, obtained by integral spectra do not depend \nexplicitly on spectral index:\n%\n\\begin{equation}\\label {cicint}\n\\Lambda _{int}(I)=\\frac{X_2-X_1}{ln\\left(\\frac{N_e(X_1)}{N_e(X_2)}\\right)}\n\\end{equation} \n%\nPractically the estimate of the attenuation length is obtained by \nfitting the $N_e$ dependence on the depth in atmosphere by the \nstraight line according to the equation (\\ref {cascade}). \nThe sequence of $N_e$ values is obtained according to the fixed \nvalues of the flux intensity, selected from the interpolation of \nthe differential or integral size spectra. \\\\\nFor each $N_e$ value, the slope index $\\gamma$ used in equation \n\\ref{cicdif}, is obtained by averaging over all used slant depths.\nSelecting equal intensities ($\\approx$ primary energies) \ncorresponding to different shower sizes $N_e$ and different \ndepths the value of $\\Lambda_{diff} (I)$ is estimated. \nIntensity values from $10^{-9}$ to $5.\\cdot 10^{-6}$\nwere used for CIC method.\n\n\\subsection{Attenuation of the size of the knee}\nA special variant of the constant intensity cut is to follow the \ndecrease of the shower size at a constant primary energy in the \nsize spectrum. Assuming that the knee phenomenon reflects a \nfeature of the primary flux, the variation shower size at the \nknee with the zenith angle provides the possibility to extract \nthe attenuation length. \\\\\nConsidering the assigned knee position of the data from various\nexperiments, differences within 30\\% are noticed for all X-bins. \\\\\nThe knee positions obtained by the differential and integral \nspectra are a bit shifted to the smaller $N_e$ values \n(see Figure \\ref{xkn}). The shift is approximately uniform over \nall investigated depths interval, therefore the estimates of \nthe attenuation length by the differential and integral \nsize spectra are very close to each other.\n\n\\subsection{The relation between the absorption and \nattenuation length}\nWe consider the quantity $I(N_e,X)dN_e$ - the number of EAS at\nthe depth $X$ which comprise $N_e$ to $N_e+dN_e$ particles: \n\\begin{equation}\nI(N_e,X)dN_e\\sim N_e^{-\\gamma}exp\\left[-\\left(\\gamma-1\\right)\n\\frac{X-X_{0}}{\\Lambda}\\right]dN_e \n\\end{equation}\n%\nWith eq.\\ref{eq-abs} we obtain:\n%\n\\begin{equation}\n\\Lambda_{diff}(N_e) = (\\gamma(N_e)-1)\\lambda_N,\n\\end{equation}\n%\nwhere, $\\gamma(N_e)$ is the differential size spectra index \n(here we indicate the $N_e$ dependence of the slope index explicitly). \nFor the integral spectra: \n%\n\\begin{equation}\\label {attfromabs}\n\\Lambda_{int}(N_e) = \\gamma(N_e)\\lambda_N,\n\\end{equation}\n%\nwhere, $\\gamma(N_e)$ is integral size spectra index. \\\\ \nFor the evaluation of the inelastic cross section and for \ncomparison of the three methods described above we propose to \nuse the calculated values of the attenuation length $\\Lambda$\n(instead of using absorption length $\\lambda_N$).\nThe attenuation of the number of particles in the individual \ncascade is more directly connected with the characteristics of the \nstrong interaction and is independent from the parameters of the\ncosmic ray flux incident on the atmosphere. In turn the absorption \nlength, i.e. the attenuation of the CR flux intensity, reflects also \ncharacteristics of the primary flux and is\ndependent on the change of the slope of the spectra. \n\n\\subsection{Estimate of the inelastic cross section} \nThe inelastic cross sections, of the primary \nnuclei with atmosphere nuclei is related by \\cite{nagano}: \n\\begin{equation}\n\\sigma^{inel}_{A-air}(mbarn) = \n\\frac{2.41\\cdot 10^4}{\\lambda_A(g\\cdot cm^{-2})}, \n\\end{equation}\nwhere A denotes the primary nuclei. The quantity $\\lambda_A$ is \nthe {\\it interaction length} of the A-nucleus in the atmosphere \n(note: in some publications the interaction length is \ndenoted by $\\lambda_N$, where N is primary nuclei, in contrast in this paper N is \nreserved for the shower size). \nThe interaction length \n$\\lambda_A$ is related with the absorption length $\\Lambda_A$ by \n%\n\\begin{equation}\n\\lambda_A = K(E) \\cdot \\Lambda_A\n\\end{equation}\n%\nThe K(E) coefficient reflects \npeculiarities of the strong interaction model used for simulation.\nThe value of the parameter K has to be determined by \nsimulations of the EAS development in the atmosphere. \nSuch studies require the development of procedures for the \nselection of EAS initiated by primaries of a definite type \n(see for example in \\cite{beam1,beam2}). \n\n\\section{Application to the data}\n\\label{disc.sec}\nThe mean values of the attenuation lengths obtained by various \nmethods from data of the ANI and KASCADE installations, \nas well as for the joint ANI \\& KASCADE data by\nthe differential ($\\Lambda_{diff}$) and integral spectra \n($\\Lambda_{int}$) are compiled in the Tables \n\\ref{gtab1},\\ref{gtab3},\\ref{gtab2}.\n\\vspace{0.15cm}\n\\input gtab \nThe alternative estimates of the attenuation length \nreflect the inherent uncertainties of the methods \nand the statistical errors, as well as the fluctuations of cascade \ndevelopment in the atmosphere, the \n%\n\\begin{figure}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\epsfig{file=lambintg3fit.epsi,width=8.cm,height=8.cm}\n\\vspace{-.4cm}\n\\caption{\\label{lamintgcas3} \\it{Attenuation Length dependence \non Spectra Intensity (Primary Energy).}}\n\\end{minipage}\n\\hspace*{0.4cm}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\vspace{-.5cm}\n\\epsfig{file=lamgtintg.epsi,width=8.cm,height=8.cm}\n\\vspace{-.4cm}\n\\caption{\\label{lamdif9} \\it{Attenuation Length dependence on \nthe Shower Size $N_e$.}}\n\\end{minipage}\n\\end{figure}\n%\n%\n\\begin{wrapfigure}[24]{r}{9.cm}\n\\vspace{-0.1cm}\n\\epsfig{file=makas2.epsi,width=9.cm,height=9.5cm}\n\\vspace{-0.4cm}\n\\caption{\\label{makas2} {\\it Attenuation length\nobtained by joint analysis of the MAKET ANI and KASCADE data.}}\n\\end{wrapfigure}\n%\nenergy dependence of \nthe inelastic cross section and possible changes in mass composition.\nAs obvious in Figure \\ref{lincas8}, the values\ncorresponding to the minimal equivalent depths of used MAKET ANI data, deviate \nsignificantly from the exponential decrease.\nThe observations reflects the flattening of the cascade curve \njust after the shower maximum in the altitude $500-600\\,g\\cdot cm^{-2}$. \nDue to these features the attenuation lengths calculated by \nMAKET ANI data appear to be \nsignificantly larger than those derived for the KASCADE \ndata (Tables \\ref{gtab1}, \\ref{gtab3}). \\\\\nTherefore, for the combined analysis of the KASCADE and ANI data \nwe omitted the first and the second zenith\nangle bins of MAKET ANI and calculate\nthe attenuation lengths by the remaining 9 (minimal equivalent depth \n$758\\,g\\cdot cm^{-2}$) and 8 (minimal equivalent depth $816\\,g\\cdot cm^{-2}$) \nangular bins. The dependences of estimated values of attenuation \nlength on the shower size and flux intensity for different \namount of the angular bins used, are displayed in Figures \n\\ref{lamintgcas3} (note, that higher intensities on the X \naxes correspond to the lower primary energies) and \\ref{lamdif9}. \nThe attenuation length estimates obtained from the differential \nand integral spectra agree fairly well.\nThe results of both CIC and recalculation from absorption \nlength agree within the error bars. \nThe results obtained by the \"attenuation of knee position\" are \nlarger for MAKET ANI and KASCADE.\nAs pointed out by S. Ostapchenko \\cite{ostap} it is the consequence of \nthe large EAS fluctuations with the tendency to\nshift the knee position to the lower energies \n(and correspondingly to higher fluxes) in a way to \"slow down\"\nthe cascade curve attenuation. \\\\\nWell below the shower development maximum starting from \n$816 g\\cdot cm^{-2}$ KASCADE and MAKET ANI\ndata could be fitted with one decay parameter\n(see Figure \\ref {makas2}). There is a concentration of the \nknee positions on the curve showing the dependence of \nthe attenuation of the flux\nintensity ($\\approx$ primary energy). \nIn turn, the curve displaying the dependence of the\nattenuation length on the shower size demonstrates a\nrather large dispersion of the \"knee positions\". These\nobservations in size\nand energy scales may be interpreted as an indication of the\nastrophysical nature of the knee phenomenon.\n\n\\section{Conclusion}\\label{conc.sec}\nExperimental studies of EAS characteristic like the depth of \nthe shower maximum $X_{max}$, the elongation rate \n$dX_{max}/dlog_{10}E$ and the attenuation length $\\Lambda$ are of \nparticular importance, since they map rather directly basic \nfeatures of the hadronic interaction. Strictly, however, the \ninterpretation of these quantities in terms of hadronic cross \nsections cannot bypass the necessity of detailed calculations \nof the shower development. Nevertheless these type of EAS \nquantities, if compared with Monte Carlo simulation results, \nprovide stringent tests of the interaction model ingredients of \nthe simulations. \\\\\nThe recent results of various experimental installations are \nsufficiently accurate to enable relevant studies of this kind, \nand combining the data from arrays situated on different \naltitudes (like MAKET ANI and KASCADE) allows a large span in \nthe atmospheric slant depth for reconstructing the development \nof the charge particle size. In fact such studies, if using a \nsufficiently large data sample, could be continued in a more \ndetailed manner by separating the muon component and taking \ninto account the deviations from the exponential shape of \nthe cascade decline. The penetrating muon component \ncontributes with smaller attenuation to the development of \nthe considered charged particle component, but hardly with \nan exponential degrading (according to eq.\\ref{cascade}). \nActually by use of methods in progress to isolate different \nprimary groups (\"pure nuclear beams\") of the size spectra \n\\cite{beam2,gagik99}, these kind of interaction studies would get \nof extreme interest. \n\n \\vspace*{3.5ex}\n{\\noindent \\bf \\Large Acknowledgment \\\\}\n\\vspace*{-.5ex}\n\n{\\it \\noindent This publication is based on experimental \nresults of the ANI collaboration. The MAKET ANI detector installation has been \nset up as collaborative project of the Yerevan Physics Institute,\nArmenia and the Lebedev Institute, Moscow. The continuous \ncontributions and assistance of the Russian colleagues in operating \nthe detector installation and in the data analyses are gratefully \nacknowledged. In particular, we thank S. Nikolski and V. Romakhin \nfor their encouraging interest and useful discussions. \\\\\nFirst perspectives of combined considerations of the KASCADE \nand ANI experimental data have been discussed in 1998 during the \nANI-98 workshop in the cosmic ray observatory station Nor-Amberd \nof Mt.Aragats (Armenia). The MAKET ANI group would like to thank \nthe German colleagues for stimulating discussions and encouragement, \nin particular H. Rebel for his numerous valuable comments and \ninteresting suggestions to the topic of this paper. We acknowledge \nthe useful discussions with K.-H. Kampert, H. Klages and \nR. Glasstetter. The suggestions of S. Ostapchenko are highly \nappreciated. \\\\ \nThe work has been partly supported by the research grant \nNo.96-752 of the Armenian Government and by the ISTC project A116. \nThe assistance of the Maintenance Staff of the Aragats Cosmic Ray \nObservatory in operating the MAKET ANI installation is \nhighly appreciated.}\n\n%\\vspace*{-0.9cm} \n\\vspace*{-0.3cm} \n\n\\begin{thebibliography}{99}\n\\renewcommand{\\baselinestretch}{0.1}\n\\parskip0.ex\n%\n\\bibitem{hayakawa}\nS. Hayakawa, {\\it Cosmic Ray Physics}, Interscience Monographs and \nTexts in Physics and Astronomy, V. 22, Wiley-Interscience, 1969\n\\bibitem{avak}\nV.V. Avakyan et al., Jadernaya Fiz. 56 (1993) 182 \n\\bibitem{hovsep98}\nG.G. Hovsepyan for the ANI collaboration., Proc. of the Workshop \nANI 98, eds. A.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, \nFZKA 6215, Forschungszentrum Karlsruhe 1998, 45\n\\bibitem{kascade}\nH.O. Klages et al. - KASCADE collaboration, \nNucl. Phys. B (Proc. Suppl.) 52B (1997) 92 \n\\bibitem{top1}\nM. Aglietta et al., Nucl. Instrum. and Meth. A336 (1993) 310 \n\\bibitem{top2}\nM. Aglietta et al., Astropart. Phys. 10 (1999) 1 \n\\bibitem{ralf1}\nR. Glasstetter et al. - KASCADE collaboration, Proc. 16{th} \nECRS (Alcala, 1998), 564 \n\\bibitem{khris}\nG.B. Khristiansen, G. Kulikov, J. Fomin, \n{\\it Cosmic Rays of Superhigh Energies}, Verlag Thiemig, M\\\"unchen,\n1979\n\\bibitem{nagano}\nM. Nagano et al., Journ. Phys. G: Nucl. Phys. 10 (1984) L235; \\\\\nGaisser T.K, {\\it Cosmic Rays and Particle Physics}, \nCambridge Univ. Press, 1992 \n\\bibitem{gagik}\nG.V. Gharagyozyan for the ANI collaboration, Proc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, 51 \n\\bibitem{hovsep99}\nS.V. Blokhin, V.A. Romakhin, G.G. Hovsepyan, \nthese proceedings\n\\bibitem{serg1}\nS.H. Sokhoyan S.H. et al. - ANI collaboration, \nProc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, 55\n\\bibitem{beam1}\nA.A. Chilingarian, H.Z.Zazyan, Yad. Fiz. 54 (1991) 128\n\\bibitem{beam2}\nA. Vardanyan et al., these proceedings \n\\bibitem{ostap} \nS. Ostapchenko , private communication, 1999\n\\bibitem{gagik99}\nG.V. Gharagyozyan et al., these proceedings \n\n\\end{thebibliography}\n \n\\end {document}\n"
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"name": "astro-ph0002076.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\renewcommand{\\baselinestretch}{0.1}\n\\parskip0.ex\n%\n\\bibitem{hayakawa}\nS. Hayakawa, {\\it Cosmic Ray Physics}, Interscience Monographs and \nTexts in Physics and Astronomy, V. 22, Wiley-Interscience, 1969\n\\bibitem{avak}\nV.V. Avakyan et al., Jadernaya Fiz. 56 (1993) 182 \n\\bibitem{hovsep98}\nG.G. Hovsepyan for the ANI collaboration., Proc. of the Workshop \nANI 98, eds. A.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, \nFZKA 6215, Forschungszentrum Karlsruhe 1998, 45\n\\bibitem{kascade}\nH.O. Klages et al. - KASCADE collaboration, \nNucl. Phys. B (Proc. Suppl.) 52B (1997) 92 \n\\bibitem{top1}\nM. Aglietta et al., Nucl. Instrum. and Meth. A336 (1993) 310 \n\\bibitem{top2}\nM. Aglietta et al., Astropart. Phys. 10 (1999) 1 \n\\bibitem{ralf1}\nR. Glasstetter et al. - KASCADE collaboration, Proc. 16{th} \nECRS (Alcala, 1998), 564 \n\\bibitem{khris}\nG.B. Khristiansen, G. Kulikov, J. Fomin, \n{\\it Cosmic Rays of Superhigh Energies}, Verlag Thiemig, M\\\"unchen,\n1979\n\\bibitem{nagano}\nM. Nagano et al., Journ. Phys. G: Nucl. Phys. 10 (1984) L235; \\\\\nGaisser T.K, {\\it Cosmic Rays and Particle Physics}, \nCambridge Univ. Press, 1992 \n\\bibitem{gagik}\nG.V. Gharagyozyan for the ANI collaboration, Proc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, 51 \n\\bibitem{hovsep99}\nS.V. Blokhin, V.A. Romakhin, G.G. Hovsepyan, \nthese proceedings\n\\bibitem{serg1}\nS.H. Sokhoyan S.H. et al. - ANI collaboration, \nProc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, 55\n\\bibitem{beam1}\nA.A. Chilingarian, H.Z.Zazyan, Yad. Fiz. 54 (1991) 128\n\\bibitem{beam2}\nA. Vardanyan et al., these proceedings \n\\bibitem{ostap} \nS. Ostapchenko , private communication, 1999\n\\bibitem{gagik99}\nG.V. Gharagyozyan et al., these proceedings \n\n\\end{thebibliography}"
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"name": "paper.tex",
"string": "\\documentclass[11pt,dvips]{article}\n\\usepackage{epsfig}\n\\usepackage{wrapfig}\n% Setting various length parameters (DO NOT ALTER):\n\\setlength{\\textheight}{9in}\n\\setlength{\\textwidth}{6.63in}\n\\setlength{\\hoffset}{-0.2in}\n\\setlength{\\voffset}{0.37in}\n\\setlength{\\topmargin}{-15pt}\n\\setlength{\\headheight}{12pt}\n\\setlength{\\headsep}{10pt}\n\\setlength{\\oddsidemargin}{0in}\n\\setlength{\\evensidemargin}{0in}\n\\setlength{\\parindent}{3ex}\n\\renewcommand{\\thefootnote}{\\fnsymbol{footnote}}\n\\renewcommand{\\bottomfraction}{0.999}\n\\renewcommand{\\topfraction}{0.999}\n\\renewcommand{\\textfraction}{0.001}\n\\setcounter{secnumdepth}{4} \n\\pagestyle{empty}\n\n\\begin{document}\n\\begin{center}\n%*********************************************\n\n{\\LARGE \\bf The Dependence of the Age Parameter from EAS Size and \nZenith Angle of Incidence}\n\\end{center}\n\n\\begin{center}\n{\\bf A.A. Chilingarian, \nG.V. Gharagyozyan\\footnote{corresponding author: \[email protected]}, S.S. Ghazaryan, G.G. Hovsepyan, \\\\\nE.A. Mamidjanyan, L.G. Melkumyan, S.H. Sokhoyan} \\\\\n{\\it Yerevan Physics Institute, Cosmic Ray Division, Armenia}\n\\end{center}\n\n\\vspace{1ex}\n\\begin{center}\n\\begin{minipage}[c]{5.5in}\nThe quality of the MAKET-ANI detector installation in view of the \nuniformity of the registration efficiency is demonstrated. \nBased on a data sample collected by the MAKET-ANI array in the \nperiod of June 1997 - March 1999, the dependencies of the age \nparameter on the zenith angle and the EAS size $(10^5-10^7)$ are \nstudied. The variation of the age parameter with the shower size \ncan be approximately related to the elongation rate.\n\\end{minipage}\n\\end{center}\n\\vspace{1ex}\n\n\n\n\\section{Introduction}\nThe lateral distribution of the charged particle component of \nextensive air showers (EAS) carries information about the height \nof maximum of the EAS development. In NKG type parameterizations \nof the lateral distribution this information is associated \nwith the so-called age parameter s, originally introduced by \nthe analytic description of purely electromagnetic cascades \nfor characterizing the actual stage of the EAS development. \\\\\nIn EAS experiments this parameter is usually extracted from \nfitting the distribution measured on observed level, assuming \nthat this lateral parameter reflects the actual longitudinal \nEAS stage. Investigations of the parameter s have been performed \non various altitudes, with the aim to gain information on the \nlongitudinal EAS development and on the composition of primary \ncosmic rays [1-7]. For example, from the \nanalysis of the zenith angle dependence of the average value of \ns it has been concluded that the mass composition gets either \nheavier primary energies larger than $10^{15}\\,$eV or the \nmultiplicity of secondary particle production in hadronic \ninteractions is unexpectedly increasing. \\\\\nIn the present contribution experimental age distributions, \ndependent on the zenith angle $\\theta$ of EAS incidence and of \nthe shower size $N_e$ as extracted from an actual data set \nof the MAKET-ANI array, are communicated. As compared to earlier \nresults \\cite{AH-avak} the statistical accuracy of the data is \nconsiderably improved thanks to various modernizations of \nthe installation \\cite{AH-gagik}. The variation of the age \nparameter with the observation depth X is considered by a \nsimplified approach.\n\n\\section{Some characteristics of the data selection}\nWith an effective running time of ca. 8000 h the array triggered \nfor $2.6\\cdot10^6$ showers. From this set 177066 showers have \nbeen selected with following criteria: $N_e\\geq1\\times10^5$,\n$\\theta<45^o$, $0.3\\leq s \\leq 1.7$. The procedures of data \nselection and further analyses are given in Ref. \\cite{AH-gagik}.\nThe effective area for EAS registration, varying from \n$28\\cdot14$m$^2$ for $N_e\\geq10^5$ to $64\\cdot32m^2$ for \n$N_e\\geq10^6$. With Monte Carlo simulations and experimental \nconsiderations of the angular accuracy following uncertainties \nof the reconstructed EAS parameters were obtained: core location: \n$\\delta R \\simeq1.5\\,$m, $\\delta N_e \\simeq 15\\%$ for $N_e<10^6$,\n$\\delta N_e \\simeq 10\\%$ for $N_e>10^6$, $\\delta s \\simeq 7\\%$,\n$\\delta\\theta<1.5^o$ and $\\delta\\varphi<5^o$. \\\\\nFigures 1 and 2 display the good uniformity of the EAS registration; \nthe maximum intensity results %\n%\n\\begin{figure}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\epsfig{file=fig1.eps,width=8.cm,height=8.cm}\n\\vspace{-1.5cm}\n\\caption{\\it{Distributions of the EAS azimuth angles \n$\\varphi$ for different EAS sizes.}}\n\\end{minipage}\n\\hspace*{0.4cm}\n\\begin{minipage}[b]{0.48\\linewidth}\n\\epsfig{file=fig2.eps,width=8.cm,height=8.cm}\n\\vspace{-1.5cm}\n\\caption{\\it{Distributions of the EAS zenith angles for different \nEAS sizes.}}\n\\end{minipage}\n\\end{figure}\n%\n%\n\\begin{wrapfigure}[26]{r}{8.cm}\n\\vspace{-.2cm}\n\\epsfig{file=fig3.eps,width=8.cm,height=13.cm}\n\\vspace{-1.7cm}\n\\caption{\\it{Distribution of the core locations of \ndifferent age classes of showers.}}\n\\vspace{-0.6cm}\n\\end{wrapfigure}\n%\nfrom the zenith angle of \n$\\overline{\\theta}\\simeq 23^o$. For more detailed analyses the \nEAS sample is divided in three classes: \"young\" showers with \n$0.3 < s < 0.8$, \"mature\" showers with $0.8 < s < 1.1$, \nand \"old\" showers with $1.1 < s < 1.7\\,$.\\\\\nFigure 3 display the uniform efficiency of the age selection\nof the procedures. \n\n\\section{Age parameter distributions}\nThe distributions of the age parameter values for various EAS \nsizes are shown in Figure 4, displayed for different ranges of \nthe zenith angles of EAS incidence.\nThe distributions get narrower and show decreasing variances with \nincreasing $N_e$ in agreement with Ref. \\cite{AH-miayke}.\nThis can be understood that small size showers penetrating in the \ndeeper atmosphere show larger fluctuations in s.\nThe average age is slightly, but systematically shifted to higher \nvalues with increasing atmospheric depth. \\\\\nFor a consideration of the dependence of the average age from $N_e$ \nand zenith angle a finer binning of the total angular range has \nbeen applied. As examples in Figure 5 the dependence of the mean \nage is shown for selected angular bins (representing ''vertical'', \n''inclined'' and all showers). The results are compared with \nthe Norikura data \\cite{AH-miayke}, which show similar tendencies, \nbut shifting the global features% \n%\n\\begin{figure}[h]\n\\begin{center}\n\\begin{minipage}[t]{0.32\\linewidth}\n\\vspace{-.1cm}\n\\epsfig{file=fig4a.eps,width=6.cm,height=6.cm} \n\\end{minipage}\n\\hspace*{0.01cm}\n\\begin{minipage}[t]{0.32\\linewidth}\n\\vspace{-.1cm}\n\\epsfig{file=fig4b.eps,width=6.cm,height=6.cm} \n\\end{minipage}\n\\hspace*{0.01cm}\n\\begin{minipage}[t]{0.32\\linewidth}\n\\vspace{-.1cm}\n\\epsfig{file=fig4c.eps,width=6.cm,height=6.cm} \n\\end{minipage}\n\\end{center}\n\\vspace{-.2cm}\n\\caption{\\it{Age parameter distributions for various EAS sizes \nand angular ranges of EAS incidence: a- vertical, \nb- inclined, c- all showers. $N_e=\\bullet-1.6\\cdot 10^5,\n\\times -4.0\\cdot 10^5, \\diamond-9.7\\cdot10^5, \\star-2.4\\cdot 10^6,\n\\ast-6.0\\cdot 10^6$.}}\n\\end{figure}\n%\n\n%\\begin{figure}\n\\begin{wrapfigure}[18]{l}{8.cm}\n\\vspace{-.7cm}\n\\epsfig{file=fig5.eps,width=8.cm,height=8.cm}\n\\vspace{-1.cm}\n\\caption{\\it{$\\overline{s}$ dependence of the shower size.}}\n\\end{wrapfigure}\n%\\end{figure}\n%\n\n\\noindent to larger and younger EAS.\nIt is not clear if this finding is due methodical effects of \ndifferent evaluation procedures in both experiments.\nThe results of MAKET-ANI agree with the observations \nRef. \\cite{AH-asaki}, \nif taking into account the different \nobservation levels, but disagrees with the data of the MSU group \n\\cite{AH-khrist}, the latter claiming an almost constant mean \nage for EAS of $N_e =10^5-10^6$. There are results of EAS \nsimulations, based on the QGSJET model as generator \\cite{AH-ostap}, \nwhich show fair agreement \\cite{AH-ost}. \\\\\nThe variation of the average age is affected by the primary energy \nspectrum, by the change of the chemical composition and the \nhadronic interaction characteristics, governing the EAS development. \nAs long as there is no noticeable change, the average depth of \nthe shower maximum is expected to be increasing monotonously. \nHence the shallow slope of the average age for $N_e> 10^6$ may \nindicate a faster EAS development due to an increasing \nmultiplicity of the secondary production and a heavier composition, \nrespectively. \n\n\\section{EAS size spectra of different ages}\nFigure 6 shows the integral size spectra for ''young'', ''mature''\nand ''old'' showers for two different angular ranges of \nshower incidence. While the young and mature shower spectra \nexhibit the knee feature, a knee is not evident for old showers, \nwhich show obviously a different variation with the shower size. \nThis behavior results also from an analysis of KASCADE \ndata classified along various types of primaries by methods of \nadvanced statistical analysis \\cite{AH-aro}. \nThe old showers are tentatively associated to iron-like showers \nwith a different knee position. \\\\ \nThe lower part of Figure 6, taken from Ref. \\cite{AH-kempa}, \nwhere the showers have been classified by an analysis of the \nappearance of the shower core, shows a good consistency.\nThere are, however some differences with the Tien-Shan data \n(given in Ref.\\cite{AH-nikol}). While the slopes are identical \nfor mature showers and equal for old showers, the young showers \ndo not display a knee in the data of Ref. \\cite{AH-nikol}. \nWhether these differences can be explained by the particular \nanalysis procedures, is not yet clarified. \\\\\nFigure 7 presents the spectra for different values of the \nage parameters and characterized by the spectral indices given \nTable 2 (extracted by the procedures of Ref. \\cite{AH-sokho}). \nWith increasing age values the spectral slope gets flatter \nbefore the knee as also evidenced by the KASCADE data \n\\cite{AH-glasster}.\nOld showers exhibit a quite different slope. \n%\n\\begin{figure}[h]\n\\begin{minipage}[t]{0.48\\linewidth}\n\\vspace{-0.2cm}\n\\epsfig{file=fig6.eps,width=8.cm,height=8.cm}\n\\vspace{-1.cm}\n\\caption{\\it Integral EAS size spectra for two different ranges \nof the zenith angles (closed symbols: $\\theta=0^\\circ -25^\\circ$, \nopen symbols: $\\theta=25^\\circ -45^\\circ$ for young, mature and \nold showers. The lower part of the figure is taken from Ref. \n\\cite{AH-kempa} for comparison.}\n\\end{minipage}\n\\hspace*{0.4cm}\n\\begin{minipage}[t]{0.48\\linewidth}\n\\vspace{-.2cm}\n\\epsfig{file=fig7.eps,width=8.cm,height=8.cm}\n\\vspace{-1.cm}\n\\caption{\\it{Differential EAS size spectra for different angular \nand age ranges.}}\n\\end{minipage}\n\\end{figure}\n%\n%\n\\begin{table}[ht]\n\\vspace{-0.05cm}\n\\caption{\\it Average age values and variances for different \nzenith angles ($\\theta<25^o$, $25^o\\leq\\theta<45^o$, $\\theta<45^o$)\nand EAS sizes together with the values of the parameters A \nand $s(\\theta = 0)$ of the parameterization of the $\\sec\\theta$ \ndependence.}\n\\vspace{0.5cm}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline\n & \\multicolumn{2}{|c|}{$\\theta<25^o$}\n & \\multicolumn{2}{|c|}{$25^o\\leq\\theta<45^o$}\n & \\multicolumn{2}{|c|}{$\\theta<45^o$}&\n &\n \\\\\n \\raisebox{1.5ex}[1.5ex]{$N_e$} &\n $\\overline{s}$&$\\sigma_s$&$\\overline{s}$&\n $\\sigma_s$&$\\overline{s}$&$\\sigma_s$&\n \\raisebox{1.5ex}[1.5ex]{$A$} & \n \\raisebox{1.5ex}[1.5ex]{$s(0)$}\\\\\n\\hline\n\n$1.6\\times10^5$&$0.96$&$0.15$&$0.98$&$0.15$&$0.97$&$0.15$&$0.126\\pm.002$&$0.968\\pm.001$\\\\\n\n$4.0\\times10^5$&$0.92$&$0.13$&$0.95$&$0.13$&$0.93$&$0.13$&$0.194\\pm.004$&$0.902\\pm.005$\\\\\n\n$9.7\\times10^5$&$0.89$&$0.11$&$0.93$&$0.12$&$0.91$&$0.12$&$0.241\\pm.006$&$0.872\\pm.007$\\\\\n\n$2.4\\times10^6$&$0.88$&$0.10$&$0.92$&$0.11$&$0.89$&$0.11$&$0.274\\pm.008$&$0.855\\pm.009$\\\\\n\n$6.0\\times10^6$&$0.87$&$0.11$&$0.92$&$0.12$&$0.89$&$0.11$&$0.316\\pm.2$&$0.852\\pm.032$\\\\\n\n$\\geq10^5$&$0.93$&$0.14$&$0.96$&$0.14$&$0.94$&$0.14$&$0.161\\pm.002$&$0.934\\pm.001$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n%\n%\n\\begin{table}[ht]\n\\vspace{-0.05cm}\n\\caption{\\it Spectral slopes ($dI/DN_e \\propto N_e^{-\\gamma}$)\nand knee positions for different \nranges of the age parameter values.}\n\\vspace{0.2cm}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n $\\theta$ & $s$ & $\\gamma_1$ & $\\gamma_2$ & $log(N_e^{knee})$ \\\\ \n\\hline\n $0^o-25^o$& $0.3-1.7$ & $2.54\\pm0.03$ & $3.08\\pm0.03$ & $6.30$\\\\\n $ $& $0.8-1.1$ & $2.45\\pm0.03$ & $2.92\\pm0.07$ & $6.13$\\\\\n $ $ & $0.3-0.8$ & $2.21\\pm0.03$ & $3.17\\pm0.14$ & $6.31$\\\\\n $ $ & $1.1-1.7$ & $3.68\\pm0.08$ & & \\\\\n\\hline\n $25^o-45^o$ & $0.3-1.7$ & $2.50\\pm0.02$ & $2.82\\pm0.04$ & $6.08$\\\\\n $ $ & $0.8-1.1$ & $2.34\\pm0.03$ & $2.81\\pm0.05$ & $5.93$\\\\\n $ $ & $0.3-0.8$ & $2.20\\pm0.02$ & $2.70\\pm0.07$ & $5.91$\\\\\n $ $ & $1.1-1.7$ & $3.31\\pm.07$ & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n%\n\n\\section{Variation of the age with the observation depth}\nFigure 8 shows the dependence of the mean age $\\overline{s}(\\theta)$ of \nparticular EAS sizes from the zenith angle $\\theta$, as \nlinear dependence from $\\sec\\theta$. \\\\\nThe parameters $\\overline{s}(0)$ and A, adjusted to the $\\sec\\theta$ \ndependence are given in Table 1. \\\\\nWith increasing $N_e$ the slope A increases while $\\overline{s}(0)$ is \ndecreasing. There is a good agreement with the%\n%\n\\begin{wrapfigure}[20]{r}{8.cm}\n\\vspace{-.7cm}\n\\epsfig{file=fig8.eps,width=8.5cm,height=8.5cm}\n\\vspace{-1.cm}\n\\caption{\\it{The dependence of the mean age $\\overline{s}$ from the \nzenith angle of EAS incidence for various shower sizes.}}\n\\end{wrapfigure}\n%\nvalues of Ref. \\cite{AH-miayke} obtained for $N_e =2.4 \\cdot 10^6$. \nThe values averaged over all EAS sizes are $A=0.161\\pm0.002$\nand $\\overline{s}(0) =0.934 \\pm 0.001$. With the approximate relation \n$\\sec\\theta=X/X_v$ where $X_v$ is depth of the observation \nlevel and X the transverse atmospheric thickness (grammage) \nA can be related to the change $d\\overline{s}/dX$ of the average age \nwith X. With the average value of A inferred from the data for \nthe observation level $X_v = 700\\,$g/cm$^2$ a value $d\\overline{s}/dX = \n2.3 \\cdot 10^{-4}\\,$cm$^2$/g. This result can be compared \nwith $d\\overline{s}/dX = 3.4 \\cdot 10^{-4}\\,$cm$^2$/g given in \n\\cite{AH-miayke}. A compilation \\cite{AH-miayke} of the data \nfrom the literature yields a range $d\\overline{s}/dX = (1.9-4.3) \\cdot \n10^{-4}\\,$cm$^2$/g. Associating the depth of the shower \nmaximum $X_m$ with $\\overline{s}=1$,\nwe reach the relation \n\\begin{equation}\n\\overline{s} -1 ={\\frac{d\\overline{s}}{dX}}\\cdot (X-X_m),\n\\end{equation}\nThus an evaluation of the $N_e$ dependence of $\\Delta X=(X-X_m)$\ncarries some information about the elongation rate, as already \nindicated by Linsley \\cite{AH-linsley}.\n\n\\section{Concluding Remarks}\nThe present results deduced from the data of the MAKET-ANI \narray are in good agreement with theoretical expectations. The analyses reveal that: \\\\\n$\\bullet$ Average age parameter gradually decreases with increasing shower size\nfrom $10^5$ to $10^6$, and for $N_e>10^6$ it becomes almost constant.\\\\\n%The dependence of the average age parameter on the EAS size\n% show rather monotonic decrease (Figures 4 and 5). \\\\\n$\\bullet$ The knee of \"young\" showers is sharper than knee of the all particle spectra.\\\\ \n$\\bullet$ The size spectra classified by different ages show \ndifferent attenuation. \\\\\n$\\bullet$ The change of age parameter with the zenith angle of \nEAS incidence can be related to the change of the EAS maximum \nwith $N_e$.\n\n\n\\vspace*{3.5ex}\n{\\noindent \\bf \\Large Acknowledgment \\\\}\n\\vspace*{-.5ex}\n\n\t{\\it The report is based on scientific results of the \n\tANI collaboration. The MAKET-ANI installation on Mt.Aragats \n\thas been setup as a collaboration project of the \nYerevan Physics Institute (Armenia) and the Lebedev Physics Institute (Moscow).\nThe continuous contributions and assistance of the Russian colleagues in \noperating of the installation and in the data analyses are gratefully \nacknowledged. In particular, we thank Prof. S. Nikolski and Dr. V. Romakhin \nfor their encouraging interest to this work and useful discussions. \\\\\n\tWe would like to thank Prof. Dr. H. Rebel pointing on the \nimportance of the elongation rate estimation, Dr. A. Haungs and Dr. Kh. Sanosyan \nfor useful remarks.\nCorrections and suggestions made by Dr. S. Ostapchenko are highly appreciated.\nThe assistance of the Maintenance Staff of the Aragats Cosmic Ray\nObservatory in operating the MAKET-ANI installation is highly appreciated.\nThe work has been partly supported by the ISTC project A116.}\n\n\n\\begin{thebibliography}{99}\n\\renewcommand{\\baselinestretch}{0.1}\n\\parskip0.ex\n\\bibitem{AH-miayke}\nS. Miayke et al., Proc. 16$^{th}$ ICRC (Kyoto) {\\bf 13} (1979) 171\\\\\nS. Miayke et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 11} (1981) 293\\\\\nB.S. Acharya et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 9} (1981) 162\n\\bibitem{AH-kempa}\nJ. Kempa and M. Samorski, J.Phys. G: Nucl. Part. Phys. {\\bf 24} (1998) 1039\n\\bibitem{AH-khrist}\nG.B. Khristiansen et al., Proc. AS USSR, Phys. {\\bf 35} (1971), 2107 (in Russian)\\\\\nG.B. Khristiansen et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 6} (1981) 39\\\\ \nN.N. Kalmykov et al., Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} (1997) 277 \n\\bibitem{AH-avak}\nV.V. Avakian et al., Soviet J. Nucl. Phys. {\\bf 56} (1993) 183 (in Russian) \n\\bibitem{AH-gagik}\nG.V. Gharagyozyan for the ANI collab., Proc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, p.51\n\\bibitem{AH-laura}\nL.G. Melkumyan for the ANI collab., ANI Workshop 1999, these proceedings\n\\bibitem{AH-asaki}\nK. Asakimori et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 11} (1981) 301\\\\\nT. Hara et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 6} (1981) 52\\\\\nK. Asakimori, Proc. 21$^{st}$ ICRC (Adelaide) {\\bf 3} (1990) 129\n\\bibitem{AH-ostap}\nN.N. Kalmykov, S.S. Ostapchenko and A.J. Pavlov, Nucl. Phys. B {\\bf 52R}\n(1997) 17\n\\bibitem{AH-ost}\nS.S. Ostapchenko, private communication\n\\bibitem{AH-aro}\nA. Vardanyan et al. - KASCADE collaboration, these proceedings\n\\bibitem{AH-nikol}\nS.I. Nikolsky, Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} (1997) 105\n\\bibitem{AH-sokho}\nS.H. Sokhoyan et al., these proceedings\n\\bibitem{AH-glasster}\nR. Glasstetter et al. - KASCADE collaboration, Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} \n(1997) 157\n\\bibitem{AH-linsley}\nJ. Linsley, Proc. 15$^{th}$ ICRC (Plovdiv) {\\bf 12} (1977) 89 \n\\end{thebibliography}\n\\setcounter{section}{0}\n\\setcounter{footnote}{0}\n\\setcounter{figure}{0}\n\\setcounter{table}{0}\n\\newpage\n\\clearpage\n\n\\end {document}\n"
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[
{
"name": "astro-ph0002077.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\renewcommand{\\baselinestretch}{0.1}\n\\parskip0.ex\n\\bibitem{AH-miayke}\nS. Miayke et al., Proc. 16$^{th}$ ICRC (Kyoto) {\\bf 13} (1979) 171\\\\\nS. Miayke et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 11} (1981) 293\\\\\nB.S. Acharya et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 9} (1981) 162\n\\bibitem{AH-kempa}\nJ. Kempa and M. Samorski, J.Phys. G: Nucl. Part. Phys. {\\bf 24} (1998) 1039\n\\bibitem{AH-khrist}\nG.B. Khristiansen et al., Proc. AS USSR, Phys. {\\bf 35} (1971), 2107 (in Russian)\\\\\nG.B. Khristiansen et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 6} (1981) 39\\\\ \nN.N. Kalmykov et al., Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} (1997) 277 \n\\bibitem{AH-avak}\nV.V. Avakian et al., Soviet J. Nucl. Phys. {\\bf 56} (1993) 183 (in Russian) \n\\bibitem{AH-gagik}\nG.V. Gharagyozyan for the ANI collab., Proc. of the Workshop ANI 98, eds.\nA.A. Chilingarian, H.Rebel, M. Roth, M.Z. Zazyan, FZKA 6215,\nForschungszentrum Karlsruhe 1998, p.51\n\\bibitem{AH-laura}\nL.G. Melkumyan for the ANI collab., ANI Workshop 1999, these proceedings\n\\bibitem{AH-asaki}\nK. Asakimori et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 11} (1981) 301\\\\\nT. Hara et al., Proc. 17$^{th}$ ICRC (Paris) {\\bf 6} (1981) 52\\\\\nK. Asakimori, Proc. 21$^{st}$ ICRC (Adelaide) {\\bf 3} (1990) 129\n\\bibitem{AH-ostap}\nN.N. Kalmykov, S.S. Ostapchenko and A.J. Pavlov, Nucl. Phys. B {\\bf 52R}\n(1997) 17\n\\bibitem{AH-ost}\nS.S. Ostapchenko, private communication\n\\bibitem{AH-aro}\nA. Vardanyan et al. - KASCADE collaboration, these proceedings\n\\bibitem{AH-nikol}\nS.I. Nikolsky, Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} (1997) 105\n\\bibitem{AH-sokho}\nS.H. Sokhoyan et al., these proceedings\n\\bibitem{AH-glasster}\nR. Glasstetter et al. - KASCADE collaboration, Proc. 25$^{th}$ ICRC (Durban) {\\bf 6} \n(1997) 157\n\\bibitem{AH-linsley}\nJ. Linsley, Proc. 15$^{th}$ ICRC (Plovdiv) {\\bf 12} (1977) 89 \n\\end{thebibliography}"
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astro-ph0002078
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NICMOS Narrow-band Infrared Photometry of TW Hya Association Stars
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[
{
"author": "David A. Weintraub\\altaffilmark{1}"
},
{
"author": "Didier Saumon\\altaffilmark{1}"
},
{
"author": "Joel H. Kastner\\altaffilmark{2}"
},
{
"author": "and Thierry Forveille\\altaffilmark{3}"
}
] |
We have obtained 1.64, 1.90 and 2.15 $\mu$m narrow-band images of five T Tauri stars in the TW Hya Association (TWA) using the Near-Infrared Camera and Multiobject Spectrometer aboard the {Hubble Space Telescope}. Most of the T Tauri stars in our study show evidence of absorption by H$_2$O vapor in their atmospheres; in addition, the low-mass brown dwarf candidate, TWA 5B, is brighter at 1.9 $\mu$m than predicted by cool star models that include the effects of H$_2$O vapor but neglect dust. We conclude that the effect of atmospheric dust on the opacity is important at 1.9 $\mu$m for TWA 5B, the coolest object in our sample. The available evidence suggests that the TWA is 5--15 MY old. Comparison of the colors of TWA 5B with theoretical magnitudes as a function of age and mass then confirms previous claims that TWA 5B is substellar with a mass in the range 0.02--0.03 $\,M_\odot$. The accurate single-epoch astrometry of the relative positions and separation of TWA 5A and TWA 5B reported here should permit the direct measurement of the orbital motion of TWA 5B within only a few years.
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"name": "re_revised.tex",
"string": "\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,epsf,/nfs/yohoia/h1/jhk/tex/aastex40/aasms4]{article}\n%\\documentstyle[12pt,/home/david/tex/aastex/aasms4]{article}\n\n\n%\\received{today}\n%\\accepted{tomorrow}\n%\\slugcomment{Version date: October 1, 1999}\n\n\\lefthead{Weintraub et al.}\n\\righthead{NICMOS Observations of TWA Stars}\n\n\n\\begin{document}\n\n\\def\\arcsec{{$^{\\prime\\prime}$}}\n\\def\\ptsec{$^{\\prime\\prime}\\mskip-7.6mu.\\,$}\n\\def\\ptdeg{$^\\circ\\mskip-7.6mu.\\,$}\n\\def\\Teff{T_{\\rm eff}}\n\\def\\wig#1{\\mathrel{\\hbox{\\hbox to 0pt{%\n \\lower.5ex\\hbox{$\\sim$}\\hss}\\raise.4ex\\hbox{$#1$}}}}\n\n\n\\def\\plottwo#1#2{\\centering \\leavevmode\n%\\epsfxsize=.45\\textwidth \\epsfbox[230 150 750 650]{#1} \\hfil\n%\\epsfxsize=.45\\textwidth \\epsfbox[230 150 750 650]{#2}}\n\\epsfxsize=.5\\textwidth \\epsfbox[100 150 750 650]{#1} \\hfil\n\\epsfxsize=.5\\textwidth \\epsfbox[100 150 750 650]{#2}}\n\n\n\n% for PREPRINTS use:\n%\\def\\captionbaselineskip{\\baselineskip 14pt}\n%\\def\\textbaselineskip{\\baselineskip 14pt}\n\n% for SUBMITTED copy use:\n\\def\\captionbaselineskip{\\baselineskip 20pt}\n\\def\\textbaselineskip{\\baselineskip 20pt}\n\n\\title{NICMOS Narrow-band Infrared Photometry of TW Hya Association Stars}\n\n\\author{David A. Weintraub\\altaffilmark{1}, Didier Saumon\\altaffilmark{1},\n Joel H. Kastner\\altaffilmark{2}, \n and Thierry Forveille\\altaffilmark{3}}\n\n\\altaffiltext{1}{Department of Physics \\& Astronomy,\nVanderbilt University, P.O. Box 1807 Station B, Nashville, TN 37235}\n\n\n\\altaffiltext{2}{Carlson Center for Imaging Science, RIT, \n 84 Lomb Memorial Drive, Rochester, NY 14623}\n\n\\altaffiltext{3}{Observatoire de Grenoble, B.P. 53X, 38041 Grenoble Cedex, France}\n\n%\\begin{center}\n%{\\em To appear in the May 20, 2000 issue of {\\rm The Astrophysical Journal}}\n%\\end{center}\n\n\\begin{abstract}\n\nWe have obtained 1.64, 1.90 and 2.15 $\\mu$m narrow-band images of five \nT Tauri stars in the TW Hya Association (TWA) using the Near-Infrared \nCamera and Multiobject Spectrometer aboard the {\\it Hubble Space \nTelescope}. Most of the T Tauri stars in our study show evidence \nof absorption by H$_2$O vapor in their atmospheres; in addition, \nthe low-mass brown dwarf candidate, TWA 5B, is\nbrighter at 1.9 $\\mu$m than predicted by cool star models \nthat include the effects of H$_2$O vapor but neglect dust. We conclude\nthat the effect of atmospheric dust on the opacity is \nimportant at 1.9 $\\mu$m for TWA 5B, the \ncoolest object in our sample. The available evidence suggests that the \nTWA is 5--15 MY old. Comparison of the colors \nof TWA 5B with theoretical magnitudes as a function of age \nand mass then confirms previous claims that TWA 5B is substellar with a mass \nin the range 0.02--0.03 $\\,M_\\odot$. The accurate single-epoch astrometry \nof the relative positions and separation of TWA 5A and \nTWA 5B reported here should permit the direct measurement of the orbital \nmotion of TWA 5B within only a few years. \n\n\\end{abstract}\n\\keywords{open clusters and associations: individual (TW Hydrae, \nCD$-$33$^\\circ$7795)\n--- stars: low-mass, brown dwarfs \n--- stars: pre-main sequence}\n\n\\section{Introduction}\n\nFor more than a decade, the young star TW Hya has been an enigma\nsince it lies in a region of sky apparently devoid of the raw materials to\nform stars, nearly 13$^\\circ$ from the nearest dark cloud, yet it is\nunambiguously a classical T Tauri star (\\cite{ruci1983}) \nsurrounded by a great deal of cold dust (\\cite{wein1989}) and \ngas (\\cite{zuck1995,kast1997}).\nRecently, the TW Hya mystery was solved: TW Hya, along with\nother T Tauri stars found in an area of $\\sim$100 square degrees \nof the southern sky (\\cite{dela1989,greg1992}),\ncompose a uniquely close association of young stars known as the TW Hya \nAssociation (\\cite{kast1997}). \n\nAt a mean distance of only $\\sim$55 pc, the TW Hya Association (hereafter \nTWA) is almost three times closer than the next nearest known region \nof recent star formation. Given the likely age ($\\sim$10 MY) of the TWA, \nthese stars could harbor very young planetary systems with fully formed\ngiant planets or low mass, brown dwarf companions, and may still be \nsurrounding by circumstellar disks. In fact, there is substantial \nevidence for circumstellar gas and dust around several of these \nstars (\\cite{wein1989,zuck1993,zuck1995,kast1997}).\nThe relative proximity and the absence of significant interstellar or \nintra-molecular cloud extinction in the direction of the TWA \nmake the prospects for detecting substellar \ncompanions around these nearest T Tauri stars much better than the \nprospects for similar searches for young low mass companions \naround T Tauri stars in Taurus-Auriga, Chamaeleon, Lupus or Ophiuchus, the\nnext closest regions of star formation. \nIn a recent study of the TWA, Webb et al.~(1999) \nidentified a total of at least 17 sources as members of the TWA. In addition,\nLowrance et al.~(1999) and Webb et al.~have reported the \ndiscovery of a likely low mass brown dwarf companion (M $\\simeq$ 0.02 \n$\\,M_\\odot$) to TWA 5A (= CD$-$33$^\\circ$7795) in a combination of \nground-based and {\\it Hubble Space Telescope} ({\\it HST}) observations. \nTWA 5B is found almost 2\\arcsec\\ from TWA 5A; thus, despite its relative \nphysical proximity ($\\sim$100 AU) to the primary, TWA 5B is amenable to \nspectroscopic and astrometric studies, uncontaminated by light from TWA 5A.\n\nIn this paper, we report results from imaging the fields \naround five stars in the TWA, including the TWA 5 system, \nusing the Near Infrared Camera and Multi-Object \nSpectrometer (NICMOS) and the {\\it HST}. The goal of this \nprogram was to search for companions \naround these stars. Our choice of three narrowband filters centered \nat 1.64, 1.90 and 2.15 $\\mu$m was designed to enable us to identify \ncool and low surface gravity objects, including substellar mass \ncompanions, through their likely strong signatures of H$_2$O absorption \nat 1.9 $\\mu$m.\n\n\\section{Observations}\n\nWe obtained images of five star systems (Table 1) in the TWA \nusing camera 1 (NIC1) and camera 2 (NIC2) of NICMOS between \n1998 May 30 and July 12 (U.T.) \n% The NIC1 plate \n% scale\\footnote{http://www.stsci.edu/ftp/instrument\\_news/NICMOS/nicmos\\_doc\\_platescale.html}\n% is $\\sim$0\\ptsec0432 per pixel in X and \n% $\\sim$0\\ptsec0430 per pixel in Y (field of view 11\\ptsec03\n% $\\times$ 10\\ptsec98) while the NIC2 plate scale is \n% $\\sim$0\\ptsec0760 per pixel in X and $\\sim$0\\ptsec0753 per pixel in Y\n% (field of view 19\\ptsec43 $\\times$ 19\\ptsec25).\n% Three of the stars (CD$-$29$^\\circ$8887 = TWA 2, USNO 21 = TWA 8, \n% Hen 600 = TWA 3) in our sample were known \n% binary star systems while a fourth (TWA 5) appears to include a\n% low mass, brown dwarf companion (Fig.~1).\nObservations of each of the five stars were made identically. \nUsing NIC1 and filter F164N, we imaged \neach target in a four position, spiral dither pattern, \nwith an integration time per position of 33.894 s. Three images\nwere obtained at each position for \na total integration time of 406.73 s. We carried out identical\nobservations using NIC1 and filter F190N, with an integration \ntime per position of 43.864 s and a total integration time of \n526.37 s. Switching to NIC2 and filter F215N, we again obtained \nthree sets of four-position dithered image suites; however, for \nthe F215N observations we changed the starting position for the\ndithered image suites in order to obtain a better median filtered\nimage for subtraction of the thermal background. The integration\ntime per position was 15.948 s for the NIC2 images, for a total \nintegration time of 191.38 s. \n% The NIC1 narrowband filters \n% F164N (central wavelength $\\lambda_c$ = 1.6353 $\\mu$m, \n% full-width-half-maximum (FWHM) = 0.0166 $\\mu$m) and \n% F190N ($\\lambda_c$ = 1.8987 $\\mu$m, FWHM = 0.0174 $\\mu$m) and \n% the NIC2 filter F215N ($\\lambda_c$ = 2.1488 $\\mu$m, FWHM = 0.0200 $\\mu$m) \n% have very sharp cutoffs such that the full-widths at 1\\% transmission are\n% barely broader than the FWHM\\footnote{see \n% filter curves in NICMOS Instrument Handbook, \n% http://www.stsci.edu/instrument-news/handbooks/nicmos/NICMOSTOC.doc.html}.\n\n\\section{Results}\n\\subsection{Imaging}\n\nWe find no sources in any of our images other than the previously \nknown five primaries and four secondaries, to limiting magnitudes \nof 18.3, 18.4 and 17.5 in the F164N, F190N and F215N images, \nrespectively, at distances beyond $\\sim$1\\ptsec3 at 1.64 and 1.90\n$\\mu$m and 2\\ptsec3 at 2.15 $\\mu$m. The images of TWA 5 (Fig.~1) \nreveal how how easy it is to detect and image young, intermediate mass, \nbrown dwarf companions around stars in the TWA, even without a\ncoronagraph.\nIn addition, all nine imaged objects appear as point \nsources (with FWHM of 0\\ptsec14, 0\\ptsec16, and 0\\ptsec18\\ in the F164N,\nF190N and F215N images, respectively), \nwith no evidence (after deconvolutions performed with point spread functions \n[PSFs] generated using the software package Tiny \nTim\\footnote{http://scivax.stsci.edu/~krist/tinytim.html}, \ndirect subtractions of PSFs, and examinations of azimuthally averaged \nradial intensity profiles [Fig.~2])\nof extended emission around any of them. \nThus, although some of these stars appear to be \nsurrounded by circumstellar material (e.g., TWA 1 is surrounded\nby a circumstellar disk of radius $\\sim$3\\arcsec\\ that is viewed nearly\nface-on; \\cite{wein1999,kris1999}), we conclude that these direct, narrow \nband images are insufficiently sensitive to image circumstellar disks \naround these stars.\n\n\\subsection{Photometry}\n\nWe report our photometry for these observations in Table~1. \nThe factors used to convert from NICMOS count rates to absolute fluxes and \nmagnitudes\\footnote{http://www.stsci.edu/ftp/instrument\\_news/NICMOS/NICMOS\\_phot/keywords.html, \nversion 1998, December 1} were 5.376665 $\\times$ 10$^{-5}$ \nJy sec ADU$^{-1}$ for the F164N filter, 4.866353 $\\times$ 10$^{-5}$\nJy sec ADU$^{-1}$ for the F190N filter, and 3.974405 $\\times$ 10$^{-5}$\nJy sec ADU$^{-1}$ for the F215N filter with zero point flux densities\nof 1033 Jy, 862 Jy, and 690 Jy, respectively.\nPhotometry was obtained by measuring the total counts within a 0\\ptsec5\nradius aperture and then applying a correction factor of 1.15 to\ncompensate for the flux that falls outside of this radius\\footnote{\nhttp://www.stsci.edu/ftp/instrument\\_news/NICMOS/nicmos\\_doc\\_phot.html}.\n\nFigure 3 shows how the photometry of TWA stars through the $J$, $H$, and $K$\nbroadband and the F164N, F190N and F215N narrowband filters relates to the\nnear infrared spectral characteristics of late-type stars. Stars with lower\neffective temperatures have increasingly strong water absorption bands centered \nat $1.4\\,\\mu$m and $1.9\\,\\mu$m which are very effectively probed by this \ncombination of broad and narrowband filters.\n\nWe find no systematic differences between the $K$ and F215N \nphotometry (see Fig.~3, right panel), despite the slight difference \nin central wavelengths and large difference in bandwidth. On the \nother hand the stars are systematically brighter at F164N than \nat $H$-band, the most extreme case being TWA 5B. Finally, \nTWA 5B is the only star with an absolute flux that is clearly\nlower at 1.9 than at 2.15 $\\mu$m.\n\nThe left hand panel of Fig.~3 clearly shows how water absorption \nin the 1.35-1.55 and 1.7 - 2.1 $\\mu$m regions will strongly affect broad \nband $H$ measurements but will have no effect on observations with the \nF164N filter (see also the library of near-infrared spectra published \nby Lan\\c con \\& Rocca-Volmerange 1992). Thus, \nthe $H$-band and F164N observations reveal the presence of different\namounts of water vapor absorption in the spectra of most of the stars\nin our sample.\n\n\\subsection{Astrometry}\n\nFor the four binary systems in our sample, we measured the intensity\ncentroids for each binary component and transformed the cartesian \npositions on the array into offsets in Right Ascension and Declination \nof the secondaries from the primaries (Table~2). \nExcept for TWA 8, for which the binary separation is such that the\ncompanion only appeared in the NIC2 images, \nthe results presented in Table~2 are those obtained using only the \nNIC1 images since the spatial \nresolution is highest when using the NIC1 array.\nThe NIC1-based results in Table~2 are the statistical average and\nstandard deviations based on measurements of the F164N and F190N \nimages. The pixel to RA and \nDec conversions were done using the plate scale measurement \nephemeris generated by the NICMOS instrument team\\footnote{\nhttp://www.stsci.edu/ftp/instrument\\_news/NICMOS/nicmos\\_doc\\_platescale.html}.\nComparison of the \nresults for the F164N and F190N images indicate that, in most cases, \nwe can determine image separations to an accuracy of 0.02 pixels ($<$ 1 milli-arcsec).\n\nBecause our astrometric results are obtained from unocculted {\\it HST}\nimages and with the highest resolution camera in NICMOS, these results \nare much more precise than offsets previously reported for these \nbinaries. They are, however, consistent with previous results (Table~2).\nIn the case of TWA 5B, Lowrance, Weinberger \\& Schneider (1999) \nrecently independently determined that the offsets reported in \nLowrance et al.~(1999) and Webb et al.~(1999) have a \nsign error in RA; the corrected values are reported in Table~2.\n\n\\section{TWA 5B} \n\n\\subsection{The age of the TWA}\n\nWe have constructed an H-R diagram for the TWA (Fig.~4) using the\npre-main sequence tracks of Baraffe et al.~(1998). This H-R diagram\nis quite similar to that presented by Webb et al.~(1999), which is\nbased on the pre-main sequence tracks of D'Antona \\& Mazzitelli (1997);\nhowever, Fig.~4 appears to constrain the cluster age more tightly \nthan does previous work on the TWA, presumably because of \nimproved physics included in the Baraffe et al.\\ tracks (see Baraffe \net al.\\ 1997 for a discussion). Specifically, virtually all of the\nstars, including TWA 5B, fall between the 3 and 10 MY isochrones. \nIn comparison, the H-R diagrams of Webb et al. and Lowrance et \nal.~(1999) indicate that the TWA stars have ages in the range 1--100 MY\nwhile Kastner et al.~(1997) suggested that \nthe likely age of the TWA stars is 10--30 MY, based on lithium studies\n(upper limit) and X-ray luminosities (lower limit).\nTWA 6 and TWA 9A, which lie together almost on the\n30 MY isochrone, and TWA 9B, which falls near the 100 MY isochrone,\nare mild outliers in our and the Webb et al.\nHR diagrams and appear to be older than the other TWA stars (however,\nsee Webb et al.~for other possible explanations).\n\nWhat other information do we have to constrain the ages of the TWA stars?\nSoderblom et al.~(1998) used the lithium abundance to place an age\nrange of 5--20 MY and a most probable age of 10 $\\pm$ 3 MY \non TWA 4 (HD 98800; EW(Li $\\lambda$6708) = 0.36 \\AA); \nStauffer, Hartmann, \\& Barrado y Navascues (1995) \nused the strength of the Li line to assign an upper limit of \n9--11 MY to TWA 11B (HR 4796B) while Jayawardhana et al.~(1998)\nassigned an isochronal age of 8 $\\pm$ 3 MY to this star; and \nWebb et al.~(1999) measured similar \nLi EW strengths for 14 of the 17 stars identified as members of the TWA \nand, on this basis, suggested that they are all less than $\\sim$10 MY.\nThe excellent agreement between the ages estimated from the Li EWs and \nthose obtained from photometry and pre-main sequence evolutionary tracks \nsuggests that the age of the TWA is well constrained to be in \nthe range 5--15 MY. \n\n\\subsection{Mass and evolutionary status of TWA 5A and 5B}\n\nTWA 5A is a M1.5 star (Webb et al. 1999) with $\\Teff=3700 \\pm 150\\,$K (Leggett et al. 1996).\nThe distance to the TWA 5 system is presently unknown but can be estimated as $55 \\pm 9\\,$pc from\nthe measured parallaxes of four members of the association (Webb et al. 1999). The range of\ndistances is consistent with the approximate angular dimension of the association. With $d=55 \\pm 9\\,$pc\nand $K=6.8 \\pm 0.1$, we find $M_K=3.10 \\pm 0.41$. By comparing these values of $\\Teff$ and $M_K$\nwith the evolution sequences of Baraffe et al. (1998), we find $M=0.75 \\pm 0.15\\,M_\\odot$ and an age\nof 2.5 to 6 MY for TWA 5A, assuming it is a single, pre-main sequence star (Fig. 4). On the other hand,\nWebb et al. report that TWA 5A is suspected to be a spectroscopic binary. If we assume that TWA 5A is\nbinary with equal mass components, the mass of each component decreases to $0.7 \\pm 0.15\\,M_\\odot$ and\nthe age range becomes 6 to 18 MY.\n\nSince the Baraffe et al. (1998) sequence does not extend to substellar masses,\nwe analyze the photometric measurements of TWA 5B with evolutionary models\ncomputed by Saumon \\& Burrows (unpublished). These models use the same interior\nphysics as Saumon et al. (1996) and Burrows et al. (1997) with the distinction that the surface\nboundary condition is provided by the ``NextGen'' sequence of atmosphere models computed by\nAllard and Hauschildt for cool stars (Allard et al. 1996, Hauschildt, Allard \\& Baron 1999).\nThe atmospheric structures provide a surface boundary condition for the interior models by giving\na relation between the interior entropy (where the convective zone becomes essentially adiabatic\nat depth) and the surface parameters $S(\\Teff,g)$. This relation plays a central role in controlling\nthe evolution of fully convective stars. Colors are computed from the synthetic spectra,\nand are therefore fully consistent with the evolution calculation.\nThis evolution sequence was calculated for objects with solar compositions and\nmasses between 0.01 and 0.3$\\,M_\\odot$, and is very similar to that of Baraffe et al. (1998) since it\nuses the same input physics (equation of state, atmosphere models, nuclear reaction screening \nfactors, etc.). A limitation of the ``NextGen'' atmospheres is that\nthey do not include dust opacity, which becomes significant for $\\Teff \\wig< 2600\\,$K.\n\nFigure 5 shows the evolution of the absolute magnitudes at $I$, $J$, $H$ and $K$ bands, from 1 to 100 MY,\nbased on the models of Saumon \\& Burrows (unpublished). Each curve shows the evolution for a fixed mass.\nThe two dashed\nlines highlight the 0.02 and 0.03$\\,M_\\odot$ models. The boxes show the photometric measurements for\nTWA 5B (Webb et al. 1999, Lowrance et al. 1999), with the height of the box representing the \n$\\pm 1 \\sigma$ photometric error and the width showing the 5--15 MY\nestimated age of the association. The absolute magnitudes of TWA 5B\nassume a distance of 55 pc and the $\\pm 9\\,$pc uncertainty is shown by the error bar in the upper\nright corner.\nAll four bandpasses indicate that the mass of TWA 5B is between 0.02 and 0.03$\\,M_\\odot$ with an upper\nlimit of $\\sim 0.06\\,M_\\odot$ if the TWA 5 system lies on the far side of the association and near the\nupper limit of our age estimate. Given this mass range and the estimated age of TWA 5B, the models\nindicate that its surface gravity is $3.8 \\wig< \\log g ({\\rm cm/s}^2) \\wig< 4.0$.\n\nStellar and substellar objects with $M \\ge 0.012\\,M_\\odot$\nundergo a phase of nearly constant luminosity which corresponds to the fusion of their primordial \ndeuterium content (D'Antona \\& Mazzitelli 1985, Saumon et al. 1996). This phase lasts for 2 - 20 MY\nand contraction --- with a consequent steady decrease in luminosity --- resumes once\nthe deuterium is exhausted. Figure 5 shows that TWA 5B is almost certainly in the deuterium burning \nphase of its evolution.\n\n\n\n\n\\subsection{Colors of TWA 5B}\n\nThe $IJK$ colors of TWA 5B are consistent with its dM8.5--dM9 spectral classification\nbased on 0.65--0.75 $\\mu$m spectra (\\cite{webb1999,legg1998}), and thus a temperature\nof $\\Teff = 2600 \\pm 150\\,$K \n(\\cite{luhm1997,legg1996}). In a $J-H$ vs. $H-K$ \ndiagram, TWA 5B falls well outside of the observed sequence of very-low \nmass stars and brown dwarf candidates in the field (\\cite{legg1998}),\nwhile all other members of the association fall along the observed sequence\nof field stars. This indicates that the $H$ magnitude for TWA 5B \nmay be erroneous (by $\\ge$ 1$\\sigma$) or that its relatively low surface gravity \nresults in a redder $H-K$ color. \n\nThe narrowband infrared colors are shown in Fig.~6 along with the \nsynthetic colors from the ``NextGen'' spectra. Each curve shows the colors \nfor $\\Teff=2600$, 2800, 3000 and 3200$\\,$K (from left to right) for a \nfixed gravity. The colors of TWA 5B are shown by the triangle with \nerror bars. \nFor the estimated $\\Teff = 2600 \\pm 150\\,$K and $\\log g = 3.9 \\pm 0.1$, \nthere is a reasonable agreement for the F164N$-$F215N color but the models \nare $\\sim 0.4$ magnitude too blue in F164N$-$F190N. Consequently,\nTWA 5B is brighter at 1.9 $\\mu$m than predicted by the models.\n\nThe F190N bandpass falls \nin the middle of a strong H$_2$O absorption band (Fig.~3) whose strength \nprobably is overestimated by the ``NextGen'' models. \nAllard et al.~(1997) compare a sequence of near-infrared \nspectra of late M dwarfs with their synthetic spectra. In all cases,\nthe models overestimate the depth of the H$_2$O band, an effect which \nincreases for later spectral types. While an inadequate H$_2$O opacity \nmay be partly responsible for this effect, Tsuji, Ohnaka, \\& Aoki \n(1996) have shown that the condensation of dust in atmospheres of low \n$\\Teff$ results in a source of continuum opacity which decreases the depth \nof the water absorption bands. New atmosphere models including dust \nopacity (Tsuji, Ohnaka, \\& Aoki; Leggett, Allard \\& Hauschildt 1998) \nindicate that its effects on the spectrum (and on broadband colors) \nbecome discernible for $\\Teff \\wig< 2800\\,$K but remain moderate \n($\\sim 0.1$ mag) at the effective temperature of TWA 5B ($\\sim 2600\\,$K). \nWhile current models including dust opacity may not fully account for the relatively\nhigh F190N flux of TWA 5B, the F164N$-$F190N color of TWA 5B is a strong \nindication of the presence of dust in its atmosphere. \n\n\n\\subsection{Astrometry of TWA 5B}\n\nAt a distance of 55 $\\pm$ 9 pc, TWA 5B \nlies at a projected distance from TWA 5A of 108 astronomical \nunits. TWA 5A has a spectral type of M1.5 and a likely \nmass for the central binary of $\\sim$1.4 M$_\\odot$ while \nTWA 5B has an estimated \nspectral type of M8.5 (\\cite{webb1999}) and a likely mass\nof $\\sim$25 M$_{jup}$. Given this information about the \nTWA 5 system, the orbital period P of TWA 5B \nshould be P $\\simeq$ 1000 years. Thus, the angular motion of \nTWA 5B, assuming a circular orbit of radius 1\\ptsec96 \nviewed nearly pole-on, would be 0\\ptsec013 yr$^{-1}$ \n(or 0\\ptsec010 yr$^{-1}$ if TWA 5A is a single star with a mass of \n0.7 M$_\\odot$ and P = 1300 years). \n\nThe NICMOS observations of TWA 5 were obtained on 25 April \n(\\cite{lowr1999a}) and 12 July 1998 (this paper), a difference of \n$\\sim$0.21 years. In only one-fifth of a \nyear, the orbital motion of TWA 5B would have changed its\nposition relative to TWA 5A by only $\\sim$0\\ptsec0027, too small for the \npositional difference to be measured at these two epochs.\nThus, the differences between the positions we measured and the \ncorrected positions from earlier epoch observations reported by \nLowrance, Weinberger, \\& Schneider (1999) are strictly\ndue to the relative accuracies of the different measurements.\n\nAlthough we have demonstrated that the positional change for TWA 5B\nis measurement error, not orbital motion, we also have shown that\nthe position reported in this paper is a very accurate ``starting'' \nposition for TWA 5B. In addition, our results show that it is possible\nto measure the relative separation of these two objects to an accuracy of\nonly a few thousandths of an arcsec. Thus, the orbital motion of TWA \n5B should be measurable to a fairly high degree of accuracy with \nground-based observing facilities equipped with adaptive optics or \nwith the refurbished NICMOS camera.\n\n\\section{Summary}\n\nTo the sensitivity limits of these data, our images \nreveal no detectable circumstellar disks or infrared reflection\nnebulae, and no low mass stellar or substellar companions around stars \nin the five \nstudied TWA systems other than the previously discovered TWA 5B.\nAs for TWA 5B itself, our results suggest that this object\nhas a mass in the range of 0.02--0.03 $\\,M_\\odot$, in good agreement with\nthe work of Lowrance et al.~(1999). Finally, while our single epoch\nobservations cannot demonstrate or measure the orbital \nmotion of TWA 5B, they are more than accurate\nenough to permit the measurement of this motion, in combination\nwith future epoch {\\it HST} or adaptive optics, ground-based \nobservations, with a baseline of only about a year. \n\n\\acknowledgments{We thank the referee for thoughtful suggestions \nwhich improved the clarity of the manuscript, \nA. Burrows for computing the evolutionary \nsequences used in this work, and F. Allard, P.H. Hauschildt, I. Baraffe \nand G. 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E. 1993, ApJ, 406, L25\n\n\\bibitem[Zuckerman et al. 1995]{zuck1995} \nZuckerman, B., Forveille, T., \\& Kastner, J.H. 1995, Nature, 373, 494\n\\end{thebibliography}\n\n\\begin{deluxetable}{cllrrrrr}\n\\tablewidth{520pt}\n\\tablenum{1}\n\\tablecaption{Measured Photometry of TWA Stars}\n\\tablehead{\n \\colhead{TWA}\n & \\colhead{Common}\n & \\colhead{Spec.}\n & \\colhead{F164N}\n & \\colhead{$H$}\n & \\colhead{F190N}\n & \\colhead{F215N}\n & \\colhead{$K$}\n\\\\\n \\colhead{Number} \n & \\colhead{Name}\n & \\colhead{Type\\tablenotemark{a}}\n & \\colhead{(mag)\\tablenotemark{b}}\n & \\colhead{(mag)\\tablenotemark{c}}\n & \\colhead{(mag)\\tablenotemark{b}}\n & \\colhead{(mag)\\tablenotemark{b}}\n & \\colhead{(mag)\\tablenotemark{c}}\n }\n\\startdata\n1 & TW Hya & K7 & 7.50$\\pm$0.01 & 7.65$\\pm$0.1 & 7.53$\\pm$0.01 & 7.41$\\pm$0.01 & 7.37$\\pm$0.07 \\nl\n2A & CD$-$29$^\\circ$8887A & M0.5& 7.26$\\pm$0.01 & \\nodata & 7.39$\\pm$0.01 & 7.20$\\pm$0.01 & 7.18$\\pm$0.07 \\nl\n2B & CD$-$29$^\\circ$8887B & M2 & 8.08$\\pm$0.01 & \\nodata & 8.12$\\pm$0.01 & 7.94$\\pm$0.01 & 7.99$\\pm$0.07 \\nl\n3A & Hen 600A & M3 & 7.52$\\pm$0.01 & 7.60$\\pm$0.1 & 7.60$\\pm$0.01 & 7.37$\\pm$0.01 & 7.28$\\pm$0.07 \\nl\n3B & Hen 600B & M3.5& 7.90$\\pm$0.01 & 8.07$\\pm$0.1 & 7.98$\\pm$0.01 & 7.79$\\pm$0.01 & 7.80$\\pm$0.07 \\nl\n5A & CD$-$33$^\\circ$7795A & M1.5& 6.93$\\pm$0.01 & 7.06$\\pm$0.1 & 7.00$\\pm$0.01 & 6.86$\\pm$0.01 & 6.83$\\pm$0.07 \\nl\n5B & CD$-$33$^\\circ$7795B & M8.5& 11.76$\\pm$0.01 & 12.1$\\pm$0.1 & 11.83$\\pm$0.01 & 11.49$\\pm$0.01 & 11.5$\\pm$0.07 \\nl\n8A & USNO 21A & M2 & 7.59$\\pm$0.01 & 7.72$\\pm$0.1 & 7.66$\\pm$0.01 & 7.53$\\pm$0.01 & 7.44$\\pm$0.07 \\nl\n8B & USNO 21B & M5 & \\nodata\\tablenotemark{d} & \\ 9.36$\\pm$0.1 & \\nodata\\tablenotemark{d} & \\ 9.13$\\pm$0.01 & \\ 9.01$\\pm$0.07 \\nl\n\\enddata\n\\tablenotetext{a}{from Webb et al.~(1999).}\n\\tablenotetext{b}{this paper.}\n\\tablenotetext{c}{from Webb et al.~(1999). Also, Lowrance, Weinberger, \\& Schneider 1999\n report $H$ = 7.2$\\pm$0.1 \n for TWA 5A and $H$ = 12.14$\\pm$0.06 and $K$ = 11.4$\\pm$0.2 for TWA 5B.}\n\\tablenotetext{d}{TWA 8A and 8B are more widely spaced than the size of the NIC1 field of view; hence, \n at F164N and F190N we were able to obtain data only for the \n primary.}\n\\end{deluxetable}\n\n\\clearpage\n\n%\\begin{deluxetable}{crrrr}\n%\\tablewidth{450pt}\n%\\tablenum{2}\n%\\tablecaption{Measured Binary Separations\\tablenotemark{a}}\n%\\tablehead{\n% \\colhead{Star}\n% & \\colhead{$\\Delta$RA}\n% & \\colhead{$\\Delta$Dec}\n% & \\colhead{Separation}\n% & \\colhead{Position}\n%\\\\\n% \\colhead{} \n% & \\colhead{(arcsec)}\n% & \\colhead{(arcsec)}\n% & \\colhead{(arcsec)}\n% & \\colhead{Angle}\n% }\n%\\startdata\n%TWA 2B\\tablenotemark{b} & $+$0.281$\\pm$0.001 &\\ $+$0.492$\\pm$0.001 &\\ 0.567$\\pm$0.001 & 29.774$^\\circ$ \\nl\n%TWA 3B\\tablenotemark{c} & $-$0.866$\\pm$0.001 &\\ $-$1.187$\\pm$0.001 &\\ 1.469$\\pm$0.001 & 216.106$^\\circ$ \\nl\n%TWA 5B\\tablenotemark{d} & $-$0.038$\\pm$0.001 &\\ $+$1.960$\\pm$0.006 &\\ 1.960$\\pm$0.006 &$-$1.117$^\\circ$ \\nl\n%TWA 8B\\tablenotemark{e} & $-$1.220$\\pm$0.014 & $-$13.162$\\pm$0.019 & 13.219$\\pm$0.021 & 185.297$^\\circ$ \\nl\n%\\enddata\n\n\n\\begin{deluxetable}{cllllc}\n\\tablewidth{510pt}\n\\tablenum{2}\n\\tablecaption{Measured Binary Separations\\tablenotemark{a}}\n\\tablehead{ \\colhead{Source}\n & \\colhead{$\\Delta$RA}\n & \\colhead{$\\Delta$Dec}\n & \\colhead{Separation}\n & \\colhead{Position}\n & \\colhead{Ref.\\tablenotemark{b}}\n\\\\\n \\colhead{} \n & \\colhead{(arcsec)}\n & \\colhead{(arcsec)}\n & \\colhead{(arcsec)}\n & \\colhead{Angle}\n & \\colhead{}\n }\n\\startdata\nTWA 2B\\tablenotemark{c} & $+$0.281$\\pm$0.001 & $+$0.492$\\pm$0.001 & 0.567$\\pm$0.001 & 29.73$^\\circ$$\\pm$0.03$^\\circ$ & 1\\nl\n & $+$0.3\\ \\ \\ $\\pm$0.1& $+$0.5\\ \\ \\ $\\pm$0.1 & 0.6\\ \\ \\ $\\pm$0.1 & 31$^\\circ$\\ \\ \\ \\ $\\pm$3$^\\circ$ & 2\\nl \nTWA 3B\\tablenotemark{d} & $-$0.866$\\pm$0.001 & $-$1.187$\\pm$0.001 & 1.469$\\pm$0.001 & 216.11$^\\circ$$\\pm$0.03$^\\circ$ & 1\\nl\n & $-$0.8\\ \\ \\ $\\pm$0.1\\ \\ \\ & $-$1.2\\ \\ \\ $\\pm$0.1 & 1.4\\ \\ \\ $\\pm$0.1 & 214$^\\circ$\\ \\ \\ $\\pm$3$^\\circ$ & 2\\nl\nTWA 5B\\tablenotemark{e} & $-$0.038$\\pm$0.001 & $+$1.960$\\pm$0.006 & 1.960$\\pm$0.006 &$-$1.11$^\\circ$$\\pm$0.03$^\\circ$ & 1 \\nl\n & $-$0.1\\ \\ \\ $\\pm$0.1\\ \\ \\ & $+$1.9\\ \\ \\ $\\pm$0.1 & 1.9\\ \\ \\ $\\pm$0.1 & $-$3$^\\circ$\\ \\ \\ $\\pm$3$^\\circ$ & 3\\nl\n & $-$0.04\\ \\ $\\pm$0.01\\ \\ \\ & $+$1.95\\ $\\pm$0.01 & 1.96\\ $\\pm$0.01 &$-$1.2$^\\circ$\\ \\ $\\pm$0.1$^\\circ$ & 3\\nl\nTWA 8B\\tablenotemark{f} & $-$1.220$\\pm$0.014 & $-$13.162$\\pm$0.019 & 13.219$\\pm$0.021 & 185.30$^\\circ$$\\pm$0.06$^\\circ$ & 1 \\nl\n & $-$1.3\\ \\ \\ $\\pm$0.1 & $-$13.0\\ \\ \\ \\ $\\pm$0.1 & 13.0\\ \\ \\ $\\pm$0.1 & 186$^\\circ$\\ \\ \\ $\\pm$3$^\\circ$ & 2\\nl\n\\tablebreak\n\\enddata\n\\tablenotetext{a}{from primary to secondary, based on centroid positions in NIC1 array images for \n TWA 2B, TWA 3B and TWA 5B. As TWA 8B was only in the field of view in the NIC2 images, this offset \n is taken from those NIC2 images.}\n\\tablenotetext{b}{ 1 = this paper. 2 = \\cite{webb1999}. 3 = \\cite{lowr1999b}. \nLowrance, Weinberger \\& Schneider report corrections of the position of TWA 5B\n originally reported in both Lowrance et al.~(1999) and Webb et al.~(1999).} \n\\tablenotetext{c}{NIC1 plate scale: X=0.0431862 arcsec px$^{-1}$, Y=0.0430120 arcsec px$^{-1}$,\n based on plate scale measurements from June 4, 1998. Observations obtained May 30, 1998.}\n\\tablenotetext{d}{NIC1 plate scale: X=0.0431887 arcsec px$^{-1}$, Y=0.0430144 arcsec px$^{-1}$,\n interpolated from plate scale measurements obtained on June 4 and August 6, 1998. Observations \n obtained July 1, 1998.}\n\\tablenotetext{e}{NIC1 plate scale: X=0.0431897 arcsec px$^{-1}$, Y=0.0430154 arcsec px$^{-1}$,\n interpolated from plate scale measurements obtained on June 4 and August 6, 1998. Observations \n obtained July 12, 1998.}\n\\tablenotetext{f}{NIC2 plate scale: X=0.0759831 arcsec px$^{-1}$, Y=0.0753005 arcsec px$^{-1}$,\n interpolated from plate scale measurements obtained on June 4 and August 6, 1998. Observations \n obtained July 9, 1998.}\n\\end{deluxetable}\n\n\n\n\n\\clearpage\n\\subsection*{FIGURE CAPTIONS}\n\n\n\n% Figure 1\n% Images of TWA 5A/B\n\\figcaption{\nNICMOS Images of TWA 5A/B, as seen through narrowband filters at 1.64 \n$\\mu$m (F164N) (1 pixel = 0\\ptsec043), 1.90 $\\mu$m (F190N) (1 pixel = \n0\\ptsec043), and 2.15 $\\mu$m (F215N) (1 pixel = 0\\ptsec076). \nAll the small scale features seen in the images except for TWA 5B \nare seen identically in the model point spread functions for NICMOS.\n% The F164N and F190N images are rotated 100.214$^\\circ$ west \n% of north; the F215 image is rotated 101.017$^\\circ$ west of north.\n}\n\n% Figure 2\n% Radial profiles of TWA stars\n\\figcaption{\nAzimuthally averaged radial intensity profiles for five of the TWA stars\nin our sample as seen in the a) F164N (1 pixel = 0\\ptsec043), b) F190N \n(1 pixel = 0\\ptsec043) and c) F215N (1 pixel = 0\\ptsec076) filters. \nEach profile is normalized to the brightness of the \ncentral pixel in that profile. All profiles look identical to the \nPSFs generated by Tiny Tim, except for the presence of known companions.\n}\n\n% Figure 3\n% Synthetic spectral sequence and photometry\n\\figcaption{\nPhotometry of TWA stars.\nLeft panel: Synthetic spectra for a gravity of $\\log g=4$ and \n$\\Teff=4000\\,$K ($\\sim$K7) to 2600$\\,$K ($\\sim$M6), from top to bottom, respectively \n(Allard et al.~1996, Hauschildt et al.~1999). Bars at the bottom show\nthe bandpasses of the Johnson-Cousin $J$, $H$ and $K$ filters and of the \nnarrowband NICMOS filters F164N, F190N and F215N. Right panel: Broadband \n(Webb et al.~1999, Lowrance et al.~1999) and narrowband photometry for a \nrepresentative sample of TWA stars. The photometry is expressed in \narbitrary flux units, normalized to the $J$ flux. Boxes show the width of\nthe broadband filters and $\\pm1\\sigma$ error bars. Solid squares \nrepresent narrowband photometry results. The stars are ordered \nby spectral type, with later types at the bottom.\n}\n\n% Figure 4\n% TWA stars and Baraffe et al.~1998 evolutionary tracks\n\\figcaption{\nEvolutionary tracks from Baraffe et al.~(1998) and the stars of \nthe TW Hya association. Solid lines show the evolution of stars of masses \nfrom 1.0 to 0.1$\\,M_\\odot$ in steps of 0.1$\\,M_\\odot$ and for 0.08$\\,M_\\odot$, \nfrom left to right, respectively. Isochrones for $\\log t{\\rm (yr)} =6.5$, \n7, 7.5, and 8 are shown by dotted curves. The effective temperatures of the \nTWA stars were obtained from the Webb et al.~(1999) spectral types and the \nLuhman \\& Rieke (1998) spectral type-$T_{\\rm eff}$ relation. The\nerror bars on $M_K$ reflect the uncertainties in the photometry \n(Webb et al.~1999) and on the distances.\n}\n\n% Figure 5\n% Evolution of I, J, H and K magnitudes from NextGen models\n\\figcaption{\nEvolution of $M_I$, $M_J$, $M_H$, and $M_K$ magnitudes for very\nlow mass stars and brown dwarfs. From top to bottom, the curves correspond \nto masses of 0.2, 0.15, 0.125, 0.1, 0.09, 0.08, 0.07, 0.06, 0.05, 0.04, 0.03, \n0.02, and 0.01$\\,M_\\odot$, respectively. Heavier curves show objects with\n$M \\ge 0.08\\,M_\\odot$ which eventually become main sequence stars. \n}\n\n% Figure 6\n%NICMOS narrowband color-color diagram of the NextGen spectra\n\\figcaption{NICMOS narrow-band color-color diagram. Colors calculated \nfrom the NextGen synthetic spectra (Hauschildt et al.~1999)\nare shown by the dots. Models with the \nsame gravity are connected by a solid line, with $\\log g\\,({\\rm cgs}) = 3.5$ \nto 5.5 from top to bottom, respectively. The effective temperatures\nshown are 2600, 2800, 3000, and 3200$\\,$K, increasing from left to right. \nThe observed colors of TWA5 B are shown by a triangle.\n}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002078.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Allard et al.\\ 1997]{alla1997}\nAllard, F., Hauschildt, P. H., Alexander, D. R., \\& Starrfield, S. 1997,\nARAA, 35, 137\n\n\\bibitem[Allard et al.\\ 1996]{alla1996}\nAllard, F. Hauschildt, P. H., Baraffe, I. \\& Chabrier, G. 1996, \nApJ, 465, L123\n\n% \\bibitem[Allard et al.\\ 1994]{alla1994}\n% Allard, F. Hauschildt, P. H., Miller, S., \\& Tennyson, J. 1994, ApJ, 426, L39\n\n\\bibitem[Baraffe et al.\\ 1997]{bara1997}\nBaraffe, I., Chabrier, G., Allard, F., \\& Hauschildt, P. H. 1997, A\\&A, 327, 1054\n\n\\bibitem[Baraffe et al.\\ 1998]{bara1998}\nBaraffe, I., Chabrier, G., Allard, F., \\& Hauschildt, P. H. 1998, A\\&A, 337, 403\n\n\\bibitem[Burrows et al.\\ 1997]{burr1997}\nBurrows, A., Marley, M. S., Hubbard, W. B., Lunine, J. I., Guillot, T.,\nSaumon, D., Freedman, R. S., Sudarsky, D., \\& Sharp, C. 1997, ApJ,\n491, 856\n\n\\bibitem[D'Antona \\& Mazzitelli 1985]{dant1985}\nD'Antona, F., \\& Mazzitelli, I. 1985, ApJ, 296, 502\n\n% \\bibitem[D'Antona \\& Mazzitelli 1994]{dant1994}\n% D'Antona, F., \\& Mazzitelli, I. 1994, ApJS, 90, 467\n\n\\bibitem[D'Antona \\& Mazzitelli 1997]{dant1997}\nD'Antona, F., \\& Mazzitelli, I. 1997, Mem. Soc. Astron. Italiana, 68, 4\n\n\\bibitem[de la Reza et al.\\ 1989]{dela1989}\nde la Reza, R., Torres, C. A. O., Quast, G., Castillo, B. V., \n\\& Vieira, G. L. 1989, ApJ, 343, L61\n\n\\bibitem[Gregorio-Hetem et al.\\ 1992]{greg1992}\nGregorio-Hetem, J., L\\'epine, J. R. D., Quast, G., Torres, C. A. O., \n\\& de la Reza, R. 1992, AJ, 103, 549\n\n\\bibitem[Hauschildt, Allard \\& Baron 1999]{haus1999}\nHauschildt, P. H., Allard, F. \\& Baron, E. 1999, ApJ, 512, 377\n\n\\bibitem[Jayawardhana et al.\\ 1998]{jaya1998}\nJayawardhana, R., Fisher, S., Hartmann, L., Telesco, C., \nPina, R. \\& Fazio, G. 1998, ApJ, 503, L79\n\n\\bibitem[Kastner et al.\\ 1997]{kast1997} \nKastner, J. H., Zuckerman, B., Weintraub, D. A., \\& Forveille, T. 1997,\nScience, 277, 67 \n\n\\bibitem[Krist et al.\\ 1999]{kris1999}\nKrist, J. E., Stapelfeldt, K. R., Burrows, C. J., Menard, F., Padgett, D. L.\n1999, BAAS, 31, 935\n\n\\bibitem[Lan\\c con \\& Rocca-Volmerange 1992]{lanc1992}\nLan\\c con, A. \\& Rocca-Volmerange, B. 1991, A\\&ASS, 96, 593\n\n\\bibitem[Leggett et al.\\ 1996]{legg1996}\nLeggett, S. K., Allard, F., Berriman, G., Dahn, C. C. \\& Hauschildt, P. H.\n1996, ApJS, 104, 117\n \n\\bibitem[Leggett, Allard \\& Hauschildt 1998]{legg1998}\nLeggett, S. K., Allard, F., \\& Hauschildt, P. H. 1998, ApJ, 509, 836\n\n\\bibitem[Lowrance et al.\\ 1999]{lowr1999a}\nLowrance, P. J. et al. 1999, ApJ, 512, L69 % note: 15 authors\n\n\\bibitem[Lowrance, Weinberger \\& Schneider 1999]{lowr1999b}\nLowrance, P. J., Weinberger, A. \\& Schneider, G., 1999, pers. comm. \n\n\\bibitem[Luhman, Liebert \\& Rieke 1997]{luhm1997}\nLuhman, K. L., Liebert, J., \\& Rieke, G. H. 1997, ApJ, 489, L165\n\n\\bibitem[Luhman, \\& Rieke 1997]{luhm1998}\nLuhman, K. L., \\& Rieke, G. H. 1998, ApJ, 497, 354\n\n\\bibitem[Rucinski \\& Krautter 1983]{ruci1983}\nRucinski, S. M., \\& Krautter, J. 1983, A\\&A, 121, 217\n\n\\bibitem[Saumon et al.\\ 1996]{saum1996}\nSaumon, D., Hubbard, W. B., Burrows, A., Guillot, T., Lunine, J. I., \n\\& Chabrier, G. 1996, Apj, 460, 993\n\n\\bibitem[Soderblom et al.\\ 1998]{sodo1998}\nSoderblom, David. R. et al. 1998, ApJ, 498, 385.\n\n\\bibitem[Stauffer, Hartmann \\& Barrado y Navascues 1995]{stau1995}\nStauffer, J. R., Hartmann, L. W., \\& Barrado y Navascues, D. 1995, ApJ, 454, 910\n\n\\bibitem[Tsuji, Ohnaka \\& Aoki 1996]{tsuj1996}\nTsuji, T., Ohnaka, K., \\& Aoki, W. 1996, A\\&A, 305, L1\n\n\\bibitem[Webb et al.\\ 1999]{webb1999} \nWebb, R. A., Zuckerman, B., Patience, J., White, R. J., Schwartz, M. J.,\nMcCarthy, C., \\& Platais, I. 1999, ApJ, 512, L63\n\n\\bibitem[Weintraub, Sandell \\& Duncan 1989]{wein1989}\nWeintraub, D. A., Sandell, G., \\& Duncan, W. D. 1989, ApJ, 340, L69\n\n\\bibitem[Weinberger et al.\\ 1999]{wein1999}\nWeinberger, A. J., Schneider, G., Becklin, E. E., Smith, B. A., Hines, D. C.\n1999, BAAS, 31, 934\n\n\\bibitem[Zuckerman \\& Becklin 1993]{zuck1993} \nZuckerman, B. \\& Becklin, E. E. 1993, ApJ, 406, L25\n\n\\bibitem[Zuckerman et al. 1995]{zuck1995} \nZuckerman, B., Forveille, T., \\& Kastner, J.H. 1995, Nature, 373, 494\n\\end{thebibliography}"
}
] |
astro-ph0002079
|
Pinpointing the Position of the Post-AGB Star at the Core of RAFGL 2688 using Polarimetric Imaging with NICMOS
|
[
{
"author": "David A. Weintraub\\altaffilmark{1}"
},
{
"author": "Joel H. Kastner\\altaffilmark{2}"
},
{
"author": "Dean C. Hines\\altaffilmark{3}"
},
{
"author": "Raghvendra Sahai\\altaffilmark{4}"
}
] |
We have used infrared polarimetric imaging with NICMOS to determine precisely the position of the star that illuminates (and presumably generated) the bipolar, pre-planetary reflection nebula RAFGL 2688 (the Egg Nebula). The polarimetric data pinpoint the illuminating star, which is not detected directly at wavelengths $\le$ 2 $\mu$m, at a position well within the dark lane that bisects the nebula, 0\farcs55 ($\sim550$ AU) southwest of the infrared peak which was previously detected at the southern tip of the northern polar lobe. The inferred position of the central star corresponds to the geometric center of the tips of the four principle lobes of near-infrared H$_2$ emission; identifying the central star at this position also reveals the strong point symmetric structure of the nebula, as seen both in the intensity and polarization structure of the polar lobes. The polarimetric and imaging data indicate that the infrared peak directly detected in the NICMOS images is a self-luminous source and, therefore, is most likely a distant binary companion to the illuminating star. Although present theory predicts that bipolar structure in pre-planetary and planetary nebulae is a consequence of binary star evolution, the separation between the components of the RAFGL 2688 binary system, as deduced from these observations, is much too large for the presence of the infrared companion to have influenced the structure of the RAFGL 2688 nebula.
|
[
{
"name": "ms_revised.tex",
"string": "\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,/home/david/tex/aastex/aasms4]{article}\n%\\documentstyle[12pt,/nfs/yohoia/h1/jhk/tex/aastex40/aasms4]{article}\n\n% Here's some slug-line data. The receipt and acceptance dates will be \n% filled in by the editorial staff with the appropriate dates. Rules \n% appear on the title page of the manuscript until these are uncommented \n% out by the editorial staff.\n\n\\received{}\n\\accepted{}\n\\journalid{337}{}\n\\articleid{11}{}\n\n\\slugcomment{Version date: August 31, 1999}\n\n\n\\lefthead{Weintraub et al.}\n\\righthead{Polarimetric Imaging of the Egg Nebula with NICMOS}\n\n\\begin{document}\n\n\\def\\arcsec{{$^{\\prime\\prime}$}}\n\n\n\\title{Pinpointing the Position of the Post-AGB Star \nat the Core of RAFGL 2688 using Polarimetric Imaging with NICMOS}\n\n\\author{David A. Weintraub\\altaffilmark{1}, Joel H. \nKastner\\altaffilmark{2}, Dean C. Hines\\altaffilmark{3}, \nRaghvendra Sahai\\altaffilmark{4}}\n\n\\altaffiltext{1}{Department of Physics \\& Astronomy,\nVanderbilt University, P.O. Box 1807 Station B, Nashville, TN 37235; \[email protected]}\n\n\\altaffiltext{2}{Carlson Center for Imaging Science, RIT, \n 84 Lomb Memorial Drive, Rochester, NY 14623; [email protected]}\n\n\\altaffiltext{3}{Steward Observatory, The University of Arizona, Tucson, \nAZ 85721; [email protected]}\n \n\\altaffiltext{4}{Jet Propulsion Laboratory, MS 183-900, California \nInstitute of Technology, Pasadena, CA 91109; [email protected]}\n\n\\begin{abstract}\n\n\nWe have used infrared polarimetric imaging with NICMOS to determine\nprecisely the position of the star that illuminates (and presumably \ngenerated) the bipolar, pre-planetary reflection nebula RAFGL 2688 \n(the Egg Nebula). The polarimetric data pinpoint the illuminating \nstar, which is not detected directly at wavelengths $\\le$ 2 \n$\\mu$m, at a position well within the dark lane that bisects the \nnebula, 0\\farcs55 ($\\sim550$ AU) southwest of the infrared peak \nwhich was previously detected at the southern tip of the northern \npolar lobe. The inferred position of the central star corresponds \nto the geometric center of the tips of the four principle lobes of \nnear-infrared H$_2$ emission; identifying the central star at this\nposition also reveals the strong point symmetric structure of the\nnebula, as seen both in the intensity and polarization structure \nof the polar lobes. The polarimetric and imaging data \nindicate that the infrared peak directly detected in the NICMOS \nimages is a self-luminous source and, therefore, is most likely a \ndistant binary companion to the illuminating star. Although present \ntheory predicts that bipolar structure in pre-planetary and planetary \nnebulae is a consequence of binary star evolution, the separation between \nthe components of the RAFGL 2688 binary system, as deduced from these \nobservations, is much too large for the presence of the infrared \ncompanion to have influenced the structure of the RAFGL 2688 nebula.\n\n\\end{abstract}\n\n\n\\keywords{stars: AGB and post-AGB --- stars: mass-loss --- \n stars: individual (RAFGL 2688) --- circumstellar matter --- \n reflection nebulae --- techniques: polarimetric}\n\n\n\n\\section{Introduction}\n\nThe bipolar structures exhibited by a substantial fraction of the known \nplanetary nebulae likely arise during the last, rapid, pre-planetary \nnebula (PPN) stage of evolution of intermediate-mass (1--8 M$_\\odot$) \nstars off the asymptotic giant branch (AGB). \nA popular, albeit largely untested, model for \nsuch bipolarity is that the central AGB star possesses a companion that \naids in the buildup of a dense, dusty equatorial torus surrounding the \ncentral star (e.g., \\cite{soke1998}). Alternatively, the fossil remnant \nof a $\\beta$ Pic-like main-sequence disk may bear responsibility for \ntriggering bipolarity during post-main sequence evolution (\\cite{kast1995}). \nWhatever the mechanism that abets their formation, bipolar PPN \ntypically show two bright reflection lobes separated by a dark \ndust lane. The star that illuminates the polar lobes presumably is located\nat or near the center of the equatorial, dust torus. While this geometry\nobscures the central star along our direct line of sight, photons readily\nescape the nebular core in the polar directions and subsequently are \nscattered by dust grains located primarily in the walls of the rarefied, \nexpanding lobes. As even the lobe walls tend to be optically thin\nin the near-infrared, such photons can be singly scattered out of the nebula\ninto our line of sight. Single scattering produces polarized light that \ncontains a record of the original direction of the unpolarized \nlight source; therefore, polarimetric maps of such polarized nebulae contain\nclues as to the locations of their illuminating sources, even if those \nstars lie hidden inside dust lanes. \n\nRecent direct imaging of RAFGL 2688 (the Egg Nebula) with the Near Infrared \nCamera and Multi-Object Spectrometer (NICMOS) aboard the Hubble Space \nTelescope ({\\it HST}) (\\cite{saha1998}) revealed a compact red source \njust south of the bottom of the northern reflection lobe. However, \ninitial analysis of the polarimetric maps from NICMOS indicated that \nthis red source was not the primary illuminator of the reflection \nnebulosity; this object is most likely a companion to the post-AGB star that\nlurks in the core of the Egg Nebula. From a preliminary examination of \nthe 2.0 $\\mu$m polarimetric map, Sahai et al. suggested that the obscured, \npost-AGB star was located $\\simeq$ 750 AU (0\\farcs75) south of the red companion.\n\nIn this paper, we present a rigorous analysis of the 2.0 $\\mu$m \npolarization map of RAFGL 2688 obtained by NICMOS. We determine\nthe precise position of the post-AGB star in the core, assess the \nrelationship of the red source to the illuminator star, and discuss\nthe implications of this work for understanding the formation \nof the Egg Nebula and of other bipolar PPN.\n\n\\section{Polarization Data Analysis}\n\nThe data and data reduction methods used in this study were first \npresented by Sahai et al.\\ (1998). In brief summary, RAFGL 2688 was imaged\nthrough the POL0L, POL120L and POL240L filters with camera 2 (NIC2) of NICMOS, using\nintegration times of 1215 s for each filter. These filters are centered\nat 1.994 $\\mu$m and have a full-width-half-maximum of 0.2025 $\\mu$m. \nThe field of view for these images is 19\\farcs5$\\times$19\\farcs3 and \nthe plate scale is 0\\farcs076/pixel (\\cite{thom1998}). The calculations of \nfractional polarization ({\\it p}) and polarization position angle \n($\\theta$) are carried out as described by Hines (1998)\\footnote{Note that the\ncoefficients for polarimetric imaging calculations have been updated; see \nhttp://www.stsci.edu/instruments/nicmos/nicmos\\_polar.html and Hines, \nSchmidt \\& Schneider 1999}; however,\nwe find that the best position angle calculations include the \naddition of a small, constant angle $\\phi$ to $\\theta$, i.e.\n$$ \\theta = {1 \\over 2}\\tan^{-1}\\biggr({U \\over Q}\\biggl) + \\phi,$$ \nwhere $U$ and $Q$ are the Stokes vectors obtained from the polarimetric\nimages. The offset angle $\\phi$ could represent a systematic rotation of the filters in \nthe polarization filter set from their nominal position angles. For example, \nif the three polarizing filters were designed to lie at position angles \n0$^\\circ$, 120$^\\circ$, and 240$^\\circ$, they actually \nare found at position angles 0$^\\circ$ + $\\phi$, 120$^\\circ$ + $\\phi$, \nand 240$^\\circ$ + $\\phi$. Alternatively, $\\phi$ could represent \nuncertainties in our knowledge of the absolute position angles assumed \nfor the polarization calibrators. We suggest that RAFGL 2688 represents \nthe best absolute position angle calibrator for NICMOS polarimetric data. \nAs explained in \\S 4.1, we have determined empirically that \n$\\phi$ = 4.0$^\\circ$ $\\pm$ 0.2$^\\circ$. \nA polarization map of RAFGL 2688, made with $\\phi$ = 4.0$^\\circ$, \nis presented in Figure~1. \n\n\\section{The Polarization Structure of the Nebula}\n\n\nA centrosymmetric pattern is the dominant single feature of\nthe polarization map (Fig.~1); however, it is apparent by careful \ninspection of Fig.~1 that the polarimetric centroid is not spatially \ncoincident with the source (labeled A) at the southern tip of the \nnorthern lobe (see \\S 4). \nOverall, the nebula is very highly polarized, with virtually\nthe entire southern lobe polarized with $p$ $>$ 0.50 (see Fig.~6 in \nSahai et al.\\ 1998 for a grayscale map of the polarized intensity).\nA second strong feature of the polarization structure is the \napparent point symmetry of the polarization pattern around \nposition B, which we describe below. \nThe implication of such a symmetry for \nthe origin of the bipolar lobes is discussed later (see \\S 4.2).\n\nThe southern lobe is more highly polarized overall than the northern \nlobe (Figure~2). In the north, only 11 pixels show vectors with \npolarization amplitudes above 0.7; all of these vectors are on or \nwest of the polar axis, with all but one at least 5\\arcsec\\ from the \ncenter of the nebula (Figure~2a). In contrast, $\\sim$300 pixels in \nthe southern lobe have $p$ $>$ 0.7; these pixels are dominantly on \nthe eastern side of the polar axis and all of them lie more than \n4\\arcsec\\ from the center of the nebula, demonstrating a strong point \nsymmetry to the polarization pattern around the nebular core. \nAn additional $\\sim$1000 pixels are polarized with 0.6 $<$ $p$ $<$ 0.7 \n(Figure~2b). In the north, virtually all these vectors lie west of \nthe polar axis, stretching inwards along the west limb of the \nreflection lobe from a distance of $\\sim$7\\arcsec\\ to just more than \n3\\arcsec\\ from the center. In the south, these vectors are uniformly\nspread across the lobe in the outer regions and more concentrated to\nthe east of the polar axis closer to the core. Most \nof the rest of the southern lobe is polarized at a level $p$ $>$ 0.50 \n(Figure~2c). In the north, the polarization vectors in the range \n0.4 $<$ $p$ $<$ 0.6 cover most of the center of \nthe lobe (Figure~2c); the region covered by these vectors \nstretches radially away from the core along the eastern side;\nthe polarization vectors in the range 0.4 $<$ $p$ $<$ 0.6 \nalso cover the center of the southern lobe at small radial distances \nand then this region stretches outwards from the core along the \nwestern side. Finally, the outer edges of the northern lobe nearest \nto the nebular core are dominated by polarization amplitudes in the \n0.15--0.40 range (Figure~2d). \n\n\n\\section{The Polarimetric Centroid}\n\n\\subsection{Method of Determination}\n\nTo determine the position of the source that illuminates the nebula,\nwe have used the method presented by Weintraub \\& Kastner (1993),\ncoded into a program in the software package IDL.\nThis method takes advantage of the fact that a dust grain that\nsingly scatters photons out of the nebula imparts a polarization\nposition angle to the scattered light that is perpendicular to\nthe scattering plane, i.e., perpendicular to the projected direction \nfrom that dust grain to the source of \nillumination. Thus, for every pair of polarization vectors in \na map, we can draw perpendiculars to each vector and determine a\npoint of intersection. Ideally, for\nnoiseless data and purely singly scattered photons, all the pairs\nof vectors would have a unique intersection, the {\\it polarimetric \ncentroid}, which should mark the intersection between the polar axis \nand the disk midplane (assuming the illuminating source is identical \nwith the central star of the nebula and that the central star lies \nat the geometric center of the nebula). \n\nEven for noisy data and a mixture of singly and multiply scattered\nphotons, one can use the method of intersections of polarization\nperpendiculars to determine the polarization centroid,\nalbeit with finite positional error bars (\\cite{wein1993}). For a given data set,\nthe accuracy with which we can determine the centroid depends on the\nabsolute calibration of the position angles and thus depends on \nour knowledge of $\\phi$. If $\\phi$ is marginally inaccurate, the \npolarimetric centroid will be poorly determined while if $\\phi$ is quite \ninaccurate, there will be no polarimetric centroid in the map at all. \nThus, we have determined $\\phi$ by examining a range of $\\phi$ values \nbetween $-10^\\circ$ and $+10^\\circ$ and adopting the value \nthat minimizes the uncertainty in determining the polarimetric centroid.\nIn calculating the polarimetric centroid, we limit the calculation to \nthe $>$8000 pixels containing flux levels with signal-to-noise ratios \ngreater than six in all three of the POL0L, POL120L, and POL240L images.\n\n\nMany of these pairs of vectors have nearly parallel position angles. \nFor vector pairs with similar position angles, especially given even a small \nerror in determining the true position angles, the intersection position\nis poorly determined. We therefore impose an additional constraint: we\nreject all vector pairs for which the angle between the vectors \n(modulo 180$^\\circ$) is less than 20$^\\circ$. This ensures that the small \nuncertainties in the position angle calculations do not produce large \nuncertainties in the actual position of the centroid. \nIn practice, in addition to noise, many of the pixels, usually those \nwith polarization vectors with lower polarization amplitudes, represent \nparts of the reflection nebula in which multiple scattering is \nprobably dominant. Thus, for our final calculations, we placed a limit \non the minimum allowable fractional polarization to be $p_{min}$ $\\ge$ 0.15 \nin order to exclude lines of sight dominated by multiple scattering. \n\nAfter calculating the intersection points for the complete set of \nallowable vectors and vector pairs, we calculate the statistical mean \nand the standard deviation of the mean ($\\sigma$) for the polarization \ncentroid. We then repeat this calculation, keeping only intersection \npoints within a 3-$\\sigma$ rejection threshold of the initially \ndetermined mean. We continue with this process, iteratively, until the \nsolution converges on the polarimetric centroid (denoted B). \nWe find that the initial calculation typically lies \nwithin 0.1 pixels ($<$ 0\\farcs01) of the final position and the calculation \nconverges after only $\\sim$five iterations and after rejecting only \n$\\sim$2\\%--4\\% of the total possible intersections. Changing the rejection \nthreshold appears to affect only the size of the uncertainty and the rate of \nconvergence, not the position of the polarization centroid itself.\n\n\n\\subsection{Results}\n\nIn Figure~3, we present the same map as shown in Figure~1 \nbut drawn with all the vectors perpendicular to the polarization position \nangles. These vectors clearly point to a single intersection point, \nthe polarimetric centroid (labeled B in Fig.~1,3-6). In addition, this \nmap illustrates, very \nclearly, the symmetry axis of the nebula, as seen in scattered light.\n\nBy examining solutions where $p_{min}$ ranges from 0.15 to 0.35, we \nfind that the centroid lies 0\\farcs52 $\\pm$ 0\\farcs02 west and 0\\farcs16 \n$\\pm$ 0\\farcs03 south (Figure 4) of the isolated intensity peak at the \nsouthern tip of the north lobe (position A), well within the dark dust \nlane that cuts across the middle of the bipolar nebula. The positional \nuncertainty is dominated by the systematic differences between solutions found\nwhen selecting different values of $p_{min}$, rather than by the statistical\nerrors in a single calculation (which are more than an order of magnitude \nsmaller). \n\nWe have used the position of the polarimetric centroid combined with \nthe vector pattern to determine the direction of the projection of the \npolar (major) axis of the Egg Nebula. One can see (Fig.~3) that the\nprojected polar axis, drawn at a position angle of 12$^\\circ$ (east \nof north), runs exactly \nparallel to the straight lines formed by the alignment of the \nperpendiculars (of the polarization vectors) along the central axis of both the\nnorth and south scattering lobes. A change in more than 1$^\\circ$ \nin the position angle of the polar axis produces a clear error in the left-right \nsymmetry of the lobes, as defined by the polarization vectors.\nThus, we believe this determination of the projected position \nangle of the polar axis represents an improvement over \nthe previously inferred angle of 15$^\\circ$ (\\cite{ney1975}).\n\nIn projection, the centroid is located \nmuch closer to the northern than the southern lobe. The fact that B lies \ncloser to the southern tip of the northern lobe than to the northern tip \nof the southern lobe is consistent with previous determinations that the \npolar axis of the system is inclined such that the northern lobe is \ntilted toward the observer. This geometry causes the optically \nthick equatorial torus to obscure the innermost part of the southern \nlobe but permits us to view most of the inner regions of the northern lobe.\n\nIt is interesting to note the point symmetry between the two \nscattering lobes. In the north, the majority of the total intensity \nof the nebula is east of the polar axis, including the brightest reflection\npeaks (see Fig.~1). In contrast, in the south, most of the reflection \nnebula is found to the west of the polar axis. In both lobes, the \nmorphologically larger side of the nebula is the side showing\nlower overall polarization levels. We also see that the polar\naxis runs through the eastern side of the inward extension of the\nsouthern lobe and through the western side of the inward extension\nof the northern lobe. The simplest mechanism for producing \npoint symmetric structure in the nebula is the operation of collimated \nbipolar outflows. Sahai \\& Trauger (1998) have argued, based on finding \na high degree of point symmetry in the morphologies of their sample of \nyoung planetary nebulae, that such outflows are the primary agent for \nproducing aspherical structure in planetary nebulae. \n\n\\section{The Illuminator Star and its Surroundings}\n\nThe polarimetric centroid presumably marks the position of the \npost-AGB star that illuminates most or all of both the northern \nand southern reflection lobes of the Egg Nebula. We now consider \nwhether this illuminator and the intensity peak A constitute a \nwidely spaced ($>$550 AU) binary system. \n\nIf a field star were at position A, such a star would reveal\nitself in an Airy pattern in the total intensity profile, as NICMOS \ngenerates such patterns even for very faint point sources. The \nabsence of such a pattern indicates that the intensity peak A \nis an extended object. Such an object could be either a region \nof enhanced dust density that reflects light from B or a star \nembedded in the nebula that illuminates and heats the local pocket \nof dust around it. \n\nIn Figure~5, we present a polarization map of the same region as \nseen in Figure~4; however, in order to focus on the polarization \nbehavior near A, we present in Fig.~5 only the polarization \nvectors with amplitudes $p$ $<$ 0.15. If a point source at \nposition A suffers little local extinction, then it becomes a \nsource of 2 $\\mu$m photons which should generate some sort of \ncentrosymmetric polarization pattern centered on A while the direct \nline of sight to A should show a low polarization level. Given the \nlocal presence of the illuminator star at B, we might expect this \npattern to be distorted by the influence of a second photon source. \n\nIn examining Fig.~5, we find neither an indication of any kind of \ncentrosymmetric pattern, even a strongly distorted one, centered on \nthe position of the intensity peak at A, nor a simple, \ncentrosymmetric pattern focused on the position of the illuminator at B, \nsimilar to that which characterizes the vectors in the rest of the \nnebula. Instead, close to A, we find \na region marked by extremely low polarization levels and a \ndisorganized polarization pattern, despite the fact that the \nsignal-to-noise ratio is high. A somewhat more \norganized vector pattern is seen in the vectors that \nlie northeast, north and northwest of A, and which appear\nto define a centrosymmetric pattern centered on B.\n\nIf intensity peak A were simply a region of enhanced density of cold dust, \nwe should see a pattern of highly polarized vectors at A suggesting \ndirect illumination from position B, as is seen at other intermediate \nintensity peaks further out in the northern lobe. The absence of \nsuch a pattern suggests that peak A is self-luminous; however, \nthe lack of any Airy profile as would be expected from a point source \nindicates that the source at A, at 2 $\\mu$m, is\nseen as a small, extended nebula. At this position in the \nnebula, the local NICMOS point spread function generated by emission \nfrom the extended source at A, combined with the illumination of dust \nin this vicinity by B, generates a disorganized polarization pattern \nmarked by relatively low polarization levels. This analysis therefore\nsupports the suggestion \nthat intensity peak A is a self-luminous near-infrared source.\n\nWhat is the nature of the self-luminous source at peak A? Is it a deeply\nembedded star or a blob of warm dust? If it is a blob of warm dust, the \nonly likely heat sources would be illumination from the former AGB star \nlocated at least 550 AU distant or shock heating. To produce significant thermal \nemission at 1.65 $\\mu$m, the wavelength at which the blob begins to appear\n(\\cite{saha1998}), would require dust with temperatures of at least 1000 K.\nThe heating of a large amount of dust when the heat source is at least \n550 AU away is highly unlikely, even for an AGB star with a luminosity of \n10$^4$ L$_\\odot$. In addition, some of the luminosity of the AGB star \nwould be expected to show up in a reflection pattern at peak A, which we do not \nsee. As for shock heating, the maps of H$_2$ \nemission (Fig.\\ 6; also, see \\cite{saha1998}) reveal no evidence of \nshocked gas within a few tenths of an arcsec (several hundred AU) of\npeak A. If the dust had been heated by a passing shock that is now\n200 AU away, having moved past at 30 km s$^{-1}$, it would have had\nat least 30 years to cool down. Thus, it appears more likely that\nintensity peak A is a star and that A and B most likely constitute a \nwidely spaced, binary star system.\n\nAssuming A and B are a binary, their minimum separation is 550 AU (taking\nd = 1 kpc). If A and B are both in the equatorial plane and the polar \naxis is tilted 15$^\\circ$ out of the plane of the sky \n(Sahai et al.\\ (1998) estimated a tilt\nof 10$^\\circ$--20$^\\circ$ from the axial ratio of the dust torus), \nthen the star at \nA would lie $\\sim$900 AU more distant than the star at B, making the \ntrue binary separation about 1000 AU. This separation is several orders \nof magnitude larger than that hypothesized (\\cite{morr1987,soke1998}) \nfor a central binary system that could trigger the formation of an \nequatorial disk and the consequent bipolar outflow. \n\nIt is remarkable that position B appears \nto be equidistant and point-symmetrically placed between \nthe apex of the western loop (E1), the apex of the middle of the \neastern loops (E3), and the most distant points in the polar \nlobes of molecular hydrogen emission (Fig.\\ 6). Thus, the \npolarimetric and molecular hydrogen emission centroids are \npositionally coincident. This result strongly indicates that \nthe nebular illuminator at B also generated the H$_2$ emission,\nwhere the H$_2$ emission regions are delineated by sharp outer \nboundaries suggestive of shocks. As shocks require fairly \nsudden changes --- in this case, perhaps the rapid turning-on of a \nfast wind from the former AGB star, perhaps triggered by the quite \nquick stripping and ejection of the stellar envelope and the \nsubsequent capture of a close companion --- the relationship between \nposition B and the H$_2$ emission lobes suggests that the shocks seen \nin the H$_2$ were caused by a very sudden event or series of events \nin the evolution of the central star. \n\nThus, while the presence of the A+B binary at the core of RAFGL 2688 does \nnot lend support to the binary trigger hypothesis for the formation \nof bipolar planetary nebulae, the relationship between the central star\nat B and the H$_2$ lobes may support such a hypothesis. \nSpecifically, absorption of a close binary companion by the atmosphere \nof the central AGB star may cause the ejection of high-velocity material;\nthe ejected material produces the shocked H$_2$ emission and \ngenerates the bipolar structure of the Egg Nebula.\n\n\\section{Summary}\n\nFrom a detailed analysis of the polarimetric images obtained using \nNICMOS and the {\\it HST}, we have precisely determined the position \nof the post-AGB star in the waist of the Egg Nebula and the projected \norientation of the polar axis (PA 12$^\\circ$) of this bipolar system. \nThis post-AGB star, which illuminates the Egg Nebula, falls \npoint-symmetrically at the center of the molecular hydrogen emission \nregions that mark the waist and the polar lobes of the nebula. \nWe find that this star lies 550 AU in projected distance, and perhaps \n1000 AU in physical distance, from the star previously identified \n(\\cite{saha1998}) at the southern tip of the northern polar lobe. \nThus, these data provide clear evidence \nfor the presence of an optically obscured, widely spaced binary system \nnear the core of the bipolar, pre-planetary nebula RAFGL 2688. However,\nthe separation between these components is orders of magnitude larger \nthan required by models postulating that companions to AGB stars \ntrigger the production of bipolar planetary nebulae.\n\n\\acknowledgments{\nDCH acknowledges support by NASA grant NAG5-3042 to the \nNICMOS instrument definition team. RS thanks NASA for support through \ngrant GO-07423.01-96A from the Space Telescope Science Institute (which \nis operated by the Association of Universities for Research in Astronomy, \nInc., under NASA contract NAS5-26555).\n}\n\n\n\\begin{thebibliography}{}\n\n%\\bibitem[Cohen \\& Kuhi 1977]{cohe1977}\n% Cohen, M. \\& Kuhi, L. V.1977, \\apj, 213, 79.\n\n%\\bibitem[Cox et al.\\ 1997]{cox1997}\n% Cox, P., Maillard, J.-P., Huggins, P. J., Forveille, T., Simons, D.,\n% Guilloteau, S., Rigaut, F., Bachiller, R., \\& Omont, A. \n% 1997, A\\&A, 321, 907\n\n\\bibitem[Hines 1998]{hine1998}\n\tHines, D. C. 1998, ``Imaging Polarimetry with NICMOS,'' NICMOS\n\tInstrument Science Report.\n\n\\bibitem[Hines et al.\\ 1999]{hine1999}\n\tHines, D. C., Schmidt, \\& Schneider 1999, \\pasp, in prep.\n\n\\bibitem[Kastner \\& Weintraub 1995]{kast1995}\n\tKastner, J. H., \\& Weintraub, D. A. 1995. \\aj, 109, 1211\n\t\n\\bibitem[Morris 1987]{morr1987}\n Morris, M. 1987, \\pasp, 99, 1115\t\n\t\n\\bibitem[Ney et al.\\ 1975]{ney1975}\n Ney, E. P., Merrill, K. M., Becklin, E. E., Neugebauer, G., \\&\n Wynn-Williams, C. G. 1975, ApJ, 198, L129\t\n\n\\bibitem[Sahai et al.\\ 1998] {saha1998} Sahai, R., Hines, D. C., Kastner, J. H.,\n Weintraub, D. A., Trauger, J. T., Rieke, M. J., Thompson, R. I., \\&\n Schneider, G. 1998, \\apjl, 492, L163\n\n\\bibitem[Sahai \\& Trauger 1998]{sata1998}\nSahai, R. \\& Trauger, J. T. 1998, AJ, 116, 1357\n\n\\bibitem[Soker 1998]{soke1998} \n\tSoker, N. 1998, \\apj, 496, 833\n\t\n\\bibitem[Thompson et al.\\ 1998]{thom1998} Thompson, R. I, Rieke, M., Schneider, G., \n Hines, D.C., \\& Corbin, M.R., 1998, \\apjl, 492, L95\n\n\\bibitem[Weintraub \\& Kastner 1993]{wein1993}\n Weintraub, D. A., \\& Kastner, J. H., 1993, \\apj, 411, 767 \n \n%\\bibitem[Yusef-Zadeh, Morris \\& White]{yuse1984}\n% Yusef-Zadeh, B., Morris, M., White, R. L. 1984, ApJ, 278, 186\n\n\n\\end{thebibliography}\n\n\\clearpage\n\n\\figcaption[fig1.eps]{\nPolarization map of RAFGL 2688, obtained from 2.0 $\\mu$m imaging from\nNICMOS. Vectors are plotted only where intensity level is greater \nthan 3-$\\sigma$ in all three Stokes images. The polarimetric centroid \nis labeled B and found at the intersection of the lines marking the \nprojected polar axis (12$^\\circ$ east of north) and equatorial\nplane of the nebula. The intensity peak is labeled A. Vectors indicate\nthe polarization strength (length) and position angles in each pixel,\nwith only vectors with $p$ $\\ge$ 0.15 plotted. \n% Pixel scale is 0\\farcs076.\nIn this and all other figures, orientation is indicated by north (N) \nand west (W) axes, offset distances are measured from \nB, absolute polarization amplitudes are indicated by a $p$ = 0.30\nfiducial vector marked in the lower right corner of panel, and intensity\ncontours are drawn at 1 magnitude intervals, with the lowest contour at\nthe 3-$\\sigma$ level in the total intensity image.\n\\label{fig1}}\n\n\\figcaption[fig2.eps]{Full view of RAFGL 2688 with polarization vectors \nin the specified range overlaid on 2.0 $\\mu$m intensity contours (same\ncontour levels as Fig.\\ 1). \na) $p$ $>$ 0.70,\nb) 0.70 $>$ $p$ $>$ 0.60, \nc) 0.60 $>$ $p$ $>$ 0.40, \nd) 0.40 $>$ $p$ $>$ 0.15. \n\\label{fig2}}\n\n\\figcaption[fig3.eps]{Same as Figure~1 but with all polarization vectors drawn \nperpendicular to their normal orientations. \\label{fig3}}\n\n\\figcaption[fig4.eps]{Polarization map of central region of nebula \nshowing position of polarimetric centroid. Only vectors with $p$ \n$\\ge$ 0.15 are plotted. Size of small plus sign at the position of\nSource B indicates 1-$\\sigma$ \nsystematic uncertainty in determination of centroid position. \\label{fig4}}\n\n\\figcaption[fig5.eps]{Close-up polarization map of same region as Figure~4, \nbut showing only vectors with $p$ $<$ 0.15. \n \\label{fig5}}\n\n\\figcaption[fig6.eps]{Molecular hydrogen emission (grayscale) overlaid \nwith 2 $\\mu$m continuum (contours).\n\\label{fig6}}\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002079.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem[Cohen \\& Kuhi 1977]{cohe1977}\n% Cohen, M. \\& Kuhi, L. V.1977, \\apj, 213, 79.\n\n%\\bibitem[Cox et al.\\ 1997]{cox1997}\n% Cox, P., Maillard, J.-P., Huggins, P. J., Forveille, T., Simons, D.,\n% Guilloteau, S., Rigaut, F., Bachiller, R., \\& Omont, A. \n% 1997, A\\&A, 321, 907\n\n\\bibitem[Hines 1998]{hine1998}\n\tHines, D. C. 1998, ``Imaging Polarimetry with NICMOS,'' NICMOS\n\tInstrument Science Report.\n\n\\bibitem[Hines et al.\\ 1999]{hine1999}\n\tHines, D. C., Schmidt, \\& Schneider 1999, \\pasp, in prep.\n\n\\bibitem[Kastner \\& Weintraub 1995]{kast1995}\n\tKastner, J. H., \\& Weintraub, D. A. 1995. \\aj, 109, 1211\n\t\n\\bibitem[Morris 1987]{morr1987}\n Morris, M. 1987, \\pasp, 99, 1115\t\n\t\n\\bibitem[Ney et al.\\ 1975]{ney1975}\n Ney, E. P., Merrill, K. M., Becklin, E. E., Neugebauer, G., \\&\n Wynn-Williams, C. G. 1975, ApJ, 198, L129\t\n\n\\bibitem[Sahai et al.\\ 1998] {saha1998} Sahai, R., Hines, D. C., Kastner, J. H.,\n Weintraub, D. A., Trauger, J. T., Rieke, M. J., Thompson, R. I., \\&\n Schneider, G. 1998, \\apjl, 492, L163\n\n\\bibitem[Sahai \\& Trauger 1998]{sata1998}\nSahai, R. \\& Trauger, J. T. 1998, AJ, 116, 1357\n\n\\bibitem[Soker 1998]{soke1998} \n\tSoker, N. 1998, \\apj, 496, 833\n\t\n\\bibitem[Thompson et al.\\ 1998]{thom1998} Thompson, R. I, Rieke, M., Schneider, G., \n Hines, D.C., \\& Corbin, M.R., 1998, \\apjl, 492, L95\n\n\\bibitem[Weintraub \\& Kastner 1993]{wein1993}\n Weintraub, D. A., \\& Kastner, J. H., 1993, \\apj, 411, 767 \n \n%\\bibitem[Yusef-Zadeh, Morris \\& White]{yuse1984}\n% Yusef-Zadeh, B., Morris, M., White, R. L. 1984, ApJ, 278, 186\n\n\n\\end{thebibliography}"
}
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astro-ph0002080
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Nearby Gas-Rich Low Surface Brightness Galaxies
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[
{
"author": "Stephen E. Schneider"
}
] |
We examine the Fisher--Tully $cz<1000$ km s$^{-1}$ galaxy sample to determine whether it is a complete and representative sample of {all} galaxy types, including low surface brightness populations, as has been recently claimed. We find that the sample is progressively more incomplete for galaxies with (1) smaller physical diameters at a fixed isophote and (2) lower HI masses. This is likely to lead to a significant undercounting of nearby gas-rich low surface brightness galaxies. However, through comparisons to other samples we can understand how the nearby galaxy counts need to be corrected, and we see some indications of environmental effects that probably result from the local high density of galaxies.
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[
{
"name": "ms.tex",
"string": "\\documentstyle[aaspp4]{article}\n \n%\\received{ }\n%\\accepted{ }\n%\\journalid{ }{ }\n%\\articleid{ }{ }\n \n%\\slugcomment{ }\n \n \n\\lefthead{Schneider \\& Schombert}\n\\righthead{Nearby LSB Galaxies}\n \n\\begin{document}\n \n\\title{Nearby Gas-Rich Low Surface Brightness Galaxies} \n\n\\author{Stephen E. Schneider}\n\\affil{Astronomy Program, University of Massachusetts,\n Amherst, MA 01003}\n\n\\author{James M. Schombert}\n\\affil{Department of Physics, University of Oregon}\n \n\\begin{abstract}\n\nWe examine the Fisher--Tully $cz<1000$ km s$^{-1}$ galaxy sample to determine\nwhether it is a complete and representative sample of {\\it all} galaxy types,\nincluding low surface brightness populations, as has been recently claimed. \nWe find that the sample is progressively more incomplete for galaxies with (1)\nsmaller physical diameters at a fixed isophote and (2) lower HI masses. This\nis likely to lead to a significant undercounting of nearby gas-rich low\nsurface brightness galaxies. However, through comparisons to other samples we\ncan understand how the nearby galaxy counts need to be corrected, and we see\nsome indications of environmental effects that probably result from the local\nhigh density of galaxies.\n\n\\end{abstract}\n \n\\keywords{galaxies: luminosity function}\n \n\\section{Introduction}\n\nTwo of the key questions in 20th century extragalactic studies have concerned\nthe density and the composition of the galaxy population in the Universe. Our\nknowledge of galaxy types and their abundance depends critically on the issue\nof completeness of our galaxy catalogs. Since our current catalogs are\nconstructed by various observational means, they are, by definition, limited by\nnatural and technological selection effects.\n\nRecently, Briggs (1997a) has argued that the Fisher \\& Tully (1981, F--T)\ncatalog of nearby galaxies is complete to its redshift and sensitivity limits,\neven for low surface brightness (LSB) galaxies. F--T examined HI emission from\na sample of 1787 angularly large galaxies accessible from the Green Bank radio\ntelescopes. They believed the sample to be very complete for late-type galaxies\nwithin a redshift of $cz=1000$ km s$^{-1}$, with angular diameters larger than\n3$'$, located in regions at $|b|>30^\\circ$ and $\\delta>-33^\\circ$. Briggs\nadditionally found a sensitivity limit depending on the HI mass and defined the\nF--T ``completeness zone'' as extending out to:\n\\begin{equation}\nz_{CZ} = \\left\\{ \\begin{array}{ll} 1000\\mbox{km s}^{-1}/c & \n\\mbox{if $M_{HI}>10^{8.45} h_{75}^{-2} M_\\odot$} \\\\\n(M_{HI}h_{75}^{2}/10^{8.45}M_\\odot)^{5/12} 1000\\mbox{km s}^{-1}/c &\n\\mbox{otherwise.}\n\\end{array} \\right. \n\\end{equation} \nThe form of the limit for sources with masses smaller than \n$10^{8.45}M_\\odot$\\footnote{We adopt $H_0=75$ km s$^{-1}$ Mpc$^{-1}$ for masses\nand distances quoted hereafter, and we use the heliocentric velocity corrected\nby 300 km s$^{-1} \\cos b \\sin l$ as in F--T and Briggs.} was based on a\nsemi-analytic, semi-empirical fit to the HI sensitivity.\n\nBriggs pointed out that surveys of low surface brightness galaxies (Schneider\net al.~1990; Schombert et al.~1992; Matthews \\& Gallagher 1996; Impey et\nal.~1996) have identified sources that are primarily at larger distances, but\nthey have added very few within the F--T ``completeness zone.'' He concluded\nthat LSB galaxies ``must already be fairly represented by nearby, previously\ncataloged examples.''\n\nThis is an interesting idea, but the conclusion does not necessarily follow\nfrom the analysis for several reasons: (1) For sources with low HI masses\n$z_{CZ}$ is so small that redshift distances are very uncertain and Galactic\nHI emission creates strong confusion. A further objection to Briggs' analysis\nis that (2) the F--T sources are themselves incomplete within Briggs'\n``completeness zone'' because of angular size selection effects. Lastly, (3)\nthe $cz<1000$ km s$^{-1}$ region around the Local Group has about twice the\naverage galactic density and therefore is not a very representive sample of the\nUniverse as a whole.\n\nIn a companion paper, Briggs (1997b) used the F--T and LSB samples to derive\nan HI mass function. He commented on the need for corrections for\nincompleteness and noted the usefulness of a ${\\cal V}/{\\cal V}_{max}$ test\nfor establishing whether the LSB samples were complete, but he did not discuss\nthe problems the F--T sample has in this regard. In this paper we explore the\nlimitations of the F--T sample and discuss how it and more recent surveys may\nbe properly used to understand the composition of galaxy populations. We show\nthat the local samples of galaxies display morphological segregation\ncharacteristics associated with high density environments. Finally, we find\nthat in all HI mass ranges the dominant class of galaxies are those with the\nsmallest angular diameters at the isophotal limits of the original Palomar Sky\nSurvey (PSS-I). These galaxies may be physically small or appear small because\nthey are LSB systems; in either case, they are greatly under-represented in\nthe F--T sample and most other optical surveys.\n\n\n\\section{Completeness Tests of the F--T Sample}\n\nThe incompleteness of the F--T sample can be demonstrated using a ${\\cal V} /\n{\\cal V}_{max}$ test. This test compares the distance $d$ of a detected source\nto the maximum distance $d_{max}$ at which it should be detectable. If the\nmaximum distance is correctly estimated, a source is equally likely to fall\nanywhere within the volume delimited by $d_{max}$. On average, then, sources\nwill be found halfway into the maximum volume, and ${\\cal V} / {\\cal V}_{max}\n\\equiv (d/d_{max})^3$ will average 0.5 (Schmidt 1968). For a sample of $N$\nsources, the probability distribution of the mean value of ${\\cal V}/{\\cal\nV}_{max}$ has a nearly normal distribution with standard deviation\n$1/\\sqrt{12N}$.\n\nWe assume the distance is proportional to the redshift $z$, so that ${\\cal\nV}/{\\cal V}_{max}=(z/z_{max})^3$. We exclude galaxies within $6^\\circ$ of the\ncenter of the Virgo cluster or $3^\\circ$ of the Fornax cluster from the\n$cz<1000$ km s$^{-1}$ sample. This eliminates the worst distance estimates,\nalthough peculiar velocities clearly must affect the rest of the sample as\nwell. We have tested how adjustments for peculiar velocity might alter our\nresults using the $POTENT$ model of Dekel, Bertschinger, and Faber (1990), and\nfind no substantive changes from the results presented below, although the\nsamples generally have somewhat lower values of ${\\cal V}/{\\cal V}_{max}$. We\nuse the redshift corrected for Local Group motion here to maintain consistency\nwith F--T and Briggs.\n\nWith $z_{max}=z_{CZ}$, the mean value of ${\\cal V}/{\\cal V}_{max}$ is\n$0.406\\pm0.016$. Values below 0.5 imply that galaxies were detected\npreferentially in the nearer portion of the survey volume, suggesting that the\nsample is not fully sensitive to sources out to $z_{CZ}$.\n\nA low value of ${\\cal V}/{\\cal V}_{max}$ can alternatively be caused by an\nactual clustering of galaxies nearby us. However, this tends to be\ncounter-balanced by the effects of morphological segregation and gas\ndepletion, which would favor HI detections in lower-density environments. In\nany case, the F--T sample is mostly confined to within the local supercluster,\nand it is not clear that there is an overall radial gradient within the\nsampled region. Moreover, these effects do not explain the dependence of\n${\\cal V}/{\\cal V}_{max}$ on HI mass.\n\n\\input tbl1.tex\n\n\nIn Table 1 we list the results for various galaxy samples and divide each\nsample into three mass ranges.\\footnote{While the upper and lower mass ranges\nare unbounded on one side, the range of detected masses is approximately one\ndecade in both cases.} Sample 1 shows that the F--T sample in the\n``completeness zone'' exhibits worse and worse completeness for lower mass\ngalaxies.\n\nUsing Briggs' functional form (eqn.~1) for the completeness limit, we could\nincrease the minimum mass for full-volume sensitivity from $10^{8.45}$ to\n$10^{9.15} M_\\odot$ to make ${\\cal V}/{\\cal V}_{max}$ close to 0.5 in all mass\nranges (sample 2 in Table 1). This revised limit would set the completeness\nzone limit to $cz<330$ km s$^{-1}$ for $M_{HI}<10^8$ so that distance\nuncertainty and confusion with Galactic HI would present significant problem\nfor an even larger portion of the sample. In addition, within such small\nredshifts ${\\cal V}/{\\cal V}_{max}$ is probably biased upward, since the\nlowest redshift sources may be lost in Galactic emission and sources detected\nat redshifts below $cz=100$ km s$^{-1}$ were set to that value for the purpose\nof estimating their distances. These limitations make the F--T sample highly\nproblematic for trying to understand properties of galaxies with HI masses\n$<10^8 M_\\odot$.\n\n\n\\section{Angular Size Limitations of Optical Samples}\n\nAnother approach to understanding the completeness of the F--T sample is to\nexamine the source selection criteria. F--T used a minimum angular size as\ntheir primary selection criterion---examining spirals with diameters $a>3'$ and\nSd--Im galaxies with $a>2'$ as determined in the UGC (Nilson 1973). Because\nother sources of angular diameters were also used for parts of the sample, some\nsmaller galaxies were also observed. To place all of the angular sizes on a\ncommon system, we use the formulas from F--T to convert to the UGC scale.\n\nBased on the expected increase of counts with angular diameter as $N\\propto\na^{-3}$, the full sample of observed galaxies (whether or not they were\ndetected in HI) begins to be incomplete for angular sizes $a<4'$\n(Fig.~\\ref{aftu}). At $a=2'$ there are $\\sim15\\times$ too few galaxies relative\nto the larger sources. This incompleteness at small angular sizes is partly\nintentional, since F--T excluded small angular diameter galaxies that they\nexpected would be distant. Unfortunately, this also introduces a degree of\nsubjectiveness to inclusion in the sample.\n\n\\begin{figure}[tbh]\n\\plotone{fig1.eps}\n\\caption{\nHistogram of F--T galaxy angular diameters. The dotted line shows the expected\nslope for a complete sample distributed uniformly throughout space.\n}\n\\label{aftu}\n\\end{figure}\n\nEven among the F--T galaxies in Briggs' ``completeness zone,'' many of the\ngalaxies have angular sizes so small that they would not have remained in the\nsample if they were at their maximum distance within the zone. The angular size\na source would have at $z_{CZ}$ is $a_{CZ}\\equiv a\\times z/z_{CZ}$. Of the 41\nsources with $M_{HI}<10^8M_\\odot$, none has $a_{CZ}>4'$; only one is $>3'$, the\nstated completeness limit of F--T; and only 8 have $a_{CZ}>2'$. Even among the\n171 intermediate mass sources, with $10^8<M_{HI}<10^9M_\\odot$, only 7\\%, 25\\%,\nand 60\\% galaxies have $a_{CZ}>4'$, $3'$, and $2'$ respectively. Only the high\nmass sources are large enough that high fractions pass the $a_{CZ}$\nrequirement---74\\%, 90\\%, and 98\\% for $a_{CZ}>4'$, $3'$ and $2'$. Clearly this\nwill tend to push ${\\cal V}/{\\cal V}_{max}$ to lower values since some galaxies\nare included only in the near portion of the search volume.\n\nTo make a more uniform selection we can restrict the F--T sample to $a_{CZ}>3'$\n(sample 3), in the intermediate and high mass ranges ${\\cal V}/{\\cal V}_{max}$\nis below 0.5 only marginally (1.3 and 1.0 $\\sigma$), but the low mass range\ncannot be tested since it has only one galaxy. Restricted to $a_{CZ}>2'$\n(sample 4) the F--T sample does not pass the ${\\cal V}/{\\cal V}_{max}$ test in\neither the low or intermediate mass ranges.\n\nOne way of addressing the omission of small galaxies is to look to samples of\nsmall galaxies. In particular the ``dwarf and LSB'' (D+LSB) sample of galaxies\nfrom Schneider et al. (1990, 1992) contains HI measurements for late-type,\ndwarf, and irregular galaxies down to a $1'$ diameter. Since this sample is\ndrawn from the UGC, it covers only the northern sky ($\\delta>-2.5^\\circ$), but\nwhen supplemented with HI measurements from the literature (Huchtmeier \\&\nRichter 1989) the HI detections are more than 85\\% complete. \n\nThe ${\\cal V}/{\\cal V}_{max}$ test results for the D+LSB sample within Briggs'\n``completeness zone'' are given in Table 1 (sample 5). The low-mass ranges\nstill do not pass the test, but they fare considerably better than the F--T\nsample. By restricting the galaxies to $a_{CZ}>1'$, which eliminates galaxies\nthat only meet the UGC size criterion because they are very nearby (sample 6),\nthe test is passed to within $2\\sigma$ in all mass ranges. This also shows\nthat large scale structure is not causing low ${\\cal V}/{\\cal V}_{max}$ test\nresults for the F--T sample.\n\nWe can combine the F--T and D+LSB samples in the hope of forming a complete\nsample of all types of galaxies as Briggs (1997b) did. In the northern sky we\nfind 248 F--T galaxies and 47 additional D+LSB galaxies that satisfy the\n``completeness zone'' criteria. This expanded sample fares only marginally\nbetter in the ${\\cal V}/{\\cal V}_{max}$ tests, yielding $0.407\\pm0.016$ for the\nfull sample, and in the separate mass ranges (Table 1, sample 7). Restricting\n$a_{CZ}$ does not generate samples that pass the ${\\cal V}/{\\cal V}_{max}$ test\neither.\\footnote{Restricting the samples to high Galactic latitudes\n($|b|>30^\\circ$) made no appreciable difference to the results presented in\nTable 1.} \n\nWe conclude that the F--T sources with high HI masses represent a relatively\ncomplete sample, but the sources with low HI masses are strongly biased to low\nredshifts. The problem with low mass galaxies may be caused in part by the\nF--T angular size criterion. However, even when the F--T sample is (1)\nrestricted to minimum physical diameters to make the galaxies relatively\nuniform within the ``completeness zone,'' or (2) supplemented by galaxies from\nother surveys, the galaxies with HI masses $<10^9 M_\\odot$ still fail the\n${\\cal V}/{\\cal V}_{max}$ test. This demonstrates that the F--T sample does\nnot provide a good basis for forming a representative cross section of galaxy\ntypes. \n\n\\section{High Mass LSB Galaxies}\n\nWhile galaxies with high HI masses ($M_{HI}>10^9 M_\\odot$) in the F--T sample\npass the ${\\cal V}/{\\cal V}_{max}$ test, this is really only an internal check\non the self-consistency of the database. To examine the broader question of\nhow representative the F--T sample is, Briggs (1997a) asked whether surveys of\nLSB galaxies had found galaxies within the ``completeness zone.'' However,\nsince these other surveys were also based on visual examination of\nphotographic plates, they do not provide a genuinely independent check of the\nF--T sample. Moreover, since the local density of galaxies is higher than\naverage, classes of galaxies that avoid high density may not be present.\n\nThe question we consider here is whether there are massive HI sources in\ndeeper surveys that would have been excluded from the F--T sample because\ntheir isophotal diameters at the PSS-I surface brightness would be less than\n3--4$'$ at the 1000 km s$^{-1}$ redshift limit for high mass galaxies in the\n``completeness zone.'' This is difficult to quantify precisely since diameters\nestimated from the PSS-I are somewhat variable in their effective depth, but\nwe will adopt the mean isophotal level found by Cornell et al.~(1987) of\n$\\mu_{PSS-I}\\equiv 25.36$ mag arcsec$^{-2}$ at $B$ for UGC diameters.\n\nThe F--T subset of high-mass galaxies are almost all physically large at\n$\\mu_{PSS-I}$. Figure 2 shows the distribution of $a_{CZ}$ for this (solid-line\nhistogram) and other samples of galaxies. Since all of the high mass galaxies\nare detectable to the 1000 km s$^{-1}$ redshift limit, $a_{CZ}=1'$ corresponds\nto 3.88 kpc. Thus 90\\% of the F--T high mass galaxies have sizes larger than\n11.6 kpc. Note that we restrict the following analyses to galaxies at high\nGalactic latitudes where interstellar extinction should not much affect the\ngalaxies' optical sizes or number counts. \\footnote{Briggs (1997ab) specifies\nthat his samples are restricted to high latitudes, but the numbers of galaxies\nhe quotes in various subsamples indicate he was using the full sky coverage\nof F--T.}\n\n\\begin{figure}[p]\n\\epsscale{0.7}\n\\plotone{fig2.eps}\n\\caption{\nNumber density of galaxies as a function of their angular diameter as\ndetermined at the ``completeness zone'' distance limit. The size distribution\nof the F--T sample is shown by a solid-line histogram; the UGC Dwarf+LSB\nsample is shown by a dashed line, and restricted to the ``completeness zone''\nby a dot-dash line; the PSS-II LSB sample is shown by a dotted line. The size\ndistribution of the HI-selected ``Slice'' sample is shown by a solid gray\nhistogram. The densities of the F--T sample and the D+LSB sample in the\nlow-mass range are divided by two to account for the local overdensity as\nexplained in the text. \n}\n\\label{massacz}\n\\end{figure}\n\n\n\nWe give the estimated number density of each size of galaxy in the figure\nbased on the areal coverage of the sample ($\\sim$5.1 sr for the high-latitude\nportion of the F--T sample). We also need to account for the local overdensity\nof galaxies when making comparisons to other samples. Briggs (1997b) estimates\nthe region inside $cz<1000$ km s$^{-1}$ has a density about a factor of 2\nabove average. This matches our results for the D+LSB sample, which has a\ndensity 2.1 times higher in the nearby portion. Densities in Fig.~2 that are\nbased on the F--T sample and other samples restricted to the local region are\ndivided by 2.\n\nThe ``HI-Slice'' sample of Spitzak \\& Schneider (1998) was found by\nsystematically observing 55 sq deg of the sky at 21 cm from Arecibo, and is\nunbiased by optical sizes. This survey contains 62 sources with $M_{HI}>10^9\nM_\\odot$. We have determined the angular sizes at $\\mu_{PSS-I}$ from the\noriginal $B$-band photometric profile fits of Spitzak \\& Schneider. Compared to\nthe F--T sample, these galaxies have lower percentages of optically large\ngalaxies, and higher percentages of small galaxies, although there appear to be\nvery few galaxies smaller than 7.8 kpc in either sample.\n\nUsing the sensitivity limit estimates from Schneider, Spitzak, \\& Rosenberg\n(1998), we can determine the volume within which each of the HI-Slice galaxies\nwas detectable in order to estimate its number density in space. The results\nare shown in Fig.~2 by the solid-gray histogram. We estimate that 75\\% of the\nHI among these massive galaxies is associated with galaxies larger than\n$a_{CZ}>4'$. Assuming the F--T sample is complete for these largest galaxies,\nthe smaller fraction of galaxies it finds at smaller sizes implies it is\nmissing about 23\\% of high-mass galaxies and 12\\% of the total HI due to the\nangular size limitations.\n\nSeveral differences between the samples may reflect environmental influences.\nThe distribution of F--T galaxy sizes in Fig.~2 suggests that the population\nhas been shifted to systematically larger sizes than the HI-Slice galaxies. In\naddition, the HI-selected sample has $1.8\\times$ less $B$-band luminosity\nrelative to the HI mass on average, based on optical data from Spitzak \\&\nSchneider and the RC3 (de Vaucouleurs et al. 1991), and 40\\% of the HI-selected\ngalaxies have $M_{HI}/L_{B}>1$ (in solar units) compared to 11\\% of the F--T\ngalaxies. Since the F--T sample is located in a region of high galaxy\ndensity, star formation induced by galaxy interactions may explain these\ndifferences.\n\nBy contrast, {\\it optically}-selected samples, even of LSB galaxies, rarely\nidentify high HI mass objects that would not have been identified in Briggs'\n``completeness zone.'' If we impose no HI-mass/redshift restrictions, the\nD+LSB sample (\\S 3) contains 586 high-HI-mass sources with $|b|>30^\\circ$, and\nit has even higher fractions of large-$a_{CZ}$ galaxies than the F--T sample.\nThis suggests that almost all UGC galaxies with large HI masses have large\nphysical dimensions at $\\mu_{PSS-I}$.\n\nHowever, the raw distribution of $a_{CZ}$ in an angular-diameter limited\nsample is not a good indicator of the population size distribution since\ngalaxies with smaller physical diameters at $\\mu_{PSS-I}$ remain larger than\n$1'$ (the UGC limit) out to smaller distances. Dividing the counts by the\nvolume in which each galaxy remains larger than $1'$, the distribution has a\nsimilar shape to the HI-selected sample (dashed-line histogram in Figure 2).\nThese galaxies also appear to have distinctly different properties from\ngalaxies in the F--T sample---their $B$-band luminosities relative to their HI\nmasses are similar to the HI-selected sample of sources. \n\nThe distribution of sizes of the subset of D+LSB galaxies within $cz<1000$ km\ns$^{-1}$ is shown by a dot-dash line. The counts have been divided by 2 (like\nthe F--T sample) and demonstrate that the density correction used earlier is\nreasonable. The nearby D+LSB galaxies show a slight shift toward larger sizes\nthan the full sample. This indicates that the distribution of sizes in a\nsample of late-type galaxies alone is little-affected by the local density\nenhancement. By contrast, the F--T and HI-selected samples contain a wide\nrange of morphological types. Since earlier-type galaxies tend to be larger at\nthe same isophotal level, the shift in the size distribution to larger\n$a_{CZ}$ within the F--T sample may reflect the effects of morphological\nsegregation, with a larger proportion of earlier types than an average sample.\n\nWithin the northern portion of the ``completeness zone'' the D+LSB sample adds\nonly 1 high-mass galaxy to the F--T sample, so the size distribution of the\ncombined sample is basically unchanged. The lack of additional\nsmall angular diameter galaxies supports the idea that the local population is\ndifferent from samples drawn from a wider variety of environments.\n\nThe PSS-II survey of Eder \\& Schombert (1999) is a deeper probe for small\ndiameter, very late-type galaxies. These objects were selected from 50 PSS-II\nplates ($\\sim$0.7 sr) to be larger than 20$''$ and to have dwarf-like\nmorphologies. We have determined the sizes on the PSS-I for each of these\nobjects; our size estimates are consistent for galaxies in common with the UGC.\nThe size distribution turns over below diameters of 0.4$'$ at $\\mu_{PSS-I}$,\nwhich we take to be the effective completeness limit.\n\nWhile aimed primarily at identifying dwarf galaxies, the PSS-II sample includes\n135 galaxies with $M_{HI}>10^9M_\\odot$. Their size distribution is shown by a\ndotted line in Fig.~2. Only 7 of these objects are smaller than $a_{CZ}<2'$,\nbut based on their angular size distance limits, such small sources comprise\nabout half of the population of high mass LSB objects with very late type\nmorphologies.\n\nExtremely high HI mass LSB systems like Malin 1 (Bothun et al.~1987) might\nhave been missed in the nearby volume of space because their disks are so\nfaint that even the central extrapolated surface brightness of the disk is\nfainter than $\\mu_{PSS-I}$. However, the bulge component of Malin 1 would\nreach $\\mu_{PSS-I}$ at about $3.75'$ at $cz=1000$ km s$^{-1}$. We can\nspeculate that a system like Malin 1 might have been identified as an E or S0\nin the UGC, and therefore omitted from consideration for the F--T sample. It\nis worth noting that a number of early-type galaxies have been found with\nextended distributions of HI (Van Driel \\& Van Woerden 1991; DuPrie \\&\nSchneider 1996), and perhaps these are the more appropriate comparison to\nMalin 1. For other giant disk systems that have been compared to Malin 1, like\nF568-6 (Bothun et al.~1990) and 1226+0105 (Sprayberry et al.~1993), the disk\nsurface brightness and size would make these objects easily exceed\n$a_{CZ}>3'$, and should thus have been included in the F--T sample if they\nwere in the ``completeness zone.''\n\nIn summary, high-HI-mass galaxies are relatively well-sampled by F--T, but\nthey do miss an interesting fraction of galaxies that have small sizes at the\nPSS-I isophotal limit. Based on intrinsic differences in the optical-to-21 cm\nemission from the nearby F--T sample versus more-distant samples, we suggest\nthat the high density of galaxies in the local environment may cause\ndifferences in the local population.\n\n\\section{Low and Intermediate Mass Galaxies}\n\nGalaxies with less than $10^9 M_\\odot$ of HI are highly incomplete in the F--T\nsample. Among the galaxies identified by F--T in this mass range, about half\nhave $a_{CZ}<2'$, and only $7\\%$ are larger than $a_{CZ}>4'$, so F--T's\nadopted angular size constraints give rise to a fundamental limitation to the\nsample's completeness. We illustrate here the degree of the incompleteness and\nattempt to extrapolate to the population of missing objects.\n\nThe distribution of sizes in the F--T sample among lower mass galaxies is shown\nin the bottom two panels of Fig.~2, divided into intermediate\n($10^8-10^9M_\\odot$) and low ($<10^7M_\\odot$) HI masses. Since $z_{CZ}$\ndeclines for galaxies with HI masses $<10^{8.45}M_\\odot$ (eqn.~1), the density\nis estimated from the corresponding volume. At $10^8 M_\\odot$, the distance\nlimit and $a_{CZ}$ are 65\\% of their value for high-mass galaxies, and at $10^7\nM_\\odot$ they are 25\\% as big.\n\nThe HI-Slice sample of Spitzak \\& Schneider (1998) contains 3 low and 10\nintermediate mass galaxies. Despite the small-number statistics, this sample\nclearly demonstrates that very small sizes are the norm among low-HI-mass\ngalaxies as shown in Fig.~2. {\\it All} of the sources are smaller than\n$a_{CZ}=2.2'$, and 5 of 6 sources with $M_{HI}<2.5\\times10^8$ are smaller than\n$a_{CZ}<1'$. One relatively high mass source ($M_{HI}=7\\times10^8M_\\odot$) has\n$a_{CZ}=0.13'$ and is nearly invisible on the PSS-I.\n\nThe size-distribution of the HI-Slice galaxies is clearly different from the\nF--T sample, exhibiting a strong peak toward the smallest diameters. The\nlowest-mass source in the HI-Slice sample (\\#75 in Spitzak \\& Schneider) was\nnot detected optically because of a foreground star, but it is certainly\nvery small. Given its low potential detection volume, it would increase the\nestimated density of the smallest-size low-mass galaxies by more than a factor\nof six. Since its contribution is not included in the histogram, the density of\nvery small low-mass galaxies may be substantially larger than shown.\n\nThe D+LSB sample contains 482 galaxies with $M_{HI} < 10^9 M_\\odot$. 22 of\nthese galaxies have $a_{CZ}<1'$, ranging down to $0.44'$ and physical diameters\nas small as 0.7 kpc at the UGC isophote. All 22 of these small galaxies fall\nwithin the F--T ``completeness zone'' but such galaxies would be overlooked\neven in the combined F--T and D+LSB samples if they were beyond the nearest\nportion of the zone.\n\nMost of the D+LSB galaxies are larger than $2'$, but after adjusting for each\nsource's maximum detectable distance according to its angular size, we find the\ndensity distribution shown by the dashed-line histogram in Fig.~2. In the\nintermediate mass range this distribution is quite similar to the HI-Slice\nsample for galaxies with small diameters.\n\nThe portion of the D+LSB sample restricted to the ``completeness zone'' (24\\%\nof 394 galaxies) is again shown with a dot-dash histogram in Fig.~2. The size\ndistribution of these galaxies begins to resemble that of the F--T sample even\nthough small-$a_{CZ}$ galaxies would be easier to detect nearby. This suggests\nagain that the nearby volume of space is atypical. \n\nAll three of the low-mass HI-Slice galaxies and 92\\% of the 88 low-mass D+LSB\ngalaxies have redshifts below $cz=1000$ km s$^{-1}$, although most are outside\nthe ``completeness zone'' distance limit at these masses. We have divided the\ndensities of the low-mass D+LSB galaxies by a factor of 2 as we did for the\nF--T sample since it mostly probes the same volume of space. The HI-Slice\nsample density estimates are already adjusted for the local large-scale\nstructure in the direction of that survey (Schneider et al. 1998).\n\nWe estimate the space density of small, LSB galaxies based on 23 low-mass and\n77 intermediate-mass galaxies that are larger than $0.4'$ in the PSS-II sample\nof Eder \\& Schombert (1999). Most of the low-mass galaxies are within $cz<1000$\nkm s$^{-1}$, so the densities should perhaps be divided by 2; however,\nthe sample is partially incomplete for the smallest sizes, so the densities may\nbe underestimated. The densities (dotted histogram in Fig.~2) assume that\nsources were detectable out to the distance where their angular diameter would\nreach $0.4'$.\n\nThe lowest-mass galaxy in the Eder \\& Schombert LSB sample (D634-3) was not\nincluded in the density estimates. For this galaxy $V_0=181$ km s$^{-1}$, so\nits distance and mass are quite uncertain. Taken at face value this source\nwould imply a density of 0.7 Mpc$^{-3}$ of very low-mass objects, comparable to\nthe large density implied by the lowest-mass source in the HI-Slice sample. \n\nIn summary, optically-selected samples of galaxies only begin to indicate the\nprevalance of small-diameter galaxies as measured at the limiting isophotal\ndepth of the PSS-I. Photographic surveys of galaxies with late-type\nmorphologies can recover the density of objects with intermediate HI masses if\nthe selection criteria are well-understood, but low mass galaxies present a\nmuch bigger challenge. Detections of two very small, low mass galaxies in an HI\nsurvey and an LSB survey imply that there may be a very large population of\nsources with $M_{HI}<10^7M_\\odot$, but the statistical uncertainties are too\ngreat to draw firm conclusions on this point.\n\n\\section{Discussion}\n\nOptically selected samples favor optically bright galaxies. This truism holds\neven for diameter-limited galaxy surveys because LSB galaxies appear small at\nthe surface-brightness limit of the optical images (Disney 1976). The HI-Slice\nsurvey (Spitzak \\& Schneider 1998), which is unbiased by galaxy diameter,\nindicates that the optically smallest galaxies are the most common. Current\nsearches on deep photographic plates for small angular diameter sources (Eder\n\\& Schombert 1999) are also uncovering indications of this population. Such\nLSB and 21 cm surveys are successfully probing sources with HI masses down to\n$\\sim10^8M_\\odot$, but for lower mass objects HI flux and angular size\nlimitations of existing surveys allow detections of these sources to only a\nfew Mpc.\n\nBecause of the small distances at which low mass and LSB sources are\naccessible, we need to consider the possible impact of the local environment\non them. Although the large scale distribution of LSB galaxies appears similar\nto that of other galaxies (Mo, McGaugh and Bothun 1994), on scales of less\nthan 2 Mpc their numbers drop off sharply. The most likely explanations are\nthat either LSB disks are fragile and easily disturbed by other galaxies, or\ntidal interactions induce star formation that converts LSB galaxies into\nnormal Hubble type objects. Regardless of the underlying cause why LSB\ngalaxies avoid high density regions, this fact produces an expectation that\nthe local region of space will be deficient in the number of LSB disk galaxies\ndue to the large number of high mass spirals and the proximity to the very\ndense Virgo Cluster.\n\nOther influences of the local environment may also play a role in the\ndistribution of galaxy types. In high density regions, galaxies are often gas\ndeficient for their morphological type because of stripping or evaporation,\nand morphological segregation favors earlier-type, less gas rich galaxies.\nBoth of these effects would tend to {\\it lower} the percentage of gas-rich\nsystems nearby.\n\nBriggs (1997a) asked ``Where are the nearby gas-rich low surface brightness\ngalaxies?'' The answer depends on the mass range of objects being studied.\nThere appears to be a local deficit of high-mass LSB systems, which is\nprobably an environmental effect. The story for low-mass systems is less\nsettled, because of the difficulty in detecting them to any significant\ndistance, but it is clear there is a much larger population of\nsmall-optical-diameter galaxies than optical surveys have previously revealed.\nAnd finally, since these low-mass objects have not yet been detected beyond\nthe local high-density environment, it is possible that they are even more\nprofuse than they appear locally.\n\n\\begin{acknowledgments}\n\n\\end{acknowledgments}\n\n\\begin{thebibliography}{}\n \n\\bibitem{}\nBothun, G. D., Impey, C. D., Malin, D. F., Mould, J. R. 1987, AJ, 94, 23\n\n\\bibitem{}\nBothun, G. D., Schombert, J. M., Impey, C. D., \\& Schneider, S. E. 1990, ApJ, 360, 427\n\n\\bibitem{}\nBriggs, F. H. 1997a, ApJ, 484, L29\n\n\\bibitem{}\nBriggs, F. H. 1997b, ApJ, 484, 618\n\n\\bibitem{}\nCornell, M. E., Aaronson, M., Bothun, G., \\& Mould, J. 1987, ApJS, 64, 507\n\n\\bibitem{}\nDekel, A., Bertschinger, E., \\& Faber, S. M. 1990, ApJ, 364, 349\n\n\\bibitem{}\nde Vaucouleurs, G., de Vaucouleurs, A., Corwin, H. C., Buta, R. J., Paturel,\nG., \\& Fouque, P. 1991, Third Reference Catalog of Bright Galaxies (New York:\nSpringer)\n\n\\bibitem{}\nDisney, M. J. 1976, Nature, 263, 573\n\n\\bibitem{}\nDuPrie, K., \\& Schneider, S. E. 1996, AJ, 112, 937\n\n\\bibitem{}\nEder, J. A., \\& Schombert, J. M. 1999, in preparation\n\n\\bibitem{}\nFisher, J. R., \\& Tully, R. B. 1981, ApJS, 47, 139\n\n\\bibitem{}\nHuchtmeier, W. K., \\& Richter, O. G. 1989, {\\it A General Catalog of HI\nObservations of Galaxies} (Berlin: Springer-Verlag)\n\n\\bibitem{}\nImpey, C. D., Sprayberry, D., Irwin, M. J., \\& Bothun, G. D. 1996, ApJS, 105, 209\n\n\\bibitem{}\nMatthews, L. D., \\& Gallagher, J. S. 1996, AJ, 111, 1098\n\n\\bibitem{}\nMo, H. J., McGaugh, S. S., \\& Bothun, G. D. 1994, MNRAS, 267, 129\n\n\\bibitem{}\nNilson, P. 1973, Uppsala Astron. Obs. Ann. 6 (UGC)\n\n\\bibitem{}\nSchmidt, M. 1968, ApJ, 151, 393\n\n\\bibitem{}\nSchneider, S. E., Spitzak, J. G., \\& Rosenberg, J. L. 1998, ApJ, 507, L9\n\n\\bibitem{}\nSchneider, S. E., Thuan, T. X., Magri, C., \\& Wadiak, J. E. 1990, ApJS, 72, 245\n\n\\bibitem{}\nSchneider, S. E., Thuan, T. X., Mangum, J. G., \\& Miller, J. 1992, ApJS, 81, 5\n\n\\bibitem{}\nSchombert, J. M., Bothun, G. D., Schneider, S. E., McGaugh, S. S. 1992, AJ, 103, 1107\n\n\\bibitem{}\nSprayberry, D., Impey, C. D., Irwin, M. J., McMahon, R. G., \\& Bothun, G. D.\n1993, ApJ, 417, 114\n\n\\bibitem{}\nSpitzak, J. G., \\& Schneider, S. E. 1998, ApJS, 119, 159\n\n\\bibitem{}\nVan Driel, W., \\& Van Woerden, H. 1991, \\aap, 243, 71\n\n\\end{thebibliography}\n\n\\end{document}\n\n\\end\n\n"
},
{
"name": "tbl1.tex",
"string": "\\clearpage\n\n\\begingroup\n\\oddsidemargin -.5in\n\\evensidemargin -.5in\n \n\\begin{deluxetable}{@{}l@{\\quad}r@{ }r@{\\quad }r@{ }r@{\\quad }r@{ }r@{\\quad }r@{ }r}\n\\renewcommand{\\arraystretch}{0.82}\n\\tablecolumns{9}\n\\tablewidth7.3in\n\\footnotesize\n\\tablecaption{${\\cal V}/{\\cal V}_{max}$ Tests. \\label{tbl-1}}\n\\tablehead{\n&\\multicolumn{2}{c}{\\hbox to 1.1in{\\hss All\\quad\\hss}}\n&\\multicolumn{2}{c}{\\hbox to 1.1in{\\hss $M_{HI}\\leq10^8 M_\\odot$\\quad\\hss}}\n&\\multicolumn{2}{c}{\\hbox to 1.1in{\\hss $10^8-10^9 M_\\odot$\\quad\\hss}}\n&\\multicolumn{2}{c}{\\hbox to 1.1in{\\hss $M_{HI}>10^9 M_\\odot$\\quad\\hss}}\\\\\nSample&\n\\colhead{$N$}&\\colhead{${\\cal V}/{\\cal V}_{max}$} &\n\\colhead{$N$}&\\colhead{${\\cal V}/{\\cal V}_{max}$} &\n\\colhead{$N$}&\\colhead{${\\cal V}/{\\cal V}_{max}$} &\n\\colhead{$N$}&\\colhead{${\\cal V}/{\\cal V}_{max}$}\n} \n\\startdata\n1. F--T in ``completeness zone'' &320&$0.406\\pm0.016$& 41&$0.299\\pm0.046$&171&$0.392\\pm0.022$&108&$0.468\\pm0.028$\\nl\n2. $\\ldots$full sensitivity to $M_{HI}>10^{9.15} M_\\odot$&190&$0.485\\pm0.021$& 15&$0.510\\pm0.075$& 69&$0.481\\pm0.035$&106&$0.484\\pm0.028$\\nl\n3. $\\ldots$restricted to $a_{CZ}>3'$ &141&$0.460\\pm0.024$& 1&$0.028\\pm0.287$& 43&$0.443\\pm0.044$& 97&$0.472\\pm0.029$\\nl\n4. $\\ldots$restricted to $a_{CZ}>2'$ &217&$0.429\\pm0.020$& 8&$0.208\\pm0.102$&103&$0.404\\pm0.028$&106&$0.469\\pm0.028$\\nl\n5. D+LSB in ``completeness zone'' &189&$0.437\\pm0.021$& 52&$0.425\\pm0.040$&116&$0.425\\pm0.027$& 21&$0.539\\pm0.063$\\nl\n6. $\\ldots$restricted to $a_{CZ}>1'$ &161&$0.462\\pm0.023$& 36&$0.459\\pm0.048$&104&$0.448\\pm0.028$& 21&$0.539\\pm0.063$\\nl\n7. F--T ($\\delta>-2.5^\\circ$) and D+LSB combined &295&$0.407\\pm0.016$& 54&$0.385\\pm0.039$&162&$0.416\\pm0.023$& 79&$0.476\\pm0.032$\\nl\n8. $\\ldots$restricted to $a_{CZ}>2'$ &172&$0.432\\pm0.022$& 6&$0.161\\pm0.118$& 88&$0.410\\pm0.031$& 78&$0.478\\pm0.033$\\nl\n9. $\\ldots$restricted to $a_{CZ}>1'$ &270&$0.435\\pm0.018$& 40&$0.382\\pm0.046$&151&$0.427\\pm0.023$& 79&$0.476\\pm0.032$\\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\\endgroup\n"
}
] |
[
{
"name": "astro-ph0002080.extracted_bib",
"string": "\\begin{thebibliography}{}\n \n\\bibitem{}\nBothun, G. D., Impey, C. D., Malin, D. F., Mould, J. R. 1987, AJ, 94, 23\n\n\\bibitem{}\nBothun, G. D., Schombert, J. M., Impey, C. D., \\& Schneider, S. E. 1990, ApJ, 360, 427\n\n\\bibitem{}\nBriggs, F. H. 1997a, ApJ, 484, L29\n\n\\bibitem{}\nBriggs, F. H. 1997b, ApJ, 484, 618\n\n\\bibitem{}\nCornell, M. E., Aaronson, M., Bothun, G., \\& Mould, J. 1987, ApJS, 64, 507\n\n\\bibitem{}\nDekel, A., Bertschinger, E., \\& Faber, S. M. 1990, ApJ, 364, 349\n\n\\bibitem{}\nde Vaucouleurs, G., de Vaucouleurs, A., Corwin, H. C., Buta, R. J., Paturel,\nG., \\& Fouque, P. 1991, Third Reference Catalog of Bright Galaxies (New York:\nSpringer)\n\n\\bibitem{}\nDisney, M. J. 1976, Nature, 263, 573\n\n\\bibitem{}\nDuPrie, K., \\& Schneider, S. E. 1996, AJ, 112, 937\n\n\\bibitem{}\nEder, J. A., \\& Schombert, J. M. 1999, in preparation\n\n\\bibitem{}\nFisher, J. R., \\& Tully, R. B. 1981, ApJS, 47, 139\n\n\\bibitem{}\nHuchtmeier, W. K., \\& Richter, O. G. 1989, {\\it A General Catalog of HI\nObservations of Galaxies} (Berlin: Springer-Verlag)\n\n\\bibitem{}\nImpey, C. D., Sprayberry, D., Irwin, M. J., \\& Bothun, G. D. 1996, ApJS, 105, 209\n\n\\bibitem{}\nMatthews, L. D., \\& Gallagher, J. S. 1996, AJ, 111, 1098\n\n\\bibitem{}\nMo, H. J., McGaugh, S. S., \\& Bothun, G. D. 1994, MNRAS, 267, 129\n\n\\bibitem{}\nNilson, P. 1973, Uppsala Astron. Obs. Ann. 6 (UGC)\n\n\\bibitem{}\nSchmidt, M. 1968, ApJ, 151, 393\n\n\\bibitem{}\nSchneider, S. E., Spitzak, J. G., \\& Rosenberg, J. L. 1998, ApJ, 507, L9\n\n\\bibitem{}\nSchneider, S. E., Thuan, T. X., Magri, C., \\& Wadiak, J. E. 1990, ApJS, 72, 245\n\n\\bibitem{}\nSchneider, S. E., Thuan, T. X., Mangum, J. G., \\& Miller, J. 1992, ApJS, 81, 5\n\n\\bibitem{}\nSchombert, J. M., Bothun, G. D., Schneider, S. E., McGaugh, S. S. 1992, AJ, 103, 1107\n\n\\bibitem{}\nSprayberry, D., Impey, C. D., Irwin, M. J., McMahon, R. G., \\& Bothun, G. D.\n1993, ApJ, 417, 114\n\n\\bibitem{}\nSpitzak, J. G., \\& Schneider, S. E. 1998, ApJS, 119, 159\n\n\\bibitem{}\nVan Driel, W., \\& Van Woerden, H. 1991, \\aap, 243, 71\n\n\\end{thebibliography}"
}
] |
astro-ph0002081
|
The Contribution of Faint Blue Galaxies to the Sub-mm Counts and Background
|
[
{
"author": "Geoff S. Busswell"
},
{
"author": "Tom Shanks"
},
{
"author": "Department of Physics"
},
{
"author": "Science Labs"
},
{
"author": "South Road"
},
{
"author": "Durham DH1 3LE"
},
{
"author": "UK"
}
] |
Observations in the submillimetre waveband have recently revealed a new population of luminous, sub-mm sources. These are proposed to lie at high redshift and to be optically faint due to their high intrinsic dust obscuration. The presence of dust has been previously invoked in optical galaxy count models which assume $\tau=9$ Gyr Bruzual \& Charlot evolution for spirals and these fit the count data well from U to K. We now show that by using either a 1/$\lambda$ or Calzetti absorption law for the dust and re-distributing the evolved spiral galaxy UV radiation into the far infra-red(FIR), these models can account for all of the `faint'($\leq1$mJy) $850\mu$m galaxy counts, but fail to fit 'bright'($\ge2$mJy) sources, indicating that another explanation for the sub-mm counts may apply at brighter fluxes(e.g. QSOs, ULIRGs). We find that the main contribution to the faint, sub-mm number counts is in the redshift range $0.5 < z < 3$, peaking at $z\approx 1.8$. The above model, using either dust law, can also explain a significant proportion of the extra-galactic background at $850\mu$m as well as producing a reasonable fit to the bright $60\mu m$ IRAS counts.
|
[
{
"name": "mypaper.tex",
"string": "%\\documentstyle[draft,epsf]{mn}\n\\documentstyle[graphicx]{mn}\n%\\usepackage{graphicx}\n%\\input{epsf}\n%\\usepackage{graphicx}\n\n%Define some symbols for fun...\n\\def\\hi{{\\rm H\\,{\\sc i} }}\n\\def\\hii{{\\rm H\\,{\\sc ii} }}\n\n%------------------------------------------------------------------------\n\n\\title{The Contribution of Faint Blue Galaxies to the Sub-mm Counts and\nBackground}\n\\author[Busswell et al.]\n{\nGeoff S. Busswell, Tom Shanks \\\\ \nDepartment of Physics, University of Durham, Science Labs, South Road, Durham\nDH1 3LE, UK}\n\n\n%------------------------------------------------------------------------\n\n\\begin{document}\n%\\date{Draft Version: \\today}\n\n\\maketitle\n\n\\begin{abstract}\nObservations in the submillimetre waveband have recently revealed a new\npopulation of luminous, sub-mm sources. These are proposed to lie at\nhigh redshift and to be optically faint due to their high\nintrinsic dust obscuration. The presence of dust has been previously \ninvoked in \noptical galaxy count models which assume $\\tau=9$ Gyr Bruzual \\& Charlot \nevolution for spirals and these fit the count data well from U to K.\nWe now show that by using either a 1/$\\lambda$\nor Calzetti absorption law\nfor the dust and re-distributing the evolved spiral galaxy UV\n radiation into the\nfar infra-red(FIR), these models can account for all of the `faint'($\\leq1$mJy)\n$850\\mu$m galaxy counts, but fail to fit 'bright'($\\ge2$mJy) sources,\nindicating that another explanation for the sub-mm counts may apply at\nbrighter fluxes(e.g. QSOs, ULIRGs). We find\nthat the main contribution to the faint, sub-mm number counts is in the\nredshift range $0.5 < z < 3$, peaking at $z\\approx 1.8$. The above model, \nusing either dust law,\n can also explain a\nsignificant proportion of the extra-galactic background at $850\\mu$m as\nwell as producing a reasonable fit to the bright $60\\mu m$ IRAS counts.\n\n\\end{abstract}\n\n%must alter\n\\begin{keywords}\ngalaxies: spiral - evolution - infrared: galaxies - ultraviolet: galaxies \n\\end{keywords}\n\n\\section{Introduction}\n \nThe SCUBA camera \\cite{holland99} on the James Clerk Maxwell Telescope\nhas transformed our knowledge of dusty galaxies in the distant Universe\nas a result of the discovery of a new population of luminous, dusty,\ninfra-red galaxies (Smail et al. 1997; Ivison et al 1998). It has been \nproposed that \nthese galaxies may be similar to IRAS\nULIRGs (ultra-luminous infra-red galaxies) \nwhich appear to be starbursting/AGN galaxies, containing large amounts\nof dust. The possibility that much star-formation is hidden by dust \nmeans that sub-mm observations can give an invaluable insight\ninto the star-formation history of the Universe. This view aided by\nthe redshifting\nof the thermal dust emission peak in starbursting galaxies into the FIR, which\nresults in a negative k-correction in the sub-mm. By this route, we can\ntherefore study our Universe all the way back to very early times and\ngain unprecedented insight into the formation and evolution of galaxies.\n\n\nThe first sub-mm galaxy to be detected by SCUBA was SMM J02399-0136\n\\cite{ivison98}, which is a massive starburst/AGN at\nz=2.8 and the current situation is\nthat the complete 850$\\mu$m sample from all the various groups\nconsists of well over 50 sources (Blain et al. 1999; Eales et al. 1999; \nHughes et al. 1998; Holland et al. 1998; Barger et al. 1998; Smail\net al. 1997). Optical and near\ninfra-red(NIR) counterparts have been identified for about a third of the\nsources, although the reliability of these\nidentifications varies greatly. This problem is due to the fact that \nthe $\\approx 15''$ FWHM of the SCUBA beam results in $_-^+3''$ \npositional errors\non a sub-mm source, so there is a reasonable chance that several \ncandidates could lie within these errors. Also, there is no guarantee\nthat the true source will be detected down to the optical flux limit as, for \nexample, many of the sources have been shown to be very red objects \n(Dey et al. 1999; Smail et al. 1999: Ivison et al. 2000) and\ntherefore have not been found in optical searches for sub-mm sources. \n\nWhat has proved extremely\n enlightening is that radio counterparts at 1.4GHz have \nnow been identified\nfor many of the sub-mm sources (Smail et al. 2000: Ivison et al. 2000) \nproviding much more accurate angular positions \n($<1''$ in some cases) and reasonably accurate photometric redshifts. \nVarious \ngroups have obtained redshift distributions of sub-mm samples\n(Hughes et al. 1998; Barger et al. 1999a; Lilly et al. 1999; Smail et al. 2000) \nand they all \nderive results that are consistent with a mean redshift in the range \n$1 < z < 3$. The fact that almost all of the sources are associated with \nmergers or interactions seems to confirm that the population of sources \ncontributing at the `bright' ($>2$mJy) sub-mm fluxes (since most of\nthe sources so far discovered are `bright') are similar to local\nIRAS ULIRG's, ie massive, starbursting/AGN galaxies \nwhich are extremely luminous \nin the far-infra-red.\nThis hypothesis is strengthened further by the fact that the only two sub-mm \nsources (SMM J02399-0136 and SMM J14011+0252) with reliable redshifts have \nbeen \nfollowed up with millimeter wave \nobservations (Frayer et al. 1998, 1999), resulting in CO \nemission being detected at the\nredshifts of both sources (z=2.8 and z=2.6), a characteristic indicator \nof large quantities of molecular gas present in IRAS galaxies.\n\nThe nature of the fainter ($\\le1$mJy) sub-mm population is, however, the focus\n of this paper. \nIt has been claimed by Peacock et al. (2000) and Adelberger et al. (2000)\nthat the Lyman Break Galaxy(LBG) population could not only contribute\nsignificantly to the faint sub-mm number counts, but could also account\nfor a substantial proportion of the background at $850\\mu$m. \nThis may indicate that ULIRG's \ncannot explain all of the sub-mm population and that the UV-selected galaxy\n population, which are predicted to be evolved spirals by the Bruzual \\&\nCharlot models, may in fact make a substantial contribution.\nIt is exactly this hypothesis our paper addresses. \n\nIn this paper we will first review the situation regarding the optical\ngalaxy counts, focusing in particular on the models of Metcalfe et al. (1996).\n These simple models which use a $\\tau =9$Gyr SFR for spirals\nand include the effects of dust give good fits to galaxy counts and\ncolours from U to K. The idea is then to see whether this\ncombination of exponential SFR and relatively small amounts of dust in the\n first instance\n(A$_B=0.3$ mag. for the $1/\\lambda$ law), which would re-radiate the spiral \nultra-violet (UV)\nradiation into the FIR, could cause a significant contribution to the\nsub-mm galaxy number counts and background at $850\\mu $m. Our modelling\nwill be described in section 3 and then in section 4 our predicted\ncontribution to the $850\\mu $m and $60\\mu m$ galaxy counts and the\nextra-galactic background in the sub-mm will be shown. Also in this\nsection we demonstrate how to get a fit to the background in the\n$100-300\\mu m$ range by using warmer, optically-thicker dust in line\nwith that typically seen in ULIRG's. We will then discuss the\nimplications of our predictions in section 5 and conclude in section 6.\n\n \n\\section{The Optical Counts}\n\nIt is well known that non-evolving galaxy count models, where number\ndensity and luminosity of galaxies remain constant with look-back\ntime, do not fit the optical number counts e.g. \\cite{shanks84}, as there\nis always a large excess of galaxies faintwards of $B\\sim 22^m$. One\nway to account for this excess of 'faint blue galaxies' is to\ninvestigate the way galaxy evolution will influence the optical number\ncounts.\n%The \n%natural ways to then proceed are to vary \n%the luminosity function \n%with look-back time\n%\\cite{guidmet90} and/or to make the number density of galaxies\n%a function of redshift as in \n%hierachial merging models of galaxy formation \\cite{cole94}.\nMetcalfe et al (1996) showed that by assuming that the number density of\ngalaxies remains constant, the Bruzual and Charlot(1993) evolutionary\nmodels of spiral galaxies with a $\\tau = 9$Gyr SFR give excellent fits\nto the optical counts. The galaxy number counts are normalised at\n$B\\sim 18^m$ so that the non-evolving models give good fits to the $B$\nband data and redshift distributions in the range $18^m < B < 22.^m5$.\nWith this high normalisation, the models of the galaxy counts\nrepresent both spiral and early-type galaxies extremely well for\n$17^m < I < 22^m$ (Glazebrook et al. 1995a, Driver et al 1995) and \nalso the less steep $H/K$ counts\nout to $K\\sim 20^m$. The evolution model then produces a reasonable\nfit to the fainter counts to $B\\sim 27^m$, $I\\sim 26^m$, $H\\sim28^m$.\n\n% \\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in]{counts_ts.eps}\n%\\caption{(The optical galaxy number count models from Shanks et al(1998).\n%of the Hubble and Herschel Deep fields. The figure shows B, I(x10), K(x100)\n%observations and the counts are modelled using the Bruzual \\& Charlot\n%evolution models with an exponentially increasing SFR, Lyman $\\alpha$\n%absorption and spiral dust\n%absorption of $A_B = 0.^m 3$. Shanks et al\n%adopt a dwarf dominated IMF(x=3) with $\\tau =2.5Gyr$ for E/SO/Sab galaxies\n%and a Salpeter IMF (x=1.35) with $\\tau =9$ Gyr, for Sbc/Scd/Sdn galaxies. The\n%$q_0 = 0.5$ models require the presence of an extra galaxy (disappearing \n%dwarf, dE) population at high redshift to fit the faint B and I counts}}\n%\\label{fig:optical}\n%\\end{figure}\n\nMetcalfe et al (1996) included a $1/\\lambda$ internal dust absorption law with\n$A_B=0.3$ for spirals to prevent the $\\tau=9$ Gyr SFR from over-predicting the\nnumbers of high redshift galaxies detected in faint B$<24$ redshift surveys \n(Cowie et al 1995). This $1/\\lambda$ dust law differs from the Calzetti(1997)\ndust law derived for starburst galaxies, in that for a given $A_B$, more\nradiation is absorbed in the UV. The Calzetti dust law is used by Steidel et\nal(1999) to model their `Lyman Break' galaxies; they find an average\nE(B-V)=0.15 which gives $A_B=0.87$mag and $A_{1500}=1.7$mag. \nThis compares to our\n$A_{1500}=0.9$mag with $A_B=0.3$mag. \n%However, we note that the differential\n%reddening between 1500A and 4500A is similar in both cases. \nBoth models also\nfail to predict as red colours as observed for the U-B colours of spirals in\nthe Herschel Deep Field (Metcalfe et al 1996). However, if we assumed\nE(B-V)=0.15 for our z=0 spirals, as compared to our E(B-V)=0.05, then the rest\ncolours of spirals as predicted by the Bruzual \\& Charlot model might start to\nlook too red as compared to what is observed. Otherwise, the main difference\nbetween these two dust laws is that the Calzetti law would produce more overall\nabsorption and hence a higher FIR flux from the faint blue galaxies. Thus in\nsome ways our first use of the $1/\\lambda$ law appears\n conservative in terms of the\npredicting the faint blue galaxy FIR flux. Later, we shall experiment by\nreplacing the $1/\\lambda$ law with the Calzetti(1997) law in our model.\n\nSo this pure luminosity evolution (PLE) model with $1/\\lambda$\ndust and $q_0=0.05$ then slightly under-estimates the faintest optical counts\nbut otherwise fits the data well, whereas for $q_0=0.5$ the underestimate (with\nor without dust) is far more striking. An extra population of galaxies has to\nbe invoked at high redshift to attempt to explain this more serious discrepancy\nfor the high $q_0$ model. This new population was postulated to have a\nconstant SFR from their formation redshift until $z\\sim 1$ and then the Bruzual\n\\& Charlot models predict a dimming of $\\sim 5^m$ in $B$ to form a red dwarf\nelliptical (dE) by the present day and therefore has the form of a\n'disappearing dwarf' model \\cite{babrees92}. No dust was previously assumed in\nthe dE population but this assumption is somewhat arbitrary.\n\nThe $\\tau=9$Gyr SFR was inconsistent with the early observations at low\nredshift from Gallego et al.(1996) and this is partly accounted for by the\nhigh normalisation of the optical number counts at $B\\sim 18^m$. There is\nstill a problem with the UV estimates from the CFRS UV data of Lilly et al at\nz=0.2. More recent estimates of the global SFR at low redshift based on the \n[OII]\nline (Gronwall et al.1998; Tresse \\& Maddox 1998; Hammer and Flores 1998)\nindicates that the decline from z=1 to the present day may not be as sharp as\nfirst thought and that the $\\tau=9$Gyr SFR in fact provides a better fit to\nthis low redshift data. Metcalfe et al (2000) have further found \nthat this model \nalso agrees well with recent estimates of the luminosity function of the z=3\nLyman break galaxies detected by Steidel et al.(1999).\n%could\n%account for the fact that the exponential SFR is larger out to $z\\approx 0.75$\n%that of Madau et al. It can be seen in fig \\ref{fig:optical} that the bright \n%counts are \n%overpredicted because of this normalisation, but this could be due to the \n%effects of local large-scale structure. At higher redshift the discrepancy \n%can be largely accounted for by the 0.3\n%mag dust absorption law as then higher luminosity densities are obtained at \n%$1620 \\AA$ for $z > 2$ UV drop-out galaxies than Madau et al.\n%The poor agreement in\n%the $0.75 < z < 1$ bin may be because Madau et al used a LF extrapolated UV\n%density for the point at $0.75 < z < 1$ (L.Tresse priv. comm.); if the \n%unextrapolated luminosity density is used then the result would be a factor \n%of two lower, and in better agreement with the $\\tau=9Gyr$ prediction. \n%Thirdly, in the\n%$2 < z < 2.75$ range, Shanks et al. obtain a luminoisity density a factor 1.56\n%larger at $1620 \\AA$ for $Z > 2$ UV drop-out galaxies than\n%Madau et al., because they measure brighter magnitudes for individual \n%galaxies. Also, the $1620 \\AA$ is increased by a factor of 1.63 if the 0.3\n%mag dust absorption law is taken into account, so the net effect is a $2.54$\n%increase, accounting for the approx. factor of 3 discrepancy. In the \n%$3.5 < z < 4.5$ bin the same two effects apply, with the increasingly serious\n%effects of luminosity function incompleteness applying at the larger distance.\n\n%In the optical $\\tau=9$ Gyr SFR used for spirals an $A_B=0.3$ 1/$\\lambda$\n%dust law is assumed, which corresponds to a relatively small amount\n%of dust and so it might seem unlikely that normal spiral galaxies\n%at high redshift could correspond to sub-mm objects with huge FIR \n%luminosities \n%of $\\sim 10^{13}\n%L_{\\odot}$. However, not all the sub-mm sources are this luminous\n%and the\n \n\nThe main question then that we will address in this paper is whether the\nsmall amount of internal spiral dust absorption assumed in these \nmodels which give an excellent fit to the optical galaxy counts, could cause \na significant contribution to the sub-mm number counts and background at $850\n\\mu$m.\n\n\\section{Modelling}\n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]{bruzual.eps}\n% \\caption{The Bruzual \\& Charlot specral energy distributions for a \n%$1M_{\\odot}$ spiral galaxy. The figure shows in descending order the model\n% rest frame\n%SED's at redshifts of 4,3,2 and 1 and also at the present day. We use a \n%star formation rate of $\\tau =9Gyr$ and the figure clearly shows how the \n%models predict the brightening behaviour of spiral galaxies as we look\n%back in time.}\n% \\label{fig:bruzual}\n%\\end{figure} \n\nUsing the optical B band parameters for spiral galaxies, we attempt to\npredict the contribution to the sub-mm galaxy counts and background at\n$850\\mu m$ by using a 1/$\\lambda$ absorption law for the dust and\nre-radiating the spiral UV radiation into the FIR. We use the Bruzual\n\\& Charlot(1993) galaxy evolution models with\n$H_0=50$km$s^{-1}$Mpc$^{-1}$ and a $\\tau$=9 Gyr SFR - with a galaxy\nage of 16 Gyr in the low $q_0$ case, and 12.7 Gyr in the high $q_0$\ncase to produce our 1M$\\odot$ galactic spectral energy\ndistribution(SED) as a function of redshift. We then use the equation\n\n\\begin{equation}\nG_{abs}(z) = \\int F_{\\lambda}(z)(1-10^{-0.4*A_B*(4500/\\lambda)})d\\lambda\n\\end{equation}\n~\n\nas used by Metcalfe et al(1996), which is used to calculate the\nradiation absorbed by the dust, $G_{abs}$($ergss^{-1}$), for our\n1M$\\odot$ model spiral galaxy as a function of z, using our\n$1/\\lambda$ absorption law with A$_B=0.3$. Since Bruzual \\& Charlot\nprovides us with a 1M$\\odot$ SED at each redshift increment, we need\nto calculate the factor required to scale this SED (after the effect\nof absorption from the dust) to obtain that of a galaxy with absolute\nmagnitude $M_B$ at zero redshift, and this factor will then remain\nconstant for $M_B$ galaxies at all other redshifts. This then provides\na zero point from which to calculate scaling factors for all the other\ngalaxies in our luminosity functions. We find the scaling factor for\nan $M_B$ galaxy by making use of a relation from Allen(1995)\n\n\\begin{equation}\nm_B = -2.5log(\\int B_{\\lambda}{\\it f}_{\\lambda}d \\lambda) - 12.97\n\\end{equation}\n~\nwhere ${\\it f}_{\\lambda}$ is the received flux($ergs^{-1}\\AA^{-1}cm^{-2}$) and \n$B_{\\lambda}$ is the B band filter function. By re-arranging, setting\n$m_B$=$M_B$ and then multiplying by $4\\pi(10pc)^2$ we obtain the total\nemitted power, $L_B$($ergs^{-1}$) in the B band from an $M_B$ galaxy\n\n\\begin{equation}\nL_B=4\\pi(10pc)^2.10^{[-0.4(M_B+12.97)]}\n\\end{equation}\n~\n\nThe intensity emitted in the B band, after absorption by the dust from\nour 1M$\\odot$ galaxy, $L_{BM_{\\odot}}$ is then calculated by\nintegrating the SED, assuming a flat B band filter, between $4000\\AA$\nand $5000\\AA$. \n\n\\begin{equation}\nL_{BM_{\\odot}}=\\int\nF_{\\lambda}(z)10^{-0.4*A_B*(4500/\\lambda)}B_{\\lambda}d\\lambda\n\\end{equation}\n~\n\nThe scaling factor to scale a Bruzual \\& Charlot $1M_{\\odot}$spectral \nenergy distribution for a galaxy of absolute magnitude, M$_B$, is then \ndefined by the ratio $L_B/L_{BM_{\\odot}}$. \n \nThe way the dust will re-radiate this absorbed flux depends on its\ntemperature, particle size and chemical composition. However the\nnormalisation of the re-radiated flux from a galaxy with absolute\nmagnitude M$_B$, at redshift z, is already determined (the quantity\n$G_{abs}$$E_B/E_{BM_{\\odot}}$). We will adopt a simple model by\nassuming a mean interstellar dust temperature of 15K, \\cite{bianchi99}\nand also a modest warmer component of 45K, (the actual luminosity\nratio we use is $L_{45K}/L_{15K}=0.162$), which would come from\ncircumstellar dust \\cite{dom99} and is needed in order to fit counts\nat shorter wavelengths eg. $60\\mu m$. The effect of varying\nthe dust parameters is explored in section 4. We then simply scale the Planck\nfunction so that\n\n\\begin{equation} \nC(z,M_B) \\int_{-\\infty}^{\\infty}\\beta(\\lambda, T)d\\lambda = \nG_{abs}L_B/L_{BM_{\\odot}}\n\\end{equation}\n~\n\nwhere C(z,M$_B$) is the scaling factor, which is a function of z and\nM$_B$, $\\beta(\\lambda, T)$ is the Planck function (in this case a sum\nof two Planck functions) and $\\kappa_d (\\lambda) \\propto\n\\lambda^{-\\beta}$, where $\\kappa_d (\\lambda)$ is an opacity law (we\nuse $\\beta=2.0$ for each Planck function to model optically thin\ndust).\n\n%We take $\\beta = 1.65$ in line with the lower limit of $\\beta$ derived\n%for the interacting galaxy pair VV114 \\cite{frayer99} and also consistent\n%with the fact that for $\\beta \\approx 2$, the sub-mm fluxes are significantly\n%higher than those expected from the IRAS data \\cite{soifer89}. \nWe then calculate the received $850\\mu m$ flux, S(z,M$_B$), from a galaxy \nwith absolute magnitude $M_B$ and redshift z using the equation\n\n\\begin{equation}\n\\ S(z,M_B)=\\frac{C(z,M_B) \\lambda_e^{-\\beta} \\beta(\\lambda_e, T)}\n{4\\pi (1+z) d_L^2} \n\\end{equation}\n~\n\nwhere C(z,M$_B$) is defined from (4) and $\\lambda_e$ is equal to $850\n\\mu m$/(1+z). We can then obtain the number count of galaxies with\nabsolute magnitude between M$_B$ and M$_B+dM_B$ and redshift between z\nand z+dz for which we measure the same flux density S(z,M$_B$) at\n$850\\mu m$ (see (4)).\n\n\n\\begin{equation}\ndN(z,M_B) = \\phi(M_B) \\frac{dV}{dz}dM_Bdz\n\\end{equation}\n~\n\nwhere $\\phi (M_B)$ is the optical Schechter function and\n$\\frac{dV}{dz}$ is the cosmological volume element. Then the integral\nsource counts N$(>S_{lim})$ are obtained, for each value of $S_{lim}$,\nby integrating (5) over the range of values of $M_B$ and $z$ such that\nS(z,M$_B)>S_{lim}$, where S(z,M$_B$) is defined in (4).\n \n%\\begin{eqnarray}\n%\\phi(M_B) & = & 0.92 \\phi^{\\star}exp[-0.92(M_B-M_B^{\\star}) (\\alpha +1) \n%\\nonumber \n% & & \\mbox{} -exp(-0.92(M_B-M_B^{\\star}))]\n%\\end{eqnarray}\n\n%\\begin{equation}\n%\\frac{dV}{dz}=\\frac{4\\pi c^3}{H_0^3q_0^4}\n%\\frac{[zq_0+(q_0-1)(-1+\\sqrt{2q_0z+1})]^2}\n%{(1+z)^3\\sqrt{2q_0z+1}}\n%\\end{equation}\t \n%~\n%and $\\Omega=0.000305$ is the number of square radians in a square degree.\n%\n%The data is traditionally plotted in cumulative source counts in units\n%of $mJy = 10^{-26}ergcm^{-2}s^{-1}Hz^{-1}$ and so we must transform from our \n%units of $ergscm^{-2}s^{-1}m$ using\n\n%\\begin{equation}\n%S(\\nu_o)=S(\\lambda_o)\\frac{d\\lambda_o}{d\\nu_o}\n%=S(\\lambda_o)\\frac{(850\\mu m)^2}{c}\n%\\end{equation}\n%~\n\\begin{equation}\nN(>S_{lim})=\\int_{M_B}\\int_{z}\\phi(M_B)\\frac{dV}{dz}dM_Bdz\n\\end{equation}\n~\n\nIt is straightforward to then obtain model predictions of the FIR\nbackground for a given wavelength. The intensity, dI, at $850\\mu m$\nfrom galaxies with absolute magnitudes between $M_B$ and $M_B+dM_B$\nand redshifts between z and z+dz is given by multiplying the number of\ngalaxies with these z's and M$_B$'s by the flux density which we would\nmeasure from each\n\n\\begin{equation}\ndI_{850}=S(z,M_B)\\phi(M_B)\\frac{dV}{dz}dM_Bdz\n\\end{equation}\n~\nand then we simply integrate over all absolute magnitudes and all redshifts\n($0 < z < 4$ in this case)\n\n\\begin{equation}\nI_{850} = \\int_{M_B}\\int_{z} S(z,M_B)\\phi(M_B)\\frac{dV}{dz}dM_Bdz\n\\end{equation}\n~\n\n\\section{Predictions}\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{60allgraphs.ps}\n\n\\caption{The $60\\mu m$ differential number counts. The graph shows\nthe evolution and no-evolution models for a low $q_0$ Universe(the\ncorresponding high $q_0$ models are indistinguishable) along with the\nobserved $60\\mu m$ counts of IRAS galaxies down to a flux limit of\n0.6Jy, plotted in the format used by Oliver et al.(1992). The crosses are from\nHacking \\& Houck(1987), the empty triangles from Rowan-Robinson et al.\n(1990), Saunders et al.(1990) are the filled triangles and the circles\nare Gregorich et al.(1995) and Bertin et al.(1997). We use a\ntwo-component dust temperature of 15K and 45K to model both\ninterstellar and circumstellar dust respectively. Other parameters\nused are $\\beta=2.0$, $H_0=50$ and a redshift of formation of $z=4$.\nThe dot-dashed line shows the same evolution model using the Calzetti dust\nlaw with three dust temperature components of 15, 25, and 32K. \nThis fits the IRAS counts less well at $<0.2$mJy, and this is because of\nthe lack of a 45K dust component meaning that there is much less\n thermal emission from\nthe dust at $60\\mu$m}.\n\\label{fig:counts60}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs.ps}\n\\caption{The $850\\mu$m integral number counts. The filled circles\nshow the results of the SCUBA Lens Survey (Blain et al. 1999); the\nopen circles are as labelled:S97 - Smail, Ivison \\& Blain(1997); B98 -\nBarger et al.(1998); H98 - Holland et al.(1998); E99 - Eales et\nal.(1999); HDF, P(D) - Hughes et al.(1998). Also shown are our\npredictions for $q=0.05$ and $q=0.5$ models with and without Bruzual\n\\& Charlot evolution, using the parameters from Fig. \\ref{fig:counts60}.\nBoth the high and low $q_0$ models, with evolution (dashed and solid\ncurves), do very well with the faint counts but fail the most luminous\nsources. In the no evolution cases(dotted and dot-dashed) the high\n$q_0$ model again predicts more galaxies then the low $q_0$ model, but\nthey both underpredict the faint $850\\mu$m counts by about an order\nof magnitude and then again fall away again at the higher flux\ndensities. The graph also shows a predicted contribution from AGN (Gunn \\& \nShanks 1999) and a model using the calzetti dust law (the two dot-dot-dot-\n dashed\n curves). The AGN model (the steeper of the curves) predicts that, at most, \nQSO's could contribute 30 percent\nof the background at $850\\mu$m, and these models\ndo much better in the number counts at brighter fluxes, but they fail to \ncontribute at the $0.5$mJy level where we predict that faint blue \ngalaxies are dominant. Our Calzetti dust law uses three dust temperature\ncomponents (see Fig. \\ref{fig:counts60}, and as\nwith our $1/\\lambda$ dust law, it can account for the faint number counts\nbut then fails the much brighter sources. }\n\\label{fig:counts}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs_dimming.ps}\n\\caption{If a galaxy has an absolute magnitude $M_B=-22.5$ at the\npresent day then these graphs show how the received flux from such a\ngalaxy would vary as a function of redshift using our model with the\nparameters described in the previous figure (Fig. \\ref{fig:counts}).\nThe solid line is for a $q_0=0.05$ Universe with Bruzual \\& Charlot\nevolution, the dashed line for $q_0=0.5$ with evolution, the\ndot-dashed line for $q_0=0.05$ without evolution and the dotted line\nfor $q_0=0.5$ without evolution. } \n\\label{fig:dimming}\n\\end{figure}\n\nFig. \\ref{fig:counts60} shows our model predictions for the $60\\mu m$\ndifferential number counts of IRAS galaxies (Saunders et al. 1990). This\nwas an all sky local survey carried out with the IRAS satellite down\nto a flux limit of 0.6Jy. It therefore provides an important test of\nour model since spiral galaxies contribute significatly to \nIRAS counts (Neugebauer et al. 1984) \nand so if we are going to assume PLE out to redshifts\nof 4 then our local galaxy count predictions at $60\\mu m$ need to be \nreasonably consistent with the data. \nThe figure shows our evolution and no evolution model(the\n$q_0$ makes no difference) and because the IRAS survey was probing\nredshifts out to z=0.2 we can see that there is very little difference\nbetween the two models and that they both fit the data reasonably well.\nThe IRAS counts below 0.2Jy are \nslightly under-predicted using both dust laws, which\ncould possibly be due to the fact our model doesn't include any fast-evolving \nAGN/ULIRG population. We use the Calzetti dust law with three\ndust components of 15, 25, and 32K and this failure of the fainter IRAS counts\nis greater than when the 1/$\\lambda$ law is used because of the absence\nof the 45K dust component, which dominates the thermal emission at $60\\mu$m..\n\n\n\nWe then go on to show in Fig. \\ref{fig:counts} our sub-mm predictions\nusing the Bruzual \\& Charlot evolution model with low and high $q_0$\n($q_0=0.05, q=0.5$) and also for the corresponding no-evolution models\nwhere we use the Bruzual \\& Charlot SED at $z=0$ for all redshifts.\nWe have used a two-component dust temperature, as described in the\nprevious section and a galaxy formation redshift, $z_f=4$. The low\n$q_0$ model reproduces the faint counts well, but fails the very\nbright counts. This makes sense since these very luminous sources\nwould require ULIRG's, having SFR's of order $\\approx$\n100-1000M$_\\odot$yr$^{-1}$, and/or AGN, in order to produce\nthese huge FIR luminosities. Indeed, the $850\\mu m$\nintegral log N:log S appears flat between 2-10mJy before rising\nagain at fainter fluxes, suggesting that 2 populations may be contributing to \nthe counts.\n\nThe high $q_0$ model contains a dwarf elliptical population in order to fit the\noptical counts, as already explained, but no dust was invoked in these\ngalaxies in the optical models and so they do not contribute to our $850\\mu m$\npredictions. Contrary to the optical number counts, the high $q_0$\nmodels predict more galaxies greater than a given flux limit than low\n$q_0$ models. The reason for this is illustrated in Fig.\n\\ref{fig:dimming}, which shows how the received flux density from a\nM$_B=-22.5$ galaxy would vary with redshift in the high and low $q_0$\ncase, with and without $\\tau$=9Gyr. Bruzual \\& Charlot evolution. In the\nno-evolution cases the two factors involved are the cosmological\ndimming and the effect of the negative k-correction, since we are\neffectively looking up the black body curve as we look out to higher\nredshift. The high $q_0$ model( dotted line) predicts greater flux\ndensities for a given redshift than with low $q_0$, explaining why the\nintegral number counts are higher for a given flux density. When the\nBruzual \\& Charlot evolution is invoked (solid and dashed lines), we\npredict more flux than in the corresponding no-evolution cases at high\nredshift, because a galaxy is significantly brighter than at the\npresent day. The high $q_0$ model(with evolution) is virtually flat\nin the redshift range $0.5 < z < 2$ and the low $q_0$ model again\npredicts slightly lower flux densities for a given redshift compared\nto high $q_0$. It may be noted that the no-evolution models in this\nplot differ slightly from\nthat of Hughes et al.(1998). This discrepancy is a result\nof the different assumed dust temperature and beta parameter. \nThe colder temperature means\nthat the peak of the thermal emission from the dust is probed at lower\nredshifts and so we lose the benefit of the negative k-correction at \nz$\\approx$2-3 instead of at z$\\approx$7-9 as in Hughes \\& Dunlop(1998).\n\n\nFig. \\ref{fig:temp} shows the effect of altering the interstellar\ndust temperature (where we have used the low $q_0$ evolving model). The\ninterstellar dust temperature, $T_{int}$ makes a big difference to our\n$850\\mu m$ number count predictions and the variation is perhaps\ncontrary to what one may expect in that the lower $T_{int}$ means that\nwe expect to see more galaxies above a given flux limit S$_{lim}$.\nThis is because, as we lower the dust temperature, although the\nintegrated energy ie the area under the Planck curve goes down, the\nflux density at $850 \\mu m$ goes up slightly because we are seeing the\nmajority of radiation at much longer wavelengths. Now recall from the\nprevious section that the normalisation of the Planck emission curve\nis already defined from the amount of flux absorbed by the dust and\nthe Planck curve is simply scaled accordingly. So because the\nnormalisation is fixed, when we lower the dust temperature, we have to\nscale the Planck curve up by a much larger factor and therefore find\nthat we obtain much larger flux densities at $850 \\mu m$, explaining\nwhy our models are very sensitive to $T_{int}$.\n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs_rd.eps}\n% \\caption{The effect of varying the galaxy formation redshift $z_f$. The \n%graph \n%shows the low $q_0$ model with $T_d=20K$ and $\\beta=2.0$ with $z_f$'s of \n%6(upper\n%curve), 4,2 and 1(lower curve). The difference betweem the top two curves is \n%negligible\n%which shows that galaxies beyond $z=4$ have no measurable effect on the sub-mm\n% number\n%counts. }\n% \\label{fig:redshift}\n%\\end{figure}\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs_smoothed_T.ps}\n\n\\caption{The effect of varying the interstellar dust temperature,\n$T_{int}$ The graph shows the low $q_0$ model with\n$T_{circ}=45K$($\\beta=2.0$) and $z_f=4$. The modest warmer dust\ncomponent is included in each plot and the interstellar dust\ntemperature, which is dominant for the $850\\mu m$ counts, is varied\nfrom $15K$(solid curve) to $30K$(dotted curve), again with\n$\\beta=2.0$. Our model predictions are sensitive to this variation\nand increasing the interstellar dust temperature in fact means we see\nless galaxies above a given flux limit. Typical interstellar dust\ntemperatures are $\\approx 15K$. This trend is perhaps the opposite of what\n you would expect when varying dust temperatures and the reasons are explained\n in section 5. } \n\\label{fig:temp}\n\\end{figure}\n\n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs_smoothed_beta.ps}\n% \\caption{The effect of varying the emissivity parameter, $\\beta$. The \n%graph \n%shows the low $q_0$ model with $T_d=20K$ and $z_f=4$ with $\\beta$ values\n%of $0$(solid curve), $1.5$(dashed), $1$(dot-dashed) and $0$(dotted curve) . \n% $\\beta$ is well\n%constrained between 1.5 and 2 for dust emission in the literature and indeed\n%if we were to push $\\beta$ down to 1.5 then we could account for all of\n%the faint number counts.}\n% \\label{fig:beta}\n%\\end{figure}\n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]\n%{850allgraphs_smoothed_dust.ps}\n% \\caption{The effect of varying the dust extinction parameter, $A_B$. The \n%graph \n%shows the low $q_0$ model with $T_d=20K$, $\\beta=2.0$ and $z_f=4$ with \n%$A_B$ values\n%of $1.0$(solid curve), $0.5$(dashed), $0.3$(dot-dashed) and $0.1$\n%(dotted curve). We\n%adopt $A_B=0.3$ in our model, which corresponds to a relatively small amount\n%of dust, but we predict many more galaxies if $A_B$ is increased in\n%the $0.3 < A_B < 2.0$ range. $A_B=100.0$ essentially corresponds to the \n%dust absorbing all of the UV radiation from the galaxies and redistributing\n%it in the FIR and altering $A_B$ in the $2 < A_B < 100$ makes very little\n%difference. }\n% \\label{fig:dust}\n%\\end{figure}\n%\n%~\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{n_z_log.ps}\n\n\\caption{The predicted number-redshift distribution of sub-mm selected faint\nblue galaxies down to flux limits, $S_{lim}$ of 4.0, 2.0, 1.0 and 0.5mJy.\nThe graph shows the low-q$_0$ model using the $1/\\lambda$ dust law with\nthe parameters described in Fig. \\ref{fig:counts60} \nAs the flux limit is increased, the peak in the n(z)\ndistribution shifts\nfrom around z=1.8 at $S_{lim}$=0.5mJy to much lower\nredshifts, reaching z$\\approx 0.2$ for $S_{lim}$=4.0mJy.\n } \n\\label{fig:n_z}\n\\end{figure}\n\nWe have used a galaxy formation redshift, $z_f=4$ which is reasonable\nsince sub-mm sources seem to exist out to at least that, but we do in\nfact find that adopting $z_f=4$ or $z_f=6$ or indeed $z_f=10$ does not\nmake any difference to the number counts. Fig. \\ref{fig:dimming}\nillustrates this, since at $z > 4$ we are observing radiation that was\nemitted beyond the peak of the black-body curve, and so cosmological\ndimming is no longer compensated for and all the curves begin to fall\naway very quickly explaining why increasing $z_f$ beyond about z=4 makes\nessentially no difference to the $850\\mu m$ number counts. Of course,\na higher assumed $T_{int}$ would extend this redshift range to beyond z=4.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=3in,totalheight=3in,angle=-90]{850allgraphs_background.ps} \n\n\\caption{The predicted contribution to the FIR background from our models. The\nlatest measurements of the extragalactic FIRB, compared with the COBE\nmeasurement of the cosmic microwave background (Mather et al. 1994). F98 -\nFixsen et al.(1998)(upper solid line) and P96 - Puget et\nal.(1996)(lower solid line); H98 - Hauser et al.(1998);\nS98 - Schlegel et al.(1998). Both the Hauser and Schlegel\ndata each have points at $240\\mu m$ and $130\\mu m$. Low and high\n$q_0$ models are shown with and without evolution, where we have used\nour standard parameters of $T_{int}=15K$, $T_{circ}=45K$, $\\beta=2.0$\nand $z_f=4.0$ The evolution model, in the low $q_0$ case can account\nfor all of the FIR background at $850\\mu m$, whereas the high $q_0$\none in fact overpredicts by about a factor of 2. The no evolution\nmodels both underpredict the sub-mm background but are consistent with\nit to within an order of magnitude. The solid curve shows a model\nwhere we have used the Calzetti dust law using $A_B=1.02$ (equivalent to\nE(B-V)=0.18 and close to the value 0.15 used by Steidel \net al for their Lyman Break Galaxies)\n for the dust obscuration \nwith a\nthree-component dust temperature of 15K, 25K and 32K. It fits the background \nand\nfaint number counts at $850\\mu m$, the IRAS $60\\mu m$ counts and also does \nmuch better in the wavelength range\n$100\\mu m < \\lambda < 500\\mu m$. }\n\\label{fig:background}\n\\end{figure}\n\nFig. \\ref{fig:background} shows what sort of contribution we get to the\nextra-galactic background, simply by integrating over the number\ncounts in each wavelength bin. The plot shows the low and high $q_0$\nmodels with and without evolution, and with our standard parameters of\n$T_{int}=15K$, $T_{circ}=45K$, $\\beta=2.0$ and $z_f=4$. All the\nmodels predict the same intensity at short wavelengths($\\lambda=60\\mu$m), \nas low\nredshift objects would dominate making the evolution and $q_0$\ndependence less significant. The low $q_0$ model is able to\naccount for all of the background at $850\\mu m$, the high $q_0$ model\nin fact overpredicts it by about a factor of 2 and the no evolution\nmodels, although underpredicting it, are still well within an order of\nmagnitude. Although we can fit the background at $850\\mu m$, we\nnoticeably fail the data between about $100$ and $300\\mu m$. We find\nthat the only way to fit these observations using our model is to use\nhigher values of $A_B$ and higher dust temperatures, as this means\ndust is absorbing more energy from each galaxy and so the contribution\nto the background in the wavelength range where warmer dust emission\ndominates($100\\mu m < \\lambda < 500\\mu m$) is much greater. The solid\ncurve in Fig. \\ref{fig:background} shows a prediction where we have tried \nthe Calzetti dust model which gives more\noverall absorption with similar amounts of reddening; this model might\nalso be expected to fit the B optical counts. We see that its larger \namount of absorbed flux allows more flexibility in terms of using more\ndust components. By using three dust temperature \ncomponents \nresults we obtain a better (though still not perfect) \nfit to Fig. \\ref{fig:background} in the\n$100\\mu m < \\lambda < 300\\mu m$ range, while still giving\nfits to the IRAS $60\\mu m$ (Fig. \\ref{fig:counts60}) and faint $850\\mu m$\n number counts (Fig. \\ref{fig:counts}).\n\n\n\n%Although the model is aimed at trying to explain a possible contribution to the\n%submm background, it is easy to make other predictions, like for example, the\n%counts and $n(z)$ distribution of IRAS galaxies. Figs \\ref{fig:iras_counts}\n% and\n%\\ref{fig:iras_n_z} respectively show these predictions and it is\n%re-assuring that we do extremely well in both cases. The figures show a low\n%$q_0$ model with and without evolution and our evolution model is within the\n%errors of all the observations, with the no-evolution model underpredicting the\n%$60\\mu m$ counts, although not nearly so seriously as in the $850\\mu m$ case.\n%This is probably because the low redshift objects are hugely dominant for our \n%models in\n%the $60\\mu m$ case, because of the high flux limit and the fact that $60 \\mu m$\n%is just beyond the peak in the thermal emission from the dust. This would then\n%mean that by the time galaxy evolution becomes important at high redshift, the\n%number count contribution becomes insignificant. \n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]{allgraphs_60counts.eps}\n% \\caption{Observed $60\\mu m$ number counts of IRAS galaxies together with\n%our predictions from a low $q_0$ model with and without evolution. The crosses\n%are\n%taken from Hacking \\& Houck(1987), the empty triangles from Rowan-Robinson \n%et al.(1990), the filled triangles from Sanders et al.(1990) and the circles\n%from Gregorich et al.(1995):see also Bertin et al.(1997)}\n% \\label{fig:iras_counts}\n%\\end{figure} \n\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=3in,totalheight=3in,angle=-90]{allgraphs_60n_z.eps}\n% \\caption{Our predicted N(z) distribution per steradian for the IRAS galaxy\n%catalogue down to a flux limit of 0.6mJy. The figure shows a low $q_0$ model\n%with and without evolution }\n% \\label{fig:iras_n_z}\n%\\end{figure}\n\n\n\\section{Discussion}\n\nWe have taken a different approach from the standard way in which\nsub-mm flux's are estimated using UV luminosities \\cite{meurer99}.\nInstead of assuming a relationship between the UV slope $\\beta$ and\nthe ratio $L_{FIR}/L_{UV}$, we proceed directly from the spiral\ngalaxy UV luminosity functions and simply re-radiate into the FIR by\nassuming a simple dust law constrained from the optical counts. A\ndirect result of this, as has already been illustrated in the\nprevious section, is that decreasing the interstellar dust temperature\nactually increases the received flux density at $850\\mu m$, firstly\nbecause the peak in the Planck emission curve moves towards longer\nwavelengths and secondly because (as the absorbed flux from the dust\nis fixed) the normalisation scaling factor goes up. The fact then\nthat we model the dust using a dominant interstellar component of\n15K, which is significantly colder than that used in models of\nstarburst galaxies (typically 30-50K), means that we are able to show\nthat the evolution of normal spiral galaxies like our own Milky Way,\nusing the Bruzual model\nwith an exponential SFR of $\\tau=9$Gyr, could make a very significant\ncontribution to the sub-mm number counts in the $S_{850} <\n2$mJy range. Indeed this sort of temperature for spirals has been\ngiven recent support from observations of ISO at $200\\mu m$ \n\\cite{alton98a} where, for a sample of 7 spirals, a mean temperature\nof 20K was found, about 10K lower than previous estimates from IRAS\nat shorter wavelengths. They found that 90 percent of the FIR\nemission came from very cold dust at temperatures of 15K. Sub-mm observations\nof spirals (Alton et al. 1998b; Bianchi et al. 1998) and observations of dust\n in our own \ngalaxy (Sodroski et al. 1994; Reach et al. 1995; Boulanger et al. 1996; \nSodroski et al. 1997) also support the claims of these sorts of dust \ntemperatures.\nOf course, at z=4\nour assumed interstellar dust temperature of 15K is comparable to that\nof the microwave background. \n\nOur models show that normal spiral galaxies (ie those that \nevolve into galaxies like our own Milky Way assuming the Bruzual model) \nfail to provide the necessary FIR\nflux of the most luminous sources($>2$mJy) and this is not surprising since the\n$\\tau=9$Gyr SFR at high redshift($z>1$), which is consistent with the UV data,\nis lower than that inferred by other models which fit the sub-mm counts by a\nfactor of about 5 or so \\cite{blain98a}. The LBG galaxies at high redshift are\npredicted to be evolved spirals by the Bruzual models and the dust we invoke\n($A_B$=0.3 implies an attenuation factor at 1500\\AA of 2.3) is enough to make\nthem low luminosity sub-mm sources at flux levels of around 0.5mJy. This\namount of dust, though, is not enough to account for the factor of 5\ndiscrepancy and there are several possible reasons for this. \n\nThe first is the possible additional contribution to the sub-mm counts from\nAGN. Modelling of the obscured QSO population has shown that they could\ncontribute, at most, about 30\\% \nof the background at $850\\mu m$ but they\ncan get much closer to the bright end of the sub-mm number counts\n\\cite{gunn99}. This is shown in Fig. \\ref{fig:counts} where we also show the\n$q_0$=0.5 model of Gunn \\& Shanks. Although the slope of the QSO count at the\nfaintest limits is too flat, at brighter fluxes the QSO model fits better than\nthe faint blue galaxy model and the combination of the two gives a better fit\noverall.\n\n%When deriving sub-mm based SFR's it is assumed that the dust is heated \n%entirely from star formation and the possible presence of an active nucleus is\n%neglected. If it were commonplace for these sub-mm sources to host AGN then\n%this would provide a further heating mechanism for the dust and lower the \n%SFR's needed to provide the required FIR luminosities and therefore help\n%reconcile the differing $z>1$ SFR estimates from the UV and sub-mm.\n\nIt is also possible that the optical and sub-mm observations are sampling a\ncompletely different population of galaxies \nas the obscured galaxies sampled\nby the sub-mm observations may well just be too red or too faint to be detected\nin the UV at the current flux limits \n(Smail et al. 1999, 2000; Dey et al. 1999). That may mean that the most \nluminous\nsub-mm sources or ULIRG's($>10^{13}L_{\\odot}$) are not the LBG galaxies (which\nthe Bruzual model predicts as evolved spirals) and so then it would not be\nsurprising if the current sub-mm and UV derived star-formation histories at\nhigh redshift were different. However, the evidence is growing that the faint\nblue galaxies {\\it are} significant contributors to the faint sub-mm counts.\nChapman et al.(1999) carried out sub-mm observations of 16 LBG's and found,\nwith one exception, null detections down to their flux limit of $0.5$mJy. But\ntheir one detection may suggest that with enough SCUBA integration time it\nmight be possible to detect LBG's that are particularly luminous in the FIR and\nindeed, while this paper was in preparation, work from Peacock et al (1999) \nsuggests that faint blue galaxies may be detected at $850\\mu m$ at around the\n0.2mJy level. This is below\nthe SCUBA confusion limit of $\\approx2$mJy (Hughes et al. 1998; Blain\net al. 1998b) and highlights\nthe problem faced by Chapman et al.(1999) in performing targetted\nsub-mm observations of LBG's. The conclusions of Peacock et al.(1999) \nsuggest that the LBG population (the faint blue galaxies in our model)\n contribute \nat least 25 percent of the\nbackground at $850\\mu m$ and Adelberger et al.(2000) also come to similar \nconclusions, namely that the UV-selected galaxy population could account\nfor all the $850\\mu$m background and the shape of\nthe number counts at $850\\mu$m. However, the conclusions of Adelberger \net al.(2000) are based on the fact\nthat the SED of SMM J14011+0252 is representative of both the LBG and sub-mm\npopulation. At present, they are only assumptions, but nevertheless \n the conclusions of all these authors\nseem to suggest that ULIRG's may not \ncontribute to the faint sub-mm number counts and background as much as \nwas first thought.\n\nThe spectral slope of the UV continuum and the strength of the H$\\beta$\nemission line in Lyman Break Galaxies support the fact that interstellar\ndust is present \n(Chapman et al. 1999),\nbut the physics of galactic dust and the way it obscures the optical radiation\nfrom a source is still very poorly understood. We started by adopting a very\nsimplistic model for the dust, treating it as a spherical screen around our\nmodel spiral galaxy. The dust might, in reality, be concentrated in the plane\nof the disk for spiral galaxies and may also tend to clump around massive\nstars. This would make the extinction law effectively grayer as suggested by \nobservations of local starburst galaxies (Calzetti, 1997). Indeed, we have\ninvestigated the effect of the grayer Calzetti extinction law and found that it\nwould produce a larger sub-mm count contribution due to the higher overall\nabsorption it would imply. Metcalfe et al (2000) have also suggested that there\nmay be evidence for evolution of the extinction law from the U-B:B-R diagram\nof faint blue galaxies in the Herschel Deep Field. \n\nWe have assumed pure luminosity evolution (PLE) throughout this paper. The\nassumption that the number density of spiral galaxies remains constant might \ncertainly not be the case if dynamical galaxy merging is important for\ngalaxy formation. However, as we have seen it is relatively easy to fit the\nsub-mm number counts with PLE models whereas it is in fact impossible to fit\nthe counts using pure density evolution models without hugely overpredicting\nthe background by 50 or 100 times \\cite{blain98a}. So, if existing sub-mm\nobservations are correct then although density evolution may also occur,\nluminosity evolution may be dominant. It is also striking how well\nthe PLE models do in the optical number counts and colour-magnitude diagrams\nand together with the fact that we observe highly luminous objects in the\nsub-mm out to at least $z=3$ , this could indicate that the biggest galaxies\ncould have formed relatively quickly, on timescales of about $1$Gyr or so. If\nthis were true, then the PLE models may be a fair approximation to the galaxy\nnumber density and evolution in the Universe out to $z\\approx 3$ in both the\noptical/near-IR and FIR.\n\n\n% However, $A_B=0.3$ corresponds to a relatively small amount\n%of dust (a UV attenuation correction of $\\sim 2.3$ from $1500\\AA$ observations\n%compared to a correction of 4.7 from LBG's of Steidel et al. 1998)\n% and it is amazing\n% that this has such a big impact on the\n%sub-mm number counts and background. If we were to increase the dust\n%extinction parameter to $A_B=0.6$ we have shown that, using a higher \n%temperature(30K), we can also get a much better \n%fit to the background in the $100-500\\mu m$ range.\n%As already discussed, the FIR emission from normal spiral galaxies \n%seem to be able to be well modelled\n%by dust temperatures of about $20K$, with $\\beta=2.0$, although many of\n%the observed sub-mm sources(which are ULIRG's) have lower values of\n%$\\beta$, around 1.5. often with a modest contribution\n%from warmer dust of $\\approx 50K $to fit emission at shorter wavelengths. \n%This would be important \n%in trying to fit, for example, the IRAS $60\\mu m$ counts, which contains\n%mostly normal spiral galaxies\n\n\nWe have not taken into account early-type galaxies as no dust was invoked in\nthese in the optical galaxy count models. In particular, we have not included\nany contribution from dust in the dE population which is invoked to fit the\nfaint optical counts in the $q_0=0.5$ model (Metcalfe et al. 1996).\n If we were to include their\npossible contribution this would increase our $850\\mu m$ counts predictions at\nthe faint end since in our models both early-type and dE star formation occurs \nat high redshift which is the region of greatest sensitivity for the sub-mm\ncounts. At brighter fluxes though, where, in our models, low redshift galaxies\nare the only possible influence, the inclusion of early-type galaxies would be\nnegligible.\n\n%So far there are few optical counterparts with reliable redshifts that have \n%been\n%identified with sub-mm sources. There are very few observations of\n% sources with flux densities of 1mJy or less \n%where\n%we predict normal spirals to be important and no optical counterparts and so,\n% according to our models, even if we cannot detect the optical \n%counterpart, \n%sources with flux densities $<$1mJy are likely to come from \n%normal spiral galaxies.\n\n\n%s problem is that the sub-mm sources which have been\n%observed are thought to be ultraluminous infrared galaxies (ULIRGs) and not\n%ordinary spiral galaxies. ULIRGs would probably form \n%from the merger of\n%two comparable mass, gas-rich spiral galaxies \\cite{mihos99} and the resulting\n%gas flow from the huge tidal forces could then induce starburst or AGN\n%activity. Although, it\n%is claimed that ULIRGs could account for vertially\n% all of the sub-mm counts\n%and background \\cite{sanders99}, the uncertainties in their\n%number densities \n%are still huge and AGN, on their own, are unlikely to contribute \n%any more than $20$ percent of the\n%counts and background \\cite{gunn99} without having to push\n%modelling parameters to\n%the extreme. \n\n%We do not claim to be modelling very accurately what may be \n%happening in reality, but I do hope that our model shows that it is not \n%necessary for \n%us to assume huge amounts of dust or star formation rates. The simplicity\n%of the model makes it very easy to make sense of what is going on and plainly\n%shows that if the dust invoked in spirals to explain the optical number\n%counts is to be believed, then normal spiral galaxies could provide a \n%significant\n%contribution to the sub-mm background and the $850\\mu m$ number counts at \n%flux %densities $< 1mJy$ \n\n\\section{Conclusions}\n\nThe aim of this paper was to investigate whether, by re-radiating the absorbed\nspiral galaxy UV flux into the FIR, the dust invoked in the faint blue\nspirals at high z\nfrom the optical galaxy count models of Metcalfe et al.(1996) could have a\nsignificant contribution to the sub-mm galaxy counts and also the FIR\nbackground at $850\\mu$m. We have found that, using a interstellar dust\ntemperature of $15K$, a modest circumstellar component of $45K$, a beta\nparameter of 2.0 and a galaxy formation redshift of $z_f\\approx4$ we can account for\na very significant fraction of the faint $850\\mu m$ source counts, both in the\nlow and high $q_0$ cases when we invoke Bruzual \\& Charlot evolution (see Fig.\n\\ref{fig:counts}). These evolutionary models give 5-10 times more contribution\nto the faint sub-mm counts than the corresponding no-evolution models. At\nbrighter fluxes, we find that the SFR and dust assumed in our normal spiral\nmodel are too low to produce the FIR fluxes of the most luminous sources. In\nthe no-evolution cases, we underpredict the number counts, even at the faint\nend. Our predicted redshift distribution of sub-mm selected faint blue \ngalaxies\nsuggests that the main contribution to the faint counts is in the \nrange $0.5 < z < 3$, peaking at $z\\approx1.8$. We have shown that our model \nfits the $60\\mu m$ IRAS data well, an\nimportant local test if we want to assume PLE and extrapolate our optical\nspiral galaxy luminosity functions out to higher redshift. With the evolution\nmodels we can easily account for 50-100\\% of the FIR background at $850\\mu m$ \nbut fail the data by nearly an order of magnitude in the $100-300\\mu m$ range. \nWe have shown that the only way to fit these observations using this optically\nbased model is to use assume more dust obscuration ($A_B=0.6$) and much warmer\ndust (T=30K). Effectively gray extinction laws such as that of Calzetti et al\n(1997) may also provide more overall absorption and hence allow more dust\ntemperature components to allow the flexibility to fit the FIR background from\n60-850 $\\mu m$. However, the bright sub-mm counts will still require a\nfurther contribution from QSO's or ULIRGs to complement the contribution of the\nfaint blue galaxies at fainter fluxes.\n\n\n% in dis-agreement to previous claims that ULIRG's would provide the required FIR \n%flux to fit all of the sub-mm background.\n\n%the sub-mm countsWe are able to account for essentially\n% all of the\n%$850\\mu m$ background despite the fact that we cannot account for the most\n% luminous\n%sub-mm sources (ie ULIRG's) with our model (see fig. \\ref{fig:counts}). This\n%then suggests that the FIR background at $850\\mu m$ is dominated by\n%evolved spiral galaxies and not ULIRG's. \n%Despite the\n%fact that we cannot account for the most luminous sources in the sub-mm\n%number counts,\n%we are still able to reproduce, at worst, half of\n% the FIR background at $850\\mu m$ and\n%this would suggest that the LBG, which the Bruzual model\n%predicts are evolved spirals \n%sub-mm background are dominated by FIR emission\n%from a low luminosity source population, which we claim would be\n%evolved spiral galaxies, similar to the LBG galaxies that have been detected \n%at high z.\n%We have shown, then, that the contribution\n%to the background at $100-500\\mu m$ would seem to come from sources which\n%are, firstly more obscured, and secondly, have much warmer dust than what is \n%typically assumed for normal \n%spiral galaxies, although only the model with $A_B=0.3$ is known to fit the \n%optical counts. \n%Our models are also re-assuringly consistent with the $60\\mu m$ \n%counts from the low redshift\n%IRAS all sky survey, providing verification of our galaxy count normalisation.\n%We slightly overpredict the model redshift distributions of Sanders et al(1990)\n% of the IRAS galaxies, but never-the-less the match is still very encouraging\n%and we obtain the peak in the redshift distribution at nearly the same value\n%of $z=0.02$\n\n \n\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\citename{Allen \\ }1995]{allen95}\nAllen, C.W. 1995, Astrophysical Quantities, pg. 197\n\n\\bibitem[\\protect\\citename{Alton et al.\\ }1998a]{alton98a}\nAlton, P.B. et al., 1998a, A\\&A, 335, 807A\n\n\\bibitem[\\protect\\citename{Alton et al.\\ }1998b]{alton98b}\nAlton, P.B. et al., 1998b, ApJ, 507, 125\n\n\\bibitem[\\protect\\citename{Babul \\& Rees \\ }1992]{babrees92}\nBabul, A. \\& Rees, M.J., 1992, MNRAS, 255, 346\n\n\\bibitem[\\protect\\citename{Barger et al.\\ }1998]{barger98}\nBarger, A.J. Cowie, L.L., Sanders, D.B. Fulton, E., Taniguchi, Y.,\nSato, Y., Kawara, K., Okuda, H., 1998, Nature, 394, 248B\n\n\\bibitem[\\protect\\citename{Barger et al.\\ }1999]{barger99}\nBarger, A.J., Cowie, L.L., Smail, I., Ivison, R.J., Blain, A.W., Kneib, J-P.\n1999 astro-ph/9903142\n\n\\bibitem[\\protect\\citename{Bertin et al.\\ }1997]{bertin97}\nBertin, E., Dennefield, M., Moshir, M., 1997, A\\&A, 323, 685\n\n\\bibitem[\\protect\\citename{Bianchi et al.\\ }1999]{bianchi99}\nBianchi, S., Alton, P.B., Davies, J.I., 1999, astro-ph/9910011\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1999]{blain99}\nBlain, A.W., Kneib, J.P., Ivison, R.J., Smail, I., 1999, ApJL, 512, L87\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1998a]{blain98a}\nBlain, A.W., Smail, I., Ivison, R.J., \\& Kneib, J-P\n1998, MNRAS, 302, 632\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1998b]{blain98b}\nBlain, A.W., Ivison, R.I., \\& Smail, I.,\n1998, MNRAS, 296, 29\n\n\\bibitem[\\protect\\citename{Boulanger et al.\\ }1996]{boulanger96}\nBoulanger, F. et al., 1996, A\\&A, 312256B \n\n\\bibitem[\\protect\\citename{Bruzual et al.\\ }1993]{bruzual93}\nBruzual, A.G. \\& Charlot, S. 1993, ApJ, 405, 538\n\n\\bibitem[\\protect\\citename{Calzetti et al.\\ }1997]{calzetti97}\nCalzetti, D., et al., 1997, AJ, 114, 1834C\n\n\\bibitem[\\protect\\citename{Cole et al.\\ }1994]{cole94}\nCole, S., Aragon-Salamanca, A., Frenk, C.S., Navarro, J.F.,\n Zepf, S.E. 1994, MNRAS 271, 781\n\n\\bibitem[\\protect\\citename{Cowie et al.\\ }19945]{cowie95}\nCowie, L.L., Hu, E.M., Songaila, A. 1995 AJ, 110, 1576C\n\n\\bibitem[\\protect\\citename{Dominigue et al.\\ }1999]{dom99}\nDominigue, D. L., Keel, W.C., Ryder, S.D., White, R.E.\n1999 astro-ph/9906281\n\n\\bibitem[\\protect\\citename{Glazebrook et al. 1995a, Driver et al 1995\\ }]\n{driver}\nDriver, S.P., Windhorst, R.A., Ostrander, E.J., Keel, W.C., Griffiths, R.E.\n\\& Ratnatunga, K.U. 1995, AJ, 449, L23\n\n\\bibitem[\\protect\\citename{Eales et al.\\ }1999]{eales99}\nEales et al., 1999, ApJ, 515, 518 \n\n\\bibitem[\\protect\\citename{\\ }1998]{fixsen}\nFixsen, D.J., Dwek, E., Mather, J.C., Bennett, C.L., Shafer, R.A.,\n 1998, ApJ, 508, 123\n\n\\bibitem[\\protect\\citename{Flores et al.\\ }1999]{flores99}\nFlores, H., Hammer, F. et al., 1999, ApJ, 517, 148\n\n\\bibitem[\\protect\\citename{Frayer et al.\\ }1999]{frayer99}\nFrayer, D.T., Scoville, N.Z., 1999, conf., Science with the Atacama Large \nMillimeter Array (ALMA), Associated Universities, Inc.\n\n\\bibitem[\\protect\\citename{Gallego et al.\\ }1996]{gallego96}\nGallego, J., Zamorano, J., Aragon-Salamanca, A., Rego, M., 1996, ApJ, \n459, 43\n\n\\bibitem[\\protect\\citename{Glazebrook et al. 1995a, Driver et al. 1995\\ }]\n{glaze}\nGlazebrook, K.,Ellis, R.S., Santiago, B. \\& Griffiths, R.E.\n1995a, MNRAS, 275, L19\n\n\\bibitem[\\protect\\citename{Gregorich et al.\\ }1995]{gregorich95}\nGregorich, D.T., Neugebauer, G., Soifer, B.T., Gunn, J.E., Hertler, T.L.,\n1995, AJ, 110, 259\n\n\\bibitem[\\protect\\citename{Gronwall et al.\\ }1998]{gronwall98}\nGronwall, C., Salzer, J.J., McKinstry, K., 1998, AAS, 193, 7606G\n\n\\bibitem[\\protect\\citename{Guiderdoni \\& Rocca-Volmerange\\ }1990]{guidmet90}\nGuiderdoni, B. \\& Rocca-Volmerange, B. 1990, A\\&A 227, 362\n\n\\bibitem[\\protect\\citename{Gunn \\& Shanks\\ }1999]{gunn99}\nGunn, K.F., Shanks, T., 1999, astro-ph/9909089\n\n\\bibitem[\\protect\\citename{Hacking et al.\\ }1987]{hacking87}\nHacking, P.B., Houck, J.R., \n1987, ApJS, 63, 311\n\n\\bibitem[\\protect\\citename{\\ }1998]{hauser}\nHauser, M.G. et al., 1998, ApJ, 508, 25\n\n\\bibitem[\\protect\\citename{Holland et al.\\ }1998]{holland98}\nHolland, W.S. et al., 1998 SPIE, 3357, 305H\n\n\\bibitem[\\protect\\citename{Holland et al.\\ }1999]{holland99}\nHolland, W.S. et al., 1999, MNRAS, 303, 659\n\n\\bibitem[\\protect\\citename{Hughes et al.\\ }1998a]{hughes98a}\nHughes et al. 1998, Nature, 394, 241H\n\n\\bibitem[\\protect\\citename{Ivison et al.\\ }1998]{ivison98}\nIvison, R.J., Smail, I., LeBorgne, J-F., Blain, A.W., Kneib, J-P., et al.\n1998, MNRAS., 298, 583\n\n\\bibitem[\\protect\\citename{Ivison et al.\\ }2000]{ivison00}\nIvison, R.J., Smail, I., Barger, A.J., Kneib, J-P. Blain, A.W., Owen, F.N.,\nKerr, T.H., Cowie, L.L. 2000, MNRAS., 315, 209\n\n\\bibitem[\\protect\\citename{Lilly et al.\\ }1996]{lilly96}\nLilly, S.J., Le Fevre, O., Hammer, F., Crampton, D., 1996, ApJ, 460L, 1\n\n\\bibitem[\\protect\\citename{Lilly et al.\\ }1999]{lilly99}\nLilly, S.J., et al., 1999, ApJ, 518, 641L\n\n\\bibitem[\\protect\\citename{Madau et al.\\ }1996]{madau96}\nMadau, P., Ferguson, H.C., Dickenson, M., Giavalisco, M., Steidel, C.C.,\nFruchter, A. 1996, MNRAS, 283, 1388\n\n\\bibitem[\\protect\\citename{Mather et al.\\ }1994]{mather}\nMather, J.C. et al., 1994, ApJ, 420, 439\n\n\\bibitem[\\protect\\citename{Metcalfe et al.\\ }1996]{metcalfe96}\nMetcalfe, N., Shanks, T., Campos, A., Gardner, J.P \\& Fong, R.\n1996, Nature, 21, 10\n\n\\bibitem[\\protect\\citename{Metcalfe et al. \\ }1990]{metcalfe90}\nMetcalfe, N., Shanks, T., Fong, R. \\& Jones L.R. 1991, MNRAS 249, 498\n\n\\bibitem[\\protect\\citename{Meurer et al.\\ }1999]{meurer99}\nMeurer, G.R., Heckman, T.M., Calzetti, D., 1999, ApJ, in press\n(astro-ph/9903054)\n\n\\bibitem[\\protect\\citename{Mihos \\ }1999]{mihos99}\nMihos, C., 1999, astro-ph 9903115 \n\n\\bibitem[\\protect\\citename{Morrison et al. \\ }2000]{morrison00}\nMorrison, G., et al., 2000, in prep \n\n\\bibitem[\\protect\\citename{Neugebauer et al.\\ }1984]{Neugebauer84}\nNeugebauer et al. 1984, 4Sci, 224, 14N\n\n\\bibitem[\\protect\\citename{Peacock \\ }1999]{peacock99}\nPeacock, J.A. et al. 1999, astro-ph/9912231\n\n\\bibitem[\\protect\\citename{Pei\\ }1992]{pei92}\nPei, Y.C., 1992, ApJ, 395, 130\n\n\\bibitem[\\protect\\citename{\\ }1996]{puget}\nPuget, J.L., Abergel, A., Bernard, J.P., Boulanger, F., Burton, W.B.,\nDesert, F.X., Hartmann, D., 1996, AAP, 308, L5\n\n\\bibitem[\\protect\\citename{Reach et al.\\ }1995]{reach95}\nReach, W.T., et al. 1995, ApJ, 451, 188\n\n\\bibitem[\\protect\\citename{Rowan-Robinson et al.\\ }1990]{rowrob90}\nRowan-Robinson, M., Hughes, J., Vedi, K., Walker, D.W., \n1990, MNRAS, 246, 273\n\n\\bibitem[\\protect\\citename{Sanders et al.\\ }1987]{sanders87}\nSanders, D.B., Star Forming Regions: IAU Symp 115 Tokyo P. 653, 1987\n\n\\bibitem[\\protect\\citename{Sanders et al.\\ }1990]{sanders90}\nSaunders, W., Rowan-Robinson M., Lawrence, A., Efstathiou, G.,Kaiser, N.,\nEllis, R.S., Frenk, C.S., 1990, MNRAS, 242, 318\n\n\\bibitem[\\protect\\citename{Sanders \\ }1999]{sanders99}\nSanders, D.B., 1999, astro-ph/9904292\n\n\\bibitem[\\protect\\citename{\\ }1998]{schlegel}\nSchlegel, D.J., Finkbeiner, D.P., Davis, M., 1998, ApJ, 500, 525\n\n\\bibitem[\\protect\\citename{Shanks et al.\\ }1984]{shanks84}\nShanks, T., Stevenson, P.R.F.,Fong, R. and MacGillivray, H.T. \n1984, MNRAS. 106 767\n\n\\bibitem[\\protect\\citename{Shanks et al.\\ }1998]{shanks98}\nShanks, T., Metcalfe, N., Fong, R., McCracken, H.J., Campos, A., Gardner, J.P.,\nASP Conference Series: Vol 146; 1998, p.102\n\n\\bibitem[\\protect\\citename{Smail et al.\\ }1997]{smail97}\nSmail, I., Ivison, R.J., Blain, A.W. 1997, ApJ, 490, L5\n\n\\bibitem[\\protect\\citename{Smail et al.\\ }2000]{smail00}\nSmail, I., Ivison, R.J.,, Owen, F.N., Blain, A.W., Kneib, J-P.\n2000, ApJ, 528, 612\n\n\\bibitem[\\protect\\citename{Sodroski et al.\\ }1994]{sodroski94}\nSodroski, T.J. et al., 1994, ApJ, 428, 638\n\n\\bibitem[\\protect\\citename{Sodroski et al.\\ }1997]{sodroski97}\nSodroski, T.J. et al., 1997, ApJ, 480, 173\n\n\\bibitem[\\protect\\citename{Soifer et al.\\ }1989]{soifer89}\nSoifer, B.T., Boehmer, L., Neigebauer, G., \\& Sanders, D.B., 1989, AJ, 98, 766\n\n\\bibitem[\\protect\\citename{Steidel et al.\\ }1996b]{steidel96b}\nSteidel, C.C., Giavalisco, M., Dickinson, M., Pettini, M., Adelberger, K.L.,\n1996b, ApJ, 462, L17\n\n\\bibitem[\\protect\\citename{Steidel et al.\\ }1998]{steidel98}\nSteidel, C.C., Adelberger, K.L., Dickinson, M., Giavalisco, M., Pettini, M.,\n1998, in proc. Xth Rencontres de Blois, The Birth of Galaxies\n\n\\bibitem[\\protect\\citename{Steidel et al.\\ }1999]{steidel99}\nSteidel, C.C., Adelberger, K.L., Giavalisco, M., Dickinson, M., Pettini, M.,\n1999, ApJ, 519, 1S\n\n\\bibitem[\\protect\\citename{Thronson \\& Telesco\\ }1986]{thronson86}\nThronson, H., Telesco, C., 1986, ApJ, 311, 98\n\n\\bibitem[\\protect\\citename{Tresse et al.\\ }1998]{tresse98}\nTresse, L., Maddox, S.J., 1998, ApJ, 495, 691T\n\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002081.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\citename{Allen \\ }1995]{allen95}\nAllen, C.W. 1995, Astrophysical Quantities, pg. 197\n\n\\bibitem[\\protect\\citename{Alton et al.\\ }1998a]{alton98a}\nAlton, P.B. et al., 1998a, A\\&A, 335, 807A\n\n\\bibitem[\\protect\\citename{Alton et al.\\ }1998b]{alton98b}\nAlton, P.B. et al., 1998b, ApJ, 507, 125\n\n\\bibitem[\\protect\\citename{Babul \\& Rees \\ }1992]{babrees92}\nBabul, A. \\& Rees, M.J., 1992, MNRAS, 255, 346\n\n\\bibitem[\\protect\\citename{Barger et al.\\ }1998]{barger98}\nBarger, A.J. Cowie, L.L., Sanders, D.B. Fulton, E., Taniguchi, Y.,\nSato, Y., Kawara, K., Okuda, H., 1998, Nature, 394, 248B\n\n\\bibitem[\\protect\\citename{Barger et al.\\ }1999]{barger99}\nBarger, A.J., Cowie, L.L., Smail, I., Ivison, R.J., Blain, A.W., Kneib, J-P.\n1999 astro-ph/9903142\n\n\\bibitem[\\protect\\citename{Bertin et al.\\ }1997]{bertin97}\nBertin, E., Dennefield, M., Moshir, M., 1997, A\\&A, 323, 685\n\n\\bibitem[\\protect\\citename{Bianchi et al.\\ }1999]{bianchi99}\nBianchi, S., Alton, P.B., Davies, J.I., 1999, astro-ph/9910011\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1999]{blain99}\nBlain, A.W., Kneib, J.P., Ivison, R.J., Smail, I., 1999, ApJL, 512, L87\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1998a]{blain98a}\nBlain, A.W., Smail, I., Ivison, R.J., \\& Kneib, J-P\n1998, MNRAS, 302, 632\n\n\\bibitem[\\protect\\citename{Blain et al.\\ }1998b]{blain98b}\nBlain, A.W., Ivison, R.I., \\& Smail, I.,\n1998, MNRAS, 296, 29\n\n\\bibitem[\\protect\\citename{Boulanger et al.\\ }1996]{boulanger96}\nBoulanger, F. et al., 1996, A\\&A, 312256B \n\n\\bibitem[\\protect\\citename{Bruzual et al.\\ }1993]{bruzual93}\nBruzual, A.G. \\& Charlot, S. 1993, ApJ, 405, 538\n\n\\bibitem[\\protect\\citename{Calzetti et al.\\ }1997]{calzetti97}\nCalzetti, D., et al., 1997, AJ, 114, 1834C\n\n\\bibitem[\\protect\\citename{Cole et al.\\ }1994]{cole94}\nCole, S., Aragon-Salamanca, A., Frenk, C.S., Navarro, J.F.,\n Zepf, S.E. 1994, MNRAS 271, 781\n\n\\bibitem[\\protect\\citename{Cowie et al.\\ }19945]{cowie95}\nCowie, L.L., Hu, E.M., Songaila, A. 1995 AJ, 110, 1576C\n\n\\bibitem[\\protect\\citename{Dominigue et al.\\ }1999]{dom99}\nDominigue, D. L., Keel, W.C., Ryder, S.D., White, R.E.\n1999 astro-ph/9906281\n\n\\bibitem[\\protect\\citename{Glazebrook et al. 1995a, Driver et al 1995\\ }]\n{driver}\nDriver, S.P., Windhorst, R.A., Ostrander, E.J., Keel, W.C., Griffiths, R.E.\n\\& Ratnatunga, K.U. 1995, AJ, 449, L23\n\n\\bibitem[\\protect\\citename{Eales et al.\\ }1999]{eales99}\nEales et al., 1999, ApJ, 515, 518 \n\n\\bibitem[\\protect\\citename{\\ }1998]{fixsen}\nFixsen, D.J., Dwek, E., Mather, J.C., Bennett, C.L., Shafer, R.A.,\n 1998, ApJ, 508, 123\n\n\\bibitem[\\protect\\citename{Flores et al.\\ }1999]{flores99}\nFlores, H., Hammer, F. et al., 1999, ApJ, 517, 148\n\n\\bibitem[\\protect\\citename{Frayer et al.\\ }1999]{frayer99}\nFrayer, D.T., Scoville, N.Z., 1999, conf., Science with the Atacama Large \nMillimeter Array (ALMA), Associated Universities, Inc.\n\n\\bibitem[\\protect\\citename{Gallego et al.\\ }1996]{gallego96}\nGallego, J., Zamorano, J., Aragon-Salamanca, A., Rego, M., 1996, ApJ, \n459, 43\n\n\\bibitem[\\protect\\citename{Glazebrook et al. 1995a, Driver et al. 1995\\ }]\n{glaze}\nGlazebrook, K.,Ellis, R.S., Santiago, B. \\& Griffiths, R.E.\n1995a, MNRAS, 275, L19\n\n\\bibitem[\\protect\\citename{Gregorich et al.\\ }1995]{gregorich95}\nGregorich, D.T., Neugebauer, G., Soifer, B.T., Gunn, J.E., Hertler, T.L.,\n1995, AJ, 110, 259\n\n\\bibitem[\\protect\\citename{Gronwall et al.\\ }1998]{gronwall98}\nGronwall, C., Salzer, J.J., McKinstry, K., 1998, AAS, 193, 7606G\n\n\\bibitem[\\protect\\citename{Guiderdoni \\& Rocca-Volmerange\\ }1990]{guidmet90}\nGuiderdoni, B. \\& Rocca-Volmerange, B. 1990, A\\&A 227, 362\n\n\\bibitem[\\protect\\citename{Gunn \\& Shanks\\ }1999]{gunn99}\nGunn, K.F., Shanks, T., 1999, astro-ph/9909089\n\n\\bibitem[\\protect\\citename{Hacking et al.\\ }1987]{hacking87}\nHacking, P.B., Houck, J.R., \n1987, ApJS, 63, 311\n\n\\bibitem[\\protect\\citename{\\ }1998]{hauser}\nHauser, M.G. et al., 1998, ApJ, 508, 25\n\n\\bibitem[\\protect\\citename{Holland et al.\\ }1998]{holland98}\nHolland, W.S. et al., 1998 SPIE, 3357, 305H\n\n\\bibitem[\\protect\\citename{Holland et al.\\ }1999]{holland99}\nHolland, W.S. et al., 1999, MNRAS, 303, 659\n\n\\bibitem[\\protect\\citename{Hughes et al.\\ }1998a]{hughes98a}\nHughes et al. 1998, Nature, 394, 241H\n\n\\bibitem[\\protect\\citename{Ivison et al.\\ }1998]{ivison98}\nIvison, R.J., Smail, I., LeBorgne, J-F., Blain, A.W., Kneib, J-P., et al.\n1998, MNRAS., 298, 583\n\n\\bibitem[\\protect\\citename{Ivison et al.\\ }2000]{ivison00}\nIvison, R.J., Smail, I., Barger, A.J., Kneib, J-P. Blain, A.W., Owen, F.N.,\nKerr, T.H., Cowie, L.L. 2000, MNRAS., 315, 209\n\n\\bibitem[\\protect\\citename{Lilly et al.\\ }1996]{lilly96}\nLilly, S.J., Le Fevre, O., Hammer, F., Crampton, D., 1996, ApJ, 460L, 1\n\n\\bibitem[\\protect\\citename{Lilly et al.\\ }1999]{lilly99}\nLilly, S.J., et al., 1999, ApJ, 518, 641L\n\n\\bibitem[\\protect\\citename{Madau et al.\\ }1996]{madau96}\nMadau, P., Ferguson, H.C., Dickenson, M., Giavalisco, M., Steidel, C.C.,\nFruchter, A. 1996, MNRAS, 283, 1388\n\n\\bibitem[\\protect\\citename{Mather et al.\\ }1994]{mather}\nMather, J.C. et al., 1994, ApJ, 420, 439\n\n\\bibitem[\\protect\\citename{Metcalfe et al.\\ }1996]{metcalfe96}\nMetcalfe, N., Shanks, T., Campos, A., Gardner, J.P \\& Fong, R.\n1996, Nature, 21, 10\n\n\\bibitem[\\protect\\citename{Metcalfe et al. \\ }1990]{metcalfe90}\nMetcalfe, N., Shanks, T., Fong, R. \\& Jones L.R. 1991, MNRAS 249, 498\n\n\\bibitem[\\protect\\citename{Meurer et al.\\ }1999]{meurer99}\nMeurer, G.R., Heckman, T.M., Calzetti, D., 1999, ApJ, in press\n(astro-ph/9903054)\n\n\\bibitem[\\protect\\citename{Mihos \\ }1999]{mihos99}\nMihos, C., 1999, astro-ph 9903115 \n\n\\bibitem[\\protect\\citename{Morrison et al. \\ }2000]{morrison00}\nMorrison, G., et al., 2000, in prep \n\n\\bibitem[\\protect\\citename{Neugebauer et al.\\ }1984]{Neugebauer84}\nNeugebauer et al. 1984, 4Sci, 224, 14N\n\n\\bibitem[\\protect\\citename{Peacock \\ }1999]{peacock99}\nPeacock, J.A. et al. 1999, astro-ph/9912231\n\n\\bibitem[\\protect\\citename{Pei\\ }1992]{pei92}\nPei, Y.C., 1992, ApJ, 395, 130\n\n\\bibitem[\\protect\\citename{\\ }1996]{puget}\nPuget, J.L., Abergel, A., Bernard, J.P., Boulanger, F., Burton, W.B.,\nDesert, F.X., Hartmann, D., 1996, AAP, 308, L5\n\n\\bibitem[\\protect\\citename{Reach et al.\\ }1995]{reach95}\nReach, W.T., et al. 1995, ApJ, 451, 188\n\n\\bibitem[\\protect\\citename{Rowan-Robinson et al.\\ }1990]{rowrob90}\nRowan-Robinson, M., Hughes, J., Vedi, K., Walker, D.W., \n1990, MNRAS, 246, 273\n\n\\bibitem[\\protect\\citename{Sanders et al.\\ }1987]{sanders87}\nSanders, D.B., Star Forming Regions: IAU Symp 115 Tokyo P. 653, 1987\n\n\\bibitem[\\protect\\citename{Sanders et al.\\ }1990]{sanders90}\nSaunders, W., Rowan-Robinson M., Lawrence, A., Efstathiou, G.,Kaiser, N.,\nEllis, R.S., Frenk, C.S., 1990, MNRAS, 242, 318\n\n\\bibitem[\\protect\\citename{Sanders \\ }1999]{sanders99}\nSanders, D.B., 1999, astro-ph/9904292\n\n\\bibitem[\\protect\\citename{\\ }1998]{schlegel}\nSchlegel, D.J., Finkbeiner, D.P., Davis, M., 1998, ApJ, 500, 525\n\n\\bibitem[\\protect\\citename{Shanks et al.\\ }1984]{shanks84}\nShanks, T., Stevenson, P.R.F.,Fong, R. and MacGillivray, H.T. \n1984, MNRAS. 106 767\n\n\\bibitem[\\protect\\citename{Shanks et al.\\ }1998]{shanks98}\nShanks, T., Metcalfe, N., Fong, R., McCracken, H.J., Campos, A., Gardner, J.P.,\nASP Conference Series: Vol 146; 1998, p.102\n\n\\bibitem[\\protect\\citename{Smail et al.\\ }1997]{smail97}\nSmail, I., Ivison, R.J., Blain, A.W. 1997, ApJ, 490, L5\n\n\\bibitem[\\protect\\citename{Smail et al.\\ }2000]{smail00}\nSmail, I., Ivison, R.J.,, Owen, F.N., Blain, A.W., Kneib, J-P.\n2000, ApJ, 528, 612\n\n\\bibitem[\\protect\\citename{Sodroski et al.\\ }1994]{sodroski94}\nSodroski, T.J. et al., 1994, ApJ, 428, 638\n\n\\bibitem[\\protect\\citename{Sodroski et al.\\ }1997]{sodroski97}\nSodroski, T.J. et al., 1997, ApJ, 480, 173\n\n\\bibitem[\\protect\\citename{Soifer et al.\\ }1989]{soifer89}\nSoifer, B.T., Boehmer, L., Neigebauer, G., \\& Sanders, D.B., 1989, AJ, 98, 766\n\n\\bibitem[\\protect\\citename{Steidel et al.\\ }1996b]{steidel96b}\nSteidel, C.C., Giavalisco, M., Dickinson, M., Pettini, M., Adelberger, K.L.,\n1996b, ApJ, 462, L17\n\n\\bibitem[\\protect\\citename{Steidel et al.\\ }1998]{steidel98}\nSteidel, C.C., Adelberger, K.L., Dickinson, M., Giavalisco, M., Pettini, M.,\n1998, in proc. 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}
] |
astro-ph0002082
|
The entropy and energy of intergalactic gas in galaxy clusters
|
[
{
"author": "E. J. Lloyd-Davies"
},
{
"author": "School of Physics and Astronomy"
},
{
"author": "Edgbaston"
},
{
"author": "Birmingham B15 2TT"
},
{
"author": "UK"
}
] |
Studies of the X-ray surface brightness profiles of clusters, coupled with theoretical considerations, suggest that the breaking of self-similarity in the hot gas results from an `entropy floor', established by some heating process, which affects the structure of the intracluster gas strongly in lower mass systems. By fitting analytical models for the radial variation in gas density and temperature to X-ray spectral images from the ROSAT PSPC and ASCA GIS, we have derived gas entropy profiles for 20 galaxy clusters and groups. We show that when these profiles are scaled such that they should lie on top of one another in the case of self-similarity, the lowest mass systems have higher scaled entropy profiles than more massive systems. This appears to be due to a baseline entropy of 70-140~${h_{50}}^{-\frac{1}{3}}$ keV cm$^{2}$ depending on the extent to which shocks have been suppressed in low mass systems. The extra entropy may be present in all systems, but is detectable only in poor clusters, where it is significant compared to the entropy generated by gravitational collapse. This excess entropy appears to be distributed uniformly with radius outside the central cooling regions. We determine the energy associated with this entropy floor, by studying the net reduction in binding energy of the gas in low mass systems, and find that it corresponds to a preheating temperature of $\sim 0.3$~keV. Since the relationship between entropy and energy injection depends upon gas density, we are able to combine the excesses of 70-140~keV~cm$^{2}$ and 0.3~keV to derive the typical electron density of the gas into which the energy was injected. The resulting value of 1-3$\times 10^{-4}{h_{50}}^{\frac{1}{2}}$\,cm$^{-3}$, implies that the heating must have happened prior to cluster collapse but after a redshift $z\sim$ 7-10. The energy requirement is well matched to the energy from supernova explosions responsible for the metals which now pollute the intracluster gas.
|
[
{
"name": "entropy.tex",
"string": "\\documentstyle[general_cite,psfig]{mn}\n\\bibliographystyle{mnras}\n\\title{The entropy and energy of intergalactic gas in galaxy\nclusters}\n\\author[E. J. Lloyd-Davies et al.]\n {E. J. Lloyd-Davies,\\thanks{E-mail: [email protected]} \n T. J. Ponman and D. B. Cannon\\\\\n School of Physics and Astronomy, University of\n Birmingham, Edgbaston, Birmingham B15 2TT, UK\\\\}\n\\date{Accepted 1999 ??.\n Received 1999 ??;\n in original form 1999 ??}\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{1999}\n\n\\newcommand{\\dd}{\\\"}\n\n\\begin{document}\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\n Studies of the X-ray surface brightness profiles of clusters, coupled\n with theoretical considerations, suggest that the breaking of\n self-similarity in the hot gas results from an `entropy floor',\n established by some heating process, which affects the structure of the\n intracluster gas strongly in lower mass systems. By fitting analytical\n models for the radial variation in gas density and temperature to X-ray\n spectral images from the \\emph{ROSAT} PSPC and \\emph{ASCA} GIS, we have\n derived gas entropy profiles for 20 galaxy clusters and groups. We show\n that when these profiles are scaled such that they should lie on top of\n one another in the case of self-similarity, the lowest mass systems have\n higher scaled entropy profiles than more massive systems. This appears\n to be due to a baseline entropy of 70-140~${h_{50}}^{-\\frac{1}{3}}$ keV\n cm$^{2}$ depending on the extent to which shocks have been suppressed in\n low mass systems. The extra entropy may be present in all systems, but\n is detectable only in poor clusters, where it is significant compared to\n the entropy generated by gravitational collapse. This excess entropy\n appears to be distributed uniformly with radius outside the central\n cooling regions.\n \n We determine the energy associated with this entropy floor, by studying\n the net reduction in binding energy of the gas in low mass systems, and\n find that it corresponds to a preheating temperature of $\\sim 0.3$~keV.\n Since the relationship between entropy and energy injection depends upon\n gas density, we are able to combine the excesses of 70-140~keV~cm$^{2}$\n and 0.3~keV to derive the typical electron density of the gas into\n which the energy was injected. The resulting value of 1-3$\\times\n 10^{-4}{h_{50}}^{\\frac{1}{2}}$\\,cm$^{-3}$, implies that the heating must\n have happened prior to cluster collapse but after a redshift $z\\sim$\n 7-10. The energy requirement is well matched to the energy from\n supernova explosions responsible for the metals which now pollute the\n intracluster gas.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: clusters: general - intergalactic medium - X-rays: general\n\\end{keywords}\n\n\\section{Introduction}\nThe hierarchical clustering model for the formation of structure in the\nuniverse predicts that dark matter halos should be scaled versions of each\nother\\cite{navarro95a}. While some energy transfer between dark matter and\ngas is possible through gravitational interaction and shock heating,\nsimulations suggest that the gas and dark matter halos will be almost\nself-similar in the absence of additional heating or cooling processes\n\\cite{eke98a}. Comparison of the structure of real galaxy systems with this\npredicted self-similarity provides an excellent probe of extra physical\nprocesses that may be taking place in galaxy clusters and groups.\n\nIt has been suggested that specific energy in cluster cores is\nhigher than expected from gravitational collapse and that this may be due\nto energy injected by supernova-driven protogalactic winds\n\\cite{white91a,david91a}. \\scite{david96a} studied the entropy in a small\nsample of galaxy systems and suggested that the entropy in their cores had\nbeen flattened due to energy injection. \\scite{ponman98a} have recently\nshown that the surface brightness profiles of clusters and groups do not\nfollow the predicted self-similar scaling. Surface brightness profiles of\ngalaxy groups are observed to be significantly flatter than those of\nclusters, indicating differences in the gas distribution.\n\n\\begin{table*}\n\\begin{minipage}{154mm}\n\\caption{Some important properties for the sample of 20 galaxy clusters and groups. Systems are\n listed in order of increasing temperature.}\n\\label{tab:sample}\n\\begin{tabular}{lccccccc}\n\\hline\n\\hline\nCluster/Group&R.A.(J2000)&Dec.(J2000)&z&$N_{H}$($10^{20}$ cm$^{-2}$)&$T$(keV)&$Z$(solar)&Data\\\\\n\\hline\nHCG 68&208.420&40.319&0.0080&0.90&0.54&0.43&PSPC\\\\\nHCG 97&356.845&-2.169&0.0218&3.29&0.87&0.12&PSPC\\\\\nHCG 62&193.284&-9.224&0.0137&3.00&0.96&0.15&PSPC\\\\\nNGC 5044 Group&198.595&-16.534&0.0082&5.00&0.98&0.27&PSPC\\\\\nRX J0123.6+3315&20.921&33.261&0.0164&5.0&1.26&0.33&PSPC\\\\\nAbell 262&28.191&36.157&0.0163&5.4&1.36&0.27&PSPC\\\\\nIV Zw 038&16.868&32.462&0.0170&5.3&1.53&0.40&PSPC\\\\\nAbell 400&44.412&6.006&0.0238&9.1&2.31&0.31&PSPC\\\\\nAbell 1060&159.169&-27.521&0.0124&5.01&3.24&0.27&PSPC+GIS\\\\\nMKW 3s&230.507&7.699&0.0453&3.1&3.68&0.30&PSPC\\\\\nAWM 7&43.634&41.586&0.0173&9.19&3.75&0.33&PSPC\\\\\nAbell 780&139.528&-12.099&0.0565&4.7&3.8&0.23&PSPC+GIS\\\\\nAbell 2199&247.165&39.550&0.0299&0.87&4.10&0.30&PSPC\\\\\nAbell 496&68.397&-13.246&0.0331&4.41&4.13&0.31&PSPC+GIS\\\\\nAbell 1795&207.218&26.598&0.0622&1.16&5.88&0.26&PSPC\\\\\nAbell 2218&248.970&66.214&0.1710&3.34&6.7&0.20&PSPC+GIS\\\\\nAbell 478&63.359&10.466&0.0882&13.6&7.1&0.21&PSPC+GIS\\\\\nAbell 665&127.739&65.854&0.1818&4.21&8.0&0.28&PSPC+GIS\\\\\nAbell 1689&197.873&-1.336&0.1840&1.9&9.0&0.26&PSPC+GIS\\\\\nAbell 2163&243.956&-6.150&0.2080&11.0&13.83&0.19&PSPC+GIS\\\\ \n\\hline\n\\end{tabular}\nNotes: Positions, hydrogen columns and redshifts are taken from\n\\scite{ebeling96a}, \\scite{ebeling98a}, \\scite{ponman96a} and\n\\scite{helsdon99a}. Emission weighted temperatures and metallicities for\nthese systems are taken from \\scite{markevitch96a}, \\scite{mushotzky97a},\n\\scite{markevitch98a}, \\scite{mchardy90a}, \\scite{fukazawa98a},\n\\scite{butcher91a}, \\scite{mushotzky97b}, \\scite{helsdon99a},\n\\scite{david96a}, \\scite{david94a} and \\scite{ponman96a}.\n\\end{minipage}\n\\end{table*}\n\nIn order to explore this effect further, it is necessary to study the\nproperties of the gas in these systems in greater detail. A particularly\ninteresting property of the gas for this purpose is its entropy, as this\nwill be conserved during adiabatic collapse of the gas into a galaxy\nsystem, but is likely to be altered by any other physical processes. For\ninstance preheating of the gas before it falls into the cluster, energy\ninjection from galaxy winds and radiative cooling of the gas in dense\ncluster cores will all perturb the entropy profiles of clusters from the\nself-similar model. Analysis of the entropy profiles of virialized systems\nof different masses should therefore allow the magnitude of such effects to\nbe studied, constraining the possible processes responsible. A key question\nto answer in this regard is how much energy is involved in any departures\nfrom self-similarity of the entropy profiles. The study of\n\\scite{ponman98a} was not able to address this issue in detail, since the\ngas was assumed to be isothermal. Here we combine \\emph{ROSAT} PSPC and\n\\emph{ASCA} GIS data to constrain temperature profiles, allowing a more\ndetailed study of entropy and energy distributions in the intergalactic\nmedium (IGM).\n\nEnergy loss from the gas due to cooling flows in the centres of clusters\nand groups will actually lead to an increase in the gas entropy outside the\ncooling region \\cite{knight97a}. This is because as gas cools out at the\ncentre of the system, gas from a larger radius, which has higher entropy,\nflows in adiabatically to replace it. However this effect will not be very\nlarge unless a significant fraction of the gas in the system cools out,\nwhich is not feasible within a Hubble time, even for systems with\nexceptionally large cooling flows. \n\nEnergy injection into the gas will also raise the entropy profiles of\nsystems. This energy injection could occur either before or after the\nsystems' collapse, but more energy is needed to get the same change in\nentropy when the gas is more dense \\cite{ponman98a}. There are several\npossible processes that might have injected energy into the intracluster\nmedium: radiation from quasars, early population III stars, or energetic\nwinds associated with galaxy formation. \n\nThere may also be transient effects on the entropy profiles of\nsystems due to recent mergers. Hydrodynamical simulations suggest that the\nentropy profiles of systems are flattened and their central entropy raised\nduring a merger, and this will last until the system settles back into\nequilibrium \\cite{metzler94a}. In order to look for the effects of extra\nphysical processes, it is advantageous to study a set of systems with a\nlarge range in system mass, as these processes will break the expected\nself-similar scaling relations. In the present paper we examine the\nproperties of the intracluster gas in systems with mean temperatures\nranging over a factor of 25, corresponding to virial masses varying by over\ntwo orders of magnitude.\n\n\\section{Sample}\nThe sample selected for this study consisted of 20 galaxy systems ranging\nfrom poor groups to rich clusters, with high quality \\emph{ROSAT} PSPC and\nin some cases \\emph{ASCA} GIS data. Basic properties of these systems are\nlisted in Table \\ref{tab:sample}. The sample was chosen to cover a wide\nrange of system masses but is not a `complete' or statistically\nrepresentative sample of the galaxy cluster/group population. It is\nnecessary that the systems be fairly relaxed and spherical in order for the\nassumption of spherical symmetry used in the analysis to be reasonable, and\nthey were selected with this in mind, although it will be seen later that\nsome of the systems are not as relaxed as we had hoped. In general, our\nsample should be representative of the subset of galaxy systems which is\nfairly relaxed and X-ray bright. Galaxy systems which are not virialized,\nor those currently undergoing complex mergers, would be expected to have\nsystematically different properties. Our sample spans the population range\nfrom small groups to rich clusters, covering a range in emission weighted\ngas temperature from 0.5 to 14 keV. It is therefore well-suited to\ninvestigating the scale dependence in cluster properties.\n\n\\section{Data reduction}\nIn general \\emph{ASCA} GIS data were used only where \\emph{ROSAT} PSPC data\nwere insufficient to constrain the models. This was generally the case for\nsystems with temperatures greater than 4 keV but the cutoff can be somewhat\nhigher for high quality \\emph{ROSAT} PSPC data (i.e. Abell 1795 and Abell\n2199). In the cases where it is possible to access the consistency of\nresults from \\emph{ROSAT} PSPC and \\emph{ASCA} GIS data it appears that\nthey are in reasonable agreement. The results of fits to \\emph{ROSAT} PSPC\ndata and joint fits to \\emph{ROSAT} PSPC and \\emph{ASCA} GIS data for Abell\n1060 are quite similar. The temperature profiles derived from \\emph{ROSAT}\nPSPC data for Abell 1795 and Abell 2199 are also consistent with the\nemission weighted temperature obtained by previous authors from \\emph{ACSA}\ndata.\n\nA similar reduction process was applied to the \\emph{ROSAT} and \\emph{ASCA}\ndata for each system. For the \\emph{ROSAT} PSPC, the data were screened to\nremove periods of high particle background, where the master veto rate was\nabove 170 counts s$^{-1}$. The background was calculated from an annulus\ntypically between 0.6-0.7$^{\\circ}$ off-axis. This annulus was moved to\nlarger radii for clusters of large spatial extent, to avoid cluster\nemission contaminating the background. Point sources of significance\ngreater than 4$\\sigma$, together with the PSPC support spokes, were removed\nand the background in the annulus was extrapolated across the detector\nusing the energy dependent vignetting function.\n\nFor the \\emph{ASCA} GIS, the data were screened to to remove periods of\nhigh particle background. The following parameters were used to select good\ndata; cut-off rigidity ($COR$) $>$ 6 GeV c$^{-1}$; radiation belt monitor\ncount rate $<$ 100; GIS monitor count rate `H02' $<$ 45.0 and $<$ 0.45 x\n$COR^{2}$ - 13 $\\times$ $COR$ + 125. Data were also excluded where the\nsatellite passed through the South Atlantic Anomaly and where the elevation\nangle above the Earth's limb was $\\leq$ 7.5$^{\\circ}$. The background was\ntaken from the sum of a number of `blank sky' fields screened in the same\nway as the source data and scaled to have the same exposure time as the\nobservation of the source.\n\nIn order to carry out our cluster modelling analysis, spectral image cubes\nwere sorted from the raw data. The \\emph{ROSAT} PSPC cubes had 11 energy\nbins covering PHA channel 11 to 230, and spatial bins $25''$ in size. The\n\\emph{ASCA} GIS cubes had 24 energy bins spanning PHA channel 120 to 839,\nand spatial bins $1.96'$ in size. Only data from within the PSPC support\nring were used. For all systems this encompassed the great majority of the\ndetectable \\emph{ROSAT} flux. PSPC radial surface brightness profiles were\nused to set the extraction radius in each case to restrict data to the\nregion where diffuse emission is apparent above the noise. \\emph{ASCA} data\nwere extracted from a regions similar in size to the corresponding PSPC\ndataset. Point sources were removed from the PSPC cubes. In the case of\n\\emph{ASCA}, the poor PSF makes this infeasible, however none of our\ntargets includes bright hard sources which might seriously affect our GIS\nanalysis.\n\nThe data cubes were background subtracted and then normalized to \ncount~s$^{-1}$. The cubes were not corrected for vignetting as this would\ninvalidate the Poisson statistics assumed in our subsequent analysis.\nInstead the vignetting was taken account of when fitting the data.\n\n\\section{Cluster Analysis}\nEach of the 20 galaxy clusters and groups in the sample has a high quality\n\\emph{ROSAT} PSPC observation available. For several of the clusters, as\ndetailed in Table \\ref{tab:sample}, \\emph{ASCA} GIS data were also used.\nThe use of \\emph{ASCA} GIS data is desirable for high temperature systems, as the\nGIS has a bandpass that extends to much higher energies than the \\emph{PSPC}.\n\nOur cluster analysis works by fitting analytical models to the spectral\nimages from one or both of the instruments. The models parametrize either\nthe gas density and temperature, or the gas density and dark matter\ndensity, as a function of radius. Dark matter as far as these models are\nconcerned is all gravitating matter apart from the X-ray emitting gas. Under\nthe assumption of hydrostatic equilibrium and spherical symmetry, the\nequation\n\\begin{equation}\nM(r)=-\\frac{T(r)r}{G\\mu}\\left[\\frac{dln\\rho}{dlnr}+\\frac{dlnT}{dlnr}\\right]\n\\end{equation}\nis satisfied \\cite{fabricant84a}, and therefore the dark matter density\ndistribution can be calculated from the temperature distribution or vice\nversa, if the gas density distribution is known. The models assume that the\nsystems are spherically symmetric and the dark matter models also assume\nhydrostatic equilibrium. It is also assumed that the densities and\ntemperatures can be reasonably represented by analytical functions and that\nthe plasma is single phase (i.e. each volume element contains gas at just a\nsingle temperature). The density in all the models is represented by a\ncore-index function of the form:\n\\begin{equation}\n\\rho(r)=\\rho(0)\\left[1+\\left(\\frac{r}{r_{c}}\\right)^{2}\\right]^{-\\frac{3}{2}\\beta}\n\\label{eq:beta}\n\\end{equation}\nwhere $r_{c}$ is the core radius and $\\beta$ is the density index. This has\nbeen shown to be a good fit to observations of clusters \\cite{jones84a}.\nThe temperature profile is parametrized using a linear function of the\nform:\n\\begin{equation}\nT(r)=T(0)-{\\alpha}r\n\\label{eq:linear}\n\\end{equation}\nwhere $\\alpha$ is the temperature gradient. In the case of the dark matter\ndensity parametrization we use a profile derived from numerical\nsimulations \\cite{navarro95a} of the form:\n\\begin{equation}\n\\rho_{DM}(r)=\\overline{\\rho}_{DM}\\left[x(1+x)^{2}\\right]^{-1}\n\\label{eq:nfw}\n\\end{equation}\nwhere $x=r/r_{s}$ and $r_{s}$ is a scale radius. Combining this with in gas\ndensity distribution results in the total mass density distribution which\nalong with a temperature normalization parameter $T(0)$ allows the gas\ntemperature distribution to be calculated. The metallicity of the gas is\nparametrized as a linear ramp in a similar way to the gas temperature.\nThe metallicity gradient was fixed at zero where only \\emph{ROSAT} PSPC\ndata were used. The aim of using models that parameterize the gas\ntemperature both directly and indirectly, is to more fully explore the\nparameter space available and so try to reduce the problem of implicit bias\nassociated with using a specific analytical model.\n\nOur analysis also allows an optional extra cooling flow component to be\nincluded in the models. This takes over from the normal density and\ntemperature parametrizations inside a cooling radius which is a fitted\nparameter of the model. The density increases and the temperature decreases\nas a powerlaw from the values at the cooling radius to the\n\\begin{table*}\n\\begin{minipage}{148mm}\n\\caption{Main parameters of the best fitting models for the sample. \n The temperature and dark matter models have slightly different\n parameters. An asterisk in the CF column specifies that the model used a\n cooling flow component.}\n\\label{tab:models}\n\\begin{tabular}{lccccccccccc}\n\\hline\n\\hline\nCluster/Group&$\\rho(0)$&$r_{c}$&$\\beta$&T(0)&$\\alpha$&$\\rho_{DM}$(0)&$r_{s}$&CF\\\\\n&(cm$^{-3}$)&(arcmin)&&(keV)&(keV arcmin$^{-1}$)&(amu cm$^{-3}$)&(arcmin)&\\\\\n\\hline\nHCG 68 & 0.0161 & 0.28 & 0.44 & 0.86 & 0.036 & - & - & \\\\\nHCG 97 & 0.119 & 0.04 & 0.41 & 1.05 & 0.020 & - & - & \\\\\nHCG 62 & 0.138 & 0.03 & 0.36 & 1.49 & 0.023 & - & - & * \\\\\nNGC 5044 Group& 0.009 & 1.66 & 0.49 & 1.21 & -0.005 & - & - & * \\\\\nRX J0123.6+3315 & 0.121 & 0.10 & 0.43 & 1.50 & 0.022 & - & - & * \\\\\nAbell 262 & 0.00725 & 1.45 & 0.39 & 1.45 & -0.081 & - & - & * \\\\\nIV Zw 038 & 0.00116 & 2.77 & 0.38 & 2.39 & 0.043 & - & - & \\\\\nAbell 400 & 0.00189 & 3.83 & 0.51 & 1.68 & -0.014 & - & - & \\\\\nAbell 1060 & 0.00319 & 7.35 & 0.70 & 3.28 & - & 0.189 & 4.92 & * \\\\\nMKW 3s & 0.0270 & 0.64 & 0.53 & 4.93 & 0.255 & - & - & \\\\\nAWM 7 & 0.00418 & 5.53 & 0.60 & 2.88 & -0.094 & - & - & * \\\\\nAbell 780 & 0.00855 & 1.69 & 0.67 & 4.05 & -0.203 & - & - & * \\\\\nAbell 2199 & 0.00990 & 2.20 & 0.61 & 3.13 & -0.103 & - & - & \\\\\nAbell 496 & 0.00504 & 3.24 & 0.64 & 6.34 & 0.140 & - & - & * \\\\\nAbell 1795 & 0.0245 & 0.75 & 0.57 & 6.74 & - & 0.109 & 2.47 & \\\\\nAbell 2218 & 0.00508 & 0.90 & 0.56 & 10.99 & 0.968 & - & - & \\\\\nAbell 478 & 0.0236 & 0.84 & 0.62 & 8.318 & 0.445 & - & - & * \\\\\nAbell 665 & 0.00754 & 0.73 & 0.52 & 13.76 & 1.465 & - & - & \\\\\nAbell 1689 & 0.0290 & 0.60 & 0.73 & 12.31 & 0.002 & - & - & * \\\\\nAbell 2163 & 0.00819 & 1.17 & 0.62 & 11.50 & 0.580 & - & - & \\\\\n\\hline\n\\end{tabular}\n\\end{minipage}\n\\end{table*}\ncentre, with fitted powerlaw indices. In the case of models that\nparametrize dark matter density rather than temperature, no explicit\ncooling flow temperature parameterization is needed, as the model permits\nthe derived temperature to drop at small radii. The density and temperature\npowerlaws were flattened inside $r$ = 10 kpc, to prevent them going to\ninfinity.\n\nThe models described above, specify the density, temperature and\nmetallicity at each point in the cluster. Using the MEKAL hot coronal\nplasma code \\cite{mewe86a} it is then possible to compute the emission from\neach volume element, and to integrate up the X-ray emission for each line\nof sight through the cluster. This predicted emission is then convolved\nwith the response of the instrument in order to calculate the predicted\nobservation for the instrument. Standard energy responses and vignetting\nfunctions were used for each instrument. Position and energy dependent\npoint spread functions were used. The \\emph{ASCA} GIS PSF is obtained by\ninterpolating between several observations of Cyg X-1 at various positions\non the detector \\cite{takahashi95a}. After folding the projected data\nthrough the spatial and spectral response of the instrument and applying\nvignetting, a predicted spectral image is obtained. This is then compared\nwith the observed spectral image, and the model parameters altered\niteratively, until a best fit is obtained. In cases where both \\emph{ROSAT}\nPSPC and \\emph{ASCA} GIS data were used, the model was fitted to both\ndatasets simultaneously. This required careful adjustment to take account\nof differences in the response and pointing accuracy of the different\ntelescopes. To achieve this the \\emph{ASCA} GIS dataset was repositioned so\nthat the models fitted to same position as the \\emph{ROSAT} PSPC. Our\nanalysis allows renormalization factors to be applied to the model\npredictions to take account of gain variations between the different\ninstruments. A maximum likelihood method was used to compare the data with\nthe model predictions, as there are low numbers of counts in many bins of\nthe spectral image, and hence $\\chi^{2}$ is inappropriate. Further details\nof this cluster analysis technique can be found in \\scite{eyles91a}.\n\nBecause of the large number of parameters in our models, typically $\\geq\n10$, the fit space for the models can be complicated. It is necessary to\nfind the global minimum of the fit statistic in the fit space. Two\ncomplementary methods were used to minimize the fit statistic and find the\nbest model fit. Initially a genetic algorithm \\cite{holland75a} was used to\ntry to get close to the global minimum in the fit space. This works by\ncreating a population of solutions randomly distributed across the fit\nspace. These solutions are then allowed to reproduce, by mutation\n(altering parameters) or sexual reproduction (crossing over or averaging\nparameters between parent solutions) with more chance of reproduction being\ngiven to solutions giving better fits. Solutions with the poorest fits are\nkilled off as new solutions are created, and in this way the fitness of the\npopulation improves through `natural selection'. This method is less likely\nto get trapped in local minima in the fit space than conventional descent\nmethods. Once the locality of the global minimum is found a more\nconventional modified Levenberg-Marquardt method \\cite{bevington69a} was\nused to find the exact position of the minimum in the fit space. By using\nthese two methods in conjunction the global minimum is much more likely to\nbe found.\n\nConfidence intervals for the model parameters were calculated by perturbing\neach parameter in turn from its best fit value, while allowing the other\nfitted parameter to optimize, until the fit statistic increased by 1. This\nwas done in the positive and negative directions for each fitted parameter,\nto obtain the parameter offsets that correspond to this change in the fit\nstatistic. A change in the fit statistic of 1 corresponds to 1$\\sigma$\nconfidence. All errors quoted below are 1$\\sigma$.\n\nThe models used to derive the results presented below were the temperature\nor dark matter model for each system that gave the best fit to the data.\nOnce the fitted models had been obtained it was possible to derive many\ndifferent system properties, including total gravitating mass and gas\nentropy profiles. Throughout the following analysis we adopt $H_{0}$=50~km\ns$^{-1}$ Mpc$^{-1}$ and $q_{0}$ = 0.5 , and show the $H_{0}$ dependence of\nkey results in terms of $h_{50}$ (=$H_{0}$/50). \n\n\\begin{figure}\n\\centering{\n\\vbox{\\psfig{figure=plot0.ps}}\\par\n}\n\\caption{$\\beta$ plotted against system temperature\n for 20 galaxy clusters and groups. The dotted line shows\n $\\beta=\\frac{2}{3}$.}\n\\label{fig:plot0}\n\\end{figure}\n\n\\section{Results}\nThe main parameters of the best fit model for each system in the sample are\nshown in Table \\ref{tab:models}. In this paper we will concentrate on the\ndepartures from self-similarity in these systems and specifically the\nentropy and energy of the intergalactic gas. A further paper is in\npreparation which deals with other results from our sample. Before deriving\nentropy profiles for the sample, the fitted parameters of the models\nthemselves were studied to see if they deviated from self-similar scaling\npredictions. The $\\beta$ parameter in Equation \\ref{eq:beta}, which is\nessentially equivalent to the $\\beta_{fit}$ parameter often used to fit\nX-ray surface brightness profiles, showed a strong departure from\nself-similarity in the low mass systems. This is shown in Fig.\n\\ref{fig:plot0}. It can be seen that the gas density profiles of the\nsystems in the sample are not simply scaled versions of one another. High\nmass systems have $\\beta$ values around the canonical value of\n$\\frac{2}{3}$. Low mass systems have significantly flatter gas density\nprofiles, with $\\beta$ dropping to $\\sim0.4$ for the galaxy groups which\nagrees well with the \\scite{helsdon99a} study of the surface brightness\nprofiles of galaxy groups. This is also supported by most recent studies of\ngalaxy clusters \\cite{arnaud98a,jones99a} and is predicted by recent\nsimulations of energy injection into clusters\n\\cite{metzler97a,cavaliere98a}. However, \\scite{mohr99a} fitted two\ncomponent core-index models to the surface brightness profiles of a sample\nof galaxy clusters and found no dependence of $\\beta_{fit}$ on temperature.\nOur analysis also allows for the presence of a second central component\nassociated with a cooling flow, where necessary. However the apparent\nconflict between Fig. \\ref{fig:plot0} and the results of \\scite{mohr99a} is\nresolved by the fact that their sample did not extend much below 3 keV, and\nit can be seen from the figure that no significant trend above 3 keV is\nseen in our sample. It should be noted that the $\\beta$ values we derive\nparametrize 3-dimensional gas density and are not directly comparable to\n$beta$ values that parameterize X-ray surface brightness as isothermality\nhas not been assumed. In general the $beta$ values that we derive are\nslightly lower than those derived from surface brightness profiles\n\\cite{mohr99a,ettori99a}. Some difference is to be expected as we do not\nassume isothermality.\n\n\\begin{figure*}\n\\begin{minipage}{140mm}\n\\centering{\n\\vbox{\\psfig{figure=plota.ps}}\\par\n}\n\\caption{Mean gas entropy against radius scaled to the virial radius for the\n sample, grouped by system temperature. The solid line represents the five\n most massive systems (6-14 keV), through dashed (3.7-6 keV) and dash-dot\n (1.3-3.7 keV), to dotted (0.5-1.3 keV) for the lowest mass systems. The\n discontinuities in slope seen in some mean profiles, occur at the outer\n boundary of a central cooling flow component in the fitted model.}\n\\label{fig:plota}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{140mm}\n\\centering{\n\\vbox{\\psfig{figure=plot2a.ps}}\\par\n}\n\\caption{Gas entropy at 0.1R$_{v}$ against system temperature\n for 20 galaxy clusters and groups. The dotted line is a S$\\propto$T fit\n to the systems above 4 keV excluding Abell 665 and Abell 2218 (see\n discussion in text). The dashed line is a constant entropy floor of\n 139$\\pm$7~keV~cm$^{2}$ fitted to the four lowest temperature systems.}\n\\label{fig:plot2a}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{140mm}\n\\centering{\n\\vbox{\\psfig{figure=plot1.ps}}\\par\n}\n\\caption{Mean gas entropy scaled by $T^{-1}(1+z)^{2}$ against radius scaled to\n the virial radius for the sample, grouped by system temperature. The solid\n line represents the five most massive systems (6-14 keV), through dashed\n (3.7-6 keV) and dash-dot (1.3-3.7 keV), to dotted (0.5-1.3 keV) for the\n lowest mass systems.}\n\\label{fig:plot1}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{minipage}{140mm}\n\\centering{\n\\vbox{\\psfig{figure=plot2.ps}}\\par\n}\n\\caption{Scaled entropy at 0.1R$_{v}$ against system temperature\n for 20 galaxy clusters and groups. The dotted line shows the weighted\n mean scaled entropy of 54$\\pm$3~cm$^{2}$ for the systems above 4\n keV excluding Abell 665 and Abell 2218 (see discussion in text).}\n\\label{fig:plot2}\n\\end{minipage}\n\\end{figure*}\n\n\\subsection{Excess entropy}\n\nGas entropy profiles as a function of radius were derived for the 20\nsystems. It is convenient to define `entropy' in terms of the observed\nquantities, ignoring constants and logarithms, as \n\\begin{equation}\nS=\\frac{T}{n_{e}^{2/3}}\n\\label{eq:entropy}\n\\end{equation}\nwhere $T$ is the gas temperature in keV and $n_{e}$ is the gas electron\ndensity. \nThe radius axis of each profile was scaled to the virial radius of the\nsystem, calculated using the formula\n\\begin{equation}\nR_{v}=2.57\\left(\\frac{T}{5.1 \\rm{keV}}\\right)^{\\frac{1}{2}}\n(1+z)^{-\\frac{3}{2}} \\rm{Mpc}\n\\end{equation}\nderived from numerical simulations \\cite{navarro95a}. The profiles were\nthen grouped together by temperature and averaged in order to \nimprove the clarity of\nthe figures and to high-light their temperature dependence. The mean\nentropy profiles for groups of systems with similar temperatures are shown\nin Fig. \\ref{fig:plota}. Each line in the figure is the average of the\nprofiles of 5 systems in a certain temperature range. It can be seen that\nthe most massive systems have the highest entropy gas. The gas entropy in\nall systems shows a general increase with radius. This is to be expected,\nas if the entropy declined with radius the gas would be convectively\nunstable. The profiles are similar to those seen in hydrodynamical\nsimulations such as those of \\scite{metzler94a} and \\scite{knight97a}. At\nsmall radii the profiles are dominated by the effects of cooling flows in\nmany systems, resulting in a lowered central gas entropy.\n\nTo investigate the dependence of gas entropy on system temperature,\nthe entropy at 0.1~$R_{v}$ has been plotted against the mean system\ntemperature for each individual system. This is shown in Fig.\n\\ref{fig:plot2a}. A radius of 0.1 $R_{v}$ was chosen to be close to the\ncluster centre (where shock heating is minimized), but to lie outside the\ncooling region in all systems. It can be seen that for the high\ntemperature systems the gas entropy is will appears to follow the expected\n$S \\propto T$ scaling. The dotted line is a powerlaw with a slope of unity\nfitted to the systems with mean temperatures above 4~keV. It is clear that\nthe low temperature systems deviate from this trend and appear to flatten\nout to a constant entropy floor. The dashed line is a constant gas entropy\nfitted to the four lowest temperature systems and has a value of\n139$\\pm$7~${h_{50}}^{-\\frac{1}{3}}$~keV~cm$^{2}$. This effect has\npreviously been noted by \\scite{ponman98a} using isothermal assumptions.\n\nIn order to study the departures from self-similar scaling in more detail,\nthe profiles were scaled by a factor $T^{-1}(1+z)^{2}$, where $T$ is the\nintegrated system temperature and $z$ is the system redshift, and\noverlayed. The $T^{-1}$ scaling should remove the effects of system mass,\nas from Equation \\ref{eq:entropy} it can be seen that `entropy' is directly\nproportional to gas temperature. The $(1+z)^{2}$ scaling removes the effect\nof the evolution of the mean density of the Universe, which has a\n$(1+z)^{3}$ dependence, and results in systems that form at higher\nredshifts being more dense. This assumes that the systems formed at the\nredshift of observation. The net result of this scaling is that the\nprofiles should fall on top of each other in the case of simple\nself-similar scaling. The profiles were then grouped as before, resulting in\nthe mean profiles shown in Fig. \\ref{fig:plot1}.\n\nIt can be seen from Fig. \\ref{fig:plot1} that the scaled entropy profiles\nof the sample do not coincide. In general the less massive systems have\nhigher scaled entropy profiles, with galaxy groups having the highest\nscaled entropy values. This can be seen more clearly in Fig.\n\\ref{fig:plot2}, where the scaled entropy at 0.1 $R_{v}$ has been plotted\nagainst the mean system temperature. The lower mass systems clearly show an\nexcess in scaled entropy over the high mass systems. In particular, systems\nwith temperatures above 4 keV appear to have a roughly constant scaled\nentropy, while for systems with temperatures below 4 keV the scaled\nentropy increases with decreasing temperature. A radius of 0.1 $R_{v}$ was\nused as this lies outside the cooling flow regions of all the systems. \n\nThree of the systems stand out as being somewhat different from the general\ntrend. These are the clusters Abell 2218 and Abell 665, and the group IV Zw\n038 (also known as the NGC 383 group). As well as lying above the trend in\nFig. \\ref{fig:plot2}, they also show unusual scaled entropy profiles \nhaving the highest central scaled entropies in the sample. Our fits\nindicate that both of the clusters have very high temperature gradients, a\nlinear temperature fit (Equation \\ref{eq:linear}) gives $\\sim$6.2 keV\nMpc$^{-1}$ for Abell 665 and $\\sim$4.3 keV Mpc$^{-1}$ for Abell 2218, which\nare which make them very unusual compared to the rest of our sample.\nNeither of these clusters has a significant cooling flow, and both Abell\n2218 \\cite{girardi97a} and Abell 665 \\cite{markevitch96a} have been\nsuggested as being on-going or recent mergers. IV Zw 038 has a somewhat\nlower temperature gradient of $\\sim$1.5 keV Mpc$^{-1}$ although this is\nstill large, given the low mean temperature of this system.\n\\scite{komossa99a} have studied the X-ray emission of IV Zw 038 and\nconcluded that it is fairly relaxed. However \\scite{sakai94a} studied\nthe distribution of galaxies around IV Zw 038 and concluded that the system\nis highly substructured. It therefore appears that IV Zw 038 may also be an\nongoing or recent merger. As noted previously, transient flattening of\nentropy profiles during mergers is seen in hydrodynamical simulations\n\\cite{metzler94a}.\n\nA mean value was calculated for the scaled entropy of the systems with\ntemperatures above 4 keV. The clusters Abell 2218 and Abell 665 were\nexcluded from this calculation due to their deviant behaviour. A weighted\nmean value of 54$\\pm$3 cm$^{2}$ was calculated. This was subtracted off the\nentropies of the 12 systems with temperatures below 4 keV to calculate\ntheir excess entropy. This (unscaled) excess entropy is plotted against\nsystem temperature in Fig. \\ref{fig:plot3}. The excess entropy shows no\ntrend with temperature and has a mean value of 68$\\pm$12 keV cm$^{2}$. This\nvalue drops slightly to 67 keV cm$^{2}$ if IV Zw 038 is excluded.\nTo investigate whether the excess gas entropy varies with radius this\nprocedure was repeated for radii from 0.0-0.2 $R_{v}$. It was not possible\nto extend this analysis beyond 0.2 $R_{v}$ reliably, because the data for\nthe lowest mass systems does not extend that far due to their low surface\nbrightness. The variation of mean excess entropy against radius is shown in\nFig. \\ref{fig:plot5}.\n\nThe mean excess entropy appears to be constant outside a central cooling\nregion which principally affects the innermost point in the figure. When\nonly the three systems without central cooling are plotted, the result is\nthe diamond in Fig. \\ref{fig:plot5}. This seems to confirm that the excess\nentropy is distributed fairly evenly with radius and it is the effect of\ncooling flows that causes the radial dependence seen in Fig.\n\\ref{fig:plot5}. The cooling radii for these systems are $<$ 0.1 $R_{v}$\nand it is to be expected that within cooling flows large amounts of entropy\nwill be lost as the gas cools. The asymptotic value of excess entropy\noutside the cooling region is $\\sim$70 ${h_{50}}^{-\\frac{1}{3}}$ keV\ncm$^{2}$.\n\n\\begin{figure}\n\\centering{\n\\vbox{\\psfig{figure=plot3.ps}}\\par\n}\n\\caption{Excess entropy at $0.1 R_{v}$ against system temperature\nfor 12 systems with temperatures below 4 keV. The dotted line shows\nthe weighted mean value of 68$\\pm$12 keV cm$^{2}$.}\n\\label{fig:plot3}\n\\end{figure}\n\n\\begin{figure}\n\\centering{\n\\vbox{\\psfig{figure=plot5.ps}}\\par\n}\n\\caption{Mean excess gas entropy against radius for the 12 systems with\n mean temperatures below 4 keV. The diamond shows the central mean excess\nentropy for the 3 systems without significant cooling.}\n\\label{fig:plot5}\n\\end{figure}\n\nTo investigate whether cooling flows are having any impact on the entropy\nprofiles of the systems at large radii (cf. discussion of the\n\\scite{knight97a} result in the introduction), excess entropy at 0.1\nR$_{v}$ was compared to cooling flow size. It was possible to derive\nreliable cooling flow mass deposition rates for 8 of the 12 systems with\ntemperatures below 4 keV (the remaining systems were consistent with no\ncooling within errors or were not constrained by the analysis). This was\ndone using the equation,\n\\begin{equation}\n\\stackrel{.}{M}(i)=\\frac{L(i)-[\\Delta{h(i)}+\\Delta{\\phi(i)}]\n\\sum_{i'=1}^{i'=i-1}\\stackrel{.}{M}(i')}\n{h(i)+f(i)\\Delta{\\phi}}\n\\end{equation}\nfrom \\scite{white97a}, where $\\stackrel{.}{M}(i)$ is the mass deposition\nrate, $L(i)$ is the luminosity, $h(i)$ is the thermal energy per particle,\nand $\\phi(i)$ is the gravitational energy per particle in the radial bin\n$i$. The $\\Delta$ symbols represent a change in a quantity across a radial\nbin. $f(i)$ is a factor that can be calculated to allow for the volume\naveraged radius at which the mass drops out in the radial bin $i$. A value\nof 1 was used for $f(i)$ for simplicity, which is consistent with previous\nanalysises \\cite{white97a}. By integrating this equation out from the\ncentre of the system the mass deposition rate within any radius can be\ncalculated. The radius at which the cooling time equals the Hubble time,\n1.3 $\\times$ 10$^{10}$yrs for $H_{0}$ = 50 km s$^{-1}$ Mpc$^{-1}$, was used for\nconsistency with previous work. \n\n\\begin{table}\n\\caption{Cooling flow mass deposition rates derived in this work compared\nto rates from the literature. Asterisks indicate systems \nshown in Fig. \\ref{fig:plot4}. The dashes in the second column indicate that\nno reliable value could be derived from our analysis and the dashes in the\nthird column indicate that no value was available in the literature.}\n\\begin{minipage}{85mm}\n\\begin{center}\n\\begin{tabular}{lcc}\n\\hline\n\\hline\nCluster/Group&$\\dot{M}$ this work&$\\dot{M}$ literature\\\\\n&($M_{\\odot}yr^{-1}$)&($M_{\\odot}yr^{-1}$)\\\\\n\\hline\nHCG 68$\\ast$& $0.7^{+1.3}_{-0.5}$& -\\\\ \nHCG 97$\\ast$& $4^{+19}_{-3}$& -\\\\ \nHCG 62& $6^{+95}_{-6}$& $\\sim$10\\\\\nNGC 5044 Group$\\ast$&$25^{+20}_{-3}$& 20-25\\\\ \nRX J0123.6+3315$\\ast$&$18^{+6}_{-3}$& -\\\\ \nAbell 262& -& -\\\\ \nIV Zw 038& -& $27^{+4}_{-3}$\\\\ \nAbell 400$\\ast$& $7.2^{+0.5}_{-0.5}$& $0^{+28}_{-0}$\\\\ \nMKW 3s$\\ast$& $50^{+5}_{-5}$& $175^{+14}_{-46}$\\\\ \nAbell 1060& -& $15^{+5}_{-7}$\\\\ \nAWM 7$\\ast$& $65^{+21}_{-21}$& $41^{+6}_{-6}$\\\\ \nAbell 780$\\ast$& $274^{+25}_{-24}$& $264^{+81}_{-60}$\\\\ \nAbell 496& $105^{+17}_{-16}$& $134^{+58}_{-85}$\\\\\nAbell 2199& $243^{+13}_{-10}$& $154^{+18}_{-8}$\\\\\nAbell 1795& -& $321^{+166}_{-213}$\\\\\nAbell 2218& -& $66^{+76}_{-30}$\\\\\nAbell 478& $974^{+162}_{-132}$& $616^{+63}_{-76}$\\\\\nAbell 665& -& $0^{+206}_{-0}$\\\\\nAbell 1689& $470^{+70}_{-180}$& $0^{+398}_{-0}$\\\\\nAbell 2163& -& $0^{+256}_{-0}$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\nNote: The cooling flow mass deposition rates from the literature were\nobtained from \\scite{peres98a}, \\scite{white97a}, \\scite{david94a} and\n\\scite{ponman93a}.\n\\end{minipage}\n\\label{tab:cooling}\n\\end{table}\n\nThe cooling flow mass deposition rates derived from our analysis for the\nwhole sample are listed in Table \\ref{tab:cooling} along with values taken\nfrom the literature. In general there is good agreement between the values\nwe derive and previously derived values. The cooling flow mass deposition\nrates for the 8 systems with temperatures below 4 keV were then scaled by\n$T^{-3/2}$, which is proportional to $M^{-1}$, to scale the cooling flows\nto the system size. The scaled mass deposition rates are therefore\nproportional to the fraction of the cluster mass that is cooling out per\nyear. These scaled mass deposition rates have been plotted against excess\nentropy in Fig. \\ref{fig:plot4}. It can be seen that there is no\nappreciable correlation between excess entropy and scaled mass deposition\nover more than an order of magnitude range in scaled mass deposition rate.\nThe weighted mean value for the excess entropy in the systems with no\nmeasurable cooling is 67 $\\pm$ 15 keV cm$^{2}$, almost identical to the\nmean for all the systems with temperatures below 4 keV. These results\nconfirm that cooling is not driving the trend seen in Fig. \\ref{fig:plot2}.\n\n\\begin{figure}\n\\centering{\n\\vbox{\\psfig{figure=plot4.ps}}\\par\n}\n\\caption{Excess entropy at $0.1 R_{v}$ against cooling flow mass\ndeposition rate scaled by $T^{-3/2}$\nfor 8 systems with temperatures below 4 keV.}\n\\label{fig:plot4}\n\\end{figure}\n\n\\subsection{Excess energy}\n\n\\scite{ponman98a} assumed that their systems were isothermal, and so\nwere unable to measure the extra energy in the IGM which gives rise to\nthis excess entropy. Their analysis was therefore based on a rough\nestimate of the likely energy injection based on the {\\it assumption}\nthat it was caused by supernova-driven galactic winds. Here,\nbecause of our spatially resolved temperature profiles, we can actually\nattempt to {\\it measure} the injected energy and then compare it to the energy\nexpected from galactic winds or other heating mechanisms.\n\n\\begin{figure*}\n\\begin{minipage}{140mm}\n\\centering{\n\\vbox{\\psfig{figure=plot6.ps}}\\par\n}\n\\caption{Mean binding energy per particle of the central 0.004$M_{200}$\n of gas against system temperature for 20 galaxy clusters and groups. The\n dashed line shows a $E \\propto T$ line fitted through the systems with\n mean temperatures greater than 4 keV. The solid line shows our best\n estimate of the $E=AT-\\Delta{E}$ relationship (for $\\Delta{E}=0.44$~keV)\n with 1$\\sigma$ errors (dotted).The dot-dashed line is the result\n obtained when the unreliable point for the cluster Abell 400 is included \n in the fit (see discussion in text).}\n\\label{fig:plot6}\n\\end{minipage}\n\\end{figure*}\n\nThe excess energy is composed of two parts: extra thermal energy, and\nreduced gravitational binding energy. Due to the fact that our data do\nnot extend beyond 0.2 $R_{v}$ for the lowest mass systems, it was not\npossible to calculate the total binding energy of the gas within the\nvirial radius for the entire sample, and since energy injection will\nchange the gas distribution, considering the binding energy of the gas\nwithin a fixed {\\it fraction} of the virial radius will be misleading.\nInstead, we investigate the binding energy of gas constituting a fixed\nfraction of the virial mass of each system. If the gas distributions\nof the systems were self-similar, this would translate into gas within\na fixed fraction of the virial radius, but it can be seen from Fig.\n\\ref{fig:plot0} the gas distributions of the systems are not\nself-similar. In order to calculate the virial masses of the systems\nfrom their mean temperatures the formula\n\\begin{equation}\nM_{200}=10^{15}\\left(\\frac{T}{5.1 \\rm{keV}}\\right)^{\\frac{3}{2}}\n(1+z)^{-\\frac{3}{2}}\\rm{M}_{\\odot}\n\\label{eq:mass}\n\\end{equation}\nwas used \\cite{navarro95a}, which is derived from numerical simulations. A\nfixed fractional gas mass of 0.004 $M_{200}$ was used, which was found to\ncorrespond to a fraction of the virial radius between 0.064 and 0.226 for\nthe systems in the sample. \n\nThe mean binding energy per particle of the central 0.004 $M_{200}$ of gas\nfor the sample is plotted against temperature in Fig. \\ref{fig:plot6}. If\nthe systems were self-similar then the binding energy per particle would be\ndirectly proportional to the temperature, and this relation, fitted to\nsystems with mean temperatures greater than 4 keV, is shown by the dashed\nline. The uniform injection of a constant amount of excess energy per unit\nsystem mass will result in a relation of the form\n\\begin{equation}\nE = AT-\\Delta{E}\n\\label{eq:phi}\n\\end{equation}\nwhere $E$ is the binding energy per particle, $T$ is the mean gas\ntemperature, $\\Delta{E}$ is the injected energy per particle and A is a\nconstant.\n\nUsing the function in Equation \\ref{eq:phi} results in a best fit value\n$\\Delta E$ = 2.2~keV per particle, shown in Fig. \\ref{fig:plot6} as a\ndot-dash line. This result is clearly unreasonably large, as it would\npreclude the presence of significant hot gas in systems with virial\ntemperatures less than $\\sim$ 1.5 keV. It can be seen from Fig.\n\\ref{fig:plot6} that this model line underestimates the observed binding\nenergy in almost all the cooler systems. This result is being driven by one\nsystem, Abell 400, which has an exceptionally small gas binding energy,\nwith a small statistical error. However, \\scite{beers92a} have studied the\ngalaxy distribution in Abell 400 in detail, and concluded that it is highly\nsubclustered, with two major subclusters essentially superposed on the\nplane of the sky. Hence the apparently relaxed X-ray morphology in this\nsystem is probably misleading, and our derived energy and entropy values\nfor the cluster are unsafe.\n\nExcluding Abell 400 from our analysis, gives a much lower value for the\nfitted value of excess energy: $\\Delta{E}$ = 0.44 keV per particle,\ncorresponding to a preheating temperature of $T = 0.3 \\pm 0.2$~keV. The fit\nis shown as a solid line in Fig. \\ref{fig:plot6}, along with a formal\n1$\\sigma$ confidence interval. Clearly this estimate of the excess energy\nis subject to large statistical and systematic errors at present, and a more\naccurate result should be available in due course from studies with the new\ngeneration of X-ray observatories. However, as we will discuss below, a\nvalue of $\\sim 0.4$~keV per particle agrees well with recently developed\npreheating models, and with estimates based on the metallicity of the IGM.\n\nTo investigate whether this measured injection energy shows any radial\ndependence, the above procedure was repeated for a number of different\nfractional gas masses. The results are plotted in Fig. \\ref{fig:plot7}. At\nsmall radii, the measured excess energy in the gas is affected by the\npresence of cooling flows, which effectively scales up the whole of the\nright hand side of Equation \\ref{eq:phi} due to the increased central\nconcentration of the gas, resulting in a higher inferred value for\n$\\Delta{E}$. However, it can be seen that the effects of this distortion\nare confined to $M_{\\rm gas}<0.003 M_{200}$, and that the asymptotic value\nof excess energy outside the cooling region is $\\sim$ 0.4 keV.\nExtrapolation of the models to larger fractional gas masses is highly\nuncertain and would result in large systematic errors as it would encompass\ngas well beyond the data in the low mass systems.\n\nSince $P d\\!V$ work and shock heating can move energy around within the\nIGM, the excess energy per particle evaluated within a subset of the total\ngas mass will not necessarily equal the value which would be obtained if we\ncould extend our analysis to cover the whole of the intracluster medium. A\nsimple model involving a flattened $\\beta$-model gas distribution in\nhydrostatic equilibrium within a NFW (Equation \\ref{eq:nfw}) potential,\nsuggests that our result derived from the innermost 0.004$M_{200}$ of the\ngas, may {\\it overestimate} the excess energy, integrated over the ICM, by\na factor of $\\sim$2.\n\nOur analysis assumes that Equation \\ref{eq:mass} holds even in the lowest\nmass systems. Semi-analytical models of the effects of preheating, by\n\\scite{balogh98a} and \\scite{cavaliere98a} indicate that preheating has\nlittle effect on gas temperature except in systems with virial temperatures\nclose to the preheating temperature. The mass-temperature relations in both\nthe \\scite{balogh98a} and \\scite{cavaliere98a} studies deviate\nsignificantly from the expected $M\\propto T^{3/2}$ only at $T<0.8$~keV.\nOnly one member of our sample, HCG\\,68, with a mean gas temperature of 0.54\nkeV, lies in this region. To investigate the possibility that this point\nin Fig. \\ref{fig:plot6} may have been significantly affected, we derived the\nmass of this system from our fitted model. Due to fact that the data extend\nto only $\\sim$ 0.2 R$_{v}$, this involves considerable extrapolation out to\nthe virial radius, with an associated (and uncertain) systematic error. The\nmass derived from our fitted model was $2.4\\times 10^{13}$~M$_{\\odot}$,\ncompared to a value of $3.45\\times 10^{13}$~M$_{\\odot}$ from Equation\n\\ref{eq:mass} using the mean temperature of the system. If we have\noverestimated $M_{200}$ for this system, then the gas mass we have\nconsidered will be too large, and its binding energy (which decreases with\nradius) will be too low. Using $M_{200}=2.36 \\times 10^{13}$M$_{\\odot}$\ninstead, would result in the derived binding energy of the 0.004$M_{200}$\nof gas being increased by 13\\%. This systematic error is much less than the\nstatistical error on the point and so should have a minimal effect on the\nfit. Any effect would be in the direction of reducing the injection energy.\n\nThe excess energy we have derived can be compared to what might reasonably\nbe available from galaxy winds. Assuming that the galaxy wind ejecta have\napproximately solar metallicity, it appears that this gas has been diluted\nby a factor of $\\sim$3-5 with primordial gas, to arrive at the typical\nmetallicities of 0.2-0.3~solar, seen in galaxy groups and clusters\n\\cite{fukazawa98a,finoguenov99a}. A final excess of $\\sim$0.4~keV per\nparticle after dilution, therefore implies an injected wind velocity of\n$\\sim 1000$~km~s$^{-1}$, assuming that the energy of the injected gas is\ndominated by its bulk flow energy. Studies of local ultraluminous starburst\ngalaxies show outflows of cool emission line gas with velocities of a few\nhundred km~s$^{-1}$, and models suggest terminal velocities for the hot gas\nof a few thousand km~s$^{-1}$ \\cite{heckman90a,suchkov94a,tenorio97a}.\nGalactic winds therefore seem capable of providing the energy we observe.\n\n\\begin{figure}\n\\centering{\n\\vbox{\\psfig{figure=plot7.ps}}\\par\n}\n\\caption{Excess gas energy derived for a range of fractional gas masses.\nSince the gas mass is integrated from the cluster centre, the points\nin the plot are not statistically independent.}\n\\label{fig:plot7}\n\\end{figure}\n\n\\subsection{Constraints on preheating}\n\nAs both the excess entropy and preheating temperature of the ICM have been\nmeasured, it can be seen from the definition of entropy in Equation\n\\ref{eq:entropy}, that it should be possible to derive the electron density\n$n_{e}$ at which the energy was injected. The details of the energy\ninjection process itself do not matter, provided that sufficient mixing of\nthe gas has subsequently occurred to distribute the energy uniformly at the\ntime of observation. The inferred injection density is\n\\begin{equation} \nn_{e}=\\left(\\frac{\\Delta{T}}{\\Delta{S}}\\right)^{\\frac{3}{2}}\n\\label{eq:ne}\n\\end{equation}\nwhere $\\Delta{T}$ and $\\Delta{S}$ are the changes in gas temperature\nand entropy. Using the values obtained above for these quantities,\nwe derive an electron density at the time of injection of\n$3\\times 10^{-4}{h_{50}}^{\\frac{1}{2}}$cm$^{-3}$. This is about an\norder of magnitude lower than the mean gas density in cores of systems\nwithout cooling flows, suggesting that the energy must have been\ninjected before these systems were fully formed.\n\nHowever, if the entropy injection took place before the systems collapsed\nit may have affected the shock heating efficiency in the low mass systems,\nreducing the amount of entropy the shocks produced. In the extreme case,\nshock heating could have been totally suppressed in the lowest mass\nsystems, in which case they would have collapsed adiabatically and their\npresent entropy would essentially be the total injected entropy. The degree\nto which shocks have increased the entropy in the lowest mass system is not\nat all clear. However it should be noted that even in the lowest mass\nsystems in Fig. \\ref{fig:plot2}, the gas entropy is rising with radius\noutside the cooling region, suggesting that some shock heating has taken\nplace. The resolution of this problem will require detailed hydrodynamic\nsimulations of the formation of galaxy groups which is not available at\npresent. We therefore consider our previous result to be a lower bound on\nthe excess entropy in these systems and the measured entropy floor ($\\sim$\n140 keV cm$^{2}$) in Fig. \\ref{fig:plot2a} to be an upper bound, applying\nin the case where shock heating is totally suppressed. For this second\ncase, Equation \\ref{eq:ne} results in an even lower value of $1\\times\n10^{-4}{h_{50}}^{\\frac{1}{2}}$cm$^{-3}$ for the density at which the\nentropy is injected.\n\nEven if the injection took place outside a collapsed system, it must have\noccurred after the mean density of the Universe dropped to 1-3$\\times\n10^{-4}$cm$^{-3}$, as before this, even uniformly distributed gas would be\ntoo dense to produce the measured entropy change from the available energy.\nUsing the value for the baryon density of the Universe derived from Big\nBang nucleosynthesis, $\\Omega_{b}h_{50}^{2}=0.076\\pm0.0096$\n\\cite{burles99a}, and the fact that the density of the Universe scales as\n$(1+z)^3$, it follows that the mean electron density of the Universe would\nbe less than $3\\times 10^{-4}$cm$^{-3}$ when $z<10$ and less than $1\\times\n10^{-4}$cm$^{-3}$ when $z<7$.\n\nHence we conclude that the entropy injection must have taken place after $z\n\\sim 7-10$, depending on the assumed amount of shock heating in low mass\nsystems, but before the galaxy systems have fully formed. In fact it is\nlikely that the baryons in these systems have always been in overdense\nregions of the Universe, and therefore the entropy injection probably took\nplace at a considerably lower redshift than this conservative upper limit.\nIf our value of 0.44 keV per particle for the excess energy is an\noverestimate, as discussed in Section 5.2, this would have the effect of\nlowering the inferred gas density at injection, and reducing our redshift\nlimit.\n\nThis all assumes that the gas cannot expand as the energy is injected, i.e\nan isodensity assumption. This will be true if the energy injection takes\nplace at high redshift when the density field of the Universe is still\nfairly smooth and there is effectively nowhere for the gas to expand to.\nHowever if the energy injection takes place at lower redshift in partially\nformed systems, the gas may expand in the potential of the system. A more\nrealistic scenario in this case is that the energy is injected under\nconstant pressure, i.e. it is isobaric. In the isobaric case the resulting\nentropy change will be higher than the isodensity case, since density drops\nas the injection proceeds.\n\nTo quantify the possible error involved in assuming that the gas does not\nexpand as the energy is injected, we investigate the difference in entropy\nchange between the case of isodensity and isobaric energy injection. The\nentropy changes for the two cases will be:\n\\begin{enumerate}\n\\item{Isodensity - As the density does not change the only effect on the\nentropy will be due to the change in temperature of the gas. The entropy\nchange ${\\Delta}S$ will therefore be:\n\\begin{equation}\n{\\Delta}S=\\frac{{\\Delta}T}{n_{e}^{2/3}}\n\\end{equation}\nwhere ${\\Delta}T$ is the change in temperature. If the gas cannot expand\nthe temperature change will be related to the injected energy by the\nequation\n\\begin{equation}\n{\\Delta}T=\\frac{2}{3}{\\Delta}E\n\\label{eq:energy}\n\\end{equation}\nwhere ${\\Delta}E$ is the injected energy per particle. The entropy change\nfor a given injected energy will therefore be\n\\begin{equation}\n{\\Delta}S=\\frac{2}{3}\\frac{{\\Delta}E}{n_{e}^{2/3}}\n\\end{equation}\n} \n\\item{Isobaric - As the pressure remains constant the equation:\n\\begin{equation}\nn_{0}T_{0}=n_{1}T_{1}\n\\end{equation}\nwill be satisfied, where $n_{0}$ and $n_{1}$ are the initial and final\nelectron densities and $T_{0}$ and $T_{1}$ are the initial and final temperatures\nand so using the definition of entropy in Equation \\ref{eq:entropy} the\nchange in entropy in terms of the change in temperature will be:\n\\begin{equation}\n{\\Delta}S=\\frac{{\\Delta}T}{n_{e}^{2/3}}\\frac{(\\gamma^{5/3}-1)}{(\\gamma-1)}\n\\end{equation}\nwhere $\\gamma=\\frac{T_{1}}{T_{0}}$ and $n_{e}=n_{0}$, the initial density.\nHowever as work is done expanding the gas, the temperature change will not\nbe related to the injected energy as in Equation \\ref{eq:energy} but will\nbe\n\\begin{equation}\n{\\Delta}T=\\frac{2}{5}{\\Delta}E,\n\\end{equation}\nand so the entropy change for a given injected energy is\n\\begin{equation}\n{\\Delta}S=\\frac{2}{5}\\frac{{\\Delta}E}{n_{e}^{2/3}}\\frac{(\\gamma^{5/3}-1)}{(\\gamma-1)}.\n\\end{equation}\n}\n\\end{enumerate}\nThe ratio of the changes in entropy between the isodensity and isobaric\ncase, for a given injected energy, is therefore:\n\\begin{equation}\n\\frac{{\\Delta}S_{isobar}}{{\\Delta}S_{isoden}}=\\frac{3}{5}\n\\frac{(\\gamma^{5/3}-1)}{(\\gamma-1)}\n\\label{eq:ratio}\n\\end{equation}\nand depends only on the value of $\\gamma$, the ratio of the final to initial\ntemperatures. This ratio, given by Equation \\ref{eq:ratio}, is shown in\nTable \\ref{tab:ratio} for a range of values of $\\gamma$.\n\\begin{table}\n\\caption{The ratio of entropy changes in the isodensity and isobaric cases\n as a function of the ratio of final to initial temperatures, $\\gamma$.}\n\\begin{center}\n\\begin{tabular}{lc}\n\\hline\n\\hline\n$\\gamma$&$\\frac{{\\Delta}S_{isobar}}{{\\Delta}S_{isoden}}$\\\\\n\\hline\n2&1.3\\\\\n5&2.0\\\\\n10&3.0\\\\\n100&13.1\\\\\n1000&60.1\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:ratio}\n\\end{table}\n\nAt high redshift, where the initial temperature of the gas is low, the\nvalue of $\\gamma$ will be large. However at high redshift the density field\nshould be fairly smooth and so the isodensity assumption should be a fairly\ngood one. At lower redshift, where the isobaric case will be more\nrealistic, the initial temperature of the gas in these partly formed\nsystems will be similar to the temperature change ($\\sim$ 0.3 keV)\nresulting from the entropy injection, and so $\\gamma$ will be close to\nunity. It can be seen from Table \\ref{tab:ratio} that when $\\gamma$ is\nclose to unity the difference between the isodensity and isobaric case is\nsmall and so the isodensity result should still be a reasonable\napproximation. We conclude that the entropy increase should only be\nslightly underestimated by the isodensity analysis given above, and hence\nthat the density limit of $3\\times 10^{-4}$cm$^{-3}$ cannot be pushed\nsignificantly higher by allowing for expansion of the gas during\npreheating.\n\n\\section{Discussion}\nIt is clear from Figures \\ref{fig:plot1} and \\ref{fig:plot2} that systems\nwith integrated temperatures below 4 keV show signs of having excess\nentropy in their intracluster gas over what would be expected from the\nsimple self-similar model. It can further be seen from Fig. \\ref{fig:plot3}\nthat the amount of excess entropy does not depend systematically on the\nsystem temperature and, from Fig. \\ref{fig:plot5}, it has an approximately\nconstant value outside the central cooling flow regions. The average\nexcess entropy outside the cooling flow region lies in the range\n70-140${h_{50}}^{-\\frac{1}{3}}$ keV cm$^{2}$. The upper limit, where shocks\nare totally suppressed in low mass systems, is comparable with the result of\n\\scite{ponman98a} who obtained a value of 100${h_{100}}^{-\\frac{1}{3}}$\n(126${h_{50}}^{-\\frac{1}{3}}$)~keV~cm$^{2}$ for the assumption of total\nshock suppression. This new upper limit on the entropy should be more\nreliable as it does not rely on the assumption of isothermality of the\nintracluster gas that \\scite{ponman98a} had to use. Our analysis also\nsets a lower bound on the entropy for the case where the shock heating\nis not affected.\n\nIt is also interesting to compare our measured value for the excess entropy\nagainst the value assumed in various theoretical models of entropy\ninjection in galaxy systems. For instance \\scite{balogh98a} assume a\nconstant entropy injection value of $\\sim $350 keV cm$^{2}$ in order to\nreproduce the steepening in the $L$-$T$ relation for galaxy groups.\n\\scite{tozzi99a} argue that to steepen $L$-$T$ at $\\sim$ 0.5-2 keV, entropy\ninjection in the range 190-960 keV cm$^{2}$ is needed. Both these values\nare somewhat higher than our measured range, but considering the \nsimplified nature of these models, the similarity is encouraging. It will\nbe interesting to see whether more sophisticated models can match the group\n$L$-$T$ relation using the lower values of entropy we observe.\n\nA number of models work on the assumption of some specific amount of energy\ninjection into the gas. These can be compared with the amount of\nexcess energy we observe to be present in galaxy systems.\n\\scite{cavaliere97a} and \\scite{cavaliere98a} assume that the gas in galaxy\nsystems is preheated to a temperature of 0.5 keV which is comparable to\nour measured value. \\scite{wu99a} obtain energy input of $<0.1$~keV\nper particle from SN heating within most of their\nhierarchical merger model runs. However, it is not clear that this\nrepresents a hard limit, since these authors assumed that gas can only\nbe heated to the escape velocity of their galaxy halos.\n\\scite{wu98a,wu99a} also find that \nan injected\nenergy per particle of $\\sim$1-2 keV is required to reproduce the slope\nof the cluster $L$-$T$ relation \\cite{david93a}. This may indicate that\nthe preheating required to match the steepening in $L$-$T$ at $T<1$~keV\ndoes not provide a solution to the departure of the cluster relation\nfrom the self-similar result, $L\\propto T^2$. For example, it is clear\nthat the model of \\scite{cavaliere98a}, which provides a good match to\nthe group data, fails to reproduce the slope of the $L$-$T$ relation at\nhigh temperatures (see their Fig.9). Additional effects may be at work\n-- for example \\scite{allen98a} have demonstrated that allowing for the\nimpact of cooling flows flattens the $L$-$T$ relation for rich clusters\ntowards $L\\propto T^2$.\n\nThe floor entropy of 70-140 ${h_{50}}^{-\\frac{1}{3}}$~keV is small compared\nto the entropy of the 8 systems with temperatures of 4 keV or above, which\naverages 380 keV cm$^{2}$ (at 0.1 $R_{v}$). Hence our results are\nconsistent with the idea that an approximately constant amount of excess\nentropy, $\\sim$70-140${h_{50}}^{-\\frac{1}{3}}$ keV cm$^{2}$, is present in\n{\\it all} of the systems, but is only noticeable in systems where it\nconstitutes a large fraction of the total entropy, i.e. in systems with\ntemperatures below 4 keV. From Fig. \\ref{fig:plot5} it can be seen that\nthere is little evidence for any dependence of the excess entropy on radius\noutside the central cooling region. This suggests that the process\ninvolved in injecting entropy into the systems does so fairly uniformly, at\nleast within $0.25 R_{v}$.\n\nFrom Fig. \\ref{fig:plot6}, the gas in low mass systems is significantly\nless tightly bound than would be expected from self-similar scaling.\nCombining the excess entropy and energy requirements leads us to conclude\nthat the energy was injected at $z<$7-10, but before cluster collapse.\nPossible candidates for the source of this extra energy are preheating by\nquasars, population III stars or galaxy winds. It is known that since\nrecombination at z $\\sim 1400$, the intergalactic medium has been\nre-ionized. This re-ionization is normally assumed to be caused by quasars\nor an early epoch of star formation. However analytical models of these\nprocesses \\cite{valageas99a,tegmark93a} suggest that the IGM will only be\nheated to $\\sim$ $10^{4}$-$10^{5}$K, resulting in an entropy change that is at\nleast an order of magnitude lower than the measured value. In contrast,\nenergy injected by supernovae associated with the formation of the bulk of\ngalactic stars should be much more significant \\cite{white91a,david91a}.\n\nThe likely energies involved can be estimated from observed metal\nabundances in the intracluster gas. The major uncertainty here lies in\nestablishing the contributions from supernovae of type Ia and type II,\nwhich have very different ratios of iron yield to energy \\cite{renzini93a}.\nRecent studies with \\emph{ASCA} \\cite{finoguenov99a,finoguenov99b} in which\ncontributions from SNIa and SNII have been mapped in a sample of groups and\nclusters, by tracing the abundance of iron and alpha elements, leads to the\nconclusion that SNIa provide a significant contribution to the iron\nabundance, particularly in galaxy groups. The supernova energy associated\nwith the observed metal masses by \\scite{finoguenov99a} are in good\nagreement with the energy of $\\sim 0.4$~keV per particle derived above on\nthe basis of the observed energy excesses. This is also similar to the\npreheating involved in the models of \\scite{cavaliere97a},\n\\scite{cavaliere98a} and \\scite{balogh98a} supporting the idea that the\nsimilarity breaking we see in the intracluster gas does result from\npreheating associated with galaxy formation.\n\nWith the forthcoming availability of data from \\emph{Chandra} and\n\\emph{XMM}, much more detailed studies of the abundance and entropy\ndistributions of galaxy systems will become possible. This will allow\ndeviations from mean trends to be studied in detail. Since galaxy winds\nwill inject both energy and metals, whereas processes such as ram pressure\nstripping will lead to metal enrichment without heating, studies with these\nnew X-ray observatories should throw a great deal of light on the\nevolutionary history of galactic systems and the galaxies they contain.\n\n\\section*{Acknowledgments}\nWe thank Peter Bourner for his contribution to the preliminary data\nanalysis, and the referee for a number of useful suggestions. Discussions\nwith Richard Bower, Mike Balogh, Alfonso Cavaliere and Kelvin Wu have\nhelped to clarify the relationship between the observations and preheating\nmodels. This work made use of the Starlink facilities at Birmingham, the\nLEDAS database at Leicester and the HEASARC database at the Goddard Space\nFlight Centre. EJLD acknowledges the receipt of a PPARC studentship.\n\n\\bibliography{entropy}\n\n\\label{lastpage}\n\n\\end{document}\n"
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{
"name": "entropy.bbl",
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}
] |
astro-ph0002083
|
A submillimetre survey of the star-formation history of radio galaxies
|
[
{
"author": "J. S. Dunlop$^{2}$"
},
{
"author": "D. H. Hughes$^{2,3}$"
},
{
"author": "S. Rawlings$^{4}$"
},
{
"author": "S. A. Eales$^{5}$"
},
{
"author": "and R. J. Ivison$^{6}$"
},
{
"author": "$^{1}$Joint Astronomy Centre"
},
{
"author": "660 N. A`oh\\={o}k\\={u} Place"
},
{
"author": "Hilo"
},
{
"author": "Hawaii"
},
{
"author": "9620"
},
{
"author": "USA"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh"
},
{
"author": "EH9 3HJ"
},
{
"author": "Scotland"
},
{
"author": "$^{3}$Instituto Nacional de Astrofisica"
},
{
"author": "Optica y Electronica (INAOE)"
},
{
"author": "Apartado Postal 51 y 216"
},
{
"author": "72000 Puebla"
},
{
"author": "Pue."
},
{
"author": "Mexico"
},
{
"author": "$^{4}$Astrophysics"
},
{
"author": "Department of Physics"
},
{
"author": "Keble Road"
},
{
"author": "Oxford"
},
{
"author": "OX1 3RH"
},
{
"author": "England"
},
{
"author": "$^{5}$Department of Physics and Astronomy"
},
{
"author": "P.O. Box 913"
},
{
"author": "Cardiff"
},
{
"author": "CF2 3YB"
},
{
"author": "Wales"
},
{
"author": "$^{6}$Department of Physics \\& Astronomy"
},
{
"author": "Gower Street"
},
{
"author": "London"
},
{
"author": "WC1E 6BT"
}
] |
We present the results of the first major systematic submillimetre survey of radio galaxies spanning the redshift range $1 < z < 5$. The primary aim of this work is to elucidate the star-formation history of this sub-class of elliptical galaxies by tracing the cosmological evolution of dust mass. Using SCUBA on the JCMT we have obtained 850-\micron{} photometry of 47 radio galaxies to a consistent rms depth of $1\;$mJy, and have detected dust emission in 14 cases. The radio galaxy targets have been selected from a series of low-frequency radio surveys of increasing depth (3CRR, 6CE, etc), in order to allow us to separate the effects of increasing redshift and increasing radio power on submillimetre luminosity. Although the dynamic range of our study is inevitably small, we find clear evidence that the typical submillimetre luminosity (and hence dust mass) of a powerful radio galaxy is a strongly increasing function of redshift; the detection rate rises from $\simeq$15 per cent at $z < 2.5$ to $\gtrsim$75 per cent at $z > 2.5$, and the average submillimetre luminosity rises at a rate $\propto (1+z)^3$ out to $z \simeq 4$. Moreover our extensive sample allows us to argue that this behaviour is not driven by underlying correlations with other radio galaxy properties such as radio power, radio spectral index, or radio source size/age. Although radio selection may introduce other more subtle biases, the redshift distribution of our detected objects is in fact consistent with the most recent estimates of the redshift distribution of comparably bright submillimetre sources discovered in blank field surveys. The evolution of submillimetre luminosity found here for radio galaxies may thus be representative of massive ellipticals in general.
|
[
{
"name": "mnpaper.tex",
"string": "\\documentstyle[amssymb,epic,epsfig,multirow,pifont]{mn}\n\n\\newif\\ifAMStwofonts\n\n%%%%% AUTHORS - PLACE YOUR OWN MACROS HERE %%%%%\n\n\\def\\fig#1{Figure~\\ref{#1}}\n\\def\\Fig#1{Figure~\\ref{#1}}\n\\def\\Tab#1{Table~\\ref{#1}}\n\\def\\tab#1{Table~\\ref{#1}}\n\\def\\sec#1{Section~\\ref{#1}}\n\\def\\chap#1{Chapter~\\ref{#1}}\n\\def\\appen#1{Appendix~\\ref{#1}}\n\n\\newcommand{\\micron}[1]{$\\mu\\rm{m}{#1}$}\n\\newcommand{\\hubble}{H$_{\\circ}$}\n\\newcommand{\\hubbleunits}{kms$^{-1}$Mpc$^{-1}$}\n\\newcommand{\\omegao}{$\\Omega_{\\circ}$}\n\\newcommand{\\luminsub}{L$_{850\\mu m}$}\n\\newcommand{\\radiopower}{P$_{151{\\rm MHz}}$}\n\\newcommand{\\alpharadio}{$\\alpha_{radio}$}\n\\newcommand{\\aj}{AJ}\n\\newcommand{\\apj}{ApJ}\n\\newcommand{\\apjs}{ApJS}\n\\newcommand{\\apjl}{ApJ}\n\\newcommand{\\mnras}{MNRAS}\n\\newcommand{\\memras}{MmRAS}\n\\newcommand{\\nat}{Nature}\n\\newcommand{\\aap}{A\\&A}\n\\newcommand{\\aaps}{A\\&AS}\n\\newcommand{\\qjras}{QJRAS}\n\\newcommand{\\procspie}{Proc. SPIE}\n\\newcommand{\\pasp}{PASP}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%BEGIN PAPER%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\title[The star-formation history of radio galaxies]{A submillimetre survey of the star-formation history of radio galaxies}\n\\author[E. N. Archibald et al.]\n {E. N. Archibald$^{1,2}$\\thanks{email: [email protected]}, J. S. Dunlop$^{2}$, D. H. Hughes$^{2,3}$, S. Rawlings$^{4}$, S. A. Eales$^{5}$, \\and and R. J. Ivison$^{6}$\\\\\n$^{1}$Joint Astronomy Centre, 660 N. A`oh\\={o}k\\={u} Place, University\nPark, Hilo, Hawaii, 9620, USA \\\\\n$^{2}$Institute for Astronomy, University of Edinburgh, Blackford Hill,\nEdinburgh, EH9 3HJ, Scotland\\\\\n$^{3}$Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), \nApartado Postal 51 y 216, 72000 Puebla, Pue., Mexico\\\\\n$^{4}$Astrophysics, Department of Physics, Keble Road, Oxford, \nOX1 3RH, England\\\\\n$^{5}$Department of Physics and Astronomy, University of Wales Cardiff,\nP.O. Box 913, Cardiff, CF2 3YB, Wales\\\\\n$^{6}$Department of Physics \\& Astronomy, University College London, Gower \nStreet, London, WC1E 6BT, England\\\\}\n\\date{Accepted ;\n Received ;\n in original form }\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{2000}\n\n\\begin{document}\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\nWe present the results of the first major systematic submillimetre\nsurvey of radio galaxies spanning the redshift range $1 < z < 5$. The\nprimary aim of this work is to elucidate the star-formation history of\nthis sub-class of elliptical galaxies by tracing the cosmological\nevolution of dust mass. Using SCUBA on the JCMT we have obtained\n850-\\micron{} photometry of 47 radio galaxies to a consistent rms\ndepth of $1\\;$mJy, and have detected dust emission in 14 cases. The\nradio galaxy targets have been selected from a series of low-frequency\nradio surveys of increasing depth (3CRR, 6CE, etc), in order to allow\nus to separate the effects of increasing redshift and increasing radio\npower on submillimetre luminosity. Although the dynamic range of our\nstudy is inevitably small, we find clear evidence that the typical\nsubmillimetre luminosity (and hence dust mass) of a powerful radio\ngalaxy is a strongly increasing function of redshift; the detection\nrate rises from $\\simeq$15 per cent at $z < 2.5$ to $\\gtrsim$75 per\ncent at $z > 2.5$, and the average submillimetre luminosity rises at a\nrate $\\propto (1+z)^3$ out to $z \\simeq 4$. Moreover our extensive\nsample allows us to argue that this behaviour is not driven by\nunderlying correlations with other radio galaxy properties such as\nradio power, radio spectral index, or radio source size/age. Although\nradio selection may introduce other more subtle biases, the redshift\ndistribution of our detected objects is in fact consistent with the\nmost recent estimates of the redshift distribution of comparably\nbright submillimetre sources discovered in blank field surveys. The\nevolution of submillimetre luminosity found here for radio galaxies\nmay thus be representative of massive ellipticals in general.\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: formation -- galaxies: elliptical and lenticular, cD -- dust, extinction -- radio continuum: galaxies -- galaxies: active -- stars: formation\n\\end{keywords}\n\n\\section{Introduction}\n\nAlthough large numbers of `normal' galaxies have now been discovered\nout to $z \\simeq 5$ (e.g. Steidel et al. 1999\\nocite{sag99}), radio\ngalaxies continue to offer the best opportunity to study examples of\n{\\em massive elliptical galaxies} (or the progenitors thereof) back to\ncomparably early cosmic epochs. The reason for this is that a powerful\nradio source requires a massive black hole, and it is relatively\ncertain that nowadays all such massive black holes reside in massive\nellipticals \\cite{magorrian98,mkd99}. Thus radio selection offers a\nrelatively efficient way of studying the properties of a sub-set of\nmassive ellipticals as a function of cosmic epoch. Moreover this\nsubset may well be representative of massive ellipticals in general,\nespecially since it can be argued that a substantial fraction of all\npresent-day ellipticals brighter than $2L^{\\star}$ must have been\nactive at $z \\simeq 2.5$ (Dunlop et al. 2000\\nocite{dunlopetal2000}).\n\nAt low redshift, radio galaxies are dominated by well-evolved stellar\npopulations \\cite{nolan2000}, have rather low\ndust/gas masses \\cite{kp91}, and lie in the same region of the\nfundamental plane as normal inactive ellipticals (McLure et al. 1999;\nDunlop et al. 2000\\nocite{mkd99,dunlopetal2000}). Moreover current\nevidence suggests that they have evolved only passively since at least\n$z \\simeq 1$ \\cite{ll84,mcd00}. This, coupled with the relatively old\nages derived for a few radio galaxies at $z \\simeq 1.5$\n\\cite{dunlophy}, points towards a high redshift of formation, $z > 3$,\nfor the bulk of their stellar populations. This means that both the\nstar-formation rate and gas mass in these galaxies should be a\nstrongly increasing function of redshift as one approaches their\nprimary formation epoch(s).\n\nAs has been argued by many authors, a massive starburst at high\nredshift is expected to produce rapid chemical enrichment and to be\nlargely enshrouded in dust. Consequently , submillimetre luminosity\nshould be a good indicator of the evolutionary state of an elliptical\ngalaxy, being expected to peak roughly half-way through the production\nof a galaxy from primordial material \\cite{ee96,frayerbrown97}, or\neven earlier (i.e. as soon as the gas receives sufficient heating)\ngiven pre-existing enrichment (Hughes, Dunlop \\& Rawlings 1997\\nocite{hdr97}).\nIndeed submillimetre luminosity, viewed as a tracer of gas mass, is\narguably the best way to assess the evolutionary status of a massive\ngalaxy. There are two reasons for this. Firstly, the sensitivity and\nbandwidth limitations of present-day instruments makes detecting\nmolecular line emission from high-redshift objects extremely\ndifficult. Secondly, in the case of radio galaxies, optical-UV\nmeasures may be confused by the direct or indirect effects of AGN\nactivity.\n\nThe detectability of high-redshift radio galaxies at submillimetre\nwavelengths was first demonstrated by Dunlop et al. \\shortcite{dhr94},\nwhen they detected 4C41.17, at the time the most distant known galaxy\nat $z=3.8$. However the observation, made with the single element\nbolometer detector UKT14 on the James Clerk Maxwell Telescope (JCMT),\nrequired 4 hours of integration in exceptional weather conditions. In\nfact, the sensitivity of UKT14 permitted only the most extreme objects\nto be detected at high redshift, and it was often a struggle to detect\neven those.\n\nThe advent of the Submillimetre Common-User Bolometer Array (SCUBA) on\nthe JCMT offered the first real opportunity to rectify this\nsituation. Although photometric observations do not fully exploit the\nmultiplex advantage offered by an array camera, the individual\nbolometers in the SCUBA array offered almost an order of magnitude\nimprovement in sensitivity over UKT14. This made it feasible to\nconsider undertaking the first major submillimetre study of radio\ngalaxies spanning a wide range of redshifts, and it is the results of\nthe first major SCUBA survey of radio galaxies which we report here.\n\nThe layout of the paper is as follows: In \\sec{samp} we give a more\ndetailed overview of pre-existing submillimetre observations of radio\ngalaxies, and explain the motivation for observing a sample of\ngalaxies compiled from flux-limited radio surveys of increasing\ndepth. The resulting sample is then described and summarized, before\nthe results of our new submillimetre observations are presented in\n\\sec{submmobs}. \\sec{synchcorrect} then gives details of the radio\nproperties of each galaxy, and explains how the total and, where\npossible, core radio spectrum has been extrapolated to submillimetre\nwavelengths to estimate (or at least constrain) the potential level of\nnon-thermal contamination at 850$\\;$\\micron{}. The coverage of the\nradio-luminosity:redshift plane provided by our observed sample is\npresented in \\sec{pzplanesec}, and then in \\sec{seclumin} we calculate\nthe rest-frame 850-\\micron{} luminosities or upper limits for all the\nobserved galaxies. In \\sec{evolstats} we present a detailed\nstatistical exploration of the evidence for genuine cosmological\nevolution of \\luminsub{} in our sample. Finally in \\sec{concsec} we\nconclude by considering our results in the context of the recently\npublished blank-field submillimetre surveys.\n\nWe have deliberately confined this paper to a determination and\ndiscussion of the relative behaviour of submillimetre luminosity in\nour sample, and have postponed our analysis and interpretation of more\nmodel-dependent properties, such as inferred gas mass and galaxy age,\nto a subsequent paper.\n\n\\subsection{Conventions}\n\nFor clarity, we summarize here a number of conventions which have been \nadopted throughout this paper.\n\\begin{enumerate}\n\\item For each galaxy in the sample, information has been collated\nfrom several references. Each reference has been given a code; for\nexample, ER93\\nocite{er93} corresponds to Eales S.A., Rawlings S.,\n1993, ApJ, 411, 67. These codes are included in the bibliography.\n\\item Throughout the paper, upper limits are calculated using the\nfollowing prescription: Consider an observation with signal S and\nstandard error $\\varepsilon$. If the signal is positive, the\n$n$-$\\sigma$ upper limit is S$+(n\\times\\varepsilon)$. If the signal\nis negative, the $n$-$\\sigma$ upper limit is $n\\times\\varepsilon$. It\ncannot be guaranteed that the upper limits taken from other papers\nwere calculated in this manner.\n\\item For a power-law spectrum, the spectral index, $\\alpha$, is\ndefined as ${\\rm S}_{\\nu}\\propto \\nu^{-\\alpha}$, where S$_{\\nu}$ is\nthe flux density at frequency $\\nu$. Thus, a radio synchrotron\nspectrum has a positive spectral index, and the Rayleigh-Jeans tail of\na thermal spectrum has a negative spectral index.\n\\item The cosmological constant, $\\Lambda$, is assumed to be zero\nthroughout the paper.\n\\end{enumerate}\n\n\n\\section{Project background and sample selection}\n\\label{samp}\n\n\\subsection{Pre-existing millimetre/submillimetre detections of high-redshift radio galaxies}\n\nThis work was carried out using SCUBA \\cite{scubapaper}, the\nsubmillimetre bolometer array mounted on the JCMT. When the project\nwas planned, SCUBA had not yet been commissioned, and only three\nhigh-redshift radio galaxies had been unambiguously detected at\nmillimetre/submillimetre wavelengths: 6C0902+34 (z=3.395), 4C41.17\n(z=3.8), and 8C1435+635 (z=4.25). While the millimetre observations\nof 6C0902+34 appeared to be dominated by non-thermal emission from the\nradio core \\cite{dss96}, the observations of 4C41.17 and 8C1435+635\nwere striking in their similarity, with high emission levels\nattributed to the presence of large reservoirs of dust. The observed\nflux densities are detailed in \\tab{previoussubmmobs}.\n\n\\begin{figure*}\n\\epsfig{file=fig1.eps,width=75mm,angle=270}\n\\caption{Radio luminosity-redshift plane as defined by radio surveys\nwith successively deeper flux-density limits. Open circles denote\ngalaxies from the 3C/3CRR survey and triangles denote galaxies from the 6CE\nsurvey. Stars indicate additional galaxies targeted as part of our\nSCUBA survey from the 4C*, 7CRS, 8C*, MIT-Green Bank MG*, and Texas\nTX* surveys. 4C41.17, 8C1435+635, and 6C0902+34 are each indicated by\na large cross surrounded by a circle. As can be seen from this\nfigure, they are some of the most distant, radio-luminous objects\nknown. Note, 53W069 is too faint to appear on this version (and all\nsubsequent versions) of the P-$z$ plane. H$_{\\circ}=50$\nkms$^{-1}$Mpc$^{-1}$, $\\Omega_{\\circ} = 1.0$.}\n\\label{prescubapz}\n\\end{figure*}\n\n4C14.17 and 8C1435+635 are both ultra-steep spectrum ($\\alpha>1.0$)\nradio galaxies, and both held the title, at the time of their\nrespective discovery, of being the most distant radio galaxy known.\nIn addition, as can be seen in \\fig{prescubapz}, they are two of the\nmost-luminous (at 151$\\;$MHz) radio sources known.\n\n4C41.17 was detected at both 800 \\micron{} and 1300 \\micron{}\n\\cite{dhr94,ck94}, with the contribution from the non-thermal radio\nspectrum being less than a few percent at these wavelengths. Further\nsupport for a thermal emission mechanism came from the submillimetre\nspectral index: $\\alpha^{800}_{1300}\\sim -4$ (for self-absorbed\nsynchrotron emission, $\\alpha\\geq -2.5$).\n\n8C1435+635 was first detected at 1250 \\micron{} \\cite{i95}. As for\n4C41.17, the contribution to the flux density from radio synchrotron\nemission is $\\sim 1$ per cent. In addition, the flux density is\nroughly the same as that detected for 4C41.17 at 1300 \\micron{}.\n\nGiven its similarity to 4C41.17, and its tantalizing detection at\n1250$\\;$\\micron{}, 8C1435+635 was a prime target for SCUBA. When this\nproject was given its initial allocation of time, 8C1435+635 was the\nfirst object attempted, and we were able to study its submillimetre\nSED in unprecedented detail. Firm detections were made at\n850$\\;$\\micron{} and 450$\\;$\\micron{}, confirming that the\nsubmillimetre spectrum rises well above the declining radio emission.\nObservations at 350$\\;$\\micron{}, 750$\\;$\\micron{}, and\n175$\\;$\\micron{} resulted in upper limits to the continuum flux\ndensity; the last observation was made with the {\\em Infrared Space\nObservatory (ISO)}. In addition, a sensitive upper limit,\n$3\\sigma<5\\times10^{10}\\;{\\rm K\\;km\\,s^{-1}pc^2}$ was obtained for the\nCO(4$-3$) line luminosity using the IRAM 30-m telescope. These data\nhave been published in Ivison et al. \\shortcite{idha98}; the observed flux\ndensities (or limits) between $\\lambda=175$\\micron{} and\n$\\lambda=1250$\\micron{} are listed in \\tab{previoussubmmobs}.\n\nIsothermal fits to the submillimetre spectrum suggest the majority of\nthe emission comes from $2\\times 10^8\\;{\\rm M_{\\odot}}$ of dust with a\ntemperature $40\\pm 5\\;$K and emissivity index $\\beta=2$ (assuming \n${\\rm H_{\\circ}=50\\;km\\,s^{-1}\\,Mpc}$ and $\\Omega_{\\circ}=1$). However,\nhigher temperatures, and correspondingly lower dust masses, are not\nruled out by the data. The far-infrared luminosity implied by the\npreferred fit is ${\\rm L_{FIR}\\sim 10^{13}L_{\\odot}}$.\n\nThe amount of gas available for future star formation can be\ncalculated from the dust mass if a gas-to-dust ratio is assumed. This\nassumption is notoriously uncertain; however, robust upper and lower\nlimits on the amount of gas present can be calculated if the highest\nand lowest reasonable values for the ratio are considered. For\n8C1435+635, such an analysis restricts the gas mass to \n${\\rm 4\\times10^{10} <M_{gas}< 1.2\\times10^{12}\\;M_{\\odot}}$. In addition,\nif the dust is heated {\\em solely} by star formation, the far-infrared\nluminosity indicates a star-formation rate of several thousand solar\nmasses per year.\n\nThe dust masses responsible for the detections of 4C41.17 and\n8C1435+635 are in excess of $10^8\\;{\\rm M_{\\odot}}$ \\cite{dhr94,i95}.\nThis is at least an order or magnitude higher than what is observed\nfor radio galaxies in the low-redshift Universe \\cite{kp91},\nindicating that, at $z=4$, a significant amount of gas is yet to be\nconverted into stars, suggesting that the host galaxies are not fully\nformed \\cite{hdr97}.\n\n\\subsection{Motivation for a complete sample of radio galaxies}\n\nThe distant radio galaxies initially detected at submillimetre\nwavelengths are some of the most distant, radio-luminous objects known\n(\\fig{prescubapz}). On their own, they cannot be used to determine\nthe evolutionary status of massive ellipticals at high redshift -\ntheir extreme submillimetre properties could be associated with either\ntheir redshift or the extreme nature of the radio source. There is a\nclear need for a proper sample of radio galaxies spanning a range of\nradio luminosities and redshifts. If the radio luminosity-redshift\nplane (the P-$z$ plane) is properly sampled, the effects of radio\nluminosity and cosmological evolution can be disentangled. The goal\nof this project was to study such a sample using SCUBA.\n\nThe galaxies were chosen based on their radio luminosity and their\nredshift. Before doing so, it was necessary to determine the\nfrequency at which the radio luminosity should be calculated.\n\nThe radio luminosity of a classical double radio source is controlled\nby three key physical parameters: the bulk kinetic power in the jets,\nthe age of the source (measured from the jet-triggering event) as it\nis observed on our light cone, and the environmental density\n(e.g. Blundell, Rawlings \\& Willott 1999\\nocite{brw99}). Provided the\nrest-frame frequency is high enough so that it exceeds the synchrotron\nself-absorption frequency, and low enough that the radiative timescale\nof electrons in the lobes is not so short that the lobes are\ncompletely extinguished, the selection effects inherent in any\nflux-limited sample lead to a reasonably close mapping between radio\nluminosity and jet power (e.g. Willott et al. 1999\\nocite{wrbl99}). These\nconsiderations render 151 MHz the rest-frame frequency of choice if\none wishes to use radio luminosity to track the underlying jet power.\n\nIn any flux-density limited sample, there is a tight correlation\nbetween luminosity and redshift: for large distances, only the\nbrightest objects will be observable - the faint objects will fall\nbelow the detection limit, and for small distances there are few\nbright sources in the small available cosmological volumes. Suppose\ngalaxies were selected from a flux-limited radio survey and observed\nwith SCUBA, with larger submillimetre flux densities measured for the\nhigh-redshift galaxies than for the low-redshift galaxies. It would\nbe impossible to determine whether this was genuine cosmological\nevolution, or if the higher-redshift galaxies were brighter in the\nsubmillimetre because, for example, they are associated with objects\nwith more powerful jets, perhaps because they are associated with more\nmassive black holes and/or dark matter haloes. This problem can be\novercome by using several radio surveys with different flux density\nlimits to select our sample. The details of the redshift surveys of\nradio sources from which the sample was selected are described in\n\\sec{actualsample}. The region of the 151$\\;$MHz radio luminosity\nversus redshift plane covered by these surveys is shown in\n\\fig{prescubapz}.\n\n\\subsection{The sample}\n\\label{actualsample}\n\nInitially, a sample of radio galaxies was compiled from the 3C\n(Bennett 1962\\nocite{bennett1962}; Laing, Riley \\& Longair\n1983\\nocite{lrl83} describe the doubly-revised version of the 3C\nsample, 3CRR) and 6CE (Eales 1985; Rawlings, Eales \\& Lacy\n2000\\nocite{eales85,rel00}) radio surveys, for which complete redshift\ninformation exists. The galaxies were chosen to span a range of\nredshifts, $0.2<z<4.5$, but to lie in a narrow band of radio\nluminosity, ${\\rm\n10^{27}\\;WHz^{-1}sr^{-1}<P_{151MHz}<10^{29}\\;WHz^{-1}sr^{-1}}$. This\nselection was made to minimise any radio luminosity bias and to\ndetermine if the submillimetre emission from radio galaxies truly\nevolves with redshift. Note that the top two decades in radio\nluminosity were chosen, allowing galaxies to be studied out to very\nhigh redshift. If there is a positive correlation between\nsubmillimetre emission and radio luminosity, perhaps via galaxy mass,\nthis choice should also maximise the chance of making detections.\n\nIn order to avoid strong radio synchrotron emission at submillimetre\nwavelengths, a further restriction was imposed on the selected\nsources: they were required to have steep radio spectra, with a\nspectral index $\\alpha>0.5$ for $\\nu \\sim 1\\;$GHz. This selection\ncriterion was aided by the fact that the radio galaxies were selected\nto be very luminous at 151$\\;$MHz - the most intrinsically luminous\nobjects in low-frequency surveys tend to be steep-spectrum sources,\nwhereas high-frequency surveys are biased towards flat-spectrum\nsources.\n\nThe 6CE galaxies have a declination limit $\\delta < 40^{\\circ}$. In\norder to minimise airmass, the criterion $\\delta < 40^{\\circ}$ was\nalso imposed on the 3CRR catalogue sources.\n\nAs the project progressed, it became apparent that sources selected\nfrom the 3CRR and 6CE samples alone could not produce an even\nspread in radio luminosity within the chosen luminosity band.\nAdditional sources, often with declinations $\\delta > 40^{\\circ}$,\nwere added to the sample from:\n\\begin{enumerate}\n\\item two flux-density limited radio surveys with complete, or\nnear-complete, redshift information: the 7C Redshift Survey (7CRS) -\nBlundell et al. (2000); Willott et\nal. (2000)\\nocite{brr00,willott7crs}; and the Leiden-Berkeley Deep\nSurvey (LBDS) - Waddington et al. (2000) and references\ntherein\\nocite{wadlbds}.\n\\item several `filtered surveys' for which a filter, spectral index\nand/or angular size for example, has been applied to identify high\nredshift galaxies in a radio survey. The names and references for\nthese filtered surveys are as follows: 4C* - Chambers et\nal. (1996)\\nocite{cmvb96}; 6C* - Blundell et al. (1998)\\nocite{bre98},\nJarvis et al. in preparation; 8C* - Lacy (1992)\\nocite{lthesis}; TX*\n(Texas) - van Ojik et al. (1996); and MG* (MIT-Green Bank) - Stern et\nal. (1999)\\nocite{sds99}, Spinrad private communication.\n\\end{enumerate}\n\n\\begin{table*}\n\\caption{Positions and redshifts of the radio galaxy sample observed with SCUBA. The parent samples, described in \\sec{actualsample}, are listed in Column 5. Column 6 (Pos. ID) indicates how the position was measured: `c' - a radio core ID exists, `mc' - a radio ID exists for a marginal radio core, `h' - the radio ID is the mid-point of the hotspot peaks, `CSS' - same as `h' but for an extremely compact radio source, `O' - an optical ID exits, `IR' - an infrared ID exists, `HST' - a Hubble Space Telescope ID exists. The position and redshift references are given in column 8, with references containing redshift information in bold. Notes: $^{\\S}$ 6C0930+38 is also referred to as 6C0929+38 in the literature. In the pre-release version of the 6C survey, astrometry indicated an RA of 09h 30m. However, in the final release of the survey, the position of the radio source appears as 09 29 59.7 +38 55 2. $^{\\#}$ The redshifts of 6C0919+38 and 6C1159+36 are not yet confirmed. For 6C0919+38, the estimate may not be too far off; for 6C1159+36, the redshift is based on a highly tentative Ly$_{\\alpha}$ emission line which is no longer considered secure (Rawlings et al. 2000). $^{\\dag}$ For 3C356 the telescope was pointed at the midpoint of the two possible identifications (BLR97). $^{\\ddag}$ The redshift of MG1744+18 is unpublished. A reference to a paper which quotes the unpublished value is included.}\n\\label{posreds}\n\\begin{tabular}{llllllll}\n\\hline\nCommon Name&IAU Name&\\multicolumn{1}{c}{RA (B1950.0)}&\\multicolumn{1}{c}{Dec (B1950.0)}&Parent&Pos.&\\multicolumn{1}{c}{z}&References.\\\\\n &(B1950.0) &\\multicolumn{1}{c}{(h m s)}&\\multicolumn{1}{c}{($^{\\circ}$ $'$ $''$)}&Sample&ID&\\\\\n\\hline\n6C0032+412 &0032+412 &00 32 10.73 &+41 15 00.2 &6C* &c &3.66 &BRE98, {\\bf Jprep}\\\\\n6C0140+326 &0140+326 &01 40 51.53 &+32 38 45.8 &6C* &h &4.41 &BRE98, {\\bf RLB96}\\\\\n4C60.07 &0508+604 &05 08 26.12 &+60 27 17.0 &4C* &mc, O &3.788 &CMvB96, {\\bf RvO97}\\\\\n4C41.17 &0647+415 &06 47 20.57 &+41 34 03.9 &4C* &c, O &3.792 &COH94, {\\bf RvO97}\\\\\n6C0820+36 &0820+367 &08 20 33.96 &+36 42 28.9 &6CE &c, IR &1.86 &ERLG97, LLA95, {\\bf REL00}\\\\\n5C7.269 &0825+256 &08 25 39.48 &+25 38 26.5 &7CRS &IR &2.218 &{\\bf ER96},{\\bf W7CRS}, BRR00\\\\\n6C0901+35 &0901+358 &09 01 25.02 &+35 51 01.8 &6CE &IR &1.904 &ERLG97, {\\bf REW90}, {\\bf REL00}\\\\\n6C0902+34 &0902+343 &09 02 24.77 &+34 19 57.8 &6CE &c, O, IR &3.395 &COH94, {\\bf L88}, {\\bf REL00}\\\\\n6C0905+39 &0905+399 &09 05 04.95 &+39 55 34.9 &6CE &c, IR &1.882 &{\\bf LGE95}, {\\bf REL00}\\\\\n3C217 &0905+380 &09 05 41.34 &+38 00 29.9 &3CRR &mc, HST &0.8975 &BLR97, Lpc, RS97, {\\bf SD84b}\\\\\n6C0919+38 &0919+381 &09 19 07.99 &+38 06 52.5 &6CE &IR &1.65$^{\\#}$ &ER96, {\\bf REL00}\\\\\n6C0930+38$^{\\S}$&0930+389 &09 30 00.77 &+38 55 09.1 &6CE &h &2.395 &NAR92, {\\bf ER96}, {\\bf REL00}\\\\\n3C239 &1008+467 &10 08 38.98 &+46 43 08.8 &3CRR &mc, HST &1.781 &Lpc, BLR97, {\\bf MSvB95}\\\\\nMG1016+058 &1016+058 &10 16 56.82 &+05 49 39.3 &MG* &c, O, IR &2.765 &{\\bf DSD95}\\\\\n3C241 &1019+222 &10 19 09.38 &+22 14 39.7 &3CRR &CSS, HST&1.617 &BLR97, {\\bf SD84b}\\\\\n8C1039+68 &1039+681 &10 39 07.75 &+68 06 06.6 &8C* &O &2.53 &{\\bf Lthesis}\\\\\n6C1113+34 &1113+349 &11 13 47.64 &+34 58 46.6 &6CE &h, IR &2.406 &LLA95, {\\bf REL00}\\\\\n3C257 &1120+057 &11 20 34.55 &+05 46 46.0 &3C &O &2.474 &Spriv, {\\bf vBS98}\\\\\n3C265 &1142+318 &11 42 52.35 &+31 50 26.6 &3CRR &c, HST &0.8108 &FBP97, BLR97, {\\bf SJ79}\\\\\n3C266 &1143+500 &11 43 04.22 &+50 02 47.4 &3CRR &mc, HST &1.272 &BLR97, LPR92, {\\bf SD84b}\\\\\n3C267 &1147+130 &11 47 22.07 &+13 03 60.0 &3CRR &c, HST &1.144 &BLR97, Lpc, {\\bf SD84b}\\\\\n6C1159+36 &1159+368 &11 59 20.94 &+36 51 36.2 &6CE &CSS &3.2$^{\\#}$ &NAR92, {\\bf REL00}\\\\\n6C1204+37 &1204+371 &12 04 21.75 &+37 08 20.0 &6CE &IR &1.779 &ERLG97, {\\bf REL00}\\\\\n6C1232+39 &1232+397 &12 32 39.12 &+39 42 09.4 &6CE &c, IR &3.221 &ERD93, NAR92, {\\bf REW90}, {\\bf REL00}\\\\\nTX1243+036 &1243+036 &12 43 05.40 &+03 39 44.5 &TX* &c, O &3.57 &{\\bf vOR96}, RMC95, {\\bf RvO97}\\\\\nMG1248+11 &1248+113 &12 48 29.11 &+11 20 40.3 &MG* &O &2.322 &{\\bf SDS99}\\\\\n3C277.2 &1251+159 &12 51 03.85 &+15 58 47.1 &3CRR &c, HST &0.766 &Lpc, McC97, {\\bf SDM85}\\\\\n4C24.28 &1345+245 &13 45 54.66 &+24 30 44.7 &4C* &O &2.879 &CMvB96, {\\bf RvO97}\\\\\n3C294 &1404+344 &14 04 34.06 &+34 25 40.0 &3CRR &c &1.786 &{\\bf MS90}\\\\\n8C1435+635 &1435+635 &14 35 27.50 &+63 32 12.8 &8C* &O &4.25 &{\\bf LMR94, SDG95}\\\\\n3C322 &1533+557 &15 33 46.27 &+55 46 47.4 &3CRR &mc &1.681 &LRL, LLA95, {\\bf SRS90}\\\\\n3C324 &1547+215 &15 47 37.14 &+21 34 41.0 &3CRR &c, HST, IR&1.2063 &BCG98, BLR97, {\\bf SD84a}\\\\\n3C340 &1627+234 &16 27 29.42 &+23 26 42.2 &3CRR &c &0.7754 &Lpc, LRL, {\\bf SD84b}\\\\\n53W002 &1712+503 &17 12 59.83 &+50 18 51.3 &LBDS &O &2.39 &{\\bf WBM91}\\\\\n53W069 &1718+499 &17 18 46.50 &+49 47 47.7 &LBDS &c, O &1.432 &Wthesis, {\\bf D99}\\\\\n3C356$^{\\dag}$\\ \\ (a)&1732+510 &17 23 06.77 &+51 00 17.8 &3CRR &c, IR &1.079 &BLR97, {\\bf S82}\\\\\n\\hspace{1.152cm}(b)& &17 23 06.95 &+51 00 14.2 &3CRR &c, IR & &LR94\\\\\n%\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\, (b)& &17 23 06.95 &+51 00 14.2 &3CRR &c, IR & &LR94\\\\\nMG1744+18 &1744+183 &17 44 55.30 &+18 22 11.3 &MG* &IR &2.28$^{\\ddag}$ &Bthesis, {\\bf S-unpub}, {\\bf ER93}\\\\\n4C13.66 &1759+138 &17 59 21.64 &+13 51 22.8 &3CRR &IR &1.45 &{\\bf RLL96}\\\\\n3C368 &1802+110 &18 02 45.63 &+11 01 15.8 &3CRR &c, HST &1.132 &BLR97, DSP87, {\\bf S82}\\\\\n4C40.36 &1809+407 &18 09 19.42 &+40 44 38.9 &4C* &O &2.265 &CMvB88, {\\bf RvO97}\\\\\n4C48.48 &1931+480 &19 31 40.03 &+48 05 07.1 &4C* &c, O &2.343 &CMvB96, {\\bf RvO97}\\\\\n4C23.56 &2105+233 &21 05 00.96 &+23 19 37.7 &4C* &c, O &2.483 &CMvB96, {\\bf RvO97}\\\\\nMG2141+192 &2141+192 &21 41 46.95 &+19 15 26.7 &MG* &h &3.592 &CRvO97, {\\bf Mprep}, \\\\\n3C437 &2145+151 &21 45 01.58 &+15 06 36.1 &3CRR &HST &1.48 &BLR97, {\\bf MSvB95}\\\\\nMG2305+03 &2305+033 &23 05 52.31 &+03 20 47.9 &MG* &O &2.457 &{\\bf SDS99}\\\\\n4C28.58 &2349+288 &23 49 26.94 &+28 53 47.2 &4C* &c, O &2.891 &CMvB96, {\\bf RvO97}\\\\\n3C470 &2356+438 &23 56 02.90 &+43 48 03.6 &3CRR &c, HST &1.653 &Lpc, BLR97, {\\bf MSvB95}\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\nNames, positions, and redshifts for the full sample observed with\nSCUBA are given in \\tab{posreds}. In total, 47 radio galaxies were\nobserved (27 from our original 3C/3CRR/6CE list). Note, for 3C356 two\nunresolved radio `cores' have been detected within 5$''$ of each\nother; they each have a galaxy at z=1.079 associated with them. It is\nnot clear which galaxy is the host of the radio source; for further\ndiscussion of the merits of the two positions, refer to Best, Longair,\n\\& R\\\"{o}ttgering \\shortcite{blr97}. SCUBA was pointed midway between\nthe two identifications, and will have been offset 2$''$ from the true\nposition of the host galaxy; the flux lost should be negligible, $<5$\nper cent at 850 \\micron{}.\n\n\\section{Submillimetre observations}\n\\label{submmobs}\n\nIn this section, the results of all the submillimetre observations of\nthe 47 galaxies in the sample are presented.\n\n\\subsection{The SCUBA survey}\n\\label{radiocontaminatedfluxes}\n\nSCUBA contains two bolometer arrays cooled to $\\sim75\\;$mK to achieve\nsky background-limited performance. Each array is arranged in a\nclose-packed hexagon with a $2.3'$ instantaneous field of view. The\ndiffraction-limited beamsizes delivered by the JCMT to SCUBA are\n$14.7''$ at 850$\\;$\\micron{} and $7.5''$ at 450$\\;$\\micron{}; the\nbolometer feedhorns are sized for optimal coupling to the beams.\nConsequently, the long-wavelength (LW) array, optimised for an\nobserving wavelength of 850$\\;$\\micron{}, contains 37 pixels. The\nshort-wavelength (SW) array, optimised for operation at\n450$\\;$\\micron{}, contains 91 pixels. A dichroic beamsplitter allows\nobservations to be made with both arrays simultaneously.\n\nFor point sources, SCUBA's photometry mode is recommended, where the\ntarget is observed with a single pixel. During commissioning, it was\ndiscovered that the best photometric accuracy could be obtained by\naveraging the source signal over a slightly larger area than the beam.\nThis is achieved by `jiggling' the secondary mirror such that the\nchosen bolometer samples a $3\\times3$ grid with 2$''$ spacing centered\non the source. The on-source integration time is 1 second per jiggle\npoint; excluding overheads, the jiggle pattern takes 9$\\;$s to complete.\nWhile making the mini jiggle map, the telescope was chopped at 45$''$ in\nazimuth at a frequency of 7Hz. After the first 9-point jiggle, the\ntelescope was nodded to the reference position, an event which\noccurred every 18 seconds thereafter.\n\nBetween June 1997 and March 1999, a total of 192 hours was used to\ncarry out the observations, all in excellent weather conditions. The\natmospheric zenith opacities were at the very most 0.3 at\n850$\\;$micron and 2.5 at 450$\\;$micron, although they were frequently\nmuch better than this. Skydips and observations of calibrators were\nobtained regularly. For each source, the data have been flatfielded,\ndespiked, and averaged over 18 seconds. The residual sky background\nthat chopping and nodding are unable to remove has been subtracted by\nusing the data taken by the off-source bolometers. The\nKolmogorov-Smirnov (KS) test has been applied to the data to check for\nconsistency, and the data have been calibrated using observations of\nMars, Uranus and several secondary calibrators.\n\nThe 850$\\;$\\micron{} and 450$\\;$\\micron{} flux densities measured for\nthe radio galaxies in the sample are listed in\n\\tab{introducingmydata}. This table includes both $3\\sigma$ upper\nlimits for sources whose signal-to-noise ratio (S/N) does not exceed\n3.0 and $2\\sigma$ upper limits for sources whose S/N does not exceed\n2.0. The reason for this is that while traditionally the detection of\na given source might only be regarded as robust if it is greater than\n$3\\sigma$, genuine $2\\sigma$ detections should be taken seriously,\nespecially given that the telescope was pointed at known galaxies\ninstead of the submillimetre source being identified in a blank-field\nsurvey. Furthermore, the adoption of a $2\\sigma$ detection level is\nnecessary to implement the statistical analysis presented in\n\\sec{survsub}. It should be noted, however, that the results\npresented in this paper hold whether a $3\\sigma$ or a $2\\sigma$\ndetection threshold is adopted.\n\n\\begin{table*}\n\\caption{Observed submillimetre flux densities (S$_{\\nu}$) and standard errors for the sample. $3\\sigma$ upper limits are shown for sources whose S/N does not exceed 3.0; $2\\sigma$ upper limits are shown for sources whose S/N does not exceed 2.0}\n\\label{introducingmydata}\n\\begin{tabular}{lllrrllrrrrr}\n\\hline\n&&&\\multicolumn{4}{c}{850$\\;$\\micron{}}&&\\multicolumn{4}{c}{450$\\;$\\micron{}}\\\\\nSource&\\multicolumn{1}{c}{$z$}&&\\multicolumn{1}{c}{S$_{\\nu}$}&\\multicolumn{1}{c}{S/N}&\\multicolumn{1}{c}{$3\\sigma$ limit}&\\multicolumn{1}{c}{$2\\sigma$ limit}&&\\multicolumn{1}{c}{S$_{\\nu}$}&\\multicolumn{1}{c}{S/N}&\\multicolumn{1}{c}{$3\\sigma$ limit}&\\multicolumn{1}{c}{$2\\sigma$ limit}\\\\\n&&&\\multicolumn{1}{c}{(mJy)}&&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}&&\\multicolumn{1}{c}{(mJy)}&&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}\\\\\n\\hline\n%%%%%%%\n%%%%%%%paper_scubatable.tex goes here\n%%%%%%%\n3C277.2 &0.766 &&$ 1.01\\pm 1.04$ &$ 1.0 $&$< 4.13 $&$< 3.09$ &&$ -10.6\\pm 10.7$ &$ -1.0 $&$< 32$&$< 21$\\\\\n3C340 &0.7754 &&$ 0.85\\pm 0.87$ &$ 1.0 $&$< 3.46 $&$< 2.59$ &&$ 6.8\\pm 9.0$ &$ 0.8 $&$< 34$&$< 25$\\\\\n3C265 &0.8108 &&$-1.41\\pm 0.98$ &$ -1.4 $&$< 2.94 $&$< 1.96$ &&$ -2.0\\pm 11.2$ &$ -0.2 $&$< 34$&$< 22$\\\\\n3C217 &0.8975 &&$ 1.03\\pm 0.83$ &$ 1.2 $&$< 3.52 $&$< 2.69$ &&$ -0.7\\pm 9.8$ &$ -0.1 $&$< 30$&$< 20$\\\\\n3C356 &1.079 &&$ 1.66\\pm 1.04$ &$ 1.6 $&$< 4.78 $&$< 3.74$ &&$ 17.3\\pm 19.8$ &$ 0.9 $&$< 77$&$< 57$\\\\\n3C368 &1.132 &&$ 4.08\\pm 1.08$ &$ 3.8 $&$ $&$ $ &&$ 39.6\\pm 15.1$ &$ 2.6 $&$< 85$&$ $\\\\\n3C267 &1.144 &&$ 1.93\\pm 0.96$ &$ 2.0 $&$< 4.81 $&$ $ &&$ 27.0\\pm 14.6$ &$ 1.8 $&$< 71$&$< 56$\\\\\n3C324 &1.2063 &&$ 1.75\\pm 0.87$ &$ 2.0 $&$< 4.36 $&$ $ &&$ 4.1\\pm 11.8$ &$ 0.3 $&$< 39$&$< 28$\\\\\n3C266 &1.272 &&$ 0.46\\pm 1.30$ &$ 0.4 $&$< 4.36 $&$< 3.06$ &&$ -2.1\\pm 30.5$ &$ -0.1 $&$< 91$&$< 61$\\\\\n53W069 &1.432 &&$-2.70\\pm 1.04$ &$ -2.6 $&$< 3.12 $&$< 2.08$ &&$ 14.7\\pm 11.5$ &$ 1.3 $&$< 49$&$< 38$\\\\\n4C13.66 &1.45 &&$ 3.53\\pm 0.96$ &$ 3.7 $&$ $&$ $ &&$ -16.2\\pm 18.2$ &$ -0.9 $&$< 55$&$< 36$\\\\\n3C437 &1.48 &&$-1.18\\pm 0.98$ &$ -1.2 $&$< 2.94 $&$< 1.96$ &&$ 2.9\\pm 17.3$ &$ 0.2 $&$< 55$&$< 37$\\\\\n3C241 &1.617 &&$ 1.81\\pm 0.94$ &$ 1.9 $&$< 4.63 $&$< 3.69$ &&$ 14.8\\pm 12.6$ &$ 1.2 $&$< 52$&$< 40$\\\\\n6C0919+38 &1.65 &&$-0.88\\pm 1.05$ &$ -0.8 $&$< 3.15 $&$< 2.10$ &&$ 10.5\\pm 10.1$ &$ 1.0 $&$< 41$&$< 31$\\\\\n3C470 &1.653 &&$ 5.64\\pm 1.08$ &$ 5.2 $&$ $&$ $ &&$ 57.8\\pm 32.9$ &$ 1.8 $&$< 156$&$< 124$\\\\\n3C322 &1.681 &&$-0.05\\pm 1.06$ &$ 0.0 $&$< 3.18 $&$< 2.12$ &&$ -37.5\\pm 16.0$ &$ -2.3 $&$< 48$&$< 32$\\\\\n6C1204+37 &1.779 &&$ 0.16\\pm 1.25$ &$ 0.1 $&$< 3.91 $&$< 2.66$ &&$ 45.1\\pm 26.6$ &$ 1.7 $&$< 125$&$< 98$\\\\\n3C239 &1.781 &&$ 0.83\\pm 1.00$ &$ 0.8 $&$< 3.83 $&$< 2.83$ &&$ -2.1\\pm 18.3$ &$ -0.1 $&$< 55$&$< 37$\\\\\n3C294 &1.786 &&$ 0.19\\pm 0.78$ &$ 0.2 $&$< 2.53 $&$< 1.75$ &&$ 5.4\\pm 13.4$ &$ 0.4 $&$< 45$&$< 32$\\\\\n6C0820+36 &1.86 &&$ 2.07\\pm 0.96$ &$ 2.2 $&$< 4.95 $&$ $ &&$ 13.6\\pm 18.0$ &$ 0.8 $&$< 68$&$< 50$\\\\\n6C0905+39 &1.882 &&$ 3.62\\pm 0.89$ &$ 4.1 $&$ $&$ $ &&$ 31.2\\pm 16.2$ &$ 1.9 $&$< 80$&$< 64$\\\\\n6C0901+35 &1.904 &&$-1.83\\pm 1.15$ &$ -1.6 $&$< 3.45 $&$< 2.30$ &&$ -19.3\\pm 8.2$ &$ -2.4 $&$< 25$&$< 16$\\\\\n5C7.269 &2.218 &&$ 1.68\\pm 1.00$ &$ 1.7 $&$< 4.68 $&$< 3.68$ &&$ 5.1\\pm 9.2$ &$ 0.6 $&$< 33$&$< 23$\\\\\n4C40.36 &2.265 &&$ 0.67\\pm 1.06$ &$ 0.6 $&$< 3.85 $&$< 2.79$ &&$ 7.3\\pm 23.2$ &$ 0.3 $&$< 77$&$< 54$\\\\\nMG1744+18 &2.28 &&$ 0.83\\pm 1.02$ &$ 0.8 $&$< 3.89 $&$< 2.87$ &&$ 13.2\\pm 17.7$ &$ 0.7 $&$< 66$&$< 49$\\\\\nMG1248+11 &2.322 &&$ 1.10\\pm 1.06$ &$ 1.0 $&$< 4.28 $&$< 3.22$ &&$ -20.9\\pm 12.9$ &$ -1.6 $&$< 39$&$< 26$\\\\\n4C48.48 &2.343 &&$ 5.05\\pm 1.05$ &$ 4.8 $&$ $&$ $ &&$ 17.9\\pm 24.9$ &$ 0.7 $&$< 93$&$< 68$\\\\\n53W002 &2.39 &&$ 1.03\\pm 1.10$ &$ 0.9 $&$< 4.33 $&$< 3.23$ &&$ 2.9\\pm 14.3$ &$ 0.2 $&$< 46$&$< 32$\\\\\n6C0930+38 &2.395 &&$ 0.36\\pm 1.00$ &$ 0.4 $&$< 3.36 $&$< 2.36$ &&$ 8.3\\pm 10.8$ &$ 0.8 $&$< 41$&$< 30$\\\\\n6C1113+34 &2.406 &&$ 0.33\\pm 1.14$ &$ 0.3 $&$< 3.75 $&$< 2.61$ &&$ -11.4\\pm 16.8$ &$ -0.7 $&$< 50$&$< 34$\\\\\nMG2305+03 &2.457 &&$ 2.31\\pm 0.99$ &$ 2.3 $&$< 5.28 $&$ $ &&$ -9.5\\pm 41.8$ &$ -0.2 $&$< 126$&$< 84$\\\\\n3C257 &2.474 &&$ 5.40\\pm 0.95$ &$ 5.7 $&$ $&$ $ &&$ 17.8\\pm 15.4$ &$ 1.2 $&$< 64$&$< 49$\\\\\n4C23.56 &2.483 &&$ 1.72\\pm 0.98$ &$ 1.8 $&$< 4.66 $&$< 3.68$ &&$ -3.3\\pm 17.0$ &$ -0.2 $&$< 51$&$< 34$\\\\\n8C1039+68 &2.53 &&$ 0.38\\pm 0.98$ &$ 0.4 $&$< 3.32 $&$< 2.34$ &&$ 31.8\\pm 17.0$ &$ 1.9 $&$< 83$&$< 66$\\\\\nMG1016+058 &2.765 &&$ 2.40\\pm 0.92$ &$ 2.6 $&$< 5.16 $&$ $ &&$ 28.7\\pm 10.1$ &$ 2.8 $&$< 59$&$ $\\\\\n4C24.28 &2.879 &&$ 2.59\\pm 1.16$ &$ 2.2 $&$< 6.07 $&$ $ &&$ 11.2\\pm 18.7$ &$ 0.6 $&$< 67$&$< 48$\\\\\n4C28.58 &2.891 &&$ 3.93\\pm 0.95$ &$ 4.1 $&$ $&$ $ &&$ 23.0\\pm 15.5$ &$ 1.5 $&$< 69$&$< 54$\\\\\n6C1232+39 &3.221 &&$ 3.86\\pm 0.72$ &$ 5.4 $&$ $&$ $ &&$ -2.4\\pm 6.1$ &$ -0.4 $&$< 18$&$< 12$\\\\\n6C1159+36 &3.2 &&$ 1.20\\pm 1.08$ &$ 1.1 $&$< 4.44 $&$< 3.36$ &&$ 28.3\\pm 16.0$ &$ 1.8 $&$< 76$&$< 60$\\\\\n6C0902+34 &3.395 &&$ 2.83\\pm 1.00$ &$ 2.8 $&$< 5.83 $&$ $ &&$ 11.6\\pm 11.5$ &$ 1.0 $&$< 46$&$< 35$\\\\\nTX1243+036 &3.57 &&$ 2.28\\pm 1.11$ &$ 2.1 $&$< 5.61 $&$ $ &&$ 1.5\\pm 19.0$ &$ 0.1 $&$< 59$&$< 40$\\\\\nMG2141+192 &3.592 &&$ 4.61\\pm 0.96$ &$ 4.8 $&$ $&$ $ &&$ 21.4\\pm 18.9$ &$ 1.1 $&$< 78$&$< 59$\\\\\n6C0032+412 &3.66 &&$ 2.64\\pm 1.20$ &$ 2.2 $&$< 6.24 $&$ $ &&$ -5.5\\pm 13.3$ &$ -0.4 $&$< 40$&$< 27$\\\\\n4C60.07 &3.788 &&$17.11\\pm 1.33$ &$ 12.9 $&$ $&$ $ &&$ 69.0\\pm 23.0$ &$ 3.0 $&$ $&$ $\\\\\n4C41.17 &3.792 &&$12.10\\pm 0.88$ &$ 13.8 $&$ $&$ $ &&$ 22.5\\pm 8.5$ &$ 2.7 $&$< 48$&$ $\\\\\n8C1435+635 &4.25 &&$ 7.77\\pm 0.76$ &$ 10.2 $&$ $&$ $ &&$ 23.6\\pm 6.4$ &$ 3.7 $&$ $&$ $\\\\\n6C0140+326 &4.41 &&$ 3.33\\pm 1.49$ &$ 2.2 $&$< 7.80 $&$ $ &&$ -20.5\\pm 17.1$ &$ -1.2 $&$< 51$&$< 34$\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\\subsection{Radio galaxies with other millimetre/submillimetre observations}\n\nSeveral attempts were made to observe the millimetre/submillimetre\nspectrum of radio galaxies before SCUBA existed. The attempts, made\nwith the IRAM 30-m telescope and UKT14 (SCUBA's predecessor), were\nlargely unsuccessful. More recently, Best et al. \\shortcite{brb98} also looked\nat 3C324 with SCUBA and Benford et al. \\shortcite{bco99} observed 4C41.17\nat 350$\\;$\\micron{} with the CSO. All of these observations,\nincluding the full submillimetre spectrum of 8C1435+635, are listed in\n\\tab{previoussubmmobs}.\n\n\\begin{table*}\n\\caption{All other millimetre and submillimetre observations of\ngalaxies in the sample. All flux densities are quoted in mJy.\nThe references are: 3C324 - BRB98; 53W002 - HDR97; 3C257 - HDR97; MG1016+058 - CFR98; 6C1232+39 - C\\&K94; 6C0902+34 - C\\&K94, DSS96, HDR97; TX1243+036 - CFR98; MG2141+192 - HDR97; 6C0032+412 - HDR97; 4C41.17 - BCO99, C\\&K94, DHR94; 8C1435+635 - HDR97, I95, IDHA98}\n\\label{previoussubmmobs}\n\\begin{tabular}{lllllllll}\n\\hline\nSource &S$_{3000\\mu m}$&S$_{1300\\mu m}$ &S$_{850\\mu m}$ &S$_{800\\mu m}$ &S$_{750\\mu m}$ &S$_{450\\mu m}$ &S$_{350\\mu m}$ &S$_{175\\mu m}$\\\\\n\\hline\n3C324 & & &$3.65\\pm1.17$ & & &$3\\sigma<21$ & &\\\\\n53W002 & & & &$6.9\\pm2.3$ & & & &\\\\\n3C257 & & & &$3\\sigma<11$ & & & &\\\\\nMG1016+058 & &$2.13\\pm0.47$ & &$14.7\\pm4.6$ & & & &\\\\\n6C1232+39 & &$3\\sigma<3.0$ & & & & & &\\\\\n6C0902+34 &$4.2\\pm0.6$ &$3.1\\pm0.6$ & &$3\\sigma<14$ & & & &\\\\\nTX1243+036 & &$3\\sigma<2.6$ & &$3\\sigma<9.3$ & & & &\\\\\nMG2141+192 & & & &$3\\sigma<11$ & & & &\\\\\n6C0032+412 & & & &$3\\sigma<14$ & & & &\\\\\n4C41.17 & &$2.5\\pm0.4$ & &$17.4\\pm3.1$ & &$3\\sigma<56$ &$37\\pm9$ &\\\\\n8C1435+643 & &$2.57\\pm0.42$ &$7.77\\pm0.76$ &$3\\sigma<13$ &$8.74\\pm3.31$ &$23.6 \\pm 6.4$ &$3\\sigma<87.0$ &$3\\sigma<40.1$\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\nIn most cases, these data are consistent with what we observed with\nSCUBA (for 3C324, although we find a lower flux density than Best et\nal. \\shortcite{brb98}, the two results are equivalent within errors).\nThere are two exceptions:\n\\begin{enumerate}\n\\item 53W002 - Even though 53W002 was detected at 800-\\micron{} with\nUKT14 \\cite{hdr97}, we have failed to detect it\nwith SCUBA. Assuming a typical submillimetre spectral index of $-4.0$,\nthe 800-\\micron{} detection of 53W002 implies a flux density of at\nleast 3.6$\\;$mJy at 850-\\micron{}. Note the spectral index is\nexpected to lie between the values of $-3.0$ and $-4.0$ (e.g. Hildebrand\n1983\\nocite{hildebrand}), and adopting a value of $-4.0$ will give the\nlowest estimate of 850-\\micron{} flux. Thus, if the UKT14 data are\ntrustworthy, we should have detected 53W002 with SCUBA, even if the\nlarge error bar on the 800-\\micron{} measurement is taken into\naccount.\n\\item MG1016+058 - For MG1016+058, previous detections existed at both\n1300$\\;$\\micron{} and 800$\\;$\\micron{} \\cite{cfr98}. The minimum\nsubmillimetre spectral index consistent with these data points and\ntheir error bars is $\\sim-2.8$. This can be used to estimate a lower\nlimit on the flux density expected at 850$\\;$\\micron{}. The\n850-\\micron{} flux density should be well in excess of 5$\\;$mJy,\neasily detectable with SCUBA. An obvious objection to this analysis\nis that the 1300-\\micron{} flux density could be solely due to radio\nsynchrotron emission. This is unlikely; the radio spectrum is highly\ncurved and dives down well below the 1300-\\micron{} flux density\n(\\appen{sedfig1}). However, assume for a moment that the\n1300-\\micron{} flux density was contaminated by radio emission.\nAgain, adopting a typical submillimetre spectral index of -4.0 and\napplying it to the 800$\\;$\\micron{} detection still predicts an\n850-\\micron{} flux density in excess of 5$\\;$mJy.\n\\end{enumerate}\n\nThese two discrepancies are perhaps not all that surprising. UKT14\nwas a single-element bolometer, relying solely on chopping and nodding\nfor sky removal. However, a chop/nod set-up is unable to account for\nquick variations in the background sky, and there will be residual sky\nnoise present in the data (Jenness, Lightfoot \\& Holland\n1998\\nocite{remskypaper}). SCUBA is an array, and the off-source\nbolometers can be used to remove this residual sky noise\n\\cite{remskypaper}. Omont et al. \\shortcite{omc96} investigated the\ndifference between single- and multi-bolometer detectors, and found\nthat the less-reliable sky-cancellation offered by single-bolometer\nsystems often resulted in fake detections of weak sources.\nFurthermore, they failed to detect three high-redshift quasars with a\nmulti-bolometer array that Andreani, La Franca \\& Cristiani\n\\shortcite{alc93} had apparently detected with a single bolometer.\n\n\\section{Correcting radio galaxy dust emission for potential contamination}\n\\label{synchcorrect}\n\nFor the majority of galaxies in the sample which we have actually\ndetected, a detection has only been obtained at one submillimetre\nwavelength (i.e. 850$\\;$\\micron{}). Without a reliable estimate of\nthe submillimetre spectral index, care needs to be taken to ensure the\ndetected submillimetre emission is clearly in excess of the radio\nsynchrotron spectrum, and can thus be safely attributed to dust.\nHowever, as will become clear, due to the fact that the sample was\nconfined to steep-spectrum lobe-dominated radio galaxies at $z>1$, for\nalmost all objects, detectability with SCUBA at 850$\\;$\\micron{}\ncorresponds to a successful detection of dust. Radio spectra have\nbeen compiled for each source with the aim of extrapolating the radio\nemission to submillimetre wavelengths and subtracting it off. This\ncorrection should give a good estimate of the flux density produced by\nthermal dust emission.\n\nIt might appear that such a correction would be excessive, or even\ncompletely unnecessary where it is known that the radio lobes lie\noutside the SCUBA beam. However, at high frequencies, $\\geq8\\;$GHz,\nexperience with individual well-studied objects (e.g. 4C41.17)\nindicates that much of the emission can arise from structures\ncoincident or close to the radio core (e.g. Carilli, Owen \\& Harris\n1994\\nocite{coh94}). Therefore we have adopted the conservative but\nconsistent approach of estimating submillimetre synchrotron\ncontamination from the extrapolation of the total high-frequency radio\nemission in every case. In practice, for radio sources larger than\nthe JCMT beam, this correction makes a significant impact on the\nestimated dust mass in only a very small number of sources. These are\ndiscussed at the end of \\sec{contam}.\n\nThe radio spectra are shown in \\appen{sedfig1}, and include both integrated\nand core radio flux densities. Core flux densities are generally much\nfainter than the integrated radio emission at low frequencies, but\nthey can also be much flatter. If the core has a flat spectral index,\nit may contribute significantly to the submillimetre flux density even\nif the integrated radio emission seems to fall well below this.\n\nFits to the radio spectra are also shown in \\appen{sedfig1}. These\nfits are described in \\sec{contam} (with full details in\n\\appen{sedfig1}) and are subsequently used to estimate the non-thermal\ncontamination at submillimetre wavelengths. Details on how the\nindividual radio spectra were compiled are given in Archibald\n\\shortcite{mythesis}.\n\nNote the radio spectrum of 53W069 has not been presented here. 53W069\nis only $3.73\\;$mJy at 1.4$\\;$GHz, and synchrotron contamination\nwill not be a problem \\cite{wvhk84}.\n\n\\subsection{Synchrotron contamination}\n\\label{contam}\n\nA simple synchrotron spectrum is a power law of the form\n$S_{\\nu}\\propto \\nu^{-\\alpha}$. However, real radio spectra turn over\nat low frequencies owing to synchrotron self-absorption, or through\nrunning out of electrons at low energies. At high frequencies the\nspectra steepen as they age - the highest-energy electrons radiate\naway their energy the fastest. In log-space, such spectra appear\ncurved.\n\nConsider, as an example, the radio spectrum of the hotspots of\nCygnus-A, described in detail by Muxlow, Pelletier \\& Roland\n\\shortcite{mpr88}. The spectrum is a power law at low frequencies\n$0.4\\;{\\rm GHz} < \\nu < 1.5\\; {\\rm GHz}$, with a spectral index\n$\\alpha\\sim 0.5$, and a low-frequency turn-over at $\\nu \\sim 0.2\n\\;{\\rm GHz}$. At $2 {\\rm GHz}$ the spectrum steepens; for $\\nu > 2\n\\;{\\rm GHz}$, the spectrum is consistent with a power law of index\n$\\alpha\\sim 1.0$. Robson et al. \\shortcite{rlsh98} and Eales,\nAlexander \\& Duncan \\shortcite{ead89} have found that this steep power\nlaw is an accurate description of the spectrum right out to\nsubmillimetre wavelengths. Thus in log-space, at high frequencies a\nstraight-line fit would be accurate. However, when fitting to the\nwhole spectrum, a model with some curvature would be required.\n\nAnother good example is the study of the dominant hotspot of 3C273, by\nMeisenheimer \\& Heavens \\shortcite{mh86}. For low frequencies, $\\nu <\n1.5\\; {\\rm GHz}$, the spectral index is $\\alpha\\sim 0.7$. For $1.5\\;\n{\\rm GHz} < \\nu < 5\\; {\\rm GHz}$, the spectrum steepens to an index of\n$\\alpha\\sim 0.9$. At high frequencies $5\\; {\\rm GHz} < \\nu < 15\\;\n{\\rm GHz}$, the spectrum steepens even further to an index of\n$\\alpha\\sim 1.0$.\n\nMore recently, Murgia et al. \\shortcite{mff99} published a study of\ncompact steep-spectrum radio sources. The majority of objects in\ntheir sample exhibit a clear spectral steepening, occurring anywhere\nfrom a few hundred MHz to tens of GHz.\n\nIn order to successfully correct for synchrotron contamination at\nsubmillimetre wavelengths, the high-frequency radio spectrum needs to\nbe well determined. Unfortunately, for most galaxies in the sample,\nthe highest-frequency observation is $\\nu \\sim 20 \\; {\\rm GHz}$. A\nstraight-line extrapolation (in log-space) from the highest frequency\ndata point could be used to decontaminate the submillimetre flux densities.\nHowever, in the interval between $20 \\; {\\rm GHz}$ and the SCUBA\nwavebands, the spectrum may steepen, and the straight-line\nextrapolation would over-correct the SCUBA flux density.\n\nEvidence to support this steepening comes from 3C324, MG1744+18, and\nMG1016+058 - the only sources in the sample with measured radio flux\ndensities at $\\nu > 20 \\; {\\rm GHz}$. In each case the high-frequency\nobservation indicates a significant steepening of the radio spectrum.\n4C23.56 and 8C1435+635, two of the higher-redshift galaxies in the\nsample, even appear significantly curved for $\\nu < 20 \\; {\\rm GHz}$.\n\nNote that if a straight-line extrapolation of the high-frequency radio\nemission is correct, three of 850-\\micron{} detections made with SCUBA\nappear to be seriously contaminated with non-thermal synchrotron -\n4C13.66, 3C470, and 3C257.\n\nMore high-frequency radio observations are needed to be certain what\nthe radio spectrum of each galaxy in the sample does as it approaches\nthe submillimetre waveband. For now, both possibilities will be\nconsidered: a {\\em linear fit}, a straight-line extrapolation of the\nhigh-frequency data, as could be accurately applied to Cygnus-A; and a\n{\\em parabolic fit} which reflects a degree of steepening, or\ncurvature, at higher frequencies. The details of the two fits,\ntogether with plots of the SEDs, are given in \\appen{sedfig1}.\n\nIt would be surprising if the radio spectra flattened off at high\nfrequencies, as this only occurs if the source has an extremely\nbright, flat radio core (except for 6C0902+34, the radio galaxies\ndiscussed here all have relatively faint cores - \\sec{cores}). Thus,\nthe linear fit is a strong upper limit on the synchrotron emission at\nsubmillimetre wavelengths, especially since a significant fraction of\nthe emission may lie outside the JCMT beam. Deviations from this\nstandard power-law take the form of a steepening at high frequencies -\nthe parabolic fit mimics this curvature and is a good lower limit on\nthe amount of synchrotron emission at submillimetre wavelengths.\nGiven the lack of high-frequency radio observations, it is often\ndifficult to determine which is the better fit. The best estimate of\nthe synchrotron contamination has been taken to be the midpoint of\nthese two models, with the error in the estimate being the difference\nbetween the midpoint and either the upper or lower limit.\n\nThese estimates of synchrotron emission were thus subtracted from the\nmeasured SCUBA flux densities, with the errors being added in\nquadrature (as prescribed by the propagation of errors). However,\nthere were four special cases for which particular care had to be\ntaken:\n\\begin{enumerate}\n\\item 3C324, MG1744+18, MG1016+058, and 4C23.56 all have\nhigh-frequency data that the linear fit has trouble fitting to. For\nthese galaxies, the parabolic fit looks to be the more realistic\nextrapolation of the radio spectra, and was used to decontaminate the\nSCUBA flux densities.\n\\item For the 14 radio sources whose lobes lie outside the JCMT beam,\nwe may have over-corrected for synchrotron contamination. However,\nfor all of these but one, the source was either undetected by SCUBA,\nor the applied correction was insignificantly small. For 3C470, the\napplied correction turned a detection into a non-detection, reducing\nthe 850-\\micron{} flux from 5.6$\\;$mJy to 3.1$\\;$mJy. However, as\nmentioned previously, our method of correction may be reasonable for\nsources that lie outside the JCMT beam. Furthermore, if the\ncorrection is not applied to 3C470, the results presented in the paper\nare unaffected.\n\\item For some galaxies SCUBA measured a negative signal. They\nhave not been corrected for synchrotron contamination; performing the\ncorrection would have unnecessarily increased the noise of the\nmeasurement and inappropriately made the signal even more negative.\n\\item For some of the undetected galaxies, the estimated synchrotron\ncontamination is larger than the signal measured by SCUBA, resulting\nin a negative submillimetre flux density if it is corrected for.\nClaiming a `negative emission' from dust is not physically\nmeaningful. It is better to set the SCUBA flux densities equal to zero: it\nappears that there is no thermal emission from dust at these\nwavelengths. This leaves the question of how to handle the errors.\nIt seems best to leave them as they are - as they have been measured\nby SCUBA. The statement then being made is that, as far as it can be\nascertained, all of the measured signal may be radio synchrotron\nemission, and any dust emission from the source is definitely less\nthan $2\\times$ the measured noise (for a $2\\sigma$ upper limit). This\nseems a good, conservative upper limit - in each case the limit is\nlarger than the original measured flux density.\n\\end{enumerate}\n\n\\subsection{Radio cores}\n\\label{cores}\n\nWhen searching for thermal dust emission, the telescope is pointed at\nthe optical/infrared ID of the galaxy. This position is coincident\nwith the radio core (if one has been detected). A flat radio core\ncould contribute at submillimetre wavelengths. A useful exercise is\nto estimate the upper limit on this contribution for each source -\nif it tends to be negligible, the SCUBA flux densities will not need\nto be corrected.\n\nOnly 8 of the galaxies in the sample have their radio core detected at\nmore than one frequency: 3C267, 3C324, 3C241, 4C23.56, 6C1232+39,\n6C0902+34, TX1243+036, and 4C41.17. 6C0902+34 is a special case that\nis excluded from the following discussion; it will be treated\nseparately at the end of this section. For the remaining 7 galaxies,\nthe radio core spectral index has been estimated using the two\nhighest-frequency core detections. 3C324 and 3C241 have relatively\nflat core spectra, with $\\alpha \\sim 0.35$. The majority, however,\nhave very steep spectra, ranging from $\\alpha \\sim 0.7$ to $\\alpha\n\\sim 1.8$. Note that no detected core appears either completely flat\nor inverted (i.e. flux density {\\em increasing} with frequency)\nbetween 1$\\;$GHz and 15$\\;$GHz. If these cores are extrapolated to\nsubmillimetre wavelengths, in all cases, save one, the core\ncontribution is negligible: $< 0.05{\\rm mJy}$ at 850$\\;$\\micron{}.\nFor 3C241, on the other hand, the core strength at 850$\\;$\\micron{} is\nlikely to be $\\sim 1{\\rm mJy}$.\n\nFor several galaxies in the sample, the radio core has been detected\nat a single frequency. Adopting the flattest measured spectral index\nof $\\alpha \\sim 0.35$, the corresponding core flux densities at\n850$\\;$\\micron{} have been estimated. This is a pessimistic estimate,\nmany of these galaxies may have steeper core spectra, but it is a good\nindication of the worst-case scenario. In all cases but three, the\npredicted core flux densities are negligible, $< 0.2{\\rm mJy}$.\nHigher 850$\\;$\\micron{} core flux densities are expected for 3C322 and\n3C265. However, for these galaxies a negative signal was measured\nwith SCUBA, and the core brightness is irrelevant. For MG1016+058, if\nthe spectrum is flat, a core flux density of $\\sim 0.8{\\rm mJy}$ is\nexpected at 850$\\;$\\micron{}. If, on the other hand, the spectral index\nis steeper, $\\alpha \\sim 0.75$ for example, the core contamination is\nnegligible.\n\nA lack of sources with core detections at more than one frequency\npotentially hinders this analysis. However, given the available\ninformation it seems unlikely that the cores are significant except\nfor 3C241 and MG1016+058. The core contribution in the case of 3C241\nhas been corrected for, as the core spectrum is definitely flat. For\nMG1016+058, on the other hand, it is impossible to know whether the\ncore is flat or steep. Given this uncertainty, the SCUBA observations\nhave not been corrected for core contamination. Instead, it is simply\nnoted that MG1016+058 may have a large core contribution at\nsubmillimetre wavelengths.\n\nIt is mentioned in the literature that three galaxies have completely\nflat (or possibly inverted) cores at $\\nu < 5\\;{\\rm GHz}$: 3C294\n(MS90\\nocite{ms90}), 6C0905+39 (LGE95\\nocite{lge95}), and 6C0032+412\n(BRE98\\nocite{bre98}; Jarvis et al., in preparation). These cores\ncould contribute significantly to the observed SCUBA flux densities.\nHowever, Rudnick, Jones \\& Fiedler \\shortcite{rjf86} have studied flat\ncores in powerful radio galaxies. They found the cores often turned\nover or steepened at $\\nu > 5\\;{\\rm GHz}$ - a completely flat core at\nlow frequencies does not mean that it will remain flat out to the\nsubmillimetre wavebands, indeed all evidence suggests it is very\nunlikely to do so.\n\nIn addition, note that for 3C356, two radio core identifications\nexist: one faint and steep, the other brighter and flat. Neither\nshould significantly contribute at submillimetre wavelengths.\n\n6C0919+38 could have a very bright radio core, $\\sim6\\;$mJy at\n5$\\;$GHz. However, it is not clear whether the bright feature\ndetected by Naundorf et al. \\shortcite{nar92} is the radio core or a\nknot in the radio jet. Given the uncertainty, the possible radio core\ncontamination is merely noted here and is not corrected for.\n\n\\subsubsection{6C0902+34}\n\\label{6c0902}\n\n6C0902+34 is a special case because of the brightness of its core,\n$\\sim 10 {\\rm mJy}$, between 1.5 and 15$\\;$GHz. In addition, two\nslightly conflicting observations at 8$\\;$GHz make it difficult to be\ncertain how steep the core spectrum is. If the flatter spectral index\nis used ($\\alpha\\sim 0.3$), the 3$\\;$mm and 1.3$\\;$mm detections of\nDownes et al. \\shortcite{dss96} and Chini \\& Kr\\\"ugel \\shortcite{ck94}\nlook to be completely dominated by the radio core. Downes et\nal. \\shortcite{dss96} came to the same conclusion, and predict the\ncontribution of dust emission at 1.3$\\;$mm to be $<0.6\\;$mJy. Even if\nthe steeper spectral index is used ($\\alpha\\sim 1.0$), the detections\ncould easily be dominated by the integrated radio spectrum (although\nhigher-frequency radio detections are needed to confirm this).\n\nWhen observed with SCUBA at 850$\\;$\\micron{}, a $3\\sigma$ upper limit of\n5.83$\\;$mJy was measured. Combining this with Chini \\& Kr\\\"ugel's\ndetection of $3.1\\pm0.6\\;{\\rm mJy}$ at 1300$\\;$\\micron{}, the\nsubmillimetre spectral index is $|\\alpha| \\leq 2.0$. This is\ninconsistent with thermal dust emission being present, for which\n$|\\alpha| > 2.0$. (Note that the submillimetre spectral indices are\nnegative).\n\n6C0902+34 appears completely dominated by radio synchrotron emission.\nIt has thus been left out of the sample. Hereafter, we discuss a\nsample of 46 radio galaxies which excludes 6C0902+34.\n\n\n\\subsection{Submillimetre confusion}\n\n\\subsubsection{Galactic cirrus confusion}\n\nExtrapolating the galactic cirrus confusion that {\\em IRAS} measured\nat 100$\\;$\\micron{} to 850$\\;$\\micron{} at SCUBA resolution yields a\ncirrus confusion noise of $<<1\\;{\\rm mJy\\,beam^{-1}}$ in the direction of\nour targets. Thus, contamination by galactic cirrus should not be a problem for this study (see Hughes et al. 1997 \\nocite{hdr97} and\nHelou \\& Beichman 1990 \\nocite{hb90} for detailed discussions).\n\n\\subsubsection{Confusion by extragalactic sources}\n\nHughes et al. \\shortcite{hdfnature} performed the deepest submillimetre survey\nwhen they mapped the Hubble Deep Field with SCUBA. For 850$\\;$\\micron{},\nconfusion was found to be a problem for sources weaker than 2$\\;$mJy. At the\n2$\\;$mJy level, the source density of their map is $\\sim 1$ source per 30\nbeams. In a large {\\em blank-field} survey reaching 2$\\;$mJy, some detections\nwill inevitably result from confusion, particularly if sources are strongly\nclustered. However, the chances that such false confusion-induced detections\nshould coincide in position with known massive objects at high redshift is\nclearly extremely small. Of course, given sufficient resolution our detected\nsources may break up into sub-components, as for example has the optical image\nof 4C41.17 under HST resolution \\cite{mcvb92}. However, since such\nsub-components are still extremely likely to be associated with the radio\ngalaxy itself, this cannot be regarded as a problem. See also Blain et al.\n\\shortcite{blainconfusion} for an in-depth discussion of source confusion at\nSCUBA wavelengths.\n\n\\subsubsection{Confusion by sources in the off-beam}\n\nThe measured flux densities could be affected by chopping onto a nearby\nsource. This is unlikely to be an important problem for this study, even\nthough SCUBA maps of the fields of radio galaxies have revealed an\nover-density of sources in some cases (Ivison et al. 2000a\\nocite{4cmap};\nIvison et al., in preparation\\nocite{rgmapping}). For the galaxies in our\nsample which have been mapped and shown to have companion sources (4C41.17 and\n8C1435+635), our chop did not land on the companions. Furthermore, our\nobservations were made with an azimuthal chop, and the off-beam will have\nmoved across a substantial angle (several degrees) of the sky as we tracked a\nsource, diluting the effect of off-beam contamination. There is also no {\\em\n a priori} reason why this possible source of confusion would result in a\nredshift bias and affect the analysis presented in \\sec{evolstats}.\n\n\n\\subsection{A final note on corrections: 6C0140+326}\n\nAs a final note on correcting the SCUBA flux densities, it appears\nthat 6C0140+326 is gravitationally lensed \\cite{rlb96}. However, the\npredicted amplification factor is small ($<2$). Given the\nuncertainties in estimating this factor and the synchrotron\ncontamination, a correction has not been applied.\n\n\\subsection{Corrected flux densities}\n\nThe final 850-\\micron{} flux densities, corrected for synchrotron\ncontamination, and in the case of 3C241 for radio core contamination,\nare presented in \\tab{decontaminateddata}. Note, we do not include\nthe corrected 450-\\micron{} flux densities; at 450$\\;$\\micron{} the\ncorrections are tiny compared with the errors. As mentioned\nearlier, we adopt a detection threshold of S/N$\\ge2.0$, with upper\nlimits taken at the $2\\sigma$ level. Out of a sample of 46 radio\ngalaxies (excluding 6C0902+34), thermal emission from dust has been\ndetected in 14 galaxies at 850$\\;$\\micron{}, and in 5 of these\ngalaxies at 450$\\;$\\micron{}.\n\n\\begin{table}\n\\centering\n\\caption{850-\\micron{} flux densities (S$_{\\nu}$) and errors corrected\nfor radio synchrotron contamination. In the case of 3C241, radio core\ncontamination has also been taken into account. A `\\ding{51}' in column 2\nindicates that applying the correction has changed the flux density by\nless than 1$\\sigma$. $2\\sigma$ upper limits are shown for sources\nwhose S/N does not exceed 2.0.}\n\\label{decontaminateddata}\n\\begin{tabular}{lcrrl}\n\\hline\n&&\\multicolumn{3}{c}{850$\\;$\\micron{}}\\\\\nSource&$<1\\sigma$&\\multicolumn{1}{c}{S$_{\\nu}$}&\\multicolumn{1}{c}{S/N}&\\multicolumn{1}{c}{$2\\sigma$ limit}\\\\\n&&\\multicolumn{1}{c}{(mJy)}&&\\multicolumn{1}{c}{(mJy)}\\\\\n\\hline\n%%%%%%%%%\n%%%%%%%%%scubatable_decontam.tex goes here!\n%%%%%%%%%\n3C277.2 &\\ding{51} &$ 0.00\\pm 1.04$ & 0.00 &$< 2.08$\\\\\n3C340 &\\ding{51} &$ 0.00\\pm 0.87$ & 0.00 &$< 1.74$\\\\\n3C265 &\\ding{51} &$-1.41\\pm 0.98$ &-1.44 &$< 1.96$\\\\\n3C217 & &$ 0.00\\pm 0.83$ & 0.00 &$< 1.66$\\\\\n3C356 & &$ 0.08\\pm 1.25$ & 0.06 &$< 2.58$\\\\\n3C368 &\\ding{51} &$ 3.70\\pm 1.11$ & 3.32 &$ $\\\\\n3C267 & &$ 0.00\\pm 0.96$ & 0.00 &$< 1.92$\\\\\n3C324 & &$ 0.80\\pm 0.89$ & 0.90 &$< 2.57$\\\\\n3C266 &\\ding{51} &$ 0.00\\pm 1.30$ & 0.00 &$< 2.60$\\\\\n53W069 &\\ding{51} &$-2.70\\pm 1.04$ &-2.60 &$< 2.08$\\\\\n4C13.66 &\\ding{51} &$ 2.62\\pm 1.24$ & 2.11 &$ $\\\\\n3C437 &\\ding{51} &$-1.18\\pm 0.98$ &-1.20 &$< 1.96$\\\\\n3C241 & &$ 0.01\\pm 1.15$ & 0.00 &$< 2.30$\\\\\n6C0919+38 &\\ding{51} &$-0.88\\pm 1.05$ &-0.84 &$< 2.10$\\\\\n3C470 & &$ 3.07\\pm 1.56$ & 1.96 &$< 6.20$\\\\\n3C322 &\\ding{51} &$-0.05\\pm 1.06$ &-0.05 &$< 2.12$\\\\\n6C1204+37 &\\ding{51} &$ 0.00\\pm 1.25$ & 0.00 &$< 2.50$\\\\\n3C239 &\\ding{51} &$ 0.00\\pm 1.00$ & 0.00 &$< 2.00$\\\\\n3C294 &\\ding{51} &$ 0.00\\pm 0.78$ & 0.00 &$< 1.56$\\\\\n6C0820+36 &\\ding{51} &$ 1.80\\pm 0.98$ & 1.83 &$< 3.76$\\\\\n6C0905+39 &\\ding{51} &$ 3.52\\pm 0.89$ & 3.95 &$ $\\\\\n6C0901+35 &\\ding{51} &$-1.83\\pm 1.15$ &-1.59 &$< 2.30$\\\\\n5C7.269 &\\ding{51} &$ 1.41\\pm 1.00$ & 1.41 &$< 3.41$\\\\\n4C40.36 &\\ding{51} &$ 0.63\\pm 1.06$ & 0.60 &$< 2.75$\\\\\nMG1744+18 &\\ding{51} &$ 0.02\\pm 1.02$ & 0.02 &$< 2.06$\\\\\nMG1248+11 &\\ding{51} &$ 0.96\\pm 1.07$ & 0.90 &$< 3.10$\\\\\n4C48.48 &\\ding{51} &$ 4.72\\pm 1.06$ & 4.44 &$ $\\\\\n53W002 &\\ding{51} &$ 0.99\\pm 1.10$ & 0.90 &$< 3.19$\\\\\n6C0930+38 &\\ding{51} &$ 0.00\\pm 1.00$ & 0.00 &$< 2.00$\\\\\n6C1113+34 &\\ding{51} &$ 0.00\\pm 1.14$ & 0.00 &$< 2.28$\\\\\nMG2305+03 & &$ 0.08\\pm 1.02$ & 0.08 &$< 2.13$\\\\\n3C257 & &$ 1.62\\pm 2.25$ & 0.72 &$< 6.12$\\\\\n4C23.56 &\\ding{51} &$ 1.68\\pm 0.98$ & 1.72 &$< 3.64$\\\\\n8C1039+68 &\\ding{51} &$ 0.02\\pm 0.99$ & 0.02 &$< 2.01$\\\\\nMG1016+058 &\\ding{51} &$ 2.31\\pm 0.92$ & 2.51 &$ $\\\\\n4C24.28 &\\ding{51} &$ 2.35\\pm 1.17$ & 2.01 &$ $\\\\\n4C28.58 &\\ding{51} &$ 3.89\\pm 0.95$ & 4.10 &$ $\\\\\n6C1232+39 &\\ding{51} &$ 3.84\\pm 0.72$ & 5.34 &$ $\\\\\n6C1159+36 &\\ding{51} &$ 0.79\\pm 1.15$ & 0.68 &$< 3.09$\\\\\nTX1243+036 &\\ding{51} &$ 2.14\\pm 1.11$ & 1.92 &$< 4.36$\\\\\nMG2141+192 &\\ding{51} &$ 4.57\\pm 0.96$ & 4.75 &$ $\\\\\n6C0032+412 &\\ding{51} &$ 2.40\\pm 1.20$ & 2.00 &$ $\\\\\n4C60.07 &\\ding{51} &$17.08\\pm 1.33$ &12.84 &$ $\\\\\n4C41.17 &\\ding{51} &$12.06\\pm 0.88$ &13.70 &$ $\\\\\n8C1435+635 &\\ding{51} &$ 7.76\\pm 0.76$ &10.21 &$ $\\\\\n6C0140+326 &\\ding{51} &$ 3.31\\pm 1.49$ & 2.22 &$ $\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nFor 3C368, MG1016+058, 4C60.07, 4C41.17, and 8C1435+635, an estimate\nof the 850-450$\\;$\\micron{} spectral index can be made. For thermal\ndust emission, the slope along the Rayleigh-Jeans tail is expected to\nbe around 3.0-4.0. The spectral indices of the lower-$z$ detected\nsources, 3C368 and MG1016+058, are consistent with this:\n$|\\alpha^{850}_{450}| \\sim 4$. The indices of 4C60.07, 4C41.17 and\n8C1435+635 are on the low side, $|\\alpha^{850}_{450}| \\leq 2$.\nHowever, this is to be expected. They have large redshifts, and for\nthermal greybody emission at 30 K, the spectral turnover should be\nredshifted into or near the 450$\\;$\\micron{} waveband. Using the\n450$\\;$\\micron{} observation would underestimate the slope along the\nRayleigh-Jeans tail in this situation.\n\n\\section{The radio luminosity-redshift plane for radio galaxies observed with SCUBA}\n\\label{pzplanesec}\n\nIt is useful to plot radio luminosity against redshift (the P-$z$\nplane) highlighting the galaxies we have observed with SCUBA. This\nensures that even luminosity coverage of the P-$z$ plane has been\nachieved, and identifies the redshifts at which submillimetre emission\nfrom radio galaxies is detected.\n\n\\begin{figure}\n\\centering\n\\epsfig{file=fig2a.eps,height=90mm,angle=270}\n\\epsfig{file=fig2b.eps,height=90mm,angle=270}\n\\caption{Radio luminosity-redshift plane for $\\Omega_{\\circ} = 1.0$ (upper plot) and $\\Omega_{\\circ} = 0.1$ (lower plot), assuming H$_{\\circ}=50$ kms$^{-1}$Mpc$^{-1}$. The solid circles indicate radio galaxies for which thermal emission from dust was detected at 850$\\;$\\micron{} with S/N$>2$, and the open circles indicate galaxies for which no dust emission was detected. For the detections, the size of the solid circle represents the brightness of the galaxy at 850 \\micron{}. The 151-MHz radio luminosities, P$_{151{\\rm MHz}}$, were estimated using the radio SEDs presented and referenced in \\appen{sedfig1}. Note, 53W069 is too faint to appear on this version of the radio luminosity-redshift plane. The dashed-line boxes depict Subset A (upper plot) and Subset B (lower plot) which are defined in \\sec{survsub}.}\n\\label{pzom_1_01}\n\\end{figure}\n\nAs previously mentioned, the radio luminosities have been calculated\nat rest-frame 151$\\;$MHz to ensure that the radio luminosity tracks\nthe power of the radio jets as accurately as possible. Simple physical\nmodels for the time development of the 151$\\;$MHz luminosity and the\nlinear size (D$_{linear}$) of a double radio source suggest that over\na large range of D$_{linear}$, the 151$\\;$MHz radio luminosity gives a\nreasonably accurate guide to the jet power Q of the vast majority of\nobjects detected in complete radio flux-limited samples \\cite{wrbl99}.\n\nBoth the 151$\\;$MHz luminosities and the linear sizes for the sample\nhave been calculated for two cosmologies: $\\Omega_{\\circ} = 1.0$, and\n$\\Omega_{\\circ} = 0.1$, where H$_{\\circ}=50$ kms$^{-1}$Mpc$^{-1}$.\nThe values are presented in \\tab{sourcesizes}. \\fig{pzom_1_01} shows\nthe corresponding P-$z$ plane for each cosmology.\n\nA proper statistical analysis of these data will be presented in\n\\sec{evolstats}, but at first glance, \\fig{pzom_1_01} seems to\nindicate that submillimetre emission is more predominant in\nhigh-redshift radio galaxies than in low-redshift radio galaxies.\n\n\\begin{table*}\n\\caption{Radio sizes and luminosities for the sample. Column 3 gives the largest angular size (LAS) of the radio source, measured in arcseconds. The corresponding linear size (D$_{linear}$) and 151-MHz radio luminosity (P$_{151{\\rm MHz}}$) have been calculated for both $\\Omega_{\\circ} = 1.0$ and $\\Omega_{\\circ} = 0.1$ (H$_{\\circ}=50$ kms$^{-1}$Mpc$^{-1}$). The radio luminosities were estimated using the radio spectral energy distributions presented and referenced in \\appen{sedfig1}. The references for the LAS values are given in column 8. Where necessary, the LAS was measured off published radio maps. For the majority of the 3CRR sources, the LAS was taken from Blundell et al. (2000), which summarises the radio properties of these sources.}\n\\label{sourcesizes}\n\\begin{tabular}{llrrcrcl}\n\\hline\n&&&\\multicolumn{2}{c}{$\\Omega_{\\circ}=1.0$}&\\multicolumn{2}{c}{$\\Omega_{\\circ}=0.1$}&\\\\\nSource&\\multicolumn{1}{c}{z}&\\multicolumn{1}{c}{LAS}&\\multicolumn{1}{c}{D$_{linear}$}&\\multicolumn{1}{c}{log P$_{151{\\rm MHz}}$}&\\multicolumn{1}{c}{D$_{linear}$}&\\multicolumn{1}{c}{log P$_{151{\\rm MHz}}$}&Refs.\\\\\n&&\\multicolumn{1}{c}{($''$)}&\\multicolumn{1}{c}{(kpc)}&\\multicolumn{1}{c}{(WHz$^{-1}$sr$^{-1}$)}&\\multicolumn{1}{c}{(kpc)}&\\multicolumn{1}{c}{(WHz$^{-1}$sr$^{-1}$)}&\\\\\n\\hline\n3C277.2 &0.766 & 58.0 & 473 &27.61 & 559 &27.76 &BRR00\\\\\n3C340 &0.7754 & 46.7 & 382 &27.46 & 452 &27.60 &BRR00\\\\\n3C265 &0.8108 & 78.0 & 643 &27.86 & 768 &28.01 &BRR00\\\\\n3C217 &0.8975 & 12.0 & 101 &27.65 & 122 &27.82 &BRR00\\\\\n3C356 &1.079 & 75.0 & 643 &27.92 & 809 &28.12 &BRR00\\\\\n3C368 &1.132 & 7.9 & 68 &28.14 & 86 &28.35 &BRR00\\\\\n3C267 &1.144 & 38.0 & 327 &28.05 & 416 &28.26 &BRR00\\\\\n3C324 &1.2063 & 10.0 & 86 &28.12 & 111 &28.34 &BRR00\\\\\n3C266 &1.272 & 4.5 & 39 &28.06 & 51 &28.29 &BRR00\\\\\n53W069 &1.432 & $<5.1 $ &$<44$ &24.54 &$<59$ &24.80 &WvHK84\\\\\n4C13.66 &1.45 & 6.0 & 51 &28.11 & 69 &28.36 &BRR00\\\\\n3C437 &1.48 & 34.4 & 294 &28.23 & 398 &28.49 &BRR00\\\\\n3C241 &1.617 & 0.9 & 8 &28.30 & 11 &28.58 &BRR00\\\\\n6C0919+38 &1.65 & 10.4 & 88 &27.55 & 122 &27.84 &NAR92\\\\\n3C470 &1.653 & 24.0 & 203 &28.16 & 283 &28.45 &BRR00\\\\\n3C322 &1.681 & 33.0 & 279 &28.19 & 390 &28.48 &BRR00\\\\\n6C1204+37 &1.779 & 51.7 & 433 &27.75 & 615 &28.06 &LLA95\\\\\n3C239 &1.781 & 11.2 & 94 &28.50 & 133 &28.81 &BRR00\\\\\n3C294 &1.786 & 15.0 & 125 &28.39 & 179 &28.70 &BRR00\\\\\n6C0820+36 &1.86 & 23.0 & 191 &27.64 & 275 &27.95 &LLA95\\\\\n6C0905+39 &1.882 & 111.0 & 920 &27.82 & 1330 &28.14 &LGE95\\\\\n6C0901+35 &1.904 & 2.7 & 22 &27.57 & 32 &27.90 &NAR92\\\\\n5C7.269 &2.218 & 7.7 & 62 &27.28 & 94 &27.64 &BRR00\\\\\n4C40.36 &2.265 & 4.0 & 32 &28.33 & 49 &28.69 &CRvO97\\\\\nMG1744+18 &2.28 & 7.5 & 60 &28.36 & 91 &28.74 &CRvO97\\\\\nMG1248+11 &2.322 & $<1.2$ &$<9$ &27.80 &$<15$ &28.18 &LBH86\\\\\n4C48.48 &2.343 & 14.0 & 110 &27.95 & 171 &28.33 &CRvO97\\\\\n53W002 &2.39 & 0.7 & 5 &27.33 & 9 &27.71 &WBM91\\\\\n6C0930+38 &2.395 & 3.7 & 29 &27.72 & 45 &28.11 &NAR92\\\\\n6C1113+34 &2.406 & 16.5 & 129 &27.68 & 201 &28.07 &LLA95\\\\\nMG2305+03 &2.457 & 3.0 & 23 &28.16 & 37 &28.55 &SDS99\\\\\n3C257 &2.474 & 12.0 & 93 &28.44 & 147 &28.83 &vBS98\\\\\n4C23.56 &2.483 & 53.0 & 411 &28.41 & 647 &28.80 &CRvO97\\\\\n8C1039+68 &2.53 & 15.0 & 116 &28.00 & 183 &28.40 &Lthesis\\\\\nMG1016+058 &2.765 & 1.3 & 10 &27.80 & 16 &28.23 &DSD95\\\\\n4C24.28 &2.879 & 2.3 & 17 &28.24 & 28 &28.68 &CRvO97\\\\\n4C28.58 &2.891 & 16.2 & 119 &28.71 & 198 &29.15 &CMvB96\\\\\n6C1232+39 &3.221 & 7.7 & 54 &28.35 & 94 &28.82 &NAR92\\\\\n6C1159+36 &3.2 & 1.2 & 8 &28.01 & 15 &28.49 &LLA95\\\\\nTX1243+036 &3.57 & 8.8 & 60 &28.49 & 107 &29.00 &vOR96\\\\\nMG2141+192 &3.592 & 8.9 & 60 &28.75 & 108 &29.26 &CRvO97\\\\\n6C0032+412 &3.66 & 2.3 & 15 &28.17 & 28 &28.69 &BRE98\\\\\n4C60.07 &3.788 & 9.0 & 59 &28.61 & 109 &29.14 &CRvO97\\\\\n4C41.17 &3.792 & 13.1 & 86 &28.78 & 159 &29.31 &COH94\\\\\n8C1435+635 &4.25 & 3.9 & 24 &28.42 & 47 &28.99 &LMR94\\\\\n6C0140+326 &4.41 & 2.5 & 15 &28.20 & 30 &28.78 &RLB96, BRE98\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\\section{Submillimetre luminosities and dust masses}\n\\label{seclumin}\n\nTo calculate the rest-frame 850-\\micron{} luminosity (\\luminsub{}) and\ndust mass (${\\rm M_{dust}}$) of each source, we adopt an optically\nthin isothermal dust emission template with $\\beta=1.5$ and ${\\rm\nT_{dust}}=40\\;$K. This template is consistent with the studies\nattempting to constrain $\\beta$ and ${\\rm T_{dust}}$ that have been\npublished in the literature. For example, Benford et\nal. \\shortcite{bco99} have observed a sample of high-redshift\nradio-quiet quasars and radio galaxies at 350-\\micron{}. Assuming a\ncritical wavelength of ${\\rm \\lambda_{\\circ}=125\\mu m}$, isothermal\nfits indicate $\\beta \\sim 1.5$ and ${\\rm T_{dust} \\sim 50 K}$. The\nstudy of {\\em IRAS} galaxies by Dunne et al. \\shortcite{dunne2000}\nindicates $\\beta \\sim 1.2$ and ${\\rm T_{dust} \\sim 36 K}$ (although\nthe value $\\beta$ is thought to have been artificially lowered by the\npresence of a cold dust component). Finally, for the handful of\ngalaxies identified in the recent SCUBA surveys that have known\nredshifts (refer to Smail et al. 2000\\nocite{sibk2000} for a review),\nthe favoured value of ${\\rm T_{dust}}$ is $\\sim 40\\;$K (e.g. Ivison et\nal. 1998b, 2000b\\nocite{islb98,isbk00}; Barger, Cowie \\& Sanders\n1999\\nocite{bargercs99}).\n\nIt is currently impossible to determine the precise values of $\\beta$\nand ${\\rm T_{dust}}$, and even though we have assumed the most likely\ntemplate, it could very well be wrong. This has important\nconsequences for the analysis presented here. For greybody emission,\nthe values of $\\beta$ and ${\\rm T_{dust}}$ determine the shape and\nposition of the spectral turnover, but have less of an effect on the\nRayleigh-Jeans tail. As the redshift of the source increases, the\nspectral peak is brought into view. Thus the K-correction used to\ncalculate the 850-\\micron{} luminosity is more sensitive to changing\nthe values of $\\beta$ and ${\\rm T_{dust}}$ at high redshift than it is\nat low redshift. If the template is wrong, the error in the\nestimations of \\luminsub{} will be larger if the source has a high\nredshift. To explore this, the analysis of evolutionary trends has\nbeen conducted using several $\\beta$-${\\rm T_{dust}}$ combinations, in\naddition to the template itself, to ensure the trends are real.\n\nFurthermore, applying a template to the entire sample assumes that the\nindividual radio galaxies all have similar dust parameters. This is a\nreasonable assumption if the same mechanisms for creating and heating\ndust are expected in each source. If, however, the dust\ncharacteristics do vary from source to source, they would have to do\nso in a redshift- (or radio power-) dependent manner to seriously\naffect the evolutionary trends presented here.\n\nThe choice of cosmology is also an important issue. As the relative\nproperties of the sample are of most interest in the analysis\npresented here, the value of the Hubble constant is irrelevant.\nChanging the Hubble constant simply scales all the luminosities up or\ndown by the same amount. However, changing the value of the density\nparameter affects the luminosities in a redshift-dependent manner. In\norder to encompass all possibilities, we thus consider two extreme\nvalues: \\omegao{}$\\;$=$\\;$1.0 and \\omegao{}$\\;$=$\\;$0.1, with\n\\hubble{}$\\;$=$\\;$50$\\;$\\hubbleunits{}. In \\sec{binningsec} a\nlow-density Universe (\\omegao{}$\\;$=$\\;$0.1) with \\hubble{}$\\;$=$\\;$67\nis also considered. The reason for this last choice is that the age\nof a Universe with \\omegao{}$\\;$=$\\;$1.0, \\hubble{}$\\;$=$\\;$50, is\n$\\sim 13\\;$Gyr. A Universe with \\omegao{}$\\;$=$\\;$0.1,\n\\hubble{}$\\;$=$\\;$67 has the same age - hence the `absolute values' of\nthe luminosities in these high and low density cases can be\nrealistically compared. Recall the cosmological constant, $\\Lambda$,\nis assumed to be zero throughout. It is worth noting that the\nevidence from the Supernova Cosmology Project is currently in favour\nof a cosmology with $\\Omega_{\\rm M} = 0.3$ and $\\Omega_{\\Lambda}=0.7$\n(e.g. Perlmutter et al. 1999\\nocite{perl99}). This cosmology produces\nintermediate results to the two cosmologies considered here.\n\n\\subsection{Implication of the adopted template}\n\n\\begin{figure}\n\\centering\n\\epsfig{file=fig3.eps,height=9cm,angle=270}\n\\caption{The 850 \\micron{} flux density that would be observed for the starburst galaxy M82 (Hughes, Gear \\& Robson 1994) if it were placed at progressively higher redshifts, assuming the dust emission template adopted here ($\\beta=1.5$, T$=40$K). The solid line represents an \\omegao{}=$\\;$1.0 Universe; the dashed line represents an \\omegao{}=$\\;$0.1 Universe (\\hubble{}=$\\;$50$\\;$km$^{-1}$Mpc$^{-1}$).}\n\\label{m82beta15temp40}\n\\end{figure}\n\nIt is worth investigating what happens to the 850-\\micron{} flux\ndensity of M82 as it is placed at progressively higher redshifts,\nassuming the chosen dust template of $\\beta=1.5$ and ${\\rm T_{dust} =\n40\\;K}$.\n\n\\fig{m82beta15temp40} demonstrates that in an \\omegao{}$\\;$=$\\;$1.0\nUniverse, the 850-\\micron{} flux density is almost flat between $z=1$\nand $z=4$; the 850-\\micron{} flux density should effectively trace the\n850-\\micron{} luminosity.\n\nIn an \\omegao{}$\\;$=$\\;$0.1 Universe, on the other hand, SCUBA is less\nsensitive to $z=4$ galaxies than it is to those at $z=1$. Thus, the\nhigher redshift objects in the sample should be more luminous than\nthose at lower redshifts if they are detected at the same level.\n\nThe act of increasing $\\beta$ and ${\\rm T_{dust}}$ will effectively\nmake SCUBA more sensitive to submillimetre emission at $z=4$ than\n$z=1$. For a given set of fluxes, the luminosities at $z=4$ will be\nreduced relative to those at $z=1$ if $\\beta$ and ${\\rm T_{dust}}$ are\nincreased. Likewise, decreasing $\\beta$ and ${\\rm T_{dust}}$\nincreases the inferred 850-\\micron{} luminosities at $z=4$ relative to\nthose at $z=1$.\n\n\n\\subsection{\\boldmath \\luminsub{} for the radio galaxy sample}\n\n\\tab{lumin850values} gives the 850-\\micron{} luminosities and dust\nmasses for the radio galaxy sample. The optically thin, isothermal\ntemplate spectrum with $\\beta=1.5$ and ${\\rm T_{dust}=40K}$ has been\nassumed. The errors on the values of \\luminsub{} and ${\\rm M_{dust}}$\nhave been calculated using the errors in the flux density measurements\nonly; they do not account for the uncertainties in cosmology, $\\beta$,\nor ${\\rm T_{dust}}$.\n\nThe dust mass of each galaxy in the sample was calculated from the\n850-\\micron{} observation using:\n\n\\begin{equation}\nM_{dust} = \\frac{S_{obs}\\;D_L^2}{(1+z)\\;\\kappa_{\\nu_{rest}}\\;B_{\\nu_{rest}}(T_{dust})}\n\\label{dustmasseq}\n\\end{equation}\n\nwhere $S_{obs}$ is the observed flux-density, $\\nu_{rest}$ is the\ncorresponding rest-frame frequency, $D_L$ is the luminosity distance\nto the source, $\\kappa_{\\nu_{rest}}$ is the mass absorption\ncoefficient of the dust at $\\nu_{rest}$, and\n$B_{\\nu_{rest}}(T_{dust})$ is the intensity of a blackbody at\n$\\nu_{rest}$ assuming isothermal emission from dust grains at a\ntemperature $T_{dust}$. The mass absorption coefficient $\\kappa$ is\npoorly constrained, with published values of $\\kappa$(800\\micron{}):\n0.04$\\;$m$^2$kg$^{-1}$ \\cite{draineandlee}, 0.12$\\;$m$^2$kg$^{-1}$\n(Chini, Kr\\\"ugel, \\& Kreysa 1986\\nocite{ckk86}),\n0.15$\\;$m$^2$kg$^{-1}$ \\cite{hildebrand}, and 0.3$\\;$m$^2$kg$^{-1}$\n\\cite{mw89}. These estimates can be extrapolated to\nother wavelengths using $\\kappa\\propto\\lambda^{-\\beta}$ \\cite{ckk86}.\nThe intermediate value of\n$\\kappa$(800\\micron{})=0.15$\\;$m$^2$kg$^{-1}$ will be assumed here. A\ndifferent choice will not affect the relative dust masses of the\nsample, and can only alter the absolute dust masses by a factor of\n$\\sim 4$ at most \\cite{hdr97}.\n\n\\begin{table*}\n\\caption{Rest-frame 850-\\micron{} luminosities (\\luminsub{}) and dust masses (${\\rm M_{dust}}$) for the radio galaxy sample. Optically thin, isothermal greybody emission has been assumed, with $\\beta=1.5$ and ${\\rm T_{dust}=40K}$. Errors have been estimated using only the standard errors on the flux density measurements; 2$\\sigma$ upper limits are given for undetected (S/N$\\;<\\;$2) sources. \\luminsub{} and ${\\rm M_{dust}}$ have been calculated for three different cosmologies: \\omegao{}=1.0, \\hubble{}=50$\\;$\\hubbleunits{}; \\omegao{}=0.1, \\hubble{}=50$\\;$\\hubbleunits{}; \\omegao{}=0.1, \\hubble{}=67$\\;$\\hubbleunits{}. Note, column 3 indicates whether the source belongs to either or the subsets defined in \\sec{survsub}.}\n\\label{lumin850values}\n\\begin{tabular}{llclrrrrrrrr}\n\\hline\n&&&&\\multicolumn{2}{c}{\\omegao{}=1.0, \\hubble{}=50}&&\\multicolumn{2}{c}{\\omegao{}=0.1, \\hubble{}=50}&&\\multicolumn{2}{c}{\\omegao{}=0.1, \\hubble{}=67}\\\\\nSource&\\multicolumn{1}{c}{z}&Subset&&\\multicolumn{1}{c}{log$\\;$L$_{850\\mu m}$}&\\multicolumn{1}{c}{log$\\;{\\rm M_{dust}}$}&&\\multicolumn{1}{c}{log$\\;$L$_{850\\mu m}$}&\\multicolumn{1}{c}{log$\\;{\\rm M_{dust}}$}&&\\multicolumn{1}{c}{log$\\;$L$_{850\\mu m}$}&\\multicolumn{\n1}{c}{log$\\;{\\rm M_{dust}}$}\\\\\n&&&&\\multicolumn{1}{c}{(WHz$^{-1}$sr$^{-1}$)}&\\multicolumn{1}{c}{(${\\rm M_{\\odot}}$)}&&\\multicolumn{1}{c}{(WHz$^{-1}$sr$^{-1}$)}&\\multicolumn{1}{c}{(${\\rm M_{\\odot}}$)}&&\\multicolumn{1}{c}{(WHz$^{-1}$sr$^{-1}$)}&\\multicolumn{1}{c}{(${\\rm M_{\\odot}}$)}\\\\\n\\hline\n%%\n%% insert file elesea/data/raulsmodels/paper_luminmasses.tex\n%%\n3C277.2 & 0.766 & && $<$ 22.70 & $<$ 8.18 && $<$ 22.85 & $<$ 8.32 && $<$ 22.59 & $<$ 8.07\\\\\n3C340 & 0.775 & && $<$ 22.63 & $<$ 8.10 && $<$ 22.77 & $<$ 8.25 && $<$ 22.52 & $<$ 8.00\\\\\n3C265 & 0.811 & && $<$ 22.69 & $<$ 8.16 && $<$ 22.84 & $<$ 8.32 && $<$ 22.59 & $<$ 8.06\\\\\n3C217 & 0.897 & && $<$ 22.63 & $<$ 8.10 && $<$ 22.80 & $<$ 8.27 && $<$ 22.54 & $<$ 8.02\\\\\n3C356 & 1.079 & && $<$ 22.84 & $<$ 8.31 && $<$ 23.04 & $<$ 8.51 && $<$ 22.78 & $<$ 8.26\\\\\n3C368 & 1.132 & && 23.00 & 8.47 && 23.20 & 8.68 && 22.95 & 8.43\\\\\n3C267 & 1.144 & && $<$ 22.71 & $<$ 8.19 && $<$ 22.92 & $<$ 8.40 && $<$ 22.67 & $<$ 8.14\\\\\n3C324 & 1.206 & && $<$ 22.84 & $<$ 8.32 && $<$ 23.06 & $<$ 8.54 && $<$ 22.81 & $<$ 8.28\\\\\n3C266 & 1.272 & && $<$ 22.85 & $<$ 8.32 && $<$ 23.08 & $<$ 8.55 && $<$ 22.82 & $<$ 8.30\\\\\n53W069 & 1.432 & && $<$ 22.75 & $<$ 8.22 && $<$ 23.00 & $<$ 8.48 && $<$ 22.75 & $<$ 8.22\\\\\n4C13.66 & 1.45 &A,B && 22.85 & 8.32 && 23.11 & 8.58 && 22.85 & 8.33\\\\\n3C437 & 1.48 &A,B && $<$ 22.72 & $<$ 8.20 && $<$ 22.98 & $<$ 8.46 && $<$ 22.73 & $<$ 8.20\\\\\n3C241 & 1.617 &A,B && $<$ 22.79 & $<$ 8.26 && $<$ 23.07 & $<$ 8.55 && $<$ 22.82 & $<$ 8.29\\\\\n6C0919+38 & 1.65 & && $<$ 22.75 & $<$ 8.22 && $<$ 23.03 & $<$ 8.51 && $<$ 22.78 & $<$ 8.25\\\\\n3C470 & 1.653 &A,B && $<$ 23.21 & $<$ 8.69 && $<$ 23.50 & $<$ 8.98 && $<$ 23.25 & $<$ 8.72\\\\\n3C322 & 1.681 &A,B && $<$ 22.75 & $<$ 8.22 && $<$ 23.04 & $<$ 8.52 && $<$ 22.79 & $<$ 8.26\\\\\n6C1204+37 & 1.779 & && $<$ 22.81 & $<$ 8.29 && $<$ 23.12 & $<$ 8.60 && $<$ 22.87 & $<$ 8.34\\\\\n3C239 & 1.781 &A,B && $<$ 22.72 & $<$ 8.19 && $<$ 23.02 & $<$ 8.50 && $<$ 22.77 & $<$ 8.25\\\\\n3C294 & 1.786 &A,B && $<$ 22.61 & $<$ 8.09 && $<$ 22.92 & $<$ 8.39 && $<$ 22.66 & $<$ 8.14\\\\\n6C0820+36 & 1.86 & && $<$ 22.99 & $<$ 8.46 && $<$ 23.30 & $<$ 8.78 && $<$ 23.05 & $<$ 8.53\\\\\n6C0905+39 & 1.882 & && 22.96 & 8.43 && 23.28 & 8.75 && 23.02 & 8.50\\\\\n6C0901+35 & 1.904 & && $<$ 22.77 & $<$ 8.25 && $<$ 23.10 & $<$ 8.57 && $<$ 22.84 & $<$ 8.32\\\\\n5C7.269 & 2.218 & && $<$ 22.93 & $<$ 8.40 && $<$ 23.29 & $<$ 8.77 && $<$ 23.04 & $<$ 8.51\\\\\n4C40.36 & 2.265 &A,B && $<$ 22.83 & $<$ 8.31 && $<$ 23.20 & $<$ 8.68 && $<$ 22.95 & $<$ 8.42\\\\\nMG1744+18 & 2.28 &A,B && $<$ 22.70 & $<$ 8.18 && $<$ 23.08 & $<$ 8.55 && $<$ 22.82 & $<$ 8.30\\\\\nMG1248+11 & 2.322 & && $<$ 22.88 & $<$ 8.36 && $<$ 23.26 & $<$ 8.73 && $<$ 23.00 & $<$ 8.48\\\\\n4C48.48 & 2.343 &A,B && 23.06 & 8.54 && 23.44 & 8.92 && 23.19 & 8.66\\\\\n53W002 & 2.39 & && $<$ 22.89 & $<$ 8.36 && $<$ 23.27 & $<$ 8.75 && $<$ 23.02 & $<$ 8.49\\\\\n6C0930+38 & 2.395 & && $<$ 22.69 & $<$ 8.16 && $<$ 23.07 & $<$ 8.55 && $<$ 22.82 & $<$ 8.29\\\\\n6C1113+34 & 2.406 & && $<$ 22.74 & $<$ 8.22 && $<$ 23.13 & $<$ 8.60 && $<$ 22.87 & $<$ 8.35\\\\\nMG2305+03 & 2.457 &A,B && $<$ 22.71 & $<$ 8.18 && $<$ 23.10 & $<$ 8.57 && $<$ 22.84 & $<$ 8.32\\\\\n3C257 & 2.474 &A,B && $<$ 23.17 & $<$ 8.64 && $<$ 23.56 & $<$ 9.04 && $<$ 23.31 & $<$ 8.78\\\\\n4C23.56 & 2.483 &A,B && $<$ 22.94 & $<$ 8.42 && $<$ 23.34 & $<$ 8.81 && $<$ 23.08 & $<$ 8.56\\\\\n8C1039+68 & 2.53 &A,B && $<$ 22.68 & $<$ 8.15 && $<$ 23.08 & $<$ 8.55 && $<$ 22.82 & $<$ 8.30\\\\\nMG1016+058 & 2.765 &B && 22.73 & 8.20 && 23.16 & 8.63 && 22.90 & 8.38\\\\\n4C24.28 & 2.879 &A,B && 22.73 & 8.21 && 23.17 & 8.65 && 22.92 & 8.39\\\\\n4C28.58 & 2.891 & && 22.95 & 8.42 && 23.39 & 8.86 && 23.13 & 8.61\\\\\n6C1232+39 & 3.221 &A,B && 22.93 & 8.40 && 23.40 & 8.88 && 23.15 & 8.62\\\\\n6C1159+36 & 3.2 &A,B && $<$ 22.83 & $<$ 8.31 && $<$ 23.31 & $<$ 8.78 && $<$ 23.06 & $<$ 8.53\\\\\nTX1243+036 & 3.57 &A && $<$ 22.97 & $<$ 8.45 && $<$ 23.48 & $<$ 8.95 && $<$ 23.22 & $<$ 8.70\\\\\nMG2141+192 & 3.592 & && 22.99 & 8.47 && 23.50 & 8.98 && 23.25 & 8.72\\\\\n6C0032+412 & 3.66 &A,B && 22.71 & 8.18 && 23.22 & 8.70 && 22.97 & 8.45\\\\\n4C60.07 & 3.788 & && 23.56 & 9.03 && 24.08 & 9.56 && 23.83 & 9.31\\\\\n4C41.17 & 3.792 & && 23.40 & 8.88 && 23.93 & 9.41 && 23.68 & 9.16\\\\\n8C1435+635 & 4.25 &A && 23.20 & 8.68 && 23.77 & 9.25 && 23.52 & 8.99\\\\\n6C0140+326 & 4.41 &A,B && 22.83 & 8.30 && 23.41 & 8.89 && 23.16 & 8.63\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\nIn \\Fig{sampledim}, the 850-\\micron{} flux density is plotted against\nredshift for the radio galaxy sample. Plots of \\luminsub{} vs. $z$ in\n\\omegao$\\;$=$\\;$1.0 and \\omegao$\\;$=$\\;$0.1 Universes are also shown.\nAs expected from \\fig{m82beta15temp40}, in the \\omegao$\\;$=$\\;$1.0\ncase the flux density traces the luminosity between $z=1$ and $z=4$ ,\nand the two plots look the same. For \\omegao$\\;$=$\\;$0.1,\nthe luminosity of the $z \\sim 4$ galaxies is higher relative to those\nat $z \\sim 1$ , as SCUBA is less sensitive to the high-redshift\nobjects.\n\nThe small dynamic range in the measured values of \\luminsub{} for this\nstudy are limited by the sensitivity of SCUBA and the characteristic\ndust mass in high-redshift objects. Note the detections of\n\\luminsub{} appear at roughly the same level as the \\luminsub{} upper\nlimits; most of the galaxies in the sample have been observed to the\nsame depth in 850-\\micron{} {\\em luminosity}. Coupled with the fact\nthat the upper limits are clustered at the low-redshift end of the\nsample, this indicates that the high-redshift radio galaxies are\nintrinsically brighter in the submillimetre than the lower-redshift\nradio galaxies. This evidence for evolution of the radio galaxy\npopulation with redshift will now be analysed in detail.\n\n\\begin{figure}\n\\centering\n\\epsfig{file=fig4.eps,height=15cm}\n\\caption{Scatter plots of 850-\\micron{} flux density and (rest-frame)\nluminosity against redshift for the radio galaxy sample. \\luminsub{}\nhas been calculated assuming $\\beta=1.5$ and ${\\rm T_{dust}=40K}$, and\nis shown for both $\\Omega_{\\circ}=1.0$ and $\\Omega_{\\circ}=0.1$\n(\\hubble{} is assumed to be 50$\\;$\\hubbleunits{}).}\n\\label{sampledim}\n\\end{figure}\n\n\n\\section{Evidence For evolution}\n\\label{evolstats}\n\n\\subsection{Survival analysis: correlations between radio properties, submillimetre properties, and redshift}\n\\label{survsub}\n\nA logical approach to finding evidence which either supports or\nrejects the evolution scenario is to run correlation tests between the\nradio properties, submillimetre properties, and redshifts of the\nsample. For example, a correlation between \\luminsub{} and redshift,\nin the absence of a correlation between \\luminsub{} and \\radiopower{},\nwill imply that radio galaxies undergo cosmological\nevolution of their submillimetre emission. Conversely, a significant\ncorrelation between \\luminsub{} and \\radiopower{} in the absence of a\ncorrelation between \\luminsub{} and redshift, would indicate that the\nsubmillimetre properties of radio galaxies are more closely tied to\nthe radio properties of the galaxy (perhaps, for example, via host mass) \nthan to cosmological epoch.\n\nThe obvious correlations to consider are between \\luminsub{},\n\\radiopower{}, and $z$. It is also instructive to investigate whether\n\\radiopower{} correlates with D$_{linear}$ (the linear size of the\nradio source), and whether the radio spectral index \\alpharadio{}\ncorrelates with either \\luminsub{}, \\radiopower{}, or $z$.\n\nAs mentioned previously, for radio sources selected from flux-limited\nsamples, the 151-MHz radio luminosity should be a good indicator of\nthe intrinsic power $Q$ of the radio jet. The size of a radio source\ndepends on its age, the medium it is expanding into, and the jet\npower. Again, considering sources from flux-limited samples, Willott\net al. \\shortcite{wrbl99} showed that the dependence of D$_{linear}$\non jet power is very weak; D$_{linear}$ correlates most strongly with\nthe age of the radio source. Although radio luminosities are expected\nto decline throughout the lifetime of radio sources (Kaiser,\nDennett-Thorpe \\& Alexander 1997\\nocite{kda97}; Blundell et\nal. 1999\\nocite{brw99}; Blundell \\& Rawlings 1999\\nocite{bs99}),\nselection effects conspire to ensure a very weak anti-correlation of\nradio luminosity with D$_{linear}$ for sources selected from a number\nof separate flux-limited samples \\cite{brw99}. Although our sample of\nSCUBA targets is not purely a combination of flux-limited samples, it\nis dominated by 3C/3CRR and 6CE targets so no strong \\radiopower{}-D\nlinks are expected.\n\nThe criterion that \\alpharadio{} is large is often used to identify\nhigh redshift sources in large radio surveys. This selection is based\non the empirical correlation observed between \\alpharadio{} and radio\nluminosity (e.g. Veron, Veron \\& Witzel 1972\\nocite{vvw72}). In a flux-limited\nsurvey, high values of \\alpharadio{} will often correspond to a large\nintrinsic luminosity and hence to a high redshift. \n\nHowever, it is possible to envisage models in which \\alpharadio{} is\nrelated closely to star-formation activity (e.g. Lilly\n1989\\nocite{lilly89}). This is relevant to the work presented here,\nas several of the high-redshift galaxies in the sample were originally\nidentified in these ultra-steep spectrum searches (e.g. Chambers,\nMiley \\& van Breugel 1988, 1990; Chambers et\nal. 1996\\nocite{cmvb88,cmvb90,cmvb96}; Stern et\nal. 1999\\nocite{sds99}). Thus, if \\luminsub{} appears correlated with\nredshift, it could be a manifestation of how the sources were selected\nin the first place, a possibility which can be tested by investigating\nwhether a correlation exists between \\luminsub{} and \\alpharadio{}.\nNote, for the correlation analysis, \\alpharadio{} was calculated at\n151$\\;$MHz.\n\n\\begin{table*}\n\\caption{Results of the survival analysis correlation tests applied to the entire sample. The significance ($P$) is the probability of the null hypothesis ({\\em no correlation}) being true. If all three tests yield $P\\leq 5$ per cent, the variables are taken to be correlated. If only some of the tests yield $P\\leq 5$ per cent, evidence for a correlation is taken to be uncertain.}\n\\label{correlationsALL}\n\\begin{tabular}{|c|cc|c|rrr|c|}\n\\hline\nCosmology&\\multicolumn{2}{|c|}{Variable}&Percentage of&\\multicolumn{3}{c|}{Significance ($P$)}&Correlation\\\\\n&Dependent&Independent&Data Censored &\\multicolumn{1}{c}{Cox}&\\multicolumn{1}{c}{Kendall}&\\multicolumn{1}{c|}{Spearman}&Present?\\\\\n\\hline\n-- &S$_{850\\mu m}$ &z &70$\\%$ &0.00$\\%$ &0.02$\\%$ &0.01$\\%$ &YES\\\\\n\\hline\n\\multirow{7}{15mm}{$\\Omega_{\\circ}=1.0$}\n &D$_{linear}$ &log(P$_{151MHz}$) &4$\\%$ &22.48$\\%$ &82.69$\\%$ &71.17$\\%$ &NO\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(P$_{151MHz}$) &z &0$\\%$ &0.01$\\%$ &0.03$\\%$ &0.07$\\%$ &YES\\\\\n &log(L$_{850\\mu m}$) &log(P$_{151MHz}$) &70$\\%$ &2.65$\\%$ &0.21$\\%$ &0.64$\\%$ &YES\\\\\n &log(L$_{850\\mu m}$) &z &70$\\%$ &0.00$\\%$ &0.19$\\%$ &0.08$\\%$ &YES\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(L$_{850\\mu m}$) &$\\alpha_{radio}$ &70$\\%$ &0.31$\\%$ &0.36$\\%$ &1.73$\\%$ &YES\\\\\n &$\\alpha_{radio}$ &log(P$_{151MHz}$) &0$\\%$ &0.64$\\%$ &1.00$\\%$ &1.36$\\%$ &YES\\\\\n &$\\alpha_{radio}$ &z &0$\\%$ &4.18$\\%$ &13.94$\\%$ &10.50$\\%$ &MAYBE\\\\\n\\hline\n\\multirow{7}{15mm}{$\\Omega_{\\circ}=0.1$}\n &D$_{linear}$ &log(P$_{151MHz}$) &4$\\%$ &32.29$\\%$ &67.59$\\%$ &50.22$\\%$ &NO\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(P$_{151MHz}$) &z &0$\\%$ &0.00$\\%$ &0.00$\\%$ &0.00$\\%$ &YES\\\\\n &log(L$_{850\\mu m}$) &log(P$_{151MHz}$) &70$\\%$ &0.53$\\%$ &0.01$\\%$ &0.08$\\%$ &YES\\\\\n &log(L$_{850\\mu m}$) &z &70$\\%$ &0.00$\\%$ &0.00$\\%$ &0.00$\\%$ &YES\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(L$_{850\\mu m}$) &$\\alpha_{radio}$ &70$\\%$ &0.18$\\%$ &0.67$\\%$ &1.88$\\%$ &YES\\\\\n &$\\alpha_{radio}$ &log(P$_{151MHz}$) &0$\\%$ &0.44$\\%$ &1.61$\\%$ &1.47$\\%$ &YES\\\\\n &$\\alpha_{radio}$ &z &0$\\%$ &4.18$\\%$ &13.94$\\%$ &10.50$\\%$ &MAYBE\\\\\n\\hline\n\\multicolumn{8}{|c|}{Total Number of Galaxies: 46}\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\\subsubsection{Survival analysis}\n\nThe submillimetre dataset for the radio galaxy sample contains a large\nnumber of upper limits, or {\\em censored data}. Running correlation\ntests on the dataset is not a trivial matter, as standard statistical\ntheory is not equipped to handle this kind of information.\n\nStatisticians have extensively studied the problem of censored\ndatasets, and a means for successfully handling them has been known\nfor decades. It is called {\\em survival analysis} and it allows\ncensored data samples to be treated in a meaningful manner with\nminimal loss of information - the values of the upper/lower limits are\nformally taken into account when calculating correlation coefficients\nand other test statistics.\n\nThe application of survival analysis to astronomical data is outlined\nin two papers: Feigelson \\& Nelson 1985\\nocite{fn85} (Paper I) and\nIsobe, Feigelson, \\& Nelson 1986\\nocite{ifn86} (Paper II). Paper I\ndeals with univariate problems. Paper II considers bivariate\ntechniques to characterise the correlation and line-regression between\ntwo variables. The test statistics described in these papers are\navailable in the software package ASURV Rev. 1.1 (Isobe \\& Feigelson\n1990\\nocite{if90}; LaValley, Isobe \\& Feigelson 1992\\nocite{lif92}).\n\nASURV contains three different correlation tests - Cox's Proportional\nHazard Model, Generalized Kendall's Tau, and Generalized Spearman's\nRho. All three methods test the null hypothesis that {\\em no\ncorrelation is present}. The ASURV routines compute the probability\nof the null hypothesis being true, $P$, also referred to as the\nsignificance of the correlation. The convention to be adopted here is\nthat X and Y are correlated if $P\\leq 5$ per cent. A correlation will\nbe treated as firm if all three tests yield $P\\leq 5$ per cent; the\nexistence of a correlation will be treated as possible, but\nunconfirmed, if only some of the tests indicate $P\\leq 5$ per cent.\n\nNote, the Cox test only allows censoring in the dependent variable;\nthe Kendall and Spearman tests allow censoring in both the dependent\nand the independent variables. The Spearman technique has not been\nproperly tested yet. It is known to give misleading results if\n$N<30$.\n\n\\begin{table*}\n\\caption{Results of the survival analysis correlation tests applied to Subset A. The significance ($P$) is the probability of the null hypothesis ({\\em no correlation}) being true. The generalized Spearman test has not been applied as it breaks down if the sample size is less than 30. If both Cox and Kendall yield $P\\leq 5$ per cent, the variables are taken to be correlated. If only one of them yields $P\\leq 5$ per cent, evidence for a correlation is taken to be uncertain.}\n\\label{correlationsluminbandA}\n\\begin{tabular}{|c|cc|c|rrc|c|}\n\\hline\nCosmology&\\multicolumn{2}{|c|}{Variable}&Percentage of&\\multicolumn{3}{c|}{Significance ($P$)}&Correlation\\\\\n&Dependent&Independent&Data Censored&\\multicolumn{1}{c}{Cox}&\\multicolumn{1}{c}{Kendall}&\\multicolumn{1}{c|}{Spearman}&Present?\\\\\n\\hline\n-- &S$_{850\\mu m}$ &z &67$\\%$ &0.29$\\%$ &4.05$\\%$ &-- &YES\\\\\n\\hline\n\\multirow{7}{15mm}{$\\Omega_{\\circ}=1.0$}\n &D$_{linear}$ &log(P$_{151MHz}$) &0$\\%$ &63.20$\\%$ &34.86$\\%$ &-- &NO\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(P$_{151MHz}$) &z &0$\\%$ &74.43$\\%$ &50.65$\\%$ &-- &NO\\\\\n &log(L$_{850\\mu m}$) &log(P$_{151MHz}$) &67$\\%$ &50.52$\\%$ &77.71$\\%$ &-- &NO\\\\\n &log(L$_{850\\mu m}$) &z &67$\\%$ &1.91$\\%$ &15.70$\\%$ &-- &MAYBE\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(L$_{850\\mu m}$) &$\\alpha_{radio}$ &67$\\%$ &70.37$\\%$ &85.01$\\%$ &-- &NO\\\\\n &$\\alpha_{radio}$ &log(P$_{151MHz}$) &0$\\%$ &21.03$\\%$ &16.40$\\%$ &-- &NO\\\\\n &$\\alpha_{radio}$ &z &0$\\%$ &21.22$\\%$ &18.32$\\%$ &-- &NO\\\\\n\\hline\n\\multicolumn{8}{|c|}{Total Number of Galaxies: 21}\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\caption{Results of the survival analysis correlation tests applied to Subset B. The significance ($P$) is the probability of the null hypothesis ({\\em no correlation}) being true. The generalized Spearman test has not been applied as it breaks down if the sample size is less than 30. If both Cox and Kendall yield $P\\leq 5$ per cent, the variables are taken to be correlated. If only one of them yields $P\\leq 5$ per cent, evidence for a correlation is taken to be uncertain.}\n\\label{correlationsluminbandB}\n\\begin{tabular}{|c|cc|c|rrc|c|}\n\\hline\nCosmology&\\multicolumn{2}{|c|}{Variable}&Percentage of&\\multicolumn{3}{c|}{Significance ($P$)}&Correlation\\\\\n&Dependent&Independent&Data Censored&\\multicolumn{1}{c}{Cox}&\\multicolumn{1}{c}{Kendall}&\\multicolumn{1}{c|}{Spearman}&Present?\\\\\n\\hline\n-- &S$_{850\\mu m}$ &z &65$\\%$ &0.81$\\%$ &5.87$\\%$ &-- &MAYBE\\\\\n\\hline\n\\multirow{7}{15mm}{$\\Omega_{\\circ}=0.1$}\n &D$_{linear}$ &log(P$_{151MHz}$) &0$\\%$ &84.35$\\%$ &49.54$\\%$ &-- &NO\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(P$_{151MHz}$) &z &0$\\%$ &34.86$\\%$ &27.00$\\%$ &-- &NO\\\\\n &log(L$_{850\\mu m}$) &log(P$_{151MHz}$) &65$\\%$ &79.95$\\%$ &96.22$\\%$ &-- &NO\\\\\n &log(L$_{850\\mu m}$) &z &65$\\%$ &0.13$\\%$ &2.01$\\%$ &-- &YES\\\\\n\\dottedline{4}(55,10)(409,10)\n &log(L$_{850\\mu m}$) &$\\alpha_{radio}$ &65$\\%$ &64.95$\\%$ &92.43$\\%$ &-- &NO\\\\\n &$\\alpha_{radio}$ &log(P$_{151MHz}$) &0$\\%$ &0.39$\\%$ &2.49$\\%$ &-- &YES\\\\\n &$\\alpha_{radio}$ &z &0$\\%$ &20.64$\\%$ &41.66$\\%$ &-- &NO\\\\\n\\hline\n\\multicolumn{8}{|c|}{Total Number of Galaxies: 20}\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\\begin{figure*}\n\\epsfig{file=fig5.eps,height=19cm}\n\\caption{Scatter plots corresponding to the correlations investigated for Subset A.}\n\\label{scatterplotsluminbandA}\n\\end{figure*}\n\n\n\\subsubsection{Correlations for the entire dataset}\n\nInitially, the entire sample was used to run the correlation tests.\nThe results of this analysis are given in \\tab{correlationsALL}.\n\n\\fig{sampledim} predicts that the 850-\\micron{} flux density will\nmirror the 850-\\micron{} luminosity if \\omegao{}=1.0. This is\nreflected by the S$_{\\rm 850\\mu m}$-z and \\luminsub{}-z correlations\nhaving similar significances. As expected, decreasing \\omegao{} to\n0.1 increases the strength of the \\luminsub{}-z correlation.\n\nThe absence of a correlation between \\radiopower{} and D$_{linear}$ is\nindicative of a combined sample in which, as discussed by Willott et\nal. \\shortcite{wrbl99}, \\radiopower{} can be taken to crudely track\njet power, and D$_{linear}$ to crudely track source age.\n\nIt is troublesome, but not unexpected, \nthat \\luminsub{}, \\radiopower{}, and $z$ are all\ncorrelated with each other. The strength of these correlations is\ngreater in a low-\\omegao{} Universe. The strong correlation between\n\\radiopower{} and $z$ could be responsible for either the\n\\luminsub{}-$z$ correlation if \\luminsub{} actually correlates with\n\\radiopower{}, or for the \\luminsub{}-\\radiopower{} correlation if\n\\luminsub{} actually correlates with $z$. Thus, if the effects of\ncosmological evolution and radio power are to be disentangled, the\nentire dataset cannot be used.\n\n\\luminsub{} also appears correlated with \\alpharadio{}. However, this may\nbe a remnant of the fact that \\alpharadio{} and \\luminsub{} are both\ncorrelated with \\radiopower{} and $z$. Again, if the entire dataset\nis used, discriminating between different effects is difficult.\n\nIt was decided to choose a strip in the P-$z$ plane that covered a large\nrange of redshifts in a single narrow band of radio power. In the absence\nof a correlation between \\radiopower{} and $z$, it could then be\ndetermined whether \\luminsub{} truly correlates with $z$ or\n\\radiopower{}. The strip was chosen to satisfy the following\ncriteria:\n\\begin{enumerate}\n\\item To cover the largest range in redshift possible whilst still maintaining even coverage of radio power. This automatically imposed the restriction that $z>1.4$ due to the 3C survey having a lack of low-redshift, very high radio-power sources.\n\\item To contain at least 20 objects to satisfy the requirements of the survival analysis techniques.\n\\end{enumerate}\n\nInitially a strip was chosen using the P-$z$ plane for \\omegao{}=1.0,\nhereafter referred to as Subset A. A different but similar strip was\nchosen from the P-$z$ plane for \\omegao{}=0.1. It will be referred to\nas Subset B. The sources included in each subset are listed in\n\\tab{lumin850values}.\n\nIt is important to note that there is nothing special about the\nstrips. They have merely been chosen to help disentangle the various\ninfluences affecting \\luminsub{}. The results found for the subsets\nshould apply to the entire sample and to radio galaxies in general.\n\n\\subsubsection{Correlations for Subset A}\n\nSubset A, shown in \\fig{pzom_1_01}, contains 21 radio galaxies and is\ndefined by $z>1.4$ and ${\\rm 27.9<log(P_{151MHz})<28.5}$ for\n\\omegao{}=1.0, \\hubble{}$\\;$=$\\;$50$\\;$\\hubbleunits{}.\n\n\\tab{correlationsluminbandA} contains the results of the survival\nanalysis applied to Subset A, and \\fig{scatterplotsluminbandA}\ncontains the corresponding scatter plots.\n\nFor \\omegao{}=1.0, the existence of a correlation between \\luminsub{}\nand redshift is hinted at, but is not confirmed by all of the\ncorrelation tests. The important point, however, is that \\luminsub{}\ndefinitely fails to correlate with \\radiopower{} and \\alpharadio{}.\nThe probability of `no correlation' between \\luminsub{} and $z$ is\nmuch lower than for \\luminsub{}-\\radiopower{} or\n\\luminsub{}-\\alpharadio{}.\n\nSurvival analysis could also be applied to Subset A for the\n\\omegao{}=0.1 case. However, for Subset A, \\radiopower{} and $z$ are\ncorrelated if \\omegao{}=0.1. This is precisely what was trying to be\navoided by selecting the subset in the first place. Thus, a separate\nsubsample will need to be chosen to study the statistics for a\nlow-\\omegao{} Universe.\n\n\n\\subsubsection{Correlations for Subset B}\n\n\\begin{figure*}\n\\epsfig{file=fig6.eps,height=19cm}\n\\caption{Scatter plots corresponding to the correlations investigated for Subset B.}\n\\label{scatterplotsluminbandB}\n\\end{figure*}\n\nSubset B, shown in \\fig{pzom_1_01}, contains 20 radio galaxies and is\ndefined by $z>1.4$ and ${\\rm 28.2<log(P_{151MHz})<28.9}$ for\n\\omegao{}=0.1, \\hubble{}$\\;$=$\\;$50$\\;$\\hubbleunits{}.\n\n\\tab{correlationsluminbandB} contains the results of the survival\nanalysis applied to Subset B, and \\fig{scatterplotsluminbandB}\ncontains the corresponding scatter plots.\n\nThe results of the survival analysis are more clear cut in a\nlow-\\omegao{} Universe. The suspected correlation between \\luminsub{}\nand $z$ is confirmed as significant by all of the correlation tests.\nNeither $z$ nor \\luminsub{} correlates with \\radiopower{}. This\nindicates that the important correlation for \\luminsub{} is most\nlikely to be with redshift, {\\em not} radio luminosity.\n\nFor Subset B, \\luminsub{} does not correlate with \\alpharadio{} or\n\\radiopower{}. However, \\alpharadio{} and \\radiopower{} correlate\nwith each other. This implies that the correlation between\n\\alpharadio{} and \\luminsub{} seen for the entire dataset is an\nartifact of their mutual correlation with \\radiopower{}.\n\n\\subsubsection{Considering the dust emission template}\n\nThe analysis described so far assumes a template for dust emission\nwith $\\beta=1.5$ and ${\\rm T_{dust} = 40K}$. However, what if this\ntemplate was incorrect? Would the results of the analysis be affected\nif the true values of $\\beta$ and ${\\rm T_{dust}}$ were different?\n\nIt has already been observed that increasing $\\beta$ and ${\\rm\nT_{dust}}$ makes SCUBA more sensitive to submillimetre emission at\n$z=4$ than it is at $z=1$. Given the measured fluxes, the\n850-\\micron{} luminosities at $z=3-4$ will be reduced relative to\nthose at $z=1-2$ if $\\beta$ and ${\\rm T_{dust}}$ are increased. As a\nresult, correlations between \\luminsub{} and $z$ should be weakened.\nLikewise, decreasing $\\beta$ and ${\\rm T_{dust}}$ should strengthen\n\\luminsub{}-$z$ correlations.\n\nChanging $\\beta$ and ${\\rm T_{dust}}$ will not alter \\luminsub{} in\na radio-power or radio-spectral index dependent manner. If the dust\ntemplate is wrong, the correlations between \\luminsub{} and\n\\radiopower{}/\\alpharadio{} should not be affected in a systematic\nway.\n\nIn order to investigate this fully, the survival analysis was re-run\nusing several different combinations of $\\beta$ and ${\\rm T_{dust}}$.\nTo examine the effect of changing $\\beta$, ${\\rm T_{dust}}$ was held\nat 40$\\;$K while $\\beta$ was increased to 2.0, and decreased to\n1.0. Likewise, $\\beta$ was held at 1.5 while ${\\rm T_{dust}}$\nwas changed to 100$\\;$K, 70$\\;$K, and 20$\\;$K.\n\nThe observed effects on the results of the correlation tests can be\nsummarised as follows:\n\\begin{enumerate}\n\\item \\luminsub{}-z: Increasing $\\beta$ or ${\\rm T_{dust}}$ destroys the marginal correlation between \\luminsub{} and $z$ for Subset A. For the entire dataset (both cosmologies) and for Subset B, the correlation is evident regardless of the values of $\\beta$ and ${\\rm T_{dust}}$. Decreasing $\\beta$ and ${\\rm T_{dust}}$ confirms the possible \\luminsub{}-z correlation for Subset A.\n\\item \\luminsub{}-\\radiopower{}: Changing $\\beta$ and ${\\rm T_{dust}}$ does not destroy the \\luminsub{}-\\radiopower{} correlation for the entire dataset, nor does it create a correlation between \\luminsub{} and \\radiopower{} for Subsets A or B.\n\\item \\luminsub{}-\\alpharadio{}: Changing $\\beta$ and ${\\rm T_{dust}}$ does not destroy the \\luminsub{}-\\alpharadio{} correlation for the entire dataset, nor does it create a correlation between \\luminsub{} and \\alpharadio{} for Subsets A or B.\n\\end{enumerate}\n\n\\subsubsection{Summary of correlation analysis}\n\n\\begin{table}\n\\centering\n\\caption{Summary of the \\luminsub{}-$z$ correlation analysis for the two cosmologies considered and for reasonable values of $\\beta$. \\ding{51} indicates the survival analysis found a correlation between \\luminsub{} and $z$, \\ding{55} indicates the survival analysis found no such correlation, and {\\bf ?} indicates that some, but not all, of the correlation tests found a correlation to be present.}\n\\label{correlationsummary}\n\\begin{tabular}{ccccc}\n\\hline\n&\\multicolumn{2}{|c|}{$\\Omega_{\\circ}=1.0$}&\\multicolumn{2}{c|}{$\\Omega_{\\circ}=0.1$}\\\\\n &Entire &Subset &Entire &Subset\\\\\n &Dataset &A &Dataset &B\\\\\n\\hline \n$\\beta=1.0$ &\\ding{51} &\\ding{51} &\\ding{51} &\\ding{51}\\\\\n$\\beta=1.5$ &\\ding{51} &{\\bf ?} &\\ding{51} &\\ding{51}\\\\\n$\\beta=2.0$ &\\ding{51} &\\ding{55} &\\ding{51} &\\ding{51}\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nFor Subsets A and B, survival analysis finds \\luminsub{} to be\ncorrelated with redshift unless the highest values of $\\beta$ and\n\\omegao{} are chosen (\\tab{correlationsummary}). Furthermore,\n\\luminsub{} is not found to correlate with either \\radiopower{} or\n\\alpharadio{} for any of the tested cosmologies or dust emission\ntemplates. Even for high values of $\\beta$ and \\omegao{}, there is\nevidence that \\luminsub{} is dependent on redshift instead of on the\nradio properties of the source: the probability of `no correlation' is\nsubstantially smaller for \\luminsub{} and $z$ than for \\luminsub{} and\n\\radiopower{} or \\alpharadio{}.\n\nThis all suggests that the correlation between \\luminsub{} and\nredshift for the entire dataset is real, and is not an artifact of\ntheir mutual correlation to \\radiopower{} (although this may affect\nthe strength of the observed \\luminsub{}-$z$ correlation).\n\nGiven the low detection threshold adopted in this paper, it is worth\nre-iterating that a detection threshold of S/N$>3$ (with upper limits\ntaken at the 3$\\sigma$ level) yields the same result.\n\n\\subsection{Further investigations of the relationship between \\boldmath L$_{850\\mu m}$ \\unboldmath and redshift}\n\\label{binningsec}\n\nSCUBA has had more success detecting the higher-redshift galaxies in\nthe sample. This is shown in \\tab{detectionrate}, which display\nthe 850-\\micron{} detection rate for $z\\;<2.5$ and $z\\;>2.5$. At\n850$\\;$\\micron{}, SCUBA is almost equally sensitive to all of the\ngalaxies in the sample. The striking result that almost none of the\ngalaxies are detected if $z<2.5$, whereas almost all of them are\ndetected if $z>2.5$, suggests a trend of increasing submillimetre\nluminosity with redshift. Note, the detection rates observed for\nSubset A and Subset B closely mirror those found for the entire\nsample, providing further evidence for the cosmological evolution of\nthe radio galaxy population irrespective of the radio source.\n\n\\begin{table}\n\\centering\n\\caption{Detection rate of radio galaxies at 850 \\micron{} for $z\\;<2.5$ and $z\\;>2.5$. For each dataset and redshift interval, the number of galaxies present is given in parenthesis. Note, 6C1159+36 may be at a lower redshift than previously published, which would increase the detection rate at $z\\;>2.5$.}\n\\label{detectionrate}\n\\begin{tabular}{llll}\n\\hline\n &&\\multicolumn{2}{c}{Detection Rate}\\\\\nDataset &&$z\\;<2.5$ &$z\\;>2.5$\\\\\n\\hline\nSubset A &&15$\\%$ (13) &63$\\%$ (8)\\\\\nSubset B &&15$\\%$ (13) &71$\\%$ (7)\\\\\nAll Data &&12$\\%$ (33) &77$\\%$ (13)\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nThere is an alternative to survival analysis for investigating the\nrelationship between \\luminsub{} and $z$. Instead of running a\ncorrelation test which only takes the strength of the detection or\nupper-limit into account, the 850-\\micron{} luminosities can be binned\nin redshift to calculate the typical submillimetre luminosity as a\nfunction of redshift. This method considers both the signal and error\nfor each source and is independent of the precise choice of detection\nthreshold. Note, for the following discussion, \\hubble{} has been\ntaken to be 67$\\;$\\hubbleunits{} for \\omegao{}$\\;$=$\\;$0.1; this\nshould give a comparable measure of luminosity to the\n\\omegao{}$\\;$=$\\;$1.0, \\hubble{}$\\;$=$\\;$50$\\;$\\hubbleunits{}\ncosmology.\n\n\\begin{figure*}\n\\epsfig{file=fig7a.eps,height=9.5cm,angle=270}\\vspace*{11pt}\n\\epsfig{file=fig7b.eps,height=9.5cm,angle=270}\n\\caption{Weighted-mean 850-\\micron{} luminosity, $<$\\luminsub{}$>$,\nbinned in redshift. $<$\\luminsub{}$>$ has been plotted at the\nmidpoint of each bin, which at most varies by 0.2 from the average\nredshift of all the objects in the bin. The error bars only represent\nthe statistical errors on the observations; they do not account for\nuncertainties in either the cosmology or the dust template. Curves of\nthe form ${\\rm L = a (1+z)^b}$ have been fit to the data using\nnonlinear least-squares fitting, and the horizontal line indicates the\norigin (or \\luminsub{} = 0.0). The upper plot displays an\n\\omegao{}$\\;$=$\\;$1.0, \\hubble{}$\\;$=$\\;$50$\\;$\\hubbleunits{}\ncosmology, and $<$\\luminsub{}$>$ is plotted for both the entire\ndataset and Subset A (diamond symbols). The solid curve is the\nbest-fit for the entire dataset, with ${\\rm a = 0.010 \\pm 0.008}$,\n${\\rm b = 4.58 \\pm 0.52}$, $\\chi^2 = 1.23$. The dashed curve is the\nbest-fit for Subset A, with ${\\rm a = 0.029 \\pm 0.034}$, ${\\rm b =\n3.67 \\pm 0.76}$, $\\chi^2 = 0.29$. Similarly, the lower plot displays\nthe entire dataset and Subset B (diamond symbols) for an\n\\omegao{}$\\;$=$\\;$0.1, \\hubble{}$\\;$=$\\;$67$\\;$\\hubbleunits{}\ncosmology. The solid curve is the best-fit for the entire dataset,\nwith ${\\rm a = 0.004 \\pm 0.003}$, ${\\rm b = 5.52 \\pm 0.53}$, $\\chi^2 =\n1.58$. The dashed curve is the best-fit for Subset B, with ${\\rm a =\n0.070 \\pm 0.099}$, ${\\rm b = 3.23 \\pm 1.01}$, $\\chi^2 = 0.32$.\nSubsets A and B do not contain any objects in the $z=1$ bin.}\n\\label{ombinning}\n\\end{figure*}\n\nFour redshift bins have been chosen which are adequately sampled by\nthe dataset and are centered as near as possible on $z =\n1,\\,2,\\,3,\\,4$: $0.45\\leq z <1.45$, $1.45\\leq z <2.45$, $2.45\\leq z\n<3.45$, and $3.45\\leq z <4.45$. The weighted-mean \\cite{bevington}\n850-\\micron{} luminosity, $<$\\luminsub{}$>$, is plotted in\n\\fig{ombinning} for the entire dataset and Subset A assuming an\n\\omegao{}$\\;$=$\\;$1.0 cosmology and for the entire dataset and Subset\nB assuming an \\omegao{}$\\;$=$\\;$0.1 cosmology. Curves of the form\n${\\rm L = a (1+z)^b}$ have been fit to $<$\\luminsub{}$>$ in order to\nhelp quantify the strength of the 850-\\micron{} luminosity evolution.\n\nThere are several important points to be made from \\fig{ombinning}:\n\\begin{enumerate}\n\\item For the entire dataset, there are clear steps in $<$\\luminsub{}$>$ between each redshift bin. If this trend is characterised by the function ${\\rm L = a (1+z)^b}$, nonlinear least-squares fitting indicates that ${\\rm b = 4.58 \\pm 0.52}$ if \\omegao{}=1.0, and ${\\rm b = 5.52 \\pm 0.53}$ for \\omegao{}=0.1.\n\\item For Subset A, there are clear steps in $<$\\luminsub{}$>$ between the $z=2$ and $z=3$ bins, and between the $z=3$ and $z=4$ bins. If this trend is characterised by the function ${\\rm L = a (1+z)^b}$, nonlinear least-squares fitting indicates that ${\\rm b = 3.67 \\pm 0.76}$. Subset A does not contain any objects in the $z=1$ bin.\n\\item For Subset B, there is a clear step in $<$\\luminsub{}$>$ between the $z=2$ and $z=3$ bins. There may also be an increase in $<$\\luminsub{}$>$ from $z=3$ to $z=4$, although the error bars do not preclude $<$\\luminsub{}$>$ flattening off between these two redshifts. If the model ${\\rm L = a (1+z)^b}$ is assumed, nonlinear least-squares fitting indicates that ${\\rm b = 3.23 \\pm 1.01}$. Subset B does not contain any objects in the $z=1$ bin.\n\\item For Subsets A and B, the correlation analysis has revealed that \\luminsub{} does not depend on the radio properties of the source. These subsamples are not special, they have been chosen to cover an even spread in radio luminosity over a range of redshifts; their selection has been dictated only by the deficiencies of the original radio surveys. Thus, the evolution of $<$\\luminsub{}$>$ with redshift observed for these two subsamples, which is consistent with ${\\rm <L>\\sim(1+z)^3}$, should apply to all radio galaxies. This is supported by the fact that for the $z=2$ and $z=3$ bins, the value of $<$\\luminsub{}$>$ for the subset mimics the value of $<$\\luminsub{}$>$ for the entire dataset. At $z\\sim4$, however, some of the most extreme objects in the Universe have been observed (e.g. 4C60.07 and 4C41.17), which are simultaneously the most radio-luminous and the most submillimetre-luminous, residing at the highest redshifts. These galaxies fall outside the subsets which have been constructed to exclude radio-luminosity bias. Thus at $z\\sim4$, $<$\\luminsub{}$>$ for the entire sample far exceeds that of the subsets.\n\\end{enumerate}\n\nAs for the correlation analysis, it is important to investigate the\nrobustness of this result to variations in the dust template. Thus,\n$\\beta$ was changed to 1.0 and 2.0, whilst ${\\rm T_{dust}}$\nwas fixed at 40K. Likewise, holding $\\beta$ constant at 1.5, ${\\rm\nT_{dust}}$ was changed to 20K, 70K, and 100K. Altering the dust\ntemplate has a larger effect on the higher redshift sources. Thus, if\n$\\beta$ and ${\\rm T_{dust}}$ are increased, the trend of increasing\n$<$\\luminsub{}$>$ with redshift is weakened; if they are decreased the\ntrend is strengthened. More specifically, it was found that:\n\\begin{enumerate}\n\\item For the entire dataset, there are always clear steps in $<$\\luminsub{}$>$ between all redshift bins, regardless of the values of $\\beta$ and ${\\rm T_{dust}}$.\n\\item For Subset A, there is always a clear step in $<$\\luminsub{}$>$ between $z=2$ and $z=3$ and between $z=3$ and $z=4$, regardless of the values of $\\beta$ and ${\\rm T_{dust}}$.\n\\item For Subset B, there is always a clear step in $<$\\luminsub{}$>$ between $z=2$ and $z=3$. The possible step between $z=3$ and $z=4$ becomes clear (i.e. the error bars do not allow $<$\\luminsub{}$>$ to remain flat) if $\\beta$ is decreased to 1.0 or if ${\\rm T_{dust}}$ is decreased to 20K.\n\\item For the $z=2$ and $z=3$ bins, $<$\\luminsub{}$>$ for the entire dataset always closely mimics $<$\\luminsub{}$>$ for the subsets, regardless of the values of $\\beta$ and ${\\rm T_{dust}}$.\n\\item Adopting the model ${\\rm L = a (1+z)^b}$, the luminosity evolution observed For Subsets A and B upon changing $\\beta$ and ${\\rm T_{dust}}$ is consistent with `b' lying between 2.5 and 5.0.\n\\end{enumerate}\n\nBinning the data has been able to confirm the relationship between\n\\luminsub{} and $z$ that was initially suggested by survival analysis.\nIt is therefore possible that binning may also reveal a relationship\nbetween \\luminsub{} and \\radiopower{} or \\alpharadio{}.\n\nIt is only necessary to check this for Subsets A and B, as \\luminsub{}\nis known to be strongly correlated with both \\radiopower{} and\n\\alpharadio{} for the entire dataset. If \\luminsub{} remains\nindependent of the radio source for Subsets A and B, the evidence for\nevolution with redshift will be strengthened.\n\nBinning \\luminsub{} against radio power and radio spectral index fails\nto reveal a dependence of \\luminsub{} on the radio source. Altering\nthe dust template does not change this result.\n\n\\subsection{Addressing potential remaining selection effects}\n\n\\subsubsection{Potential contamination by obscured quasars}\n\nCareful scrutiny of the P-$z$ plane defined by combining all the known\nhigh-redshift radio sources shows that there is a lack of\nhigh-redshift, high-radio power quasars, although this is at least\npartly due to the selection effects inherent in\nsteep-spectrum-selected radio samples (Jarvis et al., in\npreparation\\nocite{jarvisinprep}). This is also the area of the P-$z$\nplane where the 850-\\micron{} detections of the radio-galaxy sample\nare clustered.\n\nAccording to Unified Schemes, radio-loud quasars and radio galaxies\nare identical phenomena: the former is viewed within the opening angle\nof an obscuring dust torus allowing the quasar to be seen, the latter\nis viewed outside the opening angle of the dust torus which hides the\nquasar from view (e.g. Antonucci \\& Barvainis 1990\\nocite{ab90} and references\ntherein).\n\nIt can be argued that at higher redshifts, there is an increased\nchance of dust hiding the optically-bright nucleus of a radio-loud\nquasar, even though the radio-loud quasar is viewed within the opening\nangle of the dust torus. Thus, potentially, several high-redshift radio-loud\nquasars may have been mis-classified as radio galaxies. Therefore, the\nworry for the present study is that our radio galaxy sample could \nbecome progressively more contaminated by obscured quasars with increasing \nredshift.\n\nOf course, within unified schemes all powerful radio galaxies contain\na buried quasar. Thus the point of issue for the present study is\nwhether the submillimetre emission of a powerful radio source is\norientation dependent. If so, and if our sample was progressively\ncontaminated by mis-classified radio-loud quasars with redshift, it\ncould account for the observed increase of \\luminsub{} with redshift.\nGiven the above considerations, this might happen because, for\nexample, some of our high-redshift objects might be observed in a line\nof sight sufficiently close to the jet axis that the contribution from\na more face-on quasar heated torus (which may be optically thick in\nthe rest-frame mid-far infrared) becomes dominant at 850$\\mu m$.\n\nOne way to resolve this issue is to check directly whether unification\nworks at submillimetre wavelengths, and we are currently undertaking a\nprogramme of SCUBA observations of radio-loud quasars to test this\nhypothesis. However, even if radio-loud quasars and radio galaxies are\nshown to differ at submillimetre wavelengths this need not invalidate \nthe conclusions of this study, provided we can demonstrate that\nprogressive quasar contamination with increasing redshift is not a problem.\n\n\\begin{figure}\n\\centering\n\\epsfig{file=fig8a.eps,height=8cm,angle=270}\n\\epsfig{file=fig8b.eps,height=8cm,angle=270}\n\\caption{Investigation of the rest-frame 15$\\;$GHz core:lobe ratio for the objects in our sample. The top plot shows the core:lobe ratio against redshift. Solid circles represent the sources detected with SCUBA, and open circles represent the non-detections. Down arrows indicate sources for which no radio core has been detected. In order to estimate the core flux at 15$\\;$GHz rest-frame, the core spectral index is required. For sources with more than one core detection, we have measured this spectral index. For sources with only one core detection, we have assumed the core to be flat. The bottom plot compares the core:lobe ratio with the 850-\\micron{} luminosity. An \\omegao{}=1.0 cosmology is assumed; there is no significant difference between this plot and one for which \\omegao{}=0.1.}\n\\label{corelobe}\n\\end{figure}\n\nWe can in fact test the likelihood of this\nselection effect directly using the basic radio properties \nof the objects we have observed with SCUBA. In \\Fig{corelobe}, the rest-frame\n15$\\;$GHz core:lobe ratio is plotted against redshift and \\luminsub{}\nfor our sample. If the high-redshift objects in the sample are in fact\nburied radio-loud quasars masquerading as galaxies, they should be\nexpected to display systematically higher radio\ncore:lobe ratios, owing to Doppler boosting of the radio core along\nthe line of sight. The typical core:lobe ratio does not appear to\nchange significantly with redshift, and so this analysis does not\nsupport the idea of a systematic bias towards buried quasars at high\nredshift within the SCUBA radio galaxy sample studied here. Moreover,\nthere is no evidence that the more core dominated objects are more\ndetectable with SCUBA.\n\nThese mis-classified buried quasars may exist. Two of the objects in\nour sample, 6C0902+34 and 4C23.56, appear significantly more\ncore-dominated than the rest, and are likely candidates since their\ncore:lobe radio is comparable ($\\simeq 10$ per cent) to that typically\ndisplayed by radio quasars \\cite{spencer91}. Furthermore, 6C0902+34\nhas a single-sided radio jet characteristic of a radio-loud quasar\n\\cite{carilli95}. In addition to the evidence at radio wavelengths,\n4C23.56 has a polarized ultraviolet continuum consistent with\nscattered quasar light \\cite{cdv98}. It is worth noting that the\ncore:lobe ratio in these two sources is an order of magnitude higher\nthan the typical value throughout the rest of the radio galaxy\nsample. Moreover, in any case, SCUBA failed to detect dust emission\nfrom either one.\n\n\\begin{figure}\n\\centering\n\\epsfig{file=fig9.eps,height=9cm,angle=270}\n\\caption{\\footnotesize The cumulative redshift distribution of the radio galaxy sample. The dotted line is for the entire sample, the solid line only considers the galaxies detected at 850$\\;$\\micron{}. For the detections, the median redshift of the distribution is $<z>=3.1$.}\n\\label{cumulrgzdistrib}\n\\epsfig{file=fig10.eps,height=8cm,angle=270}\n\\caption{\\footnotesize Figure 2 of Smail et al. 2000b. The full caption, as it appears in the original paper, is as follows: ``Cumulative redshift distribution for the full submm sample. We have used the spectroscopic redshifts of those sources thought to be reliable (Table 1) and combined these with the probable redshift ranges of the remaining sources derived from their $\\alpha^{850}_{1.4}$ indices or limits. The solid line shows the cumulative distribution if we assume the minimum redshift distribution that is obtained if all sources lie at their lower $z_{\\alpha}$ limit given in Table 1 (dashed line is the equivalent analysis but restricted to the CY models). The effect of non-thermal radio emission, which drives down the $\\alpha^{850}_{1.4}$ indices, means that this is a very conservative assumption if some fraction of the population harbor radio-loud AGNs. The dash-dotted line assumes a flat probability distribution for the sources within their $z_{\\alpha}$ ranges and a maximum redshift of $z=6$ for those sources where we only have a lower limit on $\\alpha^{850}_{1.4}$. Finally, the dotted line is the cumulative redshift distribution from Barger et al. (1999a) with two of the source identifications corrected as in Smail et al. (1999) and all blank-field/extremely red object candidates placed at $z=4$.''} \n\\label{smailz}\n\\end{figure}\n\n\\subsubsection{Preferential selection of young radio sources at high redshift}\n\nAll realistic models of the time evolution of classical double radio\nsources (e.g. Kaiser et al. 1997\\nocite{kda97}; Blundell et\nal. 1999\\nocite{brw99}; Blundell \\& Rawlings 1999\\nocite{bs99})\npredict that their lobe luminosities decline with age once they are\nlarge enough to avoid synchrotron self-absorption. Older sources are\nthus (obviously) more likely to fall below the flux limit of a given\nsurvey if they reside at high redshift. A single flux-limited survey\nmay thus be biased towards young radio sources at high redshift,\nwhereas at lower redshifts a large range of radio source ages will be\nincluded in the same survey.\n\nThe importance of this selection effect to our SCUBA survey is\nprobably not a major concern for two reasons. First, the target\nsources are {\\em not} selected from a single flux-limited sample, but\nrather are selected rather close to the flux-density limit of\nprogressively deeper surveys - in other words at $z \\simeq 4$ the\nradio sources must be preferentially young, but the sources we have\nstudied at, say, $z \\simeq 1.5$ must also be fairly young to enter the\nbrighter 3CRR sample from which our lower-redshift targets are\nselected. This fact will undoubtedly weaken any correlation of source\nage with redshift (certainly at $ z > 1$), compared with that expected\nfrom a single flux-limited survey as described by Blundell \\& Rawlings\n(1999).\n\nSecond, even if some residual correlation between radio-source\nyouthfulness and redshift remains in our sample, it is not clear that\nthis has any implications whatsoever for this submillimetre study. For\nit to be responsible for the trend of increasing \\luminsub{} with $z$,\nradio-source age must be intimately linked to starburst luminosity.\nOur data do not provide any evidence in support of this. For example,\none of the largest radio sources, and hence possibly one of the\noldest, 6C0905+39, was detected by SCUBA. To examine this more\nthoroughly, survival analysis was applied to test for correlations\nbetween D$_{linear}$ (taken as indicative of the age of the radio\nsource), $z$, and \\luminsub{}. As found for complete samples by\nBlundell et al. (1999), we find a negative correlation between\nD$_{linear}$ and $z$. However, no evidence for a correlation between\nD$_{linear}$ and \\luminsub{} was found (correlation tests yield a\nsignificance of $\\sim 40$ per cent). We therefore find no internal\nevidence in support of the hypothesis that \\luminsub{} is closely\nlinked to radio-source age, although the mildness of the\nD$_{linear}$:$z$ correlation means that caution is advised in\nattempting to interpret D$_{linear}$ as a reliable estimator of\nradio-source age \\cite{brw99,bs99}.\n\n\\section{Concluding Remarks}\n\\label{concsec}\n\nIn summary, our attempts to investigate and quantify the various\npossible biases which might conceivably afflict this study have simply\nserved to reaffirm and strengthen our basic result, namely that the\nsubmillimetre luminosity of radio galaxies is primarily a function of\nredshift as illustrated in \\Fig{ombinning}.\n\nIt therefore seems hard to avoid the straightforward conclusion that\nthe observed increase in submillimetre detection rate and\ncharacteristic luminosity with redshift is due to the increasing\nyouthfulness of the stellar populations of the radio galaxies in our\nsample.\n\nIn a separate paper we will explore how the inferred evolution of gas\nmass and star-formation rate in these galaxies compares with the\npredictions of models of elliptical galaxy formation and evolution.\nHowever, it is interesting to briefly consider whether the apparently\nrather extreme evolution is peculiar to radio galaxies, or may in fact\nbe typical of the cosmological evolution of dust and gas in massive\nellipticals in general.\n\nIn \\Fig{cumulrgzdistrib} we show the cumulative redshift distribution\nof our radio galaxy sample, along with the cumulative redshift\ndistribution of the subset detected at submillimetre wavelengths. This\nfigure serves to re-emphasize that the high median redshift of our\ndetected galaxies ($z = 3$) does not simply reflect the median\nredshift of the sample selected for observation ($z = 2$). However,\nwhat is particularly interesting is that the redshift distribution of\nour submillimetre detected radio galaxies is statistically\nindistinguishable from current best estimates of the redshift\ndistribution of sources detected in SCUBA surveys, as illustrated in\n\\Fig{smailz} \\cite{smailzdistrib}. This comparison provides at least\ncircumstantial evidence that the submillimetre evolution of radio\ngalaxies found here may indeed be symptomatic of the evolution of\nmassive elliptical galaxies in general.\n\nAt first sight, it may appear contradictory that the average\nsubmillimetre luminosity of the radio galaxy sample continues to rise\nbeyond $z\\sim3$ while the median redshift of the sample is $z\\sim3$.\nThis results from the median redshift of our most luminous detections\nbeing higher at $z\\sim3.6$ for sources brighter than 5$\\;$mJy.\n\nThis raises the interesting possibility that the most massive\ndust-enshrouded starbursts are confined to $z>3$. Therefore the\nmedian redshift of submillimetre sources detected in blank-field\nsurveys may prove to be a function of flux density.\n\nIt will be some time before the redshift information in bright\nsubmillimetre surveys approaches that currently available for\nradio-selected samples. However, it will undoubtedly be very\ninteresting to see how this comparison evolves as\nsubmillimetre-selected samples are studied and refined in the years to\ncome.\n\n\\section*{Acknowledgments}\n\nWe wish to thank the staff of the James Clerk Maxwell Telescope,\nparticularly Wayne Holland, Tim Jenness, Graeme Watt and all the\nT.S.S.s, for all their help. Many thanks to Katherine Blundell for\nallowing us access to radio data prior to publication. Figure 2 of\nSmail et al. 2000b, and the corresponding caption text, have been\nreproduced by permission of the AAS. This research has made use of\nthe NASA/IPAC Extragalactic Database, which is operated by the Jet\nPropulsion Laboratory, Caltech, under contract with the National\nAeronautics and Space Administration. ENA, DHH and RJI acknowledge\nsupport from the UK Particle Physics and Astronomy Research Council\n(PPARC). 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Note, the linear fits were applied\nto $\\nu > 1\\; {\\rm GHz}$ observations only. In addition, if only two\ndata points were available (i.e. zero degrees of freedom), the slope\nand y-intercept of the line joining the two data points were\ncalculated instead of using a fitting algorithm. No value of\n$\\chi^2_{red}$ is given in this case. Finally, all best-fit\nparameters are quoted to two decimal places; therefore errors less\nthan 0.005 are quoted as being 0.00.}\n\\label{allradiofits}\n\\begin{tabular}{lrrrccrrrr}\n\\hline\n&\\multicolumn{3}{c}{Linear Fit: $y = mx + k$}&&&\\multicolumn{4}{c}{Parabolic Fit: $y = ax^2+bx+c$}\\\\\nSource&\\multicolumn{1}{c}{$m$}&\\multicolumn{1}{c}{$k$}&\\multicolumn{1}{c}{$\\chi^2_{red}$}&&&\\multicolumn{1}{c}{$a$}&\\multicolumn{1}{c}{$b$}&\\multicolumn{1}{c}{$c$}&\\multicolumn{1}{c}{$\\chi^2_{red}$}\\\\\n\\hline\n%%%%%%%%%%%%%%\n%%%%%%%%%%%%%% paper_allfits.tex goes here\n%%%%%%%%%%%%%%\n3C277.2 &$ -1.00\\pm 0.03$ &$ 0.41\\pm 0.02$ & 2.8 &&&$ -0.03\\pm 0.02$ &$ -0.96\\pm 0.01$ &$ 0.40\\pm 0.01$ & 1.7\\\\\n3C340 &$ -1.03\\pm 0.02$ &$ 0.56\\pm 0.01$ & 2.9 &&&$ -0.12\\pm 0.01$ &$ -0.86\\pm 0.01$ &$ 0.51\\pm 0.01$ & 2.8\\\\\n3C265 &$ -1.14\\pm 0.03$ &$ 0.63\\pm 0.01$ & 1.3 &&&$ -0.07\\pm 0.01$ &$ -1.05\\pm 0.01$ &$ 0.60\\pm 0.01$ & 0.9\\\\\n3C217 &$ -1.24\\pm 0.03$ &$ 0.52\\pm 0.01$ & 2.3 &&&$ -0.16\\pm 0.02$ &$ -1.02\\pm 0.01$ &$ 0.48\\pm 0.01$ & 2.5\\\\\n3C356 &$ -1.17\\pm 0.06$ &$ 0.33\\pm 0.04$ & 1.3 &&&$ -0.09\\pm 0.02$ &$ -1.10\\pm 0.02$ &$ 0.32\\pm 0.01$ & 1.1\\\\\n3C368 &$ -1.34\\pm 0.10$ &$ 0.23\\pm 0.05$ & 0.2 &&&$ -0.13\\pm 0.03$ &$ -1.34\\pm 0.03$ &$ 0.26\\pm 0.02$ & 1.8\\\\\n3C267 &$ -0.94\\pm 0.03$ &$ 0.49\\pm 0.02$ & 2.9 &&&$ -0.04\\pm 0.01$ &$ -0.92\\pm 0.01$ &$ 0.50\\pm 0.01$ & 1.3\\\\\n3C324 &$ -1.20\\pm 0.02$ &$ 0.59\\pm 0.01$ & 5.6 &&&$ -0.15\\pm 0.01$ &$ -1.01\\pm 0.01$ &$ 0.55\\pm 0.01$ & 1.8\\\\\n3C266 &$ -1.09\\pm 0.04$ &$ 0.30\\pm 0.03$ & 4.0 &&&$ -0.06\\pm 0.02$ &$ -1.04\\pm 0.01$ &$ 0.31\\pm 0.01$ & 3.9\\\\\n4C13.66 &$ -1.25\\pm 0.08$ &$ 0.42\\pm 0.04$ & 1.2 &&&$ -0.25\\pm 0.04$ &$ -1.04\\pm 0.03$ &$ 0.39\\pm 0.02$ & 1.4\\\\\n3C437 &$ -0.95\\pm 0.02$ &$ 0.58\\pm 0.01$ & 0.5 &&&$ -0.11\\pm 0.01$ &$ -0.83\\pm 0.01$ &$ 0.57\\pm 0.01$ & 6.2\\\\\n3C241 &$ -1.32\\pm 0.05$ &$ 0.43\\pm 0.02$ & 0.2 &&&$ -0.20\\pm 0.03$ &$ -1.09\\pm 0.02$ &$ 0.38\\pm 0.01$ & 0.5\\\\\n6C0919+38 &$ -1.16$ &$ -0.36$ & -- &&&$ -0.09\\pm 0.04$ &$ -1.06\\pm 0.03$ &$ -0.37\\pm 0.00$ & 0.1\\\\\n3C470 &$ -1.15\\pm 0.03$ &$ 0.50\\pm 0.01$ & 2.9 &&&$ -0.14\\pm 0.01$ &$ -0.94\\pm 0.01$ &$ 0.45\\pm 0.01$ & 6.0\\\\\n3C322 &$ -1.18\\pm 0.05$ &$ 0.46\\pm 0.03$ & 0.8 &&&$ -0.10\\pm 0.02$ &$ -0.99\\pm 0.02$ &$ 0.39\\pm 0.01$ & 2.3\\\\\n6C1204+37 &$ -1.17$ &$ -0.04$ & -- &&&$ -0.40\\pm 0.03$ &$ -1.10\\pm 0.02$ &$ -0.04\\pm 0.00$ & 22\\\\\n3C239 &$ -1.22\\pm 0.05$ &$ 0.34\\pm 0.02$ & 0.1 &&&$ -0.09\\pm 0.02$ &$ -1.13\\pm 0.02$ &$ 0.34\\pm 0.01$ & 0.5\\\\\n3C294 &$ -1.32\\pm 0.05$ &$ 0.32\\pm 0.03$ & 0.3 &&&$ -0.07\\pm 0.02$ &$ -1.16\\pm 0.02$ &$ 0.26\\pm 0.01$ & 2.7\\\\\n6C0820+36 &$ -1.14$ &$ -0.40$ & -- &&&$ -0.17\\pm 0.05$ &$ -1.09\\pm 0.03$ &$ -0.40\\pm 0.01$ & 2.2\\\\\n6C0905+39 &$ -1.50$ &$ -0.37$ & -- &&&$ -0.09\\pm 0.04$ &$ -1.13\\pm 0.03$ &$ -0.42\\pm 0.01$ & 7.4\\\\\n6C0901+35 &$ -1.17$ &$ -0.44$ & -- &&&$ -0.23\\pm 0.04$ &$ -1.12\\pm 0.03$ &$ -0.44\\pm 0.01$ & 7.7\\\\\n5C7.269 &$ -0.98$ &$ -1.03$ & -- &&&$ -0.01\\pm 0.10$ &$ -0.98\\pm 0.06$ &$ -1.03\\pm 0.01$ & 0.1\\\\\n4C40.36 &$ -1.62\\pm 0.03$ &$ -0.06\\pm 0.02$ & 0.7 &&&$ -0.23\\pm 0.03$ &$ -1.38\\pm 0.02$ &$ -0.10\\pm 0.01$ & 0.2\\\\\nMG1744+18 &$ -1.16\\pm 0.00$ &$ 0.30\\pm 0.00$ & 335 &&&$ -0.14\\pm 0.00$ &$ -0.94\\pm 0.00$ &$ 0.22\\pm 0.00$ & 62\\\\\nMG1248+11 &$ -1.27$ &$ -0.34$ & -- &&&$ -0.41\\pm 0.15$ &$ -0.96\\pm 0.04$ &$ -0.36\\pm 0.04$ & 0.9\\\\\n4C48.48 &$ -1.19\\pm 0.04$ &$ -0.28\\pm 0.02$ & 0.8 &&&$ -0.10\\pm 0.03$ &$ -1.10\\pm 0.01$ &$ -0.29\\pm 0.01$ & 0.8\\\\\n53W002 &$ -1.26\\pm 0.05$ &$ -1.11\\pm 0.02$ & 0.5 &&&$ -0.09\\pm 0.04$ &$ -1.15\\pm 0.03$ &$ -1.13\\pm 0.01$ & 0.5\\\\\n6C0930+38 &$ -1.00$ &$ -0.40$ & -- &&&$ -0.10\\pm 0.04$ &$ -0.99\\pm 0.02$ &$ -0.39\\pm 0.01$ & 3.5\\\\\n6C1113+34 &$ -1.14$ &$ -0.23$ & -- &&&$ -0.29\\pm 0.04$ &$ -0.98\\pm 0.03$ &$ -0.24\\pm 0.00$ & 3.9\\\\\nMG2305+03 &$ -0.97\\pm 0.09$ &$ -0.15\\pm 0.05$ & 0.2 &&&$ -0.02\\pm 0.14$ &$ -0.95\\pm 0.05$ &$ -0.15\\pm 0.03$ & 0.2\\\\\n3C257 &$ -1.03\\pm 0.06$ &$ 0.39\\pm 0.03$ & 0.4 &&&$ -0.12\\pm 0.04$ &$ -0.92\\pm 0.02$ &$ 0.37\\pm 0.02$ & 0.3\\\\\n4C23.56 &$ -1.40\\pm 0.03$ &$ -0.19\\pm 0.02$ & 18 &&&$ -0.16\\pm 0.02$ &$ -1.27\\pm 0.02$ &$ -0.20\\pm 0.01$ & 11\\\\\n8C1039+68 &$ -1.12$ &$ -0.44$ & -- &&&$ -0.08\\pm 0.05$ &$ -1.09\\pm 0.05$ &$ -0.43\\pm 0.04$ & 0.2\\\\\nMG1016+058 &$ -1.10\\pm 0.02$ &$ -0.25\\pm 0.01$ & 7.9 &&&$ -0.27\\pm 0.02$ &$ -0.79\\pm 0.02$ &$ -0.30\\pm 0.01$ & 5.4\\\\\n4C24.28 &$ -1.31\\pm 0.02$ &$ -0.08\\pm 0.01$ & 0.8 &&&$ -0.15\\pm 0.02$ &$ -1.18\\pm 0.01$ &$ -0.09\\pm 0.00$ & 7.9\\\\\n4C28.58 &$ -1.50\\pm 0.04$ &$ -0.40\\pm 0.02$ & 2.0 &&&$ -0.16\\pm 0.05$ &$ -1.37\\pm 0.03$ &$ -0.41\\pm 0.02$ & 2.3\\\\\n6C1232+39 &$ -1.70\\pm 0.00$ &$ -0.23\\pm 0.00$ & 659 &&&$ -0.30\\pm 0.00$ &$ -1.29\\pm 0.00$ &$ -0.37\\pm 0.00$ & 25\\\\\n6C1159+36 &$ -1.11$ &$ -0.27$ & -- &&&$ -0.34\\pm 0.04$ &$ -1.03\\pm 0.03$ &$ -0.27\\pm 0.01$ & 19\\\\\n6C0902+34 &$ -0.96$ &$ -0.33$ & -- &&&$ -0.14\\pm 0.03$ &$ -0.93\\pm 0.02$ &$ -0.34\\pm 0.00$ & 2.5\\\\\nTX1243+036 &$ -1.31\\pm 0.06$ &$ -0.32\\pm 0.04$ & 2.9 &&&$ -0.08\\pm 0.06$ &$ -1.33\\pm 0.03$ &$ -0.27\\pm 0.02$ & 3.4\\\\\nMG2141+192 &$ -1.57\\pm 0.00$ &$ -0.12\\pm 0.00$ & 25 &&&$ -0.27\\pm 0.02$ &$ -1.14\\pm 0.02$ &$ -0.29\\pm 0.01$ & 11\\\\\n6C0032+412 &$ -1.12\\pm 0.03$ &$ -0.85\\pm 0.02$ & 0.3 &&&$ 0.03\\pm 0.02$ &$ -1.14\\pm 0.01$ &$ -0.85\\pm 0.01$ & 0.7\\\\\n4C60.07 &$ -1.48\\pm 0.03$ &$ -0.60\\pm 0.02$ & 0.4 &&&$ -0.05\\pm 0.02$ &$ -1.44\\pm 0.01$ &$ -0.60\\pm 0.01$ & 0.7\\\\\n4C41.17 &$ -1.49\\pm 0.03$ &$ -0.41\\pm 0.02$ & 1.6 &&&$ -0.15\\pm 0.02$ &$ -1.33\\pm 0.01$ &$ -0.44\\pm 0.01$ & 1.1\\\\\n8C1435+635 &$ -1.85\\pm 0.00$ &$ 0.09\\pm 0.00$ & 4.3 &&&$ -0.35\\pm 0.01$ &$ -1.30\\pm 0.01$ &$ -0.12\\pm 0.00$ & 3.3\\\\\n6C0140+326 &$ -1.39\\pm 0.02$ &$ -0.83\\pm 0.01$ & 4.4 &&&$ -0.19\\pm 0.02$ &$ -1.21\\pm 0.01$ &$ -0.86\\pm 0.01$ & 1.1\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\nWe applied two fits to the radio spectra of our sample:\n\n{\\bf 1) Linear Fit -} In log-space, a straight line is fitted to radio\ndata with $\\nu > 1\\; {\\rm GHz}$. For all galaxies in the sample, at\nleast two data points satisfy this condition. Except for the\nnoticeably curved spectra of 3C324, MG1744+18, 4C23.56, and\nMG1016+058, the straight-line fit seems to mimic the existing\nhigh-frequency data very well. \n\n{\\bf 2) Parabolic Fit -} A physical model of synchrotron ageing could\nbe applied to the spectra in order to determine how they might\nsteepen. However, the fit is only required to accurately predict the\nshape of the expected steepening; the physics of the ageing\nsynchrotron population does not need to be extracted from the fit.\nBlundell et al. \\shortcite{brw99} have studied the\nproperties and evolution of over 300 FRII radio sources selected from\nthe 3C, 6C, and 7C surveys. They applied a Bayesian polynomial\nregression analysis to the fitting the flux densities. The process\ninvolved fitting polynomials of different degrees and associating a\nlikelihood or probability to each. In some cases a first-order\npolynomial, or straight-line was the preferred choice. However, in\nmost cases a second-order polynomial, or parabola, accurately modelled\nthe curvature of the spectrum. A parabolic fit seems to be the best\nway of parameterising the curvature, as higher-order polynomials were\nnever chosen by the regression analysis. Thus a polynomial of degree\n$m=2$ was fitted, in log space, to the entire radio spectrum.\n\nThe best-fit parameters of the two models are shown in\n\\tab{allradiofits}.\n\nFor each galaxy in the sample, the radio-submillimetre spectral energy\ndistribution (SED) is presented in \\fig{seds}. The SEDs are arranged\nin redshift order. The solid circles denote integrated continuum flux\ndensities. The open circles indicate radio core flux densities. For\n3C356, two radio core identifications exist. The fainter core is\ndenoted by open stars. If errors were unavailable, the error was\ntaken to be 10 per cent of the flux density. Upper limits have been\ntaken at the 3-$\\sigma$ level if S/N$<3$. The two models fit to the\ndata are also displayed in \\fig{seds}. The solid line is the\nparabolic fit to the spectrum, and the dash-dot line is the linear\nfit. The references for the data are:\n{\\bf 3C277.2} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C340} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C265} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C217} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C356} - BLR97\\nocite{blr97}, F93\\nocite{f93}, LP\\nocite{lp80};\n{\\bf 3C368} - BLR97\\nocite{blr97}, BRR00\\nocite{brr00}, LP\\nocite{lp80};\n{\\bf 3C267} - BLR97\\nocite{blr97}, BRR00\\nocite{brr00}, LP\\nocite{lp80};\n{\\bf 3C324} - BCG98\\nocite{bcg98}, BRB98\\nocite{brb98}, LP\\nocite{lp80}; \n{\\bf 3C266} - BLR97\\nocite{blr97}, BRR00\\nocite{brr00}, LP\\nocite{lp80}, LPR92\\nocite{lpr92};\n{\\bf 4C13.66} - BWE91\\nocite{bwe91}, GC91\\nocite{gc91}, BRR00\\nocite{brr00}, LML81\\nocite{lml81}, LRL, P90\\nocite{p90}, WB92\\nocite{wb92}; \n{\\bf 3C437} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C241} - ASZ91\\nocite{asz91}, LP\\nocite{lp80}, vBF92\\nocite{vbf92};\n{\\bf 6C0919+38} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, FGT85\\nocite{fgt85}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96};\n{\\bf 3C470} - BLR97\\nocite{blr97}, LP\\nocite{lp80}; \n{\\bf 3C322} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 6C1204+37} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, LLA95\\nocite{lla95}; \n{\\bf 3C239} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 3C294} - BRR00\\nocite{brr00}, LP\\nocite{lp80}; \n{\\bf 6C0820+36} - 6C-VI\\nocite{6cVI}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, LLA95\\nocite{lla95};\n{\\bf 6C0905+39} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, FGT85\\nocite{fgt85}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, LGE95\\nocite{lge95}; \n{\\bf 6C0901+35} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, NAR92\\shortcite{nar92}; \n{\\bf 5C7.269} - BRR00\\nocite{brr00}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GSDC96\\nocite{gsdc96};\n{\\bf 4C40.36} - C\\&C69\\nocite{cc69}, CMvB96\\nocite{cmvb96}, CRvO97\\nocite{crvo97}, FGT85\\nocite{fgt85}, TMW79\\nocite{tmw79}, WENSS\\nocite{wenss}; \n{\\bf MG1744+18} - BWE91\\nocite{bwe91}, CRvO97\\nocite{crvo97}, GC91\\nocite{gc91}, GSW67\\nocite{gsw67}, KB17\\nocite{kb17}, LML81\\nocite{lml81}, P90\\nocite{p90}, WB92\\nocite{wb92}; \n{\\bf MG1248+11} - DBB96\\nocite{dbb96}, LML81\\nocite{lml81}, LBH86\\nocite{lbh86}, WB92\\nocite{wb92};\n{\\bf 4C48.48} - 6C-V\\nocite{6cV}, CMvB96\\nocite{cmvb96}, CRvO97\\nocite{crvo97}, GSW67\\nocite{gsw67}, TMW79\\nocite{tmw79}, WENSS\\nocite{wenss}; \n{\\bf 53W002} - 6C-II\\nocite{6cII}, HDR97\\nocite{hdr97}, WBM91\\nocite{wbm91}, WvHK84\\nocite{wvhk84}, OKS87\\nocite{oks87}, OvL87\\nocite{ovl87}; \n{\\bf 6C0930+38} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, FGT85\\nocite{fgt85}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, NAR92\\shortcite{nar92}; \n{\\bf 6C1113+34} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, LLA95\\nocite{lla95}A;\n{\\bf MG2305+03} - BWE91\\nocite{bwe91}, GC91\\nocite{gc91}, GWBE95\\nocite{gwbe95}, LML81\\nocite{lml81}, P90\\nocite{p90}, WB92\\nocite{wb92};\n{\\bf 3C257} - BWE91\\nocite{bwe91}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSW67\\nocite{gsw67}, GWBE95\\nocite{gwbe95}, HDR97\\nocite{hdr97}, LML81\\nocite{lml81}, P90\\nocite{p90}, vBS98\\nocite{vbs98}, WB92\\nocite{wb92}; \n{\\bf 4C23.56} - CMvB96\\nocite{cmvb96}, CRvO97\\nocite{crvo97}, P90\\nocite{p90}, PS65\\nocite{ps65}, TMW79\\nocite{tmw79}; \n{\\bf 8C1039+68} - HWR95\\nocite{hwr95}, Lthesis\\nocite{lthesis}; \n{\\bf MG1016+058} - BWE91\\nocite{bwe91}, CC98\\nocite{cc98}, CFR98\\nocite{cfr98}, DBB96\\nocite{dbb96}, DSD95\\nocite{dsd95}, GC91\\nocite{gc91}, GSW67\\nocite{gsw67}, GWBE95\\nocite{gwbe95}, LML81\\nocite{lml81}, P90\\nocite{p90}, WB92\\nocite{wb92}; \n{\\bf 4C24.28} - CMvB96\\nocite{cmvb96}, CRvO97\\nocite{crvo97}, P90\\nocite{p90}, PS65\\nocite{ps65}, TMW79\\nocite{tmw79}, WYR96\\nocite{wyr96}; \n{\\bf 4C28.58} - CC98\\nocite{cc98}, CMvB96\\nocite{cmvb96}, DBB96\\nocite{dbb96}, PS65\\nocite{ps65}, TMW79\\nocite{tmw79}; \n{\\bf 6C1232+39} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, C\\&K94\\nocite{ck94}, CRvO97\\nocite{crvo97}, DBB96\\nocite{dbb96}, FGT85\\nocite{fgt85}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, NAR92\\shortcite{nar92}; \n{\\bf 6C1159+36} - 6C-II\\nocite{6cII}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, LLA95\\nocite{lla95}; \n{\\bf 6C0902+34} - 6C-II\\nocite{6cII}, C95\\nocite{c95}, CC98\\nocite{cc98}, C\\&K94\\nocite{ck94}, COH94\\nocite{coh94}, DBB96\\nocite{dbb96}, DSS96\\nocite{dss96}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, HDR97\\nocite{hdr97}, LLA95\\nocite{lla95}; \n{\\bf TX1243+036} - CC98\\nocite{cc98}, CFR98\\nocite{cfr98}, DBB96\\nocite{dbb96}, GSW67\\nocite{gsw67}, LML81\\nocite{lml81}, P90\\nocite{p90}, vOR96\\nocite{vor96}, WB92\\nocite{wb92}; \n{\\bf MG2141+192} - BWE91\\nocite{bwe91}, CC98\\nocite{cc98}, CRvO97\\nocite{crvo97}, DBB96\\nocite{dbb96}, GC91\\nocite{gc91}, GSW67\\nocite{gsw67}, HDR97\\nocite{hdr97}, WB92\\nocite{wb92}; \n{\\bf 6C0032+412} - 6C-VI\\nocite{6cVI}, BRE98\\nocite{bre98}, DBB96\\nocite{dbb96}, FGT85\\nocite{fgt85}, GC91\\nocite{gc91}, GSDC96\\nocite{gsdc96}, HDR97\\nocite{hdr97}; \n{\\bf 4C60.07} - 6C-V\\nocite{6cV}, CC98\\nocite{cc98}, CMvB96\\nocite{cmvb96}, CRvO97\\nocite{crvo97}, DBB96\\nocite{dbb96}, TMW79\\nocite{tmw79}, WENSS\\nocite{wenss}; \n{\\bf 4C41.17} - 6C-VI\\nocite{6cVI}, BCO99\\nocite{bco99}, CC98\\nocite{cc98}, C\\&K94\\nocite{ck94}, CMvB90\\nocite{cmvb90}, COH94\\nocite{coh94}, DBB96\\nocite{dbb96}, DHR94\\nocite{dhr94}, FGT85\\nocite{fgt85}, GSW67\\nocite{gsw67}, TMW79\\nocite{tmw79}, WENSS\\nocite{wenss}; \n{\\bf 8C1435+635} - 6C-III\\nocite{6cIII}, CC98\\nocite{cc98}, CRvO97\\nocite{crvo97}, DBB96\\nocite{dbb96}, HDR97\\nocite{hdr97}, HWR95\\nocite{hwr95}, I95\\nocite{i95}, IDHA98, LMR94\\nocite{lmr94}; \n{\\bf 6C0140+326} - 6C-VI\\nocite{6cVI}, BRE98\\nocite{bre98}, CC98\\nocite{cc98}, DBB96\\nocite{dbb96}, FGT85\\nocite{fgt85}, RLB96\\nocite{rlb96}.\n\n\\begin{figure*}\n\\epsfig{file=figA1_a.eps,height=23cm,width=18.5cm}\n\\label{seds}\n\\caption{Spectral Energy Distributions}\n\\end{figure*}\n\n\\begin{figure*}\n\\epsfig{file=figA1_b.eps,height=23cm,width=18.5cm}\n\\contcaption{}\n\\end{figure*}\n\n\\begin{figure*}\n\\epsfig{file=figA1_c.eps,height=23cm,width=18.5cm}\n\\contcaption{}\n\\end{figure*}\n\n\\label{lastpage}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002083.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\citename{{Akujor} et~al.{\\ }}{1991}]{asz91}\n{Akujor}~C.~E., {Spencer}~R.~E., {Zhang}~F.~J., {Davis}~R.~J., {Browne}~I.\n W.~A., {Fanti}~C., 1991, \\mnras, 250, 215, (ASZ91)\n\n\\bibitem[\\protect\\citename{{Andreani} et~al.{\\ }}{1993}]{alc93}\n{Andreani}~P., {La Franca}~F., {Cristiani}~S., 1993, \\mnras, 261, L35\n\n\\bibitem[\\protect\\citename{{Antonucci} \\& {Barvainis}{\\ }}{1990}]{ab90}\n{Antonucci}~R., {Barvainis}~R., 1990, \\apjl, 363, L17\n\n\\bibitem[\\protect\\citename{{Archibald}{\\ }}{1999}]{mythesis}\n{Archibald}~E.~N., 1999, The cosmological evolution of dust and gas in radio\n galaxies, Ph.D. thesis, University of Edinburgh\n\n\\bibitem[\\protect\\citename{{Barger} et~al.{\\ }}{1999}]{bargercs99}\n{Barger}~A.~J., {Cowie}~L.~L., {Sanders}~D.~B., 1999, \\apjl, 518, L5\n\n\\bibitem[\\protect\\citename{{Becker} et~al.{\\ }}{1991}]{bwe91}\n{Becker}~R.~H., {White}~R.~L., {Edwards}~A.~L., 1991, \\apjs, 75, 1,\n (BWE91)\n\n\\bibitem[\\protect\\citename{{Benford} et~al.{\\ }}{1999}]{bco99}\n{Benford}~D.~J., {Cox}~P., {Omont}~A., {Phillips}~T.~G., {McMahon}~R.~G.,\n 1999, \\apjl, 518, L65, (BCO99)\n\n\\bibitem[\\protect\\citename{{Bennett}{\\ }}{1962}]{bennett1962}\n{Bennett}~A.~S., 1962, \\memras, 68, 163\n\n\\bibitem[\\protect\\citename{{Best} et~al.{\\ }}{1997}]{blr97}\n{Best}~P.~N., {Longair}~M.~S., {R\\\"ottgering}~H. J.~A., 1997, \\mnras, 292,\n 758, (BLR97)\n\n\\bibitem[\\protect\\citename{{Best} et~al.{\\ }}{1998a}]{bcg98}\n{Best}~P.~N., {Carilli}~C.~L., {Garrington}~S.~T., {Longair}~M.~S.,\n {R\\\"ottgering}~H. J.~A., 1998a, \\mnras, 299, 357, (BCG98)\n\n\\bibitem[\\protect\\citename{{Best} et~al.{\\ }}{1998b}]{brb98}\n{Best}~P.~N. et al., 1998b, \\mnras, 301, L15, (BRB98)\n\n\\bibitem[\\protect\\citename{{Bevington}{\\ }}{1969}]{bevington}\n{Bevington}~P.~R., 1969, Data Reduction and Error Analysis for the Physical\n Sciences.\nMcGraw-Hill\n\n\\bibitem[\\protect\\citename{{Blain} et~al.{\\ }}{1998}]{blainconfusion}\n{Blain}~A.~W., {Ivison}~R.~J., {Smail}~I., {Kneib}~J.-P., 1998, in\n Colombi~S., Mellier~Y., eds, Wide Field Surveys in Cosmology, 14th IAP\n meeting held May 26-30, 1998, Paris. 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J.~A., {van Ojik}~R., {Miley}~G.~K.,\n {van Breugel}~W. J.~M., 1997, \\apjs, 109, 1, (CRvO97)\n\n\\bibitem[\\protect\\citename{{Caswell} \\& {Crowther}{\\ }}{1969}]{cc69}\n{Caswell}~J.~L., {Crowther}~J.~H., 1969, \\mnras, 145, 181, (C\\&C69)\n\n\\bibitem[\\protect\\citename{{Chambers} et~al.{\\ }}{1988}]{cmvb88}\n{Chambers}~K.~C., {Miley}~G.~K., {van Breugel}~W. J.~M., 1988, \\apjl, 327,\n L47, (CMvB88)\n\n\\bibitem[\\protect\\citename{{Chambers} et~al.{\\ }}{1990}]{cmvb90}\n{Chambers}~K.~C., {Miley}~G.~K., {van Breugel}~W. J.~M., 1990, \\apj, 363,\n 21, (CMvB90)\n\n\\bibitem[\\protect\\citename{{Chambers} et~al.{\\ }}{1996}]{cmvb96}\n{Chambers}~K.~C., {Miley}~G.~K., {van Breugel}~W. J.~M., {Bremer}~M. A.~R.,\n {Huang}~J.-S., {Trentham}~N.~A., 1996, \\apjs, 106, 247, (CMvB96)\n\n\\bibitem[\\protect\\citename{{Chini} \\& {Kr\\\"ugel}{\\ }}{1994}]{ck94}\n{Chini}~R., {Kr\\\"ugel}~E., 1994, \\aap, 288, L33, (C\\&K94)\n\n\\bibitem[\\protect\\citename{{Chini} et~al.{\\ }}{1986}]{ckk86}\n{Chini}~R., {Kr\\\"ugel}~E., {Kreysa}~E., 1986, \\aap, 167, 315\n\n\\bibitem[\\protect\\citename{{Cimatti} et~al.{\\ }}{1998a}]{cdv98}\n{Cimatti}~A., {di Serego Alighieri}~S., {Vernet}~J., {Cohen}~M.~H.,\n {Fosbury}~R. A.~E., 1998a, \\apjl, 499, L21\n\n\\bibitem[\\protect\\citename{{Cimatti} et~al.{\\ }}{1998b}]{cfr98}\n{Cimatti}~A., {Freudling}~W., {R\\\"ottgering}~H. 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}
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astro-ph0002084
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X-Ray Spectral and Timing Evolution During the Decay of the 1998 Outburst from the Recurrent X-Ray Transient 4U~1630--47
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We report on the X-ray spectral and timing behavior of the recurrent X-ray transient 4U~1630--47 for 51 RXTE observations made during the decay of its 1998 outburst. The observations began when the source was still relatively bright, and, during one of the early observations, a QPO with a non-Lorentzian profile occurred near 6~Hz. As the source decayed, the X-ray flux dropped exponentially with an e-folding time of 14.4~d. The exponential decay was interrupted by an increase in the X-ray flux, and a secondary maximum occurred 89~d after the onset of the outburst. A transition marked by significant changes in the timing and spectral properties of the source occurred 104~d after the start of the outburst. The transition is similar to soft-to-hard state transitions observed in other black hole candidate X-ray binaries. Most of the changes associated with the transition occurred in less than 2~d. The timing changes include an increase in the continuum noise level from less than 4\% RMS to greater than 10\% RMS and the appearance of a quasi-periodic oscillation (QPO) at 3.4~Hz with an RMS amplitude of 7.3\% in the 2-21~keV energy band. At the transition, the energy spectrum also changed with an abrupt drop in the soft component flux in the RXTE band pass. A change in the power-law photon index from 2.3 to 1.8, also associated with the transition, occurred over a time period of 8~d. After the transition, the source flux continued to decrease, and the QPO frequency decayed gradually from 3.4~Hz to about 0.2~Hz.
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[
{
"name": "x1630.tex",
"string": "\n\\documentclass[letterpaper]{article}\n\n\\usepackage{emulateapj}\n\\usepackage{onecolfloat}\n\\usepackage{apjfonts}\n\\usepackage{amsmath}\n\\usepackage{graphicx}\n\n%\\textheight=24.4cm\n\\textheight=23.2cm\n\n\\begin{document}\n\n\\submitted{To Appear in the Astrophysical Journal}\n\n\\twocolumn[\n\\title{X-Ray Spectral and Timing Evolution During the Decay of the\n1998 Outburst from the Recurrent X-Ray Transient 4U~1630--47}\n\n\\authoremail{[email protected]}\n\n\\author{John A. Tomsick}\n\\affil{Department of Physics and Columbia Astrophysics Laboratory, \nColumbia Univ., 550 West 120th Street, New York, NY 10027\\nl\n(Current address: Center for Astrophysics and Space Sciences, \nUniv. of California, San Diego, MS 0424, La Jolla, CA 92093)\\nl\n(e-mail: [email protected])}\n\n\\vspace{0.1cm}\n\n\\author{Philip Kaaret}\n\\affil{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, \nCambridge, MA 02138 (e-mail: [email protected])}\n\n\\begin{abstract}\n\nWe report on the X-ray spectral and timing behavior of the recurrent\nX-ray transient 4U~1630--47 for 51 \\it RXTE \\rm observations made\nduring the decay of its 1998 outburst. The observations began when the\nsource was still relatively bright, and, during one of the early \nobservations, a QPO with a non-Lorentzian profile occurred near 6~Hz. \nAs the source decayed, the X-ray flux dropped exponentially with \nan e-folding time of 14.4~d. The exponential decay was interrupted \nby an increase in the X-ray flux, and a secondary maximum occurred 89~d \nafter the onset of the outburst. A transition marked by significant \nchanges in the timing and spectral properties of the source occurred \n104~d after the start of the outburst. The transition is similar to \nsoft-to-hard state transitions observed in other black hole candidate \nX-ray binaries. Most of the changes associated with the transition \noccurred in less than 2~d. The timing changes include an increase in \nthe continuum noise level from less than 4\\% RMS to greater than 10\\% RMS \nand the appearance of a quasi-periodic oscillation (QPO) at 3.4~Hz with\nan RMS amplitude of 7.3\\% in the 2-21~keV energy band. At the transition, \nthe energy spectrum also changed with an abrupt drop in the soft \ncomponent flux in the \\it RXTE \\rm band pass. A change in the power-law \nphoton index from 2.3 to 1.8, also associated with the transition, \noccurred over a time period of 8~d. After the transition, the source flux \ncontinued to decrease, and the QPO frequency decayed gradually from 3.4~Hz \nto about 0.2~Hz. \n\n\\end{abstract}\n\n\\keywords{accretion, accretion disks --- X-ray transients: general ---\nstars: individual (4U~1630--47) --- stars: black holes --- X-rays: stars}\n\n] % twocolumn\n\n\\section{Introduction}\n\nAlthough the recurrent X-ray transient and black hole candidate (BHC) 4U~1630--47 has \nbeen studied extensively since its first detected outburst in 1969 (\\cite{priedhorsky86}), \ninterest in this source has intensified due to observations made during its \n1998 outburst. During the 1998 outburst, radio emission was detected for the first \ntime (\\cite{hjellming99}). Although the source was not resolved in the radio, the \noptically thin radio emission suggests the presence of a radio jet. Also, low \nfrequency quasi-periodic oscillations (QPOs) were discovered during the 1998 outburst \n(\\cite{dieters98a}) using the \\it Rossi X-ray Timing Explorer \\rm (\\it RXTE\\rm).\n\nHere, we report on X-ray observations of 4U~1630--47 made with \\it RXTE \\rm \n(\\cite{brs93}) during the decay of its 1998 outburst. We compare the X-ray light \ncurve to those of other BHC X-ray transients and study the evolution of the spectral \nand timing properties during the decay. Like many other X-ray transients, the light \ncurve of 4U~1630--47 shows an exponential decay and a secondary maximum (\\cite{csl97}).\nDuring the early part of the decay, when the X-ray flux was high, 4U~1630--47\nshowed canonical soft state characteristics (\\cite{v95};~\\cite{nowak95};~\\cite{ct96}),\nincluding an energy spectrum with a strong soft component and a steep power-law and \nrelatively low timing variability with a fractional RMS (Root-Mean-Square) amplitude \nof a few percent. Later in the decay, we observe a transition to a spectrally harder \nand more variable state, which has similarities to transitions observed for GS~1124--68 \n(\\cite{ebisawa94};~\\cite{miyamoto94}) and GRO~J1655--40 (\\cite{mendez98}) near the \nends of their outbursts.\n\nIn this paper, we describe the 4U~1630--47 X-ray light curve for the 1998 outburst \nand the \\it RXTE \\rm observations (\\S 2). In \\S 3 and \\S 4, we present results of \nmodeling the power and energy spectra, respectively. In \\S 5, we examine the \ntransition in more detail, and \\S 6 contains a discussion of the results. Finally, \n\\S 7 contains a summary of our findings.\n\n\\section{Observations and Light Curve}\n\nWe analyzed PCA (Proportional Counter Array) and HEXTE (High Energy X-ray \nTiming Experiment) data from 51 \\it RXTE \\rm pointings of 4U~1630--47 during the \ndecay of its 1998 outburst. The observation times, integration times and background \nsubtracted 2.5-20~keV PCA count rates are given in Table~\\ref{tab:obs}. In \nFigure~\\ref{fig:lightcurve}, we show the 1.5-12~keV PCA fluxes with the ASM \n(All-Sky Monitor) flux measurements in the same energy band. The ASM light curve was \nproduced from data provided by the ASM/\\it RXTE \\rm teams at MIT and at the \\it RXTE \\rm \nSOF and GOF at NASA's GSFC. The 1998 outburst was first detected by BATSE on Modified \nJulian Date 50841 (MJD = JD--2400000.5), and 4U~1630--47 was not detected by the ASM until \nabout MJD 50847 (\\cite{hjellming99};~\\cite{kuulkers98a}). Figure~\\ref{fig:lightcurve} \nshows that the ASM flux increased rapidly after MJD 50850, peaking at \n$1.10\\times 10^{-8}$~erg~cm$^{-2}$~s$^{-1}$ (1.5-12~keV) on MJD 50867. The flux \ndropped to about $6\\times 10^{-9}$~erg~cm$^{-2}$~s$^{-1}$ soon after the peak, and \nour \\it RXTE \\rm observations began during this time. Our observations fill a gap in the \nASM light curve near MJD 50880, showing that a flare occurred during this time. The flux \ndecayed exponentially between MJD 50883 and MJD 50902 with an e-folding time of 14.4~d. \nAfter the exponential decay, the flux increased by about 50\\% over a time period of about \n20~d, and a secondary maximum occurred near MJD 50936. After the secondary maximum, \nthe flux decay is consistent with an exponential with an e-folding time of 12~d to 13~d. \nIn Figure~\\ref{fig:lightcurve}, the vertical dashed line at MJD 50951 marks an \nabrupt change in the timing properties of the source, which is described in detail below. \nThe source flux at the transition was between 6 and \n7~$\\times 10^{-10}$~erg~cm$^{-2}$~s$^{-1}$.\n\n\\begin{figure}\n\\plotone{lightcurve.ps}\n\\caption{X-ray light curve for the 1998 outburst of 4U~1630--47. \nThe points with error bars are 1.5-12~keV ASM daily flux measurements,\nand the squares mark the 1.5-12~keV fluxes measured by the PCA \nduring 51 pointed observations. The solid lines are exponential\nfits to the light curve, and the dotted vertical line marks a transition \nin the spectral and timing properties of the source.\\label{fig:lightcurve}}\n\\end{figure}\n\nSoft $\\gamma$-ray bursts were detected from a position near 4U~1630--47 on MJD 50979 \n(\\cite{kouveliotou98}), 7~d after our last \\it RXTE \\rm observation, and the $\\gamma$-ray \nsource has been named SGR~1627--41. Although the position of SGR~1627--41 is not consistent \nwith the position of 4U~1630--47 (\\cite{hurley99}), the two sources are close enough so that \nthey were both in the \\it RXTE \\rm field of view during our observations, allowing for the \npossibility of source confusion. As described in detail in the appendix, \\it RXTE \\rm scans \nand \\it BeppoSAX \\rm observations provide information about possible source confusion.\nBased on the evidence, we conclude that it is very unlikely that SGR~1627--41 contributed \nsignificantly to the flux detected during our observations of 4U~1630--47.\n\n\\section{X-Ray Timing}\n\nFor each observation, we produced 0.0156-128~Hz power spectra to study the timing \nproperties of the system. For each 64~s interval, we made an RMS normalized\npower spectrum using data in the 2-21~keV energy band. To convert from the Leahy \nnormalization (\\cite{leahy83}) to RMS, we determined the Poisson noise level\nusing the method described in Zhang et al.~(1995) with a deadtime of 10 microseconds\nper event. For each observation, the individual 64~s power spectra were averaged,\nand the average spectrum was fitted using a least-squares technique and several different \nanalytic models. For individual 64~s power spectra, we calculated the error bars using \nequation A11 from Leahy et al.~(1983). When combining the power spectra for an entire \nobservation, we used two different methods to calculate the errors. In one method, \nwe calculated the errors by propagating the error bars for individual power spectra.\nThis method does not account for any intrinsic (i.e., non-random) changes in the power \nspectrum over the duration of the observation. We also estimated the error by calculating \n$\\sigma/\\sqrt{N}$, where $\\sigma$ is the standard deviation of the power measurements from \nthe individual spectra, and $N$ is the number of 64~s power spectra being combined. For \nall observations, the error estimates are approximately the same above $\\sim$2~Hz, indicating \nthat the shape of the power spectrum at higher frequencies does not change significantly \nduring an observation. However, below $\\sim$2~Hz, the calculated errors are significantly\nlarger using the second method, indicating that intrinsic changes in this region of \nthe power spectrum are significant. In the following, we have used the second method \nto calculate the errors.\n\nTo determine the analytic model to use for the continuum noise, we began by\nfitting the power spectrum for each observation with a power-law model. For some \nobservations, the power-law fits are acceptable ($\\chi^{2}_{\\nu} \\sim 1.0$); however,\nin most cases, the reduced $\\chi^{2}$ is significantly greater than 1.0 and\nsystematic features appear in the residuals. Strong QPOs dominate the residuals \nfor several observations, and these are discussed in detail below. For the\nobservations without obvious QPOs, the power-law residuals are similar and show a \nbroad excess peaking between 0.5 and 1.0~Hz. To model this broad excess, we focus on \nthe observation 8 power spectrum since the statistics are good for this observation and \nthere are no strong QPOs. Fitting the observation 8 power spectrum with a power-law \nalone gives a poor fit ($\\chi^{2}/{\\nu} = 680/444$). Previous studies of the power \nspectra of BHCs show that the continuum noise can be described by a model consisting of \ntwo components: A power-law and a band-limited noise component \n(e.g., Cui et al.~1997;~Miyamoto et al.~1994). In applying this model to 4U~1630--47, \nwe used a broken power-law with the lower power-law index fixed to zero for the \nband-limited component, and hereafter this model is referred to as the flat-top model. \nApplying this two-component model to the observation 8 power spectrum gives a \nsignificantly improved fit ($\\chi^{2}/{\\nu} = 486/441$). Figure~\\ref{fig:powercont}a \nshows the observation 8 power spectrum fitted with the two-component model.\n\n\\begin{figure}\n\\plotone{powercont.ps}\n\\vspace{0.7cm}\n\\caption{The power spectra for observation 8 (a) and observations 11 to \n40 (b). The observation 8 power spectrum is fitted with a model consisting \nof a power-law (dashed line) and a band-limited (or flat-top) noise component \n(dotted line). The solid line is the sum of the two components. For \nobservations 11 to 40, only the flat-top component (solid line) is necessary. \nThese power spectra have been rebinned for presentation.\n\\label{fig:powercont}}\n\\end{figure}\n\n\\begin{figure}\n\\plotone{obs3.ps}\n\\caption{Observation 3 power spectrum fitted with the continuum model\n(flat-top plus power-law) and three Lorentzians at 5.43~Hz, 6.19~Hz\nand 10.79~Hz (dashed lines). The solid line is the sum of the continuum \nand the Lorentzians.\n\\label{fig:obs3}}\n\\end{figure}\n\nFor each observation, we fitted the power spectrum using the power-law\nmodel alone, the flat-top model alone and the combination of the two components. \nFor several of the observations, the statistics are not good enough to uniquely \ndetermine the best continuum model. In these cases, we combined consecutive \nobservations, as indicated in Table~\\ref{tab:powercont}, to improve the statistics \nand refitted the power spectra with the same models. For observations 1 to 10, the \nfit using the two-component model is significantly better than using either of the \nindividual components, indicating that these power spectra require both components. \nFor observations 11 to 51, the flat-top model alone provides a significantly better \nfit than the power-law model alone, and the two-component model does not provide a \nsignificantly better fit than the flat-top component alone. We conclude that only \nthe flat-top component is necessary to fit these power spectra. The continuum \nparameters for all observations are given in Table~\\ref{tab:powercont}. In cases \nwhere the power-law component is not significantly detected, the 90\\% confidence \nupper limit on the contribution from a power-law with an index of $-1.0$ is given. \nFigure~\\ref{fig:powercont}b shows the power spectrum for observations 11 to 40 \ncombined, illustrating that the power-law component is not significant at low\nfrequencies. We note that there is some evidence for excess noise near 45~Hz, but \nthis excess is not statistically significant. For observations 41 to 51, the RMS \namplitude for the continuum noise is 10\\% to 17\\%, which is considerably higher \nthan for observations 1 to 40. In determining the continuum parameters, we \nincluded Lorentzians to model the QPOs as marked in Table~\\ref{tab:powercont}.\n\nTo determine where QPOs are present, we examined the residuals for fits with the \ncontinuum model only. For observations 1-2, 3, 6, 7, 8, 41, 42, 43, 44, 45, \n46-48 and 49, systematic features in the residuals suggest the presence of QPOs. \nTo determine if these features are statistically significant, we compared the \n$\\chi^{2}$ for a fit with the continuum model only to a fit with a Lorentzian \nadded to the continuum model. F-tests indicate that QPOs significant at greater \nthan 96\\% confidence occurred for observations 1-2, 3, 41, 42, 43 and 46-48. \nFor observation 1-2, the continuum model provides a relatively poor fit to the \ndata ($\\chi^{2}/\\nu = 561/441$), and the largest residuals occur near 11~Hz. \nThe fit is significantly improved ($\\chi^{2}/\\nu = 471/438$) when a Lorentzian \nis added to the continuum model. The QPO centroid, FWHM and RMS amplitude are \n$10.8\\pm 0.2$~Hz, $2.9\\pm 0.6$~Hz and $2.01\\%\\pm 0.16$\\%, respectively. Although \nthe features for observations 6, 7 and 8 are not as statistically significant, \nthey also have centroids between 10 and 13~Hz and may be related to the \nobservation 1-2 QPO.\n\nFor observation 3, the continuum model provides an extremely poor fit\n($\\chi^{2}/\\nu = 987/441$), and the largest residuals occur near 6~Hz. Although\nthe fit is significantly improved by the addition of a Lorentzian at 5.7~Hz, the\nfit is still relatively poor ($\\chi^{2}/\\nu = 685/438$), and systematic features\nare present in the residuals, which indicate that the 5.7~Hz QPO is not\nwell-described by a Lorentzian. As for some other BHCs \n(\\cite{belloni97};~\\cite{rtb99}), the QPO has a high frequency shoulder\nthat can be modeled using a second Lorentzian. Modeling the QPO with\nLorentzians at 5.4~Hz and 6.2~Hz improves the fit to $\\chi^{2}/\\nu = 608/435$.\nThe fit can be further improved to $\\chi^{2}/\\nu = 552/432$ by the addition of \na QPO near 11~Hz. It is possible that the 11~Hz QPO is a harmonic of the lower\nfrequency QPO, but it may also be related to the QPO that occurred during \nobservation 1-2. Table~\\ref{tab:obs3} summarizes the QPO parameters for \nobservation 3, and it should be noted that three Lorentzians were included in \nthe model in determining the continuum parameters given in \nTable~\\ref{tab:powercont}. Figure~\\ref{fig:obs3} shows the observation 3 power \nspectrum fitted with a model consisting of the continuum plus three Lorentzians \nto model the QPOs. The Lorentzians at $5.43\\pm 0.02$~Hz, $6.19\\pm 0.04$~Hz and \n$10.79\\pm 0.14$~Hz have RMS amplitudes of $2.89\\%\\pm 0.18$\\%, $2.85\\%\\pm 0.21$\\% \nand $1.85\\%\\pm 0.20$\\%, respectively. To determine if the QPO properties \nchanged during the observation, we divided observation 3 into two time segments\nwith durations of 576~s and 512~s, made power spectra for each segment and \nfitted the power spectra with a model consisting of the continuum (flat-top \nplus power-law) plus three Lorentzians. The results for these fits are given\nin Table~\\ref{tab:obs3}. There is no evidence for large changes in the QPO\nproperties between the two time segments. \n\nThe increase in the continuum noise level that occurred between observations \n40 and 41 was accompanied by the appearance of a QPO at $3.390\\pm 0.008$~Hz with \nan RMS amplitude of $7.30\\%\\pm 0.33$\\%. In subsequent observations, the QPO \nfrequency gradually shifted to lower frequency. Figure~\\ref{fig:shiftqpo} shows \nthe power spectra for observations 41, 42, 43 and 46-48. After the 3.4~Hz QPO \nappeared for observation 41, QPOs occurred at $2.613\\pm 0.012$~Hz, \n$1.351\\pm 0.012$~Hz and $0.228\\pm 0.003$~Hz for observations 42, 43 and 46-48, \nrespectively. We note that the observation 43 QPO shows some evidence \nfor a high frequency shoulder. QPOs with lower statistical significance occurred \nfor observations 44, 45 and 49 with frequencies of $0.430\\pm 0.006$~Hz, \n$0.365\\pm 0.011$~Hz and $0.182\\pm 0.005$~Hz. It should be noted that these QPOs \nare consistent with the gradual shift to lower frequencies. The QPO parameters \nfor observations 41 to 49 are given in Table~\\ref{tab:shiftqpo}. \n\n\\section{Energy Spectra}\n\nWe produced PCA and HEXTE energy spectra for each observation using the processing\nmethods described in Tomsick et al.~(1999). We used the PCA in the 2.5-20~keV\nenergy band and HEXTE in the 20-200~keV energy band. For the PCA, we used standard \nmode data, consisting of 129-bin spectra with 16~s time resolution, included \nonly the photons from the top anode layers and estimated the background using the \nsky-VLE model\\footnote{%\nSee M.J. Stark et al.~1999, PCABACKEST, available at \nhttp:// lheawww.gsfc.nasa.gov/docs/xray/xte/pca.}. We used the version 2.2.1 response \nmatrices with a resolution parameter of 0.8 and added 1\\% systematic errors to account \nfor uncertainties in the PCA response. As described in Tomsick et al.~(1999), we used\nCrab spectra to test the response matrices and found that the response matrix \ncalibration is better for PCUs 1 and 4 than for the other three Proportional\nCounter Units (PCUs); thus, we only used these two PCUs for spectral analysis and \nallowed for free normalizations between PCUs. PCU 4 was off during three observations\n(34, 39 and 48), and, to avoid instrumental differences, we did not use these \nobservations in our spectral analysis. Previously, we found that the PCA over-estimates \nthe source flux by a factor of 1.18 (\\cite{tomsick99}), and, in this paper, we\nreduced the fluxes and spectral component normalizations by a factor of 1.18 so that \nthe PCA flux scale is in agreement with previous instruments. \n\nHEXTE energy spectra were produced using standard mode data, consisting of 64-bin \nspectra with 16~s time resolution. We used the March~20,~1997 HEXTE response matrices\nand applied the necessary deadtime correction (\\cite{rothschild98}). For the spectral \nfits, the normalizations were left free between cluster A and cluster B. It is \nwell-known that the HEXTE and PCA normalizations do not agree, so the normalizations\nwere left free between HEXTE and the PCA. The HEXTE background subtraction is\nperformed by rocking on and off source. Each cluster has two background fields, \nand we checked the HEXTE background subtraction by comparing the count rates for\nthe two fields. In cases where contamination of one of the fields occurred, we \nonly used the data from the non-contaminated background field.\n\n\\begin{figure}\n\\plotone{shiftqpo.ps}\n\\vspace{1.0cm}\n\\caption{Power spectra (Power = (RMS/Mean)$^{2}$/Hz) for observations \n41 (a), 42 (b), 43 (c) and 46-48 (d) showing QPOs detected at 3.390~Hz, \n2.613~Hz, 1.351~Hz and 0.228~Hz. The power spectra are fitted with a model \nconsisting of a flat-top (dotted line) and a Lorentzian (dashed line). The \nsolid line is the sum of the two components.\n\\label{fig:shiftqpo}}\n\\end{figure}\n\nWe first fitted the energy spectra using a power-law with interstellar absorption, \nbut this model does not provide acceptable fits to any of the spectra. For most of \nthe observations, the residuals suggest the presence of a soft component, which is \ntypical for 4U~1630--47 (\\cite{tomsick98};~\\cite{parmar97}). A soft component was \nalso detected during \\it BeppoSAX \\rm observations of 4U~1630--47, which overlap \nwith our \\it RXTE \\rm observations (\\cite{oosterbroek98}). Since \nOosterbroek et al.~(1998) found that a disk-blackbody model (\\cite{makishima86}) \nprovides a good description of the soft component observed by \\it BeppoSAX\\rm, we \nadded a disk-blackbody model to the power-law component and refitted the \\it RXTE \\rm\nspectra. Although the addition of a soft component improves the fits significantly\nin most cases, the fits are only formally acceptable for a small fraction of the \nobservations, and, in the worst case, the reduced $\\chi^{2}$ is 3.1 for 106 \ndegrees of freedom. \n\nA broad iron absorption edge, associated with the Compton reflection component\n(\\cite{lw88}), is commonly observed in the energy spectra of BHCs \n(\\cite{ebisawa94} and references therein;~\\cite{sobczak99}). \nWe refitted the 4U~1630--47 spectra with the model given in equation 3 of\nEbisawa et al.~(1994), which includes a broad absorption edge in addition to\nthe disk-blackbody and power-law components. Following Ebisawa et al.~(1994),\nwe fixed the width of the absorption edge to 10~keV and left the edge energy \nfree. For all of the 4U~1630--47 observations, the fits are significantly better \nwith the absorption edge. As an example, for observation 8, the fit improved from \n$\\chi^{2}/\\nu = 179/106$ using the disk-blackbody plus power-law model without \nthe edge to $\\chi^{2}/\\nu = 110/104$, indicating that the edge is required at\nthe 99.1\\% confidence level. In addition to the absorption edge, an iron emission \nline is expected due to fluorescence of the X-ray illuminated accretion disk \nmaterial (\\cite{matt92}); thus, we have added an emission line to our model to \ndetermine whether the line is present in the spectra. We used a narrow \nemission line since the width of the emission line could not be constrained,\nand the energy of the emission line was a free parameter. \n\n\\begin{figure}\n\\plotone{energy.ps}\n\\vspace{-0.8cm}\n\\caption{PCA and HEXTE energy spectrum for observation 8\nfolded with the instrument response and fitted with a model\nconsisting of a disk-blackbody (dashed line), a power-law\n(thin solid line), a narrow emission line (dotted line) and a \nbroad iron absorption edge. The sum of these components is\nmarked with a thick solid line. The column density is fixed to \n$9.45\\times 10^{22}$~cm$^{-2}$. The bottom panel shows the \nresiduals for the fit.\\label{fig:energy}}\n\\end{figure}\n\nWe fitted the spectra with the column density free and also with the column \ndensity fixed to the mean value for the 51 observations, \n$9.45\\times 10^{22}$~cm$^{-2}$. For all observations, the quality of\nthe fit is not significantly worse with the column density fixed.\nTable~\\ref{tab:energy} shows the results for the spectral fits with the column \ndensity fixed using a model consisting of a power-law, a disk-blackbody component, \na narrow emission line and a broad absorption edge. The free parameters for the \npower-law component are the photon index ($\\Gamma$) and the normalization. For the \ndisk-blackbody component, the temperature at the inner edge of the disk ($kT_{in}$) \nand the normalization are free parameters. Rather than the power-law and \ndisk-blackbody normalizations, the component fluxes are given in \nTable~\\ref{tab:energy}. The emission line energy ($E_{line}$) and normalization \n($N_{line}$) and the edge energy ($E_{edge}$) and optical depth ($\\tau_{\\rm{Fe}}$) \nare free parameters. However, in cases where the best fit value for $E_{edge}$ \nis less than 7.1~keV (the value for neutral iron), we fixed $E_{edge}$ to 7.1~keV.\nIn Table~\\ref{tab:energy}, we do not give error estimates for $kT_{in}$ since the \nuncertainty for this parameter is dominated by systematic error due to uncertainty \nin the correct value for the column density. By comparing the values found\nfor $kT_{in}$ with the column density fixed to those with the column density\nfree, we estimate that the systematic error is 0.05~keV. For the 51 \nobservations, the largest $\\chi^{2}_{\\nu}$ is 1.32 for 102 degrees of freedom \nand $\\chi^{2}_{\\nu}<1.0$ for 44 of the observations, indicating that the spectra \nare well-described by the model. Figure~\\ref{fig:energy} shows the observation 8 \nenergy spectrum and residuals. The residuals shown in Figure~\\ref{fig:energy} \ntypify the quality obtained for the observations.\n\n\\begin{figure}\n\\plotone{line.ps}\n\\caption{Data-to-model ratio for a power-law plus disk-blackbody\nfit to the spectrum for observations 44 to 51. An emission\nline at $6.46\\pm 0.04$~keV with an equivalent width of 91~eV is \nclearly present. Although we fitted both the PCA and the HEXTE data, \nonly the PCA data are shown.\\label{fig:line}}\n\\end{figure}\n\nFor each observation, we determined the significance of the emission line by \nrefitting the spectra without the line and using an F-test. In cases where the \nsignificance of the emission line is less than 90\\%, we fixed $E_{line}$ to the \nbest fit value and determined the 90\\% confidence upper limit on $N_{line}$. \nAlthough most of the spectra do not require the emission line at a high confidence \nlevel, the line is required at greater than 90\\% confidence for 16 of the 51 \nobservations, and at greater than 95\\% confidence for 9 observations. In the \ncases where the iron line is detected at greater than 90\\% confidence, the \nequivalent width of the iron line is between 45~eV (for observation 7) and \n110~eV (for observation 47). \n\nWe also determined the significance of the disk-blackbody component using\nthe same method described above for the emission line. With the column \ndensity fixed, the disk-blackbody component is required at greater than\n97\\% confidence for every observation; however, with the column density\nfree, the disk-blackbody component is not required for several observations.\nWith the column density free, the disk-blackbody components are significant\nat only 50\\% and 65\\% confidence for observations 3 and 4, respectively, and \nat between 46\\% and 70\\% confidence for observations 41 to 51. In \nTable~\\ref{tab:energy}, the disk-blackbody fluxes for these observations are \nmarked as upper limits since the component is not detected. For observations \n41 to 51, the best fit values of $kT_{in}$ are also marked as upper limits \nsince the peak of the disk-blackbody flux falls below the PCA band pass and \nwe cannot constrain $kT_{in}$ and the column density independently.\n\nThe flux levels and line parameters are similar for observations 44 to 51 so \nwe refitted the combined spectrum for these observations. As shown in\nTable~\\ref{tab:energy}, an emission line at $6.46\\pm 0.04$~keV is detected at \n99.93\\% confidence. The line energy is consistent with emission from neutral \nor mildly ionized iron and the line equivalent width is 91~eV. We also fitted \nthe combined spectrum with a model consisting of a disk-blackbody and a \npower-law, and Figure~\\ref{fig:line} shows the data-to-model ratio, clearly \nindicating the presence of the iron line. Since 4U~1630--47 lies \nalong the Galactic ridge ($l = 336.91^{\\circ}$, $b = 0.25^{\\circ}$), we have \nconsidered the possibility that the 4U~1630--47 spectra are contaminated\nby Galactic ridge emission. It is unlikely that the ridge emission is the\nsource of the iron line detected in our spectra because the line energy\nwe observe is considerably lower than the values measured by $ASCA$, \n$Ginga$ and $Tenma$ for the Galactic ridge, which are all near 6.7~keV \n(\\cite{kaneda97} and references therein). Also, based on the spectrum \nof the Galactic ridge emission measured by \\it RXTE \\rm (\\cite{vm98}), \nthe spatially averaged Galactic ridge 2.5-20~keV flux is only 6\\% \nof the flux for the combination of observations 44 to 51, indicating that \nthe level of contamination by the Galactic ridge emission should be low.\n\n\\section{State Transition}\n\n\\begin{figure}\n\\plotone{trans.ps}\n\\vspace{1.0cm}\n\\caption{Timing and Spectral parameters for observations 33 to 51. \nPanel a is the 2.5-20~keV flux (in ergs~cm$^{-2}$~s$^{-1}$) vs. time. \nThe timing parameters are shown in panels b$_{1}$, b$_{2}$ and b$_{3}$, \nand the spectral parameters are shown in panels c$_{1}$, c$_{2}$ and \nc$_{3}$. The error bars displayed correspond to $\\Delta \\chi^{2} = 1.0$\n(68\\% confidence) and the upper limits shown are 90\\% confidence.\nThe bolometric disk-blackbody flux is shown in panel c$_{3}$. A \nvertical dotted line at MJD 50951 marks the state transition.\\label{fig:trans}}\n\\end{figure}\n\nFigure~\\ref{fig:trans} shows the evolution of the timing and spectral \nparameters for observations 33 to 51. Significant changes in the 4U~1630--47 \nemission properties occurred between observations 40 and 41, and we interpret \nthis as evidence that a state transition occurred. In Figure~\\ref{fig:trans}, \nthe transition is marked with a vertical dashed line at MJD 50951. At the \ntransition, an increase in source variability occurred with the 0.01-10~Hz\nRMS amplitude of the flat-top component increasing from between 2.1\\% and 3.9\\% \nfor observations 33 to 40 to $10.2\\%\\pm 0.6$\\% for observation 41. As shown \nin panel b$_{1}$ of Figure~\\ref{fig:trans}, the RMS amplitude continued to \nincrease after the transition, reaching a maximum value of $17.3\\%\\pm 0.8$\\% \nfor observation 46-48. In addition to the increase in the continuum noise level, \na QPO appeared for observation 41, and the centroid QPO frequency and RMS amplitude \nare shown in panels b$_{2}$ and b$_{3}$, respectively. The timing changes \noccurred in less than 2~d and with only a small change in the 1.5-12~keV flux \n(shown in panel a of Figure~\\ref{fig:trans}). \n\nTo determine if a QPO was present before the transition, we made a combined \npower spectrum for observations 33 to 40. When the 2-21~keV power spectrum is \nfitted with a flat-top model, the residuals show no clear evidence for a QPO. \nThe 90\\% confidence upper limit on the RMS amplitude for a QPO in a frequency \nrange from 0.1~Hz to 10~Hz is 2.4\\%. We performed an additional test by determining \nthe energy range where the observation 41 QPO is strongest. For observation 41,\nthe RMS amplitudes are $6.1\\%\\pm 0.4$\\% and $8.6\\%\\pm 0.4$\\% for the 2-6~keV and \n6-21~keV energy bands, respectively, indicating that the strength of the QPO \nincreases with energy. Since the QPO is stronger in the 6-21~keV energy band for \nobservation 41, we produced a 6-21~keV power spectrum for observations 33 to 40.\nAs before, when a flat-top model is used to fit the power spectrum, the residuals\ndo not show evidence for QPOs, and the 90\\% confidence upper limit on the RMS \namplitude for a QPO in a frequency range from 0.1~Hz to 10~Hz is 2.9\\%.\n\nAlthough the difference between the observation 40 and 41 energy spectra is \nnot as distinct as for the power spectra, changes occurred. In Figure~\\ref{fig:trans}, \nthe spectral parameters $\\Gamma$ and $kT_{in}$ are shown in panels c$_{1}$ \nand c$_{2}$, respectively. The power-law index hardened slightly between \nobservations 40 and 41; however, this change appears to be part of a larger \ntrend, which occurred over a span of 8~d between observations 38 and 43. \nThe inner disk temperature began to decrease near observation 37, and \nthe soft component is not confidently detected after observation 40, which\nprobably indicates that $kT_{in}$ continued to drop after observation 40.\nThe spectral changes are also illustrated in Figures~\\ref{fig:energy3}a and \n\\ref{fig:energy3}b, which show the energy spectra for observations 40 and \n41, respectively. Figure~\\ref{fig:energy3}c shows the energy spectrum\nfor observations 44 to 51, indicating that the spectrum continued to\nharden after the transition.\n\nIn summary, during the transition, the noise level increased, the power-law \nspectral index hardened and the soft component flux in the $RXTE$ band pass \ndecreased. Similar changes are typically observed in BHC systems when \nsoft-to-hard state transitions occur (\\cite{v95};~\\cite{nowak95};~\\cite{ct96}),\nand we conclude that such a transition occurred for 4U~1630--47. We also show \nthat QPOs were not present during the observations leading up to the transition, \nindicating that their appearance during observation 41 is related to the state \ntransition.\n\n\\section{Discussion}\n\n\\subsection{Comparisons to Previous 4U~1630--47 Outbursts}\n\nSince 4U~1630--47 was discovered in 1969, quasi-periodic outbursts have been observed\nfrom this source every 600 to 690~d (\\cite{kuulkers97})\\footnote{%\nHowever, the 1999 outburst significantly deviates from this periodicity \n(\\cite{mccollough99}).}. The light curve for the 1998 \n4U~1630--47 outburst is the best example of a ``fast-rise exponential-decay\" (or FRED) \nlight curve (Chen et al.~1997) that has been observed for 4U~1630--47. A FRED light \ncurve may have been observed for 4U~1630--47 by the $Vela~5B$ X-ray monitor in 1974 \n(\\cite{priedhorsky86};~Chen et al.~1997), but the temporal coverage was sparse compared to \nthe coverage obtained for the 1998 outburst. Good temporal coverage was obtained for \nthe 1996 outburst by the $RXTE$/ASM, and a FRED light curve was not observed. After \nthe start of the 1996 outburst, the flux stayed at a high level for about 100~d before \ndecaying exponentially with an e-folding time of about 14.9~d (\\cite{kuulkers97}). \nAlthough the overall light curve shapes are different for the two outbursts, it is\ninteresting that the e-folding time for the 1998 outburst, 14.4~d, is close to the\n14.9~d e-folding time for the 1996 outburst. This may suggest that the e-folding time \nis related to a physical property of the system that does not change between outbursts.\nFor example, the e-folding time may be related to the mass of the compact object \n(\\cite{ccl95}) or the radius of the accretion disk (\\cite{kr98}). \n\n\\begin{figure}\n\\plotone{energy3.ps}\n\\vspace{1.0cm}\n\\caption{Unfolded PCA and HEXTE energy spectra for (a) Observation 40; \n(b) Observation 41; and (c) Observations 44 to 51 with the spectral\ncomponents marked as for Figure~\\ref{fig:energy}. The figure shows that \nthe disk-blackbody temperature changes significantly between observations \n40 and 41, and that the disk-blackbody flux is significantly lower for \nobservations 44 to 51. Also, the power-law gradually hardens. \n\\label{fig:energy3}}\n\\end{figure}\n\nA state transition with similarities to the soft-to-hard transition we report in this \npaper was observed by $EXOSAT$ during the decay of the 1984 outburst from 4U~1630--47. \nFour $EXOSAT$ observations of 4U~1630--47 were made during outburst decay (\\cite{psw86}). \nDuring the first two observations in 1984 April and 1984 May, a strong soft component was \nobserved in the energy spectrum. The power-law was harder in May than in April and became \neven harder for two observations made in 1984 July. During the July observations, the soft \ncomponent was not clearly detected. Assuming a soft-to-hard transition occurred between\nMay and July, the transition took place at a luminosity between $10^{36}$~erg~s$^{-1}$ and \n$10^{38}$~erg~s$^{-1}$ (1-50~keV), which is consistent with the luminosity where the 1998 \nsoft-to-hard transition occurred, $7\\times 10^{36}$~erg~s$^{-1}$ (2.5-20~keV). The \nluminosities given here are for an assumed distance of 10~kpc; however, the distance to \n4U~1630--47 is not well-determined.\n\n\\subsection{Comparisons to Other Black Hole Candidate X-Ray Transients}\n\nHere, we compare the properties 4U~1630--47 displayed during the decay of its 1998 \noutburst to those observed for other X-ray transients. We have compiled a list of \ncomparison sources using Tanaka \\& Shibazaki~(1996) and Chen, Shrader \\& Livio (1997). \nThe comparison group contains the BHC X-ray transients that had strong soft \ncomponents during outburst and FRED light curves. The comparison sources from the \nabove references are GS~1124--68, GS~2000+251, A~0620--00, EXO~1846--031, Cen~X-2, \n4U~1543--47 and A~1524--617. We also include a recent X-ray transient, XTE~J1748--288, \nthat has similar properties to this group. For the eight comparison sources, the \nexponentially decaying portions of their X-ray light curves have e-folding times ranging \nfrom 15~d to 80~d (Chen et al.~1997;~Revnivtsev et al.~1999), and the mean decay time \nis 39~d. Thus, the 14.4~d e-folding time for 4U~1630--47 is shorter than average, but \nnot unprecedented.\n\nLike 4U~1630--47, secondary maxima occurred in the X-ray light curves of 4U~1543-47, \nA~0620--00, GS~2000+251 and GS~1124--68, and a tertiary maximum occurred for A~0620--00 \n(\\cite{kaluzienski77}). It is likely that the secondary and tertiary maxima are the \nresult of X-ray irradiation of the outer accretion disk or the optical companion\n(\\cite{kr98};~\\cite{clg93};~\\cite{aks93}). In this picture, the time between the start \nof the outburst and subsequent maxima depends on the viscous time scale of the disk.\nFor A~0620--00, GS~2000+251 and GS~1124--68, secondary maxima are observed 55 to 75~d \nafter the start of the outburst. These maxima, often referred to as ``glitches\", consist \nof a sudden upward shift in X-ray flux, interrupting the exponential decay. The tertiary \nmaximum observed for A~0620--00 about 200~d after the start of the outburst is significantly \ndifferent, and can be described as a broad (35 to 40~d) bump in the X-ray light curve near \nthe end of the outburst. The 4U~1630--47 secondary maximum is similar to the A~0620--00 \ntertiary maximum since it is a broad (about 25~d) increase in flux near the end of the \noutburst. However, the secondary maximum peaked about 89~d after the start of the outburst, \nwhich is considerably less than for A~0620--00.\n\nFour sources in our comparison group exhibited soft-to-hard state transitions\nduring outburst decay: A~0620--00 (\\cite{kuulkers98b}), GS~2000+251 (\\cite{ts96}), \nGS~1124--68 (\\cite{kitamoto92}) and XTE~J1748--288 (Revnivtsev et al.~1999). The \n4U~1630--47 transition occurred 104~d after the start of the outburst, while \ntransitions for the other four sources occurred 100 to 150~d, 230 to 240~d, \n131 to 157~d and about 40~d after the starts of the outbursts for A~0620--00, \nGS~2000+251, GS~1124--68 and XTE~J1748--288, respectively. Detailed X-ray spectral \nand timing information is available after the transition to the hard state for \nGS~1124--68. Like 4U~1630--47, the GS~1124--68 transition was marked by an increase \nin the RMS noise amplitude; however, in contrast to 4U~1630--47, QPOs were not observed \nfor GS~1124--68 in the hard state (\\cite{miyamoto94}). Also, during the GS~1124--68 \ntransition, the X-ray spectrum hardened with a drop in the inner disk temperature \n($kT_{in}$) and a change in the power-law photon index ($\\Gamma$) from 2.2 to 1.6 \n(\\cite{ebisawa94}). During the 4U~1630--47 transition, the change in the soft component \nwas consistent with a drop in $kT_{in}$, and $\\Gamma$ changed from 2.3 to 1.8. \nWhile the $Ginga$ observations of GS~1124--68 were relatively sparse near the \ntransition, our observations of 4U~1630--47 show that soft-to-hard transitions can \noccur on a time scale of days.\n\n\\subsection{Hard State QPOs}\n\nAlthough QPOs were not detected after the GS~1124--68 state transition, QPOs were observed \nafter a similar transition for the microquasar GRO~J1655--40 during outburst decay \n(\\cite{mendez98}). \\it RXTE \\rm observations of GRO~J1655--40 show that a state transition \noccurred between 1997 August 3 and 1997 August 14. The transition was marked by an \nincrease in the continuum variability from less than 2\\% RMS to 15.6\\% RMS, a decrease in \nthe characteristic temperature of the soft spectral component ($kT_{in}$) from 0.79~keV to \n0.46~keV and the appearance of a QPO at 6.46~Hz with an RMS amplitude of 9.8\\%. A QPO was \nalso detected at 0.77~Hz during an August 18 \\it RXTE \\rm observation of GRO~J1655--40 \nwhen the 2-10~keV flux was about a factor of four lower than on August 14; thus, the shift \nto lower frequencies with decreasing flux is common to GRO~J1655--40 and 4U~1630--47. The \ncorrelations between spectral and timing properties for the microquasar GRS~1915+105 are \nsimilar to those observed for GRO~J1655--40 and 4U~1630--47. Markwardt, Swank \\& Taam \n(1999) and Muno, Morgan \\& Remillard (1999) found that 1-15~Hz QPOs are observed for \nGRS~1915+105 more often when the source spectrum is hard. Markwardt et al.~(1999) report \na correlation between QPO frequency and disk flux, and Muno et al.~(1999) find that the \nQPO frequency is correlated with $kT_{in}$. Although these results suggest that the \nQPO is related to the soft component, the fact that the QPO strength increases with \nenergy for 4U~1630--47, GRO~J1655--40 and GRS~1915+105 indicates that the QPO mechanism \nmodulates the hard component flux. \n\nA physical model that has been used to explain the energy spectra of \nBHC systems involves the presence of an advection-dominated accretion flow \nor ADAF (\\cite{narayan97}). The model assumes the accretion flow \nconsists of two zones: An optically thin ADAF region between the black \nhole event horizon and a transition radius, $r_{t}$, and a geometrically \nthin, optically thick accretion disk outside $r_{t}$. Esin, McClintock \\& \nNarayan (1997) developed and used this model to explain the spectral changes \nobserved for GS~1124--68 during outburst decay, which are similar to the \nspectral changes observed for 4U~1630--47. The different emission states \nobserved during the decay can be reproduced by decreasing the mass accretion \nrate and increasing $r_{t}$. This model suggests that the gradual decrease \nin the QPO frequencies observed for GRO~J1655--40 and 4U~1630--47 may be \nrelated to a gradual increase in $r_{t}$ or a gradual drop in the mass \naccretion rate (or both).\n\nIn studies of the X-ray power spectra of BHC and neutron star X-ray binaries,\nWijnands \\& van der Klis~(1999) find a correlation between the frequency of \nQPOs between 0.2 and 67~Hz and the break frequency of the continuum component \n(described as a flat-top component in this paper). Such a correlation is \ninteresting since it suggests that there is a physical property of the system \nthat sets both time scales and that the physical property does not depend on the \ndifferent properties of BHCs and neutron stars. While 4U~1630--47 was in its hard \nstate, the break frequency gradually decreased from $3.33\\pm 0.36$~Hz to \n$0.48\\pm 0.03$~Hz between observations 41 and 46-48 as the QPO frequency dropped \nfrom 3.4~Hz to 0.23~Hz (cf. see Tables~\\ref{tab:powercont} and \\ref{tab:shiftqpo}). \nAs for the other sources included in the Wijnands \\& van der Klis~(1999) sample, \n4U~1630--47 exhibits a correlation between QPO frequency and break frequency. \nHowever, for 4U~1630--47, the QPO frequency is below or consistent with the \nbreak frequency, while in other sources the QPO frequency is above the break\nfrequency.\n\n\\subsection{Emission Properties During the Flare}\n\nFigure~\\ref{fig:flare} shows the 2-60~keV PCA light curves for the two observations \nmade during the flare which occurred around MJD 50880 (observations 3 and 4).\nFor observation 3, short (about 4~s) X-ray dips are observed. We have \nexamined the light curves for all 51 observations and find that X-ray dips\nare only observed for observation 3. However, 4U~1630--47 observations\nmade by another group show that short X-ray dips were observed earlier in\nthe outburst (\\cite{dieters99}). In addition to the dips, Figure~\\ref{fig:flare}\nshows that the level of variability is much higher for observation 3\nthan for observation 4. Table~\\ref{tab:powercont} details the differences \nbetween the power spectra for these two observations. For observation 3, \nthe flat-top and power-law RMS amplitudes are 3.55\\% and 4.36\\%, respectively, \nwhile, for observation 4, the flat-top and power-law RMS amplitudes are 1.83\\% \nand 1.10\\%, which are even lower than most of the nearby non-flare observations. \nAlso, QPOs are observed for observation 3 but not for observation 4. The timing \ndifferences between these two observations are especially remarkable because \nthe energy spectra for observations 3 and 4 are nearly identical \n(cf. Table~\\ref{tab:energy}). \n\n\\begin{figure}\n\\plotone{flare.ps}\n\\caption{PCA light curves for the flare observations (observations 3\nand 4). The 2-21~keV X-rays are binned in 1~s intervals, and \nbackground has not been subtracted. The figure shows that the source \nvariability was much higher during observation 3 than during \nobservation 4.\\label{fig:flare}}\n\\end{figure}\n\nThe asymmetry of the low frequency QPO peak for observation 3 is similar to\nQPOs observed for GS~1124--68 (\\cite{belloni97}) and XTE~J1748--288 \n(Revnivtsev et al.~1999). For these two sources and for 4U~1630--47, the \nasymmetric shape of the QPO can be modeled using two Lorentzians, suggesting \nthat the asymmetry may be due to a shift in the QPO centroid during the \nobservation. Revnivtsev et al.~(1999) find that some properties of the \nXTE~J1748--288 power spectra are consistent with this picture.\nThe 4U~1630--47 timing properties during observation 3 are not consistent \nwith a gradual shift in the QPO centroid during the observation since the \n5.4~Hz and 6.2~Hz Lorentzians are present in both segments of the observation\n(cf. Table~\\ref{tab:obs3}). The stability of the QPO shape may indicate that \nthe asymmetric peak is caused by an intrinsic property of the QPO mechanism.\nHowever, for observations of 4U~1630--47 containing dips, Dieters et al.~(1999) \nfind that the frequencies of some QPOs are lower within the dips than outside \nthe dips. For our observation 3, it is possible that frequency changes during \nthe dips (cf. Figure~\\ref{fig:flare}) cause the QPO profile to be asymmetric.\n\n\\section{Summary and Conclusions}\n\nWe have analyzed data from 51 \\it RXTE \\rm observations of 4U~1630--47 during \nthe decay of its 1998 outburst to study the evolution of its spectral and \ntiming properties. During the decay, the X-ray flux dropped exponentially \nwith an e-folding time of about 14.4~d, which is short compared to most other \nBHC X-ray transients. The e-folding time was nearly the same (14.9~d) for the \ndecay of the 1996 outburst, which may indicate that this time scale is set by \nsome property of the system that does not change between outbursts. For the \n1998 outburst, the decay was interrupted by a secondary maximum, which is \ncommonly observed for BHC X-ray transients.\n\nOur analysis of the 4U~1630--47 power spectra indicates that 0.2~Hz to 11~Hz \nQPOs with RMS amplitudes between 2\\% and 9\\% occurred during the observations. \nDuring one of our early observations, when the source was relatively bright, \na QPO occurred near 6~Hz with a profile that cannot be described by a single \nLorentzian. Similar asymmetric QPO peaks have been observed previously for \nGS~1124--68 (\\cite{belloni97}) and XTE~J1748--288 (Revnivtsev et al.~1999). \nFor all three sources (4U~1630--47, GS~1124--68 and XTE~J1748--288), the QPO \nis well-described by a combination of two Lorentzians. \n\nNear the end of the outburst, an abrupt change in the 4U~1630--47 spectral and \ntiming properties occurred, and we interpret this change as evidence for a \nsoft-to-hard state transition. Our observations indicate that most of the changes \nin the emission properties, associated with the transition, occurred over a time \nperiod less than 2~d. The timing properties changed after the transition with \nan increase in the continuum noise level and the appearance of a QPO. A 3.4~Hz \nQPO appeared immediately after the transition, and, in subsequent observations, \nthe QPO frequency decreased gradually to about 0.2~Hz. At the transition, the \nenergy spectrum also changed with an abrupt drop in the soft component flux in \nthe \\it RXTE \\rm band pass, which was probably due to a drop in the inner disk \ntemperature. A change in the power-law photon index from 2.3 to 1.8, also \nassociated with the transition, occurred over a time period of 8~d. Although \nmany of these changes are typical of soft-to-hard state transitions, the QPO \nbehavior and the short time scale for the transition are not part of the \ncanonical picture for state transitions (\\cite{v95};~\\cite{nowak95};~\\cite{ct96}).\nFinally, we note that 4U~1630--47 exhibits interesting behavior (e.g., state \nchanges and QPOs) below a flux level of $10^{-9}$~erg~cm$^{-2}$~s$^{-1}$, \nindicating that observing programs for X-ray transients should be designed to \nfollow these sources to low flux levels.\n\n\\acknowledgements\n\nThe authors would like to thank J.H. Swank for approving observations of \n4U~1630--47 at low flux levels, S. Dieters for providing results from \n\\it BeppoSAX \\rm observations prior to publication and an anonymous \nreferee whose comments led to an improved paper. 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9152 & 1400\\nl\n10 & 50892.6314 & 4816 & 1313\\nl\n11 & 50893.8026 & 9456 & 1212\\nl\n12 & 50895.7370 & 9424 & 992\\nl\n13 & 50899.0084 & 1200 & 822\\nl\n14 & 50900.6819 & 912 & 736\\nl\n15 & 50904.2146 & 992 & 626\\nl\n16 & 50904.6203 & 9328 & 621\\nl\n17 & 50906.5668 & 7056 & 587\\nl\n18 & 50907.5942 & 9920 & 568\\nl\n19 & 50909.5107 & 11120 & 553\\nl\n20 & 50911.3969 & 9920 & 559\\nl\n21 & 50913.3997 & 11040 & 547\\nl\n22 & 50921.5827 & 576 & 599\\nl\n23 & 50923.6826 & 9824 & 587\\nl\n24 & 50924.8245 & 10128 & 634\\nl\n25 & 50925.8665 & 1584 & 653\\nl\n26 & 50926.6551 & 400 & 692\\nl\n27 & 50927.7248 & 512 & 714\\nl\n28 & 50928.5927 & 416 & 723\\nl\n29 & 50929.6599 & 560 & 741\\nl\n30 & 50930.6609 & 608 & 772\\nl\n31 & 50931.8622 & 544 & 801\\nl\n32 & 50932.7974 & 800 & 825\\nl\n33 & 50935.1336 & 1136 & 854\\nl\n34 & 50936.1995 & 1024 & 873\\nl\n35 & 50937.6251 & 512 & 847\\nl\n36 & 50939.0651 & 736 & 799\\nl\n37 & 50942.0190 & 672 & 758\\nl\n38 & 50945.8624 & 352 & 571\\nl\n39 & 50947.8040 & 960 & 467\\nl\n40 & 50949.7373 & 864 & 404\\nl\n41 & 50951.6677 & 1328 & 397\\nl\n42 & 50952.4870 & 880 & 361\\nl\n43 & 50953.4910 & 1408 & 307\\nl\n44 & 50956.9571 & 1440 & 201\\nl\n45 & 50958.9578 & 1312 & 208\\nl\n46 & 50961.0918 & 912 & 194\\nl\n47 & 50962.9571 & 1440 & 240\\nl\n48 & 50965.9570 & 1616 & 207\\nl\n49 & 50968.2637 & 624 & 193\\nl\n50 & 50970.3910 & 720 & 145\\nl\n51 & 50972.1303 & 864 & 203\\nl\n\\tablenotetext{a}{Modified Julian Date (MJD = JD--2400000.5) at the midpoint of the observation.}\n\\tablenotetext{b}{2.5-20~keV count rate for 5 PCUs (all 3 layers) after background subtraction.}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lcccccc}\n\\footnotesize\n\\tablecaption{Power Spectra: Continuum Parameters\\tablenotemark{a}\\label{tab:powercont}}\n\\tablewidth{0pt}\n\\tablehead{ & \\multicolumn{3}{c}{Flat-top} & \\multicolumn{2}{c}{Power-law} & }\n\\startdata\nObs. & RMS\\tablenotemark{b}~(\\%) & $\\nu_{break}$~(Hz) & $\\alpha$ & RMS\\tablenotemark{b}~(\\%) & $\\alpha$ & $\\chi^{2}/\\nu$\\nl\n\\hline\n1-2\\tablenotemark{e} & $3.24\\pm 0.21$ & $0.49\\pm 0.05$ & $-0.96\\pm 0.04$ & $1.37\\pm 0.66$ \n\t& $-1.56\\pm 0.19$ & 471/438\\nl\n3\\tablenotemark{e} & $3.55\\pm 0.21$ & $2.72\\pm 0.28$ & $-1.46\\pm 0.15$ & $4.36\\pm 0.72$ \n\t& $-1.70\\pm 0.07$ & 552/432\\nl\n4 & $1.83\\pm 0.33$ & $1.52\\pm 0.66$ & $-0.73\\pm 0.11$ & $1.10\\pm 0.56$ \n\t& $-1.52\\pm 0.24$ & 495/441\\nl\n5 & $2.04\\pm 0.28$ & $2.54\\pm 0.50$ & $-1.23\\pm 0.28$ & $1.98\\pm 0.32$ \n\t& $-0.97\\pm 0.08$ & 418/441\\nl\n6\\tablenotemark{e} & $2.71\\pm 0.27$ & $1.42\\pm 0.14$ & $-1.90\\pm 0.33$ & $1.60\\pm 0.48$ \n\t& $-1.05\\pm 0.16$ & 453/438\\nl\n7\\tablenotemark{e} & $2.49\\pm 0.18$ & $1.72\\pm 0.10$ & $-2.87\\pm 0.54$ & $2.47\\pm 0.23$ \n\t& $-0.89\\pm 0.05$ & 405/438\\nl\n8\\tablenotemark{e} & $2.48\\pm 0.18$ & $1.40\\pm 0.09$ & $-2.24\\pm 0.38$ & $2.38\\pm 0.15$ \n\t& $-0.81\\pm 0.04$ & 470/438\\nl\n9-10 & $2.67\\pm 0.22$ & $1.60\\pm 0.14$ & $-1.69\\pm 0.24$ & $2.06\\pm 0.25$ \n\t& $-0.75\\pm 0.07$ & 431/441\\nl\n11-12 & $3.52\\pm 0.16$ & $0.56\\pm 0.04$ & $-1.05\\pm 0.04$ & $<1.0$\\tablenotemark{c}\n\t& $-1.0$\\tablenotemark{d} & 518/443\\nl\n13-24 & $3.65\\pm 0.12$ & $0.76\\pm 0.04$ & $-1.33\\pm 0.06$ & $<0.7$\\tablenotemark{c} \n\t& $-1.0$\\tablenotemark{d} & 421/443\\nl\n25-40 & $3.13\\pm 0.27$ & $1.57\\pm 0.14$ & $-2.82\\pm 0.71$ & $<1.0$\\tablenotemark{c}\n\t& $-1.0$\\tablenotemark{d} & 452/443\\nl\n41\\tablenotemark{e} & $10.2\\pm 0.6$ & $3.33\\pm 0.36$ & $-1.73\\pm 0.24$ \n\t& $<2.5$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 480/440\\nl\n42\\tablenotemark{e} & $11.3\\pm 0.8$ & $2.81\\pm 0.33$ & $-1.60\\pm 0.21$ \n\t& $<3.6$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 415/440\\nl\n43\\tablenotemark{e} & $13.6\\pm 0.7$ & $1.97\\pm 0.12$ & $-1.87\\pm 0.16$ \n\t& $<3.3$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 479/440\\nl\n44\\tablenotemark{e} & $15.9\\pm 1.1$ & $0.83\\pm 0.07$ & $-1.45\\pm 0.10$ \n\t& $<5.2$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 550/440\\nl\n45\\tablenotemark{e} & $16.1\\pm 1.5$ & $0.55\\pm 0.06$ & $-1.31\\pm 0.08$ \n\t& $<2.0$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 491/440\\nl\n46-48\\tablenotemark{e} & $17.3\\pm 0.8$ & $0.48\\pm 0.03$ & $-1.33\\pm 0.05$ \n\t& $<5.4$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 453/440\\nl\n49\\tablenotemark{e} & $14.9\\pm 2.2$ & $0.26\\pm 0.05$ & $-1.45\\pm 0.12$ \n\t& $<9.0$\\tablenotemark{c} & $-1.0$\\tablenotemark{d} & 550/440\\nl\n50-51 & $13.8\\pm 1.1$ & $0.19\\pm 0.02$ & $-1.28\\pm 0.08$ & $<8.3$\\tablenotemark{c}\n\t& $-1.0$\\tablenotemark{d} & 494/440\\nl\n\\tablenotetext{a}{The errors correspond to $\\Delta \\chi^{2} = 1.0$ (68\\% confidence).}\n\\tablenotetext{b}{0.01-10~Hz RMS amplitudes.}\n\\tablenotetext{c}{90\\% confidence upper limit.}\n\\tablenotetext{d}{Power-law index fixed to this value.}\n\\tablenotetext{e}{A Lorentzian is included in the model. For observation 3, three\nLorentzians are included in the model as described in the text.}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lccccc}\n\\footnotesize\n\\tablecaption{QPO Parameters for Observation 3\\tablenotemark{a}\\label{tab:obs3}}\n\\tablewidth{0pt}\n\n\\tablehead{ & \\multicolumn{3}{c}{All of Observation 3} & \n\\multicolumn{1}{c}{Time Segment 1\\tablenotemark{b}} & \n\\multicolumn{1}{c}{Time Segment 2\\tablenotemark{c}}}\n\\startdata\n & 1 Lorentzian & 2 Lorentzians & 3 Lorentzians & 3 Lorentzians & 3 Lorentzians\\nl\n\\hline\n$\\nu_{1}$ (Hz) & $5.74\\pm 0.03$ & $5.42\\pm 0.02$ & $5.43\\pm 0.02$ & $5.49\\pm 0.02$ & $5.35\\pm 0.03$\\nl\nFWHM$_{1}$ (Hz) & $1.06\\pm 0.07$ & $0.37\\pm 0.06$ & $0.41\\pm 0.06$ & $0.38\\pm 0.05$ & $0.49\\pm 0.10$\\nl\nRMS$_{1}$ (\\%) & $4.03\\pm 0.10$ & $2.76\\pm 0.19$ & $2.89\\pm 0.18$ & $2.95\\pm 0.20$ & $2.88\\pm 0.25$\\nl\n\\hline\n$\\nu_{2}$ (Hz) & --- & $6.17\\pm 0.05$ & $6.19\\pm 0.04$ & $6.17\\pm 0.06$ & $6.25\\pm 0.06$\\nl\nFWHM$_{2}$ (Hz) & --- & $0.77\\pm 0.13$ & $0.78\\pm 0.12$ & $0.71\\pm 0.16$ & $0.85\\pm 0.17$\\nl\nRMS$_{2}$ (\\%) & --- & $2.85\\pm 0.22$ & $2.85\\pm 0.21$ & $2.60\\pm 0.25$ & $3.09\\pm 0.27$\\nl\n\\hline\n$\\nu_{3}$ (Hz) & --- & --- & $10.79\\pm 0.14$ & $11.00\\pm 0.19$ & $10.57\\pm 0.18$\\nl\nFWHM$_{3}$ (Hz) & --- & --- & $1.47\\pm 0.45$ & $2.00\\pm 0.63$ & $1.56\\pm 0.53$\\nl\nRMS$_{3}$ (\\%) & --- & --- & $1.85\\pm 0.20$ & $2.11\\pm 0.24$ & $1.95\\pm 0.26$\\nl\n\\hline\n$\\chi^{2}/\\nu$ & 685/438 & 608/435 & 552/432 & 570/432 & 480/432\\nl\n\\tablenotetext{a}{The errors correspond to $\\Delta \\chi^{2} = 1.0$ (68\\% confidence).}\n\\tablenotetext{b}{First 576 seconds of Observation 3.}\n\\tablenotetext{c}{Last 512 seconds of Observation 3.}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lccc}\n\\footnotesize\n\\tablecaption{QPO Parameters for Observations 41-49\\tablenotemark{a}\\label{tab:shiftqpo}}\n\\tablewidth{0pt}\n\\tablehead{\\colhead{Observation} & \\colhead{Frequency (Hz)} & \\colhead{FWHM (Hz)} & \\colhead{RMS (\\%)}}\n\\startdata\n41 & $3.390\\pm 0.008$ & $0.14\\pm 0.02$ & $7.30\\pm 0.33$\\nl\n42 & $2.613\\pm 0.012$ & $0.17\\pm 0.03$ & $8.46\\pm 0.47$\\nl\n43 & $1.351\\pm 0.012$ & $0.22\\pm 0.04$ & $8.68\\pm 0.51$\\nl\n44 & $0.430\\pm 0.006$ & $0.07\\pm 0.02$ & $<8.2$\\tablenotemark{b}\\nl\n45 & $0.365\\pm 0.011$ & $0.11\\pm 0.04$ & $<9.6$\\tablenotemark{b}\\nl\n46-48 & $0.228\\pm 0.003$ & $0.046\\pm 0.010$ & $6.55\\pm 0.51$\\nl\n49 & $0.182\\pm 0.005$ & $0.043\\pm 0.012$ & $<10.1$\\tablenotemark{b}\\nl\n\\tablenotetext{a}{The errors correspond to $\\Delta \\chi^{2} = 1.0$ (68\\% confidence).}\n\\tablenotetext{b}{90\\% confidence upper limit.}\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{lccccccccccc}\n\\scriptsize\n\\tablecaption{Energy Spectrum Fit Parameters\\tablenotemark{a,b}\\label{tab:energy}}\n\\tablewidth{0pt}\n\\tablehead{ & \\multicolumn{2}{c}{Power-law} & \\multicolumn{2}{c}{Disk-blackbody} & \n\\multicolumn{3}{c}{Narrow Emission Line} & \\multicolumn{2}{c}{Broad Absorption Edge}}\n\\startdata\nObs. & $\\Gamma$ & $F_{PL}$\\tablenotemark{c} &\n$kT_{in}$ (keV) & $F_{DBB}$\\tablenotemark{d} & \n$E_{line}$ (keV) & $N_{line}$\\tablenotemark{e} & Signif.~(\\%) & \n$E_{edge}$ & $\\tau_{\\rm{Fe}}$ & $\\chi^{2}/\\nu$\\nl\n\\hline\n1 & $2.498\\pm 0.019$ & 7.42 & 0.955 & 7.95 & \n6.60\\tablenotemark{g} & $<2.6$\\tablenotemark{f} & 72.8 & \n$8.65\\pm 0.16$ & $0.84\\pm 0.09$ & 80/102\\nl\n2 & $2.389\\pm 0.017$ & 7.34 & 0.917 & 8.66 & \n6.68\\tablenotemark{g} & $<3.1$\\tablenotemark{f} & 78.8 & \n$9.05\\pm 0.13$ & $0.94\\pm 0.08$ & 135/102\\nl\n3 & $2.603\\pm 0.015$ & 10.6 & 1.577 & $<2.79$ & \n6.41\\tablenotemark{g} & $<2.4$\\tablenotemark{f} & 52.3 & \n$8.71\\pm 0.34$ & $0.43\\pm 0.10$ & 96/102\\nl\n4 & $2.557\\pm 0.012$ & 10.3 & 1.573 & $<5.08$ & \n6.79\\tablenotemark{g} & $<1.9$\\tablenotemark{f} & 67.0 & \n$9.15\\pm 0.32$ & $0.35\\pm 0.08$ & 107/102\\nl\n5 & $2.500\\pm 0.021$ & 3.70 & 1.049 & 11.5 & \n6.63\\tablenotemark{g} & $<2.3$\\tablenotemark{f} & 87.3 & \n$9.00\\pm 0.09$ & $1.50\\pm 0.10$ & 90/102\\nl\n6 & $2.402\\pm 0.023$ & 3.99 & 0.933 & 9.62 & \n$6.70\\pm 0.07$ & $1.9\\pm 0.5$ & 94.7 & \n$8.93\\pm 0.10$ & $1.42\\pm 0.10$ & 104/102\\nl\n7 & $2.457\\pm 0.016$ & 4.09 & 0.905 & 9.14 & \n$6.61\\pm 0.08$ & $1.7\\pm 0.5$ & 93.2 & \n$8.77\\pm 0.09$ & $1.36\\pm 0.08$ & 92/102\\nl\n8 & $2.453\\pm 0.016$ & 3.50 & 0.914 & 8.61 & \n$6.63\\pm 0.07$ & $1.6\\pm 0.4$ & 97.4 & \n$8.76\\pm 0.08$ & $1.47\\pm 0.08$ & 78/102\\nl\n9 & $2.412\\pm 0.017$ & 2.61 & 0.861 & 7.94 & \n$6.60\\pm 0.07$ & $1.2\\pm 0.3$ & 93.6 & \n$8.55\\pm 0.08$ & $1.55\\pm 0.08$ & 90/102\\nl\n10 & $2.396\\pm 0.023$ & 2.38 & 0.857 & 7.96 & \n$6.65\\pm 0.07$ & $1.2\\pm 0.3$ & 94.4 & \n$8.61\\pm 0.09$ & $1.78\\pm 0.10$ & 93/102\\nl\n11 & $2.444\\pm 0.020$ & 2.14 & 0.847 & 7.83 & \n$6.52\\pm 0.06$ & $1.3\\pm 0.3$ & 97.4 & \n$8.59\\pm 0.07$ & $1.84\\pm 0.09$ & 104/102\\nl\n12 & $2.276\\pm 0.015$ & 2.14 & 0.714 & 7.13 & \n$6.43\\pm 0.07$ & $1.0\\pm 0.3$ & 97.7 & \n$8.37\\pm 0.08$ & $1.46\\pm 0.07$ & 78/102\\nl\n13 & $2.265\\pm 0.040$ & 1.67 & 0.733 & 6.28 & \n6.49\\tablenotemark{g} & $<1.5$\\tablenotemark{f} & 88.2 & \n$8.57\\pm 0.15$ & $1.56\\pm 0.17$ & 97/102\\nl\n14 & $2.265\\pm 0.042$ & 1.63 & 0.666 & 6.30 & \n6.25\\tablenotemark{g} & $<1.3$\\tablenotemark{f} & 78.6 & \n$8.22\\pm 0.18$ & $1.43\\pm 0.19$ & 83/102\\nl\n15 & $2.264\\pm 0.050$ & 1.37 & 0.664 & 5.45 & \n6.32\\tablenotemark{g} & $<1.2$\\tablenotemark{f} & 85.1 & \n$8.37\\pm 0.18$ & $1.49\\pm 0.22$ & 87/102\\nl\n16 & $2.248\\pm 0.017$ & 1.43 & 0.636 & 5.58 & \n6.47\\tablenotemark{g} & $<0.8$\\tablenotemark{f} & 88.8 & \n$8.08\\pm 0.10$ & $1.40\\pm 0.09$ & 64/102\\nl\n17 & $2.122\\pm 0.017$ & 1.41 & 0.605 & 5.22 & \n$6.49\\pm 0.07$ & $0.6\\pm 0.2$ & 92.9 & \n$8.23\\pm 0.11$ & $1.24\\pm 0.09$ & 77/102\\nl\n18 & $2.136\\pm 0.016$ & 1.39 & 0.595 & 5.09 & \n$6.49\\pm 0.06$ & $0.7\\pm 0.2$ & 96.3 & \n$8.44\\pm 0.09$ & $1.30\\pm 0.08$ & 86/102\\nl\n19 & $2.074\\pm 0.015$ & 1.28 & 0.643 & 4.95 & \n$6.50\\pm 0.05$ & $0.7\\pm 0.2$ & 96.5 & \n$8.31\\pm 0.09$ & $1.49\\pm 0.08$ & 100/102\\nl\n20 & $2.264\\pm 0.021$ & 1.14 & 0.701 & 4.81 & \n$6.54\\pm 0.06$ & $0.7\\pm 0.2$ & 98.2 & \n$8.31\\pm 0.09$ & $1.61\\pm 0.10$ & 73/102\\nl\n21 & $2.330\\pm 0.024$ & 1.05 & 0.718 & 4.93 & \n$6.50\\pm 0.06$ & $0.7\\pm 0.2$ & 98.7 & \n$8.45\\pm 0.09$ & $1.75\\pm 0.10$ & 87/102\\nl\n22 & $2.064\\pm 0.050$ & 1.40 & 0.633 & 4.97 & \n6.38\\tablenotemark{g} & $<1.0$\\tablenotemark{f} & 63.0 & \n$8.20\\pm 0.24$ & $1.34\\pm 0.24$ & 101/102\\nl\n23 & $2.202\\pm 0.021$ & 1.24 & 0.701 & 4.20 & \n$6.56\\pm 0.05$ & $0.8\\pm 0.2$ & 99.5 & \n$8.61\\pm 0.08$ & $1.75\\pm 0.09$ & 90/102\\nl\n24 & $2.185\\pm 0.017$ & 1.43 & 0.681 & 4.68 & \n6.49\\tablenotemark{g} & $<0.8$\\tablenotemark{f} & 87.3 & \n$8.13\\pm 0.10$ & $1.35\\pm 0.09$ & 90/102\\nl\n25 & $2.180\\pm 0.036$ & 1.45 & 0.693 & 4.83 & \n6.59\\tablenotemark{g} & $<1.1$\\tablenotemark{f} & 82.6 & \n$8.32\\pm 0.18$ & $1.30\\pm 0.16$ & 88/102\\nl\n26 & $2.158\\pm 0.066$ & 1.46 & 0.723 & 4.69 & \n6.31\\tablenotemark{g} & $<1.6$\\tablenotemark{f} & 73.5 & \n$8.18\\pm 0.33$ & $1.22\\pm 0.29$ & 84/102\\nl\n27 & $2.269\\pm 0.065$ & 1.51 & 0.731 & 5.10 & \n6.48\\tablenotemark{g} & $<1.2$\\tablenotemark{f} & 60.4 & \n$8.14\\pm 0.27$ & $1.42\\pm 0.28$ & 94/102\\nl\n28 & $2.466\\pm 0.068$ & 1.64 & 0.706 & 4.74 & \n6.32\\tablenotemark{g} & $<1.1$\\tablenotemark{f} & 54.5 & \n$7.95\\pm 0.42$ & $0.99\\pm 0.29$ & 93/102\\nl\n29 & $2.320\\pm 0.071$ & 1.52 & 0.760 & 4.89 & \n6.77\\tablenotemark{g} & $<1.4$\\tablenotemark{f} & 66.4 & \n$8.71\\pm 0.28$ & $1.27\\pm 0.28$ & 92/102\\nl\n30 & $2.364\\pm 0.064$ & 1.58 & 0.762 & 5.25 & \n6.56\\tablenotemark{g} & $<1.4$\\tablenotemark{f} & 72.0 & \n$8.46\\pm 0.19$ & $1.68\\pm 0.25$ & 104/102\\nl\n31 & $2.370\\pm 0.060$ & 1.70 & 0.757 & 5.08 & \n6.33\\tablenotemark{g} & $<1.3$\\tablenotemark{f} & 65.3 & \n$8.31\\pm 0.26$ & $1.29\\pm 0.25$ & 88/102\\nl\n32 & $2.268\\pm 0.048$ & 1.73 & 0.750 & 5.40 & \n$6.35\\pm 0.08$ & $1.3\\pm 0.4$ & 90.1 & \n$8.53\\pm 0.19$ & $1.44\\pm 0.20$ & 73/102\\nl\n33 & $2.348\\pm 0.042$ & 1.73 & 0.773 & 5.68 & \n6.55\\tablenotemark{g} & $<1.3$\\tablenotemark{f} & 70.7 & \n$8.09\\pm 0.18$ & $1.52\\pm 0.19$ & 81/102\\nl\n35 & $2.367\\pm 0.067$ & 1.70 & 0.764 & 5.99 & \n6.62\\tablenotemark{g} & $<1.0$\\tablenotemark{f} & 53.2 & \n$8.24\\pm 0.18$ & $2.10\\pm 0.28$ & 111/102\\nl\n36 & $2.356\\pm 0.052$ & 1.67 & 0.738 & 5.75 & \n6.39\\tablenotemark{g} & $<1.2$\\tablenotemark{f} & 63.2 & \n$8.40\\pm 0.18$ & $1.62\\pm 0.22$ & 89/102\\nl\n37 & $2.422\\pm 0.068$ & 1.40 & 0.758 & 6.24 & \n6.36\\tablenotemark{g} & $<1.3$\\tablenotemark{f} & 73.3 & \n$8.37\\pm 0.19$ & $1.89\\pm 0.19$ & 85/102\\nl\n38 & $2.317\\pm 0.092$ & 1.12 & 0.711 & 5.01 & \n6.65\\tablenotemark{g} & $<0.8$\\tablenotemark{f} & 51.0 & \n$8.38\\pm 0.39$ & $1.28\\pm 0.39$ & 81/102\\nl\n40 & $2.072\\pm 0.058$ & 0.90 & 0.601 & 4.78 & \n$6.33\\pm 0.07$ & $0.8\\pm 0.3$ & 99.96 & \n$8.47\\pm 0.18$ & $1.73\\pm 0.27$ & 75/102\\nl\n41 & $1.916\\pm 0.027$ & 1.09 & $<0.461$ & $<4.69$ & \n6.45\\tablenotemark{g} & $<0.8$\\tablenotemark{f} & 80.1 & \n$8.06\\pm 0.22$ & $0.92\\pm 0.18$ & 107/102\\nl\n42 & $1.858\\pm 0.032$ & 1.00 & $<0.466$ & $<3.57$ & \n6.43\\tablenotemark{g} & $<0.6$\\tablenotemark{f} & 58.4 & \n$7.74\\pm 0.25$ & $1.08\\pm 0.22$ & 63/102\\nl\n43 & $1.798\\pm 0.027$ & 0.85 & $<0.487$ & $<2.42$ & \n6.51\\tablenotemark{g} & $<0.6$\\tablenotemark{f} & 71.8 & \n$7.49\\pm 0.27$ & $0.91\\pm 0.19$ & 98/102\\nl\n44 & $1.793\\pm 0.037$ & 0.56 & $<0.459$ & $<2.19$ & \n6.44\\tablenotemark{g} & $<0.4$\\tablenotemark{f} & 61.6 & \n$7.54\\pm 0.29$ & $1.05\\pm 0.26$ & 74/102\\nl\n45 & $1.675\\pm 0.031$ & 0.58 & $<0.486$ & $<1.68$ & \n6.46\\tablenotemark{g} & $<0.6$\\tablenotemark{f} & 85.6 & \n7.1\\tablenotemark{g} & $1.36\\pm 0.27$ & 89/103\\nl\n46 & $1.735\\pm 0.038$ & 0.55 & $<0.451$ & $<1.83$ & \n6.54\\tablenotemark{g} & $<0.6$\\tablenotemark{f} & 73.4 & \n7.1\\tablenotemark{g} & $1.19\\pm 0.33$ & 78/103\\nl\n47 & $1.584\\pm 0.024$ & 0.67 & $<0.452$ & $<1.70$ & \n$6.47\\pm 0.07$ & $0.5\\pm 0.2$ & 93.0 & \n7.1\\tablenotemark{g} & $0.66\\pm 0.22$ & 74/103\\nl\n49 & $1.640\\pm 0.055$ & 0.54 & $<0.493$ & $<1.27$ & \n6.34\\tablenotemark{g} & $<0.7$\\tablenotemark{f} & 68.3 & \n$7.56\\pm 0.32$ & $1.45\\pm 0.37$ & 83/102\\nl\n50 & $1.536\\pm 0.040$ & 0.50 & $<0.495$ & $<1.21$ & \n6.50\\tablenotemark{g} & $<0.7$\\tablenotemark{f} & 74.5 & \n7.1\\tablenotemark{g} & $0.98\\pm 0.36$ & 99/103\\nl\n51 & $1.605\\pm 0.031$ & 0.57 & $<0.365$ & $<3.20$ & \n6.40\\tablenotemark{g} & $<0.6$\\tablenotemark{f} & 72.7 & \n7.1\\tablenotemark{g} & $0.78\\pm 0.28$ & 94/103\\nl\n44-51 & $1.657\\pm 0.012$ & 0.58 & $<0.455$ & $<1.83$ & \n$6.46\\pm 0.04$ & $0.4\\pm 0.1$ & 99.93 & \n7.1\\tablenotemark{g} & $1.08\\pm 0.11$ & 98/103\\nl\n\\tablenotetext{a}{Column density fixed to $9.45\\times 10^{22}$~cm$^{-2}$.}\n\\tablenotetext{b}{The errors correspond to $\\Delta \\chi^{2} = 1.0$ (68\\% confidence).}\n\\tablenotetext{c}{2.5-20~keV unabsorbed flux in units of\n10$^{-9}$~erg~cm$^{-2}$~s$^{-1}$.}\n\\tablenotetext{d}{Bolometric flux in units of 10$^{-9}$~erg~cm$^{-2}$~s$^{-1}$.}\n\\tablenotetext{e}{Normalization in units of 10$^{-3}$~photons~cm$^{-2}$~s$^{-1}$.}\n\\tablenotetext{f}{90\\% confidence upper limit.}\n\\tablenotetext{g}{Fixed.}\n\\enddata\n\\end{deluxetable}\n\n\\appendix\n\n\\section{SGR~1627--41}\n\nSoft $\\gamma$-ray bursts were detected from a position near 4U~1630--47 on \nMJD 50979 (\\cite{kouveliotou98}), 7~d after our last \\it RXTE \\rm observation. \nThe soft $\\gamma$-ray repeater, SGR~1627--41, was observed with \\it RXTE \\rm on \nMJD 50990, and a 0.15~Hz QPO was detected during the observation (\\cite{dieters98b}). \nAlthough the position of SGR~1627--41 is not consistent with the position of \n4U~1630--47 (\\cite{hurley99}), the two sources are close enough so that they were \nboth in the \\it RXTE \\rm field of view during the observation made on MJD 50990\nand also during our observations, allowing for the possibility of source confusion. \nWe inspected the \\it RXTE \\rm 0.125~s light curves for our 4U~1630--47 observations, \nand there is no evidence for activity (e.g., bursts) from SGR~1627--41. An \\it RXTE \\rm \nscanning observation made on 1998 June 21 (MJD 50985) and \\it BeppoSAX \\rm observations \nmade on 1998 August 7 (MJD 51032) and 1998 September 16 (MJD 51072) provide information \nabout possible source confusion. The scanning observation indicates that 4U~1630--47 \nwas much brighter than SGR~1627--41 on June 21. Below, we present an analysis of the \ndata from the scanning observation. 4U~1630--47 was also much brighter than \nSGR~1627--41 during the \\it BeppoSAX \\rm observations. On August 7 and September 16, the \n2-10~keV unabsorbed flux for 4U~1630--47 was 30 to 40 times higher than for SGR~1627--41 \n(\\cite{woods99};~\\cite{dieters99}). It is likely that 4U~1630--47 also dominated the \nflux detected during the June 26 \\it RXTE \\rm observation and that it is responsible \nfor the 0.15~Hz QPO. Given the low persistent flux detected for SGR~1627--41 by \n\\it BeppoSAX\\rm, $6.7\\times 10^{-12}$~erg~cm$^{-2}$~s$^{-1}$ unabsorbed in the 2-10~keV \nband (\\cite{woods99}), it seems very unlikely that this source could be bright enough to \nproduce the QPOs observed during our observations.\n\nAfter soft $\\gamma$-ray bursts were detected from SGR~1627--41\nby BATSE (Burst and Transient Source Experiment) on 1998 June 15 \n(\\cite{kouveliotou98}), \\it RXTE \\rm scanning observations were \nmade to locate a source of persistent X-ray emission related to \nsoft $\\gamma$-ray repeater (SGR). When the scans were made, the \nposition of SGR~1627--41 was restricted to the IPN (3rd \nInterplanetary Network) annulus reported in Hurley et al.~(1998a),\nwhich is consistent with the position of the supernova remnant\nG337.0-0.1. \\it RXTE \\rm scans were made along the IPN annulus \non 1998 June 19 and nearly perpendicular to the IPN annulus on 1998 \nJune 21. Since other SGRs are associated with supernova remnants,\nthe perpendicular scan was centered on G337.0-0.1. In the following \nmonths, the IPN position was improved (\\cite{hurley98b}) and a\nsource of persistent X-ray emission related to the SGR was discovered\nusing \\it BeppoSAX \\rm (\\cite{woods99}). These observations restrict the \nSGR~1627--41 position to a 2$^{\\prime}$ by 16$^{\\prime\\prime}$ region \nthat is consistent with the position of G337.0-0.1, making an association \nbetween the two likely (\\cite{hurley99}).\n\n\\setcounter{figure}{0}\n\n\\begin{figure}\n\\plotone{scan.ps}\n\\caption{The PCA light curve for the scan performed on June 21,\nshowing that X-ray emission was coming from a position consistent\nwith the 4U~1630--47 position (dotted line). It is likely\nthat SGR~1627--41 is associated with the supernova remnant G337.0-0.1 \n(\\cite{hurley99}) and its position is also marked (dashed line).\n\\label{fig:scan}}\n\\end{figure}\n\nWe analyzed the \\it RXTE \\rm data from the June 21 scan to determine\nif the persistent X-ray emission from SGR~1627--41 could have been bright \nenough to contaminate our \\it RXTE \\rm observations of 4U~1630--47. \nThe linear scan passed through the positions of both G337.0-0.1 and \n4U~1630--47 for this purpose. Figure~\\ref{fig:scan} shows the background subtracted \n2-60~keV PCA count rate versus scan angle. We fitted the light curve \nusing a model consisting of a single point source and a constant count \nrate offset to account for small uncertainties in the background \nsubtraction. We used the 1996 June 5 PCA collimator response to\nmodel the scan light curve produced by a point source. A good fit is \nachieved ($\\chi^{2}/\\nu = 91/161$), indicating that the light curve \nis consistent with the presence of one source. Figure~\\ref{fig:scan} \nshows that the source position is consistent with 4U~1630--47 and not \nG337.0-0.1. Also, the source amplitude is about 187~s$^{-1}$ (2-60~keV, 5 PCUs), \nwhich is close to the count rates reported for observations 44 to 51 \nin Table~\\ref{tab:obs}. The \\it RXTE \\rm scan indicates that it is very unlikely \nthat our 4U~1630--47 observations are significantly contaminated by \nemission from SGR~1627--41.\n\n\\end{document}\n\n\n"
}
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[
{
"name": "astro-ph0002084.extracted_bib",
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astro-ph0002085
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Naturally occurring water vapor maser emission at 1.35 cm wavelength provides an accurate probe for the study of accretion disks around highly compact objects, thought to be black holes, in the centers of active galaxies. Because of the exceptionally fine angular resolution, 200 microarcseconds, obtainable with very long baseline interferometry, accompanied by high spectral resolution, $<0.1$~\kms, the dynamics and structures of these disks can be probed with exceptional clarity. The data on the galaxy NGC\_4258 are discussed here in detail. The mass of the black hole binding the accretion disk is $3.9 \times 10^7$~\msun. Although the accretion disk has a rotational period of about 800 years, the physical motions of the masers have been directly measured with VLBI over a period of a few years. These measurements also allow the distance from the earth to the black hole to be estimated to an accuracy of 4 percent. The status of the search for other maser/black hole candidates is also discussed.
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"name": "india-jmm.tex",
"string": "%\\documentstyle[12pt, aasms4]{article}\n\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[11pt]{article}\n\\pagestyle{plain}\n\n\\renewcommand{\\topfraction}{.99}\n\\renewcommand{\\bottomfraction}{.99}\n\\renewcommand{\\textfraction}{.01}\n\n\n\n\\def\\plotfiddle#1#2#3#4#5#6#7{\\centering \\leavevmode\n \\vbox to#2{\\rule{0pt}{#2}}\n \\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}\n\\newcommand{\\Mdot}{M$_{\\odot}$}\n\\newcommand{\\msun}{M$_{\\odot}$}\n\\newcommand{\\msunyr}{M$_{\\odot}\\,$yr$^{-1}$}\n\\newcommand{\\msunpc}{M$_{\\odot}\\,$pc$^{-3}$}\n\\newcommand{\\ergs}{erg s$^{-1}$}\n\\newcommand{\\gcc}{g$\\,$cm$^{-3}$}\n\\newcommand{\\kms}{km$\\,$s$^{-1}$}\n\\newcommand{\\degrees}{$^{\\circ}$}\n\\renewcommand{\\deg}{$^{\\circ}$}\n\\newcommand{\\hto}{H$_2$O}\n\\renewcommand{\\_}{$\\,$}\n\\newcommand{\\sol}{$_{\\odot}$}\n\\newcommand{\\sm}{\\scriptsize}\n\n\\newlength{\\phantomdigit}\n\\settowidth{\\phantomdigit}{8}\n\\newcommand{\\z}{\\hspace*{\\phantomdigit}}\n%---------------------------------------------\n\n\\begin{document}\n\\thispagestyle{empty}\n\\begin{center}\n\nOBSERVATIONAL EVIDENCE FOR MASSIVE BLACK HOLES\\\\\nIN THE CENTERS OF ACTIVE GALAXIES\n\nJ. M. Moran, L. J. Greenhill \n\nHarvard-Smithsonian Center for Astrophysics \n\nand J. R. Herrnstein\n\nNational Radio Astronomy Observatory\n\\end{center}\n\n\\begin{abstract}\n\nNaturally occurring water vapor maser emission at 1.35 cm wavelength provides an accurate\nprobe for the study of accretion disks around highly compact objects, thought\nto be black holes, in the centers of active galaxies. Because of the exceptionally fine\nangular resolution, 200 microarcseconds, obtainable with very long baseline interferometry,\naccompanied by high spectral resolution, $<0.1$~\\kms, the dynamics and structures of\nthese disks can be probed with exceptional clarity. The data on the galaxy NGC\\_4258 \nare discussed here in detail. The mass of the black hole binding the accretion disk \nis $3.9 \\times 10^7$~\\msun. \nAlthough the accretion disk has a rotational period of about 800 years, the physical\nmotions of the masers have been directly measured with VLBI over a period of a few years. \nThese measurements also allow\nthe distance from the earth to the black hole to be estimated to an accuracy of 4 percent. \nThe status of the search for other maser/black hole candidates is also discussed.\n\n\\end{abstract}\n\n\\section{INTRODUCTION}\n\nThe observational evidence for the existence of supermassive\nblack holes ($10^6$--$10^9$ times the mass of the sun, \\msun) \nin the centers of active galaxies\nhas been accumulating at an ever accelerating pace for the last \nfew decades (e.g., Rees 1998; Blandford \\& Gehrels 1999). Seyfert (1943) first drew attention to\na group of galaxies with unusual excitation conditions\nin their nuclei indicative of energetic activity. Among the twelve \ngalaxies in his list\nwas NGC\\_4258, which is the subject of much of this paper. \nSuch galaxies, now known as galaxies with active galactic nuclei (AGN),\nhave grown in membership and importance. Ironically, NGC\\_4258 no longer belongs\nto the class of Seyfert galaxies by modern classification standards \n(Heckman 1980), but it is still\nconsidered to have a mildly active galactic nucleus. \nMeanwhile, the study of AGN has become a major field in modern\nastrophysics. In the 1960s, galaxies with AGN were discovered with\nintense radio emission arising from jets of relativistic\nparticles often extending far beyond the optical boundaries of the \nhost galaxy. The central engine, the source of energy that powers\nsuch jets and other phenomena in the centers of galaxies, has long \nbeen ascribed to black holes (e.g., Salpeter 1964; Blandford \\& Rees 1992). \nThere are two sources of energy for these phenomena: the\ngravitational energy from material falling onto the black hole and the spin energy of the\nblack hole itself (Blandford \\& Znajek 1977).\n\nThe direct evidence for black holes in AGN has come principally from\nobservations of the motions of gas and stars in the extended environments\nof black holes. In the optical and infrared domains, the evidence\nfor black holes from stellar measurements comes from an analysis\nof the velocity dispersion of stars as a function of distance from\nthe dynamical centers of galaxies. In the case of our own Galactic center, the \nproper motions (angular velocities in the plane of the sky)\nof individual stars can be measured.\nThese data show that there is a mass of about $2.6 \\times 10^6$~\\Mdot\\ within a volume\nof radius 0.01 pc (Genzel et al. 1997; Ghez et al. 1998).\nIn addition, measurements\nby the Hubble Space Telescope of the velocity field of hydrogen gas in\nactive galaxies indicate the presence of massive centrally condensed objects. \nReviews of these data have been written by Faber (1999), Ho (1999), \nKormendy and Richstone (1995), and others. \n\nIn the X-ray portion of\nthe spectrum, there is compelling evidence for black\nholes in AGN from the detection of the highly broadened iron K$\\alpha$ line at 6.4 keV.\nThe line\nis broadened by the gravitational redshift of gas as close as 3\nSchwarzschild radii from the black hole. An example of an \niron line profile in the galaxy MCG\\_-6-30-15 is shown in Figure~1 (Tanaka et al. 1995).\nThe linear\nextent of the emission region cannot be determined directly by the X-ray\ntelescope, so it is not possible to estimate directly the mass of the\nputative black hole. Detailed analysis of the line profile suggests that the black \nhole is spinning\n(e.g., Bromley, Miller, \\& Pariev 1998).\n\n% FIGURE 1\n\\begin{figure}[t]\n\\plotfiddle{fig1.eps}{3.25in}{.2}{90}{90}{-275}{-204}\n\\caption{\\setlength{\\baselineskip}{8 pt} The X-ray spectrum of the galaxy MCG\\_-6-30-15, observed\nby the Japanese ASCA satellite. The top panel shows the total spectrum with a \nmodel of the continuum emission fitted to the data outside the range of 5--7 \nkeV. The bottom panel shows the residuals, which reveal a broad spectral \nfeature attributed to the Fe K$\\alpha$ line at 6.4 keV. The line has a width of\n100,000 \\kms. The most extreme redshifted part is thought to\narise from gas at a radius of about 3 Schwarzschild radii. (From Tanaka et al. 1995)}\n\\end{figure}\n\n\nIn the radio regime, a new line of inquiry\nhas given unexpectedly clear and compelling evidence for \nblack holes: the discovery of water masers orbiting highly massive\nand compact central objects. With the aid of very long baseline\ninterferometry (VLBI), which provides angular resolution as fine as 200~microarcseconds\n($\\mu$as) at a wavelength of 1.3~cm\nand spectral resolution of 0.1 km$\\,$s$^{-1}$ or less,\nthe structure of accreting material around \nthese central objects can be studied in detail. This paper describes \nthe observations and the significance of these measurements of water masers in AGN. \nWe begin with a brief description of cosmic masers and the interferometric\ntechniques used to observe them.\n\n\n\\section{COSMIC MASERS}\n\nIntense maser action in cosmic molecular clouds was \ndiscovered in 1965 (Weaver et al. 1965) from observations of OH, and later from \\hto, SiO, and \nCH$_3$OH. In the case of water vapor, the commonly observed masers\nemit in the 6$_{16}$--5$_{23}$ transition at 22235 MHz (1.35 cm wavelength).\nMost masers\nhave been found to be associated with one of two types of objects: newly\nformed stars or evolved stars (e.g., Elitzur 1992; Reid \\& Moran 1988). Although \nvery distinct, they share the characteristic of having envelopes of \noutflowing gas and dust (silicate material). \nThe pump source in all cases is thought to come in the form\nof either shock waves or infrared radiation.\nMore recently, masers have been found in the spiral\narms of nearby galaxies and in AGN.\n\nCosmic masers are similar to their laboratory counterparts on earth\nin that their intense radiation is produced by population inversion. However,\ncosmic masers are one-pass amplifiers and have little temporal or spatial\ncoherence. The intensity of cosmic masers varies, often erratically, on \ntimescales of hours to years. The underlying electric field is\na Gaussian random process (Moran 1981). In an unsaturated maser (in astronomical \nterminology), the pumping is sufficiently strong that the microwave intensity \ndoes not affect the level populations, and the intensity increases exponentially\nthrough the masing medium. The input signal can be either a \nbackground source or the maser's own spontaneous emission. In a saturated maser,\none pump photon is needed for each microwave photon, and in a one-dimensional\nmaser medium where beaming can be neglected, the intensity increases linearly\nwith distance.\nMaser emission is expected to be beamed. Most masers are thought to be saturated,\nand this condition requires the least pump power. However, this assertion\nis difficult to prove observationally.\n\n% FIGURE 2\n\\begin{figure}[t]\n\\plotfiddle{fig2.eps}{1.95in}{00}{55}{55}{-185}{-140}\n\\caption{\\setlength{\\baselineskip}{8 pt} A cartoon of a simple filamentary maser.\nThe pump energy\ncan be supplied by either shock waves or radiation. Pump cycles usually \ninvolve excitation to infrared rotational levels, followed by de-excitation\nto the upper level of the maser transition. In order to avoid thermalization,\nthe infrared photons emitted during the pump cycle must escape from the\nmasing medium, which favors a geometry that is thin in at least one dimension.\nIn a filamentary geometry, the masing medium is defined \neither by the physical extent of the masing gas or by the volume over which \nthe gas is coherent, that is, where the variation in the velocity projected along the \nline of sight is less than the thermal line width. The maser emission is\nbeamed into a cone of angular opening equal to $d/L$. If the maser amplifies\na background source, the radiation will be beamed in the forward direction.\nIf it amplifies its own spontaneous emission, then beamed maser emission will\nemerge from both ends, and weaker emission from the sidewalls.}\n\\end{figure}\n\nConsider a simple geometry for a maser, a filamentary tube, shown in \nFigure~2. The boundaries\nof the filament can be defined in terms of either gas density or the region where\nthe line-of-sight velocity is constant to within the thermal line width. The\ngas in the tube is predominantly molecular hydrogen, with trace amounts\nof water vapor (about one part in $10^{5}$) and other constituents. If this\nmaser medium is saturated, then the luminosity is given by\n%\n\\begin{equation}\nL = h \\nu n\\Delta P V~,\n\\end{equation}\n%\nwhere $h$ is Planck's constant, $\\nu$ is the frequency,\n$n$ is the population density in pumping level,\n$\\Delta P$ is the differential pump rate per molecule,\nand $V$ is the volume of the masing cloud. \nThis is the most luminosity a maser of given pump rate and volume can produce.\nThe emission will be beamed along the major axis of the filament into\nan angle \n%\n\\begin{equation}\n\\beta \\cong {d\\over L}~,\n\\end{equation}\n%\nwhere $d$ is the cross-sectional diameter, and $L$ is the length of the filament.\nThe beam angle and the length\nof the maser are not directly observable. Since the volume of the\nmaser is approximately $d^2L$, the observed flux density from a maser \nbeamed toward the earth is \n%\n\\begin{equation}\nF_{\\nu} = {1\\over 2} h \\nu n{{\\Delta P}\\over {\\Delta \\nu}} {V\\over {D^2\\Omega}}%\n = {1\\over 2} h \\nu n{{\\Delta P}\\over {\\Delta \\nu}} {L^3\\over D^2}~,\n\\end{equation}\n\n\\noindent\nwhere $\\Delta \\nu$ is the line width, $D$\nis the distance between the maser and the observer,\nand $\\Omega$ is the beam angle of the emission, $\\sim \\beta^2$. \nThe maximum allowable hydrogen number density is about $10^{10}$ molecules \nper cubic centimeter, above which the maser levels become thermalized by collisions. This\nmaximum allowable \ndensity ($\\rho_c = 3 \\times 10^{-13}$~\\gcc, an important parameter in much of the \nfollowing discussion) along with the maximum allowable pump rate, which equals the\nEinstein A-coefficient for infrared transitions linking the maser \nlevels, limit the luminosity of a maser of given volume.\n\nWater masers outside our Galaxy were first discovered in the spiral arms of\nthe nearby galaxy M33 by Churchwell et al. (1977). Their properties were found to \nbe similar to masers found in Galactic star-forming regions. Much more \nluminous water masers were found in the AGN associated with NGC\\_4945 and the Circinus\ngalaxy by dos Santos \\& Lepine (1979) and Gardner \\& Whiteoak (1982), respectively.\nClaussen, Heiligman, \\& Lo (1984) and Claussen \\& Lo\n(1986) conducted surveys and found five additional masers associated with AGN, including\nthe one in NGC\\_4258 (see Figure~3). They suggested that these masers might arise\nin gas associated with dust-laden molecular tori that had been proposed to\nsurround black holes by Antonucci \\& Miller (1985). Nakai, Inoue, \\& Miyoshi (1993), with a\npowerful new spectrometer of 16,000 channels spanning a velocity range\nof 3000 \\kms, observed NGC\\_4258 and discovered satellite line clusters\noffset from the systemic velocity by about $\\pm$ 1000 \\kms, which are shown in\nFigure~3 (see also Miyoshi 1999).\n\n% FIGURE 3\n\\begin{figure}[t]\n\\plotfiddle{fig3-smaller.eps}{3.2in}{0.3}{100}{100}{-295}{-253}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nThe top panel shows the maser spectrum as first discovered in NGC\\_4258 \nat velocities near the systemic velocity of the galaxy (Claussen, Heiligman, \\& Lo 1984).\nThe lower spectrum shows the observations of Nakai, Inoue, \\& Miyoshi (1993) over\na much broader velocity range. The velocities are computed from the Doppler\neffect and are based on a rest frequency of 22235.080 MHz. The effects of \nthe motions of the earth and sun with respect to the local standard of rest\nhave been removed. The bars indicate velocity ranges of emission.}\n\\end{figure}\n\n\nThe compelling reason that the radio emission from the water vapor transition\narises from the maser process is straightforward. A typical example of a maser\nline from a small part of the spectrum of NGC\\_4258 is shown in\nFigure~4. The line width is about 1 \\kms, the thermal broadening\nexpected for a gas cloud at 300~K. However, the angular size determined by\nradio interferometry is\nless than 100 $\\mu$as, implying that the equivalent blackbody \ntemperature must exceed $10^{14}$~K. The exceedingly high brightness\nof the radiation is the principal evidence for the maser process.\n(Typical molecular lines from molecular clouds have velocities of \nseveral tens of \\kms\\ --- due to thermal and turbulent broadening --- and\nbrightness temperatures of less than 100~K.)\nCosmic masers produce very bright spots of radiation but have\nlittle else in common with terrestrial masers.\nIt is difficult to use masers to determine physical conditions (e.g.,\ntemperature, density) in\nmolecular clouds because of the complexity of the maser process. However,\nas compact sources of narrowband radiation, masers are ideal probes of the\ndynamics of their environment.\n\n% FIGURE 4\n\\begin{figure}[t]\n\\plotfiddle{fig4.eps}{2.7in}{0}{68}{68}{-215}{-125}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nAn expanded view of the spectral feature near 1306 \\kms\\ in NGC\\_4258, which is typical\nof emission from an isolated maser component (see Figure~3). The line width\nis characteristic of gas at 300~K, but the intensity corresponds to that\nof a blackbody at an equivalent temperature greater than 10$^{14}$~K.}\n\\end{figure}\n\n\n\\section{VLBI}\n\n% FIGURE 5\n\\begin{figure}[t]\n\\plotfiddle{fig5.eps}{3.25in}{00}{55}{55}{-168}{-115}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nA block diagram of a two-element very long baseline interferometer.\nIt operates as a coherent interferometer. An atomic\nfrequency standard (F.S.) controls the phase of the local oscillator\nsignal at each telescope used to convert the radio frequency signal\nto a video band for recording on magnetic tape \nin digital form (without square-law detection) and sampled at the\nappropriate Nyquist rate. On playback, one\nof the signals is delayed by $\\tau$ to compensate for the differential\npropagation time from the source to the antennas. The signals are \ncorrelated and Fourier transformed\nto produce cross-power spectra, or correlated power as a function\nof frequency and time. }\n\\end{figure}\n\n\nThe most important tool for the study of the angular structure of masers\nis very long baseline interferometry (VLBI). Signals from a maser,\nor from other bright compact radio sources, are converted to a low-frequency\nbaseband and recorded in digital format on magnetic tape at Nyquist sampling\nrates of up to about\n$10^8$ samples per second at widely separated telescopes that\noperate independently. They form a radio version of the classical \nMichelson stellar interferometer,\nwhose coherence is maintained by the use of atomic frequency standards\nto preserve the signal phase and timing (see Figure~5). The received signals\n(which are proportional to the incident electric fields)\nfrom an array of two or more telescopes are cross-correlated pairwise\nto form cross-correlation functions. Taking advantage of the earth's \nrotation, the spatial \ncross-correlation function of the incident electromagnetic field, or visibility,\ncan be measured\nover a wide range of projected baseline vectors. The image and fringe\nvisibility functions are related through a Fourier transform (see Thompson,\nMoran, \\& Swenson 1986). The\ntemporal Fourier transform of the cross-correlation function gives the\ncross-power spectrum of the radiation, or visibility as a function of frequency, \nso that images at different frequencies can be obtained.\nThe intrinsic angular resolution, $\\theta$, \nof a multielement interferometer is $0.7 \\lambda/B$, where $\\lambda$ \nis the wavelength, and $B$ is the longest\nbaseline length. For water vapor, $\\lambda$ = 1.35 cm, and $B$ is typically 6000~km,\nwhich gives a resolution of 200~$\\mu$as. The spectral resolution\navailable is typically about 15~KHz, or about a fifth of the line widths (see Figure~4). \nIn maser sources, one spectral feature at a particular frequency or velocity can\nbe used as a phase reference for the interferometer, and all other\nphases referred to it. With this technique, the coherence time of the\ninterferometer can be extended indefinitely, and the relative positions\nof masers with respect to the reference feature can be measured to a small\nfraction of the fringe spacing, or intrinsic resolution. The relative \nposition of an unresolved maser component can be measured to an\naccuracy of about\n%\n\\begin{equation}\n\\Delta \\theta = {1\\over 2} {\\theta \\over {{S\\!N\\!R}}}~,\n\\end{equation}\n%\nwhere ${S\\!N\\!R}$ is the signal-to-noise ratio.\n\n\n\\section{THE STUDY OF NGC\\_4258}\n\nThe imaging of the maser in NGC\\_4258 was one of the first projects undertaken\nby a dedicated VLBI system known as the Very Long Baseline \nArray (VLBA) (see Figure~6) in the spring of 1994. \nPrevious VLBI measurements of the systemic features had shown that\nthey arose from an elongated structure with a velocity\ngradient along the major axis, highly suggestive of a rotating disk seen edge-on\n(Greenhill et al. 1995a). The VLBA measurements of all the maser components provide convincing\nevidence for a rotating disk around a massive central\nobject. \n\n% FIGURE 6\n\\begin{figure}[t]\n\\plotfiddle{fig6.eps}{2.05in}{00}{75}{75}{-228}{-174}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nThe distribution of the ten elements of the Very Long Baseline\nArray (VLBA). This network is often augmented with other radio telescopes\nsuch as the Very Large Array (a 27-element array operating as a \nphased array), shown here with the symbol {\\sf Y}, and the 100 m telescope of the Max Planck Institute for \nRadio Astronomy near Bonn, Germany.}\n\\end{figure}\n\n\n% TABLE 1 ---------------------------------------------------------------------\n\\begin{table}[th]\n\\begin{center}\n\\begin{tabular}{l@{\\hspace{1in}}l}\n%\\setlength{\\tabcolsep}{.25in}\n\\multicolumn{2}{c}{TABLE 1}\\\\[1ex]\n\\multicolumn{2}{c}{\\sc Parameters of Molecular Disk Traced by Water Vapor Masers %\n in NGC$\\,4258^a$}\\\\[1ex]\n\\hline\\hline\\noalign{\\vspace{1ex}}\nInner radius, $R_i$ \t\t\t\t& 0.14 pc (3.9 mas) \\\\\nOuter radius, $R_o$\t\t\t\t& 0.28 pc (8.0 mas) \\\\\nInner rotation velocity, $v_{\\phi}$($R_i$) \t& 1100 \\kms \\\\\nOuter rotation velocity, $v_{\\phi}$($R_o$)\t& 770 \\kms \\\\\nInner rotation period\t\t\t\t& 800 yrs \\\\\nOuter rotation period\t\t\t\t& 2200 yrs \\\\\nPosition angle of disk (at 3.9 mas radius)\t& 80\\deg \\\\\nInclination angle\t\t\t\t& 98\\deg \\\\\nPosition velocity slope\t\t\t\t& 282 \\kms $\\,$mas$^{-1}$ \\\\\nCentral mass, $M$\t\t\t\t& $3.9 \\times 10^7$ M\\sol \\\\\nDisk mass, $M_d$\t\t\t\t& $ < 10^6$ M\\sol \\\\\nCentral mass density, uniform distribution\t& $> 4 \\times 10^9$ M\\sol $\\,$pc$^{-3}$ \\\\\nCentral mass, Plummer distribution\t\t& $ > 10^{12}$ M\\sol $\\,$pc$^{-3}$ \\\\\nCentripetal acceleration, systemic features\t& $9.3$ \\kms $\\,$yr$^{-1}$ \\\\\nCentripetal acceleration, high-velocity\tfeatures & $\\le 0.8$ \\kms $\\,$yr$^{-1}$ \\\\\nDisk systemic velocity$^b$, $v_0$\t\t& 476 \\kms \\\\\nGalactic systemic velocity (optical)$^{b,c}$\t& 472 \\kms \\\\\nRadial drift velocity, $v_R$ \t\t& $< 10$ \\kms \\\\\nThickness of disk, $H$\t\t\t\t& $< 0.0003$ pc \\\\\nMaser beam angle, $\\beta$\t\t\t& 8\\deg \\\\\nDisk--galaxy angle$^d$\t\t\t\t& 119\\deg \\\\\nApparent maser luminosity\t\t\t& 150 L\\sol \\\\\nModel luminosity$^e$\t\t\t\t& 11 L\\sol \\\\\nDistance, $D$\t\t\t\t\t& $7.2\\pm 0.3$ Mpc \\\\\n\\noalign{\\vspace{.5ex}}\\hline \\noalign{\\vspace{1.5ex}}\n%-----------------------------------------------------------\n%\\multicolumn{3}{l}{\\vtop{\\parindent=0pt \\baselineskip=10pt \\raggedright\n%\t\t Extragalactic masers outside AGN are found in\n%\t\t NGC\\_253, M\\_82, M\\_33, IC\\_342, LMC, and SMC.}}\n\\multicolumn{2}{l}{$^a$Based on the distance estimate of 7.2 Mpc.} \\\\\n\\multicolumn{2}{l}{$^b$\\vtop{\\raggedright\n\t\t\t\tRadio definition, with respect to the local standard of rest.\n\t\t\t\tTo convert to heliocentric velocity (radio), subtract 8.2 \\kms;\n\t\t\t\tto convert to heliocentric (optical), subtract 7.5 \\kms.}} \\\\\n\\multicolumn{2}{l}{$^c$From Cecil, Wilson, \\& Tully (1992).} \\\\\n\\multicolumn{2}{l}{$^d$Angle between the spin axis of the molecular disk and the spin\n\t\t\taxis of the galaxy.} \\\\\n\\multicolumn{2}{l}{$^e$Radiation into a zone within $\\pm 4$\\deg of the plane of the disk.} \\\\\n\n\\end{tabular}\n\\end{center}\n\\end{table}\n%--------------------------------------------------------------------------------------------\n\n\nThe basic observational results on NGC\\_4258 obtained over the past few years \ncan be summarized as follows (see Table 1 for a list of parameters):\n\n\\begin{enumerate}\n\\item The masers appear to trace a highly elongated, although slightly curved,\n structure (Figure~7). The high-velocity, redshifted and blueshifted features\n are offset in position on the left and right sides of the systemic features,\n respectively. The velocities of the high-velocity features as a function of\n impact parameter (position along the major axis of the distribution) follow\n the prediction of Kepler's third law of orbital motion. The systemic features\n show linear dependence with impact parameter (Miyoshi et al. 1995).\n\\pagebreak\n\n\\item The distribution of maser features in the direction normal\n to the major axis is too small to be measured at present (see Figure~7).\n The upper limit\n on the ratio of thickness to radius of the disk is 0.0025 \n (Moran et al. 1995). \n\n\\item The upper limit of any toroidal component of the magnetic field in the\n masers, derived\n from searches for Zeeman splitting in the line at 1306 \\kms, is less than \n 300 mG (Herrnstein et al. 1998a).\n\n\\item The accelerations (i.e., the linear drift in the line-of-sight velocity with time) \n of the systemic features are about 9 \\kms$\\,$yr$^{-1}$\n (Haschick, Baan, \\& Peng 1994; Greenhill et al. 1995b; Nakai et al. 1995). \n The high-velocity features that have been tracked have accelerations in the range $\\pm 0.8$\n \\kms$\\,$yr$^{-1}$ (Bragg et al. 1999). \n\n\\item The high-velocity features show no proper motions with respect to a \n fixed-velocity component in the systemic range (Herrnstein 1996). The systemic features\n show proper motions of about \\mbox{32 $\\mu$as\\_yr$^{-1}$} (Herrnstein et al. 1999).\n\n\\item There is an elongated continuum radio source, which appears to be a jet \n emanating from the black hole position, parallel to the axis of rotation\n (Herrnstein et al. 1997). There is no 1.35~cm wavelength emission from the\n position of the black hole (Herrnstein et al. 1998b). \n\\end{enumerate}\n\n% FIGURE 7\n\\begin{figure}[t]\n\\plotfiddle{fig7.eps}{3.7in}{00}{90}{90}{-275}{-185}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nTop: Image of the maser emission from the nucleus of NGC\\_4258. The\nticks on the axes are in milliarcseconds. One milliarcsecond corresponds to\n0.035 pc, or $1.1 \\times 10^{17}$~cm, at a distance of 7.2~Mpc.\nBottom: The line-of-sight\nvelocities of the masers versus position along the major axis. The curved\nportions of the plot precisely follow a Keplerian dependence. Data from\nJanuary 1995 (top) and April 1994 (bottom).}\n\\end{figure}\n\n\nThere is virtually no doubt that the masers trace a very thin disk in\nnearly perfect Keplerian motion. Five of six phase-space parameters\nhave been measured for each maser spot, two spatial coordinates and\nthree velocity coordinates. The missing\ncoordinate is the position along the line of sight, which must be \ninferred from the constraint provided by Kepler's third law. \n\n\nThe approximate placement of the masers in the disk can be understood \nby considering\na simple thin, flat disk viewed edge-on. In this case the\nline-of-sight velocity, $v_z$, of a maser will be given by\n%\n\\begin{equation}\nv_z - v_0 = \\sqrt{{GM}\\over R} \\sin \\phi~,\n\\end{equation}\n%\\noindent\nwhere $v_0$ is the line-of-sight velocity of the central object (i.e., the\nsystemic velocity), $G$ is the gravitational constant, $R$ is the distance\nof a maser component from the black hole,\nand $\\phi$ is the azimuth angle in the disk, measured from the line between\nthe black hole and the observer. If the disk were randomly \nfilled with observable masers, one might \nexpect to see a velocity position diagram as shown in Figure~8.\nThe linear boundaries of the distribution are populated by masers at \nthe inner and outer edges of the annular disk. The masers on the curved boundaries \nlie on the midline, where $\\phi$ = 90\\degrees . Hence, the masers in NGC\\_4258 have a \nvery specific distribution: the high-velocity masers lie close to the\nmidline, and the systemic\nmasers lie within a narrow range of radii. From Equation 5, the radius of a\nparticular maser can be determined as\n%\n\\begin{equation}\nR = {(GM)}^{1\\over 3} {\\left[{b}\\over {v_z-v_0}\\right]}^{2\\over 3}~,\n\\end{equation}\n%\\noindent\nwhere ${b}$ is the projected distance on the sky along the major axis from the center of the\ndisk ($\\sin \\phi = b/R$). Similarly, positional offsets from the midline,\n$z$, of the high-velocity features can be determined by deviations from a Keplerian\ncurve; that is, \n%\n\\begin{equation}\nz = \\sqrt{R^2 - b^2}~.\n\\end{equation}\n%\\noindent\nThere is a two-fold ambiguity in the $z$ component of the position for the\nedge-on disk case. Unambiguous estimates of the positions of the high-velocity \nfeatures have been derived\nfrom the accelerations by Bragg et al. (1999), who showed that the masers\nlie within 15 degrees of the midline. \n\n% FIGURE 8\n\\begin{figure}[t]\n\\plotfiddle{fig8.eps}{4.2in}{00}{50}{50}{-140}{-5}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nTop: A cartoon model of a flat annular disk viewed edge-on, with randomly\ndistributed maser sources. Bottom: Each maser will appear as a point within\nthe ``bow tie'' boundary in the plot of line-of-sight velocity versus impact \nparameter. The curved portion of the boundary is populated by masers\nlocated along the midline, the diameter perpendicular to the line of sight. \nThis is a pure Keplerian curve, because the velocity vectors lie\nalong the line of sight. Masers at a fixed radius will appear \nalong a straight line. The steep and shallow lines correspond to\nmasers on the inner and outer annular boundaries of the disk.}\n\\end{figure}\n\nAn expanded plot of the Keplerian part of the velocity curve is\nshown in Figure~9. The data fit a Keplerian curve to an accuracy\nof about 3 \\kms, or less than 1 percent of the rotation speed. However,\nthere are noticeable deviations from a perfect fit. The estimate of the \ncentral mass of the disk derived from this data depends on the distance \nto the maser, and has a value of $3.9 \\times 10^7$ \\Mdot~for a distance \nof 7.2 Mpc. This mass corresponds to an Eddington luminosity (where\nradiation pressure from Thomson scattering would balance gravity) of\n$5 \\times 10^{45}$~erg s$^{-1}$. \nSince the total electromagnetic emission appears to be less than $10^{42}$~\\ergs,\nthe system is highly sub-Eddington. \n\n% FIGURE 9\n\\begin{figure}[t]\n\\plotfiddle{fig9-smaller.eps}{2.9in}{00.0}{100}{100}{-300}{-260}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nThe magnitude of the line-of-sight velocities of the masers, relative\nto the systemic velocity, versus distance from the dynamical center\nof NGC\\_4258. The filled circles are the redshifted masers, and the squares\nare the blueshifted masers. (Data from April 1994)}\n\\end{figure}\n\n%\\begin{equation}\n%M = 3.9 \\times 10^7 M \\left({7.2\\over D}\\right) .\n%\\end{equation}\n\nSince this binding mass must lie inside the inner radius of the maser\ndisk, the mass density, assuming a spherical mass distribution, is\nat least $4 \\times 10^9$ \\msunpc\\ ($3 \\times 10^{-13}$~\\gcc). \nIt is unlikely that this mass is in the form\nof a dense star cluster (Maoz 1995). The average density of stars in the solar \nneighborhood is about 1~\\msunpc, and the density of the densest\nknown star cluster is about $10^5$~\\msunpc. A star cluster will have\na mass distribution that decreases monotonically with radius.\nIn order not to disrupt the Keplerian\ncurve, the core mass for a reasonable distribution must have a peak\ndensity of at least $1 \\times 10^{12}$~\\msunpc. A cluster of massive stars at\nthis density would evaporate from gravitational interactions on\na timescale short with respect to the age of the galaxy, while a\ncluster of low-mass stars would destroy itself from collisions over\na similar timescale. Hence, it is unlikely that the central mass\nis in the form of a star cluster (see also Begelman \\& Rees 1978). \nThe best explanation is that\nthe central object is a supermassive black hole, with a Schwarzschild\nradius ($R_S$) of about $1.2 \\times 10^{13} $ cm. Hence, the masers are distributed\nin a zone between 40,000 and 80,000~R$_S$. Because the maser clouds are so far\nfrom the event horizon, deviations of their motions from the predictions of Newtonian mechanics\nare small.\nThe gravitational redshift and transverse Doppler shift are about 4~\\kms\\ (detectable),\nthe expected Lense-Thirring precession (see below)\nis less than about 3\\degrees over the maser annulus (possibly detectable), and \nthe apparent shift of the maser positions due to gravitational bending is about\n0.1 $\\mu$as (undetectable). \n\nThe disk is remarkably thin. In a disk supported against gravity by\npressure (hydrostatic equilibrium), the density distribution is expected to have \na Gaussian profile with a thickness, $H$, given by the relation\n%\n\\begin{equation}\nH/R = {(c_s^2+v_a^2)}^{1\\over 2}/v_\\phi~,\n\\end{equation}\n%\\noindent\nwhere $c_s$ is the sound speed and $v_a$ is the Alfv\\'en speed,\nwhich characterize thermal and magnetic support pressure, respectively,\nand $v_\\phi$ is the Keplerian rotational speed.\nSince $H/R < 0.0025$,\nthe quadrature sum of the sound speed and Alfv\\'en speed is less than 2.5~km s$^{-1}$. \nThe upper limit on the magnetic field of 300 mG suggests that the Alfv\\'en speed, \n$B/\\sqrt{4\\pi\\rho}$, where $\\rho$ is the density, is less than 3 \\kms\\ for $\\rho=\\rho_c$\n(the critical density for quenching maser emission). If the support were\ncompletely due to thermal pressure, the temperature would be less than 1000~K. \n\nA proper determination of the positions of the masers on the disk requires\nthat the warp and the inclination of the\ndisk to the line of sight be taken into account. An example of such a \ndisk, slightly warped (in position angle only) and slightly inclined to the line\nof sight, that fits the maser distribution in position and velocity\nis shown in Figure~10. \n\n% FIGURE 10\n\\begin{figure}[t]\n\\plotfiddle{fig10.eps}{1.75in}{90}{65}{65}{255}{-80}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nThe warped annular disk (wire mesh) modeled to the maser positions,\nvelocities, and accelerations (adapted from Herrnstein, Greenhill, \\& Moran 1996).\nThe black dot in the center marks the dynamical center\nof the disk. The continuum emission at 1.3 cm is shown in the shaded gray\ncontours. The southern jet may be weaker than the northern jet because of thermal\nabsorption in the disk. The lack of emission at the position of the black hole \nplaces constraints on any coronal or advection zone surrounding the black hole (Herrnstein\net al. 1998b).}\n\\end{figure}\n\n\n\nThe distance to the maser of 7.2 $\\pm$ 0.3 Mpc was determined from\nanalysis of the proper motions and accelerations of the systemic features\n(Herrnstein et al. 1999). Fifteen features were tracked over a period of\ntwo years to an accuracy of 0.5--10~$\\mu$as in relative position and\n0.4 \\kms\\ in velocity. The distance estimate is\nbased on simple geometric\nconsiderations. The Keplerian curve of the high-velocity masers gives\nthe mass function $GM \\sin^2 i/D$, where $i$ is the inclination of the\ndisk to the line of sight. The radius, $R$, of the systemic masers (in\nangular units) is\ndetermined from Equation (6), based on the slope of the velocity versus impact\nparameter curve shown in Figure~7. This fixes the angular velocity,\n$v_{\\phi}$, of the systemic masers under the assumption that the orbits\nare circular.\nThe expected accelerations and proper\nmotions of the systemic features are $v_\\phi^2/R$ and $v_\\phi/D$, \nrespectively.\nThe assumption that the orbits are circular is reasonable on theoretical grounds\nbecause of viscous relaxation and on observational grounds because the\ncontinuum emission arises close to the center of symmetry of the\nmaser distribution. \n\nThe distance to the 15 Cepheid variables in NGC\\,4258 has been estimated to be\n$8.1 \\pm 0.8$~Mpc (Maoz {\\it et al.} 1999). The statistical component of the\nerror is 0.4~Mpc and the systematic error associated with the calibration of \nthe Cepheid distance scale is 0.7~Mpc. The discrepancy between the two distance\nmeasurements to NGC\\,4258 may have cosmological implications (Paczynski 1999).\n\n\n\\section{INTERESTING UNANSWERED QUESTIONS}\n\n\\noindent\n1. What is the rate of radial inflow of material through the disk?\n\\nopagebreak\n\nThe accretion rate of material onto the black hole is an important\nparameter that affects our understanding of radiation processes around the black hole.\nThe maser data\nprovide some information about the accretion rate.\nKey issues are the long timescale needed for material to flow from the disk\nto the black hole and the assumption that the masers trace all the disk material. \nIt is useful to first estimate the mass of the disk. If we account for\nsystematic effects in addition to the random scatter of 3~\\kms, the deviation from\nKeplerian motion due to the finite\nmass of the disk, $\\Delta v_\\phi$, is less than about 10~\\kms\\ over the radius of the disk. \nThis limits the mass of the disk to less than about $2M\\Delta v_\\phi/v_\\phi$, or about\n$10^{6}$~\\msun. The density of the molecular gas must be less than $\\rho_c$ ($10^{10}$\nhydrogen molecules per cubic centimeter). Since $H/R < 0.0025$, the upper limit on mass\nis $10^5$~\\msun. If, in addition, the disk is stable against the effects of\nself-gravity (Toomre 1964; Binney \\& Tremaine 1987), then the mass of the disk must \nbe less than $M(H/R)$, or about $10^5$~\\msun.\n\nThe mass accretion rate of a disk in steady state is given by\n\\begin{equation}\n\\dot{M} = 2\\pi R \\Sigma v_R~,\n\\end{equation}\n%\n%\\noindent\nwhere $\\Sigma$ is the surface density of the disk, and $v_R$ is radial drift\nvelocity, which depends on the viscosity of the disk. Unfortunately, $v_R$ is\nonly weakly constrained by the observations (i.e., the possible difference between\nthe optical and radio systemic velocities) to be $<10$~\\kms. This provides a\ncrude limit on the accretion rate of 100 \\msunyr. To further constrain\nthe mass accretion rate requires an estimate of the viscosity of the disk.\nIn the standard model of \na thin, viscous accretion disk, as formulated by Shakura and Sunyaev (1973), \n$v_R$ can be written (see Frank, King, \\& Raine 1992) as\n%\n\\begin{equation}\nv_R = \\alpha v_{\\phi}{\\left(H\\over R\\right)}^2~,\n\\end{equation}\n\n\\noindent\nwhere $\\alpha$ is the dimensionless viscosity parameter ($0 \\le \\alpha \\le 1$).\nThe observational limit on the ratio $H/R$ implies that $v_R<0.006\\alpha$~\\kms.\nWith the limit on\nmass given by the deviation from Keplerian motion, the accretion rate is less that \n$10^{-1}\\alpha$~\\msunyr. \nThe infall time from the masing region is $R/v_R$, which\nfrom Equation (10) can be written as\n%\n\\begin{equation}\nT \\sim {1\\over \\alpha}{\\left ({c\\over c_S}\\right )^2}{\\left ({R_S\\over c}\\right)}%\n{\\left ({R\\over R_S}\\right )^{1\\over 2}}~.\n\\end{equation}\n\n\\noindent\nFor NGC\\_4258, with $\\alpha = 0.1$ and c$_S = 2.5$ \\kms , $T = 10^{16}$~s, or about\n$3 \\times 10^8$~yrs.\n\n\nFrom the magnetic field limit and the assumption of\nequipartition of magnetic and thermal energy, the upper limit on $\\dot{M}$\nis also $10^{-1}\\alpha$~\\msunyr. If the maser density is the maximum allowable value,\n$\\rho_c$, and the\nmaser traces all the material in the disk, then the limit on disk thickness\nleads to an upper limit on $\\dot{M}$ of $10^{-2}\\alpha$~\\msunyr. Detailed theoretical modeling\ncan give estimates for the accretion rate. For example, a model in which the\ncause of the outer radial cutoff in maser emission is attributed\nto the transition from molecular to atomic gas leads to an\nestimate of $10^{-4}\\alpha$~\\msunyr\\ (Neufeld \\& Maloney 1995). \nGammie, Narayan, \\& Blandford (1999) favor an accretion rate of $10^{-1}\\alpha$~\\msunyr,\nbased on an analysis of the continuum radiation spectrum.\n\nIf the accretion rate is high, then the relative weakness of the continuum \nradiation may be due to the process of advection (Gammie, Narayan, \\& Blandford 1999). On the\nother hand, if the accretion rate is low, then the weak emission is due to the\ndearth of infalling material. In this case the gravitational power in the \naccretion flow may be insufficient to power the jets.\n\n\n\\noindent\n2. What is the form and origin of the warp? \n\\nopagebreak\n\nThe form of the warp is difficult to determine precisely, because the\nfilling factor of the masers in the disk is so small. Better measurements\nof the positions and directions of motion of the high-velocity features are\nkey to defining the warp more accurately.\n\nThe cause of the warp is unknown, but several suggestions have been put\nforward. Papaloizou, Terquem, \\& Lin (1998) show that the warp could be\nproduced by a binary companion orbiting outside the maser disk. Its mass\nwould need to be comparable to the mass of the disk ($< 10^6$~\\Mdot ).\nAlternatively, radiation pressure from the central source will produce\ntorques on a slightly warped disk and will cause the warp to grow\n(Maloney, Begelman, \\& Pringle 1996). Finally, it is conceivable that\nin the absence of other torques, the observed warp is due to the\nLense-Thirring effect. A maximally rotating black hole\nwill cause a precession of a nonaligned orbit (weak field limit) of\n%\n\\begin{equation}\n{\\Omega}_{LT} = {{2G^2M^2}\\over {c^3R^3}}~,\n\\end{equation}\n\n\\noindent\nwhich can be rewritten in terms of the Schwarzschild radius as\n\n\\begin{equation}\n{\\Omega}_{LT} = {1\\over 2}{c\\over R_S}{\\left ({R_S\\over R}\\right )^3}~.\n\\end{equation}\n\n\\noindent\nAt the inner radius of the disk ($R/R_S = 40,000$), the precession amounts\nto $3 \\times 10^{-17}$~s$^{-1}$. This precession is very small but \nmight be significant over the lifetime of the disk. Equation~(11) suggests that the\nlifetime might be $10^{16}$~s, which would produce a\ndifferential precession of about 10\\degrees~ across the radius of the disk. \nIf the axis of the disk is inclined to the axis\nof the black hole, then the viscosity of\nthe disk is expected to twist the plane of the innermost part of the disk to the equatorial\nplane of the black hole (Bardeen \\& Petterson 1975; Kumar \\& Pringle, 1985).\n\n\\noindent\n3. Do the water masers trace the whole disk?\n\\nopagebreak\n\nThe inner and outer radii of the observed masers are undoubtedly due to\nexcitation conditions in the maser. In the vertical direction it is also possible that the\nmasers form in a thin region within a thicker disk with atomic and ionized components. \nIt has also been proposed that the high-velocity features are not indicative of \na warped disk but trace material that has been blown off a flat disk (Kartje, Konigl, \\& \nElitzur 1999). These proposals are difficult to test.\n\n% FIGURE 11\n\\begin{figure}[t]\n\\plotfiddle{fig11-smaller.eps}{3.6in}{0}{100}{100}{-310}{-224}\n\\caption{\\setlength{\\baselineskip}{8 pt}\nA cartoon of the molecular accretion disk in NGC\\_4258. The period of \nrotation at the inner edge of the disk is about 800 years. A particular\nsystemic maser is visible for about 10 years as its\nradiation beam, estimated to have a width of about 8\\degrees , sweeps\nover the earth. The high-velocity features\nmay be visible for a substantially longer time. (Adapted from \nGreenhill et al. 1995a)}\n\\end{figure}\n\n\n\\noindent\n4. What are the physical properties of the maser spots?\n\\nopagebreak\n\nThe spectrum of the maser has many discrete peaks which correspond to\nspots of maser emission on the sky. The success of measuring proper motions and \naccelerations of these masers suggests that they correspond to discrete\ncondensations or density-enhanced regions in the disk. A cartoon of the\nblobs in a disk is shown in Figure~11. The blobs in front of the\nblack hole may be visible because they amplify emission from the\ncentral region. No masers have been seen on the backside of the disk. \nOn the other hand, the high-velocity masers have no continuum emission to\namplify, and we may only see the ones near the midline, where the \ngradient in the line-of-sight velocity is small. Blobs in the rest of\nthe disk may be radiating in directions away from the earth. The\nclumpiness of the medium allows us to track \nthe individual masers. If the appearance of spots is due to blobs, or\ndensity enhancements in the disk, then\nthe minimum gradient condition would not seem to be necessary. However, intense\nhigh-velocity maser spots may occur when blobs at the same velocity\nline up to form two-stage masers (Deguchi \\& Watson 1989).\nThis situation forms a highly\nbeamed maser, like the filamentary maser described in Section~2. The probability of realizing\nthis situation is greatest along the midline, where the velocity gradient is\nsmallest. All evidence suggests that the masers arise from discrete\nphysical condensations. There have been several suggestions that\nthe apparent motions of the maser spots may be due to a phase effect\n(e.g., a spiral density wave\nmoving through the disk, Maoz \\& McKee 1998), but there is no\nobservational evidence for this.\n\n\n\\noindent\n\n\n% TABLE 2 ---------------------------------------------------------------------\n\n\\begin{table}[b]\n\\begin{center}\n\\begin{tabular}{lcccc}\n%\\setlength{\\tabcolsep}{.25in}\n\\multicolumn{5}{c}{TABLE 2}\\\\[1ex]\n\\multicolumn{5}{c}{\\sc Known AGN with Water Masers}\\\\[1ex]\n\\hline\\hline\\noalign{\\vspace{1ex}}\n%\n & Distance & Flux Density & Milliarcsecond & \\\\\nGalaxy & (Mpc) & (Jy) & Structure & Disk \\\\[.5ex]\n%\n\\hline\\noalign{\\vspace{1ex}}\nM\\_51 \t & 3 & 0.2 & \\nodata & \\nodata \t\\\\\nNGC\\_4945 & 3.7 & 4 & yes & yes \t\\\\\nCircinus & 4 & 4 & yes & yes \t\\\\\nNGC\\_4258 & 7.2 & 4 & yes & yes \t\\\\\nNGC\\_1386 & 12 & 0.9 & yes & maybe \\\\\nNGC\\_3079 & 16 & 6 & yes & maybe \\\\\nNGC\\_1068 & 16 & 0.6 & yes & yes \t\\\\\nNGC\\_1052 & 20 & 0.3 & yes & no \t\\\\\nNGC\\_613 & 20 & 0.1? & \\nodata & \\nodata\t\\\\\nNGC\\_5506 & 24 & 0.6 & \\nodata & \\nodata \t\\\\\nNGC\\_5347 & 32 & 0.1 & \\nodata & \\nodata\t\\\\\nNGC\\_3735 & 36 & 0.2 & \\nodata & \\nodata \t\\\\\nIC\\_2560 & 38 & 0.4 & yes\t & \\nodata \t\\\\\nNGC\\_2639 & 44 & 0.1 & \\nodata & \\nodata \t\\\\\nNGC\\_5793 & 50 & 0.4 & \\nodata & \\nodata \t\\\\\nESO\\_103-G035 & 53 & 0.7 & \\nodata & \\nodata\t\\\\\nMrk\\_1210 & 54 & 0.2 & \\nodata & \\nodata \t\\\\\nIRAS F01063-8034 & 57 & 0.2 & \\nodata & \\nodata \\\\\nMrk\\_1 & 65 & 0.1 & \\nodata & \\nodata\t\\\\\nNGC\\_315 & 66 & 0.05 & \\nodata & \\nodata \t\\\\\nIC\\_1481 & 83 & 0.4 & \\nodata & \\nodata \t\\\\\nIRAS F22265-1826 & 100 & 0.3 & yes & no \t\\\\\n\\noalign{\\vspace{.5ex}}\\hline \\noalign{\\vspace{1.5 ex}}\n%-----------------------------------------------------------\n\\multicolumn{5}{l}{\\parbox{4.45in}{\\parindent=0pt \\baselineskip=10pt \\raggedright\n\t\t {\\sc Note}--- Extragalactic masers outside AGN are found in\n\t\t NGC\\_253, M\\_82, M\\_33, IC\\_342, LMC, and SMC.}}\n\\end{tabular}\n\\end{center}\n\\end{table}\n%------------------------------------------------------------------------------\n\n\\section{MASERS IN OTHER AGN}\n\nAt this time (early 1999), 22 masers have been detected among about 700 galaxies\nsearched (e.g., Braatz, Wilson, \\& Henkel 1997). A list of these galaxies with\nmasers is given in Table 2. The yield rate of detections is only about 3 percent.\nThe major reason for this paucity is probably that the maser disks can\nonly be seen if they are edge-on to the line of sight. If the\ntypical beam angle, $\\beta$, is 8\\degrees, as in NGC\\_4258, then the probability\nof seeing a maser is about equal\nto $\\sin \\beta,$ or 8 percent. Braatz, Wilson, \\& Henkel (1997) have\nshown that most of the known masers are associated with Seyfert II galaxies\nor LINERs where the accretion disks are thought to be edge-on to the earth. \n\n\n% TABLE 3 ---------------------------------------------------------------------\n\n\\begin{table}[b]\n\\begin{center}\n\\begin{tabular}{l@{}ccrcccl}\n\\multicolumn{8}{c}{TABLE 3}\\\\[1ex]\n\\multicolumn{8}{c}{\\sc Water Masers with Resolved Structure}\\\\[1ex]\n\\hline\\hline\\noalign{\\vspace{2ex}}\n%\n\\multicolumn{8}{c}{Masers Without Obvious Disk Structure}\\\\[1ex]\n\\hline\\noalign{\\vspace{1ex}}\n && $D$ & \\omit{\\hfil $v_0$\\hfil} & $\\Delta v$ & $\\Delta R$ & & \\\\\nGalaxy && \\sm Mpc & \\omit{\\hfil \\sm \\kms\\hfil} & \\sm \\kms & \\sm pc & Comment & Reference \\\\\n\\hline\\noalign{\\vspace{1ex}}\nIRAS\\_22265 (S0) && 100 & \\omit{\\hfil 7570\\hfil} & 150 & 2.4 & messy & Greenhill et al. 1999a\\\\\nNGC\\_1052 (E4) && \\z 20 & \\omit{\\hfil 1490\\hfil} & 100 & 0.6 & ``jet'' & Claussen et al. 1998\\\\\nIC\\_2560 && \\z 38 & \\omit{\\hfil 2900\\hfil} & \\z 30 & 0.2 & velocity & Nakai et al. 1998 \\\\\n && & & & & gradient & \\\\\n\\noalign{\\vspace{.5ex}}\\hline\n\\hline\n\\noalign{\\vspace{2ex}}\n%-----------------------------------------------------------------------------------------------------\n\\multicolumn{8}{c}{Masers With Disk Structure}\\\\[1ex]\n\\hline\\noalign{\\vspace{1ex}}\n & $D$ & $v_{\\phi}$ & \\omit{\\hfil $R_i$/$R_o$\\hfil} & $M$ & $\\rho$ & $L_x$ & \\\\\nGalaxy & \\sm Mpc & \\sm \\kms & \\omit{\\hfil \\sm pc\\hfil} & \\sm 10$^6$ M$_{\\odot}$\n\t& \\sm 10$^7$ M$_{\\odot}\\,$pc$^{-3}$ & \\sm 10$^{42}$ erg$\\,$s$^{-1}$ & Reference \\\\ \n\\hline\\noalign{\\vspace{1ex}}\nNGC\\_4258 & \\z 7 & 1100 & 0.13/0.26 & 35 & 400 & 0.04 & Miyoshi et al. 1995\\\\\nNGC\\_1068 & 15 & \\z 330 & 0.6/1.2\\z & 17 & 3 & 40 & Greenhill \\& Gwinn 1997\\\\\nCircinus & \\z 4 & \\z 230 & 0.08/0.8\\z & \\z 1 & 40 & 40 & Greenhill et al. 1999b\\\\\nNGC\\_4945 & \\z 4 & \\z 150 & 0.2/0.4\\z & \\z 1 & 2 & 1 & Greenhill et al. 1997\\\\\nNGC\\_1386 & 12 & \\z 100 & --/0.7\\z & \\z 2 & 4 & 0.02 & Braatz et al. 1999\\\\\nNGC\\_3079 & 16 & \\z 150 & --/1.0\\z & \\z 1 & 0.2 & 0.02 & Trotter et al. 1998,\\\\\n & & & & & & & Satoh et al. 1998 \\\\\n\\noalign{\\vspace{.5ex}}\\hline\n\\noalign{\\vspace{1.5ex}}\n\\multicolumn{8}{l}{\\parbox{6.5 in}{\\parindent=0pt \\baselineskip=10pt \\raggedright\n$D$ = distance,\n$v_0$ = systemic velocity, $\\Delta v$ = velocity range, $\\Delta R$ = linear extent,\n$v_{\\phi}$ = rotational velocity, $R_i$/$R_o$ = inner/outer radius of disk, \n$M$ = central mass, $\\rho$ = central mass density, $L_x$ = X-ray luminosity.}}\\\\\n\\noalign{\\vspace{1ex}}\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nIt is difficult to make VLBI measurements on masers weaker than about 0.5 Jy because\nof the need to detect the maser within the coherence time of the interferometer.\nNine masers have been studied with VLBI. Four of these\nshow strong evidence of disk structure, and two more show \nprobable disk structure. The properties of these masers\nare listed in Table 3. Unfortunately, none of these masers \nshow the simple, well-defined structure that would make them useful for\nprecise study of the physical properties of accretion disks around black holes. \n\n\\section{SUMMARY}\n\nThe measurements of the positions and velocities of the masers in the nucleus\nof NGC\\_4258 offer compelling evidence for the existence of a supermassive black\nhole and provide the first direct image of an accretion disk within $10^5$~R$_S$\nof the black hole. Much more can be learned from this system. A measurement of\nthe disk thickness is important and may require higher signal-to-noise ratios\nthan are achievable currently or VLBI measurements from space. Measurement of\nthe continuum spectrum from the central region is very important to the\nunderstanding of the radiation process. Detection of radio emission would require\ninstruments of higher sensitivity. Continued\nmeasurements over time of the positions and velocities of the masers will refine\nthe estimates of their proper motions and accelerations, and this will better\ndefine the shape of the disk. It is even conceivable that the radial drift\nvelocity will be detected. This work will benefit immensely from new instruments\nthat are in the planning stage for centimeter wavelength radio astronomy. These\ninclude the enhanced Very Large Array, the Square Kilometer Array, and space\nVLBI missions such as ARISE. \n\nWe thank Adam Trotter and Ann Bragg for helpful discussions.\n\n\n\\begin{center}\n{\\bf REFERENCES}\n\\end{center}\n\n\\setlength{\\parindent}{0pt}\n\nAntonucci, R.~R.~J. \\& Miller, J.~S. 1985, {\\it Astrophys. J.}, {\\bf 297}, 621--632.\n\nBardeen, J.~M. \\& Petterson, J.~A. 1975, {\\it Astrophys. J.}, {\\bf 195}, L65--L67.\n\nBegelman, M.~C. \\& Rees, M.~J. 1978, {\\it Mon. Not. R. Astr. 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Wrobel (San Francisco: ASP), 237--238.\n\nNakai, N., Inoue, M., Miyazawa, K., Miyoshi, M., \\& Hall, P. 1995, {\\it Pub. Astron.\nSoc. Jap.}, {\\bf 47}, 771--799.\n\nNakai, N., Inoue, M., \\& Miyoshi, M. 1993, {\\it Nature}, {\\bf 361}, 45--47.\n\nNeufeld, D. \\& Maloney, P.~R. 1995, {\\it Astrophys. J.}, {\\bf 447}, L17--L20.\n\nPaczynski, B. 1999, {\\it Nature,} {\\bf 401}, 331--332.\n\nPapaloizou, J.~C.~B., Terquem, C., \\& Lin, D.~N.~C. 1998, {\\it Astrophys. J.}, {\\bf 497}, 212--226.\n\nReid, M.~J. \\& Moran, J.~M. 1988, in {\\it Galactic and Extragalactic Radio Astronomy},\n2d ed., ed. G.~L. Verschuur \\& K.~I. Kellermann (New York: Springer-Verlag), 255--294.\n\nRees, M. 1998, in {\\it Black Holes and Relativistic Stars}, ed. R.~M. Wald (Chicago: Univ.\nChicago Press), 79--101.\n\nSalpeter, E.~E. 1964, {\\it Astrophys. J.}, {\\bf 140}, 796--800.\n\nSatoh, S., Inoue, M., Nakai, N., Shibata, K.~M., Kameno, S., Migenes, V., \\&\nDiamond, P.~J. 1998, in {\\it Highlights of Astronomy}, {\\bf 11b}, ed. J. Andersen\n(Dordrecht: Kluwer), 972--973.\n\nSeyfert, C. 1943, {\\it Astrophys. J.}, {\\bf 97}, 28--40.\n\nShakura, N.~I. \\& Sunyaev, R.~A. 1973, {\\it Astr. Astrophys.}, {\\bf 24}, 337--355.\n\nTanaka, Y., et al. 1995, {\\it Nature}, {\\bf 375}, 659--661. \n\nThompson, A. ~R., Moran, J.~M., \\& Swenson, G.~W. 1986, {\\it Interferometry and \nSynthesis in Radio Astronomy} (New York: Wiley Interscience).\n\nToomre, A. 1964, {\\it Astrophys. J.}, {\\bf 139}, 1217--1238.\n\nTrotter, A.~S., Greenhill, L.~J., Moran, J.~M., Reid, M.~J., Irwin, J.~A., \\& Lo, K.~Y. \n1998, {\\it Astrophys. J.}, {\\bf 495}, 740--748.\n\nWeaver, H., Williams, D.~R.~W., Dieter, N.~H., \\& Lum, W.~T. 1965,\n{\\it Nature}, {\\bf 208}, 29--31.\n\n\\eject\n\n\\begin{center}\n{\\bf QUESTIONS AND ANSWERS}\n\\end{center}\n\n\\begin{list}{}{\\settowidth{\\labelwidth}{Q:~~}\n \\setlength{\\labelsep}{0pt}\n \\setlength{\\leftmargin}{\\labelwidth}\n \\addtolength{\\leftmargin}{\\labelsep}\n \\setlength{\\itemsep}{12pt}\n \\renewcommand{\\makelabel}[1]{#1\\hfill}}\n%\n\\item [Q:~~] What other measurements can one do with masers to try to get\nsensitivity to the general relativistic effects or to get information from\ndistances closer to the mass concentration?\n%\n\\item [A:~~] We have searched for masers in NGC$\\,$4258 that are closer to the central\nmass than 40,000 Schwarzschild radii and have found none. The reason for\nthe absence of masers closer to the center is unclear. Masers are very sensitive\nto local conditions such as temperature, density, and pump power,\nwhich may depend on the geometry of the warp. Water masers arise in neutral\nmedia at temperatures below a few thousand degrees, so it is unrealistic\nto expect to find masers very close to the Schwarzschild radius.\n\nOne possible general relativity effect might be the deflection of radiation\nfrom masers on the far side of the accretion disk (i.e., a distortion of the\nimage of the back side of the accretion disk). However, no such masers have\nbeen found.\n\\end{list}\n\n\n\\end{document}\n\n\n\n"
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astro-ph0002086
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BINDING ENERGY AND THE FUNDAMENTAL PLANE OF GLOBULAR CLUSTERS
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"author": "Dean E. McLaughlin\\altaffilmark{1}"
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A physical description of the fundamental plane of Galactic globular clusters is developed which explains all empirical trends and correlations in a large number of cluster observables and provides a small but complete set of truly independent constraints on theories of cluster formation and evolution in the Milky Way. In a very good first approximation, the internal structures and dynamics of Galactic globulars are described by single-mass, isotropic \markcite{kin66}King (1966) models and are thus characterized by four nominally independent physical parameters. Within this theoretical framework, it is shown that (1) 39 regular (non--core-collapsed) globulars with measured central velocity dispersions all share a common core mass-to-light ratio, $\Upsilon_{V,0}=1.45\,M_\odot\,L_\odot^{-1}$, and (2) 109 regular globulars both with and without direct observations of $\Upsilon_{V,0}$ show a very strong correlation between global binding energy and total luminosity, regulated by Galactocentric position: $E_b=7.2\times10^{39}\ {erg}\ (L/L_\odot)^{2.05}(r_{gc}/ 8\,{kpc})^{-0.4}$. The observational scatter about either of these two constraints can be attributed fully to random measurement errors, making them the {defining equations of a fundamental plane} (FP) to which real clusters are confined in the larger, four-dimensional parameter space of general King models. They are shown to underlie a pair of bivariate correlations first found, and used to argue for the existence of a globular cluster FP, by \markcite{djo95}Djorgovski (1995). A third, weaker correlation, between clusters' total luminosities and King-model concentration parameters, is related to the (non-random) distribution of globulars {on} the FP. With $L$, $\Upsilon_{V,0}$, $E_b$, and the central concentration $c$ thus chosen as the four physical quantities that define any single globular cluster, the FP equations for $\Upsilon_{V,0}$ and $E_b(L,r_{gc})$ are used to {derive} expressions for {any other} observable in terms of only $L$, $r_{gc}$, and $c$. Results are obtained for generic King models and applied specifically to the globular cluster system of the Milky Way.
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"name": "dempa.tex",
"string": "\\documentstyle[11pt,aaspp4,epsf]{article}\n\n\\begin{document}\n\n\\title{BINDING ENERGY AND THE FUNDAMENTAL PLANE OF GLOBULAR CLUSTERS}\n\\author{Dean E. McLaughlin\\altaffilmark{1}}\n\\affil{Department of Astronomy, 601 Campbell Hall\\\\\nUniversity of California, Berkeley, CA 94720-3411\\\\\[email protected]}\n\n\\altaffiltext{1}{Hubble Fellow}\n\n\\lefthead{McLaughlin}\n\\righthead{Fundamental Plane of Globular Clusters}\n\n\\begin{abstract}\n\nA physical description of the fundamental plane of Galactic globular clusters\nis developed which explains all empirical trends and correlations in a large\nnumber of cluster observables and provides a small but complete set of truly\nindependent constraints on theories of cluster formation and evolution in \nthe Milky Way.\n\nIn a very good first approximation, the internal structures and dynamics of\nGalactic globulars are described by single-mass, isotropic\n\\markcite{kin66}King (1966) models and are thus characterized by four\nnominally independent physical parameters. Within this theoretical framework,\nit is shown that (1) 39 regular (non--core-collapsed) globulars with measured\ncentral velocity dispersions all share a common core mass-to-light ratio,\n$\\Upsilon_{V,0}=1.45\\,M_\\odot\\,L_\\odot^{-1}$, and (2) 109 regular globulars\nboth with and without direct observations of $\\Upsilon_{V,0}$ show a very\nstrong correlation between global binding energy and total luminosity,\nregulated by Galactocentric position:\n$E_b=7.2\\times10^{39}\\ {\\rm erg}\\ (L/L_\\odot)^{2.05}(r_{\\rm gc}/\n8\\,{\\rm kpc})^{-0.4}$. The observational scatter about either of these two\nconstraints can be attributed fully to random measurement errors, making them\nthe {\\it defining equations of a fundamental plane} (FP) to which\nreal clusters are confined in the larger, four-dimensional parameter space of\ngeneral King models. They are shown to underlie a pair of bivariate\ncorrelations first found, and used to argue for the existence of a globular\ncluster FP, by \\markcite{djo95}Djorgovski (1995). A third, weaker correlation,\nbetween clusters' total luminosities and King-model concentration parameters,\nis related to the (non-random) distribution of globulars {\\it on} the FP. With\n$L$, $\\Upsilon_{V,0}$, $E_b$, and the central concentration $c$ thus chosen as\nthe four physical quantities that define any single globular cluster, the\nFP equations for $\\Upsilon_{V,0}$ and $E_b(L,r_{\\rm gc})$ are used to\n{\\it derive} expressions for {\\it any other} observable in terms of only $L$,\n$r_{\\rm gc}$, and $c$. Results are obtained for generic King models and\napplied specifically to the globular cluster system of the Milky Way.\n\n\\end{abstract}\n\n\\keywords{galaxies: fundamental parameters --- galaxies: star clusters ---\nglobular clusters: general}\n\n\n\\section{Introduction}\n\nThe properties of globular clusters in the Milky Way offer empirical\nconstraints not only on their own formation and evolution, but also\non the history of our Galaxy as a whole and, to a potentially large extent, on\nthe formation of generic star clusters---a key element of the star formation\nprocess itself. The many observed correlations between various internal\nstructural and dynamical parameters of the clusters (core and half-light\nradii, surface brightnesses, velocity dispersions, etc.) that have been found\nby several authors (e.g., \\markcite{bro84}Brosche \\& Lentes 1984;\n\\markcite{kor85}Kormendy 1985; \\markcite{vdb91}van den Bergh, Morbey, \\&\nPazder 1991; \\markcite{vdb94}van den Bergh 1994; \\markcite{djo94}Djorgovski \\&\nMeylan 1994; \\markcite{djo95}Djorgovski 1995; \\markcite{bel96}Bellazzini et\nal.~1996; \\markcite{mur92}Murray \\& Lin 1992) constitute an important set of\nsuch constraints.\n\nThe apparently large number of these correlations (see especially\n\\markcite{djo94}Djorgovski \\& Meylan 1994) can be somewhat misleading,\nhowever, in that it is impossible for all of them to be independent. This\nfollows from the fact that Galactic globulars are structurally and dynamically\nexceedingly simple, being very well described by single-mass, isotropic\n\\markcite{kin66}King (1966) models. Since these models are defined fully by\nthe specification of just four independent physical parameters, it is not\nunreasonable to expect that the same should be true, at least in a\nfirst-order approximation, of real clusters; but there can then be at most\nthree truly distinct correlations between their various intrinsic properties\n(although these may be supplemented, in general, by dependences on\n``external'' factors such as Galactocentric position or cluster metallicity).\n\nIt is clearly of interest, then, to systematically reduce the globular cluster\ndata in the Milky Way to the minimum number of independent physical\nrelationships required for a complete description of the observed properties\nof the ensemble. The establishment of such a compact set of empirical\nconstraints---which should serve better as a target for theories of cluster\nformation and evolution---is the main goal of this paper. To reach it, two\nimportant results will be used as starting points.\n\nFirst, the two best globular cluster correlations known to date (i.e., the\nonly two with scatter that can be fully accounted for by observational\nuncertainties) are the bivariate dependences presented by\n\\markcite{djo}Djorgovski (1995) for a subset (roughly one-third) of the\nGalactic globulars. One of these correlations involves only cluster core\nparameters, while the other includes properties measured at their half-light\nradii. \\markcite{djo95}Djorgovski found these correlations by a statistical\nprincipal-components analysis, and he offered no physical interpretation of\nthem; but he pointed out that their very existence suggests that globular\nclusters may in practice be confined---much like elliptical galaxies and\nother large stellar systems are---to a ``fundamental plane'' in the\nhigher-dimensional space of physical parameters available to them in\nprinciple.\n\nSecond, an almost completely unexamined (but, as it happens, very closely\nrelated) issue has to do with the dependence of binding energy, $E_b$, on mass\n(or luminosity) among globular clusters. This was studied some time ago by\n\\markcite{sai79}Saito (1979), who also investigated the question for dwarf\nand giant elliptical galaxies. He found that $E_b\\propto M^{1.5}$ or\nso---apparently consistent with very simple virial-theorem arguments---for\nglobulars and giant ellipticals alike. However, his observational sample\nincluded only ten relatively bright globular clusters. The data required for a\ncalculation of binding energy are now available for many more clusters than\nthis and they are obviously of higher quality than those\navailable to \\markcite{sai79}Saito. A total energy $E_b$ is the only obvious\nphysical property that is {\\it not} routinely estimated from observations of\nGalactic globulars; but it is arguably important---if for no other reason than\nto complete a systemization of the data---to clarify the empirical\nbehavior of this quantity.\n\nIn what follows, catalogued data are used to estimate binding energies within\nthe context of single-mass, isotropic \\markcite{kin66}King (1966) models for\n109 ``regular'' (non--core-collapsed) globular clusters in the Milky Way. The\ndata and necessary aspects of the models are summarized in the next Section\nand in a pair of Appendices. Section 3 presents the binding energies\nthemselves, and also derives core mass-to-light ratios, $\\Upsilon_{V,0}$, for\n39 of these clusters with measured central velocity dispersions. It is shown\nthat (1) $\\Upsilon_{V,0}$ is a constant for all clusters, and (2) $E_b$\ncorrelates tightly with total cluster luminosity (or mass), scaling as\n$E_b\\propto L^{2.05\\pm0.1}$. This is significantly (if not surprisingly)\ndifferent from \\markcite{sai}Saito's (1979) result, and perhaps also from the\nrelation obeyed by elliptical galaxies (although this also appears not\nto have been reviewed in any detail since \\markcite{sai79}Saito's work).\n\nSection 3 also establishes the choice of $L$, $E_b$, $\\Upsilon_{V,0}$,\nand the King-model concentration parameter $c\\equiv\\log\\,(r_t/r_0)$, as the\nfour ``independent'' physical properties used to define any globular cluster.\nThe tight constraints found on $\\Upsilon_{V,0}$ and $E_b(L)$ then imply that\nreal clusters have (at most) only two free parameters, and they do indeed\noccupy a fundamental plane in the theoretical space of King models. The\ninfluence of environment on this plane, as reflected in cluster Galactocentric\nradii and metallicities, is also examined in \\S3; it is shown to be confined to\na dependence on $r_{\\rm gc}$ in the {\\it normalization} of the $E_b$--$L$\nscaling.\n\nIn \\S4, an orthogonal coordinate system called $\\epsilon$-space (analogous to\nthe so-called $\\kappa$-space of elliptical galaxies; \\markcite{ben92}Bender,\nBurstein, \\& Faber 1992) is constructed to obtain a face-on view of the\nfundamental plane. This shows that globulars are not distributed uniformly\nover it; essentially, the parameter $c$, which\ndescribes the internal density profile of a cluster, is also correlated with\ntotal luminosity or mass (see also \\markcite{vdb94}van den Bergh 1994;\n\\markcite{bel96}Bellazzini et al.~1996). Alternate representations of the\nfundamental plane, in the form of a number of bivariate correlations between\ncluster core and half-light parameters, are also developed in \\S4. It is\nshown that the two correlations of \\markcite{djo95}Djorgovski (1995) are\nequivalent to the two constraints $\\Upsilon_{V,0}=constant$ and $E_b\\propto\nL^{2.05}$ and, thus, that \\markcite{djo95}Djorgovski identified the same\nfundamental plane that is developed here.\n\nSection 5 and Appendix A then use the defining equations of the fundamental\nplane, along with manipulations based on generic properties of King\nmodel, to derive a set of simple relations that ultimately describe the\nvariation of {\\it any} globular cluster observable as a function of $L$, $c$,\nand $r_{\\rm gc}$ {\\it only}. These may themselves be manipulated to explain\nany observed correlation between any other combination of cluster variables.\nThus, the fundamental plane indeed reduces a large array of globular cluster\ndata to a very small set of independent constraints for models of their\nformation and evolution. These are set out in \\S6, which summarizes the paper.\n\nIt should be noted that the choice of ``basic'' cluster properties adopted\nhere---total luminosity (mass), binding energy, mass-to-light ratio, and\nconcentration parameter---is not a unique possibility, nor is it necessary in\nany rigorous sense. It will be noted, for example, that the scaling of binding\nenergy with luminosity is essentially equivalent to other, previously known\ncorrelations between half-light radii and luminosities ($R_h\\sim L^0$;\n\\markcite{vdb91}van den Bergh et al.~1991) and between core velocity\ndispersions and luminosities ($\\sigma_0\\sim L^{0.52}$; e.g.,\n\\markcite{djo94}Djorgovski \\& Meylan 1994). However, this does not make a\ndescription in terms of $E_b$ any less correct or valid. In fact, this\nframework seems particularly amenable to theoretical studies of cluster\nevolution and formation both: Many simulations of the former follow the\nevolution of $c$ and $E_b$ over time, and a discussion of the $E_b(L,r_{\\rm\ngc})$ dependence in the latter context will be taken up in a subsequent paper\n(McLaughlin, in preparation).\n\n\\section{Data and Model Calculations}\n\nIt is well known that \\markcite{kin66}King's (1966) theoretical sequence of\nisotropic, lowered isothermal spheres of single-mass stars (see also\n\\markcite{bin87}Binney \\& Tremaine 1987) provides an excellent match to the\nluminosity profiles of most Milky Way globulars and a good description\nof their internal kinematics. This specific model framework is therefore\nadopted for analyses throughout this paper. For\nself-consistency, and in order to make use of as large an empirical database\nas possible, the complications of velocity anisotropy and multi-mass stellar\npopulations are not considered (although theoretical models incorporating\nthese features have, of course,\nbeen constructed [\\markcite{mic63}Michie 1963; \\markcite{gun79}Gunn \\& Griffin\n1979] and applied to a number of Galactic globulars [see \\markcite{pry93}Pryor\n\\& Meylan 1993]).\n\n\\markcite{har96}Harris (1996) maintains an on-line catalogue\\footnotemark\n\\footnotetext{{\\tt http://physun.physics.mcmaster.ca/Globular.html}. The\nversion used in this paper is the revision of 22 June 1999.}\nof King-model parameters and other properties of 147 Galactic globular\nclusters; it is in part a synthesis and updating of earlier compilations by\n\\markcite{tra93}Trager, Djorgovski, \\& King (1993) and\n\\markcite{dja93}Djorgovski (1993a) (see also \\markcite{tra95}Trager, King,\n\\& Djorgovski 1995). Among other quantities, the catalogue lists the\nclusters' heliocentric distances and their Galactocentric positions,\n$r_{\\rm gc}$; their foreground reddenings, $E(B-V)=A_V/3.1$, and absolute\nmagnitudes, $M_V$; metallicities, [Fe/H]; projected\nhalf-light (or effective) radii, $R_h$; central $V$-band surface brightnesses,\n$\\mu_{V,0}$ (not corrected for extinction in the raw catalogue); scale\nradii,\\footnotemark\\ $r_0$,\n\\footnotetext{The radii $r_0$ are referred to by \\markcite{har96}Harris\n(1996), and by \\markcite{tra93}Trager et al.~(1993) and\n\\markcite{dja93}Djorgovski (1993), as core radii, and they are denoted\n$r_c$ in these catalogues. However, the tabulated values in fact correspond to\nthe King-model scale radii $r_0$ defined by equation (\\ref{eq:23}), and they\nare quantitatively different from the projected half-power radii of\nlow-concentration clusters.}\nand concentration parameters, $c\\equiv\\log\\,\\left(r_t/r_0\\right)$ (with $r_t$\nthe tidal radius), derived from fits of\n\\markcite{kin66}King (1966) models to cluster surface-brightness\nprofiles; and central luminosity densities, $j_0$ (in $V$-band $L_\\odot$\npc$^{-3}$), obtained from the measured $c$, $r_0$, and extinction-corrected\n$\\mu_{V,0}$ (see, e.g., \\markcite{dja93}Djorgovski 1993a, and Appendix A\nbelow).\n\nThe \\markcite{kin66}King-model structural parameters are not available for six\nof the globulars in \\markcite{har96}Harris' (1996) tables; another cluster\n(Djorgovski 1) has no measured metallicity; and no central surface brightness\nis given for one more (the Pyxis cluster). These objects were therefore\nexcluded a priori from the data set ultimately used here. Of the 139 clusters\nremaining, 30 are identified (following \\markcite{tra93}Trager et al.~1993)\nas having obvious or suspected post--core-collapse (PCC) morphologies, i.e.,\ncentral density cusps. As \\markcite{tra93}Trager et al.~discuss,\nsuch clusters are not particularly well described by King\nmodels---a concentration parameter of $c=2.5$ has generally been assigned to\nthem {\\it arbitrarily}---and their tabulated scale radii $r_0$ and core\nsurface brightnesses $\\mu_{V,0}$ are most likely over- and underestimates,\nrespectively. Thus, although most of the calculations described below have\nbeen performed for the PCC clusters using the data as given, the results\nshould {\\it not} be taken at face value; and while these objects are shown\non many of the plots in this paper, they are never included in any more\ndetailed analyses (e.g., least-squares fits).\n\nThis leaves 109 regular, King-model clusters as the main focus of\nattention. Of these, 103 have Galactocentric radii $r_{\\rm gc} < 40$ kpc;\n4 have $65\\la r_{\\rm gc}\\la 100$ kpc; and two (the faint Palomar 4 and AM1)\nlie at $r_{\\rm gc}\\simeq110$--120 kpc. Estimates of the central line-of-sight\nvelocity dispersions, $\\sigma_{p,0}$, are given for roughly one-third (39/109)\nof this restricted sample, as well as for 17 of the 30 PCC clusters, by\n\\markcite{pry93}Pryor \\& Meylan (1993). These additional data are also\nemployed here.\n\nThe recent study of \\markcite{ros98}Rosenberg et al.~(1998) has been used\nto replace some of \\markcite{har96}Harris' (1996) numbers for the\nlow-luminosity cluster Palomar 12. Specifically, from a King-model fit to\nstar counts, \\markcite{ros98}Rosenberg et al.~derive $c=1.08$ and\n$r_0=0\\farcm63$ (or 3.5 pc, for a heliocentric distance of 19.1 kpc), as\ncompared to the $c=1.94$ and $r_0=0\\farcm20$ given by \\markcite{har96}Harris.\nWith $\\mu_{V,0}=20.6$, according to \\markcite{har96}Harris, this then\nimplies (following the procedure outlined in Appendix A below) a central\nluminosity density $j_0\\simeq32\\,L_\\odot\\,{\\rm pc}^{-3}$, lower than the\nprevious value by a factor of roughly three. After incorporating these few\nchanges for this one cluster, the final database is similar to that\nadopted by \\markcite{djo94}Djorgovski \\& Meylan (1994), and the subsets\nthereof in \\markcite{djo95}Djorgovski (1995) and \\markcite{bel98}Bellazzini\n(1998), for their recent investigations of the Milky Way globular cluster\nsystem.\n\nExpositions of observational uncertainties can be found in\n\\markcite{tra93}Trager et al.~(1993) and \\markcite{pry93}Pryor \\& Meylan\n(1993), and the situation may be summarized roughly as follows: scale and\n(projected) half-light radii are known to typical precisions of\n$\\Delta\\,\\log\\,r_0\\simeq\\pm0.1$ dex and $\\Delta\\,\\log\\,R_h\\simeq\\pm0.1$ dex;\ncentral velocity\ndispersions, to within $\\Delta\\,\\log\\,\\sigma_{p,0}\\simeq\\pm0.07$ dex; central\nsurface brightnesses, to $\\Delta\\,\\mu_{V,0}\\simeq\\pm0.3$ mag arcsec$^{-2}$;\nand concentrations, to $\\Delta\\,c\\simeq\\pm0.2$ dex.\nUncertainties in any derived quantities follow immediately from these\nestimates. For example, the central luminosity density is obtained from\n$\\mu_{V,0}=const.-2.5\\,\\log\\,\\left(j_0r_0\\right)$ (eqs.~[\\ref{eq:a2}],\n[\\ref{eq:a3}]), and thus $\\Delta\\,\\log\\,j_0\\simeq\\pm0.2$ dex. Similarly, the\naverage surface brightness within a half-light radius is defined as\n$\\langle\\mu_V\\rangle_h=const.-2.5\\,\\log\\,\\left(L/R_h^2\\right)$\n(see eq.~[\\ref{eq:a5}]), so that $\\Delta\\,\\langle\\mu_V\\rangle_h\n\\simeq\\pm0.5$ mag arcsec$^{-2}$.\nThere are also uncertainties in cluster distance moduli---$\\pm0.15$ mag\nmay be representative; see the discussion at \\markcite{har96}Harris' (1996)\nwebsite---and thus in Galactocentric distances\n$r_{\\rm gc}$ and total luminosities $L$ (note that integrated apparent $V$\nmagnitudes are generally good to a few hundredths of a magnitude). These\nare generally not dominant in the error budgets discussed here, however,\nand for the most part they can be ignored.\n\nIn order to refer cluster data to isotropic King models, it is necessary\nfirst to relate the observed velocity dispersion $\\sigma_{p,0}$ to the model\n{\\it scale velocity}, $\\sigma_0$. This latter quantity is defined through the\ndistribution function assumed for the cluster stars, $f(E)\\propto\n\\sigma_0^{-3}\\,\\left[\\exp\\left(E/\\sigma_0^2\\right)-1\\right]$, and through the\ndimensionless cluster potential, $W(r)\\equiv\\left[\\phi(r_t)-\\phi(r)\\right]/\n\\sigma_0^2$ (\\markcite{kin66}King 1966; \\markcite{bin87}Binney \\& Tremaine\n1987). $W(r)$ and a scaled density profile, $\\rho/\\rho_0$ vs.~$r/r_0$, follow\nfrom integrating Poisson's equation with this distribution function and a\nspecified value of $W_0\\equiv W(r=0)$. With $r_t$ the radius at which $W=\\rho\n=0$, there is then a one-to-one relation between $W_0$ and the concentration\nparameter $c\\equiv\\log\\,\\left(r_t/r_0\\right)$. In the limit of high\nconcentration, the King model is a normal isothermal sphere, $\\sigma_0$ is the\ntrue one-dimensional velocity dispersion inside the cluster, and $\\sigma_{p,0}=\n\\sigma_0$. For low concentrations $c\\la 1$, however, the outer, non-isothermal\nparts of a cluster influence projected quantities even at its center, and\n$\\sigma_{p,0}<\\sigma_0$. This effect is illustrated in the upper left-hand\npanel of Fig.~\\ref{fig1}. The numerical integrations summarized there have\nbeen used (given the observed concentrations $c$) to convert the central\ndispersions $\\sigma_{p,0}$ to model $\\sigma_0$-values for the\n39 regular and 17 PCC clusters in \\markcite{pry93}Pryor \\& Meylan (1993). In\nmost cases, this is not a large correction: the \\markcite{pry93}Pryor \\&\nMeylan clusters all have $c>0.75$, and $0.8<\\sigma_{p,0}/\\sigma_0<1$. It does\nhave the effect of adding slightly to the observational uncertainty, however:\nwith $\\Delta\\,c=\\pm0.2$ and $\\Delta\\,\\log\\,\\sigma_{p,0}=\\pm0.07$, the typical\nerrorbar on $\\log\\,\\sigma_0$ is roughly $\\pm0.09$ dex.\n\n\\placefigure{fig1}\n\nThe binding energies of Milky Way globulars are calculated in \\S3 from the\nbasic definition (cf.~\\markcite{kin66}King 1966; \\markcite{sai79}Saito 1979)\n\\begin{equation}\nE_b \\equiv -{1\\over{2}}\\,\\int_0^{r_t}4\\pi r^2\\rho\\phi\\,dr =\n{1\\over{2}}\\,\\int_0^{r_t}4\\pi r^2\\rho\n\\left[{{GM}\\over{r_t}}+\\sigma_0^2\\,W(r)\\right]\\ dr\\ ,\n\\label{eq:21}\n\\end{equation}\nwhere $M$ is the total mass and the sign has been chosen to make $E_b>0$ for \nbound clusters. A dimensionless binding energy follows directly from this\nand is a function only of $c$ (through $W_0$) for an isotropic and\nsingle-mass King model:\n\\begin{equation}\n{\\cal E}(c)\\equiv {{GE_b}\\over{\\sigma_0^4\\,r_0}} =\n{{81}\\over{2}}\\,{{r_0}\\over{r_t}}\\,\n\\left[\\int_0^{r_t} {{\\rho}\\over{\\rho_0}}\\,\\left({r\\over{r_0}}\\right)^2\\\n{{dr}\\over{r_0}}\\right]^2 +\n{9\\over{2}}\\,\\int_0^{r_t} {{\\rho}\\over{\\rho_0}}\\,\\left({r\\over{r_0}}\\right)^2\nW(r)\\ {{dr}\\over{r_0}}\\ .\n\\label{eq:22}\n\\end{equation}\nHere the central mass density $\\rho_0$ is related to $r_0$ and $\\sigma_0$ by\nthe {\\it model definition}\n\\begin{equation}\nr_0^2\\equiv{{9\\sigma_0^2}\\over{4\\pi G \\rho_0}}\\ .\n\\label{eq:23}\n\\end{equation}\nThe function ${\\cal E}$ is shown in the upper right panel of Fig.~\\ref{fig1}.\nOver the range $0.5\\le c\\le 2.5$ appropriate to Galactic globulars, an\nobservational uncertainty of $\\Delta\\,c=\\pm0.2$ translates to an\nr.m.s.~variation of $\\pm0.2$ dex in ${\\cal E}$ as well.\n\nIf the mass density profile $\\rho(r)/\\rho_0$ is replaced by its luminosity\nequivalent, $j(r)/j_0$, the light intensity $I$ at a given projected radius\n$R$ follows from the standard integral ${\\cal I}(R)\\equiv I(R)/\\left(j_0r_0\n\\right)=2\\,\\int_R^{r_t}\\left(j/j_0\\right)\\left(r/r_0\\right)\\left(r^2/r_0^2-\nR^2/r_0^2\\right)^{-1/2}\\,dr/r_0$. The central surface density ${\\cal I}_0$ is\nagain a function of $c$ only, and it is shown in the bottom left panel of\nFig.~\\ref{fig1}. The full profile ${\\cal I}(R)$ also uniquely predicts the\nradius ${\\cal R}(c)\\equiv R_h/r_0$ which contains half of a cluster's total\nluminosity in projection. This is plotted against the concentration parameter\nat the bottom right of Fig.~\\ref{fig1}. Both ${\\cal I}_0(c)$ and ${\\cal R}(c)$\nfigure prominently in the analysis of \\S\\S4 and 5 below.\n\nIt will also be necessary to refer to another feature of single-mass King-model\nclusters, namely, the dimensionless total luminosity ${\\cal L}(c)\\equiv\nL/j_0r_0^3=\\int_0^{r_t}\\,4\\pi\\left(j/j_0\\right)\\left(r/r_0\\right)^2\\,dr/r_0$.\nThis quantity is shown for a range of central concentrations in the top panel\nof Fig.~\\ref{fig2}. The lower half then compares the\ncalculated luminosity---$L_{\\rm mod}={\\cal L}(c)j_0r_0^3$---to that directly\nobserved for the 139 globular clusters of\n\\markcite{har96}Harris (1996). The agreement for the 109 regular\nclusters is excellent (as was also noted by \\markcite{dja93}Djorgovski 1993a):\n$\\langle\\log\\,L_{\\rm mod}-\\log\\,L\\rangle=-0.017$ with an r.m.s.~scatter,\n$\\Delta=0.25$ dex, that is less than the observational errorbar of\n$\\pm0.3$.\\footnotemark\n\\footnotetext{This errorbar, drawn in the bottom panel of Fig.~\\ref{fig2},\nfollows from (conservatively) combining in quadrature the uncertainties\nof $\\pm0.1$ in $\\log\\,r_0$; $\\pm0.12$ in $\\log\\,\\left(j_0r_0\\right)$; and\n$\\pm0.16$ dex in $\\log\\,{\\cal L}(c)$ (which follows from the shape of\n${\\cal L}$ in the interval $0.5\\le c\\le 2.5$, given $\\Delta\\,c=\\pm0.2$ dex).}\nFigure \\ref{fig2} can therefore be viewed as confirming that regular globular\nclusters are indeed well described by King models---and as showing the\ndifficulties with PCC clusters, whose luminosities are often underestimated\non the basis of their crude King-model parametrizations.\n\n\\placefigure{fig2}\n\nAs has already been suggested, the concentration parameters measured for\nGalactic globular clusters span a reasonably wide range of values, from\n$c\\simeq0.5$ to $c\\simeq2.5$ (\\markcite{har96}Harris 1996); moreover, there\nis a strong {\\it systematic} quality to the variation of $c$ from cluster\nto cluster (see, e.g., Fig.~\\ref{fig6} below). Thus, Figs.~\\ref{fig1} and\n\\ref{fig2} also serve to illustrate the {\\it dynamical and structural\nnon-homology} that characterizes the Milky Way globular cluster system: The\nrelationships between global and local properties of a cluster (i.e., any of\nthe ratios plotted in these Figures) obviously depend quantitatively on its\ninternal density and velocity profiles. But the details of these profiles\nare quite sensitive to the King-model parameter $c$ (or, equivalently,\n$W_0$), so that even {\\it dimensionless} ratios such as ${\\cal E}$,\n${\\cal R}$, and ${\\cal L}$ can differ significantly between clusters; one\nglobular cannot, in general, be turned into another simply by applying a\nsingle scaling factor to its basic physical parameters. \n\nThis is a natural consequence of the fact that globular clusters are well\ndescribed by King models (it would not be the case if, for example,\nthese objects were singular isothermal spheres), and it is clearly key\nto a full understanding of cluster structures and a complete explanation of\nthe various correlations between their properties. Although this point has\nalways been appreciated in principle (e.g., \\markcite{djo95}Djorgovski 1995;\n\\markcite{bel98}Bellazzini 1998), its consequences are fully explored for the\nfirst time in this paper. Throughout, the functions of $c$ just\ndiscussed are used repeatedly to derive and manipulate physical parameters\nof the Milky Way globulars, thus always taking into account---or, in some\nsense, correcting for---any non-homology. Whenever an evaluation of\n${\\cal E}$, ${\\cal I}_0$, ${\\cal R}$, or ${\\cal L}$ is required, it is\nobtained from an observed $c$-value by interpolating on the numerical model\ncurves plotted in Figs.~\\ref{fig1} and \\ref{fig2}. (For convenience, however,\nAppendix B also gives simple approximations to these dimensionless quantities\nas polynomial functions of the concentration $c$.)\nIt is worth noting that analogous corrections for non-homology in elliptical\ngalaxies may remove some significant part of the observed ``tilt'' of their\nfundamental plane (see \\markcite{gra97}Graham \\& Colless 1997;\n\\markcite{bus97}Busarello et al.~1997).\n\n\\section{Two Basic Properties of Galactic Globular Clusters}\n\nThe full spatial structure and internal dynamics of a single-mass, isotropic\n\\markcite{kin66}King (1966) model cluster are set by specifying four\nindependent physical parameters. The four most convenient, for purposes of\ncomparison with observations of real clusters, are the central concentration\n$c$ [or the central potential depth $W_0$, to fix the overall shape of a\nsurface brightness profile $\\mu(R)\\sim-2.5\\,\\log\\,I(R)$]; the scale radius\n$r_0$ [for horizontal normalization in a plot of $\\mu(R)$ vs.~projected radius\n$R$]; the central luminosity $j_0$ (the vertical normalization, related to\n$\\mu_0$ as described above and in Appendix A); and the core mass-to-light\nratio $\\Upsilon_0$ (for normalization of the model to observed line-of-sight\nvelocity dispersions). More generally, however, {\\it any} set of four\nlinearly independent combinations of these quantities will serve equally well\nas a physical ``basis'' for the sequence of King models. (Such additional\nfactors as metallicity or galactocentric position are quite separate from\nany model characterization of a cluster's internal structure, and they\nare best viewed as ``external'' physical parameters.) As will be described\nbelow, the basis ultimately chosen here comprises the concentration, $c$; the\n(logarithmic) mass-to-light ratio, $\\log\\,\\Upsilon_0$; total luminosity,\n$\\log\\,L$ (which agrees well with the model quantity $\\left[ \\log\\,j_0 +\n3\\,\\log\\,r_0 + \\log\\,{\\cal L}(c)\\right]$); and binding energy, $\\log\\,E_b=\nconst. + \\left[ 2\\,\\log\\,\\Upsilon_0 + 2\\,\\log\\,j_0 + 5\\,\\log\\,r_0 +\n\\log\\,{\\cal E}(c)\\right]$.\n\nAt any rate, the implication is that, insofar as Galactic globulars can be\napproximated by the simplest King models---that is, to the extent that\ninternal velocity anisotropies and a range of constituent stellar masses can\nbe ignored as second-order corrections---they constitute a nominally\nfour-parameter family of stellar systems. As was mentioned in \\S1, however,\nthere exist many\ncorrelations between various properties of globular clusters in the Milky Way,\nimplying that these objects in reality inhabit only a small part of the\nphysical space potentially available to them in principle.\nIndeed, as \\markcite{djo95}Djorgovski (1995) and \\markcite{bel98}Bellazzini\n(1998) have suggested, and as will now be shown in a different manner, there\nexist at least two (and perhaps three) independent constraints linking\nthe four basic parameters of globular clusters, so that they are confined\nto a fundamental plane (perhaps a line) in the theoretical 4-space of\nKing models.\n\n\\subsection{A Constant Core Mass-to-Light Ratio}\n\nAs was discussed in \\S2, the central line-of-sight velocity\ndispersions $\\sigma_{p,0}$ compiled for 39 regular and 17 PCC globular\nclusters by \\markcite{pry93}Pryor \\& Meylan (1993) have been converted to\nKing-model scale velocities $\\sigma_0$ using the concentration parameters\n$c$ given by \\markcite{har96}Harris (1996). With measurements of all three\nof $\\sigma_0$, $r_0$, and $j_0$\nthus in hand, self-consistent mass-to-light ratios $\\Upsilon_{V,0}$\nmay be calculated for fully one-third of the Milky Way globulars via the\ncore-fitting procedure of \\markcite{ric86}Richstone \\& Tremaine (1986): Given\n$\\sigma_0$ and $r_0$ for any one cluster, equation (\\ref{eq:23}) yields a core\nmass density $\\rho_0$, from which follows $\\Upsilon_{V,0}\\equiv \\rho_0/j_0$.\n\nFigure \\ref{fig3} plots $\\rho_0$ against $j_0$ for the \\markcite{pry93}Pryor\n\\& Meylan dataset, with the regular clusters represented by circles\n(open symbols use the directly observed $\\sigma_{p,0}$ in place of the\ncorrected $\\sigma_0$ in eq.~[\\ref{eq:23}]) and PCC objects shown as open\nsquares. The straight line traces the relation $\\log\\,\\rho_0=0.16+\\log\\,j_0$,\nobtained by a least-squares fit to the non--core-collapsed clusters (filled\ncircles) {\\it only}. Clearly, the intercept in this equation is the mean\nmass-to-light ratio $\\langle\\log\\,\\Upsilon_{V,0}\\rangle$. Moreover, the\nr.m.s.~scatter about this fit ($\\Delta=0.2$ dex) can be attributed entirely\nto random observational uncertainties;\\footnotemark\n\\footnotetext{Given $\\Delta\\,\\log\\sigma_0\\simeq\\pm0.09$, $\\Delta\\,\\log\\,r_0=\n\\pm0.1$, and $\\Delta\\,\\log\\,(j_0r_0)=0.12$, and with $\\Upsilon_{V,0}\\propto\n\\sigma_0^2/j_0r_0^2$ the uncertainty $\\Delta\\log\\,\\Upsilon_{V,0}$ is typically\n$\\pm0.24$ dex even if the constituent errors are uncorrelated.}\nthere is no evidence for any significant variation in $\\Upsilon_{V,0}$ from\none cluster to another.\n(The apparent departure of the densest core-collapsed clusters from the mean\nline in Fig.~\\ref{fig3} is certainly not entirely real,\nand it may be completely spurious: forcing a King-model fit to these objects\nleads to underestimates of their core densities $j_0$, and thus to the\nunderestimates of their total luminosities in Fig.~\\ref{fig2} and to\noverestimates of $\\Upsilon_{V,0}$ here. Once again, PCC clusters\nare never included in any of the quantitative analyses in this paper.)\n\n\\placefigure{fig3}\n\nThis result has two implications. First, almost as a practical matter, it\ncan confidently be assumed, even in the absence of direct velocity-dispersion\nmeasurements, that {\\it all other} (non-PCC) Galactic globulars share the\nsame mass-to-light ratio, viz.\n\\begin{equation}\n\\log\\,\\Upsilon_{V,0}=\\log\\,\\left(\\rho_0/j_0\\right)=0.16\\pm0.03\n\\ \\ \\ \\ \\ [M_\\odot\\,L_\\odot^{-1}]\\ ,\n\\label{eq:24}\n\\end{equation}\nwhere the uncertainty is just $0.2/\\sqrt{39}$. This mean $\\Upsilon_{V,0}=(1.45\n\\pm0.1)\\ M_\\odot\\,L_\\odot^{-1}$ is the same as the direct\naverage of the values given for individual clusters by \\markcite{pry93}Pryor\n\\& Meylan (1993), even though these authors define the mass-to-light ratio\ndifferently (as the ratio of central {\\it surface} densities) and fit\ndifferent (multi-mass) King models to the raw velocity and surface-brightness\ndata. Their numbers also show no evidence for any significant dependence of\n$\\Upsilon_{V,0}$ on $j_0$, or on cluster luminosity. Figure \\ref{fig3} is also\nroughly consistent with the mean $\\Upsilon_{V,0}\\simeq1.2\\ M_\\odot\\,\nL_\\odot^{-1}$ found by \\markcite{man91}Mandushev, Spassova, \\& Staneva (1991)\n(who, however, claim marginal evidence for a weak trend,\n$\\Upsilon_{V,0}\\propto L^{0.08\\pm0.06}$ with large scatter).\n\nThe second consequence of Fig.~\\ref{fig3} and equation (\\ref{eq:24}) is an\neffective reduction of the dimensionality of the parameter space available\nto Galactic globular clusters, from four to three; in practice, {\\it the core\nmass-to-light ratio is not a free physical variable}. This point is taken up\nagain in \\S4.2 below, where it is shown that the constraint\n$\\log\\,\\Upsilon_{V,0}\\equiv0.16$ is equivalent to one of\n\\markcite{djo95}Djorgovski's (1995) bivariate correlations defining the\nglobular cluster fundamental plane.\n\n\\subsection{Binding Energy vs.~Luminosity}\n\nFollowing the discussion at the beginning of this Section, the King-model\nparameters remaining to characterize Galactic globulars are $c$, $r_0$,\nand $j_0$---or any three linearly independent combinations of these quantities\nplus a constant $\\Upsilon_{V,0}$. The remainder of this Section, as well as\n\\S4, is devoted to establishing total luminosity $L$ (or mass\n$\\Upsilon_{V,0}L$) and binding energy $E_b$ as replacements for $r_0$ and\n$j_0$ as two of the axes\nin the parameter space of King models. There are several justifications\nfor this replacement. First, there exists a previously unrecognized,\nbut exceptionally strong, correlation between $E_b$ and $L$ in the Milky Way\ncluster system. This correlation further reduces the dimensionality of the\nspace inhabited by real globulars, and it provides an immediate\nphysical explanation for \\markcite{djo95}Djorgovski's (1995) second equation\nfor the fundamental plane (\\S4.2). Second, an emphasis on binding energy in\nparticular facilitates comparison with the expected properties of gaseous\nprotoclusters (McLaughlin, in preparation), i.e., this quantity is a natural\nfocus for theoretical investigations of the origin and evolution of the\nglobular cluster fundamental plane. And third, a view in terms of binding\nenergy might profitably be extended to galaxies and clusters of galaxies,\nperhaps to yield new insight into their fundamental planes as well.\n\nGiven equations (\\ref{eq:22}) and (\\ref{eq:23}), $E_b$ may be calculated for\na King-model globular cluster using measurements of $c$ and any two of\n$\\sigma_0$ (which, again, is inferred from the directly observed $\\sigma_{p,0}$\nand $c$), $r_0$, and $\\rho_0\\equiv \\Upsilon_{V,0}j_0$ in one of the three\nequivalent relations,\n\\begin{equation}\nE_b(\\sigma_0,r_0) = 4.639\\times10^{45}\\,{\\rm erg}\\,\n\\left({{\\sigma_0}\\over{{\\rm km\\,s}^{-1}}}\\right)^4\n\\left({{r_0}\\over{{\\rm pc}}}\\right)\\,{\\cal E}(c)\n\\label{eq:31}\n\\eqnum{\\ref{eq:31}a}\n\\end{equation}\n\\begin{equation}\nE_b(\\sigma_0,\\rho_0) = 5.995\\times10^{46}\\,{\\rm erg}\\,\n\\left({{\\sigma_0}\\over{{\\rm km\\,s}^{-1}}}\\right)^5\n\\left({{\\Upsilon_{V,0}j_0}\\over{M_\\odot\\,{\\rm pc}^{-3}}}\\right)^{-1/2}\\,\n{\\cal E}(c)\n\\eqnum{\\ref{eq:31}b}\n\\end{equation}\n\\begin{equation}\nE_b(r_0,\\rho_0) = 1.663\\times10^{41}\\,{\\rm erg}\\,\n\\left({{r_0}\\over{{\\rm pc}}}\\right)^5\n\\left({{\\Upsilon_{V,0}j_0}\\over{M_\\odot\\,{\\rm pc}^{-3}}}\\right)^2\\,\n{\\cal E}(c)\\ .\n\\eqnum{\\ref{eq:31}c}\n\\addtocounter{equation}{+1}\n\\end{equation}\nWith $\\Upsilon_{V,0}$ a constant, equation (\\ref{eq:31}c) is of\nparticular interest in that it allows for an estimate of binding energy based\nentirely on photometry, i.e., velocity-dispersion measurements are not\nexplicitly required. The function ${\\cal E}(c)$ is shown in Fig.~\\ref{fig1}\nabove, and it can be approximated by equation (\\ref{eq:b2})\nbelow. As was mentioned in \\S2, an r.m.s.~variation of $\\pm0.2$ dex in $c$\ntranslates to $\\Delta\\,\\log\\,{\\cal E}(c)=\\pm0.2$; thus, the typical\nmeasurement errors in $c$, $\\log\\,r_0$, and $\\log\\,j_0$ result in a\ntotal observational uncertainty of $\\pm0.45$--0.75 dex\n(depending on whether or not the individual errors are correlated)\nin the logarithm of $E_b$.\n\nFigure \\ref{fig4} plots the concentrations and the binding energies, calculated\nusing each of equations (\\ref{eq:31}) (supplemented by eq.~[\\ref{eq:24}]),\nagainst luminosity and mass for the\n39 King-model globulars (circles) and 17 PCC clusters (squares) with\n$\\sigma_0$ known from \\markcite{pry93}Pryor \\& Meylan (1993). Note that\nthe total masses used in this Figure are taken directly from\n\\markcite{pry93}Pryor \\& Meylan, who derived them from fits of anisotropic,\nmulti-mass King models to the cluster data. These masses are therefore highly\nmodel-dependent, and in fact it is not clear what relevance they have in the\nanalysis of this paper, which treats globulars as isotropic, single-mass\nclusters (in particular, the equality $M=\\Upsilon_{V,0} L$ is implicit here,\nbut it does not necessarily hold for the numbers of \\markcite{pry93}Pryor \\&\nMeylan 1993). Nevertheless, the right column of Fig.~\\ref{fig4} demonstrates\nthat correlations between cluster concentration and luminosity/mass, and\nbetween $E_b$ and $L$ or $M$, exist independently of specific model\nassumptions.\n\n\\placefigure{fig4}\n\nThe top row of Fig.~\\ref{fig4} shows a rough trend of increasing central\nconcentration with increasing cluster luminosity. Such a correlation has also\nbeen noted by, e.g., \\markcite{vdb94}van den Bergh (1994),\n\\markcite{djo94}Djorgovski \\& Meylan (1994), and \\markcite{bel96}Bellazzini\net al.~(1996), and it was recognized in essence long ago, by\n\\markcite{sha27}Shapley \\& Sawyer (1927). This dependence is visibly weaker\nthan that of $E_b$ on $L$, an impression that is quantified by the difference\nin the Spearman rank correlation coefficients $s$ for the various\nrelationships. (These nonparametric measures of correlation strength,\nspecified in each panel of Fig.~\\ref{fig4}, are computed for\nthe regular, King-model clusters [filled circles] only.) A linear\ndependence can be fit to these data---$c\\simeq const. +\n0.4\\,\\log\\,(L/L_\\odot)$---but the r.m.s.~scatter about it is $\\Delta=0.3$,\nsignificantly larger than the observational errorbar $\\Delta\\,c=\\pm$0.2 dex.\nClearly, $c$ is not completeley independent of $\\log\\,L$, but the relation\nbetween the two does not appear to be one-to-one (or, if such a strong link\ndoes exist, it is nonlinear).\n\nOn the other hand, $\\log\\,E_b$ and $\\log\\,L$ are very strongly correlated.\nIndeed, if the correlation coefficients $s$ in the lower six panels of\nFig.~\\ref{fig4} are compared to those given by \\markcite{djo94}Djorgovski \\&\nMeylan (1994), \\markcite{djo95}Djorgovski (1995), and\n\\markcite{bel98}Bellazzini (1998) for a large number of empirical relations\nbetween other observables of Milky Way clusters, it can quickly be seen that\n{\\it the correlation between binding energy and luminosity (or mass) is as\nstrong as or stronger than any other correlation between properties of\nGalactic globulars}. In addition to this, it is clear that a simple power-law\ndependence of $E_b$ on $L$ or $M$ completely describes the data. Least-squares\nfits (for the regular clusters only) of $\\log\\,E_b$ against either $\\log\\,L$\nor the $\\log\\,M$ from \\markcite{pry93}Pryor \\& Meylan (1993) are drawn in\nFig.~\\ref{fig4}. The r.m.s.~scatter of $\\log\\,E_b$ about the straight lines\nin these six fits always lies within the observational errorbar ($\\pm0.5$ dex)\nshown in the second row of the Figure.\n\nThe three fits of $\\log\\,E_b$ against $\\log\\,L$ are statistically\nindistinguishable. This is only to be expected; it reconfirms the main\nunderlying assumption here---that globular clusters are well described by\nisotropic, single-mass King models---and the finding of \\S3.1, that the\ncore mass-to-light ratio is an essentially constant $\\log\\,\\Upsilon_{V,0}=\n0.16$. Figure \\ref{fig5} specifically compares the binding energies computed\nusing measurements of $r_0$ and $\\rho_0$ (eq.~[\\ref{eq:31}c]) to those\ncalculated from $\\sigma_0$ and $r_0$ (eq.~[\\ref{eq:31}a]). Since the ratio\nof these is just $\\left(4\\pi G \\Upsilon_{V,0} j_0 r_0^2/9\\sigma_0^2\\right)^2$,\nit should be---and is---equal to unity in the mean, with an r.m.s.~scatter\n($\\Delta=0.4$ dex) just twice that found in Fig.~\\ref{fig3} for the basic\nidentity $\\Upsilon_{V,0}=\\rho_0/j_0$.\n\n\\placefigure{fig5}\n\nIf $\\log\\,E_b$ is then specified, for each of the 39 regular clusters in\n\\markcite{pry93}Pryor \\& Meylan's (1993) sample, as the direct mean of the\nthree values derived from equations (\\ref{eq:31}), a least-squares regression\nagainst cluster luminosity results in\n\\begin{equation}\n\\log\\,(E_b/{\\rm erg}) =\n(39.82\\pm0.75) + (2.05\\pm0.15)\\,\\log\\,\\left(L/L_\\odot\\right)\\ ,\n\\label{eq:32}\n\\end{equation}\nwith a Spearman rank correlation coefficient $s=0.92$ and an r.m.s.~scatter\nin $\\log\\,E_b$ of $\\pm0.43$ dex. This relation is significantly different (the\nuncertainties in eq.~[\\ref{eq:32}] are $\\pm1\\sigma$) from the $E_b\\propto\nL^{1.5}$ proposed by \\markcite{sai79}Saito (1979).\n\nIt is perhaps worth noting that the three fits of $\\log\\,E_b$ vs.~$\\log\\,M$\nin Fig.~\\ref{fig4} are also statistically identical to each other, but that\nthey differ formally\nfrom the $E_b(L)$ fit: $E_b\\propto M^{1.8\\pm0.1}$ is indicated, as opposed to\n$E_b\\propto L^{2.05\\pm0.15}$. At first glance, the difference in these\nexponents might seem to imply a varying {\\it global}\nmass-to-light ratio, $(M/L)_V\\propto L^{0.14\\pm0.11}$ or so. Such a result\nis obviously of very low statistical significance, however, and of dubious\norigin besides. It could well be completely an artifact of {\\it a comparison\nbetween different King models}, namely, the single-mass and isotropic version\nused here to compute $E_b$, vs.~the multi-mass and anisotropic variant used by\n\\markcite{pry93}Pryor \\& Meylan (1993) to obtain $M$. In addition, a more\ndirect inspection of the \\markcite{pry93}Pryor \\& Meylan masses shows no clear\nevidence for any systematic variation of global $(M/L)_V$ with cluster\nluminosity (consistent with the lack of any such trend in $\\Upsilon_{V,0}$\nfrom Fig.~\\ref{fig3}).\nAs a whole, then, the current data and models still show no conclusive signs\nof any variation in global mass-to-light ratios among Milky Way globulars.\nThe rest of this paper will therefore discuss cluster binding energies\nexplicitly as a function of luminosity only, and it will be taken as given\nthat $E_b$ scales with total mass in the same way.\n\nFigure \\ref{fig6} shows the concentration $c$ and the binding energy\n$E_b$ (calculated from eq.~[\\ref{eq:31}c] with $\\log\\,\\Upsilon_{V,0}\n\\equiv0.16$) as functions of luminosity for all of the 139 globulars with\ndata taken from \\markcite{har96}Harris (1996). As before, the 109 regular\nclusters are plotted as filled circles, and the 30 PCC objects as open squares.\nEvidently, the correlations seen in Fig.~\\ref{fig4} extend to the whole of the\nMilky Way cluster system. In particular, the power-law nature and high\nstatistical significance of the $E_b$ vs.~$L$ scaling are unchanged from the\nsmaller sample of \\markcite{pry93}Pryor \\& Meylan. It is now found that\n\\begin{equation}\n\\log\\,\\left(E_b/{\\rm erg}\\right) =\n(39.89\\pm0.38) + (2.05\\pm0.08)\\,\\log\\,\\left(L/L_\\odot\\right)\\ ,\n\\label{eq:33}\n\\end{equation}\nwhere the uncertainties are again $\\pm1\\sigma$ estimates. The r.m.s.~scatter\nabout this fit (to the regular clusters only) is $\\Delta=0.53$ dex in\n$\\log\\,E_b$, consistent with the combination of purely random measurement\nerrors in $c$, $\\log\\,r_0$, and $\\log\\,j_0$. With a Spearman rank statistic of\n$s=0.93$, the correlation between $E_b$ and $L$ is better by far than those\nbetween any other cluster properties in this expanded (and now essentially\ncomplete) dataset.\n\n\\placefigure{fig6}\n\nThe rough correspondence between $c$ and $\\log\\,L$ seen in Fig.~\\ref{fig4}\nalso persists for regular, King-model clusters---$c\\approx const.+0.4\\,\\log\\,L$\nis again indicated---but this remains less significant (smaller $s$) and more\nscattered (the r.m.s.~deviation deviation from the straight line in the top\nof Fig.~\\ref{fig6} is $\\Delta\\simeq0.35$ dex, again exceeding the typical\nobservational uncertainty in $c$) than the $E_b$--$L$ relation.\n\nThe cluster luminosities plotted in Figs.~\\ref{fig4} and \\ref{fig6} are\nthe integrated absolute magnitudes tabulated by \\markcite{har96}Harris (1996),\nand they are {\\it independent} of any King-model fits; they have\n{\\it not} been computed from the formula $L={\\cal L}(c) j_0 r_0^3$.\nNevertheless, Fig.~\\ref{fig2} above demonstrated that the model luminosities\ndo correspond very closely to the directly observed values. Thus, a point\nof potential concern here is that a plot of $E_b$ against $L$ is effectively\none of $(j_0^2 r_0^5)$ against $(j_0 r_0^3)$, raising the possibility\nthat any correlation might be either trivial or spurious. Figure\n\\ref{fig7} illustrates that the situation is rather more subtle than this in\nreality, and that the $E_b(L)$ dependence found here is indeed nontrivial.\nThe top two panels of this Figure show $\\log\\,r_0$ and $\\log\\,(j_0r_0)$ (which\nagain is closely related to the central surface brightness $\\mu_{V,0}$)\nvs.~total luminosity for all of \\markcite{har96}Harris' (1996) clusters.\nIt is immediately obvious that $r_0$ and $j_0r_0$ each correlate with\n$L$---the dashed lines drawn describe $r_0\\propto L^{-0.3}$ and $j_0r_0\\propto\nL^{1.25}$---but the r.m.s.~scatter $\\Delta$ in these plots is much larger\nthan the observational errorbars (drawn in the upper left corners) in either\ncase. The point of physical interest is that the {\\it scatter} in $\\log\\,r_0$\nis (anti)correlated with that in $\\log\\,(j_0r_0)$. One example of this has\nalready been shown in Fig.~\\ref{fig2}, with its plot of ${\\cal L}(c)j_0r_0^3$\nagainst $L$; another is now seen in the bottom panel of Fig.~\\ref{fig7}, which\nshows explicitly that the specific combination $(j_0^2r_0^5)\\propto E_b/\n{\\cal E}(c)$ is much more tightly correlated with cluster luminosity [the\nerrorbar in the upper left, $\\pm0.4$ dex, represents the quadrature sum of\nthe uncertainties in $\\log\\,(j_0^2r_0^2)$ and $\\log\\,r_0^3$]. This already\nsuggests that the relation between $E_b$ and $L$ is the more fundamental one,\nand that the (degraded) $r_0$--$L$ and $j_0r_0$--$L$ correlations are properly\nviewed as deriving from it.\n\n\\placefigure{fig7}\n\nThe details of this derivation are discussed in \\S5 and Appendix A, along with\nother examples of similarly weak or scattered monovariate structural\ncorrelations in the Galactic globular cluster system. A key consideration is\nthe effect of the clusters' structural non-homology (see \\S2). Thus---for\nexample---the bottom of Fig.~\\ref{fig7} is still not equivalent to the lower\nhalf of Fig.~\\ref{fig6}, because $j_0^2r_0^5$ differs from $E_b$ by a\n{\\it non-constant} factor of ${\\cal E}(c)$ (eq.~[\\ref{eq:31}c]). Indeed, the\nstraight line in Fig.~\\ref{fig7} represents the scaling $j_0^2r_0^5\\propto\nL^{1.7}$; it is only because $\\log\\,{\\cal E}\\sim 0.85\\,c$ ({\\it very}\nroughly, from Fig.~\\ref{fig1} above) and $c\\sim 0.4\\,\\log\\,L$ that\n$E_b\\propto L^{2.05}$ obtains in the end. Note also that the r.m.s.~scatter\n$\\Delta$ in $\\log\\,E_b$ vs.~$\\log\\,L$ is actually slightly {\\it smaller} than\nthat in $\\log\\,(j_0^2r_0^5)$ vs.~$\\log\\,L$, despite the large scatter in the\n$c$--$\\log\\,L$ correlation; this is further evidence that the $E_b(L)$\nrelation is nontrivial and physically significant.\n\nThere are other ways to see this dependence, however, and it might have been\nanticipated on the basis of some previous work. In particular, Fig.~\\ref{fig8}\nshows the projected half-light radii of the clusters in\n\\markcite{har96}Harris (1996) as a function of their total luminosities and\n(3D) Galactocentric radii $r_{\\rm gc}$. This comparison, which is not new\n(cf.~\\markcite{vdb91}van den Bergh et al.~1991; \\markcite{vdb95}van den Bergh\n1995), shows that $R_h$ depends only weakly on $L$ but tends to increase\nsystematically with $r_{\\rm gc}$ [the dashed line in the upper right panel of\nthis Figure has the equation $\\log\\,(R_h/{\\rm pc})=0.23+0.4\\,\\log\\,\n(r_{\\rm gc}/{\\rm kpc})$]. Moreover, it turns out that the latter variation\nis responsible for what little dependence $R_h$ does appear to have on $L$:\nas Fig.~\\ref{fig8} also shows (see also \\markcite{vdb91}van den Bergh et\nal.~1991), the normalized quantity $R_h^*\\equiv R_h(r_{\\rm gc}/8\\,{\\rm kpc})\n^{-0.4}$ is essentially independent of cluster luminosity.\\footnotemark\n\\footnotetext{The relation claimed by \\markcite{ost97}Ostriker \\& Gnedin\n(1997), $R_h\\propto L^{-0.63}$ for clusters with $5\\le r_{\\rm gc}\\le 40$ kpc,\nis not consistent with the earlier analysis of \\markcite{vdb91}van den Bergh\net al.~(1991), and it is {\\it not confirmed} here. Again, the plot of\n$R_h^*$ against $L$ shows that {\\it at a fixed Galactocentric radius}, cluster\nsizes are quite insensitive to their total masses. This point is important\nfor discussions of cluster destruction timescales, especially in the low-mass\nregime.}\nIn fact, with a rank correlation coefficient of $s\\simeq-0.1$, $R_h^*$\nand $L$ are about as close to being perfectly {\\it un}correlated ($s=0$) as\n$E_b$ and $L$ are to being perfectly correlated ($s=1$).\n\n\\placefigure{fig8}\n\nThe point of this is that $E_b\\propto j_0^2r_0^5{\\cal E}(c)$, $L=j_0\nr_0^3{\\cal L}(c)$, and $R_h=r_0{\\cal R}(c)$ together give $E_b\\propto ({\\cal E}\n{\\cal R}/{\\cal L}^2)\\,L^2/R_h$. But it happens that the non-homology factor\n$({\\cal E} {\\cal R}/{\\cal L}^2)$ varies very little over the range of\nconcentrations $0.5\\le c\\le 2.5$ appropriate for regular Galactic\nglobulars (see Figs.~\\ref{fig1} and \\ref{fig2} above, or Fig.~\\ref{fig14}\nbelow). The simple scaling $E_b\\propto L^2/R_h$, which is self-evident if the\nquestion of non-homology is ignored altogether, is then quite\naccurate; and the weak dependence of $R_h$ on $L$---even if the influence of\nGalactocentric radius is also ignored---leads inevitably to the rough\nexpectation, $E_b\\propto L^2$. That is, Figs.~\\ref{fig8} and \\ref{fig6} are\nequivalent characterizations of the Milky Way globular clusters; $E_b\\sim\nL^2$ if and only if $R_h\\sim constant$ for King-model clusters, and\nconceptually one constraint is no more correct or fundamental\nthan the other. As a practical matter, however, note that the r.m.s.~scatter\nabout the mean $\\log\\,R_h^*$ in Fig.~\\ref{fig8} is about twice the\nmeasurement uncertainty of $\\pm0.1$ dex, whereas the scatter about the\nline $E_b\\propto L^{2.05}$ in Fig.~\\ref{fig6} is basically comparable to the\nobservational errorbar. The source of the scatter in Fig.~\\ref{fig8} is\ndiscussed in \\S5 (Fig.~\\ref{fig17}), which also considers another known\ncorrelation ($\\sigma_0\\propto L^{0.52}$; see Fig.~\\ref{fig18} and\n\\markcite{djo94}Djorgovski \\& Meylan 1994) that is equivalent to the binding\nenergy--luminosity scaling found here.\n\nThe rest of this paper keeps its focus on binding energy, rather than\nhalf-light radius or velocity dispersion explicitly, as one of the four\ndefining parameters of globular clusters; and the $E_b(L)$ relation, rather\nthan the constancy of $R_h$, will be used (along with the constancy of\n$\\Upsilon_{V,0}$) to define the fundamental plane. Figure \\ref{fig8} makes it\nclear that this course is not strictly necessary, but it has been adopted for\nthe convenience and insight it offers (as has already been suggested, a\ndiscussion in terms of $E_b$ can greatly facilitate theoretical studies of\ncluster formation and evolution).\n\nBefore the globular cluster fundamental plane can be constructed explicitly,\nhowever, Fig.~\\ref{fig8} raises another issue to be addressed: Given that\n$E_b\\propto L^2/R_h$ and $R_h\\propto r_{\\rm gc}^{0.4}$, it is clear that \n``secondary'' quantities such as Galactocentric position or cluster\nmetallicity---which are extraneous to the formal King-model fitting\nprocess---are not completely disconnected from the basic cluster attributes\n$\\Upsilon_{V,0}$, $c$, $L$, and $E_b$. What, then, is the total effect\nof such environmental factors on these fundamental parameters and the\nrelationships between them?\n\n\\subsection{The Influences of Galactocentric Position and Metallicity}\n\nFigure \\ref{fig9} shows the relative insensitivity of $\\Upsilon_{V,0}$,\n$L$, and $c$ to $r_{\\rm gc}$ and [Fe/H] for globular clusters in the Milky Way.\nThe top row incorporates only the sample of \\markcite{pry93}Pryor \\& Meylan\n(1993), with $\\Upsilon_{V,0}\\equiv 9\\,\\sigma_0^2/(4\\pi G j_0r_0^2)$ as in\n\\S3.1. Clearly, a cluster's core mass-to-light ratio is quite detached from\nits metallicity. There is perhaps a hint of a slight decrease in\n$\\Upsilon_{V,0}$ towards larger Galactocentric radii, but this is not\nstatistically significant. Thus, although it would be interesting to examine\nthe question more closely by obtaining velocity data for the remaining\ntwo-thirds of the Galactic globulars, it will be assumed here that\n$\\Upsilon_{V,0}$ is completely independent of $r_{\\rm gc}$. (Note that the\nvalues for the PCC clusters [open squares] are overestimates, due to the\nunderestimation of their central densities $j_0$ [cf.~Fig.~\\ref{fig3}]. Also,\nthe point at $r_{\\rm gc}\\simeq90$ kpc corresponds to NGC 2419, which appears\nas an outlier in a plot of $\\sigma_0$ against $L$ [see Fig.~\\ref{fig18} below],\nand for which $\\Upsilon_{V,0}$ may have been underestimated as a result.)\n\n\\placefigure{fig9}\n\nThe middle panels of Fig.~\\ref{fig9} illustrate the well known facts\n(e.g., \\markcite{djo94}Djorgovski \\& Meylan 1994) that globular cluster\nluminosities are completely uncorrelated with [Fe/H]---there is no\nmass-metallicity relation---and very weakly anticorrelated with Galactocentric\nposition. However, it can be seen that the latter result does not reflect any\nclear, systematic dependence of $L$ on $r_{\\rm gc}$, but appears instead to be\ndriven by a handful of ``excess'' faint objects at large radii ($r_{\\rm gc}\\ga\n10$ kpc) which are not equally represented in the inner parts of the Galaxy.\nThis slight imbalance may be due to dynamical evolution from an initial\ndistribution of cluster luminosities which was much more insensitive to\n$r_{\\rm gc}$ (see, e.g., \\markcite{mcl96}McLaughlin \\& Pudritz 1996), with a\nlarger fraction of the low-mass clusters inside the Solar circle having been\ndisrupted by disk shocking and evaporation over a Hubble time. Or,\nalternatively, since some of the outer-halo globulars are somewhat younger\nthan average, it could be that clusters formed with lower average masses at\nlower redshifts (S.~van den Bergh, private communication). But whatever its\ncause, this effect does {\\it not} change the basic scalings inferred in\nFig.~\\ref{fig6} for concentration and binding energy as functions of\nluminosity.\n\nAlthough a plot of $c$ alone against $r_{\\rm gc}$ shows a rough\nanticorrelation (\\markcite{djo94}Djorgovski \\& Meylan 1994), this is simply\na result of the tendencies for $c$ to decrease towards lower $L$ ($c\\approx\nconst.+0.4\\,\\log\\,L$, from Figs.~\\ref{fig4} and \\ref{fig6}) and for the\nlowest-luminosity clusters to lie preferentially at large Galactocentric\nradii. The bottom panels of Fig.~\\ref{fig9} correct for this, showing that\n{\\it at a given cluster luminosity}, $c$ is essentially independent of\n$r_{\\rm gc}$. Equivalently, the mean relation between concentration and\nluminosity does not change with Galactocentric position (see also\nFigs.~\\ref{fig12} and \\ref{fig13} below). It is obvious, too, that $c$\nis---like $\\Upsilon_{V,0}$ and $L$---impervious to [Fe/H].\n\nFigure \\ref{fig10} shows that similar remarks apply to the {\\it scaling},\nthough not to the normalization, of the $E_b(L)$ relation. The top plot does\nshow a tendency for the lowest-energy King-model clusters to be found at the\nlargest radii; but this is due in part to the preponderance of faint clusters\nin the outer parts of the Galaxy. If the overall dependence $E_b\\propto\nL^{2.05}$ is removed, the influence of Galactocentric position alone can\nbe isolated: the straight line in the bottom of Fig.~\\ref{fig10} has the\nequation $\\log\\,(E_b/{\\rm erg})-2.05\\,\\log(L/L_\\odot)=40.22-0.4\\,\n\\log(r_{\\rm gc}/{\\rm kpc})$. The slope of this line is uncertain by perhaps\n$\\pm0.1$; it is, of course, just that expected from the proportionality\n$E_b\\propto L^2/R_h$ and the systematic increase of cluster radii with\n$r_{\\rm gc}$ (Fig.~\\ref{fig8}). Put another way---and as can be confirmed\neither by plotting $E_b\\,r_{\\rm gc}^{0.4}$ against $L$ or by fitting\n$E_b$ vs.~$L$ directly in a series of narrow radial bins---the {\\it slope} of\nthe $E_b(L)$ relation in the Milky Way does not vary with Galactocentric\nposition, but the normalization decreases systematically towards larger\n$r_{\\rm gc}$ (see also Fig.~\\ref{fig12}). All the data are described\ncompletely by\n\\begin{equation}\n\\log\\,\\left(E_b/{\\rm erg}\\right) =\n\\left[(39.86\\pm0.40) - 0.4\\,\\log\\,\\left(r_{\\rm gc}/8\\,{\\rm kpc}\\right)\\right]\n+ (2.05\\pm0.08)\\,\\log\\,\\left(L/L_\\odot\\right)\\ ,\n\\label{eq:34}\n\\end{equation}\nin which the errobars are $\\pm1\\sigma$ and all clusters are normalized to a\ncommon $r_{\\rm gc}=8$ kpc for convenience. Note that the r.m.s.~scatter\nabout this relation, $\\Delta=0.49$ dex, is $\\sim$10\\% lower than that in\nequation (\\ref{eq:33}) and Fig.~\\ref{fig6}, which ignored the $r_{\\rm gc}$\ndependence. It can be attributed entirely to the effects of random measurement\nerrors in $r_0$, $j_0$, and $c$, even under the most conservative assumption\nthat these uncertainties are uncorrelated. Also, the intercepts in equations\n(\\ref{eq:32}) and (\\ref{eq:33}) are consistent with equation (\\ref{eq:34})\ngiven the median Galactocentric radii of the \\markcite{pry93}Pryor \\& Meylan\n(1993) sample of regular clusters ($\\overline{r_{\\rm gc}}=8.7$ kpc) and\nthe full \\markcite{har96}Harris (1996) dataset\n($\\overline{r_{\\rm gc}}=7.0$ kpc).\n\n\\placefigure{fig10}\n\nFinally, Fig.~\\ref{fig11} shows that metallicity plays no role in setting a\ncluster's total energy, a result which is completely in keeping with the\nirrelevance of [Fe/H] to any other aspect of the internal structure and\ndynamics of globular clusters (see \\markcite{djo94}Djorgovski \\& Meylan 1994\nfor further examples).\n\n\\placefigure{fig11}\n\n\\subsection{Summary}\n\nTo a very good first approximation, Galactic globular clusters can be treated\nas realizations of single-mass, isotropic \\markcite{kin66}King (1966) models.\nA complete basis for the physical description of the ensemble is therefore\nprovided by the four quantities $\\log\\,\\Upsilon_{V,0}$, $c$, $\\log\\,L$, and\n$\\log\\,E_b$. While this particular choice of variables is not necessary---any\nset of four linearly independent King-model parameters is permissible, in\nprinciple---it is certainly sufficient. Moreover, it has the advantage of\nimmediately revealing two strong empirical constraints on the properties of\nGalactic globulars (each of which will, of course, be recovered in any\nalternative parametrization of King-model space): (1) the core mass-to-light\nratio is a constant, $\\log\\,(\\Upsilon_{V,0}/M_\\odot\\,L_\\odot^{-1})=0.16\\pm\n0.03$, and (2) clusters' binding energies are set by their total luminosities\nand Galactocentric positions, through $\\log\\,E_b=39.86-0.4\\,(\\log\\,r_{\\rm gc}/\n8\\,{\\rm kpc})+2.05\\,\\log\\,L$. As far as the current data can discriminate, the\nMilky Way cluster system appears almost {\\it perfectly} to obey these two\nrelations---deviations from them can be attributed entirely to random\nmeasurement errors---and it therefore populates a two-dimensional subspace in\nthe four-dimensional volume of King models. The effects of metallicity and\nenvironment on individual cluster properties are summarized\n{\\it completely} (again, within the limits of current data) by the\n$r_{\\rm gc}$-dependence in the normalization of the $E_b(L)$ relation. \n\nEquations (\\ref{eq:24}) and (\\ref{eq:34}) thus {\\it define} a fundamental\nplane for Galactic globulars. Various representations of this are developed in\nthe next Section. Essentially, central concentration and total luminosity or\nmass are then left to determine the distribution of clusters {\\it on} the\nplane; but even this is not random, as there also exists a rough correlation\nbetween $c$ and $\\log\\,L$ (Fig.~\\ref{fig6}). This dependence is rather weak\nby comparison with the constraints on $\\log\\,\\Upsilon_{V,0}$ and $\\log\\,E_b$,\nand a one-to-one $c(\\log\\,L)$ relation has {\\it not} yet been found in the\ndata; but, as will also be discussed in \\S4, the situation does suggest the\nintriguing possibility that Galactic globulars may actually fall along, or\nat least have evolved from, something closer to a ``fundamental straight line''\n(cf.~\\markcite{bel98}Bellazzini 1998, who suggested something similar but\nwith a much different physical interpretation).\n\n\\section{The Fundamental Plane}\n\nFor much of this Section, it will be taken as given that $\\Upsilon_{V,0}$\nis a constant for Galactic globulars, as in equation (\\ref{eq:24}). This\nimmediately removes the core mass-to-light ratio as a physical variable, and \nthe parameter space remaining available to the clusters is only\nthree-dimensional.\n\nThe preceding discussion and Fig.~\\ref{fig6} suggest a physically\ntransparent view of the globular cluster fundamental plane (FP) as a\nthin, tilted slice of $(\\log\\,L,\\log\\,E_b,c)$ space---the volume left by the\nconstraint $\\log\\,\\Upsilon_{V,0}=constant$---which is seen edge-on along the\n$c$-axis (in the $\\log\\,L$--$\\log\\,E_b$ plane) and closer to face-on along the\n$E_b$ axis (in the $c$--$\\log\\,L$ plane). As was discussed in \\S3.3, however,\nthe normalization of the $E_b(L)$ relation decreases systematically with\nincreasing Galactocentric radius. Thus, a plot of $\\log\\,E_b$ vs.~$\\log\\,L$\nfor the entire Milky Way cluster system, with its wide range of $r_{\\rm gc}$,\nactually provides an edge-on view of a {\\it collection} of separate and\ndistinct FPs which intersect the $\\log\\,E_b$ axis at different points. Figure\n\\ref{fig6} can therefore be improved by introducing the normalized quantity\n(cf.~eq.~[\\ref{eq:34}])\n\\begin{equation}\n\\log\\,E_b^* \\equiv \\log\\,E_b + 0.4\\,\\log\\left(r_{\\rm gc}/8\\,{\\rm kpc}\\right)\\ ,\n\\label{eq:40}\n\\end{equation}\nwhich simply removes all environmental influences on the FP.\n\nFigure \\ref{fig12} plots $c$ and $\\log\\,E_b^*$ against $\\log\\,L$ for the 109\nregular and 30 PCC clusters catalogued by \\markcite{har96}Harris (1996),\ndivided according to whether they lie within the Solar circle ($R_0=8$ kpc)\nor outside it. Two points are apparent from this. First, it is confirmed that\nthe $r_{\\rm gc}$ dependence in $E_b$ is adequately described by a scaling\nclose to $E_b\\propto r_{\\rm gc}^{-0.4}$, and that the mean increase of $c$\nwith $L$ is, although rough, essentially independent of Galactocentric position\n(cf.~\\S3.3). The solid straight lines in both bottom panels follow the\nrelation given by equation (\\ref{eq:34}) above; the dashed lines show the\n$3\\sigma$ limits on the fitted slope and intercept. Clearly, clusters at\n$r_{\\rm gc}<8$ kpc and $r_{\\rm gc}>8$ kpc obey this equation equally well.\nSimilarly, the dashed lines in the top right panel of Fig.~\\ref{fig12} are\nlinear least-squares fits of $c$ against $\\log\\,L$ (shallower slope) and of\n$\\log\\,L$ against $c$ (steeper slope) for the regular clusters at $r_{\\rm gc}>\n8$ kpc (excluding Palomar 1, the most obvious outlier). These same lines are\nthen re-drawn in the top left panel of the Figure, where they are seen to be\nequally acceptable as crude descriptions of $c$ vs.~$\\log\\,L$ for the\nKing-model clusters with $r_{\\rm gc}<8$ kpc.\n\n\\placefigure{fig12}\n\nSecond, it can be seen from Fig.~\\ref{fig12} that {\\it both $c$ and $\\log\\,\nE_b^*$ are more strongly correlated with $\\log\\,L$ for clusters beyond the\nSolar circle} than for those within it: the Spearman rank correlation\ncoefficients are higher, and in the case of $c$ vs.~$\\log\\,L$, the\nr.m.s.~scatter about the linear fits is smaller. This point has already been\ndiscussed in relation to the central concentrations\nby \\markcite{bel96}Bellazzini et al.~(1996) and \\markcite{ves97}Vesperini\n(1997), who note that globulars at $r_{\\rm gc}<8$ kpc have been subjected\nto much stronger dynamical evolution than have those at larger radii\n(evaporation is faster and disk shocks are more severe in denser regions of\nthe Galaxy). Thus, the very existence of a $c$--$\\log\\,L$ correlation among\nthe more distant clusters suggests that it has a largely primordial origin.\nThese authors' quantitative numerical simulations confirm in more detail that\n``evolutionary processes are unlikely to play a dominant role in establishing\nthe $c$--$\\log\\,M$ correlation'' (\\markcite{ves97}Vesperini 1997). The same\ncalculations show explicitly that the main effect of the evolution within\n$r_{\\rm gc}=8$ kpc is to increase the {\\it scatter} in the final version of\nan initial $c(\\log\\,L)$ dependence. This is consistent with the appearance of\nthe data in the top half of Fig.~\\ref{fig12}. (It must be noted again, however,\nthat the r.m.s.~scatter of measured $c$ values about the linear regressions at\n$r_{\\rm gc}>8$ kpc is still substantially larger than the typical errorbar of\n$\\pm0.2$ dex. It remains unclear whether there might exist a {\\it nonlinear}\n$c$--$\\log\\,L$ correlation that is significantly tighter, or whether there is\nsimply a real scatter in cluster concentrations at any given luminosity.)\n\nSimilarly, the very strong correlation of $\\log\\,E_b^*$ with $\\log\\,L$ for the\nglobulars at $r_{\\rm gc}>8$ kpc implies that this dependence, too, may have\nbeen set largely at the time of cluster formation. If this is correct, then it\nseems that the main effect of the stronger evolution within the Solar circle\nmay have been a greater fractional depopulation of the low-mass tail of the\ncluster distribution, rather than any significant change in a power-law\nscaling between $E_b$ and $L$. (It is emphasized again that the r.m.s.~scatter\nin the data of both lower panels of Fig.~\\ref{fig12}\nis essentially the same as, or even smaller than, the typical observational\nerrorbar on $\\log\\,E_b$.) Indeed, an initial scaling close to $E_b\\propto\nL^2$ {\\it can} be expected to be roughly preserved during the course of\ndynamical evolution of an entire cluster system. Direct calculations (see the\ndiscussion and references in \\markcite{mur92}Murray \\& Lin 1992;\n\\markcite{har94}Harris \\& Pudritz 1994) show that the half-mass radii of\nindividual clusters are fairly well preserved during dynamical evolution,\neven over the course of a Hubble time, i.e., $dR_h/dt\\approx0$; but this and\n$E_b\\propto L^2/R_h$ together imply $d\\,\\log\\,E_b/dt\\approx2\\,d\\,\\log\\,L/dt$.\nThus, as a cluster loses mass to evaporation and tidal shocking it should move\ndown and to the left in the $(\\log\\,L,\\log\\,E_b^*)$ plane, along a line roughly\nparallel to the initial correlation (if this was indeed roughly $\\sim L^2$,\nand assuming that any changes in $0.4\\,\\log\\,r_{\\rm gc}$ can be neglected).\n\nTo put this another way, it is plausible that {\\it clusters remain more or\nless in the fundamental plane as they evolve} and, thus, that globular\nclusters may have appeared on the FP as a result of the formation process.\nIn addition, the relation between $c$ and $\\log\\,L$ implies that the\ndistribution of globulars over the FP is non-random and also reflects something\nof initial conditions. To see this properly, however, requires a further\nmanipulation of the basic cluster variables.\n\n\\subsection{$\\mathbf{\\epsilon}$-Space}\n\nBy construction, the $\\log\\,L$, $\\log\\,E_b^*$, and $c$ axes are mutually\northogonal in the three-dimensional cluster parameter space selected by\n$\\log\\,\\Upsilon_{V,0}=constant$. And in the Milky Way, the view of the FP in\na plot of $\\log\\,E_b^*$ vs.~$\\log\\,L$ is nearly perfectly edge-on (again, this\nfollows from the fact that random measurement errors can account fully for the\nscatter of observed clusters about the relation $\\log\\,E_b^*=39.86+2.05\n\\log\\,L$). The FP is therefore canted at quite a steep angle [$\\arctan\\,\n(2.05)=64^\\circ$] to the $(\\log\\,L, c)$ plane, and the top panels of\nFigs.~\\ref{fig7} and \\ref{fig12} do {\\it not} offer a truly face-on view of\nit; plots of $c$ against $\\log\\,L$ suffer from strong projection\neffects and may not, in general, accurately reflect the true dispersion of\nglobulars over the actual surface of the FP. (Plots of $c$ vs.~$\\log\\,E_b^*$\nwould be better, but that plane still makes an angle of $26^\\circ$ with the FP\nand projection effects would still be present.)\nIn order to be as rigorous as possible---and hopefully to allow eventually for\nsome connection with the fundamental plane(s) of other stellar\nsystems---it desirable to correct for this. This is easily done in a\nprocedure analogous to that used by \\markcite{ben92}Bender et al.~(1992; see\nalso \\markcite{bur97}Burstein et al.~1997) to define a three-dimensional\n``$\\kappa$-space'' for elliptical galaxies. The present construct for\nglobulars is based specifically on cluster binding energies and will therefore\nbe referred to as $\\epsilon$-space.\n\nThe easiest way to a face-on view of the FP is to define a new coordinate\nsystem by rotating the $\\log\\,L$--$\\log\\,E_b^*$ plane through $64^\\circ$\n(counterclockwise) about the $c$ axis. The new (and still mutually\northogonal) axes thus obtained are proportional to\n\\begin{eqnarray}\n\\epsilon_1 & \\equiv & \\log\\,E_b^* - 2.05\\,\\log\\,L \\nonumber \\\\\n\\epsilon_2 & \\equiv & 2.05\\,\\log\\,E_b^* + \\log\\,L \\\\\n\\epsilon_3 & \\equiv & c \\nonumber\n\\label{eq:eps}\n\\end{eqnarray}\nAlternatively, of course, Galactic globulars are expected, on the basis of\nequation (\\ref{eq:34}), to lie on a line $\\epsilon_1=const.$; and the line\n$\\epsilon_2=const.$ is perpendicular to this in the original\n$\\log\\,L$--$\\log\\,E_b^*$ plane. In this $\\epsilon$-space, then, edge-on views\nof the globular cluster fundamental plane are obtained by plotting\n$\\epsilon_1$ against either $\\epsilon_2$ or $\\epsilon_3$, while the\n$(\\epsilon_2,\\epsilon_3)$ plane provides the face-on view.\n\nThis is shown in Fig.~\\ref{fig13} for the full sample of 139 globular clusters\nfrom \\markcite{har96}Harris (1996). The two edge-on views of the fundamental\nplane are drawn as the bold line $\\epsilon_1=39.86$. The scatter of the\nKing-model clusters about this line in both the $(\\epsilon_1, \\epsilon_2)$ and\nthe $(\\epsilon_1,\\epsilon_3)$ planes are just the residuals due to measurement\nerrors. The apparent tendency for the 30 PCC clusters to fall below the FP is,\nagain, probably spurious: the underestimation of $j_0$ leads to low values of\n$E_b^*$ and $L$, and thus of $\\epsilon_1$, for these objects; and\n$\\epsilon_3=c$ has been {\\it arbitrarily} set to 2.5 for many of them.\n\n\\placefigure{fig13}\n\nThe plot of $\\epsilon_3$ against $\\epsilon_2$ confirms that Galactic globulars\nare not distributed uniformly throughout their fundamental plane. The\ncorrelation of $c$ with $\\log\\,L$ clearly carries over into one between\n$\\epsilon_3$ and $\\epsilon_2$. Moreover, because the clusters do occupy a\nfairly narrow swath on the FP, the potential problems with projection in\nthe $c$--$\\log\\,L$ correlation are actually not too severe: the dashed line\ndrawn in Fig.~\\ref{fig13} has the equation $\\epsilon_3=-(12.5\\pm3.2)+(0.13\n\\pm0.03)\\,\\epsilon_2$, which corresponds (given the definition of $\\epsilon_2$\nand the scaling $E_b^*\\propto L^{2.05}$) to $c\\simeq0.68\\,\\log\\,L+const.$\n(cf.~Fig.~\\ref{fig12}). This particular relation follows from fitting only\nthe regular, King-model clusters at $r_{\\rm gc}>8$ kpc, where, again similar\nto the case for $c$ vs.~$\\log\\,L$, the correlation between $\\epsilon_3$ and\n$\\epsilon_2$ is strongest: The Spearman statistic is $s=0.8$ for the globulars\noutside the Solar circle, and the r.m.s.~scatter about the best linear fit\nis $\\Delta\\approx0.3$ dex; but $s=0.4$ and $\\Delta\\simeq0.4$ dex inside 8 kpc.\n\nAgain taking the view that cluster properties in the outer halo better\nreflect initial conditions, it seems quite clear that Galactic globulars\nformed in something more like a ``fundamental band'' than a plane per se.\nMoreover, it is\neven plausible (but not proven) that they might have been born along a {\\it\nfundamental straight line}, a one-dimensional locus in $\\epsilon$-space.\n(This is a term coined by \\markcite{bel98}Bellazzini 1998, who arrived at a\nsimilar conclusion from a very different argument. See Figs.~\\ref{fig16} and\n\\ref{fig19} below for further discussion of \\markcite{bel98}Bellazzini's\ninterpretation of the globular cluster FP.) That is, it is conceivable that\nglobular clusters formed through a simple process, governed almost completely\nby the mass and Galactocentric position of a gaseous protocluster, which\nnaturally resulted not only in $\\Upsilon_{V,0}=const.$ and $E_b^*\\propto\nL^{2.05}$, but also in some (unknown) one-to-one relation between\ncentral concentration and luminosity.\n\nThe viability of this interpretation depends to some extent---similar to what\nwas concluded above---on the possibility that there may be some nontrivial\nfunction of $\\epsilon_3=c$ which correlates very tightly with $\\epsilon_2$,\ni.e., which shows scatter within the observational uncertainties (at least for\nthe outer-halo clusters) and which would therefore serve better as the third\naxis in $\\epsilon$-space. On the other hand, while globulars at $r_{\\rm gc}>8$\nkpc should have been less influenced by dynamical evolution, it is unrealistic\nto expect that they could have been completely untouched by it. Thus, another\npossibility is that some or all of the ``excess'' scatter of\nclusters in the fundamental $(\\epsilon_2, \\epsilon_3)$ plane is indeed\nirreducible, but that it arose during evolution from an initial cluster\ndistribution that showed no intrinsic scatter. Theoretical studies of cluster\nevolution will be key in deciding this issue and will be of considerable\nimportance, whatever the outcome, for theories of cluster formation.\n\nIt is obviously also of interest to understand the relation between the\npresent $\\epsilon$-space and the corresponding $\\kappa$-space defined for\nelliptical galaxies (\\markcite{ben92}Bender et al.~1992) and studied for\nother hot stellar systems (\\markcite{bur97}Burstein et al.~1997)---or,\nequivalently, to explain the connection between the bivariate correlations\nfor globular clusters (\\markcite{djo95}Djorgovski 1995, and \\S4.2 just below)\nand the analogous relations for ellipticals (\\markcite{djo87}Djorgovski \\&\nDavis 1987; \\markcite{dre87}Dressler et al.~1987; see \\markcite{pah98}Pahre,\nde Carvalho, \\& Djorgovski 1998 for a comprehensive recent discussion). A\npotentially important difference is that one full dimension---the $\\epsilon_3\n\\equiv c$ axis---of the observational space employed here is given over to a\nparameter describing the broken homology of globulars, whereas the\ncorresponding structural factor is incorporated into all three axes of the\nspace used for ellipticals (see \\markcite{ben92}Bender et al.~1992). While\nexplicit corrections can certainly be made for the effects of non-homology in\ngalaxies (\\markcite{gra97}Graham \\& Colless 1997; \\markcite{bus97}Busarello et\nal.~1997), these are perhaps less easily pictured in $\\kappa$-space than in\n$\\epsilon$-space. The construction of an $\\epsilon$-space for galaxies would\nrequire the use of a single family of structural and dynamical models that is\nhighly accurate in its description of any individual system (in order to\nestimate total luminosities/masses and global binding energies by\nextrapolation from direct observations of the galaxy cores).\n\nThat real differences exist between the fundamental planes of globular clusters\nand elliptical galaxies is clear from contrasts in certain of their monovariate\ncorrelations, or projections of their FPs (e.g., \\markcite{kor85}Kormendy\n1985; \\markcite{djb93}Djorgovski 1993b). What remains to be seen is the extent\nto which these disparities might result from fundamentally different $E_b(L)$\nrelations, as opposed to any number of other physical distinctions (examples\nbeing a varying core mass-to-light ratio in ellipticals [\\markcite{vdm91}van\nder Marel 1991]; the presence of dark matter in the galaxies [see\n\\markcite{kri97}Kritsuk 1997]; and possibly different systematics in the\nstructural non-homology). It may be significant, in this regard, that\n\\markcite{bus97}Busarello et al.~1997 find evidence that the {\\it kinetic}\nenergy per unit mass measured within an effective radius in ellipticals scales\nas $\\left(E_k/M\\right)\\propto\\sigma_0^{1.6}$ or so, whereas the total\n$\\left(E_k/M\\right)$ in globular clusters can be roughly---although not\nperfectly---estimated as $\\left(E_b/L\\right)\\propto L^{1.05}\\sim \\sigma_0^2$\n(see Fig.~\\ref{fig18} below for the relation between $\\sigma_0$ and $L$).\n\n\\subsection{Bivariate Correlations}\n\n\\markcite{djo95}Djorgovski (1995) used a statistical, principal-components\nanalysis to infer the existence of two strong, bivariate correlations\ninvolving core and half-light properties of Galactic globular clusters\nwith measured central velocity dispersions (i.e., those in the catalogue of\n\\markcite{pry93}Pryor \\& Meylan 1993):\n\\begin{equation}\n\\log\\,\\sigma_{p,0}-0.45\\,\\log\\,r_0=-(0.20\\pm0.01)\\,\\mu_{V,0}+(4.17\\pm0.2)\n\\label{eq:djo}\n\\eqnum{\\ref{eq:djo}a}\n\\end{equation}\nand\n\\begin{equation}\n\\log\\,\\sigma_{p,0}-0.7\\,\\log\\,R_h=-(0.24\\pm0.02)\\,\\langle\\mu_V\\rangle_h+\n(4.83\\pm0.26)\\ ,\n\\eqnum{\\ref{eq:djo}b}\n\\addtocounter{equation}{+1}\n\\end{equation}\nwhere $\\langle\\mu_V\\rangle_h\\equiv26.362-2.5\\,\\log\\,\\left(L/2\\pi R_h^2\\right)$\nis the average surface brightness within a projected half-light radius;\n$\\sigma_{p,0}$ is in units of km s$^{-1}$; and $r_0$, $R_h$ are measured in pc.\nIt was the existence of these correlations that originally led\n\\markcite{djo95}Djorgovski to conclude that the Galactic globulars are\nconfined to a fundamental plane. But the statistical analysis does not,\nby itself, offer any physical insight into the FP. (\\markcite{djo95}Djorgovski\nsuggested, as did \\markcite{bel98}Bellazzini [1998] after him, that\neq.~[\\ref{eq:djo}a] is a reflection of the ``pure virial theorem'' applied to\ncluster {\\it cores}. However, as will be discussed further below, this is not\na fully satisfactory interpretation.) Indeed, note that equations\n(\\ref{eq:djo}) appear superficially to constitute two constraints on five\ndifferent observables, and thus it is not clear a priori that they need define\na plane of any kind. Now, however, with a specific physical basis\n($\\log\\,\\Upsilon_{V,0}$, $c$, $\\log\\,E_b$, and $\\log\\,L$) having been chosen\nto describe globular clusters in a King-model framework, it is possible to\nreduce the number of distinct variables in these equations to just four,\nand to show explicitly---by comparing with the bivariate $(\\sigma_0, r_0,\n\\mu_{V,0})$ and $(\\sigma_0, R_h, \\langle\\mu_V\\rangle_h)$ correlations\n{\\it expected} to arise from each of the two empirical relations defining the\nfundamental plane---that equation (\\ref{eq:djo}a) derives from equation\n(\\ref{eq:24}) above while (\\ref{eq:djo}b) is a reflection of equation\n(\\ref{eq:32}). Thus, \\markcite{djo95}Djorgovski's (1995) correlations {\\it\ntogether} identify the same globular cluster FP that has been developed here.\n\nThe basic definition of the King radius (eq.~[\\ref{eq:23}]), together with\na constant $\\log\\,\\Upsilon_{V,0}=0.16$ and the definition of surface\nbrightness, yields a relation between $\\sigma_0$ ({\\it not} exactly the\n$\\sigma_{p,0}$ used by \\markcite{djo95}Djorgovski in establishing his\ncorrelations), $r_0$, and $\\mu_{V,0}$. The details of this derivation are\ngiven in Appendix A; from equation (\\ref{eq:a9a}),\n\\begin{equation}\n\\log\\,\\sigma_0 - 0.5\\,\\log\\,r_0=-0.2\\,\\mu_{V,0}-0.5\\,\\log\\,{\\cal I}_0(c)\n+4.241\\ .\n\\label{eq:41}\n\\eqnum{\\ref{eq:41}a}\n\\end{equation}\nHere and throughout, $\\sigma_0$ is in units of km s$^{-1}$, $r_0$ is in pc,\nand $\\mu_{V,0}$ is in mag arcsec$^{-2}$. The function ${\\cal I}_0$ is the\ndimensionless central surface density for a King model of concentration $c$;\nit is given in Fig.~\\ref{fig1} above and in equation (\\ref{eq:b3}) below.\nAn equivalent expression, in terms of cluster half-light radii and surface\nbrightnesses, follows from defining $\\langle\\mu_V\\rangle_h$ and from accounting\nfor non-homology in the ratio ${\\cal R}(c)\\equiv R_h/r_0$ (see Fig.~\\ref{fig1}\nand eq.~[\\ref{eq:b4}]); according to equation (\\ref{eq:a9b}),\n\\begin{equation}\n\\log\\,\\sigma_0 - 0.5\\,\\log\\,R_h=-0.2\\,\\langle\\mu_V\\rangle_h\n-0.5\\,\\log\\,\\left[{\\cal L}(c)/{\\cal R}(c)\\right]+4.640\\ ,\n\\eqnum{\\ref{eq:41}b}\n\\addtocounter{equation}{+1}\n\\end{equation}\nwhere ${\\cal L}$ is the dimensionless luminosity given in Fig.~\\ref{fig2} and\nequation (\\ref{eq:b5}).\n\nSimilarly, the analysis in Appendix A (see eqs.~[\\ref{eq:a10a}] and\n[\\ref{eq:a10b}]) shows that the finding $\\log\\,(E_b/{\\rm erg})=39.82+2.05\\,\n\\log\\,(L/L_\\odot)$ (eq.~[\\ref{eq:32}]; for clusters in the catalogue of\n\\markcite{pry93}Pryor \\& Meylan 1993 specifically) is equivalent to\n\\begin{equation}\n\\log\\,\\sigma_0-0.775\\,\\log\\,r_0=-0.205\\,\\mu_{V,0}\n+0.25\\,\\log\\,\\left[{\\cal L}(c)^{2.05}/{\\cal E}(c)\\,{\\cal I}_0(c)^{2.05}\\right]\n+3.943\n\\label{eq:42}\n\\eqnum{\\ref{eq:42}a}\n\\end{equation}\n(with the dimensionless energy ${\\cal E}$ again discussed in \\S2 and Appendix\nB), and to\n\\begin{equation}\n\\log\\,\\sigma_0-0.775\\,\\log\\,R_h=-0.205\\,\\langle\\mu_V\\rangle_h \n- 0.25\\,\\log\\,\\left[{\\cal E}(c)/{\\cal R}(c)\\right]\n+4.352\\ .\n\\eqnum{\\ref{eq:42}b}\n\\addtocounter{equation}{+1}\n\\end{equation}\nNote that, in general, the $r_{\\rm gc}$ dependence in the normalization of\nthe $E_b(L)$ relation (eq.~[\\ref{eq:34}]) should appear as an additional\nterm ($-0.1\\,\\log\\,r_{\\rm gc}+constant$) on the right-hand side of equations\n(\\ref{eq:42}). In order to make a more direct comparison with the analysis of\n\\markcite{djo95}Djorgovski (1995), however, the effect (which is evidently\nquite small anyway) has been acknowledged only implicitly here, by using a\nnormalization of the $E_b$--$L$ scaling that is appropriate for the median\nGalactocentric position of the globulars in the \\markcite{pry93}Pryor \\&\nMeylan database.\n\nFigure \\ref{fig14} confirms the validity of equations (\\ref{eq:41}b) and\n(\\ref{eq:42}b) as a representation of the globular cluster FP in terms\nof half-light quantities. The left panels here show the non-homology\nfunctions $0.5\\,\\log\\,\\left({\\cal L}/{\\cal R}\\right)$ and $0.25\\,\\log\\,\n\\left({\\cal E}/{\\cal R}\\right)$, as obtained in general from numerical\nintegrations of King models (curves) and evaluated specifically for the\ncentral concentrations of the 39 regular clusters (points) in the sample of\n\\markcite{pry93}Pryor \\& Meylan (1993). The functions vary only slightly\namong these clusters, and the effects of non-homology happen to be effectively\nsuppressed in this projection of the FP. The mean values indicated for each\nfunction may therefore be applied to derive nearly constant intercepts in\nequation (\\ref{eq:41}b) for $\\Upsilon_{V,0}=const.$ and equation\n(\\ref{eq:42}b) for $E_b\\propto L^{2.05}$. The right panels of Fig.~\\ref{fig14}\nthen make a direct comparison between the resulting FP ``predictions''\n(solid lines) and the \\markcite{pry}Pryor \\& Meylan data. The agreement is\nclearly quite good and, as expected, the r.m.s.~scatter of the data about the\nexpected correlations is within the range of observational uncertainty.\n\n\\placefigure{fig14}\n\nThe top panels of Fig.~\\ref{fig14}, and equation (\\ref{eq:41}b), also represent\nthe basic scaling $L\\propto (\\sigma_0^2R_h)({\\cal L}/{\\cal R})$, which\nultimately---given that $\\Upsilon_{V,0}$ is a constant independent of $L$---is\njust an expression for the total {\\it mass} of a King model. Since the ratio\n${\\cal L}/{\\cal R}$ does not vary particularly strongly or systematically\nwith $c$ (or, therefore, with $L$), this result appears to differ significantly\nfrom the $L\\propto\\left(\\sigma_0^2R_h\\right)^{0.7-0.8}$ that\n\\markcite{sch93}Schaeffer et al.~(1993) find for elliptical galaxies and Abell\nclusters (although note that these authors claim that their scaling holds for\nGalactic globulars as well). This is another indication that the globular\ncluster fundamental plane may indeed differ from those of these other\nsystems. Whether this particular contrast is due to fundamentally\ndifferent trends of $\\Upsilon_{V,0}$ with $L$, or to different structural\nsystematics (i.e., to the non-homology term ${\\cal L}/{\\cal R}$ perhaps being\nmore sensitive to $L$ in the larger systems), is unclear at this point.\n\nThe two left panels of Fig.~\\ref{fig14} further show the product\n${\\cal E}{\\cal R}/{\\cal L}^2$ to be very nearly constant as a function\nof $c$, and thus they confirm that the expectation $E_b\\propto L^2/R_h$\nfor homologous clusters actually is a good approximation for King-model\nglobulars as well (as was discussed in \\S3.2 above; see Fig.~\\ref{fig8}).\n\nFigure \\ref{fig15} illustrates the accuracy of equations (\\ref{eq:41}a) and\n(\\ref{eq:42}a) for the globular cluster FP. Again, the panels on the left show\nthe appropriate non-homology functions for generic King models and for the\nregular clusters of \\markcite{pry93}Pryor \\& Meylan (1993). The top plot shows\n(as does Fig.~\\ref{fig1}) that ${\\cal I}_0$ is a very weak function of $c$.\nNon-homology is therefore a rather minor concern for this FP equation as well,\nand the mean value of ${\\cal I}_0$ can be used to estimate a roughly constant\nintercept for equation (\\ref{eq:41}a); this then compares very favorably to\nthe (non-PCC) data in the top right panel of Fig.~\\ref{fig15}. The bottom\npanels, however, show that things are not always so simple. The logarithm of\n${\\cal L}^{2.05}/{\\cal E}{\\cal I}_0^{2.05}$ in the left panel increases\nsystematically (and close to linearly, as the dashed line indicates) with\nconcentration parameter $c$, and hence with cluster luminosity (and, thus,\nwith central surface brightness as well; see eqs.~[\\ref{eq:51}] below). This\nfunction is therefore {\\it not} well approximated by a constant, and if it is\ntreated as such---if it is simply assigned its mean value in equation\n(\\ref{eq:42}a), as was done in the other examples here---the neglected\nnon-homology manifests itself as a slope in the observed correlation between\n$(\\log\\,\\sigma_0-0.775\\,\\log\\,r_0)$ and $\\mu_{V,0}$ which is steeper than the\nnaive expectation.\n\n\\placefigure{fig15}\n\nEquation (\\ref{eq:42}b) for $(\\log\\,\\sigma_0-0.775\\,\\log\\,R_h)$ vs.~$\\langle\n\\mu_V\\rangle_h$---a result of $E_b\\propto L^{2.05}$---comes closest to the\nbasic form of \\markcite{djo95}Djorgovski's (1995) equation (\\ref{eq:djo}b).\nThe fact that his analysis zeroed in on a half-light correlation with\nthe slightly different combination $(\\log\\,\\sigma_{p,0}-0.7\\,\\log\\,R_h)$ may\nitself be understood as a consequence of the fact that $E_b\\sim L^{2.05}$ for\nthe Galactic globulars: since $R_h$ is then so nearly constant as a function of\nluminosity, a correlation between $0.7\\,\\log\\,R_h$ and $\\langle\\mu_V\\rangle_h$\nis not significantly worse, statistically, than one involving $0.775\\,\\log\\,\nR_h$. Meanwhile, equation (\\ref{eq:41}a) for $(\\log\\,\\sigma_0-0.5\\,\\log\\,r_0)$\nvs.~$\\mu_{V,0}$ is clearly equivalent to equation (\\ref{eq:djo}a) from\n\\markcite{djo95}Djorgovski (1995), which therefore is another statement of the\nfact that the King-model clusters have an essentially constant\n$\\Upsilon_{V,0}=(1.45\\pm0.10)\\,M_\\odot\\, L_\\odot^{-1}$.\n\nFinally, as was noted above, it has been claimed (e.g.,\n\\markcite{djo95}Djorgovski 1995; \\markcite{bel98}Bellazzini 1998; see also\n\\markcite{djo94}Djorgovski \\& Meylan 1994) that equation (\\ref{eq:djo}a)\n(or eq.~[\\ref{eq:41}a]) might follow from globular cluster {\\it cores},\nviewed as dynamically distinct entities in their own right, being\n``virialized'' with a constant mass-to-light ratio. However,\nthis is not entirely accurate. If cores are defined as those parts\nof clusters within the volume $r\\le r_0$, direct integrations of King models\nshow that they do not satisfy the simplest version of the virial theorem; that\nis, if kinetic energy is denoted $E_k$, then $2E_k(r_0)\\ne E_b(r_0)$ in\ngeneral. This is shown in Fig.~\\ref{fig16}, which plots the ratio $2E_k/E_b$\nas a function of $r/r_0$ for three representative King models. [Binding energy\nis defined, as in eq.~(\\ref{eq:21}), by $E_b(r)=-(1/2)\\int_0^r 4\\pi r^2\\rho\n\\phi\\,dr$; the kinetic energy is computed from $E_k(r)=(3/2)\\int_0^r 4\\pi\nr^2\\rho\\sigma^2\\,dr$.] This may explain why \\markcite{bel98}Bellazzini (1998),\nwho assumed $2E_k/E_b\\equiv1$ at $r=r_0$, inferred a mass-to-light ratio of\nonly $\\Upsilon_{V,0}\\simeq0.7\\,M_\\odot\\,L_\\odot^{-1}$---a factor of two too\nsmall---from his analysis of \\markcite{djo}Djorgovski's (1995) bivariate\ncorrelation for cluster cores. This Section has shown that, while\n$\\Upsilon_{V,0}$ is indeed a constant in Galactic globulars, the precise\nform of the correlation between $(\\log\\,\\sigma_0-0.5\\,\\log\\,r_0)$ and\n$\\mu_{V,0}$ depends on the definition of $r_0$ in equation (\\ref{eq:23});\nbut although the basic scaling there does arise generically from a dimensional\nanalysis of Poisson's equation (or, equivalently, from the virial theorem {\\it\nincluding surface terms} which vanish only at the {\\it tidal} radius), the\nnormalization (which helps set the intercept in eq.~[\\ref{eq:djo}a] or\neq.~[\\ref{eq:41}a]) is a {\\it convenience} specific to \\markcite{kin66}King\n(1966) models.\n\n\\placefigure{fig16}\n\n\\section{Other Correlations}\n\nSections 3 and 4 have presented the main results of this paper: The binding\nenergies of 109 regular globular clusters in the Milky Way, calculated\nwithin the theoretical context of single-mass, isotropic \\markcite{kin66}King\n(1966) models, correlate very tightly with total luminosities, and decrease\nsystematically with increasing Galactocentric radius (eq.~[\\ref{eq:34}]). This\nresult and the fact (eq.~[\\ref{eq:24}]) that the core mass-to-light ratio\nis a constant (at least for the 39 regular clusters where it has been\ndirectly measured) then imply the existence of a fundamental plane for globular\nclusters, one which has an immediate and clear interpretation even\nwhile accounting for the bivariate cluster correlations discovered by\n\\markcite{djo95}Djorgovski (1995). This new physical view of the FP is\nexpected to aid in developing theories of cluster formation and evolution.\n\nMeanwhile, on perhaps a more pragmatic note, it is a mathematical\nnecessity, requiring no further proof once a King-model framework has been\nadopted, that {\\it any correlation} between {\\it any set of cluster\nobservables} can be obtained simply by treating only $r_{\\rm gc}$, $L$ and\n(to rather a lesser degree) $c$ as independent variables and then manipulating\nthe constraints on $E_b(L, r_{\\rm gc})$ and $\\Upsilon_{V,0}$ according to\ngeneric properties of King models. (As was concluded in \\S3.3, all cluster\nattributes are independent of metallicity, a fact which---although interesting\nin its own right---justifies the neglect of [Fe/H] in this discussion.) No\nother empirical trend contains any physical information beyond the intrinsic\nproperties of these models and the defining equations (\\ref{eq:24}) and\n(\\ref{eq:34}) of the globular cluster FP. This point is developed quite\ngenerally in Appendix A, and it is now illustrated in brief for the Milky Way\ncluster system specifically.\n\nEquations (\\ref{eq:a11})--(\\ref{eq:a16}) give expressions for various physical\nquantities in terms of the basis chosen in this paper for King-model parameter\nspace, i.e., as functions of $L$, $c$, $\\Upsilon_{V,0}$, and $E_b$, allowing\nfor arbitrary $\\Upsilon_{V,0}$ and any power-law scaling $E_b=\nA\\,(L/L_\\odot)^{\\gamma}$. Applied to the Milky Way cluster system, with\n$\\log\\,\\Upsilon_{V,0}\\equiv0.16$, $\\gamma=2.05$, and $\\log\\,(A/{\\rm erg})=\n39.86-0.4\\,\\log(r_{\\rm gc}/8\\,{\\rm kpc})$, the analysis of Appendix A\ntherefore results in the following observable dependences on $L$,\n$r_{\\rm gc}$, and $c$:\n\\begin{equation}\n\\log\\,r_0=-0.05\\,\\log\\,L + 0.4\\,\\log\\,(r_{\\rm gc}/8\\,{\\rm kpc})\n- \\log\\,\\left({\\cal L}^2/{\\cal E}\\right) + 1.681\n\\label{eq:51}\n\\eqnum{\\ref{eq:51}a}\n\\end{equation}\n%\n\\begin{equation}\n\\log\\,R_h=-0.05\\,\\log\\,L + 0.4\\,\\log\\,(r_{\\rm gc}/8\\,{\\rm kpc})\n- \\log\\,\\left({\\cal L}^2/{\\cal E}{\\cal R}\\right) + 1.681\n\\eqnum{\\ref{eq:51}b}\n\\end{equation}\n%\n\\begin{equation}\n\\log\\,j_0=1.15\\,\\log\\,L - 1.2\\,\\log(r_{\\rm gc}/8\\,{\\rm kpc})\n+ \\log\\,\\left({\\cal L}^5/{\\cal E}^3\\right) - 5.042\n\\eqnum{\\ref{eq:51}c}\n\\end{equation}\n%\n\\begin{equation}\n\\mu_{V,0}=-2.75\\,\\log\\,L + 2\\,\\log\\,(r_{\\rm gc}/8\\,{\\rm kpc})\n-2.5\\,\\log\\left({\\cal L}^3{\\cal I}_0/{\\cal E}^2\\right) + 34.766\n\\eqnum{\\ref{eq:51}d}\n\\end{equation}\n%\n\\begin{equation}\n\\langle\\mu_V\\rangle_h=-2.75\\,\\log\\,L + 2\\,\\log\\,(r_{\\rm gc}/8\\,{\\rm kpc})\n- 5\\,\\log\\,\\left({\\cal L}^2/{\\cal E}{\\cal R}\\right) + 36.761\n\\eqnum{\\ref{eq:51}e}\n\\end{equation}\n%\n\\begin{equation}\n\\log\\,\\sigma_0=0.525\\,\\log\\,L - 0.2\\,\\log\\,(r_{\\rm gc}/8\\,{\\rm kpc})\n-0.5\\,\\log\\,\\left({\\cal E}/{\\cal L}\\right) - 1.872\n\\eqnum{\\ref{eq:51}f}\n\\addtocounter{equation}{+1}\n\\end{equation}\nfor cluster radii in pc, luminosities in $L_\\odot$, surface brightnesses in\nmag arcsec$^{-2}$, luminosity densities in $L_\\odot\\,{\\rm pc}^{-3}$, and\nvelocities in km s$^{-1}$. \n\n\\markcite{djo94}Djorgovski \\& Meylan (1994) present many ``monovariate''\ncorrelations for Galactic globulars, of the type $\\log\\,r_0$ vs.~$M_V\n=4.83-2.5\\,\\log\\,L$; $\\log\\,\\sigma_0$ vs.~$\\mu_{V,0}$; $\\log\\,j_0$\nvs.~$\\log\\,r_{\\rm gc}$; and\nso on. All of these can be traced back to some combination of equations\n(\\ref{eq:51}), and thus to King-model definitions and the two\nfundamental-plane relations. (Additional quantities considered by\n\\markcite{djo94}Djorgovski \\& Meylan include dynamical relaxation\ntimes, which are derived from measurements of other cluster parameters and\nthus could easily be included in the analysis here.) Clearly, however, the\nseparation of $L$- and $r_{\\rm gc}$-dependences in many cases might give a\nskewed or degraded impression of the true, underlying physical relationship\nresponsible for a correlation; and so can the neglect of structural and\ndynamical non-homology, i.e., of the increase of (and scatter in) $c$ as a\nfunction of $L$, and the concomitant variations in ${\\cal L}(c)$,\n${\\cal E}(c)$, ${\\cal R}(c)$, and ${\\cal I}_0(c)$ from one cluster to\nanother.\n\nOne example of this is shown in Fig.~\\ref{fig17}, which follows up the FP\nprediction of equation (\\ref{eq:51}a) to improve significantly on the rather\npoor anticorrelation between scale radius and luminosity that was seen in\nFig.~\\ref{fig7} above for the full set of clusters taken from\n\\markcite{har96}Harris (1996). It is now clear\nthat the only reason {\\it any} such correlation appears is because the\nnon-homology term $\\log\\,\\left[{\\cal L}(c)^2/{\\cal E}(c)\\right]$ increases\n(very roughly) as $const.+0.7\\,c\\approx const.+0.3\\,\\log\\,L$ (top panel of\nFig.~\\ref{fig17}), far outweighing the explicit dependence on $\\log\\,L$ in\nequation (\\ref{eq:51}a). The correlation plotted in the bottom panel of\nthis Figure takes this and the expected dependence on Galactocentric position\nfully into account. The solid line drawn through the data here is just\nequation (\\ref{eq:51}a). The dashed line is a formal least-squares fit to\nthe 109 regular-cluster points. Although it has the expected slope of $-0.05$,\nits intercept is offset slightly downwards, a discrepancy which\ntraces back to the small---and purely observational---bias introduced by\nassuming that $L={\\cal L}(c)j_0r_0^3$ exactly for the Galactic globulars\n(see the discussion around Fig.~\\ref{fig2}). The r.m.s.~scatter of the data\npoints about either of these lines is a factor of almost 2 smaller than in\na plot of $\\log\\,r_0$ against $\\log\\,L$ alone and appears to be fully\nattributable to random measurement errors.\\footnotemark\n\\footnotetext{The observational errorbar on $\\log\\,r_0$ is $\\pm0.1$ dex, and\nan uncertainty of $\\pm0.2$ in $c$ translates to about $\\pm0.15$ in\n$\\log({\\cal L}^2/{\\cal E})$. In addition, the derivation of equation\n(\\ref{eq:51}a) in Appendix A involves squaring the equality $L={\\cal L}j_0\nr_0^3$, thereby introducing additional scatter of $2\\times0.25/\\sqrt{109}\n\\simeq0.05$ dex about the mean line (see Fig.~\\ref{fig2}). Even added\nconservatively, in quadrature, these three terms lead to an expected\nr.m.s.~scatter of $\\Delta\\simeq0.2$ dex, essentially that found\nin the bottom of Fig.~\\ref{fig17}.}\n\n\\placefigure{fig17}\n\nIt is worth noting that this approach also explains the ``large'' scatter of\n$\\log\\,R_h^*$ values in Fig.~\\ref{fig8} above ($\\Delta=0.21$ dex, as opposed\nto the observational errorbar of $\\pm0.1$ on $\\log\\,R_h$ alone): the\nscatter about the prediction of equation (\\ref{eq:51}b) is guaranteed to be\nthe same as that about equation (\\ref{eq:51}a), since the former comes from\nadding $\\log\\,{\\cal R}(c)$ to each side of the latter.\n\nAll of the other equations above can be similarly dissected, but it is\nparticularly worth looking at the correlation of velocity scale with total\nluminosity (eq.~[\\ref{eq:51}f]). This is compared to cluster data from the\nsmaller sample of \\markcite{pry93}Pryor \\& Meylan (1993) in Fig.~\\ref{fig18}.\nIn the top panel, non-homology and the expected variation with Galactocentric\nradius are ignored. A fairly strong correlation persists in this case,\nhowever, because the ratio ${\\cal E}/{\\cal L}$ depends only weakly\non $c$ (as can be inferred from the similar shapes of the individual curves\nin Figs.~\\ref{fig1} and \\ref{fig2} above) and because all\nbut one of the regular (non-PCC) \\markcite{pry93}Pryor \\& Meylan clusters\nlie within $2.6\\la r_{\\rm gc}\\la 29$ kpc [so that the term $0.2\\,\\log\\,\n(r_{\\rm gc}/8\\,{\\rm kpc})$ ranges only from $-0.1$ to $+0.1$ or so]. The\nexception to this is the bright cluster NGC 2419, marked on Fig.~\\ref{fig18},\nwhich is located at $r_{\\rm gc}=91.5$ kpc according to \\markcite{har96}Harris\n(1996). This partly explains its appearance as an outlier relative to the\nstraight line drawn through the top panel of the Figure:\n$$\\log\\,\\sigma_0=0.525\\,\\log\\,L-1.928\\ ,$$\nwhich follows from applying an average $0.5\\,\\log\\,({\\cal E}/{\\cal L})\\simeq\n0.049$ and a median $r_{\\rm gc}=8.7$ kpc (both evaluated using the 39 regular\nclusters in the sample) to equation (\\ref{eq:51}f). Clearly, this simple\nversion of the full relation already provides a reasonable description of the\ndata (aside from NGC 2419), and the monovariate correlation is a rather\nfaithful representation of the FP scaling $E_b^*\\propto L^{2.05}$ and the\nconstancy of $\\Upsilon_{V,0}$.\n\n\\placefigure{fig18}\n\nThe situation nevertheless improves somewhat if ${\\cal E}/{\\cal L}$ and\n$r_{\\rm gc}$ are treated properly as variables. This is done in the\nbottom panel of Fig.~\\ref{fig18}, which shows a stronger and more significant\n$\\sigma_0$--$L$ correlation (i.e., the r.m.s.~scatter $\\Delta$ is lower and\nthe Spearman rank correlation coefficient $s$ is higher), and in which NGC\n2419 appears as a less extreme outlier (though an outlier all the same).\nThe solid line plotted here traces the full equation (\\ref{eq:51}f), and it is\nstatistically indistinguishable from a formal least-squares fit to the regular\nclusters (dashed line). The scatter of these data about either line is again\nthat expected given the typical observational uncertainties.\\footnotemark\n\\footnotetext{In this case, the errorbar on $\\log\\,\\sigma_0$ is $\\pm0.09$ dex\n(\\S2). However, the intercept in equation (\\ref{eq:51}f) includes a\ncontribution from $0.5\\,\\log\\,\\Upsilon_{V,0}$ (see the general\neq.~[\\ref{eq:a16}]), which is further subject to errors in $\\log\\,\\sigma_0$\n(because $\\Upsilon_{V,0}\\propto \\sigma_0^2$; see \\S3.1). The total\nexpected scatter in Fig.~\\ref{fig18} is therefore $2\\times\\Delta\\,\n(\\log\\,\\sigma_0)=0.18$.}\n\nAs was mentioned above, equations (\\ref{eq:51}) can be combined in various\nways to produce a large number of other correlations. For instance, the\nsum of (\\ref{eq:51}a) and (\\ref{eq:51}c) gives the full dependence\nunderlying the rough correlation between $\\log\\,(j_0r_0)$ and $\\log\\,L$ seen\nin Fig.~\\ref{fig7} above. Another example---and the last to be considered\nhere---is found by eliminating $\\log\\,r_{\\rm gc}$ between equations\n(\\ref{eq:51}a) and (\\ref{eq:51}d) above:\n\\begin{equation}\n\\log\\,r_0 - 0.2\\,\\mu_{V,0} =\n0.5\\,\\log\\,L - 0.5\\,\\log\\,\\left({\\cal L}/{\\cal I}_0\\right) - 5.272\\ .\n\\label{eq:52}\n\\end{equation}\nAlternatively, the manipulations leading to equation (\\ref{eq:a13}) below\nshow that this relation is really just an expression for the total luminosity\nof a King model, combined with the definition of surface brightness; as such,\nit is completely independent of any fundmamental plane specifications.\n\nEquation (\\ref{eq:52}) relates to the correlation between scale\nradius and core surface brightness, shown in the top left panel of\nFig.~\\ref{fig19}, for the 109 regular and 30 PCC clusters from the catalogue of\n\\markcite{har96}Harris (1996). This is of interest because\n\\markcite{bel98}Bellazzini (1998) has claimed that the correlation (along with\none between $\\sigma_0$ and $\\mu_{V,0}$, which can actually be obtained from\neqs.~[\\ref{eq:51}d] and [\\ref{eq:51}f]) results from Galactic globulars having\na ``constant core mass.'' However, this conclusion was based on the assumption\nthat cores satisfy the virial theorem in the form $2 E_k(r_0)=E_b(r_0)$, and\nthis was shown above (Fig.~\\ref{fig16}) {\\it not} to be true in general.\nMoreover, the basic hypothesis of a constant $M_0\\equiv\\Upsilon_{V,0}j_0r_0^3$\nis not borne out by the data. The top right panel of Fig.~\\ref{fig19}, for\ninstance, shows clearly that measured values of $j_0r_0^3$ range over more\nthan two orders of magnitude---far in excess of the observational\nerrorbar---in the Milky Way cluster system. \\markcite{bel98}Bellazzini (1998)\nalso recognizes this but implies, in essence, that the scatter, although\nunarguably real, is consistent with more or less random excursions from a\nline of constant core mass. However, the bottom left panel of Fig.~\\ref{fig19}\nshows that this is not the case either: If it were true that $j_0r_0^3\\sim\nconst.$, such that $r_0\\sim (j_0r_0)^{-1/2}$ with some intrinsic scatter, then\nthe quantity $(\\log\\,r_0 - 0.2\\,\\mu_{V,0})$ would have to be {\\it uncorrelated}\nwith any other cluster property; but instead it shows a significant dependence\non the total cluster luminosity.\n\n\\placefigure{fig19}\n\nThe point is that {\\it both} the monovariate $r_0$--$\\mu_{V,0}$ correlation,\n{\\it and} a correlation between $\\log\\,r_0-0.2\\mu_{V,0}$ and $\\log\\,L$, are\nexpected on the basis of equation (\\ref{eq:52}). But this says nothing about a\nconstant cluster core mass; rather, it implies that King-model clusters at a\ngiven {\\it total} luminosity (and with a single central concentration) will\nalways show a correlation of the form $\\log\\,r_0\\sim0.2\\mu_{V,0}$, {\\it by\ndefinition}. The rougher trends and the large scatter in the top half of\nFig.~\\ref{fig19} reflect the superposition of many such correlations for\nclusters with a wide range of total $L$ in the Milky Way, modified somewhat by\nsystematics in the non-homology terms ${\\cal L}$ and ${\\cal I}_0$ that result\nfrom the range in $c$-values as well.\n\nThe solid line in the bottom left of Fig.~\\ref{fig19} is just equation\n(\\ref{eq:52}) with an intercept evaluated assuming a constant\n$\\log\\,({\\cal L}/{\\cal I}_0)=1.007$, the average for \\markcite{har96}Harris'\n(1996) King-model clusters; the dashed line is a least-squares fit to the\ndata. The two differ---and the scatter about either exceeds the observational\nerrorbvars on the data---because the ratio ${\\cal L}/{\\cal I}_0$ has a\nsignificant dependence on $c$, and hence on $\\log\\,L$ (see Figs.~\\ref{fig1} and\n\\ref{fig2}); the cluster non-homology cannot be ignored here. The bottom right\ncorner of Fig.~\\ref{fig19} therefore shows the full correlation expected on\nthe basis of equation (\\ref{eq:52}). The agreement with the data is now\nexcellent; the solid, ``model'' line is indistinguishable from a least-squares\nfit to the regular clusters, and the r.m.s.~scatter is fully within the realm\nof random measurement errors. [This last plot is equivalent to one of\n$({\\cal L}j_0r_0^3)^{1/2}$ against $(L/L_\\odot)^{1/2}$, so the observed and\nexpected scatter both are just half those in the bottom panel of\nFig.~\\ref{fig2} above.]\n\nThus, the observed correlation between $r_0$ and $\\mu_{V,0}$ in globular\nclusters is controlled entirely by the generic behavior of total luminosity\nin King models, and by the systematic (but scattered) increase of $c$ with\n$L$ found in the Milky Way. There is no need to postulate a constant core\nmass. Indeed, much more generally, in the scheme developed here---where\nglobulars are defined completely by $L$, $c$, $\\Upsilon_{V,0}$, and\n$E_b^*$---there is no {\\it room} for such new constraints not already provided\nby the equations of the fundamental plane.\n\n\\section{Summary}\n\nIf they are described by single-mass, isotropic \\markcite{kin66}King (1966)\nmodels, globular clusters are fully defined, in general, by specifying just\nfour independent physical parameters. These were chosen in this\npaper to be a mass-to-light ratio ($\\log\\,\\Upsilon_{V,0}$), total\nbinding energy ($\\log\\,E_b$), central concentration [$c=\\log\\,(r_t/r_0)$],\nand total luminosity ($\\log\\,L$). It has been shown that (1) all 39\nregular (non--core-collapsed) Galactic globular clusters with measured core\nvelocity dispersions have a common mass-to-light ratio (\\S3.1),\n$$\\log\\,(\\Upsilon_{V,0}/M_\\odot\\,L_\\odot^{-1})=0.16\\pm0.03\\ ;$$\nand (2) if it is assumed that this also holds for the other regular\nclusters in the Milky Way with no velocity data, but for which measured\nKing-model structural parameters are available, the full cluster system (109\nobjects in all, excluding core-collapsed members) shows a very well-defined\ndependence of binding energy on total luminosity, modulated by Galacocentric\nradius (\\S3.2):\n$$\\log\\,\\left(E_b/{\\rm erg}\\right)=\n\\left[\\left(39.86\\pm0.40\\right)-0.4\\,\\log\\,\\left(r_{\\rm gc}/8\\,{\\rm kpc}\n\\right)\\right]+\\left(2.05\\pm0.08\\right)\\,\\log\\,\\left(L/L_\\odot\\right)\\ .$$\nThe scatter about each of these relations is fully accounted for by the typical\nobservational errorbars on $\\log\\,\\Upsilon_{V,0}$ ($\\simeq0.2$ dex) and\n$\\log\\,E_b$ ($\\simeq0.5$ dex).\n\nWith $\\Upsilon_{V,0}$ essentially a fixed constant and $E_b$ known\nprecisely (at a given Galactocentric position) as a function of $L$, only\ntwo of the four basic cluster properties are truly independent; globular\nclusters in the Milky Way are confined to a narrow, two-dimensional\nsubregion---a fundamental plane (FP)---in the larger, four-dimensional space\nof King models. The distribution of clusters on the plane is then determined\nessentially by their $c$- and $L$-values. They are not scattered randomly,\nhowever, as there also exists a correlation between $c$ and $\\log\\,L$. Still,\nthis does {\\it not} necessarily mean that the locus of globular clusters is\nonly one-dimensional: a linear $c$--$\\log\\,L$ relation is of poorer quality\nthan either of the empirical constraints on $\\log\\,\\Upsilon_{V,0}$ and\n$\\log\\,E_b$, and although there {\\it might} exist some more complicated\nfunction which gives a comparably one-to-one dependence of concentration on\nluminosity, one has yet to be found (\\S\\S3 and 4).\n\nRegardless, the mean trend of $c$ vs.~$\\log\\,L$ is independent of\nGalactocentric position and cluster metallicity, as is the value of\n$\\log\\,\\Upsilon_{V,0}$ and the slope of the correlation between $\\log\\,E_b$\nand $\\log\\,L$ (\\S3.3). The normalization of the $E_b(L)$ scaling is also\nindependent of [Fe/H], but it decreases towards larger Galactocentric\nradii. The equation above accounts for this, and the $r_{\\rm gc}$ dependence\nthere describes the {\\it full extent of environmental influences} on\nthe globular cluster FP.\n\nIt was shown in \\S4 that cluster concentration parameters (and, to a\nlesser extent, binding energies) correlate more tightly with luminosity for\nglobulars at $r_{\\rm gc}>8$ kpc than for those at smaller\nradii. Thus, since dynamical evolution has likely been less effective at\nerasing initial conditions outside the Solar circle---and since simple\narguments indicate that clusters could remain on or close to the FP as they\nevolve---it may well be that most properties of the fundamental plane were set\nmore or less at the time of globular cluster formation. Quantitative\ncalculations of cluster evolution over a Hubble time in the Galactic potential\nshould be applied to check this.\n\nA three-dimensional ``$\\epsilon$-space'' was constructed in \\S4.1 from a simple\ntransformation of the cluster parameter space left after specifying\n$\\log\\,\\Upsilon_{V,0}=constant$ (and after removing the effects of\nGalactocentric radius) in order to obtain a directly face-one view of the FP.\nIt could be interesting to attempt a similar construction for elliptical\ngalaxies and clusters of galaxies, i.e., to interpret their fundamental planes\nin terms of binding energy as well, in order to make a more direct comparison\nwith the globular cluster FP.\n\nThe equations for $\\Upsilon_{V,0}$ and for $E_b$ as a function of $L$, which\ndefine the FP, were shown in \\S4.2 to be equivalent to the two strong bivariate\ncluster correlations used by \\markcite{djo95}Djorgovski (1995) to argue for\nthe existence of a fundamental plane for globular clusters.\n\\markcite{djo95}Djorgovski (and \\markcite{bel98}Bellazzini 1998) offered a\nsimple virial-theorem argument (which was shown here to be incomplete) as an\nexplanation for one of these correlations, but did not interpret the other.\nThe results of this paper have put his results on a firm physical footing.\n\nFinally, since $\\Upsilon_{V,0}$, $c$, $E_b$, and $L$ completely define\nglobular clusters, any correlations connecting any of their other properties,\nor any other trends with Galactocentric radius, necessarily derive from\ngeneric properties of \\markcite{kin66}King (1966) models combined with the\nempirical FP relations and their environmental dependence. Appendix A outlined\nsuch derivations quite generally, and specialized results for the Milky Way\ncluster ensemble were presented in \\S5.\n\nThe picture that has been developed here is a simplification in that it\nworks specifically in the context of single-mass and isotropic models for\nglobular clusters. This approximation is evidently an excellent one, but\nbecause of it the results of this paper can say nothing about the stellar mass\nfunctions or possible velocity anisotropy in observed clusters. Nor have the\nkinematics of clusters within the Milky Way (e.g., orbital\neccentricities, or bulk rotation of the metal-rich subsystem) been considered\nin any way. These issues aside, however, the preceding discussion may be\ndistilled into a small set of four main facts to be explained by theories of\ncluster formation and evolution:\n\n\\begin{itemize}\n\n\\item All cluster properties are independent of metallicity.\n\n\\item The core mass-to-light ratio, $\\Upsilon_{V,0}=(1.45\\pm0.1)\\,M_\\odot\\,\nL_\\odot$, does not vary significantly with cluster luminosity or\nGalactocentric position.\n\n\\item The concentration parameter, which controls the shape of a cluster's\ninternal density profile, correlates with luminosity. The dependence of $c$\non $\\log\\,L$ is much more significant outside the Solar circle than inside,\nbut even there the relationship is not obviously one-to-one. Its basic form\nis, however, independent of $r_{\\rm gc}$.\n\n\\item Binding energy is intrinsically a function of luminosity and is\nregulated by Galactocentric position: $E_b\\propto L^{2.05}r_{\\rm gc}^{-0.4}$.\nSince there is no evidence for significant variations in the {\\it global}\nmass-to-light ratios of clusters in the Milky Way, $E_b$ is inferred to scale\nwith total mass in the same way as with luminosity.\n\n\\end{itemize}\n\nOnce again, the balance of current evidence suggests that these characteristics\nof the fundamental plane---and, thus, most of the systematics of the Galactic\nglobular cluster system---were essentially fixed by the cluster formation\nprocess. Moreover, it is not implausible that this process was controlled\nlargely by a single intrinsic protocluster parameter---the initial gas\nmass---and adjusted by an external influence depending on Galactocentric\nradius. Further discussion along these lines is left for future work\n(McLaughlin, in preparation). Regardless of any interpretive details, however,\nit clearly will be important to determine the extent to which the globular\ncluster systems of other galaxies can be described in the same simple terms\nthat apply in the Milky Way.\n\n\\acknowledgments\n\nThis work was supported by NASA through grant number HF-1097.01-97A awarded by\nthe Space Telescope Science Institute, which is operated by the Association of\nUniversities for Research in Astronomy, Inc., for NASA under contract\nNAS5-26555.\n\n\\appendix\n\n\\section{KING MODELS AND GLOBULAR CLUSTER CORRELATIONS}\n\nThe analysis in this paper refers to eleven physical parameters\nwhich may be observed or derived for globular clusters: the central\nline-of-sight velocity dispersion $\\sigma_{p,0}$; the scale radius $r_0$,\nwhich is closely related (but not always identical) to the core radius,\nat which the luminosity surface density falls to half its central\nvalue; the central surface brightness $\\mu_{V,0}$, which is related to the\ncentral $V$-band intensity, $I_0$, in units of $L_\\odot\\,{\\rm pc}^{-2}$; the\ncentral luminosity density $j_0$ ($L_\\odot\\,{\\rm pc}^{-3}$); the central\nmass-to-light ratio $\\Upsilon_{V,0}$, which gives the central {\\it mass}\ndensity, $\\rho_0=\\Upsilon_{V,0}j_0$, and which must equal the global\nmass-to-light ratio in (idealized) clusters of single-mass stars; the\nprojected half-light radius $R_h$ and the surface brightness $\\langle\\mu_V\n\\rangle_h$ averaged within that aperture; the central concentration $c$,\nwhich describes the global shape of the cluster's surface brightness profile;\nthe total luminosity $L$; and the cluster binding energy, $E_b$.\n\nThere are, of course, other quantities of interest (e.g., core and half-mass\nrelaxation times; average velocity dispersion within the half-light radius),\nbut within the context of \\markcite{kin66}King's (1966) model for\nglobular clusters, these other parameters can all be derived from some subset\nof the eleven just listed. Indeed, if the isotropic, single-mass King models\nare adopted a priori as complete descriptions of the internal structures of\nGalactic globular clusters, then only {\\it four} of these eleven variables are\ntruly independent. These are (1) the mass-to-light ratio $\\Upsilon_{V,0}$; (2)\nthe concentration parameter $c=\\log\\,(r_t/r_0)$, which is directly related to\nthe depth of a cluster's potential well; and two other parameters---chosen\nhere to be (3) binding energy and (4) total luminosity---required to normalize\na dimensionless model to an observed object. The reduction to this\nphysical basis requires seven definitions and model relations. (See also\n\\markcite{dja93}Djorgovski 1993a for an outline of this procedure, and\n\\markcite{kin66}King 1966 or \\markcite{bin87}Binney \\& Tremaine 1987 for more\ndetailed descriptions of the models themselves.)\n\nFirst, recall that, where they are available, the directly observed central\nvelocity dispersions of Milky Way globulars (\\markcite{pry93}Pryor \\& Meylan\n1993) have {\\it already} been converted to \\markcite{kin66}King-model scale\nvelocities $\\sigma_0$ (in \\S2 above; see Fig.~1 and eq.~[\\ref{eq:b1}]). Also,\nthe so-called core radii tabulated by \\markcite{har96}Harris (1996; also\n\\markcite{tra93}Trager et al.~1993 and \\markcite{dja93}Djorgovski 1993a) are\nin fact the $r_0$ referred to here as scale radii ($r_0$ differs from the\ntrue projected half-power radius in low-concentration clusters).\n\nGiven these things, the definition of $r_0$ (\\markcite{kin66}King 1966) yields\na cluster's central {\\it mass} density:\n\\begin{equation}\n\\Upsilon_{V,0}j_0=9\\sigma_0^2/(4\\pi G r_0^2)\\ ,\n\\label{eq:a1}\n\\end{equation}\nwhere the basic scaling $\\rho_0\\propto(\\sigma_0^2/Gr_0^2)$ follows simply from\ndimensional analysis, but the coefficient $(9/4\\pi)$ is specific to the King\nmodel. A central {\\it luminosity} volume density alone is derived from an\nobserved $r_0$, $c$, and central surface brightness, by way of the trivial\n(model-independent) definition\n\\begin{equation}\n\\mu_{V,0}=26.362-2.5\\,\\log\\,(I_0/L_\\odot\\,{\\rm pc}^{-2})\n\\label{eq:a2}\n\\end{equation}\nand the model relation\n\\begin{equation}\nI_0={\\cal I}_0(c)\\,j_0r_0\\ ,\n\\label{eq:a3}\n\\end{equation}\nwhere ${\\cal I}_0$ is the dimensionless function of concentration shown in the\nbottom left panel of Fig.~\\ref{fig1} and approximated by equation\n(\\ref{eq:b3}). Equation (\\ref{eq:a1}) is used in \\S3.1 to infer the central\nmass-to-light ratio $\\Upsilon_{V,0}$ for the 39 non--core-collapsed clusters\ncatalogued by \\markcite{pry93}Pryor \\& Meylan (1993).\n\nThe projected half-light radius, King scale radius, and central concentration\nare linked through the function\n\\begin{equation}\n{\\cal R}(c)=R_h/r_0\\ ,\n\\label{eq:a4}\n\\end{equation}\nwhich is drawn in the bottom right panel of Fig.~\\ref{fig1} and approximated\nin equation (\\ref{eq:b4}) below. The average surface brightness within $R_h$\nis then given (for $L$ in $L_\\odot$ and $R_h$ in pc) by\n\\begin{equation}\n\\langle\\mu_V\\rangle_h=26.362-2.5\\,\\log\\,(L/2\\pi R_h^2)\\ ,\n\\label{eq:a5}\n\\end{equation}\nwhere the total cluster luminosity is given in terms of $c$, $j_0$ and $r_0$\nby\n\\begin{equation}\nL={\\cal L}(c)\\,j_0r_0^3\\ .\n\\label{eq:a6}\n\\end{equation}\n(See Fig.~\\ref{fig2} and eq.~[\\ref{eq:b5}] for the dimensionless function\n${\\cal L}$.) Finally, the cluster binding energy is expressed as\n(cf.~eq.~[\\ref{eq:22}])\n\\begin{equation}\nE_b ={{\\sigma_0^4r_0}\\over{G}}\\,{\\cal E}(c) =\n\\left({9\\over{4\\pi}}\\right)^{1/2}\\,{{\\sigma_0^5\n\\left(\\Upsilon_{V,0}j_0\\right)^{-1/2}}\\over{G^{3/2}}}\\,{\\cal E}(c) =\n\\left({{4\\pi}\\over{9}}\\right)^2\\,G\\left(\\Upsilon_{V,0}j_0\\right)^2r_0^5\\,\n{\\cal E}(c)\\ ,\n\\label{eq:a7}\n\\end{equation}\nwith ${\\cal E}$ the function in equation (\\ref{eq:b2}) and the top right\npanel of Fig.~\\ref{fig1}. (The last two equalities in eq.~[\\ref{eq:a7}] follow\nfrom the definition [\\ref{eq:a1}].)\n\nTo repeat, then, a King-model globular cluster is defined fully by\nits core mass-to-light ratio, central concentration, binding energy, and\ntotal luminosity. Real clusters therefore can be expected to inhabit a\nnominally four-dimensional parameter space. However, the dimensionality of\nthis space is reduced by one for every independent constraint on the four\nfundamental quantities. Thus, given relations of the type inferred in \\S3\nfor the Milky Way clusters, \n\\begin{equation}\n\\Upsilon_{V,0}={\\rm constant}\\ \\ \\ \\ \\ \\ \\ {\\rm and}\\ \\ \\ \\ \\ \\ \\ \nE_b=A\\,\\left(L/L_\\odot\\right)^{\\gamma}\\ ,\n\\label{eq:a8}\n\\end{equation}\nglobulars constitute an essentially two-parameter family\nof objects (although, in principle, $\\Upsilon_{V,0}$ or the $E_b(L)$ relation\nmay further depend on external, environmental variables; in our Galaxy, $A\n\\propto r_{\\rm gc}^{-0.4}$ according to \\S3.3 above.) That is, having\nspecified $L$ and $c$ for an object (at some given $r_{\\rm gc}$), its binding\nenergy $E_b$ and mass-to-light ratio $\\Upsilon_{V,0}$ follow immediately from\nequation (\\ref{eq:a8}). The product $\\left(j_0r_0^3\\right)$ is then given\nuniquely by equation (\\ref{eq:a6}), and the combination\n$\\left(j_0^2r_0^5\\right)$ by equation (\\ref{eq:a7}). This sets\nthe values of $j_0$ and $r_0$ individually, and all other cluster parameters\nfollow from equations (\\ref{eq:a1})--(\\ref{eq:a5}). If there exists a third\nbasic relation, $c=c(\\log\\,L)$---a situation which is strongly suggested,\nalthough not proven, by current data on the Galactic cluster system---then\nluminosity or mass alone (again, at a given $r_{\\rm gc}$ in our Galaxy)\ncontrols the globular cluster sequence.\n\nIt is clear, as a result of this, that {\\it any correlations between any\nobserved or derived cluster parameters must trace back to some\ncombination of the equations (\\ref{eq:a1})--(\\ref{eq:a7}) characterizing\nKing models, and/or to relations between the fundamental physical variables\n$\\Upsilon_{V,0}$, $c$, $E_b$, and $L$}. Several examples of such observable\ncorrelations are now derived quite generally; their application to the Milky\nWay globular cluster system specifically is discussed in \\S\\S4 and 5 above.\n\n\\subsection{Bivariate Correlations}\n\nEquation (\\ref{eq:a1}) can be viewed either as a definition of $r_0$ or as an\nexpression for $\\Upsilon_{V,0}$ in terms of $\\sigma_0$, $r_0$, and $j_0$.\nEither way, it may be re-written as\n$$\\left(4\\pi G/9\\right)\\,\\Upsilon_{V,0}\\,j_0r_0=\\sigma_0^2r_0^{-1}\\ ;$$\nor, in appropriate units,\n$$\\left({{\\sigma_0}\\over{{\\rm km}\\,{\\rm s}^{-1}}}\\right)^2\\,\n\\left({{r_0}\\over{{\\rm pc}}}\\right)^{-1} =\n5.9870\\times10^{-3}\\,\n\\left({{\\Upsilon_{V,0}}\\over{M_\\odot\\,L_\\odot^{-1}}}\\right)\\,\n\\left({{j_0r_0}\\over{L_\\odot\\,{\\rm pc}^{-2}}}\\right)\\ .$$\nTaking the logarithm of both sides and using equations (\\ref{eq:a2}) and\n(\\ref{eq:a3}) to introduce the observable $\\mu_{V,0}$ then yields\n\\begin{equation}\n\\log\\,\\sigma_0-0.5\\,\\log\\,r_0=-0.2\\,\\mu_{V,0}-0.5\\,\\log\\,{\\cal I}_0(c)\n+0.5\\,\\log\\,\\Upsilon_{V,0}+4.1610\\ .\n\\label{eq:a9a}\n\\end{equation}\nGiven a constant $\\log\\,\\Upsilon_{V,0}$ (eq.~[\\ref{eq:24}]) and a very slowly\nvarying ${\\cal I}_0(c)$, this becomes an essentially bivariate correlation\ncorresponding to one of \\markcite{djo95}Djorgovski's (1995) two equations for\nthe fundamental plane of Galactic globular clusters (\\S4.2). It may also be\nput in terms of half-light cluster radii and average surface brightness by\nnoting a relation between $\\mu_{V,0}$ and $\\langle\\mu_V\\rangle_h$ that follows\nfrom King-model definitions: Equations (\\ref{eq:a2}), (\\ref{eq:a3}),\n(\\ref{eq:a6}), (\\ref{eq:a4}), and (\\ref{eq:a5}) combined give\n\\begin{eqnarray}\n\\mu_{V,0} & = & 26.362-2.5\\,\\log\\,\n\\left[{{{\\cal I}_0(c)\\,j_0r_0}\\over{L_\\odot\\,{\\rm pc}^{-2}}}\\right]\n = 26.362-2.5\\,\\log\\,\n\\left[2\\pi\\,{{{\\cal I}_0(c){\\cal R}(c)^2}\\over{{\\cal L}(c)}}\\,\n{{L/2\\pi R_h^2}\\over{L_\\odot\\,{\\rm pc}^{-2}}}\\right] \\nonumber \\\\\n & = & \\langle\\mu_V\\rangle_h-2.5\\,\\log\\,\\left(2\\pi\\right)-\n2.5\\,\\log\\left[{{{\\cal I}_0(c){\\cal R}(c)^2}\\over{{\\cal L}(c)}}\\right]\\ ,\n\\label{eq:mumu}\n\\end{eqnarray}\nand substitution of this in equation (\\ref{eq:a9a}) yields\n\\begin{equation}\n\\log\\,\\sigma_0-0.5\\,\\log\\,R_h=-0.2\\,\\langle\\mu_V\\rangle_h-\n0.5\\,\\log\\,\\left[{\\cal L}(c)/{\\cal R}(c)\\right]\n+0.5\\,\\log\\,\\Upsilon_{V,0}+4.5601\\ .\n\\label{eq:a9b}\n\\end{equation}\nas another expression of equation (\\ref{eq:a1}).\n\nA power-law scaling of binding energy with total luminosity leads to another\npair of equivalent bivariate correlations. With $E_b=A\\,\\left(\nL/L_\\odot\\right)^{\\gamma}$ as in equation (\\ref{eq:a8}), the first\nequality in equation (\\ref{eq:a7}) reads\n$$\\sigma_0^4r_0=GA\\,\\left(L/L_\\odot\\right)^{\\gamma} {\\cal E}(c)^{-1}\\ ,$$\nwhere, again, the normalization $A$ in general may vary with Galactocentric\nposition (or with any other environmental factor appropriate to a given\ndataset). Applying equation (\\ref{eq:a6}) and inserting the usual units, this\nbecomes\n$$\\left({{\\sigma_0}\\over{{\\rm km}\\,{\\rm s}^{-1}}}\\right)^4\\,\n\\left({{r_0}\\over{{\\rm pc}}}\\right)^{1-2\\gamma} =\n2.1558\\times10^{-46}\\,\\left({A\\over{{\\rm erg}}}\\right)\\,\n\\left[{{{\\cal L}(c)^{\\gamma}}\\over{{\\cal E}(c)}}\\right]\\,\n\\left({{j_0\\,r_0}\\over{L_\\odot\\,{\\rm pc}^{-2}}}\\right)^{\\gamma}\\ ,$$\nso that taking the logarithm and using the definition of $\\mu_{V,0}$\n(eqs.~[\\ref{eq:a2}] and [\\ref{eq:a3}]) yields\n\\begin{eqnarray}\n\\log\\,\\sigma_0-0.25\\,\\left(2 \\gamma-1\\right)\\,\\log\\,r_0 & = &\n-(0.1\\,\\gamma)\\,\\mu_{V,0}\n+0.25\\,\\log\\,\\left[{\\cal L}(c)^{\\gamma}/{\\cal E}(c)\\,\n{\\cal I}_0(c)^{\\gamma}\\right] \\nonumber \\\\\n & & + 0.25\\,\\log\\,A + 2.6362\\,\\gamma - 11.4166\\ .\n\\label{eq:a10a}\n\\end{eqnarray}\nAnd finally, a version that refers to half-light cluster quantities is\nobtained by applying equations (\\ref{eq:a4}) and (\\ref{eq:mumu}):\n\\begin{eqnarray}\n\\log\\,\\sigma_0-0.25\\,\\left(2\\gamma-1\\right)\\,\\log\\,R_h & = &\n-(0.1\\,\\gamma)\\,\\langle\\mu_V\\rangle_h\n-0.25\\,\\log\\,\\left[{\\cal E}(c)/{\\cal R}(c)\\right] \\nonumber \\\\\n & & + 0.25\\,\\log\\,A + 2.8357\\,\\gamma - 11.4166\\ ,\n\\label{eq:a10b}\n\\end{eqnarray}\nwhich is shown in \\S4.2 to correspond to \\markcite{djo95}Djorgovski's (1995)\nsecond equation for the globular cluster fundamental plane in the Milky Way.\n\n\\subsection{``Monovariate'' Correlations}\n\nGiven the suite of definitions listed above\n(eqs.~[\\ref{eq:a1}]--[\\ref{eq:a7}]), plus the two fundamental-plane\nconstraints of equation (\\ref{eq:a8}), any globular cluster observables can be\nexpressed as functions of central concentration and total luminosity (and\nany environmental factors, such as $r_{\\rm gc}$, which in general can be\nsubsumed in eq.~[\\ref{eq:a8}]). Some of these relations can appear as\nmonovariate cluster correlations if non-homology and variations in $c$ are\nignored.\n\nOne such expression follows from the third equality in equation (\\ref{eq:a7}).\nTogether with equations (\\ref{eq:a8}) and (\\ref{eq:a6}), this reads\n$${{E_b}\\over{{\\rm erg}}}=1.6627\\times10^{41}\\,\n\\left({{\\Upsilon_{V,0}}\\over{M_\\odot\\,L_\\odot^{-1}}}\\right)^2\\,\n\\left({{j_0}\\over{L_\\odot\\,{\\rm pc}^{-3}}}\\right)^2\\,\n\\left({{r_0}\\over{{\\rm pc}}}\\right)^5\\, {\\cal E}(c)=\n{A\\over{{\\rm erg}}}\\,\n\\left({L\\over{L_\\odot}}\\right)^{\\gamma-2}\n\\left[{{\\cal L}(c)\\,{j_0\\,r_0^3}\\over{L_\\odot}}\\right]^2\\ ,$$\nor, after taking the logarithm of both sides,\n\\begin{equation}\n\\log\\,r_0=(2-\\gamma)\\,\\log\\,L - \\log\\,\\left[{\\cal L}(c)^2/{\\cal E}(c)\\right]\n-\\log\\,A + 2\\,\\log\\,\\Upsilon_{V,0} + 41.2208\\ .\n\\label{eq:a11}\n\\end{equation}\nAs \\S5 discusses, this does translate to a rough correlation between $r_0$\nand $L$ in the Milky Way (see Figs.~\\ref{fig7} and \\ref{fig17}). It also can\nbe used to derive the dependence of $R_h={\\cal R}(c)\\,r_0$ on $L$ and $c$:\n\\begin{equation}\n\\log\\,R_h=(2-\\gamma)\\,\\log\\,L - \\log\\,\\left[{\\cal L}(c)^2/{\\cal E}(c)\n{\\cal R}(c)\\right] - \\log\\,A + 2\\,\\log\\,\\Upsilon_{V,0} + 41.2208\\ ,\n\\label{eq:a12}\n\\end{equation}\naccounting for the behavior of observed cluster half-light radii in\nFig.~\\ref{fig8} above. (Like $r_0$, $R_h$ is measured in pc.)\n\nCorrelations involving surface brightness follow from the basic definitions\n(\\ref{eq:a2}), (\\ref{eq:a3}), and (\\ref{eq:a6}), which state that\n\\begin{eqnarray}\n\\log\\,r_0 & = & \n0.2\\,\\mu_{V,0} + 0.5\\,\\log\\,(j_0r_0^3) + 0.5\\,\\log\\,{\\cal I}_0(c) - 5.2724\n\\nonumber \\\\\n & = & 0.2\\,\\mu_{V,0} + 0.5\\,\\log\\,L -\n0.5\\,\\log\\,\\left[{\\cal L}(c)/{\\cal I}_0(c)\\right] - 5.2724\n\\nonumber\n\\end{eqnarray}\nfor $j_0$ in units of $L_\\odot\\,{\\rm pc}^{-3}$ and $r_0$ in pc. This is itself\na bivariate correlation; it is discussed further in \\S5, in connection with\na rough correlation between $r_0$ and $\\mu_{V,0}$ observed in the Milky Way\ncluster system (see Fig.~\\ref{fig19}). But it and equation (\\ref{eq:a11}) also\nlead to\n\\begin{equation}\n\\log\\,j_0=\\left(3\\gamma-5\\right)\\,\\log\\,L +\n\\log\\,\\left[{\\cal L}(c)^5/{\\cal E}(c)^3\\right]+3\\,\\log\\,A -\n6\\,\\log\\,\\Upsilon_{V,0} - 123.662\n\\label{eq:a13}\n\\end{equation}\nor to\n\\begin{equation}\n\\mu_{V,0}=2.5 \\left(3-2\\gamma\\right)\\,\\log\\,L-2.5\\,\\log\\left[{\\cal L}(c)^{3}\n{\\cal I}_0(c)/{\\cal E}(c)^2\\right]-5\\,\\log\\,A+10\\,\\log\\,\\Upsilon_{V,0}\n+232.466\\ ,\n\\label{eq:a14}\n\\end{equation}\nwhich corresponds to the correlation between $\\log\\,j_0r_0$ and $\\log\\,L$ in\nFig.~\\ref{fig7} above. In addition, equations (\\ref{eq:a14}) and\n(\\ref{eq:mumu}) together, or equations (\\ref{eq:a12}) and (\\ref{eq:a5})\ntogether, imply\n\\begin{equation}\n\\langle\\mu_V\\rangle_h=2.5\\left(3-2\\gamma\\right)\\,\\log\\,L -\n5\\,\\log\\,\\left[{\\cal L}(c)^2/{\\cal E}(c){\\cal R}(c)\\right]-5\\,\\log\\,A +\n10\\,\\log\\,\\Upsilon_{V,0} + 234.461\\ . \n\\label{eq:a15}\n\\end{equation}\n\nFinally, a correlation between core velocity dispersion and total cluster\nluminosity can be obtained directly from the definition $E_b=\\sigma_0^4\nr_0 {\\cal E}(c)/G$, the empirical scaling $E_b/{\\rm erg} = A\n(L/L_\\odot)^{\\gamma}$, and equation (\\ref{eq:a11}):\n\\begin{equation}\n\\log\\,\\sigma_0=\n0.5(\\gamma-1)\\,\\log\\,L -\n0.5\\,\\log\\,\\left[{\\cal E}(c)/{\\cal L}(c)\\right] +\n0.5\\,\\log\\,A - 0.5\\,\\log\\,\\Upsilon_{V,0} - 21.7218\n\\label{eq:a16}\n\\end{equation}\nfor $\\sigma_0$ in units of km s$^{-1}$. This version of the $E_b(L)$\nrelation in the Milky Way is compared to data in Fig.~\\ref{fig18} above.\n\nThe six quantities on the left-hand sides of equations\n(\\ref{eq:a11})--(\\ref{eq:a16}) are all expressed in terms of the\nKing-model basis $L$, $c$, $\\Upsilon_{V,0}$, and $E_b=A(L/L_\\odot)^{\\gamma}$\n(once more, any effects of, say, Galactocentric position and metallicity are\neasily allowed to enter through these variables; see \\S5). Moreover, any\ncorrelation between any other set of globular cluster observables may be\nderived from equations (\\ref{eq:a11})--(\\ref{eq:a16})---the results of\n\\S A.1, for example, could be thus obtained. As for {\\it any} collection\nof single-mass, isotropic King-model clusters, there is no {\\it new} physical\ncontent in empirical scalings beyond those existing just among $L$, $c$,\n$\\Upsilon_{V,0}$ and $E_b$. This follows necessarily from the fact that this\nchosen basis is (by definition) complete.\n\n\\section{DIMENSIONLESS FUNCTIONS OF CENTRAL CONCENTRATION}\n\nThis Appendix lists ad hoc polynomial fits that describe the variation of\ncertain derived quantities in single-mass, isotropic \\markcite{kin66}King\n(1966) models, as functions of the central concentration $c\\equiv\\log\\,\n(r_t/r_0)$. These fits have been obtained by comparing with numerical\nintegrations of King models with $0.12\\la c\\la 3.6$, or $0.5\\le W_0\\le 16$\nfor $W_0$ the (normalized) central potential. The fits generally will\n{\\it not} be reliable if extrapolated beyond this range in $c$, but all\nGalactic globular clusters are described by $0.5\\le c\\le 2.5$.\n\nThe projected, or line-of-sight, velocity dispersion at the center of a model\ncluster is given in terms of the velocity {\\it scale parameter}\n$\\sigma_0$---which differs from the true one-dimensional velocity dispersion\nfor low-concentration models---by\n\\begin{equation}\n\\log\\,\\left(\\sigma_{p,0}/\\sigma_0\\right)=-14.203\\,\\log\\,\\left[\n1+0.11313\\times10^{-1.1307\\,c}\\right]\\ ,\n\\label{eq:b1}\n\\end{equation}\nwhich deviates from the curve in Fig.~\\ref{fig1} above by less than 0.005 dex\nfor $c\\ga0.5$.\n\nThe dimensionless binding energy (eq.~[\\ref{eq:22}] above, and the top right\npanel of Fig.~\\ref{fig1}) may be fit by\n\\begin{eqnarray}\n\\log\\,{\\cal E}\\equiv \\log\\,\\left(GE_b/\\sigma_0^4r_0\\right) & = &\n-1.64893+2.82056\\,c+9.38926\\,c^2-26.0275\\,c^3+30.6474\\,c^4 \\nonumber \\\\\n & & -20.7951\\,c^5+8.61423\\,c^6-2.13978\\,c^7+0.291982\\,c^8 \\nonumber \\\\\n & & -0.0167994\\,c^9\\ ,\n\\label{eq:b2}\n\\end{eqnarray}\nwith an absolute error of $\\la0.01$ dex (relative error $\\la1\\%$) for\n$c\\ga0.5$.\n\nThe central intensity, or surface density, in terms of the central volume\ndensity $j_0$ and the King radius $r_0$, is (cf.~\\markcite{dja93}Djorgovski\n1993a, and the bottom left panel of Fig.~\\ref{fig1} above)\n\\begin{equation}\n\\log\\,{\\cal I}_0\\equiv \\log\\,\\left(I_0/j_0 r_0\\right) =\n0.3022 - 7.5726\\,\\log\\,\\left[1+0.2180\\times 10^{-1.1291\\,c}\\right]\\ ,\n\\label{eq:b3}\n\\end{equation}\nto within an absolute error of $\\la0.005$ dex in the interval $0.5\\la c\\la\n3.6$. [Note that in the limit $c\\rightarrow\\infty$, this formula gives\n${\\cal I}_0\\rightarrow 2.005$, slightly lower than the correct value for\nan isothermal sphere, ${\\cal I}_0(\\infty)=2.018$.] For these single-mass\nmodels, which have spatially constant mass-to-light ratios,\n${\\cal I}_0$ is also equal to the dimensionless central {\\it mass} surface\ndensity, $\\Sigma_0/\\rho_0r_0$.\n\nThe {\\it projected} half-light radius, $R_h$, is related to the King radius,\n$r_0\\equiv(9\\sigma_0^2/4\\pi G \\rho_0)^{1/2}$, by\n\\begin{eqnarray}\n\\log\\,{\\cal R}\\equiv\\log\\,\\left(R_h/r_0\\right) & = &\n-0.602395+1.36023\\,c-1.67086\\,c^2+2.65848\\,c^3-2.71152\\,c^4 \\nonumber \\\\\n & & +1.42555\\,c^5 -0.274551\\,c^6-0.0381277\\,c^7+0.0217849\\,c^8 \\nonumber \\\\\n & & -0.00225252\\,c^9\\ ,\n\\label{eq:b4}\n\\end{eqnarray}\nwhich differs by no more than 0.007 dex from the $\\log\\,{\\cal R}$ obtained by\nnumerically integrating any King model with $0.12\\la c\\la 3.6$ (bottom right\nof Fig.~\\ref{fig1} above).\n\nFinally, the dimensionless total luminosity (top panel of Fig.~\\ref{fig2})\nis given by\n\\begin{eqnarray}\n\\log\\,{\\cal L}\\equiv\\log\\,\\left(L/j_0r_0^3\\right) & = &\n-0.725444+1.90743\\,c+4.63720\\,c^2-13.0266\\,c^3+14.8724\\,c^4 \\nonumber \\\\\n & & -9.43699\\,c^5+3.39098\\,c^6-0.578169\\,c^7-0.00512814\\,c^8 \\nonumber \\\\\n & & +0.0162534\\,c^9-0.00165078\\,c^{10}\\ .\n\\label{eq:b5}\n\\end{eqnarray}\nThe relative error of this expression is $\\la0.5\\%$, in $\\log\\,{\\cal L}$,\nfor any $0.5\\la c\\la3.6$; it may be compared to the fit given by\n\\markcite{dja93}Djorgovski (1993a), which applies over a more restricted\nrange in central concentration. 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P. 1991, MNRAS, 253, 710\n\\reference{ves97} Vesperini, E. 1997, MNRAS, 287, 915\n\n\\end{references}\n\n\\clearpage\n\n\\figcaption[fig1.eps]{Dimensionless functions of central concentration for\nsingle-mass, isotropic King (1966) models. Analytic expressions for each are\ngiven in Appendix B. The observed concentrations of Milky Way globulars lie\nin the range $0.5\\la c\\la 2.5$.\n\\label{fig1}}\n\n\\figcaption[fig2.eps]{{\\it Top panel}: Dimensionless total luminosity\n${\\cal L}$ of King models, as a function of central concentration. See\nalso equation (\\ref{eq:b5}). {\\it Bottom panel}: Comparison of model\nluminosities ${\\cal L}(c)j_0r_0^3$ to the directly observed\n$L=0.4\\left(4.83-M_V\\right)$ for globulars from Harris (1996). Filled circles\nare regular, King-model clusters; open squares are post--core-collapse\nobjects. Straight line is the equality $\\log\\,L_{\\rm mod}=\\log\\,L$, and\nthe typical observational errorbar on $\\log\\,L_{\\rm mod}$ is shown in the\nupper left corner.\n\\label{fig2}}\n\n\\figcaption[fig3.eps]{Determination, according to equation (\\ref{eq:23}), of\nthe mean core mass-to-light ratio of globular clusters in the Milky Way. \nFilled circles correspond to 39 King-model clusters tabulated by Pryor\n\\& Meylan (1993); open circles have $\\rho_0$ computed for these objects using\nthe directly observed $\\sigma_{p,0}$ instead of the model velocity scale\n$\\sigma_0$. Open squares represent PCC clusters. The solid line has the\nequation $\\log\\,\\rho_0=0.16+\\log\\,j_0$, obtained from a least-squares fit of\nthe regular-cluster data only. The errorbars at upper left show typical\nobservational uncertainties in $\\rho_0$ and $j_0$.\n\\label{fig3}}\n\n\\figcaption[fig4.eps]{Concentration parameters and binding energies, as\nfunctions of total luminosity, for globulars with measured central velocity\ndispersions (Pryor \\& Meylan 1993). Filled circles correspond to\nregular, King-model clusters; open squares, to PCC objects. The three lower\nrows present the results of calculating $E_b$ according to each of equations\n(\\ref{eq:31}). Integrated absolute magnitudes are taken from the catalogue of\nHarris (1996), while total masses are obtained by Pryor \\& Meylan (1993)\nfrom fits of multi-mass, anisotropic King models.\n\\label{fig4}}\n\n\\figcaption[fig5.eps]{Confirmation that the binding energy computed using\nequation (\\ref{eq:31}c) (with $\\log\\,\\Upsilon_{V,0}\\equiv0.16$) is equal to\nthat obtained from (\\ref{eq:31}a) for the regular globulars (filled circles)\nin the catalogue of Pryor \\& Meylan (1993). Open squares again correspond to\nthe PCC clusters in their sample. This plot is equivalent to Fig.~\\ref{fig3}.\n\\label{fig5}}\n\n\\figcaption[fig6.eps]{Central concentrations and binding energies of 109\nKing-model globulars and 30 PCC clusters (filled circles and open squares)\nin the catalogue of Harris (1996). The straight line in the top panel traces\nthe rough relation $c=-0.57+0.4\\,\\log\\,L$. The solid line in the bottom panel\nrepresents the least-squares fit $\\log\\,E_b=39.89+2.05\\,\\log\\,L$; dashed lines\nshow the $3\\sigma$ limits (from eq.~[\\ref{eq:33}]), $\\log\\,E_b=41.09+1.8\\,\n\\log\\,L$ and $\\log\\,E_b=38.69+2.3\\,\\log\\,L$.\n\\label{fig6}}\n\n\\figcaption[fig7.eps]{Monovariate correlations $\\log\\,r_0$ vs.~$\\log\\,L$\nand $\\log\\,j_0r_0$ vs.~$\\log\\,L$ for Galactic globulars in the Harris (1996)\ncatalogue, as poor reflections of the more fundamental correlation between\n$\\log\\,E_b$ and $\\log\\,L$. Filled circles are regular clusters; open squares\nare PCC objects. The straight line in the top panel has $\\log\\,r_0=\n1.63-0.3\\,\\log\\,L$; in the middle panel, $\\log\\,j_0r_0=-2.86+1.25\\,\\log\\,L$;\nin the bottom panel, $\\log\\,j_0^2r_0^5=-1.33+1.7\\,\\log\\,L$.\n\\label{fig7}}\n\n\\figcaption[fig8.eps]{Dependence of cluster half-light radius on luminosity \nand Galactocentric radius. Point types are the same as in Fig.~\\ref{fig7}.\n$R_h$ is seen to increase systematically with $r_{\\rm gc}$ (the line in\nthe top right panel is $\\log\\,R_h=0.226+0.4\\,\\log\\,r_{\\rm gc}$), but is\nessentially independent of $L$ at a given position in the Milky Way.\n$R_h^*$ is the normalized quantity $R_h(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.4}$;\nthe dashed line in the bottom plot has $\\log\\,R_h^*\\equiv0.59$.\n\\label{fig8}}\n\n\\figcaption[fig9.eps]{Insensitivity of three of the basic King-model cluster\nparameters to the ``environmental'' factors of Galactocentric position and\ncluster metallicity. Open squares again represent PCC clusters; note that $c$\nhas been {\\it arbitrarily} set to 2.5 for many of these.\n\\label{fig9}}\n\n\\figcaption[fig10.eps]{Dependence of cluster binding energy on Galactocentric\nradius. Straight line in the bottom panel represents the fit $E_b\\,\nL^{-2.05}\\propto r_{\\rm gc}^{-0.4}$, as in equation (\\ref{eq:34}), for\nregular clusters from the Harris (1996) catalogue (filled circles). The\nobservational errorbar shown for $\\log\\,E_b$ is $\\pm0.5$ dex.\n\\label{fig10}}\n\n\\figcaption[fig11.eps]{Independence of binding energy and metallicity for the\n139 clusters taken from Harris (1996).\n\\label{fig11}}\n\n\\figcaption[fig12.eps]{Concentrations $c$ and normalized binding energies\n$E_b^*\\equiv E_b(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.4}$ for regular and PCC\nGalactic globulars within and beyond $r_{\\rm gc}=8$ kpc. Dashed lines\nin both top panels are $c=-1.03+0.5\\,\\log\\,L$ and $c=-2.44+0.8\\,\\log\\,L$.\nThe r.m.s.~scatter in $c$ is $\\Delta=0.29$ dex (excluding Palomar 1) at\n$r_{\\rm gc}>8$ kpc, and $\\Delta=0.35$ for $r_{\\rm gc}<8$ kpc. Solid line in\nthe bottom panels is the fit $\\log\\,E_b^*=39.86+2.05\\,\\log\\,L$, and dashed\nlines there are the $3\\sigma$ limits (from eq.~[\\ref{eq:34}]) $\\log\\,E_b^*\n=41.06+1.8\\,\\log\\,L$ and $\\log\\,E_b^*=38.66+2.3\\,\\log\\,L$. The r.m.s.~scatter\nin $\\log\\,E_b^*$ is $\\pm0.5$ dex.\n\\label{fig12}}\n\n\\figcaption[fig13.eps]{Fundamental plane of Galactic globular clusters (109\nregular and 30 core-collapsed) in the catalogue of Harris (1996). The\northogonal axes in $\\epsilon$-space are defined in equation (\\ref{eq:eps}).\nThe $(\\epsilon_1,\\epsilon_2)$ and $(\\epsilon_1, \\epsilon_3)$ cross-sections of\nthis volume provide edge-on views of the fundamental plane, defined by\n$\\epsilon_1=39.86$ (eq.~[\\ref{eq:34}], drawn as bold solid lines). A face-on\nview of the fundamental plane is found in the $(\\epsilon_2,\\epsilon_3)$ slice\nof $\\epsilon$-space. Clusters do not fill this plane uniformly but are\nconfined, particularly at large galactocentric distances, to a fairly narrow\nband within it. The dashed line is a fit $\\epsilon_3=-12.5+0.13\\,\\epsilon_2$\nto the globulars (excluding Palomar 1) with $r_{\\rm gc}>8$ kpc. Most of the\nPCC clusters appear to fall away from the fundamental plane here, but these\nobjects are generally {\\it not} well described by King models.\n\\label{fig13}}\n\n\\figcaption[fig14.eps]{{\\it Left panels}: Effects of cluster non-homology on\ntwo empirical, bivariate correlations involving {\\it half-light}\nparameters of Galactic globulars. The functions ${\\cal L}(c)$, ${\\cal R}(c)$,\nand ${\\cal E}(c)$ are given individually in Figs.~\\ref{fig1} and \\ref{fig2},\nand in Appendix B. Points are placed at the observed $c$-values of the 39\nregular clusters in the catalogue of Pryor \\& Meylan (1993). {\\it Right\npanels}: Observed correlations in the Pryor \\& Meylan cluster sample. Filled\ncircles are their regular clusters, and the 17 open squares are their PCC\nclusters. Open circles plot the uncorrected $\\sigma_{p,0}$ for the regular\nobjects, rather than the model velocity scales $\\sigma_0$. Solid lines in the\ntop and bottom panels represent equations (\\ref{eq:41}b) and (\\ref{eq:42}b);\ndashed lines are least-squares fits to the data (filled circles). The distant\ncluster NGC 2419 is noted as an outlier (see Fig.~\\ref{fig18}).\n\\label{fig14}}\n\n\\figcaption[fig15.eps]{{\\it Left panels}: Effects of cluster non-homology on\ntwo empirical, bivariate correlations involving {\\it core}\nparameters of Galactic globulars. The functions ${\\cal I}_0(c)$, ${\\cal L}(c)$,\nand ${\\cal E}(c)$ are given individually in Figs.~\\ref{fig1} and \\ref{fig2},\nand in Appendix B. The dashed line in the bottom panel shows the rough\nscaling $0.25\\,\\log\\,\\left({\\cal L}^{2.05}/{\\cal E}{\\cal I}_0^{2.05}\\right)\n\\approx const.+0.17\\,c$. {\\it Right panels}: Correlations observed for the\nPryor \\& Meylan (1993) clusters. Point types have the same meaning as in\nFig.~\\ref{fig14}. Solid line in the top panel represents equation\n(\\ref{eq:41}a) and is indistinguishable from a least-squares fit to the\nregular-cluster data. Solid line in the bottom panel is equation (\\ref{eq:42}a)\nwith an intercept of 4.147, estimated by assuming a constant $\\langle 0.25\\,\n\\log\\,({\\cal L}^{2.05}/{\\cal E}{\\cal I}_0^{2.05})\\rangle=0.204$ for all\n39 King-model clusters. The least-squares fit (dashed line) is quite\ndifferent ($\\log\\,\\sigma_0-0.775\\,\\log\\,r_0=-0.246\\,\\mu_{V,0}+4.860$)\nbecause of the significant non-homology in this case.\n\\label{fig15}}\n\n\\figcaption[fig16.eps]{Virial ratio $2E_k/E_b$ as a function of radius inside\nthree single-mass, isotropic King (1966) models bracketing the range of central\nconcentration observed for Galactic globulars. Cluster cores, defined by $r\\le\nr_0$, in general do {\\it not} obey a simplified virial theorem of the form\n$2E_k=E_b$.\n\\label{fig16}}\n\n\\figcaption[fig17.eps]{Source of the monovariate correlation between\n$\\log\\,r_0$ and $\\log\\,L$ in Fig.~\\ref{fig7}. {\\it Top panel}: The non-homology\nterm $\\log\\,({\\cal L}^2/{\\cal E})$ as a function of central concentration.\nSolid curve is obtained from numerical integrations of King models, points are\nplaced at the observed $c$-values of the 109 regular clusters in the catalogue\nof Harris (1996), and the dashed line shows $\\log\\,({\\cal L}^2/{\\cal E})\\approx\nconst.+0.7\\,c$. {\\it Bottom panel}: The full correlation involving $\\log\\,r_0$,\n$c$, $\\log\\,L$, and $\\log\\,r_{\\rm gc}$. Data for 30 PCC clusters from Harris\n(1996) are also shown (open squares). Solid line is equation (\\ref{eq:51}a):\n$\\log\\,r_0+\\log\\,({\\cal L}^2/{\\cal E})=1.681-0.05\\,\\left[\\log\\,L-8\\,\n\\log(r_{\\rm gc}/8\\,{\\rm kpc})\\right]$; the dashed line, with an intercept of\n1.63, is the least-squares fit to the regular-cluster data (filled circles).\n\\label{fig17}}\n\n\\figcaption[fig18.eps]{{\\it Top panel}: Monovariate correlation between\n$\\log\\,\\sigma_0$ and $\\log\\,L$ for clusters from Pryor \\& Meylan (1993).\nPoint types have the same meaning as in Fig.~\\ref{fig14}. The observational\nerrorbar on $\\log\\,\\sigma_0$ is $\\pm0.09$ dex. The straight line is equation\n(\\ref{eq:51}f) after substituting appropriate averages for the ratio\n${\\cal E}(c)/{\\cal L}(c)$ and $r_{\\rm gc}$ (see text). {\\it Bottom panel}: The\nfull correlation expected on the basis of the fundamental-plane constraints on\n$\\Upsilon_{V,0}$ and $E_b^*$. Solid line is equation (\\ref{eq:51}f); dashed\nline is a least-squares fit to the regular-cluster data (filled circles).\n\\label{fig18}}\n\n\\figcaption[fig19.eps]{{\\it Top left}: Monovariate correlation between\n$\\log\\,r_0$ and $\\mu_{V,0}$ for globulars in the catalogue of Harris (1996).\nSolid points refer to the 109 King-model clusters; open squares, to the 30 PCC\nobjects. The observed r.m.s.~scatter in $\\log\\,r_0$ exceeds the observational\nerrorbar of $\\pm0.1$ dex. {\\it Top right}: Real variations in the ``core\nmass,'' $M_0\\propto j_0r_0^3$. {\\it Bottom left}: Deviations from the line\nexpected if core mass were a constant are not random, but correlated with\ntotal luminosity. {\\it Bottom right}: The first three panels are explained as\nresults of the behavior of {\\it total} luminosity as a function of $c$ in King\nmodels, combined with the definition of core surface brightness. The straight\nline is equation (\\ref{eq:52}).\n\\label{fig19}}\n\n\\setcounter{figure}{0}\n\n\\plotone{fig1.eps}\n\\figcaption[fig1.eps]{}\n\n\\plotone{fig2.eps}\n\\figcaption[fig2.eps]{}\n\n\\plotone{fig3.eps}\n\\figcaption[fig3.eps]{}\n\n\\plotone{fig4.eps}\n\\figcaption[fig4.eps]{}\n\n\\plotone{fig5.eps}\n\\figcaption[fig5.eps]{}\n\n\\plotone{fig6.eps}\n\\figcaption[fig6.eps]{}\n\n\\plotone{fig7.eps}\n\\figcaption[fig7.eps]{}\n\n\\plotone{fig8.eps}\n\\figcaption[fig8.eps]{}\n\n\\plotone{fig9.eps}\n\\figcaption[fig9.eps]{}\n\n\\plotone{fig10.eps}\n\\figcaption[fig10.eps]{}\n\n\\plotone{fig11.eps}\n\\figcaption[fig11.eps]{}\n\n\\plotone{fig12.eps}\n\\figcaption[fig12.eps]{}\n\n\\plotone{fig13.eps}\n\\figcaption[fig13.eps]{}\n\n\\plotone{fig14.eps}\n\\figcaption[fig14.eps]{}\n\n\\plotone{fig15.eps}\n\\figcaption[fig15.eps]{}\n\n\\plotone{fig16.eps}\n\\figcaption[fig16.eps]{}\n\n\\plotone{fig17.eps}\n\\figcaption[fig17.eps]{}\n\n\\plotone{fig18.eps}\n\\figcaption[fig18.eps]{}\n\n\\plotone{fig19.eps}\n\\figcaption[fig19.eps]{}\n\n\\end{document}\n"
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astro-ph0002087
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The Formation History of Globular Clusters
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[
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"author": "Dean E. McLaughlin\\inst{1,2}"
}
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The properties of old globular cluster systems in galaxy halos are used to infer quantitative constraints on aspects of star formation that are arguably as relevant in a present-day context as they were during the protogalactic epoch. First, the spatial distribution of globulars in three large galaxies, together with trends in total cluster population vs.~galaxy luminosity for 97 early-type systems plus the halo of the Milky Way, imply that bound stellar clusters formed with an essentially universal efficiency throughout early protogalaxies: by mass, always $\epsilon_{cl}=0.26\%\pm0.05\%$ of star-forming gas was converted into globulars rather than halo field stars. That this fraction is so robust in the face of extreme variations in local and global galaxy environment suggests that any parcel of gas needs primarily to exceed a {relative} density threshold in order to form a bound cluster of stars. Second, it is shown that a strict scaling between total binding energy, luminosity, and Galactocentric position, $E_b=7.2\times10^{39} \,{erg}\,(L/L_\odot)^{2.05}\,(r_{gc}/8\,{kpc})^{-0.4}$, is a defining equation for a fundamental plane of Galactic globular clusters. The characteristics of this plane, which subsumes {all other} observable correlations between the structural parameters of globulars, provide a small but complete set of facts that must be explained by theories of cluster formation and evolution in the Milky Way. It is suggested that the $E_b(L,r_{gc})$ relation specifically resulted from star formation efficiencies having been systematically higher inside more massive protoglobular gas clumps. \keywords{galaxies: fundamental parameters -- galaxies: star clusters -- globular clusters: general -- stars: formation}
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{
"name": "dempb.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\n% sample.tex -- ESLAB Conference Proceedings tutorial paper\n% ----------------------------------------------------------\n% Lines starting with \"%\" are comments; they will be ignored by LaTeX.\n%\n% NB! Use the LaTeX2e style packages!\n% You need the file EslabStyle.cls. Please, download by ftp at\n% ftp://astro.estec.esa.nl/pub/ESLAB/proceedings\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass[a4paper]{EslabStyle}\n\\usepackage{graphics}\n\n\\begin{document}\n\n\\title{The Formation History of Globular Clusters}\n\n\\author{Dean E. McLaughlin\\inst{1,2}}\n \\institute{Department of Astronomy, 601 Campbell Hall, University\n of California, Berkeley, CA 94720\n \\and Hubble Fellow}\n\n\\maketitle \n\n\\begin{abstract}\n\nThe properties of old globular cluster systems in galaxy halos are used to\ninfer quantitative constraints on aspects of star formation\nthat are arguably as relevant in a present-day context as\nthey were during the protogalactic epoch. First, the spatial distribution of\nglobulars in three large galaxies, together with trends in total cluster\npopulation vs.~galaxy luminosity for 97 early-type systems plus the halo of\nthe Milky Way, imply that bound\nstellar clusters formed with an essentially universal efficiency throughout\nearly protogalaxies: by mass, always $\\epsilon_{\\rm cl}=0.26\\%\\pm0.05\\%$ of\nstar-forming gas was converted into globulars rather than halo field stars.\nThat this fraction is so robust in the face of extreme variations\nin local and global galaxy environment suggests that any parcel of gas needs\nprimarily to exceed a {\\it relative} density threshold in order to form a bound\ncluster of stars. Second, it is shown that a strict scaling between total\nbinding energy, luminosity, and Galactocentric position, $E_b=7.2\\times10^{39}\n\\,{\\rm erg}\\,(L/L_\\odot)^{2.05}\\,(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.4}$, is a\ndefining equation for a fundamental plane of Galactic globular clusters. The\ncharacteristics of this plane, which subsumes {\\it all other} observable\ncorrelations between the structural parameters of globulars, provide a\nsmall but complete set of facts that must be explained by theories of cluster\nformation and evolution in the Milky Way.\nIt is suggested that the\n$E_b(L,r_{\\rm gc})$ relation specifically resulted from star formation\nefficiencies having been systematically higher inside more massive\nprotoglobular gas clumps.\n\n\\keywords{galaxies: fundamental parameters -- galaxies: star clusters --\nglobular clusters: general -- stars: formation}\n\\end{abstract}\n\n\\section{Introduction}\n\\label{sec:1}\n\nThe old globular cluster systems (GCSs) in galaxy halos are of especial\ninterest in a conference such as this, as they stand potentially to \nshed light on both local and global star formation in both\nprotogalactic and present-day settings. Because of their great age, their\nubiquity in galaxies of most any Hubble type, and their impressive spatial\nextent (globulars can be found as far as 100 kpc away from the centers of\nlarge galaxies), the integrated properties of GCSs clearly had to have been\ninfluenced by very general, large-scale star-formation processes in the\nearly universe. But at the same time, most new stars today, whether in\nthe Galactic disk or in galaxy mergers and starbursts, are born not in\nisolation\nbut in groups. To be sure, the formation of a bona fide star cluster is a\n{\\it rare} event (only a very small fraction of young stellar groups emerge\nfrom their natal clumps of gas as gravitationally bound units) but, as will be\nargued here, it is one that occurs {\\it regularly}. Thus, individual globular\nclusters must also be viewed---even if in a limit---as the products of a\nrobust mode of smaller-scale star formation that has always been viable.\n\nIt should come as no surprise, then, that there is no definitive\ntheoretical description of the formation history of globular clusters;\nwhile some concepts have been identified that do seem likely to survive as\nelements of a correct theory in the future, at this point there is simply no\nmodel that can claim completeness. Detailed discussions of the many theories\nalready in the literature may be found in, e.g., \\cite*{ash98} or\n\\cite*{mey97}. The focus here will instead be on recent progress in\nextracting quantitative and (as nearly as possible) model-independent\nconstraints from the data on many GCSs. A similarly empirical discussion is\ngiven by \\cite*{har00}, with an eye mostly to implications for large-scale\naspects of galaxy formation and evolution (see also \\cite{ash98}). In what\nfollows, particular emphasis will be placed on applications to the\nproblem of {\\it generic} star formation on subgalactic scales.\n\nA serious concern, when trying to use GCSs in this way, is the influence of\ndynamical evolution on the gross properties of cluster systems that\nhave been immersed for a Hubble time in the tidal fields of their parent\ngalaxies. Two-body relaxation and evaporation, disk- and bulge-shock heating, \nchaotic scattering or disruption by a compact nucleus, and\ndynamical friction: all of these processes whittle away at clusters\nindividually and collectively (\\cite{spi87}; \\cite{agu88}; \\cite{ost89};\n\\cite{cap93}; \\cite{mwa97}; \\cite{mwb97}; \\cite{mwc97}; \\cite{ves97}). In the\ncase of the Milky Way particularly, the net effect is to define a roughly\ntriangular region in mass--radius space, within which globulars are predicted\nto survive a 10-Gyr dynamical onslaught (\\cite{fal77})---the implication\nbeing that any clusters born outside such a ``survival triangle'' would have\ndisappeared, taking with them vital information on their birth properties.\nHowever, further investigation shows that Milky Way clusters located at large\nGalactocentric radii ($r_{\\rm gc}\\ga 3$ kpc, roughly the effective radius of\nthe bulge) {\\it do not fill} their expected survival triangles (\\cite{cap84}; \n\\cite{gne97}). Similarly, evolutionary calculations geared to conditions in\nthe giant elliptical M87 (\\cite{mwb97}) suggest that the damage done to an\ninitial GCS may be largely confined to within an effective radius in that\ngalaxy as well. Thus, there are some features of globular clusters, and of\nGCSs, that are {\\it not} dictated purely by evolution from some completely\nobscured initial conditions, and while care must be taken in identifying such\nobservables, the task is not an impossible one.\n\nFollowing the suggestion that large fractions of the GCSs in ellipticals may\nhave formed in major mergers (e.g., \\cite{sch87}; \\cite{ash92}), and the\nrelated discovery of young, massive star clusters in systems like the Antennae\ngalaxies (\\cite{whi95}), much recent discussion in this field has centered on\nthe interpretation of (often) bi- and multimodal distributions of globular\ncluster colors (as indicators of integrated metallicity) in relation to their\nhost galaxies' dynamical histories (e.g., \\cite{zep93}; \\cite{for97};\n\\cite{cot98}; \\cite{kis98}; \\cite{kig99}; \\cite{cot00}).\nHowever, as will be discussed further in \\S\\ref{sec:3}, metallicity is\ncompletely decoupled from the other basic properties of\nindividual globulars in the Milky Way; thus, while GCS colors are of interest\nin the context of galaxy formation and chemical evolution, they seem to be of\nmarginal importance to the star-formation process itself. In this connection,\nit is worth noting explicitly that literally thousands of genuinely old\nglobulars have now been identified, in many galaxies besides our own, with\ncolors as red as or redder than solar: {\\it high metallicity has never posed\nany apparent obstacle to the formation of massive star clusters}. This\ncautions against theories of globular formation such as those of\n\\cite*{fal85} and \\cite*{mur93}, which, at least in their current form, are\nable to account only for metal-poor objects.\n\nOf rather more direct relevance to the small-scale problem are the\nluminosity or mass functions of cluster systems. It is well known that the\noverall range of Galactic globular cluster masses, $m\\sim 10^4$--$10^6\\\nM_\\odot$, and the mean value $\\langle m\\rangle=2.4\\times10^5\\ M_\\odot$,\nare essentially universal properties of other GCSs.\nTraditionally, theories of globular cluster formation attempted to explain\njust this basic mass scale (e.g., \\cite{pee68}; \\cite{fal85}).\nMore recently, however, attention has turned to the full {\\it\nmass spectrum}, $d{\\cal N}/dm$ (the number of clusters with mass $m$ in a\nsingle galaxy), which---in the regime usually observed, $m\\ga 10^5\\ \nM_\\odot$---is similar (though not identical) from galaxy to galaxy; shows no\ndetectable variations with radius in any one system; and is remarkably similar\nto the mass function, $d{\\cal N}/dm\\propto m^{-1.7}$ or so, of the dense gas\nclumps currently forming stars in the giant molecular clouds of the Milky Way\ndisk (\\cite{har94}). These facts have suggested a general physical picture,\ndeveloped by \\cite*{har94} building on earlier arguments by\n\\cite*{lar88} and \\cite*{lar93}, in which handfuls of globulars form in each\nof many protogalactic fragments whose gas masses (of order $10^9\\ M_\\odot$),\nsizes, and internal velocity dispersions correspond to disk GMCs scaled up by\nsome three orders of magnitude in mass. Such a picture has the obvious appeal\nof being at least conceptually consistent both with current models of\nhierarchical galaxy formation (there is clearly some affinity with the classic\npicture of \\cite{sea78} as well) and with the observed pattern of present-day\nstar formation. It also has more specific attractions (e.g., the\nprotogalactic fragments and their protoglobulars are presumed to be supported\nlargely by nonthermal mechanisms, thus allowing for metal-rich protoglobulars\nwith the correct mass scale) but many details remain to be worked out.\nSee \\cite*{mcl96} (and compare the rather different view of \\cite{elm97}) for\nan attempt at a quantitative theory for GCS mass spectra which, with the\n\\cite*{har94} framework as a backdrop, makes explicit use of the emerging links\nbetween present-day and protogalactic star formation.\n\nIn addition to color and luminosity distributions, photometric studies of\nextragalactic GCSs yield estimates of their specific frequencies (total\ncluster populations, normalized to the parent galaxy luminosity) and spatial\nstructures (number density of globulars as a function of galactocentric\nposition). These are the focus of \\S\\ref{sec:2}, where it is shown that a large\nsample of early-type galaxies display a common ratio of GCS mass to\ntotal mass in stars and (hot) gas---an apparently universal efficiency for the\nformation of globular clusters (\\cite{mcl99}). Finally, \\S\\ref{sec:3}\ndiscusses the binding energies of\nglobular clusters in the Milky Way (\\cite{mcl00}). It is\nshown that a strong correlation between binding energy, total cluster\nluminosity, and Galactocentric position is instrumental in defining a\nfundamental plane for Galactic globulars---which, by incorporating every\none of their many other structural correlations, systematically reduces these\ndata to the smallest possible set of {\\it independent} physical constraints\nfor theories of cluster formation and evolution.\n\n\\section{The Efficiency of Cluster Formation}\n\\label{sec:2}\n\nThe possibility that globular cluster systems can be connected not only to\ngalaxy formation, but to ongoing star formation as well, is suggested by the\nfact that this latter process operates largely in a {\\it clustered\nmode}. One dramatic example of this is the situation in the Orion B (L1630)\nmolecular cloud, where 96\\% of a complete sample of young stellar\nobjects are physically associated with just four dense clumps of gas, each\ncontaining $>300\\,M_\\odot$ of material (\\cite{lad91}; \\cite{lad92}). More\ngenerally, \\cite*{pat94} note that this is just a result of the\ndifferent power-law slopes in the mass function of molecular clumps (as above,\n$d{\\cal N}/dm\\propto m^{-1.7}$, so that the largest clumps, which always weigh\nin at $10^2$--$10^3\\,M_\\odot$, contain most of the star-forming gas mass in\nany molecular cloud) and the stellar initial mass function ($d{\\cal N}/dm\n\\propto m^{-2.35}$, putting most of the mass in young stars into $\\la1\\,\nM_\\odot$ objects). In more extreme environments, the ``super''\nstar clusters---luminous, blue, compact associations with integrated properties\nroughly consistent with those expected of young globulars---found in many\nmerging and starburst galaxies can account for as much as $\\sim$20\\% of the\nUV light from such systems (\\cite{meu95}).\n\nAgain, however, this is not to say that all, or even most, stars are born\ninto true clusters that exist for any length of time as systems with negative\nenergy. At some point during the collapse and fragmentation of a cluster-sized\ncloud of gas, the massive stars which it has formed will expel any remaining\ngas by the combined action of their stellar winds, photoionization, and\nsupernova explosions. If the {\\it cumulative} star formation efficiency (SFE)\nof the cloud, $\\eta\\equiv M_{\\rm stars}/(M_{\\rm stars}+M_{\\rm gas})$, is below\na critical threshold when the gas is lost, then the blow-out removes\nsufficient energy that the stellar group left behind is unbound and disperses\ninto the field. The precise value of this threshold depends on details of the\ndynamics and magnetic field in the gas cloud before its self-destruction, and\non the timescale over which the massive stars dispel the gas; but various\nestimates place it in the range $\\eta_{\\rm crit}\\sim 0.2$--0.5 (e.g.,\n\\cite{hil80}; \\cite{mat83}; \\cite{elm85}; \\cite{ver90}; and see \\cite{goo97}\nfor a discussion of globulars specifically).\n\nA general theory of star formation must therefore be able to anticipate the\nfinal cumulative SFE in any single piece of gas with (say) a given mass and\ndensity, and thereby predict whether or not it will form a bound cluster. No\nsuch theory yet exists. It is possible, however, to empirically estimate the\n{\\it probability} that a cluster-sized cloud of gas is able to achieve\n$\\eta>\\eta_{\\rm crit}$. This probability---or, equivalently, that fraction of\nan ensemble of massive star-forming clouds which manages to produce bound\nstellar systems---is referred to here as the efficiency of cluster formation.\nTo get a handle on this for globulars in particular, \\cite*{mcl99} works in\nterms of the {\\it mass} fraction\n\n\\begin{equation}\n\\hfil\n\\epsilon_{\\rm cl}\\equiv M_{\\rm gcs}^{\\rm init}/M_{\\rm gas}^{\\rm init}\\ \\ ,\n\\hfil\n\\label{eq:1}\n\\end{equation}\n\n\\noindent where $M_{\\rm gas}^{\\rm init}$ refers to the total gas supply that\nwas available to form stars in a protogalaxy---whether in a monolithic\ncollapse or a slower assembly of many distinct, subgalactic clumps is\nunimportant---and $M_{\\rm gcs}^{\\rm init}$ is the total mass of all globulars\nformed in that gas. The advantage of this definition for $\\epsilon_{\\rm cl}$\nis that the total mass of a GCS is expected to be very well preserved over\nthe course of dynamical evolution in a galaxy; presently observed values are\nreasonable indicators of the initial quantities. This is ultimately due to the\nfact that GCS mass spectra are shallow enough that (again, like the clumps in\nGalactic molecular clouds) most of any one system's mass is contained in its\nmost massive clusters. But most of the destruction processes mentioned in\n\\S\\ref{sec:1} operate most effectively against {\\it low}-mass globulars, which\nmay be lost in great numbers (substantially affecting the total GCS population,\n${\\cal N}_{\\rm tot}$) while decreasing the integrated $M_{\\rm gcs}$ by\nas little as $\\sim$25\\% (\\cite{mcl99}).\n\nUntil very recently, it was generally assumed that a galaxy's total luminosity,\nor stellar mass, was an adequate stand-in for $M_{\\rm gas}^{\\rm init}$. Thus,\nthe number of globulars per unit of halo light has long been taken as a direct\ntracer of the efficiency of globular cluster formation in galaxies. However,\nthis approach leads quickly to two interesting problems.\n\n\\subsection{global and local specific frequencies}\n\\label{sec:21}\n\nSpecific frequency was originally defined by \\cite*{hvd81} as a global\nproperty of galaxies. It is nominally the ratio, modulo a convenient\nnormalization, of the total GCS population to the total $V$-band light\nintegrated over an entire galaxy:\n\n\\begin{equation}\n\\hfil\nS_N\\equiv{\\cal N}_{\\rm tot}\\times 10^{0.4(M_V+15)} =\n8.55\\times10^7\\,\\left({\\cal N}_{\\rm tot}/L_{V,{\\rm gal}}\\right)\n\\hfil\n\\label{eq:2}\n\\end{equation}\n\n\\noindent Most subsequent studies of GCSs have therefore estimated their total\npopulations and cited $S_N$-values according to equation (\\ref{eq:2}). It is\nmore useful, however, following the discussion just above, to refer to total\nGCS and stellar masses; thus,\n\n\\begin{equation}\n\\hfil\nS_N \\simeq 2500\n\\left({{\\langle m\\rangle}\\over{2.4\\times10^5\\ M_\\odot}}\\right)^{-1}\n\\left({{\\Upsilon_{V,{\\rm gal}}}\\over{7\\ M_\\odot\\,L_\\odot^{-1}}}\\right)\n{{M_{\\rm gcs}}\\over{M_{\\rm stars}}}\n\\hfil\n\\label{eq:3}\n\\end{equation}\n\n\\noindent for a standard mean globular cluster mass $\\langle m \\rangle$ and a\nrepresentative stellar mass-to-light ratio, $\\Upsilon_{V,{\\rm gal}}$,\nappropriate to the {\\it cores} of large ellipticals (which value is used so as\nnot to include any nonbaryonic dark matter in the galaxy mass). Note that\n$\\langle m\\rangle$ is not observed to deviate significantly from the Milky Way\nvalue, either from galaxy to galaxy or from place to place within any one\nsystem, but that $\\Upsilon_{V,{\\rm gal}}$ {\\it does} vary systematically, as\na function of luminosity, among large ellipticals (e.g.,\n\\cite{vdm91}).\n\n\\begin{figure}[!b]\n\\resizebox{\\hsize}{2.6truein}\n{\\includegraphics{dempbf1.eps}}\n\\caption{\\rm First specific frequency problem in 97 early-type galaxies.\n\\label{fig1}}\n\\end{figure}\n\nGlobal specific frequencies in a large sample of early-type galaxies are\nshown in Fig.~\\ref{fig1}. (The GCSs of spirals are generally less populous,\nand often more difficult to identify, than those in elliptical systems; thus,\nthe data on late-type galaxies are relatively sparse.) The square points\ncorrespond to dwarf ellipticals and spheroidals, some in the Local Group (the\ntwo faintest objects are the Fornax and Sagittarius dwarfs) and others in the\nVirgo cluster (\\cite{dur96}; \\cite{mil98}); filled circles represent regular\ngiant ellipticals in a wide range of field and cluster environments (see, e.g.,\n\\cite{har91} and \\cite{kis97}); and open circles stand for the centrally\nlocated galaxies (which often are also the brightest) in a large\nnumber of groups and clusters (\\cite{bla97}; \\cite{btm97}; \\cite{har98}).\n\nThree points are immediately apparent. First, among normal gE's an average\n$S_N\\approx 5$ (roughly, $M_{\\rm gcs}/M_{\\rm stars}\\sim 0.002$) is\nindicated. Second, the specific frequencies of central\ngalaxies in groups and clusters show a systematic departure from this\n``typical'' value, increasing strongly towards brighter galaxy magnitudes.\nAnd third, while the brightest of the dwarf ellipticals have $S_N$ comparable\nto the giants, the ratio increases towards {\\it fainter} luminosities in these\nsmall systems. All in all, $S_N$ ranges over more than a factor of 20 in\nearly-type galaxies. If the ratio $M_{\\rm gcs}/M_{\\rm stars}$ were a good\napproximation to $\\epsilon_{\\rm cl}$ in equation (\\ref{eq:1}), the implication\nwould be that the basic efficiency of cluster formation also varied\ndrastically---and in a {\\it non-monotonic} fashion---from galaxy to galaxy.\nThis is the first specific frequency problem. Although it has been much\ndiscussed in the literature (see \\cite{mcl99}, \\cite{elm00}, or\n\\cite{har00} for recent reviews and references), no satisfactory explanation\n(or prediction) of it has ever been advanced.\n\nVery closely related to this, {\\it local} specific frequencies may be defined\nat different projected radii within a single galaxy, by taking the ratio\nof its GCS surface (number) density profile, $N_{\\rm cl}(R_{\\rm gc})$, and\nits $V$-band light intensity, $I_V(R_{\\rm gc})$, normalized as in equation\n(\\ref{eq:2}). (This is then proportional to the ratio of cluster and field-star\n{\\it mass} densities, just as in eq.~[\\ref{eq:3}].) Beyond an effective radius\nor so (where the effects of dynamical evolution on the GCS are presumably\nminimized), it is found in {\\it some} galaxies that local specific frequencies\n{\\it increase outwards}; in others, they remain constant. Equivalently,\nsome galaxies' GCSs are significantly more extended than their stellar halos,\nwhile others' GCS and field-star distributions trace each other accurately on\nlarge spatial scales. If the simple assumption $S_N\\propto\\epsilon_{\\rm cl}$\nwere applied here, it would appear to suggest that bound stellar\nclusters were sometimes (but not always, and for reasons completely unknown)\n{\\it more} likely to form at {\\it larger} distances from the centers of\ngalaxies, in gas that was presumably at lower ambient densities and pressures.\nThis is the second specific frequency problem.\n\n\\begin{figure}[!t]\n\\resizebox{\\hsize}{2.9truein}\n{\\includegraphics{dempbf2.eps}}\n\\caption{\\rm Second specific frequency problem as seen in M87. A distance of\n15 Mpc to the galaxy has been assumed.\n\\label{fig2}}\n\\end{figure}\n\nFigure \\ref{fig2} illustrates this situation in M87, the cD\ngalaxy at the center of the Virgo Cluster and the first system for which the\neffect was shown convincingly to exist (\\cite{har86}). The solid line in the\ntop panel is the galaxy light profile, derived from the surface photometry of\n\\cite*{dvn78}, and the points trace the projected GCS number\ndensities (in units of pc$^{-2}$ and scaled up for a direct\ncomparison with the stellar densities) from the combined data of\n\\cite*{mcl93}, \\cite*{mcl95}, and \\cite*{har86} (see \\cite{mcl99}). It is\nclear that the radial gradient of $N_{\\rm cl}$ is significantly shallower than\nthat of $I_V$, leading directly to the strongly increasing local specific\nfrequency profile in the bottom panel.\n\nThe horizontal line in the bottom of Fig.~\\ref{fig2} marks the globally\naveraged $S_N$ for M87 as a whole: $14.1\\pm1.6$, three times higher than\n``normal'' for giant ellipticals (\\cite{har98}). That is, M87 also suffers\nfrom the first specific frequency problem. This is one strong hint that the two\n$S_N$ problems are really just different aspects of a single basic phenomenon.\nWhat this might be has become clear only with a\nhomogeneous survey of the central galaxies (simply BCGs hereafter)\nin 21 Abell clusters by \\cite*{bla97}, \\cite*{btm97}, and \\cite*{bla99}.\n\n\\subsection{x-ray gas and a universal $\\epsilon_{\\rm cl}$} \n\\label{sec:22}\n\nBlakeslee has found (see also \\cite{wes95}) that the global specific\nfrequencies of BCGs increase systematically with the soft X-ray luminosity\n(averaged over $\\sim$500-kpc scales) of the hot gas in their parent clusters.\nHe then uses the details of this correlation to argue that the number of\nglobulars in the cores of galaxy clusters scales in direct proportion to the\ntotal mass there, with one found for every 1--$2\\times10^9\\,M_\\odot$ of\nstars, gas, {\\it and dark matter}. This implies that the first $S_N$ problem\nstems (in BCGs, at least) from a tendency for brighter galaxies\nto be ``underluminous,'' for the amount of gas and dark matter associated with\nthem, rather than overabundant in globular clusters. Strictly from a\nstar-formation point of view, however, only the baryons are of interest; thus,\n\\cite*{har98} suggest, in essence, that if the dark matter were left out,\nthe global mass ratio\n\n\\begin{equation}\n\\hfil\n\\widehat{\\epsilon}_{\\rm cl}=M_{\\rm gcs}/(M_{\\rm gas}+M_{\\rm stars})\n\\hfil\n\\label{eq:4}\n\\end{equation}\n\n\\noindent might itself be constant, not only among BCGs but in other galaxies\nas well.\\footnotemark\n\\footnotetext{As \\cite*{bla99} discusses at length, his\nratio of globulars per unit total mass and the ratio of equation\n(\\ref{eq:4}) can {\\it both} be constants in BCGs if the baryon fraction in\nthe cores of galaxy clusters is also roughly universal (on the order of\n10\\%). But as reasonable as it may seem, this possibility is in general\nunproven, and it is not obvious a priori that the two efficiencies are\nnecessarily equivalent. Also, the constancy of Blakeslee's ratio has been\ndemonstrated neither globally for objects other than BCGs nor locally as a\nfunction of position inside any one galaxy. The behavior of $\\widehat{\\epsilon}\n_{\\rm cl}$ {\\it in general} can therefore not be anticipated from Blakeslee's\nwork.}\nThe first specific frequency problem would still arise more or less\nas Blakeslee suggested, with the (observed) larger gas fractions\n$M_{\\rm gas}/M_{\\rm stars}$ in brighter galaxies resulting also in\na higher global $S_N\\propto M_{\\rm gcs}/M_{\\rm stars}$. In addition,\n\\cite*{mcl99} notes that if the local $\\widehat{\\epsilon}_{\\rm cl}$---defined\nin the obvious way as a ratio of densities---were also constant\nas a function of radius in galaxies, then the fact that the X-ray gas in\nellipticals tends to be hotter and more spatially extended than the stellar\ndistribution could cause the second specific frequency problem in\ngas-rich galaxies that also have a high global $S_N$.\n\nThe underlying idea here is, of course, that the present-day sum $(M_{\\rm gas}\n+ M_{\\rm stars})$ should be a better indicator of the ``initial'' gas mass in\nlarge galaxies, and that equation (\\ref{eq:4}) may therefore be more accurate\nthan $S_N$ as an estimate of the true cluster formation efficiency in equation\n(\\ref{eq:1}). Admittedly, $\\widehat{\\epsilon}_{\\rm cl}$ is still only an\nobservable {\\it approximation} to $\\epsilon_{\\rm cl}$; indeed, in a\nhierarchical universe it may be difficult to say precisely what is meant by\n$M_{\\rm gas}^{\\rm init}$ in the first place. Particularly in a large galaxy\nwhich may have accreted gas (and stars and globulars) over extended lengths of\ntime, the observable $\\widehat{\\epsilon}_{\\rm cl}$ must be viewed as a\nmass-weighted average over a complex evolutionary history including a\npotentially large number of galaxy interactions and many discrete\nstar-formation episodes. However, the current ratio of $M_{\\rm gcs}$ to\n$(M_{\\rm gas}+M_{\\rm stars})$ does have an essentially universal value in old\nGCSs---including those in regular gE's and early-type dwarfs as well as\nBCGs---arguing that it may be a good reflection after all of the real\n$\\epsilon_{\\rm cl}$.\n\n\\begin{figure}[!t]\n\\resizebox{\\hsize}{2.9truein}\n{\\includegraphics{dempbf3.eps}}\n\\caption{\\rm Constant {\\it local} cluster formation efficiency in M87, M49,\nand NGC 1399 (McLaughlin 1999). Bold lines in all panels trace the {\\it sum}\nof star and gas surface densities. Broken vertical lines mark the stellar\neffective radius of each galaxy.\n\\label{fig3}}\n\\end{figure}\n\nFigure \\ref{fig3} shows this first for the {\\it local} $\\widehat{\\epsilon}\n_{\\rm cl}$ in M87 and in the bright ellipticals M49 (also in the Virgo\nCluster) and NGC 1399 (BCG in the Fornax Cluster): The ratio of\nprojected GCS mass densities ($\\Sigma_{\\rm cl}\\equiv\\langle m\\rangle\\,N_{\\rm\ncl}$) to the sum of stellar and gas mass densities ($\\Upsilon_{V,{\\rm gal}}\\,\nI_V + \\Sigma_{\\rm gas}$, with $\\Upsilon_{V,{\\rm gal}}$ measured separately for\neach system) is constant beyond an effective radius in the\ngalaxies.\\footnotemark\n\\footnotetext{The departure of the GCS densities from the stellar profiles at\nsmaller radii in M87 and M49 is undoubtedly significant, but it is not clear\nwhether this is due to a real decrease in the true cluster formation\nefficiency there, or to dynamical depletion of the initial GCS, or to\nsubstantial dissipation in the gas that formed the field stars (after the\nglobulars were already in place) in the innermost regions of the galaxies.}\nThe construction of the individual density profiles is discussed in detail by\n\\cite*{mcl99}, where a comparison of the deprojected quantities is also made,\nconfirming the basic result and giving essentially the same numbers\nfor $\\widehat{\\epsilon}_{\\rm cl}$.\nEvidently, including the gas does alleviate the second specific frequency\nproblem, in just the sense suggested above: $S_N$ increases with radius in M87\nbecause of a locally varying gas-to-star mass ratio, rather than any change in\nthe fundamental $\\widehat{\\epsilon}_{\\rm cl}$; and in the\ncomparatively gas-poor M49 and NGC 1399, there is no $S_N$ problem in the\nfirst place. Moreover, the first $S_N$ problem is similarly removed when the\nX-ray gas is taken into account: Although the total specific frequencies of\nM87, M49, and NGC 1399 are significantly different (at 14.1, 4.7, and\n6--7), their local GCS mass ratios at large radii are consistent with a\nsingle value: $\\widehat{\\epsilon}_{\\rm cl}=0.0026\\pm0.0005$ in the\nmean. Finally, since this is also independent of galactocentric radius, it\nis the same as the {\\it global} cluster formation efficiency in each case.\n\nThese specific examples clearly are consistent with the notion of a universal\n$\\epsilon_{\\rm cl}$. Figure \\ref{fig4}, which essentially re-plots the\n$S_N$ data in Fig.~\\ref{fig1}, confirms it in detail on a global scale.\nTo understand the bold curves in this Figure, note that equation (\\ref{eq:4})\nand the definition ${\\cal N}_{\\rm tot}=M_{\\rm gcs}/(2.4\\times10^5\\,M_\\odot)$\ncan be written as\n\n\\begin{equation}\n\\hfil\n{\\cal N}_{\\rm tot}=4.17\\times10^6\\,\\widehat{\\epsilon}_{\\rm cl}\\,\n\\left(1+{{M_{\\rm gas}}\\over{M_{\\rm stars}}}\\right)\\,\n\\left({{M_{\\rm stars}}\\over{10^{12}\\,M_\\odot}}\\right)\\ .\n\\hfil\n\\label{eq:5}\n\\end{equation}\n\n\\noindent The heavy solid line in Fig.~\\ref{fig4} is just this equation, with\n(i) $\\widehat{\\epsilon}_{\\rm cl}=0.0026$ fixed; (ii) $V$-band galaxy\nluminosities converted to stellar masses according to the relation\n$\\Upsilon_{V,{\\rm gal}}=\n6.3\\ M_\\odot\\,L_\\odot^{-1}\\,(L_{V,{\\rm gal}}/10^{11}\\,L_\\odot)^{0.3}$\n(\\cite{vdm91}); and (iii) galaxy-wide gas-to-star mass ratios\nestimated from a combination of fundamental-plane scalings and\nthe X-ray--optical\nluminosity correlation: $M_{\\rm gas}/M_{\\rm stars}\\approx 0.55 \\times\n(L_{V,{\\rm gal}}/10^{11}\\,L_\\odot)^{1.5}$ (\\cite{mcl99}). The\nsteep upturn in ${\\cal N}_{\\rm tot}$ at high $L_{V,{\\rm gal}}$ (or the\nsharp increase in BCG specific frequency) is thus due to the fast-growing\ndominance of gas over stars, in\nthe face of a {\\it constant} GCS mass fraction. Towards lower luminosities,\nglobal gas masses become negligible and $S_N$ decreases steadily because of the\nsystematic decrease in $\\Upsilon_{V,{\\rm gal}}$ for fundamental-plane\nellipticals. As a result, at the luminosity of the Milky Way spheroid (disk\nexcluded), an $\\widehat{\\epsilon}_{\\rm cl}$ of 0.0026 also accounts for the\nnumber of halo (metal-poor) Galactic globulars (open square in\nFig.~\\ref{fig4}; see \\cite{mcl99}).\n\n\\begin{figure}[!t]\n\\null\\vskip-0.2truein\n\\resizebox{\\hsize}{2.9truein}\n{\\includegraphics{dempbf4.eps}}\n\\caption{\\rm Total GCS populations and galaxy luminosities for the same systems\nplotted in Fig.~\\ref{fig1}. Bold lines are the relations predicted by a\nconstant {\\it global} cluster formation efficiency of $\\epsilon_{\\rm cl}\\equiv\n0.0026$. Light, dotted lines represent constant specific frequencies of\n$S_N=15$, 5, and 1.5. From McLaughlin (1999).\n\\label{fig4}}\n\\end{figure}\n\nFor the early-type dwarf galaxies with $L_{V,{\\rm gal}}\\le 2\\times10^9\\ \nL_\\odot$, the gas-to-star mass ratio in equation (\\ref{eq:5}) has a different\nmeaning: The energy of supernova explosions in a single burst of star\nformation in one of these small galaxies may have sufficed to expel all\nremaining gas from its dark-matter well, and while any such gas would, of\ncourse, no longer be directly observable, a proper estimate of\n$\\epsilon_{\\rm cl}$ must still account for it. The bold, dashed line in\nFig.~\\ref{fig4} is one attempt to do this. It represents equation (\\ref{eq:5})\ngiven (i) the relation $(1+M_{\\rm gas}^{\\rm lost}/M_{\\rm stars})\\simeq\n(L_{V,{\\rm gal}}/2\\times10^9\\,L_\\odot)^{-0.4}$, from the {\\it theory} of\n\\cite*{dek86}; (ii) a constant\n$\\Upsilon_{V,{\\rm gal}}=2\\ M_\\odot\\,L_\\odot^{-1}$ for the stellar\npopulations; and (iii) once again, a fixed $\\widehat{\\epsilon}_{\\rm cl}=\n0.0026$.\n\nAlthough scatter remains (at the level of factors of $\\sim$2) in the observed\n${\\cal N}_{\\rm tot}$ at any given $L_{V,{\\rm gal}}$ in\nFig.~\\ref{fig4}, it is important that this is more or less random; the\nmean {\\it trends} in GCS population as a function of luminosity---the essence\nof the first specific frequency problem---can be simply explained if the\nefficiency of globular cluster formation were constant to first order. Indeed,\ndeviations in Fig.~\\ref{fig4} may reflect the scatter of individual galaxies\nabout either the fundamental plane or the $L_X$--$L_B$ correlation used to\nderive the bold lines there, rather than any significant variations in\n$\\epsilon_{\\rm cl}$. This requires further study on a case-by-case basis, as\ndoes the situation in spirals other than the Milky Way. Similarly, there is\nsome indication (e.g., \\cite{mac99}) that the simple treatment of galactic\nwinds (i.e., the model of \\cite{dek86}) used to correct for the gas lost from\ndwarf galaxies may be inadequate. At this point, however, it is more than\nplausible to assert that globular clusters formed in dE's and dSph's as in\nlarger galaxies, always in the same proportion to the total mass of gas that\nwas initially on hand.\n\nOne important consequence of this is that the efficiency of {\\it unclustered}\nstar formation in protogalaxies could {\\it not} have been universal.\nIn both the faintest dE's and the brightest BCGs, globular clusters\napparently formed in precisely the numbers expected of them, while anomalously\nlow fractions of the initial gas mass were converted into field stars. In\nthe case of the dwarfs specifically, if even just the idea of the feedback\ncorrection above is basically correct then all the globulars had to have\nformed by the time a galactic wind cleared the remaining gas; but this must\nhave happened before normal numbers of field stars appeared. Thus,\n{\\it the gas which formed bound star clusters had to have collapsed more\nrapidly than that which produced unbound groups and associations}. This implies\nthat it was only those pieces of gas which locally exceeded some critical\ndensity that were able to attain the cumulative star formation efficiency of\n$\\eta\\ga20\\%$--50\\% required to form a bound stellar cluster. In addition to\nthis, the uniformity of $\\widehat{\\epsilon}_{\\rm cl}$\nargues---applying as it does over large ranges of radius inside M87, M49, and\nNGC 1399, and from dwarfs in the field to BCGs in the cores\nof Abell clusters---that the probability of realizing such a high SFE\ndepended very weakly, if at all, on local or global protogalactic\nenvironment. Quantitative theories of cluster formation should therefore seek\nto identify a {\\it threshold in relative density}, $\\delta\\rho/\\rho$, that\nis always exceeded by $\\simeq$0.26\\% of the mass fluctuations in any\nlarge body of star-forming gas.\n\nThe ``relative'' aspect of such a criterion is crucial; the GCS data militate\nstrongly against any model relying on parameters that are too sensitive to\nenvironment. One such example is the scenario of \\cite*{elm97}, in which\nthe pressure exerted by a diffuse medium surrounding a dense clump\nof gas must exceed a fixed, absolute value in order to produce a\nhigh local $\\eta$ and a bound stellar cluster. However, since pressures vary\nby orders of magnitude in going from dE's to BCGs, or from large to small\nradii in any one galaxy, this idea seems to imply {\\it systematic} variations\nin $\\epsilon_{\\rm cl}$ that are not observed.\n\nBCGs present a complex problem in larger-scale galaxy formation, but it is\nworth noting that a feedback argument like that applied to dwarfs may also be\nrelevant to central cluster galaxies like M87 (cf.~\\cite{har98}; \\cite{mcl99}).\nThat is, globulars likely also appeared quickly, and in normal numbers,\nin the densest of star-forming clumps (perhaps embedded in dwarf-sized\nfragments) in these deep potential wells. The gas more slowly forming field\nstars could have been virialized thereafter, or moved outwards in slow,\npartial galactic winds. The unused gas in this case would have to remain hot\nto the present day, and more or less in the vicinity of the parent galaxy,\nin order to appear as the X-ray emitting gas that makes $\\widehat{\\epsilon}_\n{\\rm cl}$ so constant in Fig.~\\ref{fig4}; but this requirement is certainly\nconsistent with the BCGs being at the centers of clusters. In addition, the\nfeedback in this scenario would have more effectively truncated the star\nformation in the lower-density environs at larger galactocentric radii in\nthese very large systems, thus giving rise to the second specific frequency\nproblem as well. There are other possibilities for BCGs, however. It is\nconceivable, for instance, that their ``excess'' gas and globulars were both\nproduced elsewhere in galaxy clusters (in failed dwarfs?) and fell together\nonto the central galaxies over a long period of time. These questions need to\nbe examined in much more detail.\n\nFinally, \\cite*{mcl99} argues that the current efficiency of {\\it open}\ncluster formation in the Galactic disk is also $\\sim$0.2--0.4\\% by mass. This\nfigure is much more uncertain than it is in GCSs, and it is essentially an\n{\\it instantaneous} variant of the time-averaged quantity measured for globular\nclusters. Nevertheless, it clearly suggests that whatever quantitative\ncriterion is ultimately required to explain $\\epsilon_{\\rm cl}=0.26\\%$ in\nGCSs may very well prove to be of much wider applicability. (One exception\n{\\it may} be the formation of massive clusters in mergers and starbursts,\nwhere it has been suggested that $\\epsilon_{\\rm cl}\\sim1$--10\\% [e.g.,\n\\cite{zep99}; \\cite{sch99}]. However, this conclusion is very uncertain and\nrequires more careful investigation.)\n\n\n\\section{Globular Cluster Binding Energies}\n\\label{sec:3}\n\nThe focus to this point has been on the {\\it frequency} with which\n$\\sim$$10^5$--$10^6\\,M_\\odot$ clumps of gas were able to form stars with a\ncumulative efficiency $\\eta$ high enough to produce a bound globular cluster.\nThe impressive regularity of this occurrence is clearly important, as has just\nbeen discussed, and its rarity is significant as well: the small value of\n$\\epsilon_{\\rm cl}=0.26\\%$ implies that the local SFE\nin an {\\it average} bit of protogalactic gas was much lower than\n$\\eta_{\\rm crit}\\sim0.2$--0.5 (a fact which is also true of molecular gas in\nthe Galaxy today). However, these results say nothing of {\\it how} an extreme\n$\\eta$ comes about in any individual gas clump. This is another open\nproblem in star formation generally. Its solution requires both an\nunderstanding of local star formation laws ($d{\\rho}_*/dt$ as a function of\n$\\rho_{\\rm gas}$) and a self-consistent treatment of feedback on\nsmall ($\\sim$10--100 pc) scales.\n\nThe whole issue is essentially one of energetics in a compact,\ngravitationally bound association of gas and embedded young stars: When does\nthe combined energy injected by all the massive stars equal the binding energy\nof whatever gas remains? This point of equality and the corresponding $\\eta$\ncan in principle be identified for any given star formation law and a set of\ninitial conditions in the original gas. The difficulty lies, of course, in\ndeciphering what these are; but once this is done, progress will also have been made\nin understanding the probability of obtaining $\\eta > \\eta_{\\rm crit}$, i.e.,\nthe overall efficiency of cluster formation in \\S\\ref{sec:2}.\nOne way to begin addressing this complex set of problems empirically is to\ncompare the final binding energies of stellar clusters with the initial\nenergies of their gaseous progenitors. This is a straightforward exercise for\nthe ensemble of globular clusters in the Milky Way.\n\n\\cite*{sai79a} evaluated the binding energies $E_b$ for about 10 bright\nGalactic globulars, along with a number of dwarf and giant ellipticals. He\nclaimed that $E_b\\propto M^{1.5}$ for gE's and globulars alike, while the\ndwarfs fell systematically below this relation (a fact which he subsequently\nattributed to the effects of large-scale feedback such as discussed above\n[\\cite{sai79b}; but cf.~\\cite{ben92}]). Twenty years later, the data\nrequired for a calculation of binding energy are available for many more\nthan ten globular clusters, and they are of higher quality than those\navailable to Saito.\n\n\\cite*{mcl00} computes the binding energies of 109 ``regular'' Galactic\nglobulars and 30 objects with post--core-collapse (PCC) morphologies. The main\nassumption is that single-mass, isotropic \\cite*{kin66} models provide a\ncomplete description of the clusters' internal structures. Within this\nframework, the fundamental definition $E_b\\equiv -(1/2)\\int_0^{r_t}\n4\\pi r^2\\rho\\phi\\,dr$ (with $r_t$ the tidal radius of the cluster) may be\nwritten as\n\n\\begin{equation}\n\\hfil\nE_b=1.663\\times10^{41}\\,{\\rm erg}\\,\n\\left({{r_0}\\over{{\\rm pc}}}\\right)^5\n\\left({{\\Upsilon_{V,0}\\,j_0}\\over{M_\\odot\\,{\\rm pc}^{-3}}}\\right)^2\n{\\cal E}(c)\\ \\ ,\n\\hfil\n\\label{eq:6}\n\\end{equation}\n\n\\noindent where $r_0$ is the model scale radius (\\cite{kin66})\n$\\Upsilon_{V,0}$ is the core mass-to-light ratio; $j_0$ is the central $V$-band\nluminosity density; and ${\\cal E}(c)$ is a well defined, nonlinear function of\n$c\\equiv\\log\\,(r_t/r_0)$, obtained by numerically integrating King models\n(\\cite{mcl00}).\n\nValues of $r_0$, $j_0$, and $c$ are given for all Milky Way clusters in the\ncatalogue of \\cite*{har96}. However, a determination of $\\Upsilon_{V,0}$\nrequires measurements of velocity dispersions $\\sigma_0$, and these are\navailable for only a third of the sample, in the compilation of \\cite*{pry93}.\nFor these objects, application of the King-model relation $\\Upsilon_{V,0}=\n9\\sigma_0^2/(4\\pi G\\,r_0^2\\,j_0)$ gives the results shown in the top panel of\nFig.~\\ref{fig5}. The regular globulars there (the 39 filled circles) share\na single, {\\it constant} core mass-to-light ratio: $\\langle \\log\\,\n\\Upsilon_{V,0} \\rangle = 0.16\\pm0.03$ in the mean, and the r.m.s.~scatter\nabout this is less than the 1-$\\sigma$ observational errorbar shown for\n$\\log\\,\\Upsilon_{V,0}$. (The results for 17 PCC clusters, plotted as open\nsquares, are almost certainly spurious [see \\cite{mcl00}]. They are shown for\ncompleteness but not included in any quantitative analyses here.) This is\nconsistent with separate work by \\cite*{man91} and \\cite*{pry93}.\n\nIt can safely be assumed that this same $\\Upsilon_{V,0}$ applies to all other\n(non-PCC) Galactic globulars, so that $E_b$ can be computed from equation\n(\\ref{eq:6}) given only $r_0$, $j_0$, and $c$, i.e., on the basis of cluster\nphotometry or star-count data alone. If this is done for the full \\cite*{har96}\ncatalogue, a very tight correlation between binding energy, total cluster\nluminosity, and Galactocentric position is found:\n\n\\begin{equation}\n\\hfil\\quad\nE_b=7.2\\times10^{39}\\,{\\rm erg}\\ (L/L_\\odot)^{2.05}\\,(r_{\\rm gc}/\n8\\,{\\rm kpc})^{-0.4}\\ ,\n\\hfil\n\\label{eq:7}\n\\end{equation}\n\n\\noindent with uncertainties of about $\\pm$0.1 in the fitted powers on $L$ and\n$r_{\\rm gc}$. This relation is drawn as the line in the middle panel of\nFig.~\\ref{fig5}. The r.m.s.~scatter of the regular-cluster data\n(filled and open circles) about it is no larger than the typical 1-$\\sigma$\nobservational uncertainty on $\\log\\,E_b$.\n\n\\begin{figure}[!hb]\n\\null\\vskip-0.46truein\n\\resizebox{\\hsize}{2.72truein}\n{\\includegraphics{dempbf5a.eps}}\n\\resizebox{\\hsize}{2.72truein}\n{\\includegraphics{dempbf5b.eps}}\n\\resizebox{\\hsize}{2.72truein}\n{\\includegraphics{dempbf5c.eps}}\n\\caption{\\rm The fundamental plane of Galactic globular clusters (after\nMcLaughlin 2000). Top panels are two edge-on views; bottom is nearly the\nface-on view. All correlations between any other combinations of cluster\nobservables follow directly from these three relations between\n$\\Upsilon_{V,0}$, $E_b$, $c$, $L$, and $r_{\\rm gc}$.\n\\label{fig5}}\n\\end{figure}\n\nSo far as current data can tell, the constancy of $\\Upsilon_{V,0}$ and the\nscaling of $E_b$ with $L$ and $r_{\\rm gc}$ are essentially perfect. Now, in\nthe context of \\cite*{kin66} models, any globular cluster is fully defined\nby the specification of just four (nominally) independent physical quantities.\nGiven the results just presented, it is natural to choose these to be\n$\\log\\,\\Upsilon_{V,0}$, $\\log\\,E_b$, the total $\\log\\,L$, and the concentration\nparameter $c=\\log\\,(r_t/r_0)$. (Additional factors such as Galactocentric\nposition or cluster metallicity are quite separate from the model\ncharacterization of a cluster, and they are to be viewed as external\nparameters.) But the tight empirical constraints on $\\Upsilon_{V,0}$ and $E_b$\nmean that they are not actually ``free'' in any real sense; in practice, \nGalactic globulars are only a {\\it two-parameter} family, with all internal\nproperties set by $\\log\\,L$ and $c$. Equivalently, the clusters are confined\nto a {\\it fundamental plane} in the larger, four-dimensional space of King\nmodels available to them in principle. The top plots in Fig.~\\ref{fig5} are\nthen just two edge-on views of this plane. Its properties are discussed in\ndetail by \\cite*{mcl00}, where this physical approach to it is also compared\nto the more statistical tack taken by \\cite*{djo95}, who first claimed its\nexistence, and to the different interpretation suggested by \\cite*{bel98}.\n\nThe bottom panel shows the third plot possible in the physical cluster\n``basis'' chosen here: concentration vs.~total luminosity. (This is\nclose to, but not quite, a face-on view of the fundamental plane; see\n\\cite{mcl00}.) Although it is not one-to-one like those in\nthe top panels, there is clearly a dependence of $c$ on $\\log\\,L$ (see also\n\\cite{vdb94} or \\cite{bel96}): roughly, $c\\approx -0.55+0.4\\,\\log\\,L$, but the\nscatter about this line exceeds the observational errorbar on $c$. Neither\nthe slope nor the normalization of this rough correlation changes with\nGalactocentric position, i.e., the distribution of globulars {\\it on} the\nfundamental plane is independent of $r_{\\rm gc}$.\n\nThe mean core mass-to-light ratio is also independent of Galactocentric\nradius, and {\\it none of the distributions in Fig.~\\ref{fig5} depend on\ncluster metallicity}. Moreover, since any other property of a\nKing-model cluster is known once values for $\\Upsilon_{V,0}$, $E_b$, $c$,\nand $L$ are given, it follows that {\\it all} interdependences between {\\it any}\nglobular cluster observables (and there are many; see, e.g., \\cite{djo94}) are\nperforce equivalent to a combination of (i) a constant $\\Upsilon_{V,0}=1.45\\\nM_\\odot\\,L_\\odot^{-1}$; (ii) equation (\\ref{eq:7}) for $E_b$ as a function of\n$L$ and $r_{\\rm gc}$; (iii) the rough\nincrease of $c$ with $L$; and (iv) generic King-model definitions.\n\\cite*{mcl00} derives a complete set of\nstructural and dynamical correlations to confirm this basic point: {\\it only}\nthe quantitative details of Fig.~\\ref{fig5}---and their insensitivity to\nmetallicity---need be explained in any theory of globular cluster formation\nand evolution in our Galaxy.\n\n\\begin{figure}[!b]\n\\resizebox{\\hsize}{2.9truein}\n{\\includegraphics{dempbf6.eps}}\n\\caption{\\rm Binding energy vs.~mass for globulars (points; solid\nline) and their gaseous progenitors (broken line) in the Galaxy.\nTotal cluster luminosities are converted to masses by applying the constant\nmass-to-light ratio indicated.\n\\label{fig6}}\n\\end{figure}\n\nIt is then important that the $E_b(L,r_{\\rm gc})$ and\n$c(L)$ correlations are stronger among clusters outside the Solar circle\n(filled circles in the plots) than among those within it (open circles).\nGiven the relative weakness of dynamical evolution at such large $r_{\\rm gc}$,\nthis is one indication that these fundamental properties of the Galactic\nGCS were set largely by the cluster {\\it formation} process (see also\n\\cite{mur92}; \\cite{bel96}; \\cite{ves97}).\n\nFigure \\ref{fig6} finally compares the globular cluster energies to estimates\nfor the initial values in their progenitors. This is done for the specific\nmodel of \\cite*{har94}, in which protoglobular clusters are embedded in\nlarger protogalactic fragments and have properties analogous to those of the\ndense clumps inside present-day molecular clouds (see \\S\\ref{sec:1}). In\nparticular, the column densities of the protoclusters are postulated to be\nindependent of mass but decreasing with Galactocentric radius: $M/\\pi R^2\n\\simeq10^3\\\nM_\\odot$ ${\\rm pc}^{-2}\\,(r_{\\rm gc}/8\\,{\\rm kpc})^{-1}$, which follows\nfrom the clumps being in hydrostatic equilibrium and from their parent clouds\nbeing themselves surrounded in a diffuse medium virialized in a ``background''\nisothermal potential well with a circular velocity of 220 km s$^{-1}$.\nThis relation then implies $E_b\\equiv GM^2/R = 4.8\\times10^{42}\\ \n{\\rm erg}\\,(M/M_\\odot)^{1.5}\\,(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.5}$, which is\ndrawn as the broken line in Fig.~\\ref{fig6}. {\\it By construction, this is\nprecisely the mass-energy relation obeyed today by the massive clumps in\nmolecular clouds in the Solar neighborhood.} Intriguingly, it is also\nthe $M$--$E_b$ scaling originally claimed by \\cite*{sai79a} for giant\nelliptical galaxies and (bright) globular clusters.\n\nThe dependence of $E_b$ on $r_{\\rm gc}$ in such protoclusters is nearly the\nsame as that actually found for the globulars today. (It similarly accounts\nfor the observed increase of cluster radii with $r_{\\rm gc}$\n[\\cite{har94}; cf.~\\cite{mur92}]---a trend which is, in fact, equivalent to\nthe behavior of $E_b$ in eq.~[\\ref{eq:7}].) In Fig.~\\ref{fig6}, the two are\ntaken for convenience to be identical, so that the comparison between model\nand observed binding energies there is valid at any given Galactocentric\nposition.\n\nThe difference in the {\\it slopes} of the two $E_b(M)$ relations is\nsignificant: The ratio of the initial energy of a gaseous clump to the\nfinal $E_b$ of a stellar cluster is unavoidably a function of its cumulative\nstar formation efficiency $\\eta$; but Fig.~\\ref{fig6} shows that this ratio of\nenergies changes systematically as a function of mass, and thus that $\\eta$\nvaried as well. Moreover, the fact that the difference between initial and\nfinal $E_b$ is largest at the lowest masses implies that {\\it $\\eta$ had to\nhave been lower in lower-mass protoglobulars}. The details of this behavior\nmust rely on the density and velocity structure of the initial gas; the\ntimescale over which feedback expels unused gas; re-expansion of the stars\nafter such gas loss; and other such specifics which are model-dependent to\nsome extent. The inference on the qualitative behavior of $\\eta$ as a function\nof protocluster gas mass is, however, robust.\n\nA more quantitative discussion of Fig.~\\ref{fig6}---including its implications\nfor the mass function of GCSs, which will differ from the mass functions of\ngaseous protoclusters if $\\eta$ varied systematically from one to the \nother---has to be deferred (McLaughlin, in progress). But this evidence for a\nvariable star formation efficiency\nin protoclusters is itself a new target for theoretical attack, most likely\nthrough a general calculation of star formation and feedback such as that\ndescribed at the beginning of this Section. 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C., \\& Schweizer, F. 1995, AJ, 109, 960\n\n\\bibitem[\\protect\\astroncite{Zepf \\& Ashman}{1993}]{zep93}\nZepf, S. E., \\& Ashman, K. M. 1993, MNRAS, 264, 611\n\n\\bibitem[\\protect\\astroncite{Zepf et al.}{1999}]{zep99}\nZepf, S. E., Ashman, K. M., English, J., Freeman, K. C., \\& Sharples, R. M.\n1999, AJ, 118, 752\n\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002087.extracted_bib",
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}
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astro-ph0002088
|
Constraints on Cluster Formation from Old Globular Cluster Systems
|
[
{
"author": "Dean E. McLaughlin\\altaffilmark{1}"
}
] |
The properties of old globular cluster systems (GCSs) in galaxy halos offer unique insight into the physical processes that conspire to form any generic star cluster, at any epoch. Presented here is a summary of the information obtained from (1) the specific frequencies (total populations) and spatial structures (density vs.~galactocentric radius) of GCSs in early-type galaxies, as they relate to the efficiency (or probability) of bound cluster formation, and (2) the fundamental role of a scaling between cluster mass and energy among Galactic globulars in setting their other structural correlations, and the possible implications for star formation efficiency as a function of mass in gaseous protoclusters.
|
[
{
"name": "dempc.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{McLaughlin}\n{Constraints on Cluster Formation from Globular Clusters}\n\\pagestyle{myheadings}\n\n\\begin{document}\n\n\\title{Constraints on Cluster Formation from Old Globular Cluster Systems}\n\n\\author{Dean E. McLaughlin\\altaffilmark{1}}\n\n\\affil{Department of Astronomy, 601 Campbell Hall, University of California,\nBerkeley, CA 94720}\n\n\\altaffiltext{1}{Hubble Fellow}\n\n\\begin{abstract}\nThe properties of old globular cluster systems (GCSs) in galaxy halos offer\nunique insight into the physical processes that conspire to form any generic\nstar cluster, at any epoch. Presented here is a summary of the information\nobtained from (1) the specific frequencies (total populations) and spatial\nstructures (density vs.~galactocentric radius) of GCSs in early-type galaxies,\nas they relate to the efficiency (or probability) of bound cluster\nformation, and (2) the fundamental role of a scaling between cluster mass and\nenergy among Galactic globulars in setting their other structural correlations,\nand the possible implications for star formation efficiency as a function of\nmass in gaseous protoclusters.\n\\end{abstract}\n\n\\keywords{galaxies: star clusters -- globular clusters: general --\nstars: formation}\n\n\\section{Introduction}\n\nUntil quite recently, it was commonly assumed that the old globular clusters\nin galaxy halos were the remnants of a unique sort of star formation that\noccurred only in a cosmological context. The discovery of young, massive,\n``super'' star clusters in local galaxy mergers and starbursts has clearly\ndone much to change this perception; but at least as important is the parallel\nrecognition that star formation in the Milky Way itself proceeds---under\nmuch less extreme conditions---largely in a clustered mode. Observations of\nentire starbursts (Meurer et al.~1995) and individual Galactic molecular\nclouds (e.g., Lada 1992), as well as a more general comparison of the mass\nfunction of molecular cloud clumps and the stellar IMF (Patel \\& Pudritz 1994),\nall argue convincingly that (by mass) most new stars are born in groups rather\nthan in isolation. The production of a true stellar cluster---one that\nremains bound even after dispersing the gas from which it formed---is\nundoubtedly a {\\it rare} event, but it is an exceedingly {\\it regular} one.\n\nSeen in this light, the globular cluster systems (GCSs) found in most galaxies\ncan be used to good effect as probes not only of galaxy formation but also\nof an important element of the generic star-formation process at any epoch.\nThis is arguably so even in cases where newly formed clusters may not be\n``massive'' according to the criteria of this workshop (the main issue\nbeing simply the formation of a {\\it self-gravitating} stellar system), and\neven though GCSs have been subjected to $10^{10}$ yr of dynamical evolution in\nthe tidal fields of their parent galaxies (see O.~Gerhard's contribution to\nthese proceedings, and note that theoretical calculations geared specifically\nto conditions both in the Milky Way [Gnedin \\& Ostriker 1997] and in the giant\nelliptical M87 [Murali \\& Weinberg 1997] suggest that GCS properties are most\naffected by evolution inside roughly a stellar effective radius in each case).\n\n\\section{The Efficiency of Cluster Formation}\n\nAt some point during the collapse and fragmentation of a cluster-sized\ncloud of gas, the massive stars which it has formed will expel any remaining\ngas by the combined action of their stellar winds, photoionization, and\nsupernova explosions. If the star formation efficiency\nof the cloud, $\\eta\\equiv M_{\\rm stars}/(M_{\\rm stars}+M_{\\rm gas})$, is below\na critical threshold just when the gas is lost, then the blow-out removes\nsufficient energy that the stellar group left behind is unbound and disperses\ninto the field. The precise value of this threshold depends on details of the\ninternal density and velocity structure of the initial gas cloud, and\non the timescale over which the massive stars dispel the gas; but various\nestimates place it in the range $\\eta_{\\rm crit}\\sim 0.2$--0.5 (e.g., Hills\n1980; Verschueren 1990; Goodwin 1997, and these proceedings). There is no\ntheory which can predict whether any given piece of gas can ultimately achieve\n$\\eta>\\eta_{\\rm crit}$, but it is straightforward to evaluate {\\it\nempirically} the frequency---or efficiency---with which this occurs.\n\nTraditionally, this has been discussed for GCSs in terms of {\\it specific\nfrequency}, defined by Harris \\& van den Bergh (1981) as the normalized ratio\nof a galaxy's total GCS population to its $V$-band luminosity:\n$S_N \\equiv {\\cal N}_{\\rm tot}\\times 10^{0.4(M_V+15)}$. As is well known\n(see, e.g., Elmegreen 2000 for a recent review), there are\nsubstantial and systematic variations in this ratio from one galaxy to\nanother: Global specific frequencies {\\it decrease} with increasing galaxy\nluminosity for early-type dwarfs, then {\\it increase} gradually with\n$L_{V,{\\rm gal}}$ in normal giant ellipticals, and finally increase rapidly\nwith galaxy luminosity among the central ellipticals (BCGs) in groups and\nclusters of galaxies. In addition, the more extended spatial distribution\nof GCSs relative to halo stars in some (but not all) bright ellipticals leads\nto {\\it local} specific frequencies (ratios of GCS and field-star densities)\nthat increase with radius inside the galaxies (see McLaughlin 1999).\n\nHowever, McLaughlin (1999) shows (following related work by Blakeslee et\nal.~1997 and Harris et al.~1998) that these trends in\n$S_N$ do {\\it not} reflect any such behavior in the ability\nto form globulars in protogalaxies. To see this, it is best to work in terms\nof an efficiency per unit {\\it mass}, $\\epsilon_{\\rm cl}\\equiv\nM_{\\rm gcs}^{\\rm init}/M_{\\rm gas}^{\\rm init}$,\nwhere $M_{\\rm gas}^{\\rm init}$ is the total gas supply that was available to\nform stars in a protogalaxy (whether in a monolithic collapse or a slower\nassembly of many distinct, subgalactic clumps is unimportant) and\n$M_{\\rm gcs}^{\\rm init}$ is the total mass of all globulars formed in that\ngas. As McLaughlin (1999) argues, the integrated mass of an entire GCS should\n{\\it not} be much affected by dynamical evolution, and it is most appropriate\nto include any gas presently associated with galaxies, as well as their\nstellar masses, in estimating their initial gas contents. The {\\it observable}\nratio $M_{\\rm gcs}/(M_{\\rm gas}+M_{\\rm stars})$ should therefore\nimprove on $S_N\\propto M_{\\rm gcs}/M_{\\rm stars}$ as an estimator of\n$\\epsilon_{\\rm cl}$.\n\nFigure \\ref{fig1} shows the total GCS populations vs.~galaxy luminosity in\n97 early-type galaxies and the metal-poor spheroid of the Milky Way and\ncompares the expectations for a {\\it constant} $\\epsilon_{\\rm cl}=\n0.26\\%$, given both the variation of stellar mass-to-light ratio with\n$L_{V,{\\rm gal}}$ on the fundamental plane of ellipticals and the\nincrease of $M_{\\rm gas}/M_{\\rm stars}$ with $L_{V,{\\rm gal}}$ for regular\ngE's and BCGs inferred from the correlation between their X-ray and optical\nluminosities (bold solid curve; see McLaughlin 1999), and after correcting\n(according to the model of Dekel \\& Silk 1986) for the gas mass lost in\nsupernova-driven winds from early bursts of star formation in faint dwarfs\n($L_{V,{\\rm gal}}\\le 2\\times 10^9\\,L_\\odot$; bold dashed line). All {\\it\nsystematic} variations in GCS specific frequencies reflect only different\nrelations, in different magnitude ranges, between $M_{\\rm gas}^{\\rm init}$ and\nthe present-day $L_{V,{\\rm gal}}$.\n\n\\begin{figure}[!b]\n\\plotfiddle{dempcf1.eps}{3.0truein}{0}{50}{40}{-150}{-60}\n\\caption{\\rm Constant efficiency of cluster formation,\n$\\epsilon_{\\rm cl}\\equiv 0.0026$ (bold lines) in 97 early-type systems and the\nspheroid of the Milky Way. Light, dotted lines represent constant specific\nfrequencies ($S_N=8.55\\times 10^7\\,{\\cal N}_{\\rm tot}/L_{V,{\\rm gal}}$) of\n15, 5, and 1.5. From McLaughlin (1999).\n\\label{fig1}}\n\\end{figure}\n\nMcLaughlin (1999) also shows that the ratio of local densities,\n$\\rho_{\\rm gcs}/(\\rho_{\\rm gas}+\\rho_{\\rm stars})$, is constant as a function\nof galactocentric position (beyond a stellar effective radius) in each of the\nlarge ellipticals M87, M49, and NGC 1399, and that this ratio is the same\nin all three systems: $\\epsilon_{\\rm cl}=0.0026\\pm0.0005$. Moreover, it seems\n(although the data are much less clear in this case) that the same efficiency\nalso applies to the ongoing formation of open clusters in the Galactic disk.\nIt therefore appears that there is a {\\it universal efficiency for cluster\nformation}, whose value should serve as a strong constraint on very general\ntheories of star formation. (Note that one exception to the figure of\n0.26\\% by mass {\\it may} be the formation of massive clusters in\nmergers and starbursts, where it has been suggested that $\\epsilon_{\\rm cl}\n\\sim1$--10\\% [e.g., Meurer et al.~1995; Zepf et al.~1999]. However, this\nconclusion is very uncertain and requires more careful investigation.)\n\nWhile this result certainly has interesting implications for aspects of\nlarge-scale galaxy formation (McLaughlin 1999; Harris et al.~1998),\nthe main point to be emphasized here is that the variations in early-type\nGCS specific frequencies are now understood to result from\nvariations in the gas-to-star mass ratio in galaxies, rather than from any\npeculiarities in their GCS abundances per se (cf.~the similar suggestion of\nBlakeslee et al.~1997). That is, the efficiency of {\\it unclustered} star\nformation was {\\it not} universal in protogalaxies: while globulars apparently\nalways formed in just the numbers expected of them, the formation of a normal\nproportion of field stars was subsequently disabled in many cases. The clumps\nof gas which formed bound clusters therefore must have\ncollapsed before those forming unbound groups and associations, i.e.,\nthey must have been denser than average. This and the insensitivity of\n$\\epsilon_{\\rm cl}$ to local or global galaxy environment together suggest that\nquantitative theories of cluster formation should seek to identify a {\\it\nthreshold in relative density}, $\\delta\\rho/\\rho$, that is always exceeded\nby $\\simeq$0.26\\% of the mass fluctuations in any large star-forming complex.\n\n\\section{Globular Cluster Binding Energies}\n\nEven as they clarify the {\\it probability} that a $\\sim$$10^5$--$10^6\\,M_\\odot$\nclump of gas was able to form stars with cumulative efficiency $\\eta$ high\nenough to produce a bound globular cluster, the integrated GCS mass ratios in\ngalaxies say nothing of {\\it how} this was achieved in any individual case.\nThis more ambitious question is essentially one of energetics---When does the\nenergy injected by the massive stars in an embedded young cluster overcome the\nbinding energy of whatever gas remains, thus expelling it and terminating star\nformation?---and its answer requires both an understanding of local\nstar formation laws ($d{\\rho}_{\\rm stars}/dt$ as a function of\n$\\rho_{\\rm gas}$) and a self-consistent treatment of feedback on small\n($\\sim$10--100 pc) scales. One way to begin addressing this complex problem\nempirically is to compare the energies of globular clusters with the initial\nenergies of their gaseous progenitors.\n\nMcLaughlin (2000) has calculated the $V$-band mass-to-light ratios of 39\nregular (non--core-collapsed) Milky Way globulars, and finds that they are all\nconsistent with a single $\\Upsilon_{V,0}=(1.45\\pm0.10)\\ M_\\odot\\,L_\\odot^{-1}$.\nApplying this to all other Galactic globulars, and adopting single-mass,\nisotropic King (1966) models for their internal structure, then allows binding\nenergies $E_b$ to be estimated for a complete sample of 109 regular (and\n30 post--core-collapse) objects. This exercise reveals a very tight\ncorrelation between $E_b$, total cluster luminosity $L$ (or mass\n$M=\\Upsilon_{V,0}L$), and Galactocentric position: $E_b=7.2\\times10^{39}\\\n{\\rm erg}\\,(L/L_\\odot)^{2.05}\\,(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.4}$, with\nuncertainties of roughly $\\pm$0.1 in each of the fitted exponents on $L$\nand $r_{\\rm gc}$ (cf.~Saito 1979, who claimed $E_b\\propto M^{1.5}$ on the\nbasis of a much smaller dataset).\n\n\\begin{figure}[!b]\n\\plotfiddle{dempcf2.eps}{3.0truein}{0}{50}{40}{-150}{-60}\n\\caption{Binding energy vs.~mass for globular clusters (points and solid\nline; see McLaughlin 2000) and their gaseous progenitors (broken line) in the\nGalaxy. Total cluster luminosities are converted to masses by applying the\nconstant mass-to-light ratio indicated.\n\\label{fig2}}\n\\end{figure}\n\nThese constraints on $\\Upsilon_{V,0}$ and for $E_b(L,r_{\\rm gc})$ are, in\nfact, two edge-on views of a {\\it fundamental plane} in the (four-dimensional)\nparameter space of King models, to which real globulars are confined in the\nMilky Way (cf.~Djorgovski 1995; Bellazzini 1998). The full characteristics of\nthis plane subsume {\\it all other observable correlations} between any\ncombination of other cluster parameters (see McLaughlin 2000), and they\ntherefore provide a {\\it complete} set of independent facts to be explained in\nany theory of globular cluster formation and evolution. In fact, the\n$E_b$--$L$ correlation is stronger among clusters at larger Galactocentric\nradii (where dynamical cluster evolution is weaker), suggesting that it was\nset largely by the cluster {\\it formation} process. The same is true of a\nweaker correlation between cluster concentration and luminosity (see Vesperini\n1997), which is related to the distribution of globulars {\\it on} the\nfundamental plane.\n\nAny collection of critically stable, virialized gas spheres under a surface\npressure $P_s$ have a common column density, $\\Sigma\\equiv M/(\\pi R^2)\n\\propto P_s^{0.5}$, and thus $E_b^{\\rm gas}\\equiv GM^2/R \\propto M^{1.5}\nP_s^{0.25}$. Harris \\& Pudritz (1994) have developed a physical framework in\nwhich protoglobular clusters in the Milky Way were massive analogues of the\ndense clumps in disk molecular clouds today; in particular, their column\ndensities were the same: $\\Sigma\\simeq 10^3\\ M_\\odot$ pc$^{-2}$ at\n$r_{\\rm gc}=8$ kpc. In addition, it is natural to expect $P_s \\propto\nr_{\\rm gc}^{-2}$ for such protocluster clumps embedded in larger (but\nsubgalactic) star-forming clouds that were themselves surrounded by a diffuse\nmedium virialized in a ``background'' isothermal potential well (Harris \\&\nPudritz 1994). Together, these basic hypotheses imply $E_b^{\\rm gas}=4.8\\times\n10^{42}\\ {\\rm erg}\\,(M/M_\\odot)^{1.5}\\,(r_{\\rm gc}/8\\,{\\rm kpc})^{-0.5}$.\nNote that the $r_{\\rm gc}$ scaling is essentially that observed directly for\nGalactic globulars today, enabling a direct comparison of the (model)\ninitial and final $E_b(M,r_{\\rm gc})$ relations in Fig.~\\ref{fig2}.\n\nTo explain the relative $E_b(M)$ normalizations in Fig.~\\ref{fig2}\nrequires quantitative modelling of the initial structure and feedback dynamics\nin the gaseous protoclusters. Meanwhile, the different {\\it slopes} of the\ntwo relations are significant: The ratio of the initial energy of a gaseous\nclump to the final $E_b$ of a stellar cluster is a non-decreasing\nfunction of the cumulative star formation efficiency $\\eta$; but this Figure\nshows that it is also an increasing function of cluster mass, and thus that\n$\\eta$ {\\it was systematically higher in more massive protoclusters}. The \nquantitative details of this dependence are also model-dependent (McLaughlin,\nin preparation), but the inference on the qualititative behavior of $\\eta$ is\nrobust and presents a new constraint for theories of cluster formation.\nOnce the behavior of $\\eta$ as a function of initial gas mass is understood,\nprogress will have been made in explaining the universal $\\epsilon_{\\rm cl}$ of\n\\S2, and there will be further implications for other global properties of\nGCSs---such as their mass functions, which, contrary to current modelling\n(McLaughlin \\& Pudritz 1996; Elmegreen \\& Efremov 1997), can no longer simply\nbe assumed proportional to those of their gaseous protoclusters.\n\n\\begin{acknowledgements}\n\nThis work was supported by NASA through grant number HF-1097.01-97A awarded by\nthe Space Telescope Science Institute, which is operated by the Association of\nUniversities for Research in Astronomy, Inc., for NASA under contract\nNAS5-26555.\n\n\\end{acknowledgements}\n\n\\begin{references}\n\n\\reference Bellazzini, M. 1998, New Astronomy, 3, 219\n\n\\reference Blakeslee, J. P., Tonry, J. L., \\& Metzger, M. R. 1997, AJ, 114, 482\n\n\\reference Dekel, A.., \\& Silk, J. 1986, ApJ, 303, 39\n\n\\reference Djorgovski, S. 1995, ApJ, 438, L29\n\n\\reference Elmegreen, B. G. 2000, in Toward a New Millennium in Galaxy\nMorphology, ed. D. L. Block, I. Puerari, A. Stockton, and D. Ferreira\n(Dordrecht: Kluwer), in press ({\\tt astro-ph/9911157})\n\n\\reference Elmegreen, B. G., \\& Efremov, Y. N. 1997, ApJ, 480, 235\n\n\\reference Gnedin, O. Y., \\& Ostriker, J. P. 1997, ApJ, 474, 223\n\n\\reference Goodwin, S. P. 1997, MNRAS, 284, 785\n\n\\reference Harris, W. E. 1996, AJ, 112, 1487\n\n\\reference Harris, W. E., \\& Pudritz, R. E. 1994, ApJ, 429, 177\n\n\\reference Harris, W. E., \\& van den Bergh, S. 1981, AJ, 86, 1627\n\n\\reference Harris, W. E., Harris, G. L. H., \\& McLaughlin, D. E. 1998,\nAJ, 115, 1801\n\n\\reference Hills, J. G. 1980, ApJ, 225, 986\n\n\\reference King, I. R. 1966, AJ, 71, 64\n\n\\reference Lada, E. A. 1992, ApJ, 393, L25\n\n\\reference McLaughlin, D. E. 1999, AJ, 117, 2398\n\n\\reference McLaughlin, D. E. 2000, ApJ, in press\n\n\\reference McLaughlin, D. E., \\& Pudritz, R. E. 1996, ApJ, 457, 578\n\n\\reference Meurer, G. R., Heckman, T. M., Leitherer, C., Kinney, A., Robert,\nC., \\& Garnett, D. R. 1995, AJ, 110, 2665\n\n\\reference Murali, C., \\& Weinberg, M. D. 1997, MNRAS, 288, 767\n\n\\reference Patel, K., \\& Pudritz, R. E. 1994, ApJ, 424, 688\n\n\\reference Saito, M. 1979, PASJ, 31, 181\n\n\\reference Verschueren, W. 1990, A\\&A, 234, 156\n\n\\reference Vesperini, E. 1997, MNRAS, 287, 915\n\n\\reference Zepf, S. E., Ashman, K. M., English, J., Freeman, K. C., \\&\nSharples, R. M. 1999, AJ, 118, 752\n\n\\end{references}\n\n\\appendix\\section*{Discussion}\n\n\\noindent{\\bf G.~Meurer:}\nConcerning the two-orders-of-magnitude difference between\n$\\epsilon_{\\rm cl}$ and the fraction of UV light in starbursts: One order of\nmagnitude may be explainable by the gas content in starbursts.\n\n\\\n\n\\noindent{\\bf McLaughlin:}\nThat does seem plausible (e.g., Zepf et al.~1999), although it\nshould of course be checked in detail in every individual case. But the gas\nmass in starbursts really does have to enter as much more than a factor-of-ten\neffect if there is no boost in the cluster formation efficiency\nin starbursts vs.~old galaxy halos. A real question remains as to whether or\nnot that is the case.\n\n\\\n\n\\noindent{\\bf G.~\\\"Ostlin:}\nSince none of the fundamental properties of globular clusters depend on\nmetallicity, including the core mass-to-light ratio which appears constant,\nI guess this requires them to have had a universal stellar IMF, independent\nof metallicity.\n\n\\\n\n\\noindent{\\bf McLaughlin:}\nI think that's exactly right.\n\n\\end{document}\n"
}
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astro-ph0002089
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Relic Neutrinos and Z-Resonance Mechanism for Highest-Energy Cosmic Rays
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[
{
"author": "James L. Crooks"
},
{
"author": "James O. Dunn and Paul H. Frampton"
}
] |
The origin of the highest-energy cosmic rays remains elusive. The decay of a superheavy particle (X) into an ultra-energetic neutrino which scatters from a relic (anti-)neutrino at the Z-resonance has attractive features. Given the necessary X mass of $10^{14\sim15}$ GeV, the required lifetime, $10^{15\sim16}$ y, renders model-building a serious challenge but three logical possibilities are considered: (i) X is a Higgs scalar in $SU(15)$ belonging to high-rank representation, leading to {power}-enhanced lifetime; (ii) a global X quantum number has {exponentially}-suppressed symmetry-breaking by instantons; and (iii) with additional space dimension(s) localisation of X within the real-world brane leads to {gaussian} decay suppression, the most efficient of the suppression mechanisms considered.
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{
"name": "AUGER2.tex",
"string": "\\documentstyle[preprint,aps]{revtex}\n\n\\begin{document}\n\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\\newcommand{\\ba}{\\begin{array}}\n\\newcommand{\\ea}{\\end{array}}\n\\newcommand{\\sprime}{^\\prime}\n\\newcommand{\\dprime}{^{\\prime\\prime}}\n\\newcommand{\\tprime}{^{\\prime\\prime\\prime}}\n\n\n%\\draft\n%\\tighten\n%\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname\n%@twocolumnfalse\\endcsname\n\\preprint{\\vbox{\\hbox{IFP-778-UNC}\n\\hbox{astro-ph/0002089} \n\\hbox{February 2000}\n}\n}\n\n\n\\title{Relic Neutrinos and Z-Resonance Mechanism\nfor Highest-Energy Cosmic Rays}\n\\author{James L. Crooks, James O. Dunn and Paul H. Frampton}\n\n\n\\address{{\\it Department of Physics and Astronomy}}\n\n\\address{{\\it University of North Carolina, Chapel Hill, NC 27599-3255}}\n\n\n\\maketitle\n\n\n\\begin{abstract}\nThe origin of the highest-energy cosmic rays remains elusive.\nThe decay of a superheavy particle (X) into an ultra-energetic \nneutrino which scatters from a relic (anti-)neutrino\nat the Z-resonance has attractive features.\nGiven the necessary X mass of $10^{14\\sim15}$ GeV, \nthe required lifetime, $10^{15\\sim16}$ y, renders model-building a \nserious challenge but three logical \npossibilities are considered: \n(i) X is a Higgs scalar in $SU(15)$ belonging \nto high-rank representation, leading to\n{\\it power}-enhanced lifetime;\n(ii) a global X quantum number has \n{\\it exponentially}-suppressed symmetry-breaking\nby instantons; and (iii) with additional space dimension(s) \nlocalisation of X within the real-world brane leads to\n{\\it gaussian} decay suppression, the most \nefficient of the suppression mechanisms considered.\n\\end{abstract} \n\n\\newpage\n\nThe confluence of cosmology and particle phenomenology\nbenefits both disciplines and can lead to important new\ninsights.\n\nFor protons propagating through the cosmological \nbackground radiation there\nis an energy cut-off, as discussed in {\\it e.g.} \\cite{FKN},\nwell-known as the GKZ \neffect\\cite{Greisen,KZ}, at\nan energy of $E \\sim 5 \\times 10^{19}$ eV. \nAbove this energy, the photoproduction\nof pions at the 3-3 resonance \nprovides an energy attenuation that prohibits\ntravel over a distance greater than $\\sim 50$ Mpc.\n\nNevertheless, air showers initiated by a proton (or \nphoton) with energies above the GKZ bound have \nbeen observed\\cite{YD}, and this fact needs explanation.\n\nOne possibility is that the origin involves the decay of a superheavy particle\nas in \\cite{FKN} (for related earlier works, see {\\it e.g.} \\cite{BKV,BS})\nbut that the decay now produces a high energy neutrino\nwhich scatters from a relic background neutrino at the $Z$ pole\nand produces the primary. This Z-burst scenario was suggested in\n\\cite{Weiler} and further analysed in \\cite{GK1,GK2}.\n\nThe kinematics of the neutrino-neutrino collision at the\n$Z$ pole requires an energy $E_{resonance} = M(Z)^2/(2 M(\\nu))$\nand taking $M(\\nu) = 0.07~eV$ as suggested by the SuperKamiokande\ndata gives $M_{resonance} \\simeq 10^{23}~eV$, just as needed to explain the\ndata. This is the most attractive feature of the model.\n\nWe first estimate the mass and lifetime of the superheavy particle\nneeded to fit the data. This requires two relationships\nderived in \\cite{GK2}. Namely the flux of\ncosmic rays beyond the GKZ cut-off is estimated as:\n\\begin{eqnarray}\n\\Phi_{CR} & = & \\frac{C_1}{(4 \\pi sr) km^2 (100 y)} \\nonumber \\\\\n & \\times & \\left( \\frac{N}{10} \\right) \n\\left( \\frac{\\eta}{0.14} \\right) \n\\left( \\frac{\\Omega_X}{0.2} \\right)\n\\left( \\frac{h}{0.65} \\right)^{2} \\nonumber \\\\\n& \\times & \\left( B_{\\nu} \\frac{10^7 t_0}{\\tau_X} \\right) \n\\left( \\frac{0.07 eV}{M(\\nu)} \\right)^{3/2}\n\\left( \\frac{10^{14} GeV}{M(X)} \\right)^{5/2}\n\\label{flux}\n\\end{eqnarray}\nand\n\\begin{equation}\n\\frac{\\tau_X}{t_0} B_{\\nu}^{-1} > C_2 \\times 10^5 \n\\left( \\frac{\\Omega_X}{0.2} \\right) \n\\left( \\frac{h}{0.65} \\right)^2 \n\\left( \\frac{10^{14} GeV}{M(X)} \\right)^{3/4}\n\\label{limit}\n\\end{equation}\nFor the numerical dimensionless coefficients \nwe find the values $C_1 = 0.33$ and $C_2 = 12.8$\nwhich we use in the following analysis.\nThe notation is: $N$ is the number of \nprotons and photons per annihilation event;\n$\\eta$ is the relic neutrino density relative \nto the present photon number density\n$\\eta = (n_{\\nu,relic}/n_{\\gamma,0})$;\n$\\Omega_X$ is the contribution of $X$ particles \nto the energy density, relative to the\ncritical density;\n$h$ is the Hubble constant in units of \n$100 km/s/Mpc$; $B_{\\nu}$ is the\nbranching ratio of $X$ into neutrinos;\n$t_0$ is the age of the universe; \n$\\tau_X$ is the lifetime of $X$; $M(\\nu)$ is\nthe neutrino mass; and $M(X)$ is the mass of $X$.\n\n\\bigskip\n\\bigskip\n\nAssuming central values of all other parameters we \nplot the allowed region of $M(X)$ and $\\tau_X$ in Figure 1;\nvariations in $N, \\eta, \\Omega_X, h, B_{\\nu}, M(\\nu)$\ncan extend the allowed region but here we need\nonly the order of magnitude estimate.\n\n\\bigskip\n\\bigskip\n\nThe value of $M(X)$ must certainly exceed $2E_{resonance}$\nso that a two body decay can lead to a neutrino acquiring \nenough energy. Higher energies\ncan be red-shifted down to $E_{resonance}$ if the \nprogenitor $X$ particle\nis at a red shift $z > 0$.\n\nThe resultant spectrum will cut-off at $M(X)/2$ \nand will be expected to provide a two-component type\nof overall spectrum, with a dip around \n$E \\sim E_{GKZ}$ as can be seen in the data\\cite{YD}.\n\n\\bigskip\n\\bigskip\n\nSince $Z$ decay gives rise to approximately 10 times \nas many photons as nucleons the model predicts\na concomitant number of high-energy photons as cosmic-ray\nprimaries. Because the data is sparse, it is not \nyet possible to discriminate \non this basis, as discussed in \\cite{Weiler2}; \nthis is an important prediction of the Z-burst scenario.\n\n\\bigskip\n\\bigskip\n\nFrom the above analysis we conclude that the required particle properties\n$M(X)$ and $\\tau_X$\nfor the hypothetical state X are well defined in order of magnitude. \nNamely, the\nmass M(X) should lie between $10^{14}$ and $10^{15}$ GeV and the lifetime\n$\\tau(X)$ should lie between $10^{16}$ and $10^{17}$ years.\n\nThe remainder of the paper will discuss three possible microscopic\ntheories or, better, scenarios for this combination of M(X) and $\\tau(X)$.\nWe present these three scenarios in what we regard as their increasing\nappeal, from (i) to (iii).\n\n\\newpage\n\n(i) {\\bf Power suppression.}\n\nThe expectation for a particle of this mass is that, unless it is absolutely\nstable due to some exact conservation law, it will decay exceedingly quickly\nwith a lifetime expected to be $\\tau \\leq 10^{-24}$ seconds.\nSince the required lifetime is larger by some 46 or so orders of magnitude,\nthe longevity is the principal difficulty, as emphasized in \\cite{FKN}.\n\nOne viewpoint is that this extraordinary suppression of the decay is\nan argument against the model, as is the problem, already mentioned, of super-high-energy\nphotons concomitant with the protons.\n\nLet us here take the viewpoint, as discussed in \\cite{Weiler2}\nthat the photons are a {\\it prediction} of the model, to be tested\nin future experiments, rather than a fatal flaw. The data on\nHECR is probably too sparse to reach any stronger conclusion.\n\nTherefore the only remaining question is longevity.\n\nThe first scenario (i) is that considered (in a different model)\nin \\cite{FKN}. We assume the particle X is a boson and posit a coupling\n\\[\n\\frac{g}{M^p} X^{\\alpha_1 \\alpha_2 .....\\alpha_n}_{\\beta_1 \\beta_2 .....\\beta_n}\n(\\bar{\\psi}^{\\beta_1}\\psi_{\\alpha_1})\n(\\bar{\\psi}^{\\beta_2}\\psi_{\\alpha_2})\n.........\n(\\bar{\\psi}^{\\beta_n}\\psi_{\\alpha_n})\n\\]\nwhere the power is $p = 3(n-1)/2$. Let us assume that such a coupling is\ngravity-induced and that M is the reduced Planck mass $M \\sim M(Pl) \\simeq 10^{18} GeV$. \nThen one expects the\nlifetime $\\tau(X)$ to be of the order of magnitude\n\\[\n\\tau(X) \\sim (10^{-24} sec.) \\times \\left( \\frac{M(X)}{M(Pl)} \\right)^{2p}\n\\]\nin which the mass ratio is $\\frac{M(X)}{M(Pl)} \\simeq 10^{-3}-10^{-4}$. To arrive at a suppression\nof $10^{-46}$ thus requires $2p \\sim 12-15$ and $n\\sim 5-6$. Thus the X field must\nhave a high tensorial rank. If this is too much for the reader, skip to\nscenario (ii). \n\nIn \\cite{FKN} the case $n = 2$ was considered. \nIn the spontaneous breaking of $SU(15)$\ntheory \\cite{FLee} such a tensor appears \"naturally\" \nin the Higgs sector. There is no apparent\nneed for such a high rank as n = 5 or 6, \nbut equally no reason for their absence.\nThe dimensions of such scalar representations in \nSU(15) are astronomical -\neven for n=2 the dimension\\cite{FKN,FK} \nis 14,175 while for n=5 and 6 this becomes \nrespectively 125,846,784 and 1,367,127,216. \n\nIt is difficult to believe that such power \nsuppression could be responsible for\nthe longevity. It is a logical possibility \nwhich appears highly contrived.\nThus exponential or gaussian suppression is more appealing.\n\n\\bigskip\n\\bigskip\n\n(ii) {\\bf Exponential suppression.}\n\nLet us assume that the superheavy particle X carries a conserved\nquantum number $Q_X$ (analagous to baryon number, \nB) and that in perturbation theory\nthe quantum number is exactly conserved. If there is no open channel\nwhich conserves $Q_X$ then the state will be absolutely stable.\n\nIn the case of B in the standard model, it was first shown in 1976 by\n't Hooft\\cite{Hooft1,Hooft2} that nonperturbative instanton effects\nviolate conservation and lead to decay of otherwise stable states\nsuch as the proton. The resutant rate is typically exponentially suppressed\nby an exponential of the form $exp(-constant/g^2)$ where $g$ is the\ngauge coupling constant. Many other examples of such \nsuppression are covered in \\cite{Shifman}.\n\nThus, one scenario is that $Q_X$ generates a symmetry of the lagrangian\nbut $X$ decays with exponential suppression due to instanton effects.\nWe mention this only for completeness - any quantitative estimation\nwould require many hypotheses.\n\n\\bigskip\n\\bigskip\n\n(iii) {\\bf Gaussian suppression.}\n\nThis scenario which is, in our opinion, the most\nappealing involves the assumption of at least one extra spatial dimension.\nWe will take five space-time dimensions, four space and one time.\n\nLet the coordinates be $(x_0, {\\bf x}, y)$ with $y$ as the\nhypothetical extra dimension on which we now focus.\n\nIt used to be thought, up to a decade ago, that any such $y$ must be\ncompactified at or beyond the GUT scale of $(10^{16} GeV)^{-1}~\\sim\n~10^{-32}~m$ (recall $1 (GeV)^{-1}~\\sim~2 \\times 10^{16}~m$).\nIn 1990, Antoniadis\\cite{antoniadis} was the first to\nentertain very much larger compactification \nscales $\\sim~(1~TeV)^{-1}\\sim~10^{-19}~m$. In 1998 it\nwas pointed out \n\\cite{ADD1,ADD2,ADD3,ADD4} that, although the strong\nand electroweak interactions of the quarks and leptons need be confined\nto a region of $y$ not exceeding $10^{-19}~m$ (the real-world \nbrane on which we live), the gravitational interaction\ncould be decompactified even out to $1~mm~=10^{-3}~m$ without\ncontradicting experimental data, offering\nthe possibility of detecting such additional dimensions by deviation\nfrom Newton's Law of Gravity at millimeter scales.\n\nModels in which the fifth dimension contains \na real-world brane and a suitably separated \nPlanck brane which delimits gravitational\npropagation have \nbeen discussed in \\cite{verlinde,RS}.\nSuch models are of interest mainly because they\nsuggest how to incorporate gravity\nin the conformality approach\\cite{conf1,conf2,conf3,conf4,conf5,conf6}\nwhich {\\it ab initio} describes a flat (gravitationless) space-time.\n\nLet us assume, therefore, that the standard model states are\nall confined within a real-world brane with a thickness\nof order $10^{-19}~m$ in the $y$ direction. Following \\cite{AS}\n(see also \\cite{MS} and, for the many fold universe, \\cite{ADDK})\na scalar field $\\Phi(x_{\\mu},y)$ which has a $\\Phi$\ndomain wall in the $y$ dimension. In the vicinity of\nthe wall centered by convention at $y = 0$, \nand with the normalizations of \\cite{AS}\nthe field has the value\n\\begin{equation}\n\\Phi(y) = 2 \\mu^2 y\n\\end{equation}\n\nFirst consider chiral fermions \n(after all, $X$ could be a fermion but we will consider\nthe boson possibility later). \nIn this case we write the five-dimensional action\n\\begin{equation}\nS = \\int d^4x dy \\bar{\\Psi}_i \n[i\\gamma_{\\mu}\\partial/\\partial y_{\\mu} \n+ \\Phi(y) - m_i] \\Psi_i + ...\n\\label{fermion}\n\\end{equation}\nThe fermion $\\Psi_i$ is now localised at $y = m_i/(2 \\mu^2)$.\nIf the Higgs $H(y)$ is unlocalised inside the domain wall then the \nresulting coupling of $\\Psi_i$ to $\\Psi_j$ and $H$ has a gaussian\nsuppression\n\\begin{equation}\nexp ( - C(m_i- m_j)^2)/\\mu^2) \n\\end{equation}\nwhere C is a coefficient of order unity. \nThis is the gaussian overlap of the gaussian tails\nof the two wave functions. \nThe thickness of the real-world brane is $\\tau \\sim (\\mu)^{-1}$\nwhile the separation of the two fermion wave functions is \n$\\sigma \\sim (\\Delta y)_{ij}$. \nTo obtain the required suppression of \n$\\sim 10^{-46}$ we need $\\tau/\\sigma \\sim 10$. For example, if\n$\\tau \\sim 10^{-19}~m$, one needs $\\sigma \\sim 10^{-20}~m$.\nClearly only the ratio $\\tau/\\sigma$ matters, \nbut need not be a large number, in\norder to obtain the necessary suppression.\n\nIt is worth remarking that this gaussian \nsuppression of Yukawa couplings by\nlocalization in the fifth dimension\nhas a long historical counterpart in the \nlocalization of states on orbifold singularities\nstarting with \\cite{DFMS,HV,cvetic} in 1987 and subsequent derivative\nliterature\\cite{orb1,orb2,orb3,orb4,orb5,orb6}.\n \nThe superheavy particle $X$ may not be a fermion \nbut a boson, {\\it e.g.} the Higgs scalar considered in\nscenario (i) above. Fortunately\nwe can easily extend the localization argument of \\cite{AS} to\nthe case of a boson and obtain a similar result for\nthe gaussian suppression of the decay amplitude and consequent longevity.\nWe replace Eq.(\\ref{fermion}) by the following:\n\\begin{equation}\nS = \\int d^4x dy \\phi^{\\dagger}_i [\\Box - m_S^2 + \\Phi(y)^2]\\phi_i + .... \n\\label{boson}\n\\end{equation}\nand, analagously to the fermion $\\Psi$, the boson $\\phi$ is localized\naround $y = m_S/2\\mu^2$ when $\\Phi$ again \nhas a domain wall centered at $y = 0$.\nIdentifying $\\phi$ with $X$ then provides \nthe required longevity by\nthe same mechanism.\nIt would be amusing if the highest-energy cosmic\nrays provided the first evidence\nfor an extra spatial dimension!\n\n\\bigskip\n\\bigskip\n\nTo summarize the Z-burst mechanism for the highest energy\ncosmic rays, it has two positive features:\n\n1) The resonant energy derived from the \n$Z$ mass and the SuperKamiokande neutrino mass is numerically\nclose to the required energy.\n\n2) The spectrum is predicted to have the two-component shape\nsuggested by the present data.\n\nOn the other hand, there are also two {\\it apparently} negative features:\n\n3) The concomitant high-energy photons are not confirmed by present\ndata. Better data will confirm or refute this important prediction.\n\n4) The longevity of the superheavy particle is such a \nchallenge to microscpic model- building\nthat it may render the model less credible.\n\n\\bigskip\n\\bigskip\n\nIt is point (4) which we have attempted to ameliorate in the present article.\n\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\n{\\bf Acknowledgments } \\hspace{0.5cm} \n\n\nThis work was supported in part by the US Department of Energy\nunder the Grant No. DE-FG02-97ER-41036. We thank \nIgnatios Antoniadis, \nDon Ellison, Markus Luty and Tom Weiler\nfor discussions.\n\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\n\\begin{thebibliography}{99}\n\\bibitem{FKN}\nP.H. Frampton, B. Keszthelyi and Y.J. Ng, \nInt. J. Mod. Phys. {\\bf D8,} 117 (1999).\n\\bibitem{Greisen} \nK. Greisen, Phys. Rev. Lett. {\\bf 16,} 748 (1966);\n\\bibitem{KZ}\nG.T. Zatsepon and V.A. Kuzmin, Pisma Zh. Eksp. Theor. Fiz. {\\bf 4,} 114 (1966).\n\\bibitem{YD}\nS. Yoshida and H. Dai, J. Phys. {\\bf G24,} 905 (1998).\n\\bibitem{BKV}\nV. Berezinsky, M. Kachelriess and A. Vilenkin, Phys. Rev. Lett. {\\bf 79,} 4302 (1997).\n\\bibitem{BS}\nM. Birkal and S. Sarkar, Astropart. Phys. {\\bf 9,} 297 (1998).\n\\bibitem{Weiler}\nD. Fargion, B. Mele and A. Salis, Ap. J. {\\bf 517,} 725 (1999).\\\\\nT.J. Weiler, Astropart. Phys. {\\bf 11,} 303 (1999).\n\\bibitem{GK1}\nG. Gelmini and A. Kusenko, Phys. Rev. Lett. {\\bf 82,} 5202 (1999).\n\\bibitem{GK2}\nG. Gelmini and A. Kusenko. {\\tt hep-ph/9908276.}\n\\bibitem{Weiler2}\nT.J. Weiler. {\\tt hep-ph/9910316.}\n\\bibitem{FLee}\nP.H. Frampton and B.H. Lee, Phys. Rev. Lett. {\\bf 64,} 619 (1990).\n\\bibitem{FK}\nP.H. Frampton and T.W. Kephart, Phys. Rev. {\\bf D42,} 3892 (1991).\n\\bibitem{Hooft1}\nG. 't Hooft, Phys. Rev. Lett. {\\bf 37,} 8 (1976).\n\\bibitem{Hooft2}\nG. 't Hooft, Phys. Rev. {\\bf D14,} 3432 (1976).\n\\bibitem{Shifman}\nInstantons in Gauge Theory. Editor: M. Shifman. World Scientific (1994).\n\\bibitem{antoniadis}\nI. Antoniadis, Phys, Lett. {\\bf B249,} 263 (1998).\n\\bibitem{ADD1}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. {\\bf B429,} 263 (1998).\n\\bibitem{ADD2}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. {\\bf 436,} 257 (1998).\n\\bibitem{ADD3}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Rev. {\\bf D59,} 086004 (1999).\n\\bibitem{ADD4}\nArkeni-Hamed, S. Dimopoulos and G. Dvali. {\\tt hep-ph/9911386}.\n\\bibitem{verlinde}\nH. Verlinde. {\\tt hep-th/9906182}.\n\\bibitem{RS}\nL. Randall and R. Sundrum, Phys. Rev. Lett. {\\bf 83,} 3370 (1999).\n\\bibitem{conf1}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 041901 (1999).\n\\bibitem{conf2}\nP.H. Frampton and W.F. Shively, Phys. Lett. {\\bf B454,} 49 (1999).\n\\bibitem{conf3}\nP.H. Frampton and C. Vafa. {\\tt hep-th/9903226}.\n\\bibitem{conf4}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 085004 (1999).\n\\bibitem{conf5}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 121901 (1999).\n\\bibitem{conf6}\nP.H. Frampton and T.W. Kephart. {\\tt hep-th/9912028} and in preparation.\n\\bibitem{AS}\nN. Arkani-Hamed and M. Schmaltz. Phys. Rev. {\\bf D61,} 033005 (2000).\n{\\tt hep-ph/9903417.}\n\\bibitem{MS}\nE.A. Mirabelli and M. Schmaltz. {\\tt hep-ph/9912265.} \n\\bibitem{ADDK}\nN. Arkani-Hamed, S. Dimopoulos, G. Dvali and N. Kaloper.\n{\\tt hep-ph/9911386}.\n\\bibitem{DFMS}\nL.~Dixon, D.~Friedan, E.~Martines and S.~Shenker, Nucl. Phys. {\\bf B282,} 13 (1987).\n\\bibitem{HV}\nS.~Hamadi and C.~Vafa, Nucl. Phys. {\\bf B279,} 465 (1987).\n\\bibitem{cvetic}\nM. Cvetic, Phys. Rev. Lett. {\\bf 59,} 2829 (1987).\n\\bibitem{orb1}\nM. Dine and N. Seiberg, Nucl. Phys. {\\bf B306,} 137 (1988).\n\\bibitem{orb2}\nA. Font, L.E. Ibanez, F.Quevedo and A. Sierra, Nucl. Phys. {\\bf B307,} 109 \n(1988); {\\it ibid}. {\\bf B331,} 421 (1990).\n\\bibitem{orb3}\nA. Font, L.E. Ibanez, H.P. Nilles and F. Quevedo, Phys. Lett. {\\bf 210B,} 101 (1988).\n\\bibitem{orb4}\nL.J. Dixon, V. Kaplanovsky and J. Louis, Nucl. Phys. {\\bf B329,} 27 (1990).\n\\bibitem{orb5}\nY. Katsuki, Y. Kawanura, T. Kobayashi, N. Ohtsubo, Y. Ono and T. Tanioka,\nNucl. Phys. {\\bf B341,} 611 (1990).\n\\bibitem{orb6}\nA.E. Faraggi, Nucl. Phys. {\\bf B487,} 55 (1997).\n\\end{thebibliography}\n\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\\bigskip\n\n{\\bf Figure 1.}\n\n\\bigskip\n\nAllowed region of $M(X)~-~\\tau_X$ from Eq.(\\ref{flux}) and\nEq.(\\ref{limit}) of the text.\nIn the Figure $a_X = \\tau_X(10^7 t_0)^{-1}$ where $t_0$ \nis the age of the universe\nand $b_X = M(X)/(10^{14}GeV)$. Variations in \n$N, \\eta, \\Omega_X, h, B_{\\nu}, M(\\nu)$ can extend the allowed region\nbut we use only such order of magnitude estimates.\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002089.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{FKN}\nP.H. Frampton, B. Keszthelyi and Y.J. Ng, \nInt. J. Mod. Phys. {\\bf D8,} 117 (1999).\n\\bibitem{Greisen} \nK. Greisen, Phys. Rev. Lett. {\\bf 16,} 748 (1966);\n\\bibitem{KZ}\nG.T. Zatsepon and V.A. Kuzmin, Pisma Zh. Eksp. Theor. Fiz. {\\bf 4,} 114 (1966).\n\\bibitem{YD}\nS. Yoshida and H. Dai, J. Phys. {\\bf G24,} 905 (1998).\n\\bibitem{BKV}\nV. Berezinsky, M. Kachelriess and A. Vilenkin, Phys. Rev. Lett. {\\bf 79,} 4302 (1997).\n\\bibitem{BS}\nM. Birkal and S. Sarkar, Astropart. Phys. {\\bf 9,} 297 (1998).\n\\bibitem{Weiler}\nD. Fargion, B. Mele and A. Salis, Ap. J. {\\bf 517,} 725 (1999).\\\\\nT.J. Weiler, Astropart. Phys. {\\bf 11,} 303 (1999).\n\\bibitem{GK1}\nG. Gelmini and A. Kusenko, Phys. Rev. Lett. {\\bf 82,} 5202 (1999).\n\\bibitem{GK2}\nG. Gelmini and A. Kusenko. {\\tt hep-ph/9908276.}\n\\bibitem{Weiler2}\nT.J. Weiler. {\\tt hep-ph/9910316.}\n\\bibitem{FLee}\nP.H. Frampton and B.H. Lee, Phys. Rev. Lett. {\\bf 64,} 619 (1990).\n\\bibitem{FK}\nP.H. Frampton and T.W. Kephart, Phys. Rev. {\\bf D42,} 3892 (1991).\n\\bibitem{Hooft1}\nG. 't Hooft, Phys. Rev. Lett. {\\bf 37,} 8 (1976).\n\\bibitem{Hooft2}\nG. 't Hooft, Phys. Rev. {\\bf D14,} 3432 (1976).\n\\bibitem{Shifman}\nInstantons in Gauge Theory. Editor: M. Shifman. World Scientific (1994).\n\\bibitem{antoniadis}\nI. Antoniadis, Phys, Lett. {\\bf B249,} 263 (1998).\n\\bibitem{ADD1}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. {\\bf B429,} 263 (1998).\n\\bibitem{ADD2}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. {\\bf 436,} 257 (1998).\n\\bibitem{ADD3}\nArkeni-Hamed, S. Dimopoulos and G. Dvali, Phys. Rev. {\\bf D59,} 086004 (1999).\n\\bibitem{ADD4}\nArkeni-Hamed, S. Dimopoulos and G. Dvali. {\\tt hep-ph/9911386}.\n\\bibitem{verlinde}\nH. Verlinde. {\\tt hep-th/9906182}.\n\\bibitem{RS}\nL. Randall and R. Sundrum, Phys. Rev. Lett. {\\bf 83,} 3370 (1999).\n\\bibitem{conf1}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 041901 (1999).\n\\bibitem{conf2}\nP.H. Frampton and W.F. Shively, Phys. Lett. {\\bf B454,} 49 (1999).\n\\bibitem{conf3}\nP.H. Frampton and C. Vafa. {\\tt hep-th/9903226}.\n\\bibitem{conf4}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 085004 (1999).\n\\bibitem{conf5}\nP.H. Frampton, Phys. Rev. {\\bf D60,} 121901 (1999).\n\\bibitem{conf6}\nP.H. Frampton and T.W. Kephart. {\\tt hep-th/9912028} and in preparation.\n\\bibitem{AS}\nN. Arkani-Hamed and M. Schmaltz. Phys. Rev. {\\bf D61,} 033005 (2000).\n{\\tt hep-ph/9903417.}\n\\bibitem{MS}\nE.A. Mirabelli and M. Schmaltz. {\\tt hep-ph/9912265.} \n\\bibitem{ADDK}\nN. Arkani-Hamed, S. Dimopoulos, G. Dvali and N. Kaloper.\n{\\tt hep-ph/9911386}.\n\\bibitem{DFMS}\nL.~Dixon, D.~Friedan, E.~Martines and S.~Shenker, Nucl. Phys. {\\bf B282,} 13 (1987).\n\\bibitem{HV}\nS.~Hamadi and C.~Vafa, Nucl. Phys. {\\bf B279,} 465 (1987).\n\\bibitem{cvetic}\nM. Cvetic, Phys. Rev. Lett. {\\bf 59,} 2829 (1987).\n\\bibitem{orb1}\nM. Dine and N. Seiberg, Nucl. Phys. {\\bf B306,} 137 (1988).\n\\bibitem{orb2}\nA. Font, L.E. Ibanez, F.Quevedo and A. Sierra, Nucl. Phys. {\\bf B307,} 109 \n(1988); {\\it ibid}. {\\bf B331,} 421 (1990).\n\\bibitem{orb3}\nA. Font, L.E. Ibanez, H.P. Nilles and F. Quevedo, Phys. Lett. {\\bf 210B,} 101 (1988).\n\\bibitem{orb4}\nL.J. Dixon, V. Kaplanovsky and J. Louis, Nucl. Phys. {\\bf B329,} 27 (1990).\n\\bibitem{orb5}\nY. Katsuki, Y. Kawanura, T. Kobayashi, N. Ohtsubo, Y. Ono and T. Tanioka,\nNucl. Phys. {\\bf B341,} 611 (1990).\n\\bibitem{orb6}\nA.E. Faraggi, Nucl. Phys. {\\bf B487,} 55 (1997).\n\\end{thebibliography}"
}
] |
astro-ph0002090
|
Measuring the Size of the Vela Pulsar's Radio Emission Region
|
[
{
"author": "C.R. Gwinn"
}
] |
We describe the expected distribution of intensity for a scintillating source of finite size observed through a scattering medium, including systematic and instrumental effects. We describe measurements of the size of the Vela pulsar, using this technique.
|
[
{
"name": "iau177.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Gwinn et al.}{Vela Size}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Measuring the Size of the Vela Pulsar's Radio Emission Region}\n\\author{C.R. Gwinn}\n\\affil{Physics Department, UC Santa Barbara,\nSanta Barbara, California, USA}\n\\author{J.E. Reynolds, D.L. Jauncey}\n\\affil{Australia Telescope National Facility, Epping, New South Wales, Australia}\n\\author{H. Hirabayashi, H. Kobayashi, Y. Murata, P.G. Edwards}\n\\affil{Institute of Space and Astronautical Science, Sagamihara, Kanagawa, Japan}\n\\author{B. Carlson, S. Dougherty, D. Del Rizzo}\n\\affil{Dominion Radio Astronomy Observatory, Hertzberg Institute of Astrophysics, \nNational Research Council of Canada, Penticton, British Columbia, Canada}\n\\author{M.C. Britton}\n\\affil{Swinburne Centre for Astrophysics and Supercomputing, \nSwinburne University of Technology, Hawthorn, Victoria, Australia}\n\\author{P.M. McCulloch, J.E.J. Lovell}\n\\affil{Physics Department, University of Tasmania, Hobart, Tasmania, Australia}\n\n\\begin{abstract}\nWe describe the expected distribution \nof intensity for a scintillating source of finite size observed through a scattering\nmedium, including systematic and instrumental effects.\nWe describe measurements of the size of the Vela pulsar,\nusing this technique.\n\\end{abstract}\n\n\\section{Theoretical Background}\n\nWaves from a pointlike source observed through a scattering medium\nwill suffer random phase changes. If the phase changes are much\nlarger than 1 radian, the observer will receive radiation from many\nFresnel zones, and the scattering is said to be ``strong''. In this\ncase the electric field at the plane of the observer \nis the sum of the electric field from many lines of sight, \ndiffering random phases\n(Goodman 1985). \nThe net electric field is the result of a\nrandom walk. The electric field is thus drawn from a Gaussian\ndistribution. Its square modulus, the intensity, is drawn from an\nexponential distribution (Scheuer 1968).\n\nThe region from which the observer receives radiation is known as the\nscattering disk. Scattering changes\nphases in the Fresnel zones, and thus acts somewhat like\na lens. If the source is resolved by this ``lens'', the\nobserved intensity is an incoherent sum from each\npart of the source. \nFor a source\nof small but finite size, the resulting distribution of intensity is the sum of\n3 exponentials. The scales of the smaller exponentials are\napproximately the size of the source along either direction on the\nsky, in units of the linear resolution of the scattering disk\n(Gwinn et al. 1998). Figure 1 shows\nexample of the resulting intensity distributions for a point source,\nand for a small but resolved source. When the source is resolved, the\nlowest intensities are absent.\n\n% ~/tex/vela/optics/figs/3exp.ps\n% /home/cgwinn/vela/prod/TP_hists_22/figure/gate_2_.1f2t.binvar.cvf_10.bcut_01.ps\n\\begin{figure}\n\\plottwo{fig1a.eps}{fig1b.eps}\n\\caption{Left: Expected distribution of intensity\nfor a point source in strong scintillation (dashed line);\nand for a source of small but finite size (solid line).\nFrom Gwinn et al. (1998).\nRight upper: Observed distribution of correlated flux density \non a short baseline, for \nthe Vela pulsar.\nLower: Histogram shows \nresidual to the best-fitting distribution for point source,\ntaking into account the expected noise level. Solid curve\nshows best-fitting model including source size.\nFrom Gwinn et al. (2000a).\n}\n\\end{figure}\n\n\\section{Observations}\n\nWe compare the observed distribution of intensity with theoretical\nmodels to find the size of the Vela pulsar. The Vela pulsar is a\nfavorable object for such observations because it is strong and\nheavily scattered. Observations at decimeter wavelengths easily\ncapture many independent scintles in time and frequency. We observe\nthe source interferometrically, rather than with a single dish, to\navoid interference and effects of the substantial\nnoise baseline seen in single-dish observations. Details of the\nobservations are described elsehwere (Gwinn et al. 2000a).\n\nFigure 1 shows an example of the observed distribution of correlated\nflux density on the short Tidbinbilla-Parkes baseline for the Vela\npulsar. \nWe find a size of $340\\pm 80$~km for the data shown in the figure.\n\nNoise affects the distribution shown in Figure 1 strongly. Like\nfinite source size, noise reduces the number of points at small\namplitude. Noise can be measured accurately from observations of\nquasars, blank sky, or between pulses. Its effects can then be\nremoved. \nThe effects of changes in spectral structure on noise from digitization\ncan also be caculated\n(Gwinn et al. 2000b).\n\nSeveral effects other than noise can also affect the observed\ndistribution. Among these are correlator saturation, shot noise,\npulse-to-pulse variability, and gain variations. These can be either\ncalculated theoretically, measured from observations, or inferred from\nthe distribution of intensity. Gwinn et al. (2000a) discuss these\neffects in detail.\n\n\\section{Modulation Index}\n\nThe fact that source size affects the distribution of intensity, in\nscintillation, has long been known. (``Stars twinkle, planets do\nnot.'') The modulation index, $m=\\sqrt{<I^2>-<I>^2}/<I>$, quantifies\nthe effect (Salpeter 1967, Cohen, Gundermann, \\& Harris 1967).\nFor a point source $m=1$; for an extended source $m<1$,\nwith smaller modulation $m$ for a larger source,\nother factors being equal.\nSingle-dish observers\nused measurements of modulation index to infer source sizes before the\nadvent of radio interferometry, and \nthis technique remains standard at low frequencies\n(Hewish, Readhead, \\& Duffett-Smith 1974, Hajivasiliou 1992). \nHowever, it is more subject to scintillation shot\nnoise, and less immune to systematic effects, than a direct comparison\nof distribution functions.\n\nA finite observation necessarily samples a finite number of scintles.\nAverages over this sample approximate the statistical\naverages $<I^2>$ and $<I>$.\nBecause the nearly-exponential distribution falls off rapidly\nat high intensity, these sums (particularly $<I^2>$) are dominated by \nthe relatively rare scintles with the highest intensities.\nOn the other hand, the effects of source structure are\nmost important at the lowest intensities,\nwhere the number of scintillations is large,\nbut the contribution to $<I>$ and $<I^2>$ is small.\nThus, direct estimation of the modulation index\nis relatively insensitive to source size and\nrelatively more sensitive to scintle shot noise\nthan a direct comparison of the forms of distribution functions.\n\nCorrelator saturation also affects the modulation index\nstrongly, because its effects are largest at high intensity.\nMoreover, since the observable is a single number,\nrather than a distribution,\nit is more difficult to know what effects are playing signficant roles.\n\nInterestingly, Roberts \\& Ables (19)\nmeasured the modulation index, as well as the characteristic\ntime and frequency scales of scintillation,\nin their classic study of scattering of southern-hemisphere pulsars.\nThey report a modulation index of $0.97\\pm 0.03$ for the Vela pulsar\nat 18~cm wavelength, and of $0.90\\pm 0.02$ at\n9~cm wavelength.\nInterpolation between these values is consistent with our results\nquoted above.\n\nInterestingly, Roberts \\& Ables find that the modulation index\nis smaller at shorter observing wavelengths,\nsuggesting that the source size is greater.\nThis conclusion is surprising from the standpoint\nof the standard radius-to-frequency mapping.\n(Note, however,\nthat these measurements are\nof size rather than emission height.)\nThe larger inferred size\nmight reflect on the more complicated pulse\nprofile of this pulsar at shorter wavelengths (Kern et al. 2000).\nOn the other hand, it might also reflect systematic effects;\nat short wavelengths the scintles have wide bandwidths but\nthe source remains quite strong, so that correlator saturation should\nbecome more serious.\nIn contrast, self-noise\nand gain variations might be expected to be more important at lower\nfrequencies. \nObservations of the full distribution of intensity in scintillation,\nas a function of wavelength, should indicate the origin of\nthis variation of modulation index.\n\n\\begin{references}\n\\reference Cohen, M.H., Gundermann, E.J., \\& Harris, D.E. 1967, ApJ, 150, 767\n\\reference Goodman, J.W. 1985, Statistical Optics,\nNew York: Wiley\n\\reference Gwinn, C.R., Britton, M.C., Reynolds,\nJ.E., Jauncey, D.L., King, E.A., McCulloch, P.M., Lovell, J.E.J., \\&\nPreston, R.A. 1998, ApJ, 505, 928\n\\reference Gwinn, C.R., Britton, M.C.,\nReynolds, J.E., Jauncey, D.L., King, E.A., McCulloch, P.M., Lovell,\nJ.E.J., Flanagan, C.S., \\& Preston, R.A. 2000, ApJ, in press\n\\reference Gwinn, C.R., Britton, M.C.,\nCarlson, B., Dougherty, S., Del Rizzo, D.,\nReynolds, J.E., Jauncey, D.L., McCulloch, P.M., \nHirabayashi, H., Kobayashi, H., Murata, Y., \\& Edwards, P.G.\n2000, in preparation\n\\reference Hajivassiliou, C.A. 1992, Nature, 355, 232\n\\reference Hewish, A., Readhead, A.C.S., \\& Duffett-Smith, P.J., 1974, Nature, 252, 657\n\\reference Kern, J., Hankins, T., \\& Rankin, J. 2000, these proceedings\n\\reference Roberts, J.A., \\& Ables, J.G. 1982, MNRAS, 201, 1119\n\\reference Salpeter, E.E. 1967, ApJ, 147, 433\n\\reference Scheuer, P.A.G. 1968, Nature, 218, 920\n\\end{references}\n\n\\end{document}\n\n\n\n\n\n\n"
}
] |
[] |
astro-ph0002091
|
Current cosmological constraints from a 10 parameter CMB analysis
|
[
{
"author": "\\Huge SOME PERMUTATION OF:"
}
] |
We compute the constraints on a ``standard'' 10 parameter cold dark matter (CDM) model from the most recent CMB data and other observations, exploring 30 million discrete models and two continuous parameters. Our parameters are the densities of CDM, baryons, neutrinos, vacuum energy and curvature, the reionization optical depth, and the normalization and tilt for both scalar and tensor fluctuations. % Our strongest constraints are on spatial curvature, $-0.24<\Ok<0.38$, and CDM density, $h^2\Oc<0.3$, both at 95\%. Including SN 1a constraints gives a positive cosmological constant at high significance. % We explore the robustness of our results to various assumptions. We find that three different data subsets give qualitatively consistent constraints. Some of the technical issues that have the largest impact are the inclusion of calibration errors, closed models, gravity waves, reionization, nucleosynthesis constraints and 10-dimensional likelihood interpolation. % although the possibility of reionization %and gravity waves substantially weakens the %constraints on CDM and baryon density, tilt, Hubble constant %and curvature, allowing {\eg} a closed Universe, %open models with vanishing cosmological constant are still strongly %disfavored.
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[
{
"name": "10par.tex",
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k}}\n\\def\\ol{\\omega_\\Lambda}\n\\def\\om{\\omega_{\\rm m}}\n\\def\\on{\\omega_\\nu}\n\\def\\Cl{C_\\l}\n\\def\\dT{\\delta T}\n\\def\\T{{\\bf d}}\n\\def\\ns{n_s}\n\\def\\nt{n_t}\n%\\def\\Qs{Q_s}\n%\\def\\Qt{Q_t}\n\\def\\As{A_s}\n\\def\\At{A_t}\n\\def\\dA{d_{\\rm lss}}\n\\def\\zlss{z_{lss}}\n\n%\\def\\data{{\\bf\\delta T}}\n\\def\\data{{\\rm data}}\n\\def\\L{{\\cal L}}\n\n\n\\def\\p{{\\bf p}}\n\\def\\x{{\\bf x}}\n\\def\\xh{\\widehat{\\bf x}}\n\n\\def\\C{{\\bf C}}\n\\def\\I{{\\bf I}}\n\\def\\M{{\\bf M}}\n\n\n\n\\def\\l{\\ell}\n\\def\\llo{\\l_{\\rm low}}\n\\def\\lhi{\\l_{\\rm high}}\n\\def\\Cl{C_\\ell}\n\\def\\Clo{C_\\ell^{low}}\n\\def\\Chi{C_\\ell^{high}}\n\\def\\lstar{\\l^*}\n\\def\\ith{i^{th}}\n\\def\\first{1^{st}}\n\\def\\second{2^{nd}}\n\n\n\n\\documentstyle[emulateapj,danonecolfloat]{article}\n%\\documentstyle[aasms4]{article}\n\\def\\NoApjSectionMarkInTitle#1{#1.\\ }\n%\\draft\n\\begin{document}\n\\twocolumn[%%% Begin front material\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%\\tighten\n%\\eqsecnum\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n\\journalid{337}{15 January 1989}\n\\articleid{11}{14}\n\n\n\\submitted{Submitted to ApJ February 11 2000, accepted April 6}\n%\\submitted{\\today. To be submitted to ApJ.}\n%\\submitted{Submitted to ApJL September 16; accepted February 2}\n\n\\title{Current cosmological constraints from a 10 parameter CMB analysis}\n\n%\\author{\\Huge SOME PERMUTATION OF:}\n\\author{\nMax Tegmark\n\\footnote{Dept. of Physics, Univ. of Pennsylvania, \nPhiladelphia, PA 19104;\[email protected]}$^{,\\>b}$\nand \nMatias Zaldarriaga\n\\footnote{Institute for Advanced Study, Princeton, \nNJ 08540; [email protected]}\n}\n\\keywords{cosmic microwave background---methods: data analysis}\n\n\n\\begin{abstract}\n\nWe compute the constraints on a ``standard'' 10 parameter \ncold dark matter (CDM) model from the most recent \nCMB data and other observations, \nexploring 30 million discrete models and \ntwo continuous parameters.\nOur parameters are the densities of CDM, baryons, neutrinos, \nvacuum energy and curvature, the reionization optical depth, and the\nnormalization and tilt for both scalar and tensor fluctuations.\n%\nOur strongest constraints are on spatial curvature,\n$-0.24<\\Ok<0.38$, and CDM density,\n$h^2\\Oc<0.3$, both at 95\\%.\nIncluding SN 1a constraints gives a\npositive cosmological constant at high significance.\n%\nWe explore the robustness of our results to various\nassumptions. We find that three different data subsets \ngive qualitatively consistent constraints.\nSome of the technical issues that have the largest impact\nare the inclusion of calibration errors, closed models,\ngravity waves, reionization, nucleosynthesis constraints \nand 10-dimensional likelihood interpolation.\n\n% although the possibility of reionization\n%and gravity waves substantially weakens the \n%constraints on CDM and baryon density, tilt, Hubble constant\n%and curvature, allowing {\\eg} a closed Universe,\n%open models with vanishing cosmological constant are still strongly \n%disfavored.\n\\end{abstract}\n\n\\keywords{cosmic microwave background --- methods: data analysis}\n\n]%%% End front material\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\n\\section{INTRODUCTION}\n\nThe past year has yet again seen dramatically improved measurements\nof the Cosmic Microwave Background (CMB) power spectrum, \nwith the Python, Viper, Toco and Boomerang experiments suggesting \na first acoustic peak with a fairly well-defined height and position.\nFurther great improvements are expected shortly from the Antarctic \nBoomerang flight, the MAP satellite and other experiments, with the potential \nto accurately measure about ten cosmological parameters\n(Jungman {\\etal} 1996; \nBond {\\etal} 1997; Zaldarriaga {\\etal} 1997;\nEfstathiou \\& Bond 1998),\nespecially when combined with galaxy redshift surveys\n(Eisenstein {\\etal} 1999), supernovae 1a (SN 1a) \nobservations (White 1998) or gravitational Lensing\n(Hu \\& Tegmark 1999).\n\\begin{table}\n\\noindent\n%\\fcolorbox{blue}{yellow}\n{\n%\\footnotesize\n\\small\n{\\bf Table 1} -- CMB data used\\\\\n}\n\\smallskip\n{\\footnotesize\n\\begin{tabular}{|l|r|r|}\n\\hline\nExperiment\t&$\\dT$\t&$\\l$\\\\\n\\hline\n\\input tab1.tex\n\\hline\t\t\n\\end{tabular}\n}\n\\end{table}\n\n\n\n\\begin{figure}[tb] \n%\\vskip-1.5cm\n%\\centerline{\\epsfxsize=7cm\\epsffile{f1.eps}}\n\\centerline{\\epsfxsize=7cm\\epsffile{pipeline4.eps}}\n%\\vskip-1.5cm\n\\caption{\\label{PipelineFig}\\footnotesize%\nThe analysis of a large CMB data set is conveniently \nbroken down into four steps: mapmaking, foreground removal, \npower spectrum extraction and parameter estimation.\n}\n\\end{figure}\n\n\nComparing these observations with theoretical predictions to achieve this goal\nin practice is highly non-trivial, even aside from the experimental challenge\nof controlling systematic errors, and is often broken down into several steps,\nschematically illustrated in \\fig{PipelineFig}:\n\\begin{enumerate}\n\\itemsep0cm\n\\item Compress the time-ordered data set into sky maps at various \nfrequencies, so as to minimize the effect of \ncorrelated detector noise, scan-synchronous offsets, and other non-sky signals\n(Wright 1996; Tegmark 1997a).\n\\item Compress the multi-frequency maps into a single CMB map so as to minimize\nthe contribution of detector noise and foreground contamination \n(see Tegmark {\\etal} 2000 and references therein).\n\\item Compress this CMB map into measurements of the angular power spectrum\non various angular scales\n(Tegmark 1997b; Bond, Jaffe \\& Knox 1998), \na step nicknamed ``radical compression'' by Bond {\\etal}\n\\item Convert these power spectrum measurements into constraints on cosmological \nparameters.\n\\end{enumerate}\nThis paper is focused on the last of these four steps,\ndescribing a method and applying it to all currently available data.\n\nSince fast and accurate software is now available for computing how the \ntheoretically predicted power spectrum depends on the cosmological parameters,\nthis last step may at first appear rather trivial: just run a code such as\nCMBfast (Seljak \\& Zaldarriaga 1996) at a fine grid of points in parameter space and \nperform a $\\chi^2$ fit of the corresponding theoretical power spectra to \nthe observed data. The problem is that the currently most popular \ncosmological model has of order $N=10$ free parameters, making such \nan $N$-dimensional parameter grid rather huge and unwieldy.\nThere are also additional challenges related to evaluating the\nlikelihood function (Bond {\\etal} 1998; Bartlett {\\etal} 1999) \nthat we will discuss in more detail below.\n\nThe first analyses based on \nCOBE DMR used $N=2$ parameters, the scalar quadrupole normalization \n$\\As$ and tilt $\\ns$ of the power spectrum\n(\\eg, Smoot {\\etal} 1992; Gorski {\\etal} 1994; Bond 1995; \nBunn \\& Sugiyama 1995; Tegmark \\& Bunn 1995).\nSince then, many dozens of papers have extended this\nto incorporate more data and parameters, with recent work including \nBunn \\& White (1997); de Bernardis {\\etal} (1997); Ratra {\\etal} (1999); Hancock\n{\\etal} (1998); Lesgourges {\\etal} (1999); Bartlett {\\etal} (1998); \nWebster {\\etal} (1998); Lineweaver \\& Barbosa (1998ab); \nWhite (1998); Bond \\& Jaffe (1998); \nGawiser \\& Silk (1998); Contaldi {\\etal} (1999),\nGriffiths {\\etal} 1999; Melchiorri {\\etal} (1999);\nRocha (1999).\n\nIn an important paper, Lineweaver (1998) \nmade the leap up to $N=6$ parameters:\n$n_s$, $\\As$, the Hubble constant $h$ and\nthe relative densities $\\Oc$, $\\Ob$ and $\\Ol$\nof CDM, baryons and vacuum energy, thereby setting a new standard. \nTegmark (1999, hereafter T99)\npushed on to $N=8$ by adding the reionization optical depth $\\tau$\nand the gravity wave amplitude $\\At$. \nEfstathiou {\\etal} (1999), Efstathiou (1999), \nBahcall {\\etal} (1999),\nDodelson \\& Knox (2000) \nand Melchiorri {\\etal} (2000) performed analyses with \ndifferent techniques, better data and around 6 parameters, all finding\ninteresting joint constraints on $\\Ol$ and the matter density.\nDespite this progress, however, \na number of issues still need to be improved to do justice to \nthe ever-improving data.\n\nPerhaps the most glaring problem is that no closed models \n(White \\& Scott 1996) \nhave ever been\ncomputed exactly in these analyses, \nexcept for that of Melchiorri {\\etal} (2000), \nsince the CMBfast software \nwas limited to flat and open models. We remedy this in the present paper\nby using version 3.2 of CMBfast (Zaldarriaga \\& Seljak 1999), which is\ngeneralized to closed models. A new code by Challinor {\\etal} (2000), \nbased on CMBfast, also does closed models, agreeing well with CMBfast.\n \nAnother problem with all previous analyses is that they assumed the \nmassive neutrino density $\\On$ to be zero, although there is strong \nevidence from both the atmospheric and solar neutrino anomalies that \n$\\On>0$. Since these particle physics constraints are only sensitive\nto the {\\it differences} between the (squared) masses of the various\nneutrinos, they do not imply that neutrinos are \nastrophysically uninteresting. \nIndeed, because the CMB and matter power spectra \ncan place some of the most stringent \nupper limits on neutrino masses (Hu {\\etal} 1998), \nit would be a real pity \nto omit this aspect of the analysis.\nJust as increasing $\\Oc$\nsuppresses the acoustic peaks, \nincreasing $\\On$ suppresses does so by a comparable amount.\nIndeed, these two parameters become nearly degenerate for large $\\On$, \ncorresponding to neutrinos massive enough to be fairly nonrelativistic at \nthe relevant redshifts, so the inclusion of neutrinos will, among other things, \nweaken the lower limit on $\\Oc$.\n\nAnother weakness of the T99 analysis was that it assumed \nthat the relative amplitude \n$r\\equiv\\At/\\As$ \nof gravity waves was linked to the tensor spectral index by the\ninflationary consistency relation \n$r = -7\\nt$ (Liddle \\& Lyth 1992),\nalthough one of the most exciting applications of CMB data \nwill be to test this relation. We will remedy both of these problems \nby extending our parameter space to $N=10$ dimensions, including \nboth $\\On$ and $\\nt$ as free parameters.\n\nFinally, as we will discuss at length below, there are \na number of areas where accuracy has been unsatisfactory and \ncan be substantially improved.\n\n\nThe rest of this paper is organized as follows.\nWe describe our method in \\sec{MethodSec}, apply it to the available data in\n\\sec{ResultsSec} and summarize our conclusions in \\sec{ConclusionsSec}.\nSome technical details regarding marginalization are derived in the Appendix.\n\n\n\n\\section{METHOD}\n\n\\label{MethodSec}\\\n\n\\begin{figure}[tb] \n\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.5cm\\epsffile{experiments.ps}}\n%\\centerline{\\epsfxsize=9.5cm\\epsffile{f2.ps}}\n\\vskip-1.0cm\n\\caption{\\label{DataFig}\\footnotesize%\nThe band power measurements used.\n}\n\\end{figure}\n\n\n\\subsection{The problem}\n\nOur data consists of the $n=65$ band power measurements $\\dT^2_i$\nlisted in Table 1 and shown in \\fig{DataFig}, $i=1,...,n$.\nThe band power measurement $d_i\\equiv \\dT^2_i$ probes a weighted average\nof $\\delta T_\\l^2\\equiv\\l(\\l+1)C_\\l/2\\pi$,\n\\beq{WindowEq}\n\\expec{d_i} = \\expec{\\dT^2_i} =\n\\sum_\\l {1\\over\\l}W^i_\\l \\delta T_\\l^2,\n\\eeq\nwhere $W^i_\\l$ is the band-power window function (distinct from\nthe variance window function; see Knox 1999).\nThese known weights $W^i_\\l$\nreflect which angular scales the measurement is sensitive to.\n\nThe power spectrum in turn depends on our vector of cosmological \nparameters $\\p$ in a complicated fashion $C_\\l(\\p)$ that we use CMBfast to\ncompute. The scatter in the relation between $d_i$ and $\\expec{d_i}$\ndue to detector noise and sample variance is described by \na likelihood function $\\L_i(d_i;C_\\l(\\p))$, the probability\ndistribution for $d_i$ given $\\p$.\nIf the errors in the different data points were all independent, \nthen the combined likelihood of observing the set of all data\ngiven $\\p$ would be simply\n\\beq{Leq}\n\\L(\\data;\\p) = \\prod_{i=1}^n \\L_i(d_i;C_\\l(\\p)).\n\\eeq\nThis is complicated by the fact that some measurements are correlated, \nas will be discussed in \\sec{LikelihoodSec}.\n\nOur problem is to evaluate this likelihood function in the 10-dimensional \nparameter space that $\\p$ inhabits. To obtain Bayesian constraints on \nindividual parameters or joint constraints on interesting\npairs (such as $\\Om$ and $\\Ol$), we then marginalize over the remaining\nparameters with appropriate priors.\n \n \n\\subsection{Breaking it into four sub-problems}\n\nIf we had infinite computing resources, the solution would be \nstraightforward: compute the theoretical CMB power spectrum $C_\\l(\\p)$\nwith the CMBfast software (Seljak \\& Zaldarriaga 1996) and the corresponding\nlikelihood at a fine grid of points in \nthe $N$-dimensional parameter space. \nIn practice, this is inconvenient. With $M$ grid points in each \ndimension, $M^N$ power spectra must be computed.\nEven if we take $M$ as low as 10, the amount of \nwork thus grows by an order of magnitude for \neach additional parameter. With 1 minute per power spectrum\ncalculation, $N=10$ would translate to over $10^4$ years of \nCPU time. \n\nFortunately, the underlying physics\n(see {\\eg} Hu {\\etal} 1997 for a review) \nallows several numerical simplifications to be made.\nWe will adopt the approximation scheme used in T99 with additional\nimprovements as described below.\nOur method conveniently separates into four separate steps.\n\\begin{itemize}\n\\item {\\bf Step 1:} Run CMBfast many times for three particular subsets of\nthe parameter grid. The results are three large files: one with tensor \npower spectra, one with scalar power spectra for $\\ell\\simlt 100$\nand one with scalar power spectra for $\\ell\\simgt 100$.\n\\item {\\bf Step 2:} Interpolate these spectra \nonto larger subsets of the\nparameter grid. The results are two huge files with 7-dimensional\nmodel grids, one for scalars and one for tensors.\nThese two files allow any power spectrum in the full 10-dimensional \nmodel grid to be computed almost instantaneously. \n\\item {\\bf Step 3:} Compute and save the likelihood $\\L$ for each model.\n\\item {\\bf Step 4:} Perform 10-dimensional interpolation and marginalize\nto obtain constraints on individual parameters, constraints in the\n$(\\Om,\\Ol)$-plane, \\etc\n\\end{itemize}\nBelow we will describe each of these four steps in turn.\nBefore doing this, however, it is interesting to contrast this \n``huge grid'' approach with an alternative strategy.\nDodelson \\& Knox (2000) and Melchiorri {\\etal} (2000)\nperformed their analyses without computing and \nstoring such a grid. Instead, they found the maximum-likelihood \nparameter vector $\\p$ by a direct numerical maximum search, \ncomputing power spectra with CMBfast on the fly as needed. \nSimilarly, constraints in say the $(\\Om,\\Ol)$-plane were obtained by\nperforming a numerical maximum search over the remaining parameters\nfor each $(\\Om,\\Ol)$ grid point.\nOne drawback of this approach is that everything needs to be repeated \nfrom scratch if the data set is changed, whereas steps 1 and 2 \nin our method are independent of the data set and need only be done\nonce and for all. The same drawback applies to exploring different\npriors.\nThere is also no guarantee that CMBfast gets run fewer times with this\ndirect search approach, as a numerical search in the high-dimensional space\ntends to require large numbers of likelihood evaluations\n(Dodelson 1999, private communication; see also Hannestad 1999).\n\n\n\\subsection{Parameter space}\n\nWe choose our 10-dimensional parameter vector to be\n\\beq{pEq}\n\\p\\equiv(\\tau,\\Ok,\\Ol,\\oc,\\ob,\\on,\\ns,\\nt,\\As,\\At),\n\\eeq\nwhere the physical densities \n$\\omega_i\\equiv h^2\\Omega_i$, $i=$cdm, b, $\\nu$. The advantage of this \nparameterization (see Bond {\\etal} 1997)\nwill become clear in \\S\\ref{HighLowSec}.\n$\\Ok$ is the spatial curvature, so \nin terms of these parameters,\n\\beq{hEq}\nh = \\sqrt{\\oc+\\ob+\\on\\over 1-\\Ok-\\Ol}.\n\\eeq\nThis parameter space is identical to that used in T99 except that we have \nadded $\\on$ and replaced $h$ by $\\Ol$ as a free parameter.\n\nWe wish to probe a large enough region of parameter space to cover\neven quite unconventional models. This way, constraints from non-CMB\nobservations can be optionally included by explicitly multiplying \n$\\L(\\p)$ by a Bayesian prior after Step 3 rather than being \nhard-wired in from the outset.\nTo avoid prohibitively large $M$,\nwe use a roughly logarithmic\ngrid spacing for $\\om$, $\\ob$ and $\\on$, \na linear grid spacing for $\\Ok$ and $\\Ol$,\na hybrid for $\\tau$, $\\on$, $\\ns$ and $\\nt$, \nand (as described below) no grid at all for $\\As$ and $\\At$.\nWe let the parameters take on the following values:\n\\begin{itemize}\n\\item $\\tau=0, 0.05, 0.1, 0.2, 0.3, 0.5, 0.8$ %(7 values)\n\\item $\\Ol=-1.0, -0.8, -0.6, -0.4, ...., 1.0$ %(11 values)\n\\item $\\Ok$ such that $\\Om\\equiv 1-\\Ok-\\Ol = 0.2, 0.4, ..., 2.0$\n\\item $\\oc=0.02, 0.03, 0.05, 0.08, 0.13, 0.2, 0.3, 0.5, 0.8$ %(9 values)\n\\item $\\ob=0.003, 0.005, 0.008, 0.013, 0.02, 0.03, 0.05, 0.08, 0.13$ %(9 values)\n\\item $\\on=0, 0.02, 0.05, 0.08, 0.13, 0.2, 0.3, 0.5, 0.8$ %(9 values)\n\\item $\\ns=0.50, 0.70, 0.90, 1.00, 1.10, 1.20, 1.30, 1.50, 1.70$ %(9 values)\n\\item $\\nt=-1.00, -0.70, -0.40, -0.20, -0.10, 0$ %(6 values)\n\\item $\\As$ is not discretized\n\\item $\\At$ is not discretized\n\\end{itemize}\nNote that the extent of the $\\Ok$-grid depends on $\\Ol$, giving \na total of $10\\times 11=110$ points in the $(\\Om,\\Ol)$-plane.\nOur discrete grid thus contains \n$7\\times 110\\times 9\\times 9\\times 9\\times 9\\times 6=30,311,820$ models.\nAs will become clear from our discussion below, the main limitation on\nthis grid size is the disk space used in Step 2 rather than the \nCPU time used in Step 1, so it will probably be desirable to further\nrefine it as CMB data gets better.\n\n\n\\subsection{Separating scalars and tensors}\n\nIf we were to run CMBfast in the standard way, computing scalar and tensor\nfluctuations simultaneously, we would have to explore a 9-dimensional \nmodel grid since only $\\As$ drops out as an overall normalization factor. \nInstead, we compute \nthe scalar fluctuations $\\Cl^{scalar}$ and \nthe tensor fluctuations $\\Cl^{tensor}$\nseparately, normalize them to both have a quadrupole of unity, and \ncompute the combined power spectrum as\n\\beq{TensorComboEq}\n\\Cl = \\As\\Cl^{scalar} + \\At\\Cl^{tensor}.\n\\eeq\nWe therefore only need to compute two \n7-dimensional grids with CMBfast, one over\n$(\\tau,\\Ok,\\Ol,\\oc,\\ob,\\on,\\ns)$\nand the other over\n$(\\tau,\\Ok,\\Ol,\\oc,\\ob,\\on,\\nt)$. The other advantage of calculating \nscalars and tensors separately is that tensors only need to be\ncalculated up to an $l$ of 400, which saves additional time. \n\nAllowing 1 minute per model, the scalar grid alone would still\ntake about 10 years of CPU time. Most models take substantially longer\nto run, since reionization, curvature and neutrinos slow CMBfast down.\nIt is therefore useful to take advantage of the underlying physics to make further\nsimplifications.\n\n\n\\subsection{Separating small and large scales}\n\\label{HighLowSec}\n\n\n% The tensor power spectrum depends only \n% weakly on $\\oc$ and $\\ob$, and essentially not at all on \n% $\\on$ if the total dark matter density $\\oc+\\on$ stays\n% constant. We therefore compute \n% the tensor power spectrum\n% with the fine grid restricted to \n% $(\\tau,\\Ok,\\Ol,\\nt)$, setting $\\on=0$ and \n% using only ultra-course three-point grids for \n% $\\oc$ and $\\ob$. We then fill in the rest of the \n% $(\\oc,\\ob)$-values using cubic spline interpolation.\n% To fill in the missing $\\on$-values, we \n% first use the above-mentioned fact that $\\oc+\\on$ is all that matters\n% to produce models with neutrinos from the ones without neutrinos,\n% then interpolate. For instance, if $\\oc'$ and $\\oc''$ are two \n% values of $\\oc$ in our grid, then the power spectrum\n% for $(\\oc,\\on)$ = $(\\oc',0)$ will be essentially the same as\n% that for $(\\oc,\\on)=(\\oc'',\\oc'-\\oc'')$.\n\nThe tensor power spectrum depends only \nweakly on $\\oc$, $\\ob$ and $\\on$.\nWe therefore compute \nthe tensor power spectrum\nwith the fine grid restricted to \n$(\\tau,\\Ok,\\Ol,\\nt)$, \nusing only ultra-course three-point grids for \n$\\oc$, $\\ob$ and $\\on$. \nWe then fill in the rest of the \n$(\\oc,\\ob,\\on)$-values using cubic spline interpolation.\n\n% Dude, what is $\\l\\ll 100/\\Om^{1/2}$, is that l=1???\n% :):):)\nThe scalar power spectrum $\\Cl$ for $\\l\\ll 100/\\Om^{1/2}$ corresponds\nto fluctuations on scales outside the\nhorizon at recombination. This makes it almost independent of \nthe causal microphysics that create the familiar acoustic peaks, \n\\ie, independent of $\\om$, $\\on$ and $\\ob$. We therefore compute \nthe scalar power spectrum\non large scales with the fine grid restricted to \n$(\\tau,\\Ok,\\Ol,\\ns)$, using only ultra-course \nthree-point grids for $\\oc$, $\\ob$ and $\\on$ to \nto pick up weak residual effects aliased down \nfrom larger $\\l$. \nWe then fill in the rest of the $(\\oc,\\ob,\\on)$-values\nusing cubic spline interpolation.\n\nFor the remaining (high $\\l$) part of the power spectrum, \nmore radical simplifications can be made.\nFirst of all, the effect of reionization is mainly\nan overall suppression of $\\Cl$ by a constant factor \n$e^{-2\\tau}$ on these small scales.\nSecond, the effect of changing both $\\Ok$ and $\\Ol$ \nis merely to shift the power spectrum sideways. This is because the\nacoustic oscillations at $z\\simgt 1000$ \n(at which time $\\Ok\\approx\\Ol\\approx 0$ regardless of their present value)\ndepend only on \n$\\om$, $\\ob$ and $\\on$, and the geometric projection \nof these fixed length scales onto angular scales $\\theta$ in the sky\nobeys %(REF)\n$\\theta\\propto 1/\\dA$, where\n$\\dA$ is the angular diameter distance to the last scattering surface.\nIn T99 and Efstathiou {\\etal} (1999), \n$\\dA$ was estimated analytically by integrating out to the\nredshift of last scattering given by the fit of Hu \\& Sugiyama (1996).\nSince CMBfast automatically computes this quantity anyway, we \neliminate this approximation by simply using this numerical value.\n\n$\\Om$ and $\\Ol$ also modify the\nlate integrated Sachs-Wolfe effect, but this is important\nonly for $\\l\\simlt 30$ (Eisenstein {\\etal} 1999). \nThe only other effect is a small correction due to gravitational lensing\n(Metcalf \\& Silk 1997; Stompor \\& Efstathiou 1999), which we ignore here because of \nthe large error bars on current small-scale data.\nTo map the model $\\p^*$ into the model $\\p$ with all parameters \nexcept $\\tau$, $\\Ok$ and $\\Ol$ unchanged,\n% $(\\tau^*,\\Ok^*,\\Ol^*)$ into the model \n% $(\\tau,\\Om,\\Ol)$ with all other parameters unchanged,\nwe thus multiply its high $\\l$ power spectrum\nby $e^{2(\\tau^*-\\tau)}$ and shift it to the right by an $\\l$-factor of \n$\\dA/\\dA^*$.\n% $\\theta(\\Om^*,\\Ol^*)/\\theta(\\Om,\\Ol)$.\n \nWe therefore adopt the following procedure for the first two steps. \nIn Step 1, we compute\n\\begin{itemize}\n\\item scalar power spectra out to $\\l=5000$ for the subgrid with\n$\\tau=\\Ok=\\Ol=0$ (merely 6,561 models),\n\\item scalar power spectra out to $\\l=400$\nwith the subgrid restricted to\n$\\tau=0, 0.1, 0.8$, \n$\\om=0.02, 0.2, 0.8$, \n$\\ob=0.003, 0.02, 0.13$,\n$\\on=0, 0.2, 0.8$\n(80,190 models), and\n\\item tensor power spectra with the matter densities restricted to \nthis same subgrid (80,190 models).\n\\end{itemize}\n\nIn Step 2, we use cubic spline interpolation separately for each $\\l$\nto extend the tensor models and the low-$\\ell$ scalar models \nto the full parameter grid. \nTo account for the effects of $\\tau$, $\\Ok$ and $\\Ol$, \nwe then shift the high-$\\ell$ scalar models vertically and horizontally \nas described above and splice them together with the corresponding\nlow-$\\l$ models at a cutoff value $\\lstar$.\nFor a given model, we choose $\\lstar$ to be 100 multiplied by the horizontal \nshifting factor. In other words, the high-$\\ell$ model always gets spliced\nat the location that corresponded to $\\l=100$ before shifting it sideways,\nso open models get spliced at higher $\\l$ and closed at lower.\nWhen computing the low-$\\ell$ models in Step 1, we therefore \nadjust the accuracy flag ``ketamax'' in CMBfast \nto be 400 times this same shifting factor.\n\n\nThe public releases of CMBfast normalize the power spectra $C_\\l$ \nto COBE automatically. \nThis normalization scheme is not appropriate for our merging technique,\nsince we need a convention\nindependent of the cosmological parameters so that when we combine the\nhigh and low grids, \nthe relative normalization of the models is correct. To achieve this, we\nremoved the COBE normalization from CMBfast and normalized the\npower spectrum in both the flat and non-flat codes to agree on scales \nmuch smaller than the curvature scale. \n\nFor the reader interested in implementing this scheme, it is worth noting\nthat almost all the time in Step 1 is spent on the low scalar grid.\nFor this grid, substantial time is saved by only computing the \npower spectrum for the low $\\l$-values where it is needed.\nNote that the loop over tilts ($\\ns$ or $\\nt$) is essentially\nfree, since CMBfast can compute multiple tilts simultaneously.\nThe only reason we have used so few tilt values is because \nof disk space considerations in Steps 2 through 4.\nIncluding various test runs, we filled up more than\nhalf of a 200 GB disk array.\n\n\n\\subsection{Testing step 2}\n\nTo test the accuracy of the resulting scalar and tensor model grids\nproduced in Step 2, we drew a random sample of $\\sim 10^3$ of \nthe models and recomputed them from scratch with CMBfast.\nFor most models, we found our results to be accurate to a within \na few percent. The remainder generally had very early reionization\n(high $\\tau$ and low $h\\Ob$),\nwhich causes a broad bump of regenerated power from motions on the\nnew last scattering surface. Since our approximation simply suppresses the\nsmall scale power by $e^{-2\\tau}$, it therefore underpredicts the\npower on the angular scale corresponding to the horizon size at reionization.\nIn addition, the interpolation performed poorly at the lowest $\\l$\nfor some quite crazy models, which could be remedied by running CMBfast \non a finer grid.\n\nAs data quality improves further, it will probably be worthwhile to \nsimply include $\\tau$ explicitly in the high-$\\l$ grid.\nIn this case, the remaining errors introduced by our\napproximation scheme can of course be continuously reduced to zero by\nrefining the $(\\oc,\\ob,\\on)$-grid for low \n$\\l$ and shifting the splicing point upwards from $\\l\\sim 100$.\n\n\\subsection{Step 3: computing likelihoods}\n\\label{LikelihoodSec}\n\nWe use the CMB data and window functions listed in Table 1\nand shown in \\fig{DataFig}. \nThis is taken from the compilation of Lineweaver (1998) with the\naddition of the new results from QMAP\n(Devlin {\\etal} 1998; Herbig {\\etal} 1998; de Oliveira-Costa {\\etal} 1998),\nMSAM (Wilson {\\etal} 1999), \nToco (Torbet {\\etal} 1999; Miller {\\etal} 1999), \nPython V (Coble 1999), Viper (Peterson {\\etal} 2000) and\nBoomerang (Mauskopf {\\etal} 1999). \nFor an up-to-date annotated compilation of all current data, \nsee Gawiser \\& Silk (2000).\nFor the COBE data, we use the exact window function from Tegmark (1997b).\nIn all other cases, we approximate the window functions by a Gaussian\nof FWHM=$\\lhi-\\llo$ from Table 1.\nThis approximation does not appear to have much of an effect on the\nresults: we repeated the analysis with the much more extreme approximation\nwhere the windows are delta functions at $(\\llo+\\lhi)/2$ and obtained\nessentally unchanged results.\nKnox \\& Page (2000) compared full window functions with delta functions\nand came to the same\nconclusion.\n\n\n\\def\\Cuc{\\C^{\\rm (meas)}}\n\\def\\Cic{\\C^{\\rm (ical)}}\n\\def\\Csc{\\C^{\\rm (scal)}}\n\nAs discussed in great detail by Bond, Jaffe \\& Knox (1998) and also by \nBartlett {\\etal} (1999), \nan accurate calculation of the likelihood function \n$\\L(\\data|\\p)$ is nontrivial. If the band-power measurement\n$d_i$ is a quadratic function of the sky temperatures measured by the\nexperiment in question, then $\\L_i(d_i;C_\\l(\\p))$ is a generalized \n$\\chi^2$ distribution when viewed as a function of $d_i$ \n(Wandelt {\\etal} 1998), but sufficient details to compute this function\nexactly are rarely published when band power measurements are released.\nUseful approximations have therefore been derived that require only \nthe asymmetry between upper and lower error bars as input \n(Bond, Jaffe \\& Knox (1998), Bartlett {\\etal} (1999).\nThe former approximation is implemented by a nice publicly available\npackage called RADPACK, maintained by Lloyd Knox at \n{\\it http://flight.uchicago.edu/knox/radpack.html}, which was used in \nthe analyses of Dodelson \\& Knox (2000) and Melchiorri {\\etal} (2000).\nIn this paper, we will stick with the cruder Gaussian approximation\n\\beq{chi2eq}\n\\L(\\T;C_\\l(\\p))\\approx\n% \\exp\\left[-{1\\over 2}\\left({\\dT_i^2-\\expec{\\dT_i^2}\\over\\sigma_i}\\right)\\right],\ne^{-{1\\over 2}(\\T-\\expec{\\T})^t\\C^{-1}(\\T-\\expec{\\T})},\n\\eeq\nwhere $\\T$ is the vector of measurements $d_1,d_2,...d_n$ \nand $\\C$ is the associated $n\\times n$ covariance matrix of\nmeasurement errors.\nThis means that the full likelihood function\n$\\L=e^{-\\chi^2/2}$, where $\\chi^2$ is simply the chi-squared goodness \nof fit of the model to the data.\n\nWe have chosen to keep things \nthis simple because we are currently unable to eliminate a \nthird major source of inaccuracy: many of the recent multi-band measurements\nreleased (which dominate the constraining power) have non-negligible correlations\nbetween their different bands, but these correlations have not yet been\npublished by the experimental teams. An alternative approach would be to\nconvert these data sets to uncorrelated measurements, as was done with \nthe 8 COBE points we use.\nIn the interim, an alternative\nis to simply use only \nthose experiments which either have very small correlations,\nor significant correlations which are publically available,\nas was done in Dodelson \\& Knox (2000) and Knox \\& Page (2000).\n\nWe model $\\C$ as a sum of three terms, \n$\\C=\\Cuc + \\Csc + \\Cic$, corresponding to\nmeasurement errors, \nsource calibration errors and \ninstrument calibration errors, \nrespectively.\n$\\Cuc$ reflects the part of the errors which are uncorrelated\nbetween the different experiments and is due to detector noise and \nsample variance. We approximate it by\n\\beq{uncorrCueq}\n\\Cuc_{ij}\\equiv\\delta_{ij}\\sigma_i^2,\n\\eeq\nwhere $\\sigma_i$ is defined as the average of the upper and lower error\nbars quoted for $d_i\\equiv\\dT^2$ (not for $\\dT$) in Table 1. \n\nThe last two terms reflect the correlations between measurements due\nto calibration errors. $\\Cic$ is the part specific to a single \nmulti-band experiment and $\\Csc$ is the part that is correlated with\nother experiments that are calibrated off of the same (slightly uncertain) source.\nBoth QMAP and Saskatoon calibrate off of Cass A, \nand we assume that a 8.7\\% error due to the flux uncertainty\nof this object is common to these experiments.\nMAT, MSAM and Boomerang all calibrate off of Jupiter.\nTo be conservative, we assume that the full 5\\% \ncalibration uncertainty from \nJupiter's antenna temperature is shared by these experiment.\nThe true correlation should be lower, since the three experiments \nobserved Jupiter at different frequencies.\nThe remaining multi-band experiments do not have any such \ninter-experiment correlations:\nCOBE/DMR calibrated off of the dipole, Viper off of the moon\nand Python V off of internal loads.\nThis contribution to the noise matrix is therefore\n\\beq{CscEq}\n\\Csc_{ij}\\equiv (2s_{ij})^2 d_i d_j,\n\\eeq\nwhere \n\\beq{rEq}\ns_{ij} = \\cases{\n8.7\\% &if $i$ and $j$ refer to QMAP or Saskatoon,\\cr\n5\\% &if $i$ and $j$ refer to MAT, MSAM or Boom,\\cr\n0 &otherwise.\\cr\n}\n\\eeq\nThe factor of 2 in \\eq{CscEq} stems from the fact that the percentage \nerror on $\\dT_i^2$ is roughly twice that for $\\dT_i$ as long as \nit is small. \nSimilarly, the remaining term is \n\\beq{uncorrCieq}\n\\Cic_{ij}\\equiv (2r_{ij})^2 d_i d_j,\n\\eeq\nwhere $r_{ij}=0$ if $i$ and $j$ refer to different experiments.\nIf band powers $i$ and $j$ are from the same experiment, then\n$r_{ij}$ is the quoted quoted calibration error with\nthe source contribution $s_{ij}$ subtracted off in quadrature.\nWe use \n$r=$0.063 for Saskatoon, \n7.9\\% for QMAP, \n14\\% for Python V,\n8\\% for Viper, \n8.7\\% for Toco 97,\n6.2\\% for Toco 98,\n0 for MSAM\nand\n6.4\\% for Boomerang.\n\nThere is certainly ample room for improvement of in this 3rd step.\nTo put all these statistical issues in perspective, however, \nthe authors feels that an even more pressing challenge will be to test the \ndata sets for systematic errors, \\eg, by comparing them pairwise\nwhere they overlap in sky coverage and angular resolution \n(Knox {\\etal} 1998; Tegmark 1999a). \n\n\n\n\\subsection{Step 4: Marginalizing}\n\nFor a Bayesian analysis, the 10-dimensional likelihood should be multiplied\nby a prior probability distribution reflecting all non-CMB information,\nthen rescaled so that it integrates to unity and can be interpreted as\na probability distribution.\nTo obtain constraints on some subset of the parameters \n($\\Ok$ and $\\Ol$, say), one would then marginalize over all other\nparameters by integrating over them.\nSuch a direct integration was performed by Efstathiou {\\etal} (1999)\nwhere the parameter space had fewer dimensions. Since such integration\nis quite time-consuming in a high-dimensional space, most other \nmulti-parameter analyses published have adopted the alternative approach\nof maximizing rather than integrating over the unwanted parameters. \nFor instance, the reduced likelihood function for $\\tau$ is obtained\nby looping over a grid of $\\tau$-values and choosing the remaining parameters\nso that they maximize the likelihood in each case.\nThese two approaches are equivalent if the full likelihood function is \na multivariate Gaussian, as shown in Appendix A. \nIf Gaussianity is a poor approximation, \nthe maximization approach can tend to underestimate the error bars\n(Efstathiou {\\etal} 1999). The Gaussianity approximation is\nindeed a poor one at the moment, especially for the case with no \npriors, but it should gradually improve as\nfuture data and non-CMB priors reduce the size of the allowed parameter \nregion.\n\nIn the published grid-based implementations of the maximization method\n(\\eg, Lineweaver 1998; T99),\nthe minimization was performed by simply looking at the\nlikelihoods in the pre-computed model grid and picking the largest \none. Since the true maximum does generally not reside exactly at a grid point, \nthis method always underestimates the true maximum. Unfortunately, \nthe magnitude of this underestimation will vary in a rather random way,\ndepending on how close to the constrained maximum happens to be to\nthe nearest grid point. This effect can cause jagged-looking and\nsomewhat misleading results,\nas shown in \\fig{MargMethodFig}. Note that even an error as small as\n0.5 in $\\chi^2$ changes the likelihood by more than 20\\%.\nSome of the jaggedness/ringing seen in the plots in, \\eg, \nLineweaver (1998) and T99 is likely to be due to this effect.\nIn contrast, the ringing seen in many of the \n$(\\Om,\\Ol)$ exclusion plots\nfurther on in this paper is a purely \ncosmetic problem, due to instability in the IDL interpolation\nroutine used to generate the contour plots.\n\n\\begin{figure}[tb] \n\\vskip-1.2cm\n\\centerline{\\epsfxsize=9.5cm\\epsffile{margtest.ps}}\n%\\centerline{\\epsfxsize=9.5cm\\epsffile{f3.ps}}\n\\vskip-1.0cm\n\\caption{\\label{MargMethodFig}\\footnotesize%\nMarginalization method comparison.\n$\\chi^2$ is plotted as a function of $\\Ol$ when maximizing \nover all other parameters with no priors. The squares show the\nresult of using multidimensional spline interpolation when maximizing\nand the crosses show the result of simply picking the smallest $\\chi^2$-value\nin the model grid. Note that a seemingly small error of unity \nin $\\chi^2$ changes the likelihood by a factor of 1.6.\n}\n\\end{figure}\n\n\nThe problem at hand is to find the maximum of some hypersurface\nin a high-dimensional space. It is easy to see that if we approximate\nthe surface by multilinear interpolation between the grid points\nwhere we know its height, we will recover this unsatisfactory method, \nsince the interpolated surface can only have maxima at grid points.\nWe have chosen to use cubic spline interpolation instead. \nAs seen in \n\\fig{MargMethodFig}, this works substantially better and eliminates \nthe random jaggedness of the simpler method.\n\nFor the reader interested in implementing this method, we give some \nadditional practical details below. \nOther readers may wish to skip directly to the next subsection.\n\nWe perform the cubic spline interpolation and subsequent \nmaximization one dimension at a time. Just as for multilinear \ninterpolation, the result of this procedure is independent of the order\nin which we interpolate over the different parameters.\nWe start by maximizing over the scalar and tensor normalizations, \nwhich is readily done analytically since $\\chi^2$ depends \nquadratically on $\\As$ and $\\At$.\nWe save the remaining 8-dimensional grid in a huge file together\nwith the optimal values of $\\As$ and $\\At$ and the corresponding \n$\\chi^2$ value.\nTo marginalize over any given parameter $p_i$, we first sort\nthis file so that this parameter varies fastest. \nIn each block where the remaining parameters are fixed, \nwe then spline over this parameter and find the maximum $p_i^*$\nanalytically from the spline coefficients.\nSince it is interesting to keep track of the physical \nparameters of the best fit models, we save not only the\n$\\chi^2$-value but also the other parameter values \nspline interpolated to the point where $p_i=p_i^*$, \nreplacing the entire block of models in the file \nby this interpolated one.\n\nWe found that when $\\chi^2$ varies rapidly, a standard cubic\nspline occasionally causes unwanted oscillations. Such a rapid \nrise in $\\chi^2$ occurs only in the extreme parts of the parameter\ngrid that we do not care about (since they are completely ruled out),\nyet the resulting ringing easily propagates to the region that we\nare interested in near the minimum. We therefore adopted \na scheme where we through away irrelevant distant points before splining\nif they were too extreme. Specifically, before performing a 1-dimensional \ncubic spline, we first located the lowest grid point.\nWe then included all points to the left of it until we reached one\nwhose $\\chi^2$ was higher by 10 or more. \nPoints to the right were included analogously.\nWe found this simple scheme to work quite well in practice. Indeed, the\nslight wiggliness of the contour plots shown in the next section is\ncaused mainly by the plotting software itself (the 2D interpolation\nroutine of IDL), not by our marginalization from 10 to 2 dimensions.\n\n\n\\section{RESULTS}\n\n\\label{ResultsSec}\n\n\\subsection{Basic results}\n\nTo avoid having our constraints severely diluted by \n``silly'' models, we include two prior pieces of information\nwhen presenting our basic results. We assume that the Hubble parameter\n$h=0.65\\pm 0.07$ at $1-\\sigma$ (see Freedman 1999 for a recent \nreview of $h$-measurements) and\nthat the baryon density \n$\\ob=h^2\\Ob\\approx 0.02$ \n(Burles {\\etal} 1999\nreport $\\ob=0.019\\pm 0.0024$, and we approximate the $\\ob$ error bars by zero\nsince they are much smaller than our $\\ob$ grid spacing).\nThis value of $\\ob$ is roughly consistent with\nthat measured by Wadsley {\\etal} (1999) using the Helium Lyman-Alpha Forest.\nWe assume that the error distribution for $h$ is Gaussian.\n%Burles, Nollett, Truran and Turner: 0.019 +/- 0024\n\n\\begin{figure}[tb] \n\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.5cm\\epsffile{bestfits.ps}}\n%\\centerline{\\epsfxsize=9.5cm\\epsffile{f4.ps}}\n\\vskip-1.0cm\n\\caption{\\label{BestFitFig}\\footnotesize%\nThe best fit model is shown for the case of \nno prior (solid red/dark grey)\nand with the priors $h=0.65\\pm 0.07$, $h^2\\Ob=0.02$\nand $\\tau=r=0$ (solid green/light grey).\nThe dotted lines show the decomposition of the former curve\ninto scalar and tensor fluctuations. The model parameters are\nlisted in Table 2.\nAlthough all 65 measurements were used in the fits, \nthey have been averaged into 14 bands in this plot to \navoid cluttering. The band powers whose central $\\l$-value \nfell into any given band were average with minimum-variance weighting,\nand their corresponding window functions were averaged as well.\nThis binning was used only in this plot, not in our analysis.\n}\n\\end{figure}\n\n\n\\begin{table}\n\\def\\Qrmsps{Q_{rms,ps}}\n\\def\\lm#1#2#3{$#1^{+#2}_{-#3}$}\n\\def\\na{$-$}\n\\def\\lpeak{\\l_{peak}}\n\n\\bigskip\n\\noindent\n%\\fcolorbox{blue}{yellow}\n{\\footnotesize\n{\\bf Table 2} -- Maximum-likelihood values and 95\\% confidence limits\n}\n\\smallskip\n{\n\\begin{tabular}{|l|ccc|ccc|}\n\\hline\n\t\t\t&\\multicolumn{3}{c|}{10 free parameters}\n\t\t\t&\\multicolumn{3}{c|}{$h$ \\& $\\ob$ prior}\\\\\nQuantity\t\t&Min\t&Best\t&Max\t&Min\t&Best\t&Max\\\\\n\\hline\n$\\tau$\t\t\t&0.0\t&0.0\t&$-$\t&0.0\t&0.0\t&$-$\\\\\t\n$\\Ok$\t\t\t&$-$1.74&$-$1.03&0.49\t&$-$0.24&.09\t&0.38\\\\\t\n$\\Ol$\t\t\t&$-$\t&.16\t&$-$\t&$-$0.19&.67\t&0.89\\\\\t\n$h^2\\Oc$\t\t&0.0\t&.53\t&$-$\t&0.0\t&.036\t&0.30\\\\\t\n$h^2\\Ob$\t\t&.11\t&.13\t&$-$\t&{\\it .02}&{\\it .02}&{\\it .02}\\\\\t\n$h^2\\On$\t\t&0.0\t&.012\t&$-$\t&0.0\t&.051\t&.29\\\\\t\n$\\ns$\t\t\t&.55\t&1.69\t&$-$\t&0.80\t&1.05\t&1.53\\\\\t\n$\\nt$\t\t\t&$-$\t&0.00\t&$-$\t&$-$\t&0.03\t&$-$\\\\\t\n\\hline\t\t\n\\end{tabular}\n}\n\\end{table}\n\n%\\begin{table}\n%\\def\\Qrmsps{Q_{rms,ps}}\n%\\def\\lm#1#2#3{$#1^{+#2}_{-#3}$}\n%\\def\\na{$-$}\n%\\def\\lpeak{\\l_{peak}}\n%\n%\\bigskip\n%\\noindent\n%%\\fcolorbox{blue}{yellow}\n%{\\footnotesize\n%{\\bf Table 2} -- Maximum-likelihood values and 95\\% confidence limits\n%}\n%\\smallskip\n%{\n%\\begin{tabular}{|l|ccc|ccc|}\n%\\hline\n%\t\t\t&\\multicolumn{3}{c|}{10 free parameters}\n%\t\t\t&\\multicolumn{3}{c|}{$h$ \\& $\\ob$ prior}\\\\\n%Quantity\t\t&Min\t&Best\t&Max\t&Min\t&Best\t&Max\\\\\n%\\hline\n%$\\tau$\t\t\t&0.0\t&0.0\t&$-$\t&0.0\t&0.0\t&$-$\\\\\t\n%$\\Ok$\t\t\t&$-$1.74&$-$1.03&0.49\t&$-$0.24&.09\t&0.38\\\\\t\n%$\\Ol$\t\t\t&$-$\t&.16\t&$-$\t&$-$0.19&.67\t&0.89\\\\\t\n%$h^2\\Oc$\t\t&0.0\t&.53\t&$-$\t&0.0\t&.036\t&0.30\\\\\t\n%$h^2\\Ob$\t\t&.11\t&.13\t&$-$\t&{\\it .02}&{\\it .02}&{\\it .02}\\\\\t\n%$h^2\\On$\t\t&0.0\t&.012\t&$-$\t&0.0\t&.051\t&.29\\\\\t\n%$\\ns$\t\t\t&.55\t&1.69\t&$-$\t&0.80\t&1.05\t&1.53\\\\\t\n%$\\nt$\t\t\t&$-$\t&0.00\t&$-$\t&$-$\t&0.03\t&$-$\\\\\t\n%\\hline\t\t\n%\\end{tabular}\n%}\n%\\end{table}\n\n\nThe parameters of the best fit model\nare listed in Table 2 both with and without these priors.\nThe corresponding no-prior power\nspectrum is shown in \\fig{BestFitFig} together\nwith the ``vanilla'' version with \nthe above-mentioned priors and $\\tau=r=0$.\nAs can be seen, \nthe fitting procedure uses the additional freedom \nto match features in the data in quite amusing ways.\nSince the data dip at $\\l\\sim 50$ and rise very sharply\nthereafter, a feature that simpler models cannot match,\nthe minimization procedure finds the best fit model\nto have a dramatic blue-tilt ($\\ns\\sim 1.7$) and \nalmost the entire COBE signal due to gravity waves.\nAlthough this particular model is ruled out by other constraints\n--- for instance, \nprimordial black hole abundance (Green {\\etal} 1997) and \nspectral distortions (Hu {\\etal} 1994) give upper bounds $\\ns\\simlt 1.3$) ---\nit illustrates the importance of fitting for all 10 parameters \njointly. Indeed, it is the inclusion of gravity waves in\nour models that makes the constraints on $\\ns$ so weak.\n\nThe 1-dimensional likelihood functions for six of the best constrained \nparameters are shown in \\fig{1Dfig}, marginalized over the \nother 9 parameters. \nAlthough none of these parameters are very tightly constrained, \nit is encouraging that CMB observations are already sufficiently\npowerful to place upper and lower limits on \n$\\Om$, $\\Ol$ and $\\ns$ at the $2-\\sigma$ level.\nBecause $\\oc$ and $\\on$ are by definition non-negative, these \ndensity parameters are also bounded from both sides. \nOn the other hand, better data will be required \nto place interesting constraints on $\\tau$,\nsince this parameter is almost degenerate with the overall normalization\n(see, \\eg, Eisenstein {\\etal} 1999). \nThe best constrained parameter so far is seen to be \nthe spatial curvature $\\Ok$, with $-0.24<\\Ok<0.38$ at 95\\% confidence.\nFor comparison, using Figure 2 in Dodelson \\& Knox (2000) to read \noff the point where the likelihood drops to $e^{-2^2/2}\\approx 0.14$ \ngives the 95\\% upper limit $\\Ok<0.38$.\nAlthough the exact numerical agreement is likely to be \ncoincidental (since we use more data, etc),\nthis is nonethetheless very reassuring evidence that the basic\nresult is robust.\n \n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.0cm\\epsffile{all65_nucleo_1d.eps}}\n%\\centerline{\\epsfxsize=9.0cm\\epsffile{f5.eps}}\n%\\vskip-4.0cm\n\\caption{\\label{1Dfig}\\footnotesize%\nThe marginalized likelihood is shown for six individual parameters\nusing all 65 band power measurements and priors only\nfrom nucleosynthesis ($h^2\\Ob=0.02$)\nand the Hubble parameter ($h=0.65\\pm 0.07$).\nThe $2\\sigma$ limits (see Table 2) are roughly where \nthe curves cross the horizontal lines.\n%The triangles show the actual calculations.\n% --- the smooth\n% curves are merely splines from sm and exhibit a certain amount\n% of undesirable ringing. \n}\n\\end{figure}\n\nBecause of the well-known angular diameter distance degeneracy, \nwhere increasing $\\Ok$ shifts the acoustic peaks to the right and \nincreasing $\\Ol$ can shift them back to the left, we also plot\nour constraints marginalized onto the 2-dimensional \n$(\\Om,\\Ol)$-plane.\n\\Fig{all65_2Dfig} shows the results using all the data, \nand Figures~\\ref{lyman2Dfig}--~\\ref{boom2Dfig} shown the constraints\nfrom various subsets that will be described below.\nIn all cases, the shaded regions show what is ruled out at \n95\\% confidence ($2-\\sigma$). For our 2-dimensional parameter space, this\ncorresponds to $\\Delta\\chi^2=6.18$ (not 4), \nas in Press {\\etal} (1992) \\S 15.6. \n\nWe show four nested contours. The least constraining one is when all 10\nparameters are treated as unknown. The second includes our Hubble parameter\nprior $h=0.65\\pm 0.07$. The third (what we call our ``basic result'') \nadds the nucleosynthesis constraint\n$\\ob\\approx 0.02$ and the fourth imposes $r=\\tau=0$. Although the first two\npriors are observationally well-motivated, the last one is completely ad hoc,\nand has only been included to illustrate the importance of including \nreionization and gravity waves in analyses of this kind. \n\nWhen removing a prior constraint ($\\ob=0.02$) \nfrom our basic result, we reduce all $\\chi^2$-values by unity \nbefore plotting the corresponding contour, to account for the added \ndegree of freedom. Similarly, we subtract 2 when dropping \nboth constraints and add 2 when imposing $\\tau=r=0$.\n\n\n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.0cm\\epsffile{all65_2d.eps}}\n%\\centerline{\\epsfxsize=9.0cm\\epsffile{f6.eps}}\n%\\vskip-4.0cm\n\\caption{\\label{all65_2Dfig}\\footnotesize%\nThe regions in the $(\\Om,\\Ol)$-plane \nthat are ruled out at $2\\sigma$ using all the data are shown \nusing no priors (red/dark grey), \nthe prior $h=0.65\\pm 0.07$ (orange red/grey),\nthe additional nucleosynthesis constraint $h^2\\Ob=0.02$ (orange/light grey)\nand the additional constraints $r=\\tau=0$ (yellow/very light grey). \n}\n\\end{figure}\n\n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.0cm\\epsffile{lyman_2d.eps}}\n%\\centerline{\\epsfxsize=9.0cm\\epsffile{f7.eps}}\n%\\vskip-4.0cm\n\\caption{\\label{lyman2Dfig}\\footnotesize%\nSame as previous figure, but\nusing only the COBE and the ``East Coast''\ndata sets (Saskatoon, QMAP and Toco).\n}\n\\end{figure}\n\n\n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.0cm\\epsffile{snake_2d.eps}}\n%\\centerline{\\epsfxsize=9.0cm\\epsffile{f8.eps}}\n%\\vskip-4.0cm\n\\caption{\\label{snake2Dfig}\\footnotesize%\nSame as Figure~\\ref{all65_2Dfig}, but\nusing only COBE and ``Snake'' data sets\n(Python V and Viper).\n}\n\\end{figure}\n\n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\epsfxsize=9.0cm\\epsffile{boom_2d.eps}}\n%\\centerline{\\epsfxsize=9.0cm\\epsffile{f9.eps}}\n%\\vskip-4.0cm\n\\caption{\\label{boom2Dfig}\\footnotesize%\nSame as Figure~\\ref{all65_2Dfig}, but\nusing only COBE and Boomerang data sets. The yellow/light grey contour\ncorresponds to the result of Melchiorri et al (2000) if we impose\n$\\on=0$.\n}\n\\end{figure}\n\n\\Fig{all65_2Dfig} shows that the CMB data alone is able to rule\nout very open ($\\Om\\simlt 0.4$) models with $\\Ol=0$. \nAdding the $h$-constraint tightened the limits somewhat, mainly on \nvery closed models. A more important prior at at this stage is \nthat from nucleosynthesis, which helps eliminate most of the remaining \nclosed models and places the first {\\it lower} limit on $\\Ol$.\nThis makes the allowed region in the $(\\Om,\\Ol)$-plane bounded, which\nis important: otherwise all other constraints, which are marginalized over\n$\\Ol$, would depend sensitively on the poorly \nmotivated prior $\\Ol\\ge -1$ that was hard-wired into our parameter grid.\n\nAdding the additional prior $\\tau=r=0$, which we recommend against for\nthe reasons described in the introduction, is seen to rule out\nabout half of the remaining models.\nThe exclusion of these parameters is seen to \npredominantly rule out closed models, whose \nfirst acoustic peak is too far to the left.\nThis is because it can be shifted back to the right by\ntilting the power spectrum (increasing $\\ns$), after which the\npeak height can be brought back down to allowed levels \nusing reionization or gravity waves.\nIn contrast, it is not possible to salvage too open\nmodels with this trick: decreasing $\\ns$ would \nrequire raising the first peak, but there is of course\nno such thing as negative reionization or negative \ngravity waves.\n\n\\subsection{Is everything consistent?}\n\nThe plots we have shown so far are Bayesian in nature, and can only be\ninterpreted as advertised if the data are consistent with the best fit model.\nThis is indeed the case, since we obtain\n$\\chi^2 = 49$ for the best fit model. Dropping the\nconstraints on $h$ and $\\ob$ reduces $\\chi^2$ by as much as 6,\ncorresponding to the rather unphysical model shown in \\fig{BestFitFig}.\nFor comparison, 65 data points and 10 parameters gives 55 degrees of \nfreedom\\footnote{In fact, our parameters do not span a full 10-dimensional \nsubspace of the 65-dimensional data space when they range over physically \nreasonable values, since some of them have only a minor impact \n(say $\\nt$) or are subject\nto near degeneracies like $(\\As,\\tau)$, $(\\Ok,\\Ol)$ and $(\\oc,\\on)$.\nThe effective number of degrees of freedom to subtract off\nmay therefore be closer to 6 than 10.\n}, so we should expect $\\chi^2=55\\pm 21$ at $2\\sigma$.\n\n\n\n\\subsection{Robustness to choice of data}\n\nTo investigate the relative constraining power of different data sets and the degree\nto which they give consistent results, we repeated our analysis for three subsets\nof the observations. Specifically, we partitioned the most recent observations reporting \nmultiple band powers into three disjoint sets and combined each one of them with \nthe COBE measurements:\n\\begin{enumerate}\n\\item The ``East Coast'' sample contains Saskatoon, QMAP, TOCO and COBE.\n\\item The ``snake'' sample contains Python, Viper and COBE.\n\\item The Boomerang sample contains Boomerang-97 and COBE.\n\\end{enumerate}\nAs seen in \nFigures~\\ref{lyman2Dfig}--\\ref{boom2Dfig}, they all allow flat models and \ndisfavor very open ($\\Ok\\gg 0$) models, \nwhich would place the first acoustic peak too far to the right. \nAs more priors get added, they are seen to disfavor very closed models as well.\nIn all cases, the best fit model has an acceptable $\\chi^2$-value.\n\n\n\\subsection{Importance of calibration errors}\n\nTo assess the importance of calibration uncertainties, \nwe repeated our analysis with all calibration errors set to zero.\nWe found that in this case, {\\it no} model provided a very good fit \nto the data, with $\\chi^2\\approx 76$ for the best fit.\nThis is only a problem at the $2\\sigma$-level\nfor 65-10=55 degrees of freedom, and perhaps even less in light\nof footnote 1.\nHowever, it nonetheless caused the the Baysean constraints \nto become quite misleading, suggesting that \nmost parameters were very tightly constrained around\ntheir maximum-likelihood values --- for instance, that $\\on=0$ was ruled out \nat high significance. In conclusion, it is of paramount importance to include \ncalibration errors. This was done in the above-mentioned analyses \nof Dodelson \\& Knox (2000) and Melchiorri {\\etal} (2000), \nbut not in most earlier work.\n\nThe main discrepancies pushing up the $\\chi^2$ were localized to two places in \\fig{DataFig}.\nThe first trouble spot was at $40\\simlt\\ell\\simlt 70$, where\nthe low Python V points conflicted with the\nhigher measurements on a similar scale from, \\eg, Toco, QMAP and Saskatoon.\nThe second problem occurred at $\\ell\\simlt 300$, where the models\nfailed to fall rapidly enough from the high Toco detections down to the\nlower power levels seen by MSAM, CAT, OVRO, Viper\nand Boomerang.\n\n\n\\subsection{Are the data internally consistent?}\n\nBased on visual inspection of the data, it has been suggested\nthat all CMB measurements cannot be consistent with \nany model, since some measurements disagree with others on a comparable\nangular scale. Although we saw above that the $\\chi^2$-value\nis acceptable, the distribution of residuals could in principle be non-Gaussian \nwith the a few severe outliers being averaged down beyond recognition in the\n$\\chi^2$-calculation.\nTo investigate this possibility, we fit a 10-parameter model with no \nunderlying physical model to the data. Our model curve \nis simply a cubic spline interpolated between 10 \ngrid points. \n\\Fig{ResidualFig} shows the 65 residuals $(d_i-\\expec{d_i})/\\sigma_i$,\nignoring calibration errors, and reveals no striking outliers at all.\n\nThis fit gives a $\\chi^2\\approx 67$ ignoring calibration errors, \\ie, \neven lower than for the CMB case.\nIn view of footnote 1, we repeated this test with merely six spline points.\nThis gave $\\chi^2\\approx 95$ for logarithmically equispaced spline points,\nbut as low a $\\chi^2$ as before when more points were shifted to be near the\n1st acoustic peak.\n\nIn the future, as CMB data gets still better, one would expect the correct\nphysically based model to provide a substantially better \nfit than ``any old smooth curve'' with the same number of free parameters.\nUntil then, \\ie, until our physical theory provides the most economical\nexplanation of the observations, \nwe cannot interpret the good fit of the model to the data as \noverwhelming evidence that our theory is correct.\n\n\n\\begin{figure}[tb] \n%\\vskip-1.5cm\n\\centerline{\\epsfxsize=9.7cm\\epsffile{spline_resid.ps}}\n%\\centerline{\\epsfxsize=9.7cm\\epsffile{f10.ps}}\n\\vskip-1.0cm\n\\caption{\\label{ResidualFig}\\footnotesize%\nResiduals. \nThe top panel shows a cubic spline interpolated between 10 equispaced \ngrid points (large squares) that are adjusted vertically to \nmake the window function convolved curve (small squares)\nfit the observations (triangles) as well as possible.\nThe middle panel shows the residuals \n$(d_i-\\expec{d_i})/\\sigma_i$, the differences between the \ntriangles and small squares in units of the error bars. The bottom panel shows a histogram of these residuals\ncompared with a unit Gaussian. The reduced $\\chi^2$-value is simply\nthe second moment of this distribution.\n}\n\\end{figure}\n\n\n\\section{CONCLUSIONS}\n\n\\label{ConclusionsSec}\n\n\nWe have presented a method for rapid calculation of large numbers of CMB models\nand used it to jointly constrain 10 cosmological parameters from current \nCMB data. Our results on individual parameters are summarized in Table 2. \nArguably the most interesting constraints at this point are those on the\ngeometry of spacetime, summarized in \\fig{EverythingFig}.\nThis figure zooms in on the upper left quarter of \\Fig{all65_2Dfig}\nand shows the joint constraints on $\\Om$ and $\\Ol$ from a variety of\nastrophysical observations. The SN 1a constraints are from White 1998,\ncombining the data from both search teams \n(Perlmutter {\\etal} 1998; Riess {\\etal} 1998; Garnavich {\\etal} 1998).\nAs can be seen, the CMB and SN 1a constraints imply a positive \ncosmological constant ($\\Ol>0$) when combined. If the \nFalco {\\etal} (1998) constraints from \ngravitational lens statistics are included, the allowed region\nin parameter space is further reduced.\n\nThis claim that $\\Ol>0$ is of course old hat (Kamionkowski \\& Buchalter 2000), \noriginally being made over a year ago\n(see Sahni \\& Starobinsky 2000 for a recent review).\nWhat is new here,\nand quite striking, is its robustness. Since the first such\njoint analysis (White 1998), the number of CMB band power\nmeasurements has roughly doubled, with experiments such \nas Toco, Python V, Viper and Boomerang greatly improving the\naccuracy on acoustic peak scales. In addition, the CMB \ntreatments has been gradually refined; for example, several\ngroups have added calibration errors and this analysis has\nweakened the constraints further by fitting for 10 parameters\njointly. Yet despite these major improvements in both data and modeling,\nthe cosmological constant remains alive and well, stubbornly refusing\nto vanish.\n\n\n\\begin{figure}[tb] \n%\\vskip-1.0cm\n\\centerline{\\hglue6.0cm\\epsfxsize=15.0cm\\epsffile{everything.eps}}\n%\\centerline{\\hglue6.0cm\\epsfxsize=15.0cm\\epsffile{f11.eps}}\n\\vskip-4.5cm\n\\caption{\\label{EverythingFig}\\footnotesize%\nConstraints in the $\\Om-\\Ol$ plane.\nThe regions in the $(\\Om,\\Ol)$-plane \nthat are ruled out by our analysis at \n$2\\sigma$ using all the data are shown \nusing no priors (red/dark grey), \nthe prior $h=0.65\\pm 0.07$ (orange/grey), and the\nadditional nucleosynthesis constraint $h^2\\Ob=0.02$ \n(light orange/light grey).\nThe SN 1a constraints are from White (1998) and\nthe lensing constraints are from Falco et al (1998).\nThe CMB contours for $\\Om<0.2$ are extrapolations.\n}\n\\end{figure}\n\nSince CMB data is likely to continue to improve at a\nrapid pace, with exciting new balloon, interferometer and satellite data\njust around the corner, it will be important to further improve on \nthe type of analysis that we have presented here.\nThere are a number of areas in which the accuracy off our treatment \ncan be improved:\n\\begin{itemize}\n\n\\item The problem of regenerated power from very early reionization\ncan be eliminated by explicitly looping over $\\tau$ \nfor the high $\\l$ models in Step 1\ninstead of using the $e^{-2\\tau}$ suppression approximation.\n \n\\item In Steps 1 and 2, the effect of gravitational lensing can be included.\n\n\\item In Steps 1 and 2, further speed-up can be attained by taking advantage\nof the fact that the tensor fluctuations are essentially \nindependent of $\\on$ as long as \nthe total dark matter density $\\oc+\\on$ stays constant. \n\n\\item The accuracy in Step 2 can probably be further improved by \nusing some form of morphing technique as suggested by \nSigurdson \\& Scott (2000).\nThe basic idea is to interpolate not the power spectrum itself\nbut some cleverly chosen parametrization thereof. We have done this to \na certain extent by computing and interpolating the amount by which\nthe acoustic peaks should be shifted sideways, but more ambitious\nreparametrizations are clearly possible.\n\n\\item In Step 3, the likelihoods can be computed more accurately\nby incorporating non-Gaussianity corrections as in\nBond, Jaffe \\& Knox (1998) or Bartlett {\\etal} (1999)\nand by including correlations between different \ndata points. The former is particularly important for \nupper limits, which were simply excluded from the\npresent analysus. The latter includes correlations between \ndifferent experiments that overlap in sky coverage and angular scale.\nCalibrations can be treated as multiplicative \nparameters to be marginalized over (as in Dodelson \\& Knox 2000) rather\nthan as correlated noise (our approximation is accurate as\nlong as the relative calibration errors are much less than unity).\n\n\\item Step 3 should ideally use the exact band power window functions.\nUnfortunately, most window functions available in the literature \nare variance window functions, and using them as band-power window \nfunctions is an approximation which is not\nalways good. Experimentalists are strongly encouraged\nto publish their band power window functions!\n\n\\item The overall accuracy of our technique can be improved\nwith brute force, by computing a finer grid of models in step 1.\nIndeed, the errors introduced in Step 2 can in principle\nbe continuously reduced toward zero by\nrefining the $(\\oc,\\ob,\\on)$-grid for low \n$\\l$ and shifting the splicing point upwards from $\\l\\sim 100$.\n\n\\item The accuracy in Step 4 can be improved\nby integrating instead of maximizing when marginalizing.\nThis will make a difference mainly early on when the 10-dimensional \nprobability distribution in parameter space is widely extended and\ndiffers greatly from a multivariate Gaussian distribution.\nIf this integration approach is used, it should be applied\neven for the normalizations $\\As$ and $\\At$, for consistency.\n\n\\end{itemize}\n\n\n\nA second general area of improvement will be to include more prior \ninformation than Hubble parameter measurements and \nnucleosynthesis constraints.\nAs data improves in a wide variety of areas, \nthis will not only help break parameter degeneracies, but also\nallow important cross-checks.\nA very large number of such multi-dataset studies have been carried \nout in the past (Bahcall {\\etal} 1999 and Bridle {\\etal} 1999 \nprovide good recent entry points into the literature), \nbut rarely for more than a few parameters at a time.\nHere is a necessarily incomplete list\nof such constraints: \n\n\\begin{itemize}\n\n\\item Measurements of the matter power spectrum and its time-evolution \n$P(k,z)$ from galaxy redshift surveys.\n\n\\item\nMeasurements of $P(k,z)$ from weak gravitational lensing\n(\\eg, Narayan \\& Bartelmann 1996)\n\n\\item \nMeasurements of $P(k,z)$ from\nthe abundance of galaxy clusters \n(\\eg, Carlberg 1997; Bahcall \\& Fan 1998; Eke {\\etal} 1998.)\n\n\\item\nConstraints om $P(k)$ from peculiar velocity measurements\n(\\eg, Zehavi \\& Dekel 1999).\n\n\\item Limits on $(h, \\Ok, \\Ol)$ from SN 1a.\n\n\\item Limits on $(h, \\Ok, \\Ol)$ from lens statistics\n(\\eg, Kochanek 1996; Falco {\\etal} 1998; Bartelmann {\\etal} 1998;\nHelbig 1999)\n\n\\item Limits on $(h, \\Ok, \\Ol)$ from \nlimits on the age of the Universe and various other \nclassical cosmological tests (Peebles 1993).\nFor instance SZ cluster distance measurements provide promising\nnew constraints of this type (Reese {\\etal} 2000).\n\n\\item Direct measurements of $\\Om$ and \nthe baryon fraction $\\Ob/\\Om$ from cluster studies\n(Carlberg {\\etal} 1999; White {\\etal} 1993; Danos \\& Pen 1998; Cooray 1998) \n\n\\end{itemize}\n \nFinally, adding more physics can both weaken and tighten constraints.\nAdding further parameters (say an equation of state for a scalar field \ncomponent) can weaken constraints on other semi-degenerate\nparameters. On the other hand, \nadding an astrophysical model for, say, how $\\tau$ \ndepends on the other parameters can substantially\ntighten constraints (Venkatesian 2000).\n\nIn conclusion, as CMB experimentalists continue to \nforge ahead, CMB theorists will need to work hard to keep up.\n\n\n% * Quote a limit on peak value??? Or is that silly?\n\n\n\n\\bigskip\nThe authors wish to thank Lloyd Knox for helpful comments about\ncalibration errors\nand Ang\\'elica de Oliveira-Costa, \nMark Devlin, Charley Lineweaver and Amber Miller for useful \ndiscussions.\nSupport for this work was provided by NSF grant AST00-71213, \nNASA grant NAG5-9194,\nthe University of Pennsylvania Research Foundation, and \nHubble Fellowships HF-01084.01-96A and HF-01116.01-98A from \nSTScI, operated by AURA, Inc. \nunder NASA contract NAS5-26555. \n\n\\appendix\n\n\\section{Conditional marginalization}\n\n\\def\\fmax{f_{\\rm max}}\n\\def\\fint{f_{\\rm int}}\n\\def\\x{{\\bf x}}\n\\def\\y{{\\bf y}}\n\\def\\z{{\\bf z}}\n\\def\\xb{\\bar\\x}\n\\def\\yb{\\bar\\y}\n\\def\\zb{\\bar\\z}\n\\def\\D{{\\bf D}}\n\\def\\E{{\\bf E}}\n\\def\\F{{\\bf F}}\n\\def\\G{{\\bf G}}\n\\def\\I{{\\bf I}}\n\\def\\J{{\\bf J}}\n\\def\\K{{\\bf K}}\n\\def\\L{{\\bf L}}\n\\def\\M{{\\bf M}}\n\nIn this Appendix, we show that maximizing is equivalent to integrating \nwhen marginalizing multidimensional Gaussians in arbitrary dimensions. \nAlthough this useful property is undoubtedly derived in the statistics\nliterature, we present a brief derivation here for completeness. \n\nA multivariate Gaussian distribution in $n$ dimensions takes the form\n\\beq{GaussEq}\nf(\\x) = (2\\pi |\\C|)^{-n/2} e^{-{1\\over 2}(\\x-\\xb)^t\\C^{-1}(\\x-\\xb)},\n\\eeq\nwhere $\\xb$ is the mean vector and $\\C$ is the $n\\times n$ covariance matrix.\nLet us partition the $n$ parameters in $\\x$ into two subsets $\\y$ and $\\z$\nof size $n_x$ and $n_y$ ($n_x+n_y=n$) and write \n\\beq{DecompEq}\n\\x\\equiv\\left(\\y\\atop\\z\\right),\n\\quad\n\\C^{-1}=\\left(\\begin{tabular}{cc}\n$\\D$&$\\E$\\\\\n$\\E^t$&$\\F$\n\\end{tabular}\\right).\n\\eeq\nWe can now define a probability distribution \nfor $\\y$ in two different ways, by either integrating or maximizing over $\\z$:\n\\beq{fintDefEq}\n\\fint(\\y)\\equiv\\int f(\\x)d^{n_z} z,\n\\eeq\n\\beq{fmaxDefEq}\n\\fmax(\\y)\\equiv c \\max_{\\z} f(\\x),\n\\eeq\nwhere the normalization constant $c$ is chosen so that $\\fmax$ \nintegrates to unity.\nMaximizing $f$ is equivalent to minimizing the quadratic\nform $(\\x-\\xb)^t\\C^{-1}(\\x-\\xb)$. Inserting \\eq{DecompEq} and differentiating with\nrespect to $\\z$ shows that this minimum is attained for \n\\beq{optzEq}\n\\z = \\zb - \\F^{-1}\\E^t(\\y-\\yb).\n\\eeq\nSubstituting this back into \\eq{fmaxDefEq} gives\n\\beq{fmaxEq}\n\\fmax(\\y) \\propto e^{-{1\\over 2}(\\y-\\yb)^t[\\D-\\E\\F\\E^t](\\y-\\yb)},\n\\eeq\n\\ie, a Gaussian with mean $\\yb$ and covariance matrix $[\\D-\\E\\F\\E^t]^{-1}$.\nAs is well known, integrating over $\\z$ also gives a Gaussian with\nmean $\\y$ and a covariance matrix which is simply the upper left\nsubmatrix of the full covariance matrix $\\C$.\nThe identity\n\\beqa{MonsterEq}\n&&\\hskip-0.7cm\\left(\\begin{tabular}{cc}\n$\\D$&$\\E$\\\\\n$\\E^t$&$\\F$\n\\end{tabular}\\right)^{-1}\n= \\\\\n&&\\hskip-0.7cm\\left(\\begin{tabular}{cc}\n$[\\D-\\E\\F^{-1}\\E^t]^{-1}$&$-\\D^{-1}\\E[\\F-\\E\\D^{-1}\\E^t]^{-1}$\\\\\n$-\\F^{-1}\\E^t[\\D-\\E\\F^{-1}\\E^t]^{-1}$&$[\\F-\\E\\D^{-1}\\E^t]^{-1}$\n\\end{tabular}\\right)\n\\nonumber\n\\eeqa\ntherefore shows that the covariance matrix is $[\\D-\\E\\F^{-1}\\E^t]^{-1}$,\n\\ie, the same as for the maximization case.\nThis proves that $\\fint=\\fmax$, \\ie, that the two methods of marginalization\ngive identical results when the probability distribution is Gaussian.\nThe identity given by \\eq{MonsterEq} is readily proven by simply\nmultiplying the matrices on the left and right hand sides together\nand verifying that their product is the identity matrix.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%% REFERENCES: %%%%%%%%%%%%%%%%%%%%%%%%%\n\n%\\clearpage\n%\\end{multicols}\n\n\\vskip-1.0cm\n\n\\begin{references} % \n\n\\bigskip\n\n\\rf\\nnn Bahcall N A\\dualand\\nn Fan X;1998;ApJ;504;1\n% astro-ph/9803277\n% Title: The Most Massive Distant Clusters: Determining Omega and sigma_8\n% Authors: Neta A. 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W.\n% The Omega_M-Omega_Lambda Dependence of the Apparent Cluster Omega\n\n\\rf\\nn Challinor A, \\nn Lewis A\\multiand\\nn Lasenby A;2000;ApJ;538;473\n% astro-ph/9911177\n% Title: Efficient Computation of CMB anisotropies in closed FRW models\n% Authors: Antony Lewis, Anthony Challinor, Anthony Lasenby\n% Comments: 4 pages, 1 figure. For the F90 source code see this http URL\n\n\\rfprep\\nnn Coble K A;1999;astro-ph/9911419\n% Title: Data Reduction and Analysis of the Python V Cosmic Microwave Background Anisotropy Experiment\n% Authors: Kimberly Ann Coble\n% Comments: PhD Thesis, 109 pages, includes cross-modulation analysis\n \n\\rfprep\\nn Contaldi C, \\nn Hindmarsh M\\multiand\\nn Magueijo J;1999;Phys. Rev. Lett.;82;2034\n% astro-ph/9809053\n% Title: CMB and density fluctuations from strings plus inflation\n% Authors: Carlo Contaldi, Mark Hindmarsh, Joao Magueijo\n\n\\rf\\nn Cooray A;1998;A\\&A;333;L71\n\n\\rf\\nn{de Bernardis} P {\\etal};1997;ApJ;480;1\n\n\\rf\\nn{de Oliveira-Costa} A \\etal;1998;ApJL;509;L77\n% , \\nn Devlin M, \\nn Herbig T,\n% \\nnn Miller A D, \\nnn Netterfield C B, \n% \\nnn Page L A\\multiand\\nn Tegmark M;1998;ApJL;509;L77\n% astro-ph/9808045\n% Mapping the Cosmic Microwave Background Anisotropy: Combined Analysis of QMAP Flights\n% Authors:\n% DE OLIVEIRA-COSTA, ANGELICA; DEVLIN, MARK J.; HERBIG, TOM;\n% MILLER, AMBER D.; NETTERFIELD, C. BARTH; PAGE, LYMAN A.; TEGMARK, MAX\n% Journal:\n% The Astrophysical Journal, Volume 509, Issue 2, pp. L77-L80.\n\n\\rfprep\\nn Danos R\\dualand\\nnn Pen U L;1998;astro-ph/9803058\n% Rebecca Danos, Ue-Li Pen\n% Comments: 12 pages incl. 4 figures\n% We apply a unique gas fraction estimator to published X-ray cluster properties and we compare the derived gas fractions of observed\n% clusters to simulated ones. The observations are consistent with a universal gas fraction of 0.15+/-0.01h_{50}^{-3/2} for the low redshift\n% clusters that meet our selection criteria. The fair sampling hypothesis states that all clusters should have a universal constant gas fraction for\n% all times. Consequently, any apparent evolution would most likely be explained by an incorrect assumption for the angular-diameter distance\n% relation. We show that the high redshift cluster data is consistent with this hypothesis for \\Omega_0<0.63 (95% formal confidence, flat\n% $\\Lambda$ model) or \\Omega_0<0.60 (95% formal confidence, hyperbolic open model). The maximum likelihood occurs at \\Omega_0=0.2 for a\n% spatially flat cosmological constant model. \n \t\t \n\\rf\\nn Devlin M \\etal;1998;ApJL;509;L69\n% , \\nn{de Oliveira-Costa} A, \\nn Herbig T,\n% \\nnn Miller A D, \\nnn Netterfield C B, \n% \\nnn Page L A\\multiand\\nn Tegmark M;1998;ApJL;509;L69\n% astro-ph/9808043\n% Mapping the Cosmic Microwave Background Anisotropy: The First Flight of the QMAP\n% Experiment\n% Authors:\n% DEVLIN, MARK J.; DE OLIVEIRA-COSTA, ANGELICA; HERBIG, TOM;\n% MILLER, AMBER D.; NETTERFIELD, C. BARTH; PAGE, LYMAN A.; TEGMARK, MAX\n% Journal:\n% The Astrophysical Journal, Volume 509, Issue 2, pp. L69-L72.\n\n\\rf\\nn Dodelson S\\dualand\\nn Knox L;2000;Phys. Rev. Lett;84;3523\n% astro-ph/9909454\n% Title: Dark Energy and the CMB\n% Authors: S. Dodelson (1), L. Knox (2) ((1) Fermilab (2) U. Chicago)\n% Comments: 4+ pages, submitted to PRL, software package for calculating \\chi^2 from all CMB data available at this http URL \n \n\\rf\\nn Efstathiou G;1999;MNRAS;310;842\n% Efstathiou, G.\n% Constraining the equation of state of the Universe from distant Type Ia supernovae and cosmic microwave\n% background anisotropies\t\t\t\t\t\t \n\n\\rf\\nn Efstathiou G, \\nnn Bridle S L, \\nnn Lasenby A N, \n\\nnn Hobson M P\\multiand\\nnn Ellis, R S;1999;MNRAS;303;47\n% Efstathiou, G.; Bridle, S. L.; Lasenby, A. N.; Hobson, M. P.; Ellis, R. S.\n% Constraints on Omega_Lambda and Omega_m from distant Type IA supernovae and cosmic microwave\n% background anisotropies\n\t\t\t\t\t\t \t\t\t\t\t \n\\rf\\nn Efstathiou G\\dualand\\nnn Bond J R;1999;MNRAS;304;75\n% astro-ph/9807103 [abs, src, ps, other] :\n% Title: Cosmic Confusion: Degeneracies among Cosmological Parameters Derived from Measurements of Microwave Background\n% Anisotropies\n% Authors: G. Efstathiou, J.R. Bond\n% Comments: Submitted to MNRAS 25 pages 17 Figures latex mn.sty\n \n\\rf\\nnn Eisenstein D J, \\nn Hu W\\multiand Tegmark M;1999;ApJ;518;2\n% astro-ph/9807130\n% parameters2\n\n\\rfprep\\nnn Eke V R, \\nn Cole S, \\nnn Frenk C S\\multiand\\nnn Henry J P;1998;astro-ph/9802350\n% Measuring Omega_0 using cluster evolution\n% Authors: V. R. Eke, S. Cole, C. S. Frenk, J. P. Henry\n% Comments: 17 pages, 15 figures, submitted to MNRAS\n% The evolution of the galaxy cluster abundance depends sensitively on the value of the cosmological density parameter, Omega_0. Recent\n% ASCA data are used to quantify this evolution as measured by the X-ray temperature function. A chi^2 minimization fit to the cumulative\n% temperature function, as well as a maximum likelihood estimate (which requires additional assumptions about cluster luminosities), lead to\n% the estimate Omega_0 \\approx 0.45+/-0.2 (1-sigma statistical error). Various systematic uncertainties are considered, none of which\n% enhance significantly the probability that Omega_0=1. These conclusions hold for models with or without a cosmological constant. The\n% statistical uncertainties are at least as large as the individual systematic errors that have been considered here, suggesting that additional\n% temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest\n% redshift clusters to place an upper limit on Omega_0 is also presented and tentatively applied, with the result that Omega_0=1 can be ruled\n% out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are\n% still modeling uncertainties that preclude a firmer conclusion at this time.\n \n\\rf\\nnn Falco E E, \\nnn Kochanek C S\\multiand\\nnn Munoz J A;1998;ApJ;494;47\n% 1998ApJ...494...47F\n% Falco, E. E.; Kochanek, C. S.; Munoz, J. A.\n% Limits on Cosmological Models from Radio-selected Gravitational Lenses\n\n\\rf\\nn Freedman W;1999;Phyd. Rep.;333;13\n% astro-ph/9909076\n% Title: The Hubble Constant and the Expansion Age of the Universe\n% Authors: Wendy L. 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D;56;7559\n% astro-ph/9705166\n% Title: Primordial black hole constraints in cosmologies with early matter domination\n% Authors: Anne M Green, Andrew R Liddle, Antonio Riotto\n% Comments: 7 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at this http URL\n% Journal-ref: Phys.Rev. D56 (1997) 7559-7565 \n \n\\rf\\nnn Gorski K M {\\etal};1994;ApJL;430;L89\n% astro-ph/9403067 [abs, ps] :\n% On Determining the Spectrum of Primordial Inhomogeneity from the COBE DMR Sky\n% Maps: II. Results of Two Year Data Analysis, K.M. Gorski, G. Hinshaw, A.J. Banday, C.L. Bennett, E.L. Wright, A. Kogut, G.F.\n% Smoot & P. Lubin. 13 pages, 4 figures included, uuencoded Postscript file. Submitted to ApJ Letters, COBE Preprint #94-08.\n\n% astro-ph/9608054 [abs, src, ps, other] :\n% Title: COBE-DMR-Normalized Open CDM Cosmogonies\n% Authors: K. M. Gorski (TAC), B. Ratra (KSU), R. Stompor (Oxford), N. Sugiyama (Kyoto), A. J. Banday (MPI fur Astrophysik)\n% Comments: 49 pages, uses aaspp4.sty; 2 Postscript files of tables; uuencoded format. Complete paper including text, tables and 24\n% figures available at this ftp URL\n% APPEARED IN APJS TWO YEARS LATER.\n\n% astro-ph/9512148 [abs, src, ps] :\n% Title: CMB Anisotropy in COBE-DMR-Normalized Open CDM Cosmogony\n% Authors: Bharat Ratra, Anthony J. Banday, Krzysztof M. Gorski, Naoshi Sugiyama\n% Comments: 9 pages including 2 figures, one table: two uuencoded postscript files\n% \n% astro-ph/9511087 [abs, src, ps, other] :\n% Title: Flat Dark Matter Dominated Models with Hybrid Adiabatic Plus Isocurvature Initial Conditions\n% Authors: R.Stompor (CAMK), K.M. Gorski (GSFC), A.J. Banday (GSFC)\n% Comments: Two uuencoded compressed Postscript files containing (1) 19 pages manuscript, (2) four figures (tarred together).\n% Submitted to The Astrophysical Journal\n% \n% astro-ph/9506088 [abs, ps] :\n% Title: COBE-DMR-normalization for inflationary flat dark matter models\n% Authors: R. Stompor, K.M. Gorski, A.J. Banday\n% Comments: uuencoded postscript file (complete text and figures). Accepted for publication in MNRAS\n% \n% astro-ph/9502035 [abs, src, ps] :\n% Title: COBE-DMR-normalization for Cosmological Constant Dominated Cold Dark Matter Models.\n% Authors: Radoslaw Stompor, Krzysztof M. Gorski, Anthony J. Banday.\n% Comments: uuencoded file containing 6 postscript files (10 pgs text, 4 figures, 1 table).\n% \n% astro-ph/9502034 [abs, src, ps] :\n% Title: COBE-DMR-normalized Open Inflation, CDM Cosmogony.\n% Authors: Krzysztof M. Gorski, Bharat Ratra, Naoshi Sugiyama, Anthony J. Banday.\n% Comments: uuencoded file containing 6 postscript files (11 pgs text, 4 figures, 1 table).\n% Journal-ref: Astrophys. J. 444 (1995) L65\n\n% astro-ph/9502033 [abs, src, ps] :\n% Title: COBE-DMR-normalization for Cold and Mixed Dark Matter Models Inflationary Cosmogony.\n% Authors: Krzysztof M. Gorski, Radoslaw Stompor, Anthony J. Banday.\n% Comments: uuencoded file containing 5 postscript files (11 pgs text, 3 figures, 1 table).\n\n\\rf\\nnn Griffiths L M, \\nn Barbosa D\\multiand\\nnn Liddle A R;1999;MNRAS;308;854\n% 1999MNRAS.308..854G\n% Griffiths, Louise M.; Barbosa, Domingos; Liddle, Andrew R.\n% Cosmic microwave background constraints on the epoch of reionization\t\t\t\t\t \n\t\t\t\t\t \n\\rf\\nn Hancock S {\\etal};1998;MNRAS;294;L1\n% astro-ph/9708254 [abs, src, ps, other] :\n% Title: Constraints on cosmological parameters from recent measurements of CMB anisotropy\n% Author: S. Hancock (1), G. Rocha (1,3), A.N. Lasenby (1), C.M. Gutierrez (2) ((1) Mullard Radio Astronomy Observatory,\n% Cavendish Laboratory (MRAO), (2) Instituto de Astrofisica de Canarias (IAC), (3) Department of Physics, Kansas State University\n% (KSU))\n% Comments: 7 pages LaTeX, including 6 PostScript figures. Accepted for publication in MNRAS\n\n\\rfprep\\nn Hannestad S;1999;astro-ph/9911330\n% * astro-ph/9911330 [abs, src, ps, other] :\n% Title: Stochastic optimization methods for extracting cosmological parameters from CMBR power spectra\n% Authors: Steen Hannestad\n% Comments: 7 pages revtex, 3 figures, to appear in PRD \n% - Simulated annealing for searching in parameter space\n\n\\rf\\nn Helbig P;1999;A\\& A;350;1\n% 1999A&A...350....1H\n% Helbig, Phillip\n% Gravitational lensing statistics with extragalactic surveys. III. Joint constraints on lambda_ {0} and Omega_\n% {0} from lensing statistics and the m-z relation for type IA supernovae\t\t\t\t\t \t\t\t\t\t \n\n\\rf\\nn Herbig T {\\etal};1998;ApJL;509;L73\n% astro-ph/9808044\n\n\\rf\\nn Hu W, \\nnn Eisenstein D J\\multiand\\nn Tegmark M;1998;Phys. Rev. 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D;54;1332\n% preprint astro-ph/9512139.\n% JUNGMAN G; KAMIONKOWSKI M; KOSOWSKY A; SPERGEL DN.\n% COSMOLOGICAL-PARAMETER DETERMINATION WITH MICROWAVE BACKGROUND MAPS.\n% PHYSICAL REVIEW D, 1996 JUL 15, V54 N2:1332-1344.\n\n\\rfprep\\nn Kamionkowski M\\dualand\\nn Buchalter A;2000;astro-ph/0001045\n% Title: The Second Peak: The Dark-Energy Density and the Cosmic Microwave Background\n% Authors: Marc Kamionkowski, Ari Buchalter\n% Comments: 4 pages, 3 PostScript figures\n\n\\rf\\nn Knox L;1999;Phys.Rev. D;60;103516 \n% astro-ph/9902046\n% Title: Cosmic Microwave Background Anisotropy Window Functions Revisited\n% Authors: Lloyd Knox (University of Chicago)\n% Comments: 5 pages, 1 included .eps figure, PRD in press---final published version\n% Journal-ref: Phys.Rev. D60 (1999) 103516 \n \n\\rf\\nn Knox L {\\etal};1998;Phys. Rev. D;58;083004\n% astro-ph/9803272\n% \\rfprep\\nn Knox L, \\nnn Bond J R, \\nnn Jaffe A H, \n% \\nn Segal M\\multiand\\nn Charbonneau D;1998;astro-ph/9803272\n% Comparing Cosmic Microwave Background Datasets\n% Journal-ref: Phys.Rev. D58 (1998) 083004\n \n\\rf\\nn Knox L\\dualand\\nnn Page L A;2000;Phys. Rev. Lett.;85;1366\n% astro-ph/0002162\n% Title: Characterizing the Peak in the CMB Angular Power Spectrum\n% Authors: Lloyd Knox, Lyman Page\n% Comments: 4 pages, submitted to PRL \n\n\\rf\\nnn Kochanek C S;1996;ApJ;466;638\n\n\\rf\\nn Lesgourgues J, \n\\nn Polarski D\\multiand\\nnn Starobinsky A A;1999;MNRAS;308;281\n% astro-ph/9807019\n% Large primordial gravitational wave background in a class of BSI Lambda-CDM models\n% Authors: J. Lesgourgues (Tours), D. Polarski (Tours, Meudon), A. A. Starobinsky (Landau I.)\n% Comments: Final (revised and shortened) version to appear in MNRAS. Title changed, conclusion unchanged. 9 pages, 2 color ps figures,\n% uses mn.sty\n% Journal-ref: Mon.Not.Roy.Astron.Soc. 308 (1999) 281-288\n\n\\rf\\nnn Liddle A R\\dualand\\nnn Lyth D H;1992;Phys. Lett. B;291;391\n\n\\rf\\nnn Lineweaver C H;1998;ApJL;505;L69\n% {astro-ph/9805326 (``L98'')}\n% Title: The Cosmic Microwave Background and Observational Convergence in the Omega_m - Omega_lambda Plane\n% Author: Charles H. Lineweaver (UNSW,Sydney)\n% Comments: This version conforms to the version accepted by the Astrophysical Journal Letters. Minor revisions include references,\n% typos and phrasing. 13 pages including 3 Figures\n% The Astrophysical Journal, Volume 505, Issue 2, pp. L69-L73.\n\t\t \n\\rf\\nnn Lineweaver C H\\dualand\\nn Barbosa D;1998a;A\\&A;329;799\n\n\\rf\\nnn Lineweaver C H\\dualand\\nn Barbosa D;1998b;ApJ;496;624\n% astro-ph/9706077 [abs, src, ps, other] :\n% What Can Cosmic Microwave Background Observations Already Say About Cosmological Parameters in Open and\n% Critical-Density Cold Dark Matter Models?\n% Authors: Charles H. Lineweaver (UNSW, Sydney & Strasbourg), Domingos Barbosa (Sussex & Strasbourg)\n% Comments: 18 pages with 7 figures, conforms to accepted version in press: Astrophysical Journal, 496, (April 1, 1998). Three of the\n% figures have been modified, references updated, typos corrected. This version includes a table of current CMB measurements\n\n\\rf\\nnn Mauskopf P D {\\etal};2000;ApJ;536;L59\n% astro-ph/9911444\n% Title: Measurement of a Peak in the Cosmic Microwave Background Power Spectrum from the North American test flight of BOOMERANG\n% Authors: P.D. Mauskopf, P.A.R. Ade, P. de Bernardis, J.J. Bock, J. Borrill, A. Boscaleri, B.P. Crill, G. DeGasperis, G. De Troia, P. Farese, P. G. Ferreira, K.\n% Ganga, M. Giacometti, S. Hanany, V.V. Hristov, A. Iacoangeli, A. H. Jaffe, A.E. Lange, A. T. Lee, S. Masi, A. Melchiorri, F. Melchiorri, L. Miglio, T.\n% Montroy, C.B. Netterfield, E. Pascale, F. Piacentini, P. L. Richards, G. Romeo, J.E. Ruhl, E. Scannapieco, F. Scaramuzzi, R. Stompor, N. Vittorio\n% Comments: 5 pages, 1 figure LaTeX, emulateapj.sty\n\n\\rf\\nn Melchiorri A, \\nnn Sazhin M V, \\nnn Shulga V V,\n\\nn Vittorio N;1999a;ApJ;518;562\n% astro-ph/9901220\n% Title: The Gravitational-Wave contribution to the CMB anisotropies\n% Authors: A. Melchiorri, M. V. Sazhin, V.V. Shulga, N. Vittorio\n% Comments: 21 pages, 3 figures, to appear in ApJ\n% Journal-ref: Astrophys.J. 518 (1999) 562\n \n\\rf\\nn Melchiorri A {\\etal};2000;ApJL;536;L63\n% astro-ph/9911445\n% Title: A measurement of Omega from the North American test flight of BOOMERANG\n% Authors: A. Melchiorri, P.A.R. Ade, P. de Bernardis, J.J. Bock, J. Borrill, A. Boscaleri, B.P. Crill, G. De Troia, P. Farese, P. G. Ferreira, K. Ganga, G. de\n% Gasperis, M. Giacometti, V.V. Hristov, A. H. Jaffe, A.E. Lange, S. Masi, P.D. Mauskopf, L. Miglio, C.B. Netterfield, E. Pascale, F. Piacentini, G. Romeo, J.E.\n% Ruhl, N. Vittorio\n% Comments: 4 pages, 3 figures LaTeX, emulateapj.sty\n\n%\\bibitem{Metcalf}\n\\rf\\nnn Metcalf R B\\dualand\\nn Silk J;1997;ApJ;489;1\n% astro-ph/9708059\n% Title: Gravitational Magnification of the Cosmic Microwave Background\n% Authors: R. Benton Metcalf, Joseph Silk (University of California, Berkeley)\n% Comments: to be published in November 1 Astrophysical Journal, 11 pages, two figures\n% Astrophysical Journal v.489, p.1\n\n\\rf\\nnn Miller A D {\\etal};1999;ApJ;524;L1\n% astro-ph/9906421\n% Title: A Measurement of the Angular Power Spectrum of the CMB from l = 100 to 400\n% Authors: A. D. Miller, R. Caldwell, M. J. Devlin, W. B. Dorwart, T. Herbig, M. R. Nolta, L. A. Page, J. Puchalla, E. Torbet, H. T. Tran\n% Comments: 4 pages, 2 figures. Revised version; includes Ned Wright's postscript fix. Accepted by ApJL. Website at this http URL\n\n\\rfprep\\nn Narayan R\\dualand\\nn Bartelmann M;1996;astro-ph/9606001\n% Title: Lectures on Gravitational Lensing\n% Authors: Ramesh Narayan (1), Matthias Bartelmann (2) ((1) CfA, (2) MPA)\n% Comments: revised version: references updated, some new results included; 53 pages without any figures; complete versions can be found at this http URL\n\n\\rfbook\\nnnn Peebles P J E;1993;Principles of Physical \nCosmology;Princeton University Press;Princeton\n \n\\rf\\nn Perlmutter S {\\etal};1998;Nature;391;51\n\n\\rfprep\\nnn Peterson J B {\\etal};2000;ApJ;532;L83\n% astro-ph/9910503\n% From: Jeffrey B Peterson <[email protected]>\n% Date: Thu, 28 Oct 1999 01:47:44 GMT (64kb)\n% First Results from Viper: Detection of Small-Scale Anisotropy at 40 GHZ\n% Authors: J. B. Peterson, G. S. Griffin, M. G. Newcomb, D. L. Alvarez, C. M. Cantalupo, D. Morgan, K. W. Miller, K. Ganga, D. Pernic, M. Thoma\n% Comments: 5 pages, 4 figures, uses emulateapj.sty, submitted to ApJ Letters \n \n\\rfbook\\nnn Press W H {\\etal};1992;Numerical Recipes, 2nd ed.;Cambridge Univ. Press;Cambridge\n \n% \\rf\\nn Ratra B {\\etal};1997;ApJ;481;22 \n\n\\rf\\nn Ratra B {\\etal};1999;ApJ;510;11\n% astro-ph/9807298\n% Title: ARGO CMB Anisotropy Measurement Constraints on Open and Flat-Lambda CDM Cosmogonies\n% Authors: Bharat Ratra, Ken Ganga, Radoslaw Stompor, Naoshi Sugiyama, Paolo de Bernardis, Krzysztof M. Gorski\n% Comments: 21 pages of latex. Uses aaspp4.sty. 8 figures included. ApJ in press\n\n\\rf\\nnn Reese E D {\\etal};2000;ApJ;533;38\n% astro-ph/9912071\n% , \\nnn Mohr R R, \\nnn Carlstron J E, \n% * Perhaps use/reference \n% astro-ph/9912071 [abs, src, ps, other] :\n% Title: Sunyaev-Zel'dovich Effect Derived Distances to the High Redshift Clusters MS 0451.6-0305 and CL 0016+16\n% Authors: E. D. Reese, J. J. Mohr, J. E. Carlstrom, M. Joy, L. Grego, G. P. Holder, W. L. Holzapfel, J. P. Hughes, S. K. Patel,\n% M. Donahue\n% Comments: 14 pages, 4 figures, uses emulateapj.sty, to appear in the April 20, 2000 ApJ \n% - joint constraints on (Om,Ol,h) \n \n\\rf\\nnn Riess A G {\\etal};1998;Astron. J.;116;1009\n% Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant% astro-ph/9805201\n% The Astronomical Journal, Volume 116, Issue 3, pp. 1009-1038.\n\n\\rfprep\\nn Rocha G;1999;astro-ph/9907312\n% Title: Constraints on the Cosmological Parameters using CMB observations\n% Author: Graca Rocha (1,2) ((1) KSU, Kansas State University, USA, (2) CAUP, Centro de Astrofisica da Universidade do Porto, Portugal)\n% Comments: 67 pages, 13 figures, 10 tables. Invited review to appear in the proceedings of the `Early Universe and Dark Matter Conference', DARK98,\n% Heidelberg, 1998 \n\n\\rf\\nn Sahni V\\dualand\\nn Starobinsky A;2000;Int.J.Mod.Phys.;D9;373\n% astro-ph/9904398\n% Title: The Case for a Positive Cosmological Lambda-term\n% Authors: Varun Sahni, Alexei Starobinsky\n% Comments: 84 pages, latex, 17 figures. Revised and updated. More material added including a new section and several new figures. Invited\n% review article, to appear in: International Journal of Modern Physics D\n% Journal-ref: Int.J.Mod.Phys. D9 (2000) 373-444 \n\n\\rf\\nn Seljak U\\dualand\\nn Zaldarriaga M;1996;ApJ;469;437\n% A line of sight approach to Cosmic Microwave Background anisotropies by\n\n\\rf\\nn Sigurdson K\\dualand\\nn Scott D;2000;NewA;5;91\n% astro-ph/9911346\n% Title: Morphing the CMB: a technique for interpolating power spectra\n% Authors: Kris Sigurdson, Douglas Scott\n% Comments: 18 pages, including 6 figures, uses elsart.cls\n\n\\rf\\nnn Smoot G F {\\etal};1992;ApJ;396;L1\n% \\rf Smoot, G.F.; Bennett, C.L.; Kogut, A.; Wright, E.L.; and others.\n% Structure in the COBE Differential Microwave Radiometer first-year maps.\n\n\\rfprep\\nn Stompor R\\dualand\\nn Efstathiou G;1999;MNRAS;302;735\n% astro-ph/9805294\n% Title: Gravitational lensing of CMB anisotropies and cosmological parameters estimation\n% Authors: R. Stompor, G. Efstathiou (Institute of Astronomy, Cambridge)\n% Comments: 13 pages, 8 figures, uses mn.sty, submitted to MNRAS (5/5/1998)\n \n% \\rf\\nn Tegmark M;1997;Phys. Rev. Lett.;79;3806\n% galfisher, preprint astro-ph/9706198\n\n\\rf\\nn Tegmark M;1997a;ApJ;480;L87\n% How to make maps from cosmic microwave background data without losing information.\n% ASTROPHYSICAL JOURNAL, 1997 MAY 10, V480 N2 PT2:L87-L90.\n\n\\rf\\nn Tegmark M;1997b;Phys. Rev. D;55;5895\n% preprint astro-ph/961113.\n% cl\n\n\\rf\\nn Tegmark M;1999a;ApJ;519;513\n% astro-ph/9809001 \n% comparing\n\n\\rg\\nn Tegmark M;1999;ApJL;514;L69;T99\n% astro-ph/9809001\n% Title: Cosmological constraints from current CMB and SN 1a data: a brute force 8 parameter analysis\n% Author: Max Tegmark\n% Comments: 4 pages, with 3 figs included. Revised to match accepted ApJL version. Links, data and color figs at this http URL or from [email protected]\n% Journal-ref: Astrophys.J. 514 (1999) L69-L72\n% 9par\n \n\\rf\\nn Tegmark M\\dualand\\nnn Bunn E F;1995;ApJ;455;1\n% brute\n\n\\rf\\nn Tegmark M, \\nnn Eisenstein D J, \n\\nn Hu W\\multiand\\nn {de Oliveira Costa} A;2000;ApJ;530;133\n% astro-ph/9905257\n% foregpars\n\n%\\rfprep\\nn Tegmark M, \\nnn Eisenstein D J, \\nn Hu W\\multiand\\nn Kron R;1998;astro-ph/9805117\n\n\\rf\\nn Torbet E {\\etal};1999;ApJL;521;L79\n% astro-ph/9905100 [abs, src, ps, other] :\n% Title: A Measurement of the Angular Power Spectrum of the Microwave Background Made from the High Chilean Andes\n% Authors: E. Torbet, M. J. Devlin, W. B. Dorwart, T. Herbig, A. D. Miller, M. R. Nolta, L. Page, J. Puchalla, H. T. Tran\n% Comments: 5 pages, 3 figures, 2 tables; revised 10 June. Submitted to ApJL. Website at this http URL\n% Journal-ref: Astrophys.J. 521 (1999) L79-L82\n\n\\rf\\nn Venkatesan A;2000;ApJ;521;55\n% astro-ph/9912401\n% Title: The Optical Depth to Reionization as a Probe of Cosmological and Astrophysical Parameters\n% Authors: Aparna Venkatesan (The University of Chicago)\n% Comments: 24 pages (LaTeX) with 13 embedded postscript figures; submitted to ApJ\n\n\\rfprep\\nnn Wadsley J W, \\nnn Hogan C J\\multiand\\nnn Anderson S F;1999;astro-ph/9911394\n% From: James W. Wadsley <[email protected]>\n% Date: Sun, 21 Nov 1999 02:44:30 GMT (21kb)\n% Measuring Omega Baryon from the Helium Lyman-Alpha Forest\n% Authors: James W. Wadsley, Craig J. Hogan, Scott F. Anderson (University of Washington)\n% Comments: 7 Pages, 2 Figures, to appear in the proceedings of Clustering at High Redshift, IGRAP International\n% Conference, Marseilles, June 29-July 2, 1999\n% A new method to extract Omega_b from high redshift intergalactic absorption is described, based on the\n% distribution of HeII Ly-alpha optical depths in the voids in the ionization zone of quasars. A preliminary\n% estimate from recent HST-STIS spectra of PKS 1935-692 at z=3 gives Omega_b h^2 =\n% 0.013^{+0.002}_{-0.001} (1-sigma statistical errors, for a Lambda-CDM cosmology with additional\n% systematic uncertainties) consistent with other estimates. \n\n\\rfprep\\nnn Wandelt B D, \\nn Hivon E\\multiand\\nnn Gorski K M;1998;astro-ph/9808292\n% Title: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology\n% Authors: Benjamin D. Wandelt, Eric Hivon, Krzysztof M. Gorski (TAC, Copenhagen)\n% Comments: 4 pages, 3 figures. Also available at this http URL\n \n\\rf\\nn Webster M {\\etal};1998;ApJL;509;L65\n% astro-ph/9802109\n% Joint Estimation of Cosmological Parameters from\n% Cosmic Microwave Background and IRAS Data\n% Authors: WEBSTER, A. M.; BRIDLE, S. L.; HOBSON, M. P.; LASENBY, A. N.; LAHAV, O.; ROCHA, G.\n% Journal: The Astrophysical Journal, Volume 509, Issue 2, pp. L65-L68.\n\n\\rf\\nn White M;1998;ApJ;506;495\n% astro-ph/9802295\n% Complementary Measures of the Mass Density and Cosmological Constant\n% Astrophys.J. 506 (1998) 495\n\n\\rf\\nn White M\\dualand\\nn Scott D;1996;ApJ;459;415\n% astro-ph/9508157 [abs, ps] :\n% Title: Why Not Consider Closed Universes?\n% Authors: Martin White, Douglas Scott\n% Comments: 24 pages, including 13 figures in a uuencoded self-unpacking shell script. Submitted to ApJ\n% Journal-ref: Astrophys.J. 459 (1996) 415\n\n\\rf\\nnnn White S D M {\\etal};1993;Nature;366;429\n \n\\rfprep\\nnn Wilson G W {\\etal};1999;astro-ph/9902047\n% astro-ph/9902047\n% From: Lloyd Knox <[email protected]>\n% Date: Wed, 3 Feb 1999 01:53:10 GMT (75kb)\n% New CMB Power Spectrum Constraints from MSAMI\n% Authors: G.W. Wilson, L. Knox, S. Dodelson, K. Coble, E.S. Cheng, D.A. Cottingham, D.J. Fixsen, A.B. Goldin, C.A. Inman, M.S. Kowitt, S.S. Meyer, L.A. Page, J.L.\n% Puchalla, J.E. Ruhl, R.F. Silverberg\n\n\\rn Wright, E. L. 1996, preprint astro-ph/9612006.\n% Title: Scanning and Mapping Strategies for CMB Experiments\n% Author(s): Edward L. Wright (UCLA Astronomy)\n% Comments: 21 pages of LaTex with 11 included figures. Paper presented at the IAS\n% CMB Data Analysis Workshop in Princeton on 22 Nov 96 \n \n\\rf\\nn Zaldarriaga M, \\nn Spergel D\\multiand \\nn Seljak U;1997;ApJ;488;1\n% Microwave Background Constraints on Cosmological Parameters\n% Author(s): M. Zaldarriaga, D. Spergel, U. Seljak\n\n\\rfprep\\nn Zaldarriaga M\\dualand\\nn Seljak U;1999;astro-ph/9911219\n% Title: CMBFAST for spatially closed universes\n% Authors: Matias Zaldarriaga (IAS), Uros Seljak (Princeton University)\n% Comments: 6 pages, 2 figures, new version of CMBFAST can be found this http URL\n \n\\rf\\nn Zehavi I\\dualand\\nn Dekel A;1999;Nature;401;252\n% astro-ph/9904221 [abs, src, ps, other] :\n% Title: Evidence for a Positive Cosmological Constant from Flows of Galaxies and Distant Supernovae\n% Authors: Idit Zehavi (Hebrew U, Fermilab), Avishai Dekel (Hebrew U)\n% Comments: 8 pages, 1 figure. Slightly revised version. Letter to Nature\n% Journal-ref: Nature, 401, 252\n\n%%% HERE ARE MORE OLD MODEL TESTING/PARAMETER FITTING PAPERS:\n\n%%% THE RATRA ZONE: ONE PAPER PER EXPERIMENT\n\n% astro-ph/9406069 [abs, src, ps, other] :\n% CBR ANISOTROPY IN AN OPEN INFLATION, CDM COSMOGONY, by Marc Kamionkowski, Bharat Ratra, David N. Spergel,\n% and Naoshi Sugiyama, (12 pages, plain TeX; 3 figures available upon request from the authors), IASSNS-HEP-94/39, PUPT-1470,\n% POP-568, CfPA-TH-94-27, UTAP-185.\n% \n% astro-ph/9512157 [abs, src, ps] :\n% Title: CMB Anisotropy in COBE-DMR-Normalized Flat $\\Lambda$ CDM Cosmogony\n% Authors: Bharat Ratra, Naoshi Sugiyama\n% Comments: 9 pages including 2 figures, one 5 pages table: two uuencoded postscript files\n% \n% astro-ph/9512168 [abs, ps] :\n% Title: Tentative Appraisal of Compatibility of Small-Scale CMB Anisotropy Detections in the Context of COBE-DMR-Normalized\n% Open and Flat $\\Lambda$ CDM Cosmogonies\n% Authors: Ken Ganga, Bharat Ratra, Naoshi Sugiyama\n% Comments: 15 page PostScript file, including 6 included figures. Also available via anonymous ftp from this ftp URL\n% \n% astro-ph/9602141 [abs, src, ps] :\n% Title: UCSB South Pole 1994 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies\n% Author: Ken Ganga, Bharat Ratra, Josh Gundersen, Naoshi Sugiyama\n% Comments: Substantially shortened and rewritten. Accepted by ApJ. PostScript. 49 pages of text + tables. 16 pages of figures\n% \n% astro-ph/9702082 [abs, src, ps, other] :\n% Title: Large-scale structure in COBE-normalized cold dark matter cosmogonies\n% Authors: Shaun Cole (Durham), David H. Weinberg (Ohio), Carlos S. Frenk (Durham), Bharat Ratra (MIT & Kansas)\n% Comments: Accepted for publication in MNRAS. (shortened abstract) Also available at this ftp URL \n% \n% astro-ph/9702186 [abs, src, ps, other] :\n% Title: Using SuZIE arcminute-scale CMB anisotropy data to probe open and flat-\\Lambda CDM cosmogonies\n% Authors: K. Ganga, Bharat Ratra, S.E. Church, Naoshi Sugiyama, P.A.R. Ade, W.L. Holzapfel, A.E. Lange, P.D. Mauskopf\n% Comments: 17 pages including 4 postscript figures. Latex. Uses aaspp4. ApJ, in press\n% \n% astro-ph/9708202 [abs, src, ps, other] :\n% Title: MAX 4 and MAX 5 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies\n% Author: Ken Ganga, Bharat Ratra, Mark A. Lim, Naoshi Sugiyama, Stacy T. Tanaka\n% Comments: Latex, 37 pages, uses aasms4 style \n% \n% astro-ph/9710270 [abs, src, ps, other] :\n% Title: Using White Dish CMB Anisotropy Data to Probe Open and Flat-Lambda CDM Cosmogonies\n% Author: B. Ratra, K. Ganga, N. Sugiyama, G.S. Tucker, G.S. Griffin, H.T. Nguyen, J.B. Peterson\n% Comments: 17 pages of latex. Uses aasms4.sty. 4 figures included. Submitted to ApJS \n% \n% astro-ph/9807298 [abs, src, ps, other] :\n% Title: ARGO CMB Anisotropy Measurement Constraints on Open and Flat-Lambda CDM Cosmogonies\n% Authors: Bharat Ratra, Ken Ganga, Radoslaw Stompor, Naoshi Sugiyama, Paolo de Bernardis, Krzysztof M. Gorski\n% Comments: 21 pages of latex. Uses aaspp4.sty. 8 figures included. ApJ in press \n% \n\n% MORE LINEWEAVER:\n% astro-ph/9706215 [abs, src, ps, other] :\n% Title: Cosmic Microwave Background Anisotropies from Scaling Seeds: Fit to Observational Data\n% Authors: R. Durrer, M. Kunz, C. Lineweaver, M. Sakellariadou\n% Comments: LaTeX file 4 pages, 4 postscript figs. revised version, to appear in PRL\n% Journal-ref: Phys.Rev.Lett. 79 (1997) 5198-5201\n\n\\end{references}\n\n\\end{document}\n"
},
{
"name": "tab1.tex",
"string": "COBE &$ 8.5^{+16.0}_{- 8.5}$ &$ 2.1^{+ 0.4}_{- 0.1}$\\\\\nCOBE &$ 28.0^{+ 7.5}_{-10.3}$ &$ 3.1^{+ 0.6}_{- 0.6}$\\\\\nCOBE &$ 34.0^{+ 6.0}_{- 7.2}$ &$ 4.1^{+ 0.7}_{- 0.7}$\\\\\nCOBE &$ 25.1^{+ 5.3}_{- 6.6}$ &$ 5.6^{+ 1.0}_{- 0.9}$\\\\\nCOBE &$ 29.4^{+ 3.6}_{- 4.1}$ &$ 8.0^{+ 1.3}_{- 1.2}$\\\\\nCOBE &$ 27.7^{+ 3.9}_{- 4.5}$ &$ 10.9^{+ 1.3}_{- 1.2}$\\\\\nCOBE &$ 26.1^{+ 4.4}_{- 5.2}$ &$ 14.4^{+ 1.3}_{- 1.6}$\\\\\nCOBE &$ 33.0^{+ 4.6}_{- 5.4}$ &$ 19.4^{+ 2.7}_{- 2.8}$\\\\\nFIRS &$ 29.4^{+ 7.8}_{- 7.7}$ &$ 11.0^{+ 17.0}_{- 9.0}$\\\\\nTenerife &$ 32.5^{+10.1}_{- 8.5}$ &$ 20.0^{+ 10.0}_{- 8.0}$\\\\\nIACB &$111.9^{+65.4}_{-60.1}$ &$ 33.0^{+ 26.0}_{- 16.0}$\\\\\nIACB &$ 54.6^{+27.2}_{-21.9}$ &$ 53.0^{+ 26.0}_{- 19.0}$\\\\\nSP &$ 30.2^{+ 8.9}_{- 5.5}$ &$ 61.0^{+ 41.0}_{- 31.0}$\\\\\nSP &$ 36.3^{+13.6}_{- 6.1}$ &$ 61.0^{+ 41.0}_{- 31.0}$\\\\\nBAM &$ 55.6^{+29.6}_{-15.2}$ &$ 74.0^{+ 82.0}_{- 47.0}$\\\\\nPython &$ 60.0^{+15.0}_{-13.0}$ &$ 88.0^{+ 17.0}_{- 39.0}$\\\\\nPython &$ 66.0^{+17.0}_{-16.0}$ &$170.0^{+ 69.0}_{- 50.0}$\\\\\nARGO &$ 39.1^{+ 8.7}_{- 8.7}$ &$ 95.0^{+ 78.0}_{- 44.0}$\\\\\nARGO &$ 46.8^{+ 9.5}_{-12.1}$ &$ 95.0^{+ 78.0}_{- 44.0}$\\\\\nIAB &$ 94.5^{+41.8}_{-41.8}$ &$120.0^{+101.0}_{- 55.0}$\\\\\nMAX &$ 49.4^{+ 7.8}_{- 7.8}$ &$139.0^{+108.0}_{- 67.0}$\\\\\nSaskatoon &$ 49.0^{+ 8.0}_{- 5.0}$ &$ 87.0^{+ 44.0}_{- 35.0}$\\\\\nSaskatoon &$ 69.0^{+ 7.0}_{- 6.0}$ &$166.0^{+ 39.0}_{- 48.0}$\\\\\nSaskatoon &$ 85.0^{+10.0}_{- 8.0}$ &$237.0^{+ 36.0}_{- 48.0}$\\\\\nSaskatoon &$ 86.0^{+12.0}_{-10.0}$ &$286.0^{+ 33.0}_{- 44.0}$\\\\\nSaskatoon &$ 69.0^{+19.0}_{-28.0}$ &$349.0^{+ 51.0}_{- 46.0}$\\\\\nCAT &$ 50.8^{+15.4}_{-15.4}$ &$397.0^{+ 84.0}_{- 65.0}$\\\\\nCAT &$ 49.0^{+19.1}_{-13.6}$ &$615.0^{+102.0}_{- 72.0}$\\\\\nCAT &$ 54.0^{+ 9.5}_{- 6.4}$ &$397.0^{+ 84.0}_{- 65.0}$\\\\\nCAT &$ 43.6^{+13.6}_{-13.1}$ &$615.0^{+102.0}_{- 72.0}$\\\\\nOVRO &$ 56.0^{+ 8.5}_{- 6.6}$ &$537.0^{+267.0}_{-205.0}$\\\\\nQMAP &$ 47.0^{+ 6.0}_{- 7.0}$ &$ 80.0^{+ 41.0}_{- 41.0}$\\\\\nQMAP &$ 59.0^{+ 6.0}_{- 7.0}$ &$126.0^{+ 54.0}_{- 54.0}$\\\\\nPyth5/9911419 &$ 22.0^{+ 4.0}_{- 5.0}$ &$ 44.0^{+ 25.0}_{- 15.0}$\\\\\nPyth5/9911419 &$ 24.0^{+ 6.0}_{- 7.0}$ &$ 75.0^{+ 15.0}_{- 15.0}$\\\\\nPyth5/9911419 &$ 34.0^{+ 7.0}_{- 9.0}$ &$106.0^{+ 15.0}_{- 15.0}$\\\\\nPyth5/9911419 &$ 50.0^{+ 9.0}_{-23.0}$ &$137.0^{+ 15.0}_{- 15.0}$\\\\\nPyth5/9911419 &$ 61.0^{+13.0}_{-17.0}$ &$168.0^{+ 15.0}_{- 15.0}$\\\\\nPyth5/9911419 &$ 77.0^{+20.0}_{-28.0}$ &$199.0^{+ 15.0}_{- 15.0}$\\\\\nViper/9910503 &$ 61.6^{+31.1}_{-21.3}$ &$108.0^{+121.0}_{- 78.0}$\\\\\nViper/9910503 &$ 77.6^{+26.8}_{-19.1}$ &$173.0^{+114.0}_{-101.0}$\\\\\nViper/9910503 &$ 66.0^{+24.4}_{-17.2}$ &$237.0^{+ 99.0}_{-111.0}$\\\\\nViper/9910503 &$ 80.4^{+18.0}_{-14.2}$ &$263.0^{+185.0}_{-113.0}$\\\\\nViper/9910503 &$ 30.6^{+13.6}_{-13.2}$ &$422.0^{+182.0}_{-131.0}$\\\\\nViper/9910503 &$ 65.8^{+25.7}_{-24.9}$ &$589.0^{+207.0}_{-141.0}$\\\\\nIAC/9907118 &$ 43.0^{+13.0}_{-12.0}$ &$109.0^{+ 19.0}_{- 19.0}$\\\\\nToco97/9905100 &$ 40.0^{+10.0}_{- 9.0}$ &$ 63.0^{+ 18.0}_{- 18.0}$\\\\\nToco97/9905100 &$ 45.0^{+ 7.0}_{- 6.0}$ &$ 86.0^{+ 16.0}_{- 22.0}$\\\\\nToco97/9905100 &$ 70.0^{+ 6.0}_{- 6.0}$ &$114.0^{+ 20.0}_{- 24.0}$\\\\\nToco97/9905100 &$ 89.0^{+ 7.0}_{- 7.0}$ &$158.0^{+ 22.0}_{- 23.0}$\\\\\nToco97/9905100 &$ 85.0^{+ 8.0}_{- 8.0}$ &$199.0^{+ 38.0}_{- 29.0}$\\\\\nToco98/9906421 &$ 55.0^{+18.0}_{-17.0}$ &$128.0^{+ 26.0}_{- 33.0}$\\\\\nToco98/9906421 &$ 82.0^{+11.0}_{-11.0}$ &$152.0^{+ 26.0}_{- 38.0}$\\\\\nToco98/9906421 &$ 83.0^{+ 7.0}_{- 8.0}$ &$226.0^{+ 37.0}_{- 56.0}$\\\\\nToco98/9906421 &$ 70.0^{+10.0}_{-11.0}$ &$306.0^{+ 44.0}_{- 59.0}$\\\\\nMSAM123/9902047 &$ 35.0^{+15.0}_{-11.0}$ &$ 84.0^{+ 46.0}_{- 45.0}$\\\\\nMSAM123/9902047 &$ 49.0^{+10.0}_{- 8.0}$ &$201.0^{+ 82.0}_{- 70.0}$\\\\\nMSAM123/9902047 &$ 47.0^{+ 7.0}_{- 6.0}$ &$407.0^{+ 46.0}_{-123.0}$\\\\\nBoom/9911444 &$ 29.0^{+13.0}_{-11.0}$ &$ 58.0^{+ 17.0}_{- 33.0}$\\\\\nBoom/9911444 &$ 49.0^{+ 9.0}_{- 9.0}$ &$102.0^{+ 23.0}_{- 26.0}$\\\\\nBoom/9911444 &$ 67.0^{+10.0}_{- 9.0}$ &$153.0^{+ 22.0}_{- 27.0}$\\\\\nBoom/9911444 &$ 72.0^{+10.0}_{-10.0}$ &$204.0^{+ 21.0}_{- 28.0}$\\\\\nBoom/9911444 &$ 61.0^{+11.0}_{-12.0}$ &$255.0^{+ 20.0}_{- 29.0}$\\\\\nBoom/9911444 &$ 55.0^{+14.0}_{-15.0}$ &$305.0^{+ 20.0}_{- 29.0}$\\\\\nBoom/9911444 &$ 32.0^{+13.0}_{-22.0}$ &$403.0^{+ 72.0}_{- 77.0}$\\\\\n"
}
] |
[
{
"name": "astro-ph0002091.extracted_bib",
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Minor revisions include references,\n% typos and phrasing. 13 pages including 3 Figures\n% The Astrophysical Journal, Volume 505, Issue 2, pp. L69-L73.\n\t\t \n\\rf\\nnn Lineweaver C H\\dualand\\nn Barbosa D;1998a;A\\&A;329;799\n\n\\rf\\nnn Lineweaver C H\\dualand\\nn Barbosa D;1998b;ApJ;496;624\n% astro-ph/9706077 [abs, src, ps, other] :\n% What Can Cosmic Microwave Background Observations Already Say About Cosmological Parameters in Open and\n% Critical-Density Cold Dark Matter Models?\n% Authors: Charles H. Lineweaver (UNSW, Sydney & Strasbourg), Domingos Barbosa (Sussex & Strasbourg)\n% Comments: 18 pages with 7 figures, conforms to accepted version in press: Astrophysical Journal, 496, (April 1, 1998). Three of the\n% figures have been modified, references updated, typos corrected. This version includes a table of current CMB measurements\n\n\\rf\\nnn Mauskopf P D {\\etal};2000;ApJ;536;L59\n% astro-ph/9911444\n% Title: Measurement of a Peak in the Cosmic Microwave Background Power Spectrum from the North American test flight of BOOMERANG\n% Authors: P.D. Mauskopf, P.A.R. Ade, P. de Bernardis, J.J. Bock, J. Borrill, A. Boscaleri, B.P. Crill, G. DeGasperis, G. De Troia, P. Farese, P. G. Ferreira, K.\n% Ganga, M. Giacometti, S. Hanany, V.V. Hristov, A. Iacoangeli, A. H. Jaffe, A.E. Lange, A. T. Lee, S. Masi, A. Melchiorri, F. Melchiorri, L. Miglio, T.\n% Montroy, C.B. Netterfield, E. Pascale, F. Piacentini, P. L. Richards, G. Romeo, J.E. Ruhl, E. Scannapieco, F. Scaramuzzi, R. Stompor, N. Vittorio\n% Comments: 5 pages, 1 figure LaTeX, emulateapj.sty\n\n\\rf\\nn Melchiorri A, \\nnn Sazhin M V, \\nnn Shulga V V,\n\\nn Vittorio N;1999a;ApJ;518;562\n% astro-ph/9901220\n% Title: The Gravitational-Wave contribution to the CMB anisotropies\n% Authors: A. Melchiorri, M. V. 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Hughes, S. K. Patel,\n% M. Donahue\n% Comments: 14 pages, 4 figures, uses emulateapj.sty, to appear in the April 20, 2000 ApJ \n% - joint constraints on (Om,Ol,h) \n \n\\rf\\nnn Riess A G {\\etal};1998;Astron. J.;116;1009\n% Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant% astro-ph/9805201\n% The Astronomical Journal, Volume 116, Issue 3, pp. 1009-1038.\n\n\\rfprep\\nn Rocha G;1999;astro-ph/9907312\n% Title: Constraints on the Cosmological Parameters using CMB observations\n% Author: Graca Rocha (1,2) ((1) KSU, Kansas State University, USA, (2) CAUP, Centro de Astrofisica da Universidade do Porto, Portugal)\n% Comments: 67 pages, 13 figures, 10 tables. Invited review to appear in the proceedings of the `Early Universe and Dark Matter Conference', DARK98,\n% Heidelberg, 1998 \n\n\\rf\\nn Sahni V\\dualand\\nn Starobinsky A;2000;Int.J.Mod.Phys.;D9;373\n% astro-ph/9904398\n% Title: The Case for a Positive Cosmological Lambda-term\n% Authors: Varun Sahni, Alexei Starobinsky\n% Comments: 84 pages, latex, 17 figures. Revised and updated. More material added including a new section and several new figures. Invited\n% review article, to appear in: International Journal of Modern Physics D\n% Journal-ref: Int.J.Mod.Phys. D9 (2000) 373-444 \n\n\\rf\\nn Seljak U\\dualand\\nn Zaldarriaga M;1996;ApJ;469;437\n% A line of sight approach to Cosmic Microwave Background anisotropies by\n\n\\rf\\nn Sigurdson K\\dualand\\nn Scott D;2000;NewA;5;91\n% astro-ph/9911346\n% Title: Morphing the CMB: a technique for interpolating power spectra\n% Authors: Kris Sigurdson, Douglas Scott\n% Comments: 18 pages, including 6 figures, uses elsart.cls\n\n\\rf\\nnn Smoot G F {\\etal};1992;ApJ;396;L1\n% \\rf Smoot, G.F.; Bennett, C.L.; Kogut, A.; Wright, E.L.; and others.\n% Structure in the COBE Differential Microwave Radiometer first-year maps.\n\n\\rfprep\\nn Stompor R\\dualand\\nn Efstathiou G;1999;MNRAS;302;735\n% astro-ph/9805294\n% Title: Gravitational lensing of CMB anisotropies and cosmological parameters estimation\n% Authors: R. Stompor, G. Efstathiou (Institute of Astronomy, Cambridge)\n% Comments: 13 pages, 8 figures, uses mn.sty, submitted to MNRAS (5/5/1998)\n \n% \\rf\\nn Tegmark M;1997;Phys. Rev. Lett.;79;3806\n% galfisher, preprint astro-ph/9706198\n\n\\rf\\nn Tegmark M;1997a;ApJ;480;L87\n% How to make maps from cosmic microwave background data without losing information.\n% ASTROPHYSICAL JOURNAL, 1997 MAY 10, V480 N2 PT2:L87-L90.\n\n\\rf\\nn Tegmark M;1997b;Phys. Rev. D;55;5895\n% preprint astro-ph/961113.\n% cl\n\n\\rf\\nn Tegmark M;1999a;ApJ;519;513\n% astro-ph/9809001 \n% comparing\n\n\\rg\\nn Tegmark M;1999;ApJL;514;L69;T99\n% astro-ph/9809001\n% Title: Cosmological constraints from current CMB and SN 1a data: a brute force 8 parameter analysis\n% Author: Max Tegmark\n% Comments: 4 pages, with 3 figs included. Revised to match accepted ApJL version. Links, data and color figs at this http URL or from [email protected]\n% Journal-ref: Astrophys.J. 514 (1999) L69-L72\n% 9par\n \n\\rf\\nn Tegmark M\\dualand\\nnn Bunn E F;1995;ApJ;455;1\n% brute\n\n\\rf\\nn Tegmark M, \\nnn Eisenstein D J, \n\\nn Hu W\\multiand\\nn {de Oliveira Costa} A;2000;ApJ;530;133\n% astro-ph/9905257\n% foregpars\n\n%\\rfprep\\nn Tegmark M, \\nnn Eisenstein D J, \\nn Hu W\\multiand\\nn Kron R;1998;astro-ph/9805117\n\n\\rf\\nn Torbet E {\\etal};1999;ApJL;521;L79\n% astro-ph/9905100 [abs, src, ps, other] :\n% Title: A Measurement of the Angular Power Spectrum of the Microwave Background Made from the High Chilean Andes\n% Authors: E. Torbet, M. J. Devlin, W. B. Dorwart, T. Herbig, A. D. Miller, M. R. Nolta, L. Page, J. Puchalla, H. T. Tran\n% Comments: 5 pages, 3 figures, 2 tables; revised 10 June. Submitted to ApJL. Website at this http URL\n% Journal-ref: Astrophys.J. 521 (1999) L79-L82\n\n\\rf\\nn Venkatesan A;2000;ApJ;521;55\n% astro-ph/9912401\n% Title: The Optical Depth to Reionization as a Probe of Cosmological and Astrophysical Parameters\n% Authors: Aparna Venkatesan (The University of Chicago)\n% Comments: 24 pages (LaTeX) with 13 embedded postscript figures; submitted to ApJ\n\n\\rfprep\\nnn Wadsley J W, \\nnn Hogan C J\\multiand\\nnn Anderson S F;1999;astro-ph/9911394\n% From: James W. Wadsley <[email protected]>\n% Date: Sun, 21 Nov 1999 02:44:30 GMT (21kb)\n% Measuring Omega Baryon from the Helium Lyman-Alpha Forest\n% Authors: James W. Wadsley, Craig J. Hogan, Scott F. Anderson (University of Washington)\n% Comments: 7 Pages, 2 Figures, to appear in the proceedings of Clustering at High Redshift, IGRAP International\n% Conference, Marseilles, June 29-July 2, 1999\n% A new method to extract Omega_b from high redshift intergalactic absorption is described, based on the\n% distribution of HeII Ly-alpha optical depths in the voids in the ionization zone of quasars. A preliminary\n% estimate from recent HST-STIS spectra of PKS 1935-692 at z=3 gives Omega_b h^2 =\n% 0.013^{+0.002}_{-0.001} (1-sigma statistical errors, for a Lambda-CDM cosmology with additional\n% systematic uncertainties) consistent with other estimates. \n\n\\rfprep\\nnn Wandelt B D, \\nn Hivon E\\multiand\\nnn Gorski K M;1998;astro-ph/9808292\n% Title: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology\n% Authors: Benjamin D. Wandelt, Eric Hivon, Krzysztof M. Gorski (TAC, Copenhagen)\n% Comments: 4 pages, 3 figures. Also available at this http URL\n \n\\rf\\nn Webster M {\\etal};1998;ApJL;509;L65\n% astro-ph/9802109\n% Joint Estimation of Cosmological Parameters from\n% Cosmic Microwave Background and IRAS Data\n% Authors: WEBSTER, A. M.; BRIDLE, S. L.; HOBSON, M. P.; LASENBY, A. N.; LAHAV, O.; ROCHA, G.\n% Journal: The Astrophysical Journal, Volume 509, Issue 2, pp. L65-L68.\n\n\\rf\\nn White M;1998;ApJ;506;495\n% astro-ph/9802295\n% Complementary Measures of the Mass Density and Cosmological Constant\n% Astrophys.J. 506 (1998) 495\n\n\\rf\\nn White M\\dualand\\nn Scott D;1996;ApJ;459;415\n% astro-ph/9508157 [abs, ps] :\n% Title: Why Not Consider Closed Universes?\n% Authors: Martin White, Douglas Scott\n% Comments: 24 pages, including 13 figures in a uuencoded self-unpacking shell script. Submitted to ApJ\n% Journal-ref: Astrophys.J. 459 (1996) 415\n\n\\rf\\nnnn White S D M {\\etal};1993;Nature;366;429\n \n\\rfprep\\nnn Wilson G W {\\etal};1999;astro-ph/9902047\n% astro-ph/9902047\n% From: Lloyd Knox <[email protected]>\n% Date: Wed, 3 Feb 1999 01:53:10 GMT (75kb)\n% New CMB Power Spectrum Constraints from MSAMI\n% Authors: G.W. Wilson, L. Knox, S. Dodelson, K. Coble, E.S. Cheng, D.A. Cottingham, D.J. Fixsen, A.B. Goldin, C.A. Inman, M.S. Kowitt, S.S. Meyer, L.A. Page, J.L.\n% Puchalla, J.E. Ruhl, R.F. Silverberg\n\n\\rn Wright, E. L. 1996, preprint astro-ph/9612006.\n% Title: Scanning and Mapping Strategies for CMB Experiments\n% Author(s): Edward L. Wright (UCLA Astronomy)\n% Comments: 21 pages of LaTex with 11 included figures. Paper presented at the IAS\n% CMB Data Analysis Workshop in Princeton on 22 Nov 96 \n \n\\rf\\nn Zaldarriaga M, \\nn Spergel D\\multiand \\nn Seljak U;1997;ApJ;488;1\n% Microwave Background Constraints on Cosmological Parameters\n% Author(s): M. Zaldarriaga, D. Spergel, U. Seljak\n\n\\rfprep\\nn Zaldarriaga M\\dualand\\nn Seljak U;1999;astro-ph/9911219\n% Title: CMBFAST for spatially closed universes\n% Authors: Matias Zaldarriaga (IAS), Uros Seljak (Princeton University)\n% Comments: 6 pages, 2 figures, new version of CMBFAST can be found this http URL\n \n\\rf\\nn Zehavi I\\dualand\\nn Dekel A;1999;Nature;401;252\n% astro-ph/9904221 [abs, src, ps, other] :\n% Title: Evidence for a Positive Cosmological Constant from Flows of Galaxies and Distant Supernovae\n% Authors: Idit Zehavi (Hebrew U, Fermilab), Avishai Dekel (Hebrew U)\n% Comments: 8 pages, 1 figure. Slightly revised version. Letter to Nature\n% Journal-ref: Nature, 401, 252\n\n%%% HERE ARE MORE OLD MODEL TESTING/PARAMETER FITTING PAPERS:\n\n%%% THE RATRA ZONE: ONE PAPER PER EXPERIMENT\n\n% astro-ph/9406069 [abs, src, ps, other] :\n% CBR ANISOTROPY IN AN OPEN INFLATION, CDM COSMOGONY, by Marc Kamionkowski, Bharat Ratra, David N. Spergel,\n% and Naoshi Sugiyama, (12 pages, plain TeX; 3 figures available upon request from the authors), IASSNS-HEP-94/39, PUPT-1470,\n% POP-568, CfPA-TH-94-27, UTAP-185.\n% \n% astro-ph/9512157 [abs, src, ps] :\n% Title: CMB Anisotropy in COBE-DMR-Normalized Flat $\\Lambda$ CDM Cosmogony\n% Authors: Bharat Ratra, Naoshi Sugiyama\n% Comments: 9 pages including 2 figures, one 5 pages table: two uuencoded postscript files\n% \n% astro-ph/9512168 [abs, ps] :\n% Title: Tentative Appraisal of Compatibility of Small-Scale CMB Anisotropy Detections in the Context of COBE-DMR-Normalized\n% Open and Flat $\\Lambda$ CDM Cosmogonies\n% Authors: Ken Ganga, Bharat Ratra, Naoshi Sugiyama\n% Comments: 15 page PostScript file, including 6 included figures. Also available via anonymous ftp from this ftp URL\n% \n% astro-ph/9602141 [abs, src, ps] :\n% Title: UCSB South Pole 1994 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies\n% Author: Ken Ganga, Bharat Ratra, Josh Gundersen, Naoshi Sugiyama\n% Comments: Substantially shortened and rewritten. Accepted by ApJ. PostScript. 49 pages of text + tables. 16 pages of figures\n% \n% astro-ph/9702082 [abs, src, ps, other] :\n% Title: Large-scale structure in COBE-normalized cold dark matter cosmogonies\n% Authors: Shaun Cole (Durham), David H. Weinberg (Ohio), Carlos S. Frenk (Durham), Bharat Ratra (MIT & Kansas)\n% Comments: Accepted for publication in MNRAS. (shortened abstract) Also available at this ftp URL \n% \n% astro-ph/9702186 [abs, src, ps, other] :\n% Title: Using SuZIE arcminute-scale CMB anisotropy data to probe open and flat-\\Lambda CDM cosmogonies\n% Authors: K. Ganga, Bharat Ratra, S.E. Church, Naoshi Sugiyama, P.A.R. Ade, W.L. Holzapfel, A.E. Lange, P.D. Mauskopf\n% Comments: 17 pages including 4 postscript figures. Latex. Uses aaspp4. ApJ, in press\n% \n% astro-ph/9708202 [abs, src, ps, other] :\n% Title: MAX 4 and MAX 5 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies\n% Author: Ken Ganga, Bharat Ratra, Mark A. Lim, Naoshi Sugiyama, Stacy T. Tanaka\n% Comments: Latex, 37 pages, uses aasms4 style \n% \n% astro-ph/9710270 [abs, src, ps, other] :\n% Title: Using White Dish CMB Anisotropy Data to Probe Open and Flat-Lambda CDM Cosmogonies\n% Author: B. Ratra, K. Ganga, N. Sugiyama, G.S. Tucker, G.S. Griffin, H.T. Nguyen, J.B. Peterson\n% Comments: 17 pages of latex. Uses aasms4.sty. 4 figures included. Submitted to ApJS \n% \n% astro-ph/9807298 [abs, src, ps, other] :\n% Title: ARGO CMB Anisotropy Measurement Constraints on Open and Flat-Lambda CDM Cosmogonies\n% Authors: Bharat Ratra, Ken Ganga, Radoslaw Stompor, Naoshi Sugiyama, Paolo de Bernardis, Krzysztof M. Gorski\n% Comments: 21 pages of latex. Uses aaspp4.sty. 8 figures included. ApJ in press \n% \n\n% MORE LINEWEAVER:\n% astro-ph/9706215 [abs, src, ps, other] :\n% Title: Cosmic Microwave Background Anisotropies from Scaling Seeds: Fit to Observational Data\n% Authors: R. Durrer, M. Kunz, C. Lineweaver, M. Sakellariadou\n% Comments: LaTeX file 4 pages, 4 postscript figs. revised version, to appear in PRL\n% Journal-ref: Phys.Rev.Lett. 79 (1997) 5198-5201\n\n"
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astro-ph0002092
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Fragmentation Instability of Molecular Clouds: Numerical Simulations\altaffilmark{1}
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[
{
"author": "R\\'{e}my Indebetouw\\altaffilmark{2}"
}
] |
We simulate fragmentation and gravitational collapse of cold, magnetized molecular clouds. We explore the nonlinear development of an instability mediated by ambipolar diffusion, in which the collapse rate is intermediate to fast gravitational collapse and slow quasistatic collapse. Initially uniform stable clouds fragment into elongated clumps with masses largely determined by the cloud temperature, but substantially larger than the thermal Jeans mass. The clumps are asymmetric, with significant rotation and vorticity, and lose magnetic flux as they collapse. The clump shapes, intermediate collapse rates, and infall profiles may help explain observations not easily fit by contemporary slow or rapid collapse models.
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[
{
"name": "pp.tex",
"string": "\\documentclass[preprint2,eqsecnum]{aastex}\n\\usepackage{amssymb,amsbsy,graphics}\n\n\\begin{document}\n\\newlength{\\colw}\n\\setlength{\\colw}{3.2in}\n\n\\title{Fragmentation Instability of Molecular Clouds: \nNumerical Simulations\\altaffilmark{1}}\n\\author{R\\'{e}my Indebetouw\\altaffilmark{2}}\n\\affil{CASA, University of Colorado, Boulder, CO, 80309}\n\\and\n\\author{Ellen G. Zweibel\\altaffilmark{3}}\n\\affil{JILA, University of Colorado, Boulder, CO, 80309}\n\\altaffiltext{1}{in press, ApJ 532, April 1, 2000}\n\\altaffiltext{2}{[email protected]}\n\\altaffiltext{3}{[email protected]}\n\n\\begin{abstract}\nWe simulate fragmentation and gravitational collapse of cold, \nmagnetized molecular\nclouds. We explore the nonlinear development of an \ninstability mediated by ambipolar \ndiffusion, in which the collapse rate is intermediate to \nfast gravitational collapse and slow quasistatic collapse. \nInitially uniform stable clouds fragment into elongated\nclumps with masses largely determined by the cloud \ntemperature, but substantially larger than the thermal Jeans mass. \nThe clumps are asymmetric, with significant \nrotation and vorticity, and lose magnetic flux as they collapse.\nThe clump shapes, intermediate collapse rates, and infall profiles \nmay help explain observations \nnot easily fit by contemporary slow or rapid collapse\nmodels.\n\\end{abstract}\n\n\\section{Introduction}\n\nThe interstellar magnetic field \nplays an important role in the dynamics of molecular clouds \nand the collapse of dense cloud cores into protostars. \nMagnetic pressure and tension combine with thermal and turbulent \nkinetic pressure to resist gravitational collapse. The role of \nthe magnetic field is \noften simply characterized by a critical mass $M_{\\rm crit}$\nwhich depends on the magnetic flux threading the cloud \n\\citep{ms56,ms76,tin88,mckee93,m99}.\nClouds with $M > M_{\\rm crit}$ are termed\nsupercritical and collapse on a dynamical time-scale: \nthe magnetic field can have a moderate effect on the morphology of \ncollapse and can slow collapse in the cloud envelope\n\\citep[{\\it e.g.} ][]{black82}, but cannot significantly slow collapse in \nthe core. \nClouds with $M < M_{\\rm crit}$ are termed subcritical, and\nevolve on a longer \ntime-scale as magnetic support is lost due to ambipolar diffusion. \nThe magnetic field is redistributed within the cloud\nso that the inner parts become supercritical. \nThe cloud is then differentiated\ninto a dynamically collapsing core with a magnetically supported\nenvelope \\citep{cm93,fm93,bm94,cm94,sms97,ck98}.\nMuch progress has been made in following this\ntype of evolution through 6 or more orders of magnitude of increase in\ncentral density, including the effects of rotation as well as detailed\nchemistry and grain physics. The outcomes of these calculations include\ndetailed density, bulk velocity, ion-neutral drift velocity, \nmagnetic field, and grain and\nion abundance profiles in axisymmetric clouds, as well as an appreciation of\nthe timescales, rate of magnetic flux loss, and role of magnetic braking in\nthis mode of isolated star formation. \n\nThis theoretical picture can be\nobservationally tested \\citep[see recent reviews by ][]{evans99,meo99}.\nSo far, the results are ambiguous. Flow toward an isolated infrared source \nin the Bok globule B335 is well described by an inside-out collapse model \n\\citep{z90,z93,z95}.\nThe density distribution and measured magnetic\nfieldstrength in the cloud B1 have been fit by a model with a subcritical\nenvelope and a core which has evolved to a supercritical state by ambipolar\ndrift \\citep{c94}. On the other hand, in some respects the existing models\nappear to be incomplete. Clumps and cores are not axisymmetric; \\citet{m91} \nsurveyed 16 dense\ncores a few tenths of a parsec in size and pointed out that at least 6 of\nthem are likely to be prolate. \\citet{r96} made a statistical \nargument, based on a larger sample, that clumps and globules are more likely\nprolate or triaxial than\noblate. \\citet{wt99} showed that asphericity appears also at \nsmaller scales. Collapse guided by a magnetic field could produce oblate\nclouds, but not prolate ones. \nIt also appears unlikely that rotation accounts for the flattening;\nthis has been shown quantitatively in the case of L1527 \\citep{o97}.\nThus, the shapes are unexplained. Moreover,\nin some cases in which infall has been measured directly, it is more spatially\nextended, with faster velocities in the outer parts, than expected from\nthe standard models of inside-out collapse or gravitational motion driven by\nambipolar drift. This has been shown in the case of L1544 by \\citet{t98}, and\nfor 6 other starless cloud cores by \\citet{greg}. \n%rev8\n(Interestingly, a model of L1544 has been recently constructed by \n\\citet{cb2000} to match the observations of \\citet{t98}. The model \nrequires a mass-to-flux ratio more nearly critical than previously published \nmodels by the same authors, and appears to display the same intermediate\ncollapse discussed in this paper, although the authors do not call it out as \nsuch.)\n%rev8\nFinally, there are observations which relate to the timescale for collapse \nof molecular clouds into protostars. \\citet{lm99} find \ncollapse timescales of $\\sim$ 0.3-1.6 Myr from the ratio of the \nnumbers of starless cores to cores with embedded young stellar \nobjects. They state that this requires collapse 2-44 times \nfaster than ambipolar drift models.\nThese observations suggest that another ingredient may be required\nto explain the collapse of molecular clouds: the decay of turbulent \nsupport \\citep{mlazar}, or, as we explore in this\npaper, a magnetogravitational instability mediated by ambipolar drift.\n\nThe magnetic field likely also plays an important role in other\naspects of collapse, which are still incompletely understood.\nThe mechanism by which molecular clouds fragment,\nand the masses and morphology of those fragments, is clearly of\nimportance to the stellar initial mass function and the origin of\nbinary systems. The magnetic\nfield can exert strong forces on many scales, affecting fragmentation\n\\citep[{\\it e.g.} ][]{boss97,boss99}. \nThe field may also be a source of kinetic energy in the cloud,\nif the free energy of an ordered field can be released as turbulent\nmotions. \nThese issues have not been studied \nthoroughly in the detailed\naxisymmetric models of gravitational contraction with\nambipolar drift referenced above because they would require\ncalculations with no constraints on spatial symmetry.\n\nIn this paper, we address some of these issues by studying a simple problem:\nthe evolution of small perturbations to an initially uniform, \nmagnetically subcritical sheet of\nweakly ionized gas with a\nuniform magnetic field perpendicular to\nits plane. The perturbations evolve under the influence of magnetic tension,\nself gravity, thermal pressure, and ambipolar drift. Typically the sheet\nbreaks up into a small number of fragments of elongated shape which are\ncollapsing, losing magnetic flux through ambipolar drift, and\ninteracting gravitationally with one another. The magnetic\nfields associated with these asymmetric clumps generate local vorticity (the\nnet angular momentum of the sheet is identically zero). The characteristic\nvorticity structure is a vortex pair which flanks each clump and is\nassociated with strong streaming motions along it. The clump masses are\ntypically of order 1-10 $M_{\\odot}$, and scale with temperature like the Jeans\nmass, but are typically larger because of magnetic support. \nThe main features of collapse in this geometry were predicted \nby the linear stability analysis of Zweibel (1998; hereafter Z98); there is\nalso some overlap with the earlier stability analysis in 3D by \n\\citet{langer78}. \nHere we follow the evolution into the nonlinear regime and follow the growth\nof density fluctuations from .01 to up to 10 times the mean surface \ndensity.\nCollapse occurs on an intermediate time-scale, slower than the dynamical \nor free-fall time-scale, but faster than the ambipolar diffusion \ntime-scale. As noted above, \nthis intermediate collapse rate may be observed in \nsome clouds \\citep[{\\it e.g.} ][]{lm99,greg} .\nAs no restrictions are placed on the \nmorphology of the clumps, we can begin to explore\nthe nature of flux loss and collapse in more complicated geometries \nthan isolated axisymmetric clouds. One outcome suggested by linear\ntheory which we have not resolved \nis whether stored magnetic energy is converted to turbulence, as there\nis no stored magnetic energy in the system initially. \n\nThe unperturbed initial geometry, governing equations, and linear \ntheory are described in \\S\\ref{setup}. Section \n\\ref{num} contains a \ndescription of the numerical method and main results: \nthe collapse rate is discussed in \\S\\ref{gamgam}, \nthe relationship between magnetic field {\\bf B} and density \n$\\rho$ or surface density\n$\\sigma$ in \\S\\ref{brho}, size of fragments in \\S\\ref{clump}, \nvelocity structure in \\S\\ref{vel}, \nand distribution of energy in \\S\\ref{energy}.\nThe validity of the approximations is discussed in \\S\\ref{discuss}, \nand the summary and conclusions are in \n\\S\\ref{summary}.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Governing Equations and Linear Theory}\\label{setup}\n\nWe simulate a flat slab of cold gas with the \nmagnetic field initially \nperpendicular to the slab (the $\\hat{z}$ direction). \nZ98 discusses the linear theory for \nthis model when the cloud temperature T equals 0. \nIn this section we review the model in the more \ngeneral case T$>$0. We recall the results of the linear theory \nand discuss the consequences of adding thermal pressure.\n\nA flat slab-like model has observational and theoretical motivation: \nmolecular clouds commonly have sheet or filament-like \nstructure (although detailed, high-resolution \ninformation on the field orientation in such structures \nis not yet available for many objects). In a fairly quiescent environment, a\nroughly spherical molecular cloud with a large-scale, \ndynamically significant,\nordered magnetic field will relax into a pancake or slab\nas matter drains down the field lines. Magnetic forces \nwill allow comparatively little contraction perpendicular \nto the field direction, resulting in a slab with a predominantly \nperpendicular field. Such slabs could also be formed by shock waves \npropagating parallel to the local magnetic field. \n\nWe use a simple initial state with small ($<$1\\%) \nperturbations. The boundary conditions are periodic in the horizontal \n($\\hat{x}$ and $\\hat{y}$) directions and the initial surface \ndensity $\\sigma_0$ and magnetic field $B_{z0}$ are uniform. \n%rev8\nThe unperturbed initial state was chosen for computational \nsimplicity, as self-consistent finite disk and slab-like equilibrium \nstates cannot generally be described by simple expressions in closed form.\n\\citep[{\\it e.g.} ][]{park74,mous76,bau89,mestel85}.\nWe note that our initial state is not technically one of static equilibrium, \nbut rather a version of the commonly used Jeans swindle, in which \nthe unperturbed gravitational potential is discarded\n(see {\\it e.g.} discussion in \\citet{bt}).\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Governing Equations}\n\nWe begin with the equations of ideal magnetohydrodynamics \nfor two inviscid, non-resistive, interacting, magnetized fluids, \none charged and the other neutral. Since sources and sinks are \nexpected to dominate advection in the ion continuity equation, \nwe treat directly only the continuity equation for neutrals, \nand parameterize the ion behavior through equation \n(\\ref{eqn_alpha}).\nThe governing MHD equations are thus the equation of continuity\nfor neutral particles,\n\\begin{mathletters}\n\\begin{equation} \n{{\\partial\\rho_n}\\over{\\partial t}} + \n\t\\boldsymbol\\nabla\\cdot\\left(\\rho_n\\mathbf{v}\\right) = 0,\n\\end{equation}\nequations of motion for the two species, \n\\begin{eqnarray}\n\\rho_n{{ D_n\\mathbf{v}_n}\\over{ D_nt}}\n\t+ \\boldsymbol\\nabla P_n \n\t+ \\rho_n\\boldsymbol\\nabla\\Phi_G \\\\\\nonumber\n\t+ \\rho_n\\nu_{ni}(\\mathbf{v}_n-\\mathbf{v}_i) &=& 0, \\\\\n\\rho_i{{ D_i\\mathbf{v}_i}\\over{ D_it}}\n\t+ \\boldsymbol\\nabla P_i \n\t+ \\rho_i\\boldsymbol\\nabla\\Phi_G \\\\\\nonumber\n\t- \\rho_i\\nu_{in}(\\mathbf{v}_n-\\mathbf{v}_i) &=& \n\t{{(\\boldsymbol\\nabla\\times\\mathbf{B})\\times\\mathbf{B}}\n\t\\over{ 4\\pi}}, \n\\end{eqnarray}\nthe induction equation\n\\begin{equation}\n{{\\partial\\mathbf{B}}\\over{\\partial t}} \n= \\boldsymbol\\nabla\\times\\left(\\mathbf{v}_i\\times\\mathbf{B}\\right),\n\\end{equation}\nand Poisson's equation\n\\begin{equation}\n \\nabla^2\\Phi_G = 4\\pi G\\rho. \n\\end{equation}\n\\end{mathletters}\n\nSubscripts $i$ and $n$ denote ions and neutral particles respectively.\n$D_{\\alpha}/D_{\\alpha}t$ is the convective derivative for species $\\alpha$.\nThe ion-neutral collision frequency is \n$\\nu_{in} = \\rho_n \\langle \\sigma v \\rangle/(m_i + m_n)$,\nand $\\nu_{ni}$ is the neutral-ion \ncollision frequency $(\\rho_i \\nu_{in} = \\rho_n \\nu_{ni})$. In the context\nof collision rates only, the\nsymbol $\\sigma$ represents the cross-section for elastic collisions; elsewhere\nit represents surface density.\nThe gravitational potential is $\\Phi_G$, and $\\mathbf{v}$, $\\rho$, $P$, and \n$\\mathbf{B}$ are the \nvelocity, density, pressure, and magnetic field, respectively.\nWe work on large scales and at low temporal frequencies for which the \nions and electrons are coupled. \n\nWe assume that the ionization fraction in the cloud is low. For\ndense molecular gas which is ionized by cosmic rays and recombines on grains,\n$n_i/n_n \\sim K n_n^{-1/2}$, where $K\\sim 1.1\\times 10^{-5}$ \\citep{mckee93}\nDepartures from and generalizations of this ionization law are discussed\nbelow, see eq. [\\ref{eqn_alpha}].\nTherefore, \n$\\rho_n \\approx \\rho$ and $\\mathbf{v}_n \\approx \\mathbf{v}$. If the neutral-ion\ncollision time is much less than a dynamical time, \nthe ambipolar drift velocity \n$\\mathbf{v}_D$ can be written in the standard form \\citep{shu83}:\n\\begin{equation}\n\\mathbf{v}_D\\equiv\\mathbf{v}_i-\\mathbf{v}_n = \n{{(\\boldsymbol\\nabla\\times\\mathbf{B})\\times\\mathbf{B}}\n\\over{4\\pi\\nu_{in}\\rho_i}}.\n\\end{equation}\n\nThe flat geometry allows significant simplification of the equations\nby taking a vertical integral in the limit of \ninfinitesimal vertical thickness. For example, the \nmagnetic force simplifies to:\n\\begin{eqnarray}\n\\lim_{\\epsilon\\rightarrow 0}\\int\\limits_{-\\epsilon}^{+\\epsilon} dz\n{{(\\boldsymbol\\nabla\\times\\mathbf{B})\\times\\mathbf{B}}\n\\over{ 4\\pi}} &=& \\\\\n\\lim_{\\epsilon\\rightarrow 0}{{ B_z}\\over{ 4\\pi}}\n\\left[B_x\\hat{x} + B_y\\hat{y}\\right]_{-\\epsilon}^{+\\epsilon} &=&\n{{ B_z\\mathbf{B}_h}\\over{ 2\\pi}}.\n\\end{eqnarray}\nIn the limit of an infinitesimally thin disc or slab, \nthe vertical component of the magnetic field $B_z$ is \ncontinuous with\nrespect to the plane of the slab (the $\\hat{z}$ direction), and \nthe horizontal component $\\mathbf{B}_h$ is \nantisymmetric (reverses sign) with respect to the plane of the slab.\n\nIn addition, we assume the vertical component of the velocity is \nnegligible compared to the\nhorizontal components $(v_z \\ll v_x, v_y)$. \\citet{lz97} found that \nthin disks are generally stable to warping modes, so we expect \npredominantly horizontal motion.\n\nIn the limit of zero gas density and thermal pressure outside the \nslab, the external magnetic field relaxes instantaneously to \nan equilibrium state, shown in Z98 to be a current-free or \npotential field state.\nWe therefore assume that the magnetic field at $z \\neq 0$ is a potential field.\nThis allows us to calculate only the \nvertical part of the magnetic field in the disc, rather than all \nthree components in a three-dimensional domain, a\ntremendous simplification. Limitations of this \napproximation, and corrections\nto it, are discussed in more detail in \\S\\ref{potfield}\nand the Appendix.\n\n\nThe resulting system of 2-dimensional equations are as follows:\nThe equation of continuity \n\\begin{mathletters}\n\\begin{equation}\n\\label{gov1}\n{{\\partial\\sigma}\\over{\\partial t}}\n\t+\\boldsymbol\\nabla_h\\cdot(\\sigma\\mathbf{v}_h) = 0,\n\\end{equation}\nof motion\n\\begin{eqnarray}\n\\label{gov2}\n\\sigma{{ D\\mathbf{v}_h}\\over{ D t}}\n\t+ \\boldsymbol\\nabla_h P\n\t+ \\sigma\\boldsymbol\\nabla_h\\Phi_G &=& \n\t{{\\mathbf{B}_h B_z}\\over{ 2\\pi}}, \\\\\nv_z &=& 0,\n\\end{eqnarray}\nthe definition of the ambipolar drift velocity\n\\begin{equation}\n\\mathbf{v}_{Dh} =\n\t{{ B_z\\mathbf{B}_h}\\over\n\t{ 2 \\pi\\nu_{in}\\sigma_i}},\n\\end{equation}\nthe induction equation\n\\begin{equation}\n{{\\partial B_z}\\over{\\partial t}} =\n\t-\\boldsymbol\\nabla_h\\cdot\\left[(\\mathbf{v}_h+\\mathbf{v}_{Dh})\n\tB_z\\right], \n\\end{equation}\nthe potential field equations\n\\begin{eqnarray}\nB_z &=& {{\\partial\\Phi_M}\\over{\\partial z}}, \\\\\n\\mathbf{B}_h &=& \\mathbf\\nabla_h\\Phi_M, \n\\end{eqnarray}\nand Poisson's equation\n\\begin{equation}\n\\label{gov}\n{{\\partial\\Phi_G}\\over{\\partial z}}=2\\pi G\\sigma.\n\\end{equation}\n\\end{mathletters}\n%\nThe gravitational and magnetic potentials are $\\Phi_G$ and $\\Phi_M$ \nrespectively, \n$\\sigma$ is the surface density, and $h$ denotes horizontal components \n({\\it e.g.}, $\\mathbf{v}_{Dh}$ is the horizontal drift velocity).\nWe assume an isothermal equation of state\n\\begin{math}P = a^2\\sigma \\end{math}. \n\nEquations for an\naxisymmetric disk of small but finite half thickness $Z$ were derived by\n\\citet{cm93}. Their equations contain correction terms of order $Z/R$, where\n$R$ is the distance from the axis of symmetry; these terms include magnetic\npressure, which provides a restoring force which we neglect, and corrections\nto the normal direction, which is tilted slightly from the vertical because\n$Z$ depends on $R$. These terms go smoothly to zero in the limit \n$Z/R\\rightarrow 0$. For canonical values of physical parameters in dense\nmolecular clouds, we find $Z/R < 1/10$. Strictly speaking, we should retain\nthe magnetic pressure gradient, as \\citet{cm93} do, because it is of the\nsame order as, although generally less than, the thermal pressure gradient,\nand also provides a restoring force. \nHowever, magnetic tension clearly dominates magnetic pressure at \nthe long wavelengths of greatest interest here, while as the wavenumber \nincreases the rate of ambipolar drift increases as well, so that the \nmagnetic pressure force at short wavelengths is less than it would be \nif the magnetic field were frozen in. Moreover, we know that there\nis a 3D version of the instability which is driven by magnetic pressure \nalone. We study the instability driven by tension, but the existence \nand nature of the instability should be the same whether it is driven \nby tension or pressure.\nFor all these reasons, we think that the neglect of magnetic \npressure is not a major source of error.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Nondimensionalization}\n\\label{nondim}\n\nAll quantities in the problem are scaled by a self-consistent set of \ncharacteristic quantities. \nGiven an initial vertical magnetic field\n$B_{z0}$, we choose as the characteristic surface density that which is \nmarginally stable \nto collapse in the zero temperature limit \\citep{nn78},\n\\begin{equation}\n\\label{eqn_critical}\n \\sigma_{c0} \\equiv\n\t{{ B_{z0}}\\over{ 2\\pi G^{1/2}}}.\n\\end{equation} \nIn a 3-dimensional model \nof a cold magnetized molecular cloud, one logical choice would be to\nuse the Alfv\\'{e}n velocity as a characteristic velocity.\nThe 2-dimensional geometry precludes this approach, because the \nquantity $B_z /\\sqrt{2\\pi\\sigma}$ which arises naturally has dimensions not\nof (a 2-D Alfv\\'{e}n) velocity but rather of \nlength\\textsuperscript{1/2}/time. A length\nscale is thus required. A logical choice in this geometry is the scale height\nof the slab, $H = a^2 / 2 \\pi \\sigma G$, but this is undesirable because \nthe problem of most interest is a cold cloud, in which the isothermal sound\nspeed $a^2 \\rightarrow 0$. \nInstead we choose a characteristic length scale $L$, which\nwill be the horizontal domain size, or equivalently the largest spatial\nwavelength in the simulation (Of course, $L$ scales out of all final results\nwhen expressed in dimensional units). \nThe characteristic velocity is the \nAlfv\\'{e}n speed for the critical surface density and magnetic field\n\\begin{equation}\n\\label{eqn_alfven}\n v_{a0} \\equiv B_{z0}\\sqrt{{ L}\n\t\\over{ 2\\pi\\sigma_{c0}}}, \n\\end{equation}\nand the characteristic time is simply\n\\begin{equation}\n\\label{eqn_time}\n t_{c0} \\equiv {{ L}\\over{ v_{a0}}}. \n\\end{equation}\nThe nondimensionalized variables are as follows:\n\\begin{equation}\n\\begin{array}{rclrcl}\n\\omega &\\equiv& {{\\sigma}\\over{\\sigma_{c0}}}, &\n\t\\boldsymbol\\beta &\\equiv&\n\t{{\\mathbf{B}}\\over{ B_{z0}}}, \\\\\n\\tau &\\equiv& {{ t}\\over{ t_{c0}}}, &\n\t(\\mu,\\nu) \\;=\\; \\boldsymbol\\nu &\\equiv&\n\t{{\\mathbf{v}}\\over{ v_{a0}}}, \\\\\n\\nabla_h &\\leftarrow&\n\t{{\\nabla_h}\\over{ L}}, &\n\t\\xi,\\eta,\\zeta &\\equiv& \n\t{{ x,y,z}\\over{ L}}, \\\\\n\\phi_G &\\equiv& \n\t{{ t_{c0}^2}\\over{ L^2}}\\Phi_G, & \\mbox{and}\\hspace{3ex}\n\t\\phi_M &\\equiv& \n\t{{\\Phi_M}\\over{ B_{z0}L}}.\n\\end{array}\n\\end{equation}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Parameterization of Ambipolar Drift}\n\nWe assume that the product of the ion surface density $\\sigma_i$\nand the ion-neutral collision frequency $\\nu_{in}$ is \nrelated to the surface density $\\sigma\\simeq\\sigma_n$ according to the simple\n{\\it ansatz}:\n\\begin{equation}\n\\label{eqn_alpha}\n{{\\delta(\\sigma_i\\nu_{in})}\\over\n\t{\\sigma_i\\nu_{in}}} =\n\t\\alpha{{\\delta\\sigma}\\over{\\sigma}}.\n\\end{equation}\n%%%\nIf the ionization fraction $x$ scales as the\nneutral density $n_n^{-q}$, and the scale height $H$ scales as $\\sigma^{-1}$,\nthen $\\alpha=3-2q$. Often $q$ is taken to be 0.5 \n\\citep{mckee93}, but a detailed treatment\nof grain dynamics in contracting cores \\citep{cm94,cm95,cm98}\nshows that the parameter $q$ continuously decreases throughout contraction, \nand may\nrange from $\\sim 0.6$ to less than $0.1$ as the central density increases by\nabout 6 orders of magnitude.\nWe have tested the sensitivity of our\nresults to the value of $\\alpha$ by comparing models with $\\alpha$\n ranging from\n0 to 3, and find that the results differ by less than 5\\% as the density\nperturbations grow from .01 to 1.5 times the\nmean density (This is consistent with linear \nperturbation theory, which predicts that the value of $\\alpha$ enters only if\n%rev8\nthe unperturbed initial state has an inclined magnetic field; Z98). In view of\nthe insensitivity of the results to $\\alpha$, as well as the fact that the\nvolume density increases by less than 2 orders of magnitude in our\ncalculations, we regard the {\\it ansatz} \nequation (\\ref{eqn_alpha}) as adequate.\n\nTo compare with the linear theory, we use a nondimensional form of \nthe drift frequency \n$\\Gamma = t_{c0} k B_{z0}^2 / 2\\pi\\sigma_i\\nu_{in}$.\n(Z98 uses the {\\it dimensional} \n$\\Gamma = k B_{z0}^2 / 2\\pi\\sigma_i\\nu_{in}$.)\nIn the simulation, it is convenient to compute the evolution of \nthe drift independent of spatial wavenumber $k$. We use the \nquantity \n$\\Gamma/kL$, which is $\\Gamma/2\\pi$ for the lowest spatial \nwavenumber $k=2\\pi/L$.\n\nThe full set of governing equations in conservative form are \nas follows:\n\\begin{mathletters}\n\\begin{eqnarray}\n{{\\partial\\omega}\\over{\\partial\\tau}} \n\t&=& -\\boldsymbol\\nabla_h\\cdot(\\omega\\boldsymbol\\nu_h), \\\\\n{{\\partial}\\over{\\partial\\tau}}\\omega\\boldsymbol\\nu_h &=&\n\t-\\boldsymbol\\nabla_h\\cdot(\\omega\\boldsymbol\\nu_h\\boldsymbol\\nu_h)\n\t-a^2\\boldsymbol\\nabla_h\\omega \\nonumber\\\\&&\n\t-\\omega\\boldsymbol\\nabla_h\\phi_G\n\t+\\beta_z\\boldsymbol\\beta_h, \\\\\n\\omega &=& \\left.{{\\partial\\phi_G}\\over\n\t{\\partial\\zeta}}\\right|^+, \\\\\n\\boldsymbol\\beta_h &=& \\boldsymbol\\nabla_h\\phi_M, \\\\\n\t\\beta_z &=& \n\t{{\\partial\\phi_M}\\over{\\partial\\zeta}}, \\\\\n{{\\partial\\beta_z}\\over{\\partial\\tau}} &=& \n\t-\\boldsymbol\\nabla_h\\cdot\\left[\\beta_z(\\boldsymbol\\nu\n\t+\\boldsymbol\\nu_D)\\right], \\\\\n\\boldsymbol\\nu_D &=& \\beta_z\\boldsymbol\\beta_h\n\t{{\\Gamma}\\over{ kL}}, \\\\\n{{\\partial}\\over{\\partial\\tau}}\n\\left({{ kL}\\over{\\Gamma}}\\right) &=&\n\\label{eqn_drift}\n\t{{ kL}\\over{\\Gamma}}\n\t{{\\alpha}\\over{\\omega}}\n\t{{\\partial\\omega}\\over{\\partial\\tau}}.\n\\end{eqnarray}\n\\end{mathletters}\n\nNote that we interpret\nequation (\\ref{eqn_alpha})\nas an Eulerian relation in equation (\\ref{eqn_drift}).\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5\n\\subsection{Physically Reasonable Parameter Regime}\n\\label{phys_par}\n\nThe input parameters for the model are the sound speed $a$, \nthe strength of the initial magnetic field relative to the \nsurface density $B_{z0}/2\\pi G^{1/2}\\sigma_0 = 1/\\omega_0$, \nthe drift parameter $\\Gamma$, and the constant $\\alpha$\nwhich determines the perturbation to the collision\nrate (see eq. [\\ref{eqn_alpha}]).\n\nTypical magnetic fields in dense clouds are 30$\\mu$G \\citep{88.329}, \nand we choose the nondimensionalization length scale\n(see \\S\\ref{nondim}) to be 1pc, a typical \nsize for a dense cloud or cloud core and its \nclose neighborhood. A typical cold \ncloud temperature is 10K, and the average molecular weight is \nthat of molecular hydrogen with 10\\% helium, $m_n$ = \n3.9$\\times$10\\textsuperscript{-24}g. \nThis yields the following expressions for the Alfv\\'{e}n and \nsound speeds:\n\\begin{mathletters}\n\\begin{eqnarray}\nv_{a0}^2 &=& B_{z0}^2{L\\over{2\\pi\\sigma_{c0}}} \\\\\n\t&=& B_{z0}LG^{1/2} \\nonumber\\\\\n\t&=& 2.4\\times 10^{10} {{{\\rm cm}^2}\\over{{\\rm s}^2}}\n\t\t\\left({B_{z0}\\over{30\\mu {\\rm G}}}\\right)\n\t\t\\left({L\\over{\\rm pc}}\\right), \\nonumber\\\\\na^2 &=& {{k_BT}\\over{m},} \\\\\n{{ a^2}\\over{ v_{a0}^2}} \n\t&\\simeq& 0.02 \\left({T\\over{10 {\\rm K}}}\\right)\n\t\\left({{\\rm pc} \\over L}\\right)\n\t\\left({{30\\mu {\\rm G}}\\over{B_{z0}}}\\right) \\nonumber\\\\&&\\times\n\t\\left({{3.9\\times 10^{-24}{\\rm g}}\\over{m_n}}\\right).\n\\end{eqnarray}\n\\end{mathletters}\nFrom now on, $a^2$ will be given in units of $v_{a0}^2$.\n\nThe initial surface density is chosen to be\n$\\simeq$ 0.02 g cm\\textsuperscript{-2}, or about 100 M$_{\\odot}$ pc$^{-2}$. \nThis corresponds not only to a typical column density for a dense\ncold cloud ($N_H\\sim 10^{22}$ cm$^{-2}$), but also to the surface \ndensity that would result if \na spherical cloud of typical number density \n(10\\textsuperscript4 cm\\textsuperscript{-3}) \nand typical size (several 10\\textsuperscript{18}cm) collapsed \nalong a large-scale magnetic field into a thin pancake or disc. \nThe following expression for the normalized surface density \nresults:\n\\begin{eqnarray}\n\\label{eqn_omega_0}\n\\omega_0 &=& {{2\\pi G^{1/2}\\sigma_0}\\over{B_{z0}}} \\\\\n\t&\\simeq& 1.0 \\left({{30\\mu {\\rm G}}\\over{B_{z0}}}\\right)\n\t\\left({{\\sigma_0}\\over{0.02\\ {\\rm g}\\ {\\rm cm}^{-2}}}\\right).\\nonumber\n\\end{eqnarray}\nThermal pressure raises the critical surface \ndensity for gravitational collapse, and for a cloud at\nT = 10K the value of $\\omega_0$ for the fiducial parameters in equation \n(\\ref{eqn_omega_0})\nis 0.864 of that critical surface density $\\omega_{\\rm crit}$.\n%%%\n\nThermal pressure imparts a finite scale height to the disk \n\\begin{eqnarray}\n\\label{eqn_H}\nH &=& {{a^2}\\over{2\\pi\\sigma_0 G}} \\\\\n &\\simeq& 4\\times10^{16}{\\rm cm} \\left({T\\over{10 {\\rm K}}}\\right)\n \\left({{0.02\\ {\\rm g}\\ {\\rm cm}^{-2}}\\over{\\sigma_0}}\\right) \\nonumber\\\\&&\\times\n \\left({{3.9\\times 10^{-24} {\\rm g}}\\over{m_n}}\\right).\\nonumber\n\\end{eqnarray}\n\nClearly, $H\\ll L$. An inclined magnetic field exerts a pinching force,\ncompressing the disk and reducing $H$ further \\citep{wardle93}.\n\nDetermination of the drift parameter $\\Gamma$ requires an expression \nfor the neutral-ion collision frequency, \n$\\nu_{ni}\\simeq2\\times 10^{-9} n_i$ cm\\textsuperscript{3} \ns\\textsuperscript{-1} \n\\citep{draine83} and the density of ions. We assume\n$n_i = Kn_n^{1/2}$, where $K \n\\simeq 1.1\\times 10^{-5}\\ n_n^{1/2}$ cm\\textsuperscript{-3/2}\n\\citep{mckee93}. Using these relations\n\\begin{eqnarray}\n\\label{eqn_Gamma}\n\\Gamma &=& {k t_{c0}{B_{z0}^2}\\over{2\\pi\\sigma_i\\nu_{in}}} \\\\\n\t&=& {k t_{c0}{B_{z0}^2}\\over{2\\pi\\sigma_0\\nu_{ni}}} \\nonumber\\\\\n\t&\\sim& 0.059 \\left({{\\rm pc}\\over L}\\right)^{1\\over 2}\n\t\t\\left({{B_{z0}}\\over{30\\mu {\\rm G}}}\\right)^{3\\over 2}\n\t\t\\left({{0.02\\ {\\rm g}\\ {\\rm cm}^{-2}}\\over{\\sigma_0}}\\right) \\nonumber\\\\&&\\times\n\t\t\\left({{5\\times 10^4\\ \n {\\rm cm}^{-3}}\\over{n_n}}\\right)^{1\\over 2}\n\t\t\\left({k\\over{2\\pi/L}}\\right).\\nonumber\n\\end{eqnarray}\nThe fiducial value of $n_n$ which appears here is consistent with the other\nparameters: $n_n = \\pi G\\sigma_0^2/k_BT$.\n\nAlthough equation (\\ref{eqn_Gamma}) shows that $\\Gamma$ does\nnot depend on the scale height $H$, since the temperature of molecular clouds\nis quite well determined it is useful to rewrite $\\Gamma$ in a way\nwhich does depend on $H$ and suppresses the dependence on some of the other\nparameters. We have\n\\begin{eqnarray}\n\\label{eqn_Gamma_alt}\n\\Gamma &=& {{4\\pi^{3/2}(m_n G)^{3/2}}\\over {K\\langle\\sigma v\\rangle\\omega_0^{\n3/2}}}\\Bigg({{H}\\over {L}}\\Bigg)^{1/2}\\\\\n&=&0.56\\Bigg({{H}\\over {L}}\\Bigg)^{1/2},\\nonumber\n\\end{eqnarray}\nwhere we have used the standard values for all the constants. Equations\n(\\ref{eqn_H}) and \n(\\ref{eqn_Gamma_alt}) suggest $\\Gamma\\le 0.1$ for typical parameters. \n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Linear Theory}\n\\label{lin_th}\n\nThe collapse rate for a linear perturbation with positive thermal pressure \ncan be easily calculated (see Z98 for the calculation at T=0K).\nThe physical quantities $\\omega$, $\\beta_z$, $\\boldsymbol\\nu$\nand governing equations \n(\\ref{gov1}-\\ref{gov}) are linearized and reduced to one horizontal spatial \ndimension. Assuming a single Fourier mode\n\\begin{mathletters}\\begin{eqnarray}\n\\omega &\\rightarrow& \\omega_0 + \\omega e^{\\gamma\\tau+ik\\xi-k|\\zeta|}, \\\\\n\\beta_z &\\rightarrow& 1 + \\beta_z e^{\\gamma\\tau+ik\\xi-k|\\zeta|}, \\\\\n\\nu &\\rightarrow& \\nu e^{\\gamma\\tau+ik\\xi-k|\\zeta|}\n\\end{eqnarray}\\end{mathletters}\nleads to the dispersion relation \n\\begin{equation}\n\\gamma^3 + \\Gamma\\gamma^2 + \n\\left[\\gamma_G^2\\left({1\\over{\\omega_0^2}}-1\\right)+\\gamma_T^2\\right]\\gamma\n\t- \\gamma_G^2\\Gamma + \\gamma_T^2\\Gamma = 0, \n\\label{disp_rel}\n\\end{equation}\nwhere $\\gamma_G = \\sqrt{\\omega_0kL}$ is the nondimensionalized gravitational \nfrequency, and $\\gamma_T = akL$ is the nondimensionalized \nthermal frequency.\n%%%\n\nEquation (\\ref{disp_rel}) has two limits which provide some insight into what\nfollows. In the limit $\\Gamma = 0$ we recover the dispersion relation for\nwaves driven by magnetic tension, thermal pressure, and self-gravity; the\nfirst two forces are stabilizing and the last is destabilizing. The system is\nstable for all wavenumbers if $\\omega_0 < 1$, but if $\\omega_0 > 1$, the\nsystem is unstable for wavenumbers $k < k_c(\\Gamma=0)\\equiv \n H^{-1}(\\omega_0^2-1)/\\omega_0^2$. (In\na system of finite size $L$, $k$ is bounded from below by $2\\pi/L$, leading to\nthe absolute stability criterion $\\omega_0 < \\omega_{crit}$ which we present\nbelow).\n The maximum growth rate, in dimensional form\n(recall that in equation (\\ref{disp_rel}), \n$\\gamma$ is given in units of $t_{c0}^{-1}$\n), is $\\gamma_{max}(\\Gamma=0)=\\pi G\\sigma_0(\\omega_0^2-1)/(a\\omega_0^2)$, and\noccurs at a wavenumber $k_m(\\Gamma = 0) = {{1}\\over {2}}k_c(\\Gamma=0)$ (in\nthese dimensional expressions, $a$ is the {\\it dimensional} sound speed).\n\nIn the limit of large $\\Gamma$, the magnetic field is uncoupled from the gas,\nand the dispersion relation reverts to that of an unmagnetized slab. The\nsystem is unstable for $\\gamma_G^2 > \\gamma_T^2$, or $k < \nk_c(\\Gamma\\rightarrow\\infty) \\equiv 2\\pi G\\sigma_0/a^2\n= H^{-1}$. The maximum growth rate, which occurs at \n$k_m(\\Gamma\\rightarrow\\infty)={{1}\\over {2}}k_c(\\Gamma\\rightarrow\n\\infty)$, is $\\gamma_{max}(\\Gamma\\rightarrow\\infty)=\\pi G\\sigma_0/a$. (Again,\nin these dimensional expressions, $a$ is dimensional).\n\nThe maximum growth rate, and the wavenumber at which it occurs, is always less\nfor a magnetized but supercritical cloud than for an unmagnetized cloud, and,\nas expected, the supercritical case approaches the unmagnetized case as the\nmagnetic fieldstrength decreases to zero.\n\nIn this paper we are interested in clouds which are magnetically subcritical,\nso that they would be stable in the limit $\\Gamma=0$, but would be unstable\nif the magnetic field were removed. That is, we are\ninterested in clouds with a length much\nlarger than the unmagnetized Jeans length. A small but nonzero $\\Gamma$ \ndestabilizes a cloud to\nperturbations which are stabilized by magnetic fields in the absence of\nambipolar drift, but would be unstable to the Jeans instability in the\nabsence of magnetic fields.\n\n%%%\nFor small sound speeds, the dispersion relation shows the same \nbehavior seen for zero temperature in Z98: \nat low values of the drift parameter \n$\\Gamma$, the growth rate of the perturbation $\\gamma$ is \nproportional to $\\Gamma$. At higher $\\Gamma$, however, \n$\\gamma\\propto\\Gamma^{1/3}$. As surface densities $\\omega$ and wavenumbers\n$k$ depart from the critical values for stability, more ambipolar drift is\nrequired for the system to show $\\gamma\\propto\\Gamma^{1/3}$ behavior. \nTo quantify these\nstatements with an example, at $\\omega_0$ = 1.1, $a^2$ = 0.02, $\\Gamma$ = 0,\nthe critical $k$ below which ideal perturbations are unstable is $k$ = 9.5455.\nVery close to criticality, $k$ = 9.6, the $\\gamma\\propto \\Gamma^{1/3}$\nscaling holds for $\\Gamma$ as small as .001. At $k$ = 10, $\\gamma$ increases\nwith $\\Gamma$ faster than $\\Gamma^{1/3}$, but much slower than linearly, for $\n.001 < \\Gamma < .01$, but approaches the $\\Gamma^{1/3}$ scaling for $.01 <\n\\Gamma < .1$. As $\\Gamma$ is increased from .001 to .1, $\\gamma$ increases\nfrom .378 to 1.75, which is $\\Gamma^{.33}$ scaling. At $k$ = 4$\\pi$, this\nscaling has broken down noticeably: as\n $\\Gamma$ is increased from .001 to .1, $\\gamma$ increases\nfrom .170 to 1.93, which is $\\Gamma^{.53}$ scaling. Most of the deviation\noccurs for small values of $\\Gamma$; for $\\Gamma$ between .01 and .1, $\\gamma\n\\propto \\Gamma^{.36}$. Thus, for reasonable values of $a^2$ and $\\Gamma$, the\n$\\Gamma^{1/3}$ scaling law holds quite well even when $k$ is\nas much as 30\\% below the\ncritical value.\n\nThe addition of thermal pressure increases the stability of the disk;\n%and suppresses modes with high spatial wavenumbers. \nmore drift (larger $\\Gamma$) is required for collapse, and more \nis required to reach the \ntransition from $\\gamma\\propto\\Gamma$ to $\\gamma\\propto\\Gamma^{1/3}$. \nAn approximate value for the critical surface density \nfor collapse, with positive \nthermal pressure, is obtained from solving the dispersion relation \n(see eq. [\\ref{disp_rel}]) for $\\Gamma$=0:\n\\begin{mathletters}\\begin{eqnarray}\n{{1}\\over{\\omega_{\\rm crit}}} \n\t&=& -\\pi a^2 + \\sqrt{1+\\pi^2a^4} \\\\\n\t&\\simeq& 1-\\pi a^2, \\nonumber\\\\\n\\omega_{\\rm crit} &\\simeq& 1 + \\pi a^2,\n\\end{eqnarray}\\end{mathletters}\nwhere the approximations hold for small sound speed.\nSolution of the dispersion relation also shows that for a given sound \nspeed and drift parameter, there is a single mode with a\nmaximal growth rate, and that the modes above a certain wavenumber\nare acoustically suppressed. Figure \\ref{ak} shows the \ngrowth rate as a function of wavenumber for $\\Gamma$ = 0.1, and most\nunstable wavenumber, over a range of sound speeds. \nFigure \\ref{ak} also shows that the stability boundary is very near the \nthermal Jeans stability boundary, while the fastest growing mode has a\nmuch longer wavelength than the Jeans wavelength.\n%\n\\begin{figure}[hbpt]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{ak1.eps}}}\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{ak2.eps}}}\n\\caption{\\label{ak}\nDamping of short-wavelength modes due to thermal pressure. The \nfirst graph shows the linear growth rate $\\gamma$ of the fastest\ngrowing mode as a function \nof spatial frequency $f=k/2\\pi$, for different sound speeds $a^2$. \nThe second graph shows the spatial frequency of maximal growth \nrate (the peak of each curve in the first graph), and the highest \nundamped spatial frequency (where each curve in the \nfirst graph crosses the x-axis). \nFor both figures, $\\Gamma$ = 0.1, and $\\omega_{crit}$ is approximately \nconstant: $\\omega_0$ = 0.864(1+$\\pi a^2$).\n}\\end{figure}\n%%%\n\nAs we will see later, the wavenumber at which the growth rate is maximized\ndominates the structure of clumps even into the nonlinear regime. Numerical\nsolution of the dispersion relation equation (\\ref{disp_rel}) shows that $k_m$\nis always less than $k_m(\\Gamma\\rightarrow\\infty)$, the fastest\ngrowing wavenumber for the Jeans instability, but also scales with temperature\nas $1/T$. Therefore, we expect the fragment mass to be larger than the\nthermal Jeans mass, but to have the same $T^2$ temperature scaling. This is\nborne out by Figures \\ref{ak} and \\ref{clumpfig}.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Numerical Simulation}\\label{num}\n\nIn order to follow the instability into the nonlinear regime we have \ncarried out a numerical simulation.\nWe use a Fourier collocation pseudo-spectral method \\citep{canuto} to\nsolve the governing equations. Values of physical quantities are stored \nat discrete points in physical space (known as collocation points), and \nspatial derivatives are evaluated in Fourier spectral space (hence the name\n``Fourier pseudo-spectral''). \nThis particular method is well adapted to this\nproblem for several reasons. Calculating a spatial derivative in Fourier \nspace simply requires multiplication of each Fourier component by $i$ times\nits wavenumber. All terms involving the horizontal magnetic field \n$\\mathbf{B}_h$ or gravitational potential $\\Phi_G$ are trivial to evaluate\nin Fourier space due to the simple form of the magnetic and gravitational\npotentials. Nonlinear terms, on the other hand, are trivial to evaluate in\nphysical space by simple multiplication. Finally, growth of different \nFourier modes can be monitored and controlled explicitly, simplifying \ncomparison between the nonlinear numerical model and the single-wavenumber\nlinear analytic results.\n\nWe use a Bulirsh-Stoer time-stepping routine with Richardson extrapolation\n\\citep{fourn2}. The routine performs several modified midpoint method\nintegrations at sub-intervals of the desired time-step. It then attempts \nto extrapolate to an infinite number of sub-intervals. The routine varies\nthe number of explicit (calculated) sub-intervals based on the estimated \nerror. In general, the full set of governing equations for this problem\ncan be integrated with $\\sim$ 5 explicit subintervals for each time-step of\n$\\delta\\tau = 0.1$.\n\nWe tested convergence by running the code at increasing \nspatial resolution \nwith the same initial conditions. Figure \\ref{conv} shows \nthe amplitude of a density perturbation, computed at\ndifferent resolutions, as a function of time. \nThe initial conditions had a single wavenumber density perturbation\nin each direction, \nforming a ``checkerboard'' pattern. (Collapse is described in \ndetail below.)\nA 16$^2$ grid is sufficient to resolve the collapse of \nsuch a single wavenumber, from the linear regime (exponential\ngrowth) into the nonlinear regime.\nUse of a 32$^2$ or 64$^2$ grid changes the solution by less than 0.1\\%\nover most of the time period plotted. Finer grids are required to \nresolve collapse of smaller structures, and in runs which \ncontain a spectrum of wavenumbers, a 64$^2$ grid was used.\n%\n\\begin{figure}[hbt]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{conv.eps}}}\n\\caption{\n\\label{conv}\nConvergence of model with increasing numerical resolution.\nMagnitude of the density perturbation for the same initial \nconditions, using grid sizes of $4^2$, $8^2$, $16^2$, $32^2$, \nand $64^2$.\nThis particular run had $\\Gamma$ = 0.1, $a^2$ = 0.1, \n$\\omega_0$ = 0.864 $\\omega_{crit}$ = 1.135). The oscillations at early times\nare due to the presence of frictionally damped oscillatory modes which were\npresent in the initial conditions.}\n\\end{figure}\n\n%%\nWe have also verified that the code reproduces the results of linear theory.\nIf the initial condition corresponds to an eigenfunction of a growing mode\ncalculated according to linear perturbation theory, with an amplitude of a few\npercent or less, then the disturbance initially grows at the exponential rate\npredicted by the linear theory. This is shown in Figure \\ref{lincomp}, which\ncompares the growth rates measured from the code (discrete symbols) with the\ncontinuous curve obtained from solving the dispersion relation \nequation (\\ref{disp_rel}).\nThe agreement is generally excellent. \n%\n\\begin{figure}\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{gg1.eps}}}\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{gg2.eps}}}\n\\caption{\nComparison of linear analytical growth rate (solid line) with the \ninitial growth rate in our simulations \n($\\gamma$ when the density perturbation $\\delta\\omega$ is \n$<$10\\% of mean density $\\omega$), for a \nrepresentative sound speed $a^2$ = 0.033.\nLeft, the growth rate in the simulation (points with error bars)\nagrees with the linear theory (solid line) for \na range of initial surface density $\\omega_0$ ($\\Gamma$ = 0.1). Right,\n the growth rate in the simulation is seen to agree \nwith the linear theory over a 4 order of magnitude range in $\\gamma$.\n($\\Gamma$ varies from 0.01 to 0.3 and $\\omega_0$ from 0.3 to 0.95)\n\\label{lincomp}}\n\\end{figure}\n\nThe model is numerically stable until such time as power in the higher \norder wavenumbers grows to overwhelm power in the Fourier modes of \ninterest. \nAt that time, the simulation develops a ``sawtooth'' instability, \nwith large variation between alternating collocation points. \nPower grows in these short-wavelength modes from numerical \nnoise, whose magnitude is about 10\\textsuperscript{-8} compared to the \npower in the principal mode (measured in simulations whose initial \nconditions contained a single mode). Higher wavenumber modes are\nalso driven by the nonlinearity of the problem, and this is the\ndominant physical source of power in those modes. \n\nGrowth of high-order modes can be controlled in several ways. \nThermal pressure will stabilize high order modes, as was seen \nin Figure \\ref{ak}. In most cases, a physically reasonable \nfinite cloud temperature of $\\lesssim$ 10 K will stabilize the \nsimulation long enough to follow the collapse well into the nonlinear regime.\nThe problem of high-order mode stabilization \nis nearly independent of the drift parameter $\\Gamma$ because\nan increase (decrease) in ambipolar diffusion increases\n(decreases) the growth rate of all modes similarly. \nThus the entire physically interesting part of parameter space is\nnumerically accessible and numerically stable in this model.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Collapse Rate}\\label{gamgam}\n\nMany runs were computed\nwith initial conditions corresponding to the eigenfunction \nof the fastest-growing solution of the 3 modes present, at each\nwavenumber, in linear theory. This initial perturbation has a \nsingle initial wavenumber in each direction. \nGrowth initially proceeds exponentially, with faster\nnonlinear collapse occurring as higher order spatial modes \nare driven. Nonlinear behavior is typically seen when the \ndensity enhancement associated with a perturbation has \ngrown to 75\\%-100\\% of the mean density. We were able to follow the evolution\nof the system to peak surface densities about 10 times larger than the mean\ndensity (corresponding to a peak volume density about 100 times larger than\nthe mean).\n\n\\begin{figure}[hptb]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{gam.eps}}}\n\\caption{Collapse rate for single-wavenumber initial conditions, \n$a^2 = 0.033$, and $\\omega_0 = 0.954 = 0.864$ $\\omega_{\\rm crit}$\n(lower three curves).\nThese initial conditions would be stable in the absence of \nambipolar drift.\nThe solid line is the linear growth rate $\\gamma$ as a function of \nthe strength of the ambipolar drift $\\Gamma$. \nThe stars connected by a dotted line is the collapse rate for the nonlinear\nsimulation. The dashed line is the ambipolar drift rate. \nThe pluses connected by a dotted line \nare the collapse rates for the nonlinear \nsimulation with a high initial surface density\n$\\omega_0 = 1.278 = 1/0.864$ $\\omega_{\\rm crit}$. For such supercritical \ncollapse, the magnetic field and strength of ambipolar drift should have \nminimal effects.\n\\label{tau}\n}\\end{figure}\n%\nWe made a detailed comparison with linear theory and \nwith simple drift and collapse models by\nstudying the early collapse of a perturbation with a \nsingle spatial wavenumber.\nFigure \\ref{tau} shows how the growth of a fully nonlinear \ndensity perturbation depends on the drift parameter\n$\\Gamma$. The lower three curves describe collapse in \nsubcritical clouds, which would be stabilized by the \nmagnetic field in the absence of ambipolar drift. \nThe initial surface density (normalized to the vertical magnetic field) \nis $\\sim$ 86\\% of the critical surface density for collapse. \nThe growth rate of perturbations in the nonlinear simulation \n(calculated from the time for the central density of the \nperturbation to grow from 1\\% to 100\\% of the mean density) is \ncompared to the predicted growth rate $\\gamma$ for linear perturbations, \nand to the ambipolar drift rate $\\Gamma$. \nClearly, for the physically expected value\nof $\\Gamma$ ($\\sim$ 0.05 - 0.10), \\S\\ref{phys_par}), the collapse due to \nthis instability is several times faster than simple collapse due to \nloss of magnetic support on a diffusive ambipolar drift time-scale.\nFor\nexample, when $\\Gamma$ = 0.1, the ambipolar drift rate is 0.1 and the\nunmagnetized collapse rate is 10. The rate of contraction found from the\nsimulation is 0.4. At larger values of $\\Gamma$, the drift rate comes closer to\nthe unmagnetized collapse rate. The collapse rate in the simulation approaches\nthe unmagnetized collapse rate because the coupling between the magnetic\nfield and the gas is weak. \nWhen the drift becomes very important ($\\Gamma\\sim 10$), the drift \ntimescale is very short, and the intermediate instability described in this\npaper is \nless significant. Even for the moderate sized density perturbations used to\ncreate Figure \\ref{tau}, ($\\delta\\omega\\sim\\omega$), the growth rate is \nlarger in the nonlinear simulation than in the\nlinear problem, especially at relatively large values of\n$\\Gamma$, showing that the collapse is accelerated by the \nnonlinearity.\nIt is important to note, however, that the growth rate shows the\nsame dependence on ambipolar drift in both the linear theory\nand the nonlinear simulation: at low $\\Gamma$,\n$\\gamma\\propto\\Gamma$, and at higher $\\Gamma$,\n$\\gamma\\propto\\Gamma^{1/3}$.\n\nThe top curve in Figure \\ref{tau} describes collapse in supercritical\nclouds, in which the magnetic field would be insufficient to prevent\ncollapse even if it were frozen to the matter. The collapse\nrate depends only weakly on the strength of the ambipolar\ndrift, as expected since the magnetic field is dynamically less\nimportant. When the ambipolar drift strength $\\Gamma$ becomes\nlarge, the drift timescale becomes comparable to the\ncollapse timescale, and the subcritical and supercritical\ncases converge. Rapid collapse occurs in supercritical\nclouds due to the dynamical weakness of the field, and\nin subcritical clouds rapid diffusion removes magnetic\nsupport, quickly rendering them supercritical.\n\n\nThe evolution of self gravitating, subcritical disks\nwith ambipolar drift was studied previously by \\citet{cm94}\nand \\citet{bm95}. \\citet{cm94} began with a \nsubcritical ($\\omega_0$ = .256),\ncentrally condensed equilibrium state - the central surface density is 16\ntimes the mean density. Thus, this model is more centrally condensed even\ninitially than our models are when we terminate the simulation. \nThe initial ambipolar drift time is 10 times the\ninitial free fall time, which corresponds on Figure \\ref{tau} to\n$\\Gamma\\sim 1$. The evolutionary timescale in the subcritical, \nquasistatic phase is well estimated by the initial ambipolar drift time; after\nthe cloud becomes supercritical its collapse rate approaches the freefall rate.\nAlthough we can extrapolate our results to this model only with caution,\nbecause the initial conditions are so different from ours, it does not\nsurprise us that such a subcritical disk shows no evidence for the blending\nof dynamical and drift effects that we observe closer to criticality.\n\n\\citet{bm95} carried out a parameter study to determine the effects of the\ndegree of criticality on the rate of evolution to a critical state. They\nalso began with centrally condensed equilibrium models, forming a sequence in\nwhich the criticality parameter varied from 0.1 to 0.5. They found that the\ntimescale for evolution to the critical state decreased by about a factor of\n1.5 along this sequence, from somewhat longer than the estimated drift time\nto about 25\\% shorter (another, marginally critical model, collapsed at once). \nAlthough again a quantitative comparison of our models\nwith theirs is difficult because of the different initial conditions, it\nis possible that the\nintermediate contraction rates which they see are a manifestation of the\ncoupling between dynamical and ambipolar drift effects seen in our models.\nIt may also be due to the increased central concentration of the initial\nequilibrium states along their sequence of models.\n\nThe nature and rate of collapse is observable in molecular clouds\n\\citep{evans99,meo99}, \nand an instability with an intermediate growth rate \nsuch as this one can help to explain observations that do not \nfit either of the classical scenarios - dynamical collapse \nor slow diffusive contraction.\nOur simulated cloud cores collapse \nwith slower velocities and on larger physical scales \nthan the dynamical inside-out collapse predicted when the \nmagnetic field is unimportant, as in \\citet{shu77}. \\citet{t98} and \n\\citet{greg} have observed cores that appear to have such behavior; they find \nthat the regions of inflow are too large to fit dynamical \ninside-out collapse models, but that the inflow velocities \nare too large for quasistatic diffusion models.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{{\\bf B}-$\\rho$ relation}\\label{brho}\n\nThe correlation between fieldstrength and density is an observable quantity\nwhich can provide insight into the manner in which the magnetic field \nevolves. It is\nuseful to parameterize this relation as a power law\n\\begin{equation}\n|\\mathbf{B}|\\propto\\rho^\\kappa.\n\\end{equation}\nObservations find $\\kappa\\simeq$ 0.5 \\citep{troland86,c99} over\nseveral orders of magnitude in density.\nIn the case of a highly flattened cloud such as we simulate here, \nit is more convenient to define a\nmagnetic field - surface density relation\n\\begin{equation}\n |\\mathbf{B}|\\propto\\sigma^\\lambda. \n\\end{equation}\nIf the slab scale height $H$ remains constant throughout the \nevolution, then $\\lambda=\\kappa$. If the scale height is determined \nby a balance between self-gravity and thermal pressure alone, \nthen an isothermal slab obeys $H\\sim 1/\\sigma$, and \n$\\sigma\\sim\\rho H$ implies $\\sigma\\sim\\rho^{1/2}$, or \n$\\kappa=0.5\\lambda$ \\citep{c99,spit42}.\n\nIf the magnetic field is frozen to the matter but not dynamically \nimportant, so contraction is isotropic,\n conservation of flux $\\Phi_{mag}\\propto L^2|\\mathbf{B}|$\nand mass $M\\propto L^3\\rho$ requires $|\\mathbf{B}|\\propto\\rho^{2/3}$\n($\\kappa=$\\ 2/3). If the field is so strong that matter moves one\ndimensionally, parallel to the fieldlines, then $\\kappa\\rightarrow 0$.\nCalculations in which a cloud condenses to magnetohydrostatic equilibrium\nfrom a uniform initial state, with frozen in magnetic flux of a magnitude\nappropriate to the ISM, show anisotropic contraction, and the central values\nof $B$ and $\\rho$ in the\ninitial and final states are related by $\\kappa\\sim 0.5$ \\citep{ms76,tin88}.\nIf a cloud is already flattened and shrinks transversely, $M\n\\propto L^2\\sigma$, and flux\nfreezing implies $|\\mathbf{B}|\\propto\\sigma^1$ ($\\lambda$=1, $\\kappa$=0.5). \nHowever, rather\ndifferent input physics leads to a similar exponent: simulations of supersonic\nmagnetized turbulence, without self-gravity, produce $\\kappa\\sim 0.4$ if\nthe field is not too strong \\citep{pn99}. \n\nAmbipolar drift generally reduces $\\kappa$ below the value it would have if\nthe field were frozen in. In the models of \\citet{fm93}, \n$\\kappa$ averages\nabout 0.2 during the so-called quasistatic phase. After the quasistatic phase\nends, the mean value of $\\kappa$ is 0.3 as $\\rho$ increases by more than 5\norders of magnitude. In the highly flattened models of \n\\citet{cm94}, $\\kappa$\nincreases smoothly as the cloud evolves from subcritical to supercritical,\nreaching peak values between 0.4 and 0.5 and being about 0.3 at criticality.\nIn our simulations the magnetic field - surface density exponent $\\lambda$ \nvaries between 0.35 and 0.65. As shown in Figure \\ref{brhofig}, \nthe exponent decreases as the central density of a clump increases. \nAs collapse proceeds, not only does the density increase, but the magnetic \nfield curvature also increases as fieldlines are dragged into the \ncondensation. Both effects increase the ambipolar drift \nvelocity $\\mathbf{v}_D = B_z\\mathbf{B}_h/2\\pi\\sigma\\nu_{ni}$ \nand thus the rate of flux loss \nfrom the clump. Our models do not show the increase of\n$\\lambda$ toward its frozen flux value as the central density increases\nseen in \\citet{cm94}, \nbecause we follow only the early stages of contraction, in which the\nvelocity is well below the freefall value.\nThe exponent $\\lambda$ also decreases as the \namount of ambipolar drift $\\Gamma$ increases, as would be expected, and as the \ncloud temperature increases. The latter effect results from \nthe decreased efficiency of this instability in warm clouds. \nThe collapse rate $\\gamma$ decreases with increasing temperature\nas shown in \\S\\ref{lin_th}, and the collapse time is longer \nrelative to the ambipolar drift time, so more flux can leak \nfrom the clump as it collapses. \n%\n\\begin{figure}[hbpt]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{brho.om.eps}}}\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{brho.gam.eps}}}\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{brho.t.eps}}}\n\\caption{\nThe magnetic field - density exponent $\\lambda$.\n($|\\mathbf{B}|\\propto\\sigma^\\lambda$). The exponent \ndecreases (increased flux loss from a collapsing clump)\nwith increasing central density $\\delta\\omega$, \nincreasing ambipolar drift strength $\\Gamma$, or \nincreasing cloud temperature T.\nThe first graph shows variation with \n$\\delta\\omega$, the second variation \nwith $\\Gamma$ at constant $a^2=$ 0.05, and the third,\nvariation with T at constant $\\Gamma=$ 0.1.\nIn all simulations, $\\omega_0$ = 0.864 $\\omega_{crit}$.\n\\label{brhofig}\n}\\end{figure}\n\nComparison with observations depends on the assumed disc \nscale height $H$ and the central densities of observed cloud cores.\n\\citet{c99} finds $\\kappa$ = 0.47 for cloud cores with densities \n10\\textsuperscript{2.5}cm\\textsuperscript{-3} $\\lesssim n_H\\lesssim$\n10\\textsuperscript{7.5}cm\\textsuperscript{-3}. His data are \nstrongly weighted by observations which only measure upper limits \nfor the magnetic fieldstrength, and omission of those data points \nresults in an exponent of \n$\\kappa$ = 0.3 over the same range of densities. \nWe measure 0.3 $\\lesssim\\lambda\\lesssim$ 0.7 in simulated cores.\nIf the slab scale height $H$ is constant, \nthen 0.3 $\\lesssim\\kappa\\lesssim$ 0.7, but\nif the slab obeys $H\\sim 1/\\sigma$, then 0.2 $\\lesssim\\kappa\\lesssim$ 0.35.\nOur simulations are thus\nconsistent with the small number of available observations.\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Clumps and Fragments}\\label{clump}\n%%%%%\nReal molecular \nclouds have density variations on many scales, or a spectrum of \nspatial wavenumbers. The linear theory for this instability\n(\\S\\ref{lin_th}) predicts that a single mode \nwill dominate collapse. Fragments of a single mass \nwill form, with that mass depending on the temperature and degree of \ncriticality, with little dependence on the \nstrength of ambipolar drift, provided that it is small. We have simulated \nmany ($\\sim$ 100) clouds in which the initial density perturbations \nhave a broad spatial Fourier spectrum and random phase.\nThe real part of the \ninitial Fourier spectrum of the density perturbation \nis a Gaussian centered on $k$ = 0 (with the omission of the $k$ = 0 \nmode itself). The FWHM is 0.33 $k_{max}$, where $k_{max}$ is \nthe highest spatial mode in the simulation, so a range of low-order modes\nhave similar initial strength, and there is significant initial power \neven in some acoustically damped (high $k$) modes. \nAfter some time, the clouds coalesce into a small number of fragments, each\nof which\nwe define to be a region with $\\sigma > \\sigma_0$.\nThe size of the fragments is well-predicted by the linear theory.\nFor example, when $a^2$ = 0.02, the \nfastest linearly growing mode is $k/2\\pi \\simeq 2.5$, and in the \nsimulation, the modes ($k_x,k_y$)$/2\\pi$ = (1,3) and (3,1) have\nmuch larger amplitudes than other spatial modes.\n\nOur simulations produce a wide variety of clumps and fragments, \nas expected for systems with random initial density fluctuations.\nFigure \\ref{clumpfig} shows the fragment masses at a fairly early \nstage of collapse (the density perturbation is $\\sim$ 50\\% greater\nthan the mean density). There is considerable scatter, but the linear \ntheory is a good guide to the average fragment mass.\nThe clump masses are similar to the masses \nof the supercritical cores formed in some previous simulations\n\\citep{fm93,bm94,cm94,ck98}.\n\nAt sufficiently large $T$, \nthe spatial mode with the largest linear growth rate is the fundamental \nmode in the simulation domain \n($\\lambda=L$), and fragments larger than this cannot form \nin a periodic simulation. \nThis explains the apparent flattening of the clump mass --\ntemperature relation seen at the higher temperatures, as clump masses\nare bounded above by the mass of that ``lowest mode''.\n%\n\\begin{figure}[hbpt]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{mass2.eps}}}\n\\caption{\\label{clumpfig}\nMasses of cloud fragments as a function of temperature. \nMasses in the simulation (crosses) follow the mass of the \nfastest growing mode in linear theory (solid line) unless that \nmode exceeds the size of the simulation. (see text)\nThese runs have $\\Gamma$ = 0.1, $\\omega_0$ = 0.864 $\\omega_{crit}$.\nMasses from the simulation are plotted assuming $L$ = 1 pc, but\nthe agreement between the mass predicted by linear theory and \nthe mass in the simulation is independent of $L$.\n}\\end{figure}\n\nThe question of whether there is a characteristic mass for molecular cloud\nsubstructure is an important one. Several observational studies have found\na power law distribution of clump masses over several orders of magnitude, \n$dN/dM\\propto M^{-p}$, where $p\\sim\n1.5 - 1.7$ \\citep{b93}. \\citet{k98} present evidence that the power law extends\nfar below 1 $M_{\\odot}$.\nHowever, in the Taurus molecular cloud there is evidence \nof a minimum scale of a few tenths of a parsec, corresponding to several solar\nmasses \\citep{bw97}. \\citet{g98} have argued for an inner scale of 0.1 pc,\nwhich they identify with a transition to what they term ``velocity coherence\".\nThese inner scales are of the same order as the thermal Jeans length, and\nalso close to the cutoff wavelength below which Alfv\\'{e}n waves are critically\ndamped due to strong ambipolar drift \\citep{mckee93}. \nOur results suggest that there is\nanother scale, which is somewhat larger, in magnetically subcritical clouds\nwith weak ambipolar drift.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Velocity Structure}\\label{vel}\n\nUnlike axisymmetric collapse models, these simulations allow \nthe study of asymmetric collapse, clumps with complicated \nmorphology, relative motion of clumps, and their internal \nvelocity and vorticity fields. We find that collapse is often \nasymmetric and that significant vorticity is generated by the \ninstability (although of course the net angular momentum remains zero\nin our simulations; its absolute value is more than an order of magnitude \nsmaller than the estimated numerical errors).\n\nFigure \\ref{swirl} shows four examples of collapsing fragments. The left\npanels show contours of constant surface density, arrows indicating the local\ndirection and magnitude of velocity, and bold arrows indicating the center of\nmass motion of each clump. The velocity field shows infall towards clumps,\nbut there is also a visual impression of ``swirling\" or rotational motion.\nThis is borne out by the right panels of Figure \\ref{swirl}, which show\ncontours of constant vertical vorticity overlaid on contours of constant\ndensity. We show below that the magnetic field generates local vorticity.\n\nThe velocity field \nindicates that the collapse is in most cases asymmetric, with {\\it e.g.} much \ngreater infall velocities on one side of the clump than the other, and\nsignificant nonradial motion. \nClump mergers are possible - one is quite likely taking place in the bottom\npanel of Figure \\ref{swirl} - but the bulk motions are significantly slower\nthan the infall velocities internal to clumps. The reverse is generally true\nin molecular clouds \\citep[{\\it e.g.} ][]{b93}, \nand this result in our simulations is\na manifestation of the fact that the velocity field in the system is weak.\nWe return to this point in \\S 3.5. Sometimes the clumps move apart, but this\nis ambiguous in a periodic domain. The infall velocities within individual\nclumps are of order 0.25 $a$, and are more consistent with observations \n\\citep{evans99,meo99}.\n%\n\\onecolumn\n\\begin{figure}[p]\n\\centerline{\\resizebox{\\colw}{\\colw}{\\includegraphics{rha.eps}}\n\t\\resizebox{\\colw}{\\colw}{\\includegraphics{rhb.eps}}}\n\\centerline{\\resizebox{\\colw}{\\colw}{\\includegraphics{rka.eps}}\n\t\\resizebox{\\colw}{\\colw}{\\includegraphics{rkb.eps}}}\n\\caption[Velocity and Vorticity]{\n\\renewcommand{\\baselinestretch}{1}\n\\small\\normalsize\nVelocity, density, and vorticity for some typical simulations.\n\nThe left panel of each row shows the velocity field and density contours.\nContour levels denser than the mean density are solid, \nthose less dense than the mean are dashed.\nThe velocity scale is indicated by the arrow in the lower left hand \ncorner, whose length is 25 m/s. The density-weighted mean velocity \nof each clump is indicated with a thick arrow, and the scale is 10 \ntimes the general velocity scale (the arrow in the lower left would \nrepresent 2.5 m/s)\n\nThe right panel shows contours of vertical vorticity \n$(\\mathbf{\\nabla}\\times\\mathbf{v})_z$ for the same cloud. Positive \n(solid) and negative (dashed) vorticity are plotted along with \nthe surface density (dotted).\n\nFor all runs, $a^2$ = 0.025, $\\Gamma$ = 0.1, \n$\\omega_0$ = 1 = 0.927 $\\omega_{crit}$. \n\\label{swirl}}\n\\end{figure}\n\\addtocounter{figure}{-1}\n%\n\\begin{figure}[p]\n\\centerline{\\resizebox{\\colw}{\\colw}{\\includegraphics{rpa.eps}}\n\t\\resizebox{\\colw}{\\colw}{\\includegraphics{rpb.eps}}}\n\\centerline{\\resizebox{\\colw}{\\colw}{\\includegraphics{roa.eps}}\n\t\\resizebox{\\colw}{\\colw}{\\includegraphics{rob.eps}}}\n\\caption[Velocity and Vorticity]{continued.}\n\\end{figure}\n\\clearpage\n\\twocolumn\n\nVisual inspection of Figure \\ref{swirl} \nshows that the clumps are distinctly noncircular\nand quite elongated in shape. Accounting for the third dimension, our clumps\nshould be considered triaxial or prolate. These shapes are consistent with\nthe measured and inferred shapes reported by \\citet{m91}, \\citet{r96}, and\n\\citet{wt99}.\n\nFigure \\ref{cross} shows a cross section of the surface density and velocity\nprofiles across the short axis of one particular collapsing clump. The density\nis much more peaked than the velocity at this early stage of collapse; the\nFWHM of the infall speed is several times larger than the FWHM of the density\npeak. Both the velocity and density profiles are clearly, but not grossly,\nasymmetric. \nAlthough it is premature to compare these density and velocity profiles\nwith observations of infall, it is encouraging that we see evidence for\nextended inward motions as have been reported \n\\citep{t98,greg,evans99,meo99}. A general feature of infall onto a line mass\nsuch as a filament or strongly prolate object is that the velocity decays\nmore slowly with distance from the mass centroid than for infall onto a\nspherically symmetric,\ncentrally concentrated object. This may be the main effect that produces the\nextended infall.\n%\n\\begin{figure}[hbt]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{vc.eps}}}\n\\caption[]{\n\\renewcommand{\\baselinestretch}{1}\n\\small\\normalsize\nCross section of density perturbation $\\delta\\omega$ (solid)\nand infall velocity (dotted) across a clump. Infall velocity\nincreases towards the center of the clump (see text). This run is\nthe third example in Figure \\ref{swirl} - $\\Gamma$ = 0.1, $a^2$ = 0.025,\n$\\omega_0$ = 1. = 0.927 $\\omega_{crit}$. The collocation points are separated\nby about 5 $\\times$ 10$^{16}$ cm in this run, so the density and velocity\nprofiles are quite well resolved, except at the very center of the density\npeak.\n\\label{cross}}\n\\end{figure}\n\n\nThe vorticity generated in swirling motions is $\\nabla\\times v\\sim$\n5/$t_{c0}\\sim$ 8/Myr. Collapse proceeds on a timescale of \nseveral Myr, so the swirling and \nrotation of clumps is not insignificant, although it is dominated by infall \nand we have not found evidence for clumps\ntorn apart by shear. Magnetic braking, which is excluded from our\ncalculation by the potential field approximation, would reduce rotation.\nWe estimate the magnetic braking rate in \\S 4.1. \n\nFigure \\ref{swirl} shows that the vorticity maxima are displaced from the\ndensity maxima. In order to understand this, we derive an evolution\nequation for the $\\hat z$ component of vorticity, $\\omega_z$, by taking the\ncurl of the equation of motion (\\ref{gov2})\n%\n\\begin{equation}\n\\label{vorticity}\n{{\\partial\\omega_z}\\over {\\partial t}}+\\boldsymbol\\nabla_h\\cdot(\\omega_z\n\\mathbf{v}_h)=\\mathbf{B}_h\\times\\boldsymbol\\nabla_h {{B_z}\\over {2\\pi\\sigma}}.\n\\end{equation}\n\nAccording to equation (\\ref{vorticity}), the generation of vorticity is second \norder in the amplitude of the fluctuation. There is generation of vorticity to \nfirst order only if there is a zero-order inclined field (Z98). We can\nunderstand the spatial pattern of vorticity as follows. Despite\nambipolar drift, the contours of\nconstant $B_z$ track the contours of constant $\\sigma$ quite well. Therefore,\nthe gradient of $B_z/\\sigma$ is maximized toward the outer edge of a clump,\nnot at its center. Note that if the magnetic flux were perfectly frozen to the\nmatter, $B_z/\\sigma$ would retain its initial constant value and there\nwould be no vorticity production at all. However, real clouds probably have\nspatially varying $B_z/\\sigma$, so in general, vorticity\nproduction does not require ambipolar drift. \nThe maximum of $\\mathbf{B}_h$, like the maximum gradient of $B_z/\\sigma$,\n is displaced from the\nclump center. Equation (\\ref{vorticity}) shows that \ntherefore vorticity is generated\noff-center as well, and generally changes sign across the clump, so that clumps\nare associated with vortex pairs. Moreover, equation (\\ref{vorticity}) \nshows that\nan axisymmetric clump does not generate vorticity. The dynamical pressure\nof the vortices accentuates the non-axisymmetric nature of clump contraction,\nand appears as streaming motions along the major axis of the clump. Although in\nprinciple equation (\\ref{vorticity}) \nsuggests that the vortical velocity is scaled\nby the Alfv\\'{e}n speed, in\nour numerical models the vortical\nvelocities are rather small, somewhat less\nthan the infall velocities. This is\nlarge enough to noticeably elongate the clumps, but not enough to tear them \napart by shear. \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Energy Redistribution}\\label{energy}\n\nZ98 suggested that this magneto-gravitational instability \nmight generate significant turbulent kinetic energy\nby releasing energy contained in the background magnetic field. \nAnalysis of the total gravitational, magnetic, and kinetic \nenergy (Fig. \\ref{efig})\nin these simulations shows that the absolute values of \nall three forms of \nenergy grow exponentially during collapse. The magnetic \nenergy, which is the fluctuation energy integrated over the space outside the\ndisc, dominates at all stages of collapse in these clouds, \nwhich would be stabilized by the magnetic field in the absence \nof ambipolar drift. \n%Kinetic energy is generated along with \n%the significant vorticity discussed above, but\n%there does not appear to be a preferential generation of kinetic \n%energy or turbulent motions. \nThe initial magnetic field is uniform in these\nsimulations, and so there is no stored magnetic energy available for\nconversion to turbulent motions. The relatively low kinetic energy in the\nmodels is a signature of the importance of diffusive, as opposed to dynamical,\neffects.\nIn ideal MHD turbulence with self gravity one would expect \nequipartition between the kinetic and potential energies \\citep{zm95}. In this\ncase the potential energy is the sum of the gravitational and magnetic \nenergies, but Figure 9 shows that the kinetic energy is about an order of \nmagnitude less than the equipartition value.\n%\n\\begin{figure}[hbtp]\n\\centerline{\\resizebox{\\colw}{!}{\\includegraphics{energy.eps}}}\n\\caption{\\label{efig} Total energies in the simulation domain. \nMagnetic (dashed) and kinetic (dotted) energies are plotted \nwith the absolute value of the gravitational (solid) energy.\nThe absolute values of all forms of energy increase exponentially\nas collapse progresses, but the relative distribution does not \nchange significantly (see text.) For this particular run, \n$\\Gamma$ = 0.1, $\\omega_0$ = 0.973 = 0.864 $\\omega_{crit}$, \nand $a^2$ = 0.04.\n}\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Discussion of Approximations}\\label{discuss}\n\nIt is difficult and computationally\nexpensive to simulate the evolution of magnetized,\nself gravitating molecular clouds in three dimensions with sufficient \nresolution to capture all the relevant physical processes. \nIn this study we focussed on the two-dimensional\ninstabilities of a sheetlike cloud surrounded by a conducting medium without\ninertia. This allowed us to approximate the external magnetic field as current\nfree, and to work in only two spatial dimensions. In the next two \nsubsections we discuss the accuracy of these approximations.\n \n\\subsection{Potential Field Approximation}\\label{potfield}\n\nIn the Appendix, we show how to extend each Fourier component of the\nmagnetic and velocity \nperturbations above and below the sheet. Although the perturbations become \nhighly nonlinear within the cloud, nonlinear effects outside the cloud \nare weak as long as the velocities inside the cloud are sub-Alfv\\'{e}nic \nwith respect to the intercloud medium, which is expected for low ambient\ndensity.\nThe compressive part of the cloud velocity field\ngenerates evanescent, fast magnetosonic waves which decay exponentially\naway from the disc, while the vortical part generates Alfv\\'{e}n waves which\npropagate away from the disc. \n\nBoth the magnetosonic and Alfv\\'{e}n waves slightly change the horizontal \nmagnetic field perturbation in the disc, thereby changing the magnetic \nforce from its value in the potential approximation. If we define\nan external Alfv\\'{e}n timescale $\\tau_{Ae}\\equiv (kv_{Ae})^{-1}$ \nfor wavenumber \n$k$ in the disc, and let the timescale for the perturbation in the \ncloud be $\\tau_c$, then according to equation (\\ref{A9}) the correction to \nthe force due to compressive motion is of order $(\\tau_{Ae}/\\tau_c)^2$, \nwhile the correction due to vortical motion is of order \n$(\\tau_{Ae}/\\tau_c){\\cal C}_0/{\\cal D}_0$, where ${\\cal C}_0/{\\cal D}_0$ \nis the ratio of the amplitude of compressive to noncompressive motion. \nIf the motions in the disc were Alfv\\'{e}nic, $\\tau_{Ae}/\\tau_c$ \nwould be of order the ratio of the cloud density to external density \n$(\\rho_c/\\rho_e)^{1/2}$, but the perturbation\nfrequency is sub-Alfv\\'{e}nic, so the ratio of timescales is even larger. \nMoreover, the perturbations are primarily compressive rather than vortical. \nThus, the error in the force incurred by the potential approximation is \nlikely to be small. Even if the density contrast were only 10$^2$, and the\nmotions in the disk were Alfv\\'{e}nic and purely vortical, the \npotential field approximation would still be accurate to 10\\%.\n\nThe Alfv\\'{e}n wave flux tends to suppress the instability, and removes \nvorticity from the cloud, at a rate that we can quantify. We define \nan energy damping time $\\gamma_d$ as the ratio of outward propagating \nenergy flux to the vertically integrated wave energy in the disc. \nFrom equation (\\ref{A10}),\n\\begin{equation}\n\\label{eqn_damp}\n\\gamma_d = {{2\\rho_ev_{Ae}}\\over{\\sigma}}\n\t{{\\mid{\\cal C}_0^2\\mid}\\over{(\\mid{\\cal C}_0^2\\mid + \n\t\\mid{\\cal D}_0^2\\mid)}}.\n\\end{equation}\n\nIf we replace $\\sigma$ by the critical surface density $B_{0z}/2\\pi G^{1/2}$ \nand assume that the vertical fields inside and outside the cloud are the \nsame then $\\gamma_d$ is just the gravitational frequency for the intercloud \nmedium, reduced by the ratio of vortical to total kinetic energy\n\\begin{equation}\n\\gamma_d = (4\\pi G\\rho_e)^{1/2}{{\\mid{\\cal C}_0^2\\mid}\\over {(\\mid{\\cal\nC}_0^2\\mid + \\mid{\\cal D}_0^2\\mid)}}.\n\\end{equation}\n\nSince self gravity is presumably negligible in the low density \nintercloud medium, the energy loss rate is negligible as well. \nLoss of vorticity is measured by the magnetic braking rate \n$\\gamma_{mb}$, which can be shown by a similar argument to be\n$\\gamma_{mb} = (4\\pi G\\rho_e)^{1/2}$.\n\nWe thus see how the potential field limit is approached as the density contrast\nbetween the cloud and intercloud medium increases. At the late stages of clump\nformation the potential field becomes highly distorted and develops partially\nclosed topology, but we can ignore this for the relatively mild density\ncontrasts studied in this paper.\n\n\\subsection{Approximations to the Gas Physics}\n\nThe two dimensional approximation has a long and venerable history in galactic\ndynamics and accretion disc theory, as well as in studies of molecular \nclouds, and its errors for self gravitating systems are reasonably well \nunderstood. We expect the approximation to be reasonably good\nas long as the clump diameters exceed the disc thickness. The instability \ndiscussed in this paper \nhas a 3D analog (Z98), but it must be treated by other means.\n\nWe assumed that the gas has an isothermal equation of state. This is a \nreasonable description of the kinetic pressure - density relationship, \nbecause of the high radiative efficiency of molecular gas. However, if \nthe pressure were due to unresolved turbulence the medium would \ngenerally be less compressible; for example, Alfv\\'{e}n wave pressure follows \ndensity according to a 3/2 law \\citep{mz95}. This would make the medium \nmore stable by increasing the value of $\\gamma_T$ (see eq. [\\ref{disp_rel}]),\nas would retention of magnetic pressure.\n\nWe took a uniform sheet at rest as an initial condition. This has the \nadvantage of simplicity, but it means that there is no free energy stored \nin the background magnetic field. Thus, we have not tested the conjecture \nthat the instability can convert magnetic free energy to turbulent energy, \nwhich was proposed in Z98.\n\nWe have treated ambipolar drift in the strong coupling approximation, and have\nimplicitly assumed that $v_D <$ 20 km s$^{-1}$ (otherwise the rate coefficient\nwould change). This is reasonable as long as the ion-neutral collision time,\nwhich is of order $5\\times 10^9 n_n^{-1}$ s, is\nless than other timescales in the problem.\n\nWe have parameterized the relationship between the collision rate and the\nsurface density by an exponent $\\alpha$. In order to do better we would need a\nthree dimensional model of the sheet and might need to follow the ionization\nas well. The results of linear theory are rather insensitive to the value of\n$\\alpha$, which suggests that it need not be calculated very accurately\nin the present models.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Summary}\\label{summary}\n\nThe study of axisymmetric \ncontraction of weakly ionized,\nself gravitating, magnetized clouds has proceeded quite far\n\\citep{bm94,cm93,cm94,sms97,ck98}. In this paper,\nour emphasis has been on the initial breakup of a cold magnetized cloud \ngas into fragments and the early stages of their magnetic flux loss and\ncontraction.\nWe include self gravity,\nmagnetic tension, and ambipolar drift, but we do not include detailed\nchemistry of grain physics, choosing instead a simple parameterization of the\nionization. We follow the\nevolution for a shorter time than the isolated cloud collapse studies, but\nwe impose no symmetry constraints or initial density or velocity structure.\n\nWe study highly flattened clouds, with \nan initially perpendicular magnetic field, which are slightly subcritical. \nThe linear theory of \ncollapse in such geometry (Z98, T=0; this work, T$>$0) predicts\ncollapse on an intermediate timescale, faster than the \ndiffusive timescale set by ambipolar drift, but slower than \nthe dynamical timescale of free-falling inside-out collapse. \nThe linear theory also predicts the existence of a single \nspatial wavenumber with maximal growth rate, with sufficiently short \nwavelengths stabilized by thermal pressure. This naturally suppresses power\nat short wavelengths, which is important for the success of the spectral\nmethod we employ in the simulations.\n\nWe simulate collapse in clouds with random initial density perturbations\nwhich grow from $<$0.1\\% of the mean density to 5-10 times the mean \ndensity. We confirm the intermediate collapse rate predicted by \nlinear theory (\\S\\ref{gamgam}), although the\nnonlinear collapse rate is faster than the linear rate. These intermediate\nrates are consistent with some recent observations of infall in molecular\nclouds \\citep{evans99,meo99}.\n \nWe show that clouds fragment into \nclumps with size corresponding to the wavelength of the spatial \nmode of maximal linear growth rate (\\S\\ref{clump}), generally 1-10 \n$M_{\\odot}$. Collapse \nis asymmetric and complex (\\S\\ref{vel}), and\ngenerally forms prolate clumps, for which there is observational evidence\n\\citep{m91,r96,wt99}. Sometimes the clumps are in\nmutual orbit, although the typical clump separation, a few tenths of a parsec,\nis too large to be relevant to the formation of binary stars. The magnetic\nfield drives the growth of local vorticity, typically in the form of vortex\npairs which straddle the clumps and are associated with streaming motions along\nthem. \n\nConsiderable magnetic\nflux is lost from the collapsing clumps, consistent with the \nobservationally determined $|\\mathbf{B}|\\propto\\rho^{0.5}$ \n\\citep{troland86,c99} (see also \\S\\ref{brho}). \nThis flux loss is consistent with other calculations of cloud \nevolution \\citep{fm93,cm94}\n(although ambipolar drift is not necessary to bring \nabout this relationship, either for isolated \\citep{mous76} or \nturbulent, highly structured \\citep{pn99} clouds). As magnetic flux is lost\nand the surface density increases in the central regions of a contracting\ncore, further fragmentation might ensue. \n\nOne prediction of the linear theory, namely that the instability could \nconvert magnetic free energy to turbulence, has not been borne out by \nthe simulations. This may be due to the fact that the initial magnetic \nfield is completely uniform and therefore carries no free energy. Although \nsignificant magnetic curvature develops late in the runs, the cloud has \nalready become quite dynamical. This prediction awaits future tests with \na more stressed initial state. The relative motions of the clumps shown\nin Figure 7 are about an order of magnitude less than the relative motions\nof clumps separated by a few tenths of a parsec in real clouds \\citep{g98}, \nalthough the infall velocities in the simulation are comparable to \nmeasured velocities \\citep{meo99}.\n\nAn interesting area of future work would be to extend this \nstudy to true three-dimensional clouds. \nThe linear theory (Z98) indicates that this\ninstability exists in three as well as two dimensions,\nand that the growth rate is still intermediate to slow \ndiffusive contraction and fast dynamical collapse. \nConstruction of a nonlinear model in three dimensions would be more difficult\nthan the two dimensional models developed here,\nbut could prove interesting. In this vein, we find the recent successful\nfit of observations of L1544 with a nearly critical model\n\\citep{cb2000} encouraging.\n\n\\acknowledgements\nWe are happy to acknowledge support by NSF grant AST 9800616, \na 3-year NSF Graduate Research Fellowship to R.I., and NASA \ngrant NAG 5-4063 to the University of Colorado, as well as discussions with\nNeal Evans and comments by an anonymous referee.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\renewcommand{\\baselinestretch}{1.}\n\\begin{thebibliography}{}\n\\bibitem[Basu \\& Mouschovias(1994)]{bm94}Basu, S., \\& Mouschovias, T. Ch . \n1994, \\apj, 432, 720.\n%\n\\bibitem[Basu \\& Mouschovias(1995)]{bm95} Basu, S. \\& Mouschovias, T. Ch. \n1995, \\apj, 453, 271.\n%\n\\bibitem[Baureis {\\it et al.}(1989)]{bau89} Baureis, P., \nEbert, R., \\& Schmitz, F. 1989, \\aap, 225, 405. \n%\n\\bibitem[Bertholdi \\& McKee(1992)]{bm92} Bertholdi, F. \\&\nMcKee, C. 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II, \\& \nOhashi, N. 1999, to appear in {\\it Protostars \\& Planets IV}, eds. V.G.\nMannings, A.P. Boss, \\& S. Yorke (Tucson, U. of Arizona Press).\n%\n\\bibitem[Myers {\\it et al.}(1991)]{m91} Myers, P.C., Fuller, G.A., \nGoodman, A.A., \\& Benson, P.J. 1991 \\apj, 376, 561.\n%\n\\bibitem[Myers \\& Goodman(1988a)]{88.326} Myers, P. C., \\&\nGoodman, A. A. 1988, \\apj, 326, L27.\n%\n\\bibitem[Myers \\& Goodman(1988b)]{88.329} -----. \n1988, \\apj, 329, 392.\n%\n\\bibitem[Myers \\& Lazarian(1998)]{mlazar} Myers, P. C. \\& Lazarian, A.\n1998, \\apj, 507, L157.\n%\n\\bibitem[Nakano(1998)]{nakano98}Nakano, T. 1998, \\apj, 494, 587.\n%\n\\bibitem[Nakano \\& Nakamura(1978)]{nn78} Nakano, T., \\& Nakamura, T. 1978,\n\\pasj, 30, 681.\n%\n\\bibitem[Ohashi {\\it et al.}(1997)]{o97} Ohashi, N., Hayashi, M., Ho, P.T.P., \\&\nMomose, M. 1997, \\apj, 475, 211.\n%\n\\bibitem[Padoan \\& Norlund(1999)]{pn99} Padoan, P., \\& Norlund, A.\n1999, \\apj, in press.\n%\n\\bibitem[Parker(1974)]{park74} Parker, D. A. 1974, \\mnras, \n 168, 331.\n% \n\\bibitem[Press {\\it et al.}(1986)]{fourn2} Press, W. H., Flannery, B. P., \nTeukolsky, S. A., \\& Vetterling, W. T. 1986, \n{\\it Numerical Recipes}, \\S16.4, 724. \n%\n\\bibitem[Ryden(1996)]{r96} Ryden, B.S. 1996, \\apj, 471, 822.\n%\n\\bibitem[Safier, McKee, \\& Stahler(1997)]{sms97} Safier, P. N., McKee, C. F., \n\\& Stahler, S. W. 1997, \\apj, 485, 660. \n%\n\\bibitem[Shu, Adams, \\& Lizano(1987)]{shual87} Shu, F. H., Adams, F. C., \n\\& Lizano, S. 1987, \\araa, 25, 23.\n%\n\\bibitem[Shu(1977)]{shu77} Shu, F. H. 1977, \\apj, 214, 418.\n\n\\bibitem[Shu(1983)]{shu83} -----. 1983, \\apj, 273, 302.\n%\n\\bibitem[Spitzer(1942)]{spit42} Spitzer, L., Jr. 1942, \\apj, \n 95, 329.\n%\n\\bibitem[Tafalla {\\it et al.}(1998)]{t98} Tafalla, M., Mardones, D., \nMyers, P.C., Caselli, P., Bachiller, R., \\& Benson, P.J. 1998, \\apj, 504, 900.\n%\n\\bibitem[Troland \\& Heiles(1986)]{troland86} Troland, T.H. \\& Heiles, C. 1986,\n\\apj, 301, 339.\n%\n\\bibitem[Tomisaka, Ikeuchi, \\& Nakamura (1988)]{tin88} \nTomisaka, K., Ikeuchi, S., \\& Nakamura, T. 1988, \\apj, 335, 239.\n%\n\\bibitem[Ward-Thompson, Motte, \\& Andr\\'e(1999)]{wt99}\n Ward-Thompson, D., Motte, F.,\n\\& Andr\\'e, P. 1999, \\mnras, 305, 143.\n% \n\\bibitem[Wardle \\& K\\\"onigl(1993)]{wardle93} Wardle, M. \\& K\\\"onigl, A. 1993,\n\\apj, 410, 218.\n%\n\\bibitem[Zhou {\\it et al.}(1990)]{z90} Zhou, S., Evans, N.J. II, Butner, H.M.,\nKutner, M.L., Leung, C.M., \\& Mundy, L.G. 1990, \\apj, 363, 168.\n%\n\\bibitem[Zhou {\\it et al.}(1993)]{z93} Zhou, S., Evans, N.J. II, \nK\\\"ompe, C., \\& Walmsley, C.M. 1993, \\apj, 404, 232.\n%\n\\bibitem[Zhou(1995)]{z95} Zhou, S., 1995, \\apj, 442, 685.\n%\n\\bibitem[Zweibel(1998)]{z98} Zweibel, E. G. 1998, \\apj, 499, 746.\n%\n\\bibitem[Zweibel \\& McKee(1995)]{zm95} Zweibel, E.G. \\& McKee, C.F. 1995, \n\\apj, 439, 779.\n\\end{thebibliography}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\appendix\n\\section{Appendix}\n\nIn this Appendix we drop the potential field approximation and calculate the\nresponse of the intercloud medium to motions within the cloud. This allows us\nto estimate the errors incurred by assuming a potential field.\n\nWe carry out the estimate using linearized, ideal MHD theory. This\nis more accurate in the intercloud medium than it would be\nin the disc, because the intercloud or external Alfv\\'{e}n \nspeed $v_{Ae}$ is relatively high while\nion-neutral friction is weak. We assume the equilibrium intercloud\nfield is uniform and vertical (${\\bf B_0}=\\hat z B_0$). We\nchoose to work in the half space $z>0$ (the results are similar in\nthe other half space). In linear\ntheory, the motions are purely horizontal, and we can derive the\nfollowing pair of decoupled equations for the divergence ${\\cal D}$\nand vertical component ${\\cal C}$ of the curl of the velocity\n\\begin{mathletters}\n\\begin{eqnarray}\n\\Bigg({{\\partial^2}\\over {\\partial t^2}} - v_{Ae}^2\\nabla^2\\Bigg)\n{\\cal D} &=& 0,\\label{A1} \\\\\n\\Bigg({{\\partial^2}\\over {\\partial t^2}} - v_{Ae}^2\n{{\\partial^2}\\over {\\partial z^2}}\\Bigg){\\cal C}&=&0\\label{A2}.\n\\end{eqnarray}\n\\end{mathletters}\nEquations (\\ref{A1}) and (\\ref{A2}) represent fast magnetosonic waves and\nAlfv\\'{e}n waves, respectively. In general, both types of waves are\ngenerated by the motions in the cloud.\n\nIn order to make progress, we assume plane wave horizontal behavior\nand exponential behavior in time, so that all perturbations \ndepend on ($x$, $y$, $t$) as\n$\\exp(\\gamma t + ik_x x + ik_y y)$, where $\\gamma$ may be\ncomplex: $\\gamma = i\\omega + \\nu$ with both $\\omega$, $\\nu > 0$. Then\n\\begin{equation}\n{\\cal C}=i(k_xv_y-k_yv_x);\\quad {\\cal D}=i(k_xv_x+k_yv_y)\n\\end{equation}\ncan be calculated at $z=0$ in terms of the motions on the disc.\nThe vertical extensions of these quantities can be found from \nequations (\\ref{A1}) and (\\ref{A2}), choosing outward\ngoing or exponentially decaying wave solutions. For the Alfv\\'{e}nic part,\n\\begin{equation}\n{\\cal C}={\\cal C}_0e^{-ik_Az};\\quad k_A\\equiv{{\\gamma}\\over {v_{Ae}\n}},\\label{A3}\n\\end{equation}\nwhere ${\\cal C}_0$ is the value of ${\\cal C}$ at $z=0$.\nFor the magnetosonic part,\n\\begin{equation}\n{\\cal D}={\\cal D}_0e^{-k_Mz};\\quad k_M\\equiv k_{\\perp}\\Bigg(1+\n{{\\gamma^2}\\over {k_{\\perp}^2v_{Ae}^2}}\\Bigg)^{1/2} \\label{A4},\n\\end{equation}\nwhere $k_{\\perp}^2\\equiv k_x^2 + k_y^2$.\nIn equation (\\ref{A3}) we have written the vertical dependence as a propagating\nwave, and in equation (\\ref{A4}) as an evanescent wave. Although both $k_A$\nand $k_M$ are complex, because $\\gamma$\nis complex, our notation reflects the salient aspects\nof their behavior. The magnetosonic wave is almost purely evanescent\nbecause the wave frequency is much less than the disc Alfv\\'{e}n \nfrequency, which in turn is much less than the intercloud Alfv\\'{e}n\nfrequency. The Alfv\\'{e}n wave has a substantial propagating component\nand decays in space as long as the disturbance is growing in time,\nwhich is purely a result of causality.\n\nWe now calculate the perturbed magnetic field components\n${\\bf\\delta B}$ at the\ndisc. According to the linearized induction equation,\n\\begin{mathletters}\n\\begin{eqnarray}\n{{\\partial{\\bf\\delta B}_{\\perp}}\\over {\\partial t}} &=& B_0\n{{\\partial{\\bf v}_{\\perp}}\\over {\\partial z}},\\label{A5}\\\\\n{{\\partial\\delta B_z}\\over {\\partial t}} &=& -B_0{\\cal D}.\\label{A6}\n\\end{eqnarray}\n\\end{mathletters}\nInverting the definitions of ${\\cal C}$ and ${\\cal D}$ for the\nvelocity components gives\n\\begin{equation}\nv_x={{i}\\over {k_{\\perp}^2}}(k_y{\\cal C}-k_x{\\cal D});\\quad v_y =\n-{{i}\\over {k_{\\perp}^2}}(k_x{\\cal C}+k_y{\\cal D}).\\label{A7}\n\\end{equation}\nUsing equations (\\ref{A3}), (\\ref{A4}), and (\\ref{A7}) \nin equations (\\ref{A5}) and (\\ref{A6}) \ngives the field components at $z=0$\n\\begin{mathletters}\n\\begin{eqnarray}\n\\delta B_x &=&{{B_0}\\over {k_{\\perp}^2\\gamma}}(k_Ak_y{\\cal C}_0 +\nik_Mk_x{\\cal D}_{0}),\\label{A8a} \\\\\n\\delta B_y &=&{{B_0}\\over {k_{\\perp}^2\\gamma}}(-k_Ak_x{\\cal C}_0 +\nik_Mk_y{\\cal D}_{0}),\\label{A8b}\\\\\n\\delta B_z&=&-{{B_0}\\over {\\gamma}}{\\cal D}_0.\\label{A8c}\n\\end{eqnarray}\n\\end{mathletters}\n\nWe can use equations (\\ref{A8a}-\\ref{A8c}) \nto compare the MHD solution with the potential\nfield limit. The ratios of the perturbed horizontal to vertical\nfield components at $z=0$ can be written as\n\\begin{equation}\n{{\\delta{\\bf B}_{\\perp}}\\over {\\delta B_z}}=-i\\hat k_{\\perp}\\Bigg(1\n+{{\\gamma^2}\\over {k_{\\perp}^2 v_{Ae}^2}}\\Bigg)^{1/2} + (\\hat z\\times\n\\hat k_{\\perp}){{\\gamma}\\over {k_{\\perp}v_{Ae}}}{{{\\cal C}_0}\\over {{\\cal\nD}_0}}.\\label{A9}\n\\end{equation}\nEquation (\\ref{A9}), together with equation (\\ref{A3}), \nshows that in the limit\n$v_{Ae}\\rightarrow\\infty$ the potential field solution is exact.\n\nThe Alfv\\'{e}nic part of the disturbance, as a propagating wave, removes\nboth energy and angular momentum from the cloud. The energy flux\n${\\cal F}_W$\n(accounting for both kinetic and electromagnetic energy, and for\nwaves propagating in both directions away from the disc) is\n\\begin{equation}\n{\\cal F}_W=2\\rho_e{{\\mid{\\cal C}_0^2\\mid}\\over {k_{\\perp}^2}}v_{Ae}.\n\\label{A10}\n\\end{equation}\nIn \\S\\ref{potfield} we use equation (\\ref{eqn_damp}) \nto derive the rate at which the perturbation in the\ndisc is damped by outgoing waves.\n\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002092.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Basu \\& Mouschovias(1994)]{bm94}Basu, S., \\& Mouschovias, T. Ch . \n1994, \\apj, 432, 720.\n%\n\\bibitem[Basu \\& Mouschovias(1995)]{bm95} Basu, S. \\& Mouschovias, T. Ch. \n1995, \\apj, 453, 271.\n%\n\\bibitem[Baureis {\\it et al.}(1989)]{bau89} Baureis, P., \nEbert, R., \\& Schmitz, F. 1989, \\aap, 225, 405. \n%\n\\bibitem[Bertholdi \\& McKee(1992)]{bm92} Bertholdi, F. \\&\nMcKee, C. F. 1992, \\apj, 395, 140.\n%\n\\bibitem[Binney \\& Tremaine(1987)]{bt} Binney, J. \\& Tremaine, S., \n{\\it Galactic Dynamics} (Princeton, Princeton U. Press), 287.\n%\n\\bibitem[Black \\& Scott(1982)]{black82} Black, D. C., \\& \nScott, E. H. 1982, \\apj, 263, 696.\n%\n\\bibitem[Blitz(1993)]{b93} Blitz, L. 1993, in {\\it Protostars \\& Planets III},\neds E.H. Levy \\& J.I. Lunine (Tuscson, U. of Arizona Press), 125.\n%\n\\bibitem[Blitz \\& Williams (1997)]{bw97} Blitz, L., \\& Williams, J.P. 1997, \n\\apj, 488, L145.\n%\n\\bibitem[Boss(1997)]{boss97} Boss, A. P. 1997, \\apj, 483, 309.\n%\n\\bibitem[Boss(1999)]{boss99} Boss, A. P. 1999, \\apj, in press.\n%\n\\bibitem[Canuto {\\it et al.}(1988)]{canuto} Canuto, C., Hussaini, M. Y., \nQuarteroni, A., \\& Zang, T. A. 1988, {\\it Spectral Methods in \nFluid Dynamics} (New York: Springer-Verlag).\n%\n\\bibitem[Ciolek \\& Basu(2000)]{cb2000}Ciolek, G. E., \\& Basu, S. 2000\n\\apj, 529 (in press).\n%\n\\bibitem[Ciolek \\& K\\\"{o}nigl(1998)]{ck98}Ciolek, G. E., \\& K\\\"{o}nigl, A. \n1998 \\apj, 504, 257.\n%\n\\bibitem[Ciolek \\& Mouschovias(1993)]{cm93}Ciolek, G. E., \\& \nMouschovias, T. Ch. 1993, \\apj, 418, 774.\n%\n\\bibitem[Ciolek \\& Mouschovias(1994)]{cm94}Ciolek, G. E., \\& \nMouschovias, T. Ch. 1994, \\apj, 425, 142.\n%\n\\bibitem[Ciolek \\& Mouschovias(1995)]{cm95}Ciolek, G.E., \\& \nMouschovias, T. Ch. 1995, \\apj, 454, 194.\n%\n\\bibitem[Ciolek \\& Mouschovias(1998)]{cm98}Ciolek, G.E., \\& \nMouschovias, T. Ch. 1998, \\apj, 504, 280.\n%\n\\bibitem[Crutcher(1999)]{c99}Crutcher, R. M. 1999, \\apj, 520, 706.\n%\n\\bibitem[Crutcher {\\it et al.}(1994)]{c94} Crutcher, R.M., \nMouschovias, T., Troland, T.H., \\& Ciolek, G.E. 1994, \\apj, 427, 839.\n%\n\\bibitem[Draine, Roberge, \\& Dalgarno(1983)]{draine83} Draine, B. T., \nRoberge, W. G., \\& Dalgarno, A. 1983, \\apj, 418, 774\n%\n\\bibitem[Evans(1999)]{evans99} Evans, N.J. II, to appear in \\araa, 1999.\n%\n\\bibitem[Fiedler \\& Mouschovias(1993)]{fm93}Fiedler, R. A., \\& Mouschovias, \nT. Ch. 1993, \\apj, 415, 680.\n%\n\\bibitem[Goodman {\\it et al.}(1998)]{g98} Goodman, A.A., Barranco, J.A., \nWilner, D.J., \\& Heyer, M. 1998, \\apj, 504, 223.\n%\n\\bibitem[Graeves \\& Holland(1999)]{g99}Graeves, J. S., \\& Holland, W. S.\n1999, \\mnras, 302, L45.\n%\n\\bibitem[Gregersen(1998)]{greg} Gregersen, E. 1998, \nPh.D. Thesis, U. Texas.\n%\n\\bibitem[Kramer {\\it et al.}(1998)]{k98} Kramer, C., Stutzki, J., \nRohrig, R., \\& Corneliussen, U. 1998, \\aap, 329, 249.\n%\n\\bibitem[Langer(1978)]{langer78} Langer, W.D. 1978, \\apj, 225, 95.\n%\n\\bibitem[Lee \\& Myers(1999)]{lm99} Lee, C. W., \\& Myers, P. C. 1999, \\apjs, \nHarvard-Smithsonian Preprint No. 4765.\n%\n\\bibitem[Lovelace \\& Zweibel(1997)]{lz97} Lovelace, R. V. E. \\& Zweibel, E. G.\n1997, \\apj, 485, 285.\n%\n\\bibitem[McKee {\\it et al.}(1993)]{mckee93} McKee, C. F., Zweibel, E.G., \nHeiles, C., \\& Goodman, A.A. 1993, in {\\it Protostars and \nPlanets III}, ed. E.H. Levy \\& J.I. Lunine\n(Tucson: Univ. Arizona Press), 327.\n%\n\\bibitem[McKee \\& Zweibel(1995)]{mz95} McKee, C. F., \\& Zweibel, E. G.\n1995, \\apj, 440, 686.\n%\n\\bibitem[Mestel(1999)]{m99} Mestel, L. 1999, \n{\\it Stellar Magnetism} (Oxford University Press).\n%\n\\bibitem[Mestel \\& Ray(1985)]{mestel85} Mestel, L. \\&\nRay, T. P. 1985, \\mnras, 212, 275.\n%\n\\bibitem[Mestel \\& Spitzer(1956)]{ms56} Mestel, L. \\& \nSpitzer, L. Jr. 1956, \\mnras, 116, 505.\n%\n\\bibitem[Mouschovias(1976)]{mous76} Mouschovias, T. Ch. 1976, \n\\apj, 207, 141.\n%\n\\bibitem[Mouschovias \\& Morton(1991)]{mous91} Mouschovias, T. Ch., \n\\& Morton, S. A. 1991, \\apj, 371, 296.\n%\n\\bibitem[Mouschovias \\& Spitzer(1976)]{ms76} Mouschovias, T. Ch., \n\\& Spitzer, L. Jr. 1976 \\apj, 210, 326.\n%\n\\bibitem[Myers, Evans, \\& Ohashi(1999)]{meo99} Myers, P.C., \nEvans, N.J. II, \\& \nOhashi, N. 1999, to appear in {\\it Protostars \\& Planets IV}, eds. V.G.\nMannings, A.P. Boss, \\& S. Yorke (Tucson, U. of Arizona Press).\n%\n\\bibitem[Myers {\\it et al.}(1991)]{m91} Myers, P.C., Fuller, G.A., \nGoodman, A.A., \\& Benson, P.J. 1991 \\apj, 376, 561.\n%\n\\bibitem[Myers \\& Goodman(1988a)]{88.326} Myers, P. C., \\&\nGoodman, A. A. 1988, \\apj, 326, L27.\n%\n\\bibitem[Myers \\& Goodman(1988b)]{88.329} -----. \n1988, \\apj, 329, 392.\n%\n\\bibitem[Myers \\& Lazarian(1998)]{mlazar} Myers, P. C. \\& Lazarian, A.\n1998, \\apj, 507, L157.\n%\n\\bibitem[Nakano(1998)]{nakano98}Nakano, T. 1998, \\apj, 494, 587.\n%\n\\bibitem[Nakano \\& Nakamura(1978)]{nn78} Nakano, T., \\& Nakamura, T. 1978,\n\\pasj, 30, 681.\n%\n\\bibitem[Ohashi {\\it et al.}(1997)]{o97} Ohashi, N., Hayashi, M., Ho, P.T.P., \\&\nMomose, M. 1997, \\apj, 475, 211.\n%\n\\bibitem[Padoan \\& Norlund(1999)]{pn99} Padoan, P., \\& Norlund, A.\n1999, \\apj, in press.\n%\n\\bibitem[Parker(1974)]{park74} Parker, D. A. 1974, \\mnras, \n 168, 331.\n% \n\\bibitem[Press {\\it et al.}(1986)]{fourn2} Press, W. H., Flannery, B. P., \nTeukolsky, S. A., \\& Vetterling, W. T. 1986, \n{\\it Numerical Recipes}, \\S16.4, 724. \n%\n\\bibitem[Ryden(1996)]{r96} Ryden, B.S. 1996, \\apj, 471, 822.\n%\n\\bibitem[Safier, McKee, \\& Stahler(1997)]{sms97} Safier, P. N., McKee, C. F., \n\\& Stahler, S. W. 1997, \\apj, 485, 660. \n%\n\\bibitem[Shu, Adams, \\& Lizano(1987)]{shual87} Shu, F. H., Adams, F. C., \n\\& Lizano, S. 1987, \\araa, 25, 23.\n%\n\\bibitem[Shu(1977)]{shu77} Shu, F. H. 1977, \\apj, 214, 418.\n\n\\bibitem[Shu(1983)]{shu83} -----. 1983, \\apj, 273, 302.\n%\n\\bibitem[Spitzer(1942)]{spit42} Spitzer, L., Jr. 1942, \\apj, \n 95, 329.\n%\n\\bibitem[Tafalla {\\it et al.}(1998)]{t98} Tafalla, M., Mardones, D., \nMyers, P.C., Caselli, P., Bachiller, R., \\& Benson, P.J. 1998, \\apj, 504, 900.\n%\n\\bibitem[Troland \\& Heiles(1986)]{troland86} Troland, T.H. \\& Heiles, C. 1986,\n\\apj, 301, 339.\n%\n\\bibitem[Tomisaka, Ikeuchi, \\& Nakamura (1988)]{tin88} \nTomisaka, K., Ikeuchi, S., \\& Nakamura, T. 1988, \\apj, 335, 239.\n%\n\\bibitem[Ward-Thompson, Motte, \\& Andr\\'e(1999)]{wt99}\n Ward-Thompson, D., Motte, F.,\n\\& Andr\\'e, P. 1999, \\mnras, 305, 143.\n% \n\\bibitem[Wardle \\& K\\\"onigl(1993)]{wardle93} Wardle, M. \\& K\\\"onigl, A. 1993,\n\\apj, 410, 218.\n%\n\\bibitem[Zhou {\\it et al.}(1990)]{z90} Zhou, S., Evans, N.J. II, Butner, H.M.,\nKutner, M.L., Leung, C.M., \\& Mundy, L.G. 1990, \\apj, 363, 168.\n%\n\\bibitem[Zhou {\\it et al.}(1993)]{z93} Zhou, S., Evans, N.J. II, \nK\\\"ompe, C., \\& Walmsley, C.M. 1993, \\apj, 404, 232.\n%\n\\bibitem[Zhou(1995)]{z95} Zhou, S., 1995, \\apj, 442, 685.\n%\n\\bibitem[Zweibel(1998)]{z98} Zweibel, E. G. 1998, \\apj, 499, 746.\n%\n\\bibitem[Zweibel \\& McKee(1995)]{zm95} Zweibel, E.G. \\& McKee, C.F. 1995, \n\\apj, 439, 779.\n\\end{thebibliography}"
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astro-ph0002093
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Numerical simulation of accretion discs in close binary systems and discovery of spiral shocks
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The history of hydrodynamic numerical simulations for accretion disks in close binary systems is reviewed, in which emphasis is placed, in particular, on the facts that spiral shock waves were numerically found in 1986 by researchers including one of the present authors and that spiral structure was discovered in IP Pegasi in 1997 by Steeghs et al. The results of our two and three-dimensional numerical simulations in recent years are then summarized, with comparison being made with observations.
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[
{
"name": "xxxbarmat.tex",
"string": "\\documentclass[epsf]{kluwer}\n\\usepackage{epsfig}\n\\begin{document}\n\\begin{article}\n\\begin{opening}\n\\title{Numerical simulation of accretion discs in close binary systems and\ndiscovery of spiral shocks}\n\\author{Takuya \\surname{Matsuda} \\email{[email protected]}}\n\\author{Makoto \\surname{Makita}}\n\\author{Hidekazu \\surname{Fujiwara}}\n\\author{Takizo \\surname{Nagae}} \n\\author{Kei \\surname{Haraguchi}}\n\\author{Eiji \\surname{Hayashi}}\n\\institute{Department of Earth and Planetary Sciences, Kobe University, Kobe,\nJapan}\n\\author{H.M.J. \\surname{Boffin}}\n\\institute{Royal Observatory, Brussels, Belgium}\n\n\\begin{abstract}\nThe history of hydrodynamic numerical simulations for accretion disks in\nclose binary systems is reviewed, in which emphasis is placed, in particular,\non the facts that spiral shock waves were numerically found in 1986 by\nresearchers including one of the present authors and that spiral structure\nwas discovered in IP Pegasi in 1997 by Steeghs et al. The results of our two\nand three-dimensional numerical simulations in recent years are then\nsummarized, with comparison being made with observations.\n\\end{abstract}\n\\keywords{Accretion disk, numerical simulation, spiral shock, IP Pegasi,\nDoppler map}\n\\end{opening}\n\n\\section{Introduction}\nThe term ``accretion'' used in astrophysics means the infall of gas onto a\ncelestial body due to the gravitational attraction of the body. On this\noccasion, the gravitational energy of the gas is released and, eventually,\ntransformed into radiation and emitted to space.\n\nThe accretion process may be classified into two types depending on the momentum\npossessed by the gas, i.e. whether the gas has a large angular momentum with\nrespect to the accreting object or not. In the former case, a thin gaseous\ndisk, ``accretion disk'', is formed around the accreting object. In such a\ndisk, the gas gradually loses its angular momentum by some mechanism and\naccretes onto the central object. On the other hand, a gas with less angular\nmomentum rapidly accretes onto the object directly and this is called ``wind\naccretion'', a process characterized by, when the wind is supersonic,\nthe formation of ``bow shock'' in the forepart of the accreting object. The\npresent paper deals with accretion disks.\n\nAccretion disks are further classified into those in which the accreting body\nhas a mass comparable to that of typical star and those in which the\naccreting body is a giant black hole expected to be present at the central\ncore of galaxy. Our subject in this paper relates to the former. With the\nmass-accreting star being what is known as a compact star, which has a very\nsmall size compared to its mass, such as black hole, neutron star or white\ndwarf, a large amount of energy is released on accretion. Such accretion\ndisks are present in close binaries, including cataclysmic variables, novae\nand X-ray stars.\n\nIn accretion disks, for gas to accrete onto the central body, the gas must\nlose, by some mechanism or another, its angular momentum. The standard model\nproposed by Shakura \\& Sunyaev (1973) states that the angular momentum is\ntransported from the inner parts of the disk to the outer parts, due to some\nkind of viscosity (see also Shakura 1972a, b, Pringle \\& Rees 1972). \nThe gas of the inner parts, having lost angular momentum, accretes onto \nthe central star,\nwhile a fraction of the outer gas, having obtained larger angular momentum,\ntransports it to infinity. The gas can thus, almost entirely, accrete, while\nconserving the total angular momentum.\n\nA generally accepted candidate for this viscosity is turbulent viscosity. \nThe standard model is often called the ``$\\alpha$-disk model'', since the\nmagnitude of the turbulent viscosity has been characrerized by a\nphenomenological parameter, $\\alpha$. For accretion disks, the Reynolds\nnumber is as large as \\(10^{11-14} \\). The usual hydrodynamical common sense\nexpects a flow with such a large Reynolds number to be turbulent. With a\nrotational fluid, however, the situation is not so simple. Keplerian disks,\nwith angular momentum increasing outwards, amply satisfy the Rayleigh\ncriterion of stability. That is, where the gas rotates with nearly Keplerian\nmotion, there is no convincing evidence so far for the accretion disk to\nbecome unstable. In contrast, there is available theoretical and numerical\nevidence of the stability of Keplerian disks (Balbus, Hawley \\& Stone, 1996).\nBalbus \\& Hawley (1991) concludes that a small magnetic field present in the\ndisk will be amplified during differential rotation and, eventually, generate\nmagnetic turbulence. This has become one of the most popular models in recent\nyears.\n\nApart from the standard model, Sawada, Matsuda \\& Hachisu (1986a, b, 1987)\nconducted two-dimensional numerical simulations of accretion disk, to\ndiscover the presence of spiral shock waves in the disk. Spruit (1987) found\nself-similar solutions having spiral shock waves. They proposed a model in\nwhich the spiral shock waves absorb angular momentum from the gas. This\nis, eventually, transported to the orbital angular momentum of the binary\nsystem, due to the axial asymmetry of the density distribution in the disk of\nthe gas and to the torque caused by the tidal force of the companion star. \nWe call this the ``spiral shock model'', and we describe it in detail in the\npresent paper.\nMany textbooks and reviews of accretion disks are available (for example,\nPringle 1981, Frank, King \\& Raine 1992, Spruit 1995, Hartmann 1998,\nKato, Fukue \\& Mineshige 1998).\n\n\\section{Historical overview of numerical simulation}\n\\subsection{two-dimensional hydrodynamic simulation of accretion disk}\nThe particle model was mainly used in early stages of numerical study for\naccretion disks in close binaries. Particles differ from fluid elements in\nthat the trajectories of the former can cross each other, while those of the\nlatter cannot. Prendergast (1960) was the first to carry out numerical\nsimulation of gaseous flows, while ignoring the pressure. His model\nexpressed the two constituent stars as two mass points and ignored either\nrelease or accretion of the gas (see also Huang 1965, 1966). These drawbacks\nwere corrected by Prendergast \\& Taam (1974), who used the beam scheme and,\nwith the mass-accreting star having a large size, were unable to find\nformation of any accretion disk. Biermann (1971) conducted simulation by the\ncharacteristic line method, for models which were close to wind\naccretion rather than accretion disks.\n\nS\\o rensen, Matsuda \\& Sakurai (1974, 1975) made calculations using the Fluid in Cell\nmethod (FLIC) and Cartesian coordinates. They took both the mass-losing star\nand the mass-accreting star into consideration and assumed the latter to be of\nsuch a sufficiently small size as to allow formation of an accretion disk. \nThe results of their calculation showed a gas stream from the L1 point\ntowards the compact star and formation of an accretion disk. Flannery (1975)\nperformed a similar calculation and suggested the presence of a hot spot.\n\nIn contrast to the finite-difference method used by them, Lin \\& Pringle\n(1976) and Hensler (1982) performed calculations with a particle method, the former in\nparticular using the sticky particle method, which can be called a\npredecessor of the SPH method. All these calculations, having incorporated\nan artificial viscosity to stabilize the calculation, could not reveal the\ndetailed structure of the inside of an accretion disk.\n\n Eleven years after the S\\o rensen et al. (1975), Sawada, Matsuda \\& Hachisu\n(1986a, b, 1987) made the second challenge to the same problem, with use of\nsuch state-of-the-art techniques as the Osher upwind finite-difference method\nwith 2nd order accuracy, generalized curvilinear coordinates and a super\ncomputer of vector type. The Osher upwind difference method can run the\ncalculation stably while suppressing the artificial viscosity at a low level\nand is a predecessor of the TVD method, which is a representative modern\ncomputational fluid dynamics scheme. As a result, they discovered in the\naccretion disk the presence of spiral shocks---the very feature having been\nnever discovered with use of other more dissipative schemes.\n\nSince then, various authors have been carrying out two-dimensional simulations for\naccretion disks by various methods and they all obtained spiral shocks\n(Spruit et al. 1987, Rozyczka \\& Spruit 1989, Matsuda et al. 1990, Savonije,\nPapaloizou \\& Lin 1994, Godon 1997).\n\nFigure 1 shows the results of the two-dimensional simulation performed\nrecently by Makita, Miyawaki \\& Matsuda (1998). The mass ratio of the binary\nis 1. The region of calculation, which is limited to the surroundings of\nthe mass-accreting star, is in the range $[-0.5a, 0.5a] \\times [-0.5a, 0.5a]$,\nwhere $a$ denotes the separation of the binary. The number of grid points is\n$200 \\times 200$. Calculation is made for the specific heat ratio, $\\gamma$, of\n1.01, 1.05, 1.1 and 1.2, while using the equation of state for a perfect gas.\nThe lower $\\gamma$ is used to take somehow cooling effects into account.\n\n\\begin{figure*}\n\\begin{center}\n\\begin{tabular*}{1.0\\columnwidth}{p{0.5\\columnwidth}p{0.5\\columnwidth}}\n\\leavevmode\n\\epsfig{file=12lr7g.eps, width=50mm}&\n\\hspace{-3mm}\\epsfig{file=11lr7g.eps, width=50mm}\\\\\n\\vspace{-5mm}\\hspace{12mm}{\\Large $\\gamma=1.2$}&\n\\vspace{-5mm}\\hspace{10mm}{\\Large$\\gamma=1.1$}\\\\\n\\epsfig{file=105lr7g.eps, width=50mm}&\n\\hspace{-3mm}\\epsfig{file=101lr7g.eps, width=50mm}\\\\\n\\vspace{-5mm}\\hspace{1.2cm}{\\Large$\\gamma=1.05$} & \n\\vspace{-5mm}\\hspace{1cm}{\\Large$\\gamma=1.01$} \\\\\n\\end{tabular*}\n\\end{center}\n\\caption{Density distribution in two-dimensional calculation. Logarithmic\ndensity of gas is shown at t=44, corresponding to about 7 revolution periods,\nfor four cases of $\\gamma$, {\\it i.e.} 1.2, 1.1, 1.05, 1.01. Bar on the right\nside shows the scale range.}\n\\end{figure*}\n The gas is assumed to flow into through a hole placed at the L1 point. The\ndensity of the gas in the hole is 1 and the sonic velocity is $0.1a \\Omega$,\nwhere $\\Omega$ is the angular velocity of rotation. Specifying the sonic\nvelocity means specifying the gas temperature. The sonic velocity used in\nthis calculation is very large, thus indicating that the gas has a\nconsiderably high temperature. The gas ejected through the hole expands into\na surrounding atmosphere having high temperature, low density and low\npressure, thereby forming so called ``under-expanded jet''. This results in\nthe strange form of the inflow from the L1 point, which phenomenon turns out,\nhowever, not to be a serious drawback according to our later study.\n\nWhat the calculations revealed is that the spiral shocks are generated in\nany case and that the pitch angle of the spiral arms has a clear correlation\nwith the specific heat ratio. A smaller specific heat ratio thus leads to a\ntighter winding-in angle of the resulting shock waves. This is because that the\nsmaller specific heat ratio causes lower gas temperature and hence smaller\nsonic velocity, whereby the spiral shock waves having been generated in the\nperipheral region wind in more tightly while propagating into the inner parts. \nIn three-dimensional calculations to be described later herein, the problem\nis that such a clear correlation is not seen.\n\n\\subsection{Spiral shocks in the universe}\nThe presence of spiral shocks was discovered by Sawada, Matsuda \\&\nHachisu(1986a, b, 1987) in accretion disks. Spiral structures themselves are,\nhowever, rather common phenomena in astrophysics. In particular, spiral arms\nof galaxies attracted much attention in the 60-70's. Lin \\& Shu (1964)\ncontended that spiral density waves are formed in galactic disks under\ninfluence of self-gravity. This is the famous density wave theory of spiral\narms. Fujimoto (1968) suggested that the spiral arms, actually shining, is a\ngas rather than the constituent stars and that spiral\nshock waves composed of the gas have been formed. Shu, Milione \\& Roberts (1973) discussed\nthe motion of gas in the {\\it spiral gravitational potential} formed by stars\nand showed that the spiral gravitational potential with its amplitude\nexceeding a specific level causes the gas to form spiral shock waves.\n\nS\\o rensen, Matsuda \\& Fujimoto (1976) conducted numerical simulations for gas\nflow in a barred galaxy and showed that shock waves had been formed both\ninside and outside the corotation radius. The outside shock waves are spiral\nand correspond to the spiral arms, while the inside shocks are linear and\ncorrespond to the dark lane where cosmic dust has gathered. \n\nS\\o rensen \\& Matsuda (1982) and Matsuda et al. (1987) showed that a barred \ngalaxy with a small deviation from\naxisymmetry of gravitational potential, i.e. a weak bar, causes the shock\nwaves inside the corotation radius also to become of spiral form. They\ninvestigated the correlation between the presence of spirals and that of\nLindblad resonance, and concluded that the Lindblad resonance is essential to\ngenerate spirals. An important fact is that spiral shocks are generated by the \n{\\it barred gravitational potential} rather than the {\\it spiral\ngravitational potential}. This mechanism is essentially the same as that for\nthe formation of the spiral structure in accretion disks of close binaries\ndiscussed in the present paper. \n\nMatsuda \\& Nelson (1977) suggested that the presence of, if any, a weak bar\nstructure at the center of our Galaxy would cause spiral shock waves to\ngenerate, whereby gas around the waves loses its angular momentum and energy\nand falls towards the center. They called this mechanism ``vacuum cleaner''.\nThis mechanism is important in considering gas supply to the central core in\nAGN.\n\nBesides the galaxy scale, formation of spiral structure due to tidal force is\nseen on various objects. For instance, various simulations have shown, with\nthe primordial solar nebula after formation of Jupiter, appearance of spiral\nshock waves in the gaseous disk. These spiral shocks remove gases from the\nprimordial solar nebula eventually.\n\nIn essence spiral shock waves are generated in an accretion disk \nby an oval deformation of the\ngravitational potential and the Lindblad resonances associating with\nit. We stress that spiral shocks are not formed by the collision\nof the stream from L1 point with the disk gas.\n\n\\subsection{Does a spiral shock appear on three-dimensional scale?}\nAs described above, the presence of spiral shocks in two-dimensional\naccretion disk has been verified by various simulations. For\nthree-dimensional disks, it has been argued that waves once formed\nin the periphery of a disk diffract upwards and do not move into the inside\nof the disk and that, as a result, spiral shocks cannot appear in the disk\n(Lin, Papaloizou \\& Savonije 1990a, b, Lubow \\& Pringle 1993).\n \nAs regards numerical simulation, Molteni, Belvedere \\& Lanzafame (1991) and Lanzafame, Belvedere \\& Molteni (1992) conducted three-dimensional simulations by the SPH method and could\nnot find any spiral shock. They further argued that, with the specific heat\nratio appearing in the equation of state, \\( \\gamma \\), being larger than\n1.1-1.2, accretion disk itself cannot be formed. Attention should however be\npaid to the fact that they used in their calculation particles in as small a\nnumber as 1159 (\\( \\gamma = 1.2 \\)) or 9899 (\\( \\gamma = 1.01 \\)). Since then\nfor some time, many simulations have been performed mainly with use of the\nSPH method (Hirose, Osaki \\& Mineshige 1991, Nagasawa, Matsuda \\& Kuwahara 1991, Lanzafame, Belvedere \\& Molteni 1993), but none of them obtained spiral shocks.\n\nOnly in recent years, Yukawa, Boffin \\& Matsuda (1997) showed that shock waves are\nobtained by the SPH method when the number of particles is increased so that\nthe resolution is enhanced. They obtained spiral shocks with the binary\nhaving a mass ratio of 1 and with a specific heat ratio, \\( \\gamma \\), of 1.2,\nalthough they did not with \\( \\gamma \\) of 1.1 or 1.01. Thereafter,\nLanzafame \\& Belvedere (1997, 1998), Boffin, Haraguchi \\& Matsuda (1999)\nobtained basically similar results.\n\nWith respect to three-dimensional calculation by the finite difference/volume\nmethod, Sawada \\& Matsuda (1992) performed the calculation with use of the\nTVD method and generalized curvilinear coordinates, and obtained spiral\nshocks for \\( \\gamma = 1.2 \\). They calculated, however, only up to half the\norbital rotation period, and hence it is still doubtful if the generation of\nshock waves is an established phenomenon or merely a transient one. Our\ngroup therefore conducted a series of three-dimensional simulations as\ndescribed in the following section (see Makita \\& Matsuda 1999, Matsuda,\nMakita \\& Boffin 1999).\n\nBisikalo et al. have performed a series of three-dimensional calculations\nsimilar to ours (1997a, b, 1998a, b and c). Their study is very much like ours\nand therefore particularly worth commenting. They used the TVD method and\nCartesian coordinates. The region of calculation was $[-a, 2a] \\times [-a, a]\n\\times [0,a]$, where $a$ is the separation, and the region was divided with a\nnon-uniform lattice of $78 \\times 60 \\times 35$ or $84 \\times 65 \\times 33$. \n(In our calculation given later, the region is $[-a, a] \\times [-0.5a, 0.5a]\n\\times [0, 0.5a]$, which is divided into $200 \\times 100 \\times 50$.) They\nused the equation of state of a perfect gas and calculated with the specific\nheat ratio \\( \\gamma = 1.01, 1.2 \\). They calculated over a sufficiently\nlong period of 12-20 orbital periods. One of the main points concluded by\nthem is the absence of ``hot spot'', i.e. high-temperature region generated on\ncollision of the gas inflowing from the L1 point with the accretion disk. As\ndescribed later, our results also support this conclusion. They also\nconclude that no accretion disk forms with \\( \\gamma = 1.2 \\), while our\nresults show the formation. In addition, they mention, as the cause for the\ngeneration of spiral shocks, rather than the tidal force of the companion,\nthe interaction between the L1 flow and an expanded atmosphere, to which we\ndo not agree.\n\\nopagebreak \n\\section{Method of calculation}\n\\subsection{Basic assumptions}\nWe consider a mass-accreting star (main star) with mass $M1$ and a\nmass-losing star (companion) with mass $M2$. The mass ratio is limited to $q\n= M2/M1 = 1$ only in the present work. The companion is assumed to have\nfilled the critical Roche lobe. The motion of the gas flow having \nblown out from the\nsurface of the companion is calculated by solving the time-dependent Euler\nequations.\n\nThe basic equations governing the motion of the gas are the Euler equations\nwith no viscous term. We consider only numerical viscosity which is\nincorporated into calculation from the scheme employed, and consider neither\nmolecular viscosity nor \\( \\alpha \\) viscosity. We further assume that the\nequation of state of the gas is expressed by that of a perfect gas and take\nthe specific heat ratios 1.01 and 1.2. With accretion disks, radiative\ncooling plays an important role. Judging from the present-day computer power,\nit is, however, very difficult to incorporate the effect of the radiative\ncooling into three-dimensional calculation. We therefore try to simulate the\ngas cooling to some extent, by using a small specific heat ratio $\\gamma$.\n\nThe calculation method used is the Simplified Flux Vector Splitting (SFS)\nmethod (Jyounouchi et al. 1993, Shima \\& Jyounouchi 1994, 1997). A\nMUSCL-type approach is used, with the calculation accuracy being of 2nd order\nfor both time and space.\n\nWith the centers of the main star and the companion being at $(0,0,0)$ and $\n(-1,0,0)$, respectively, the region of calculation is $[-1.5,0.5] \\times\n[-0.5,0.5] \\times [0,0.5]$, where the lengths are scaled by the separation\n$a$. The region is divided by grid points of $201 \\times 101 \\times 51$. \nThe main star is represented by a hole of $3 \\times 3 \\times 2$, while the \ncompanion by a surface along the critical Roche lobe.\n \n\\subsection{Initial conditions and boundary conditions}\n\\subsubsection{Initial condition}\nThe entire space except the companion is filled with a gas having a density \n\\( 10^{-7} \\) and a sonic velocity of $c_0=0.02$. Here the density is, as\ndescribed later, is normalized by that of the gas on the surface of the\ncompanion. The sonic velocity value is sufficiently smaller than that in Makita, Miyawaki \\& Matsuda (1998), who assumed the density and\nthe sonic velocity to be \\( 10^{-5} \\) and \\( 10^{1/2} \\), respectively. In\ntheir case the gas initially placed in the region of calculation has a low\ndensity, but a high temperature. These values are not so important in\ntwo-dimensional calculations, since the initial gas will be removed from the\nregion of the accretion disk eventually.\n\nIn three-dimensional calculations, however, the initial gas will partially\nremain in a space above the disk. In the inner regions where the disk is\nthin, the disk gas and the initial gas may mix with each other numerically,\nthereby increasing the disk temperature artificially. As a result, inner spiral\narms may wind-in more loosely than in the actual case. In\norder to prevent this, we assume the density and temperature of the initial\ngas to be at sufficiently low levels. \n\n\\subsubsection{Boundary conditions}\nThe inside of the hole representing the main star is always filled with the\nabove-described initial gas. The gas having reached the vicinity of the main\nstar therefore accretes due to the low pressure inside the star. The outer\nboundary is also fixed at these values. At the outer boundary, the\nartificial reflection of waves is suppressed to a minimum, so that the\ncalculation can proceed stably. \n\nThe inside of the companion is assumed to be always filled with a gas having\na density of 1 and a sonic velocity of 0.02. The inside of the companion is\nassumed to be free from the gravity. The pressure difference between\nthe inside and outside of the companion surface causes the inside gas to flow\nout, the mass flux of which is evaluated by solving the corresponding Riemann problem.\n\n\\section{Results of calculation}\n\\subsection{Density distribution and spiral shocks}\nFigures 2 show the density distribution on the orbital plane at $t=72$,\nfor \\( \\gamma \\) =1.01 and 1.2, respectively. Figures 3 show the\niso-density surfaces for the same cases. The L1 flow, i.e. a flow coming out\nof the L1 point, penetrates into the inside of the accretion disk and does\nnot slow down on collision with the disk or form a ``hot spot''. \nThis is discussed in detail later. \n%\\vspace{5mm}\n\\begin{figure}\n\\centerline{\n\\epsfig{file=fig2a.eps,width=55mm} \\qquad\n\\epsfig{file=fig2b.eps,width=55mm}\n}\n\\caption{Density contours in logarithmic scale of the gas on the\nrotational plane at $t=72$. Left: the case for $\\gamma=1.01$. Right: the \ncase for $\\gamma=1.2$.}\n\\end{figure}\n\\begin{figure}\n\\centerline{\n\\epsfig{file=fig3a.eps,width=55mm} \\qquad\n\\epsfig{file=fig3b.eps,width=55mm}\n}\n\\caption{Iso-density surface at $log \\rho=-4.2$. Left: the case for\n$\\gamma=1.01$. Right: the case for $\\gamma=1.2$.\n}\n\\end{figure}\n Another point to be noted is that, while a nearly circular accretion disk\nand a pair of spiral shocks are observed for $ \\gamma=1.01$, the shape of the\naccretion disk is considerably deformed for $\\gamma =1.2$. These results\ndiffer from the preceding results obtained by Makita et al. (1998), who\nobserved a clearly circular accretion disk and spiral shocks for both\n$\\gamma=1.01, 1.2$. Our calculations differ from those of Makita et al. in\nthe size of calculation region, the mechanism of L1 flow formation, and the\ndensity and temperature of initial gas. Of these, the former two may not\ninfluence much, and the differences in the conditions of initial gas may have\ncaused the difference of the results. Bisikalo et al. (1998a, b, c) argue \nthat, for $\\gamma=1.2$, a considerably large part of the gas flowing in \nthrough the L1 point will flow out of the region, so that no accretion disk \ncan be formed.\nOur results stand in-between those of Makita et al. and Bisikalo et al. The\nquestion of knowing who is right remains to be answered.\n\n\\subsection{Penetration of L1 flow into accretion disk}\nIt is difficult to visualize a velocity field, which is a vector field. We\nuse the Line Integral Convolution (LIC) method to visualize the velocity\nfield. For LIC, see Cabral \\& Leedom (1993). The details of the \nvisualization will be given in a separate paper (Nagae, Fujiwara, Makita, \nHayashi \\& Matsuda, in preparation). \nFigure 4a shows the stream lines on the whole rotational plane.\nFigure 4b shows the iso-density surface of $\\log \\rho =-4.0$ with stream lines\non it. The stream lines on the rotational plane are also shown.\nIn Figs. 4c and d a portion of\nthe space between the L1 point and the main star has been expanded, so that\n one can easily see how the L1 flow penetrates into the accretion disk. As\n seen from Figures 4, the L1 flow coming smoothly through the L1 point\n does, without slowing down on encounter with the disk, penetrate into the\n inside of the disk.\n\\begin{figure*}\n\\begin{center}\n\\epsfig{file=g101h001lic.eps,width=9cm}~a. \\\\\n\\vspace{5mm}\n\\epsfig{file=g101r-4.0lic.eps,width=9cm}~b. \\\\\n\\vspace{5mm}\n\\epsfig{file=g101r-2.8l1lic.eps,width=5cm}~c. \\qquad\n\\epsfig{file=g101r-3.3l1lic.eps,width=5cm}~d.\n\\end{center}\n\\caption{Iso-density surface and flow lines on it for the case of\n$\\gamma=1.01$ at $t=72$. a) Flow lines on the whole rotational plane. \nb) Flow lines on the iso-density surface of $\\log \\rho=-4.0$ about the mass-accreting star. c) Blow up of L1 stream with $\\log \\rho=-2.8$, d) Same as c except $\\log \\rho=-3.3$.\n}\n\\end{figure*}\nFigure 4a shows that the rotational flow inside the disk changes, \non the orbital plane,\nits direction rapidly on collision with the L1 flow. Figures 4b, c, d \nshow that the\ngas placed a little above the orbital plane, along the z-axis, gets over the\nL1 flow on collision therewith. That is, the L1 flow looks like a bar\ninserted into the accretion disk, and the disk flow collides with the L1 flow\nto form a bow shock on the upstream side (upper side in the Figure). Figure\n4b shows that the iso-density surface swells along a spiral arm. \nFigure 4b shows an iso-density surface with the lowest density, where one can\nsee that the L1 flow penetrates the accretion disk, like a spear.\n\nBath et al. (1983) studied the penetration of the L1 flow into the accretion\ndisk. Whether or not the L1 flow penetrates into the disk depends on the\nrelative magnitude of density between the L1 flow and the disk. An L1 flow\nhaving a larger density will penetrate, while one having a smaller density\nwill not. Chochol et al. (1984) argued that such a penetration of the L1 stream\nwas observed in a symbiotic star CI Cyg.\n\n\\section{Comparison with observations}\nEleven years after the numerical discovery of spiral shocks by Sawada et al. (1986), Steeghs, Harlaftis \\& Horne (1997), using a method called ``Doppler\nTomography'' for observation, discovered the presence of spiral structure on\nan accretion disk of IP Pegasi for the first time. Since then, spiral\nstructures have been found successively in other accretion disks : SS Cyg (Steeghs et al. 1996), V347 Pup (Still, Buckley \\& Garlick 1998), EX Dra (Spruit in preparation).\n\nThe Doppler tomography method comprises at first observing the time history\nof the emission line spectrum of hydrogen or helium for 1 orbital\nperiod, on a binary system close to edge-on. The method then makes a\ndistribution map of the emission lines on the velocity space $(V_x, V_y)$ by\nan ingenious technique, the maximum entropy technique. The obtained map is called Doppler map and basically\ncorresponds to a hodograph in hydrodynamics. Presence of a spiral distribution\nin a Doppler map corresponds to a spiral distribution of emission lines in\nthe physical (configuration) space. The shape of the physical-space\nbrightness distribution, however, cannot be derived from the corresponding\nDoppler map. \n\nOn the other hand, numerical simulations can give the physical-space\ndistribution of a physical quantity, from which a Doppler map can be\nprepared. Obtaining a distribution of emission lines of an element in the\nreal space needs both the knowledge of temperature and complex radiative\ntransfer calculations, and is not easy. We therefore prepare a Doppler chart,\nwhich maps the density distribution, not the emission line distribution, on\nthe velocity space. This procedure may be deemed valid from expectation that\na high-density region be of high brightness.\n\nFigures 5a, b are Doppler maps, prepared in the above-described manner, for \\(\n\\gamma \\) =1.01 and 1.2, and show the presence of widely opened spiral\nstructures. Matsuda, Makita, Yukawa \\& Boffin (1999) and Makita, Yukawa, Matsuda \\& Boffin (1999) performed two-dimensional SPH calculations and prepared Doppler\nmaps. The maps thus prepared agree well with those based on our two-dimensional finite-difference calculations, and also very well with the observations. \n\nThis agreement is remarkable, since the results of these two-dimensional\ncalculations show that, in particular for \\( \\gamma \\) = 1.2, the obtained\nMach number is as small as less than 10, which means that the disk has a\nconsiderably high temperature. On the other hand, observations expect much\nlower temperatures and a Mach number of 20-30 for the accretion disks of\ncataclysmic variables. For such a high Mach number case, numerical\nsimulation would give spiral shocks with tightly winding, so that no Doppler\nmap agreeing with observations can be prepared (Godon, Livio \\& Lubow 1998).\n\nSteeghs et al. (1997) observed spiral structures in the outburst phases of a\ncataclysmic variable, but not in the quiescent phases. This suggests that\nonly with the disk having a high temperature, spiral shocks winding to such\nmodest angle as to be observable can be formed.\n\\begin{figure*}\n\\centerline{\n\\epsfig{file=101dop2d5.eps, width=48mm}~a. \\qquad\n\\epsfig{file=12dop2d5.eps, width=48mm}~b.\n}\n\\caption{Doppler map prepared based on two-dimensional calculation; a): \n\\( \\gamma \\) = 1.01 b): \\( \\gamma \\) = 1.2\n}\n\\end{figure*}\nIt is hard to prepare a correct, meaningful Doppler map based on the results\nof three-dimensional calculations, since the distribution observed is that of\nthe emission component at an optical depth of 1, i.e. on the photosphere of\nthe accretion disk. The preparation thus requires complex calculations of\nradiative transfer, which is beyond the scope of the present paper. One\npoint of interest here is that the three-dimensional calculations with a\nsmall \\( \\gamma \\) = 1.01 have given moderately loosely winding spiral shocks,\nwhich means that even with accretion disks with comparatively low temperature\nthe winding-in shape tends to agree with observations.\n\n\\section{Summary}\n\\begin{enumerate}\n\\item Spiral shock waves on accretion discs in close binary systems were\nfound numericaly by Sawada et al. (1986a, b, 1987) in their two-dimensional\nhydrodynamic finite difference simulation.\n\\item Spiral shock waves are generated by an oval deformation of the\ngravitational potential and the Lindblad resonances associating with\nit. Spiral shocks are seen in galactic disks and the primordial solar\nnebula as well as accretion disks.\n\\item Three-dimensional simulations also exhibit the presence of spiral\nshocks despite of some counterarguments.\n\\item The stream from L1 point penetrates into the accretion disk rather\nthan being blocked by it. Therefore, so-called hot spot is not formed\nin our present case, which fact agrees with the results by Bisikalo\net al. (1997a, b, 1998a, b, c).\n\\item Spiral structure was found in the accretion disk of a dwarf nova\nIP Pegasi by Steeghs et al. (1997) using Doppler tomography technique.\n\\item Theoretical Doppler maps are made based on two-dimensional simulations,\nand they agree well with observed ones despite of high temperature of gas\nin the simulation. \n\\end{enumerate}\n\n\\begin{acknowledgements}\nT.M. has been supported by the Grant-in-Aid for Scientific Research\nof Ministry of Education, Science and Culture in Japan (11134206)\nand (10640231) of JSPS. 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{
"name": "astro-ph0002093.extracted_bib",
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}
] |
astro-ph0002094
|
Water Ice in 2060 Chiron and its Implications for Centaurs and Kuiper Belt Objects
|
[
{
"author": "Jane X. Luu"
}
] |
We report the detection of water ice in the Centaur 2060 Chiron, based on near-infrared spectra (1.0 - 2.5 $\micron$) taken with the 3.8-meter United Kingdom Infrared Telescope (UKIRT) and the 10-meter Keck Telescope. The appearance of this ice is correlated with the recent decline in Chiron's cometary activity: the decrease in the coma cross-section allows previously hidden solid-state surface features to be seen. We predict that water ice is ubiquitous among Centaurs and Kuiper Belt objects, but its surface coverage varies from object to object, and thus determines its detectability and the occurrence of cometary activity.
|
[
{
"name": "paper.tex",
"string": "\\documentclass[aasms,tighten,psfig,graphicx,11pt,a4]{aastex}\n\\slugcomment{Submitted to {\\it Ap. J. Letters}, accepted 31 Jan 2000}\n\n\\begin{document}\n\n\\title{Water Ice in 2060 Chiron and its Implications for Centaurs\nand Kuiper Belt Objects}\n\\author{Jane X. Luu}\n\\affil{Sterrewacht Leiden\\\\\nPostbus 9513,\n2300RA Leiden, The Netherlands}\n\n\\author{David C. Jewitt\\altaffilmark{1}}\n\\affil{Institute for Astronomy\\\\\n2680 Woodlawn Drive, Honolulu, HI 96822}\n\n\n\\and\n\n\\author{Chad Trujillo\\altaffilmark{1}}\n\\affil{Institute for Astronomy\\\\\n2680 Woodlawn Drive, Honolulu, HI 96822}\n\n\n\\altaffiltext{1}{Visiting Astronomer, W. M. Keck Observatory,\njointly operated by California Institute of Technology and the University\nof California.}\n\n\\newpage\n\n\\begin{abstract}\n\nWe report the detection of water ice in the Centaur 2060 Chiron, based\non near-infrared spectra (1.0 - 2.5 $\\micron$) taken with the\n3.8-meter United Kingdom Infrared Telescope (UKIRT) and the 10-meter\nKeck Telescope. The appearance of this ice is correlated with the\nrecent decline in Chiron's cometary activity: the decrease in the coma\ncross-section allows previously hidden solid-state surface features to\nbe seen. We predict that water ice is ubiquitous among Centaurs and\nKuiper Belt objects, but its surface coverage varies from object to\nobject, and thus determines its detectability and the occurrence of cometary\nactivity.\n\n\\end{abstract}\n\n\\keywords{comets -- Kuiper Belt -- solar system: formation}\n\n\\newpage\n\n\\section{Introduction}\n\nThe Centaurs are a set of solar system objects whose orbits are\nconfined between those of Jupiter and Neptune. Their planet-crossing\norbits imply a short dynamical lifetime ($10^6\n- 10^7$ yr). The current belief is that Centaurs are objects\nscattered from the Kuiper Belt that may eventually end up in the inner\nsolar system as short-period comets. The first discovered and\nbrightest known Centaur, 2060 Chiron, is relatively well studied. The\nobject is firmly established as a comet, with a weak but persistent\ncoma. It is well documented that Chiron possesses neutral colors\n(e.g., Hartmann et al. 1990, Luu and Jewitt 1990), and a low albedo of\n$0.14^{+0.06}_{-0.03}$ (Campins et al. 1994). (It must be noted that\nmost of these measurements were made when Chiron clearly exhibited a\ncoma so that the measurements are likely to have been contaminated by\ndust scattering from the coma. The albedo, in particular, should be\nviewed as an upper limit). Chiron has a rotation period of $\\sim 6$\nhr (e.g., Bus et al. 1989) and a photometric amplitude that is\nmodulated by the cometary activity level (Luu and Jewitt 1990,\nMarcialis and Buratti 1993, Lazzaro et al. 1997). Published optical\nand near-IR spectra of Chiron show a nearly solar spectrum, varying from\nslightly blue to completely neutral (Hartmann et al. 1990, Luu 1993,\nLuu et al. 1994, Davies et al. 1998), and devoid of specific\nmineralogical features.\n\nAs a group, the Centaurs display remarkable spectral diversity (e.g.,\nLuu and Jewitt 1996). The Centaur 5145 Pholus is among the reddest bodies\nin the solar system (Mueller et al. 1992, Fink et al. 1992), and shows\nabsorption features at 2.00 and 2.25 $\\micron$ (see, e.g., Davies et\nal. 1993a, Luu et al. 1994). Cruikshank et al. (1998) interpreted the\n2.0 $\\micron$ feature as due to water ice, and the 2.27 $\\micron$ due\nto methanol. They derived a best fit to the spectrum which consisted\nof carbon black and an olivine-tholin-water-methanol mixture.\nPholus's extreme red color and low albedo ($0.044 \\pm 0.013$, Davies\net al. 1993b) strongly suggest that long-term irradiation of carbon-\nand nitrogen-bearing ices has resulted in an organic-rich, dark\n\"irradiation mantle\" (e.g., Johnson et al. 1987). The spectral\ndifferences between Chiron and Pholus have been attributed to\nthe presence of cometary activity in Chiron and the lack thereof in\nPholus (Luu 1993, Luu et al. 1994). A continuous rain of sub-orbital\ncometary debris falling onto the surface of Chiron may have buried a\nmore primordial irradiation mantle with unirradiated matter ejected\nfrom the interior. In this paper we show further evidence supporting\nthis hypothesis, and that scattering effects by coma dust particles\nalso eliminate spectral features seen in solid surface reflection.\n\n\n\\section{Observations}\n\n\\noindent {\\bf (a) Keck observations}. The Keck near-infrared\nobservations were made on UT 1999 April 03, at the $f$/25 Cassegrain\nfocus of the Keck I telescope, using the NIRC camera (Matthews and\nSoifer 1994). The NIRC detector is a 256 x 256 pixel InSb array that\ncan be switched from direct imaging to slit spectroscopy. In imaging\nmode the pixel scale is 0.15 arcsec per pixel (38\" x 38\" field of\nview), and in spectroscopy mode the resolution is $\\lambda /\n\\Delta\\lambda \\approx 100$. We used a 0.68\" $\\times$ 38\" north-south\nslit for all spectral observations. Uneven illumination of the slit\nand pixel-to-pixel variations were corrected with spectral flat fields\nobtained from a diffusely illuminated spot inside the dome.\n\nSince the target was not visible during spectral observations,\nChiron's position was confirmed by centering it at the location of the\nslit and taking an image. The slit, grism, and blocking filter were\nthen inserted in the beam for the spectroscopic observation.\nSpectra were made in pairs dithered along the slit by 13\". We\nobtained spectra in two different grating positions, covering the JH\nwavelength region (1.00 - 1.50 $\\micron$) and the HK region (1.4 -\n2.5 $\\micron$). Non-sidereal tracking at Keck showed a slight drift\nwith time, so we recentered Chiron in the slit every 15-20 minutes.\n\n\\noindent {\\bf (b) UKIRT observations}. The UKIRT observations were\nmade on UT 1996 Feb 7 and 8 with the CGS4 infrared spectrometer\nmounted at the Cassegrain focus. The detector was a 256 $\\times$ 256\npixel InSb array, with a 1.2\" per pixel scale in the spatial\ndirection. An optical TV camera fed by a dichroic beam splitter gave\nus slit viewing capability and thus we were able to guide on the\ntarget during all observations. The conditions were photometric and\nthe image quality was $\\sim$ 1\" Full Width at Half Max (FWHM), so we\nused a 1.2'' $\\times$ 80'' slit aligned North-South on the sky at all\ntimes. A 75 line per mm grating was used in first order for all\nobservations, yielding a dispersion of 0.0026 $\\micron$/pixel in the H\nand K band ($\\lambda / \\Delta\\lambda \\approx 850$). However, the\ndetector was dithered by 1/2 pixel during each observation, so the\nspectra were oversampled by a factor of 2. The effective spectral\ncoverage in the H band was 1.4 -- 2.0 $\\micron$ and in the K band 1.9\n-- 2.4 $\\micron$. Sky background removal was achieved by nodding the\ntelescope 30\" (23 pixels) along the slit. Dark frames and calibration\nspectra of flat fields and comparison lamps (Ar) were also taken every\nnight.\n\nBoth the Keck and UKIRT observations were calibrated using stars on the\nUKIRT Faint Standards list (Casali and Hawarden 1992). At both\ntelescopes, we took care to observe the standard stars at airmasses\nsimilar to those of Chiron (airmass difference $\\leq$\n0.10), to ensure proper cancellation of sky lines. \n\nThe separate reflectance spectra from each night of observation are\nshown in Fig. 1. \n\n\n\\section{Discussion}\n\n\\subsection{The spectra}\n\nThe Chiron spectra (Fig. 1) show that: (a) Chiron is nearly neutral in\nthe 1.0 -- 2.5 $\\micron$ region; (b) there is a subtle but definite\nabsorption feature at 2 $\\micron$ ($\\sim$ 0.35 $\\micron$ wide, $\\sim\n10\\%$ deep) in spectra from 1996 and 1999, and a marginal absorption\nfeature near 1.5 $\\micron$ in the 1999 spectrum; and (c) the spectral\nslope and the strength of the 2 $\\micron$ feature change with time.\n\nReflectivity gradients in the JHK region span the range $S'$ = -2\n\\%/1000~\\AA\\ to $S' =$ 1\\%/1000~\\AA\\ (Table 2). In Fig. 2 we compare\nChiron spectra from 1993 (from Luu et al. 1994) with the present\nobservations. The flat and featureless 2 $\\micron$ spectrum from 1993\nstands in sharp contrast with the later spectra. The presence of the\n2 $\\micron$ feature in different spectra taken with different\ntelescopes, instruments, and spectral resolutions provides convincing\nevidence that it is real.\n\nThe 2 $\\micron$ and 1.5 $\\micron$ features are clear signatures of\nwater ice, and the shallowness of the features (compared to that of\npure water ice) indicates that this ice is mixed with dark impurities\n(see Clark and Lucey 1984). We note that the Chiron spectra are very\nsimilar to spectra of minerals and water ice (compare the spectra in\nFig. 2 with Fig. 14 and 15 of Clark 1981, respectively). In Fig. 3 we\nshow that the Keck Chiron spectrum is well fitted by a model\nconsisting of a linear superposition of a water ice spectrum and an\nolivine spectrum. The olivine spectrum is needed to provide the\nrequired continuum slope, and at the very small grain size used, the\nspectrum of olivine is essentially featureless. The water ice\nspectrum was calculated based on the Hapke theory for diffuse\nreflectance (Hapke 1993) and used a grain diameter of 1 $\\micron$. A\ndescription can be found in Roush (1994). However, we caution that\nthe model is non-unique, and due to the many free parameters in the\nmodel (e.g., grain albedo, porosity, roughness), the $1 \\micron$ grain\nsize should not be taken literally. Similarly, olivine could also be\nreplaced in the fit by other moderately red, featureless absorbers.\n\nThe 2 $\\micron$ feature in Chiron is clearly time-variable: it was not\napparent in 1993 but changed to a depth of 8 - 10\\% in 1996\nand 1999. Chiron's lightcurve variations can be\nexplained by the dilution of the lightcurve by an optically thin coma\n(Luu and Jewitt 1990). Based on this model, we estimate that the 1993\ncoma cross-section was $\\sim 1.5$ times larger than in 1996 or now.\nThe likeliest explanation for the time-variability of the $2 \\micron$\nfeature is the degree of cometary activity in Chiron. In 1993,\nChiron's activity level was high (Luu and Jewitt 1993, Lazzaro et\nal. 1997), resulting in a featureless spectrum dominated by scattering\nfrom the coma. By 1996, when the UKIRT observations were made,\nChiron's total brightness had dropped by $\\sim 1$ mag to a minimum level\n(comparable to that of 1983--1985, Lazzaro et al. 1997), leaving \nspectral contamination by dust at a minimum.\n\n\\subsection{Implications of water ice on Chiron}\n\n\\subsubsection{Cometary activity in Centaurs}\n\nConsidering (1) Chiron's time-variable spectrum, (2) the\npresence of surface water ice, and (3) Chiron's persistent cometary\nactivity, we conclude that Chiron's surface coverage is {\\it not}\ndominated by an irradiated mantle but more probably by a layer of\ncometary debris. Occultation observations suggest that\nsublimation by supervolatiles (e.g., CO, N$_2$) on Chiron occurs in a\nfew localized icy areas (Bus et al. 1996). Dust grains ejected at\nspeeds $< 100$ m s$^{-1}$ (the escape velocity) will reimpact the\nsurface, building a refractory layer which tends to quench sublimation.\nNevertheless, the outgassing is still sustained by the sporadic\nexposure of fresh ice on the surface. Sublimation experiments with\ncometary analogs illustrate this phenomenon: outgassing produces a\ndust layer, but fresh icy material can still be periodically exposed\nby avalanches and new vents created by impacts from large dust\nparticles (Gr\\\"un et al. 1993). If, in keeping with a Kuiper Belt\norigin, Chiron once possessed an irradiation mantle, we suspect that\nit has been either blown off by sublimation or buried under a dust\nlayer thick enough to mask its features. If so, the present low albedo of\nChiron would be due to cometary dust particles rather than irradiated\nmaterial.\n\nIn contrast, the lack of cometary activity in the Centaur Pholus is\nconsistent with an encompassing surface coverage by the irradiation\nmantle -- witness the extreme red color and absorption features\nassociated with hydrocarbon materials. Although water ice may exist\nlocally on the surface (Cruikshank et al. 1998), Pholus's spectral\nproperties are still dominated by the organic irradiated crust. If\nthis hypothesis is correct, cometary activity should be uncommon among\nCentaurs with very red colors (irradiated material), and more common\namong those with neutral (ice) colors. As the observational sample of\nCentaurs grows, this is a simple prediction that can be directly tested.\nHowever, it remains unclear\nwhy cometary activity was activated on Chiron and not on Pholus, even\nthough the two Centaurs are at similar heliocentric distances. One\npossibility is that Pholus was recently expelled from the Kuiper Belt\nand has not yet been heated internally to a degree sufficient to blow\noff the irradiation mantle, but this hypothesis cannot be easily\ntested, given the chaotic nature of the orbits of Centaurs.\n\n\\subsubsection{Centaur and Kuiper Belt surfaces}\n\nWe summarize the spectral properties of Centaurs and KBOs in Table 3.\nThus far, water ice has been reported in 3 Centaurs (Chiron, Pholus,\n1997 CU$_{26}$) and 1 KBO (1996 TO$_{66}$). The existing data are too sparse to establish whether a correlation exists\nbetween color and the abundance of water ice among Centaurs and KBOs. \nHowever, water ice is\npresent in all three Centaurs for which near-IR spectra are available,\nand in 1 out of 3 studied KBOs. The preponderance of water ice among\nCentaurs makes us suspect that that the \"low\" rate of detection of\nwater ice in KBOs has more to do with the faintness of the targets and\nthe resulting low-quality spectra than with the intrinsic water\ncontents in KBOs. Considering the existing data and the high cosmochemical \nabundance of water ice, we predict that water ice is ubiquitous\namong {\\it all} objects that originated in the Kuiper Belt, although\nthe amount might vary from one object to another and thus determines\nthe possibility for cometary activity in these bodies. \n\nIn short, it would be a good idea to re-observe those\nKBOs which show no apparent water ice feature (1993 SC and 1996\nTL$_{66}$) at higher signal-to-noise ratios. Water ice might be\npresent after all.\n\n\\section{Summary}\n\n\\begin{enumerate}\n\n\\item The near-infrared reflectance spectrum of Chiron is\ntime-variable: in 1996 and 1999 it shows an absorption feature at 2\n$\\micron$ due to water ice. Another absorption\nfeature due to water ice at 1.5 $\\micron$ is also marginally detected\nin 1999. The features were not present in spectra taken in 1993.\n\n\\item Chiron's time-variable spectrum is consistent with variable\ndilution by the coma. During periods of low-level outgassing, surface\nfeatures are revealed.\n\n\\item Chiron's nearly neutral spectrum suggests the surface dominance of\na dust layer created from cometary debris, consisting of\nunirradiated dust particles from the interior. Chiron's original\nirradiation mantle has either been blown off or buried under this\nlayer. \n\n\\item Chiron is the third Centaur in which water ice has been\ndetected. This trend suggests that water ice is common on the surface\nof Centaurs. We predict that water ice is ubiquitous in {\\it all}\nobjects originating in the Kuiper Belt. The surface coverage of this\nwater ice determines its detectability. \n\n\n\\end{enumerate}\n\n\\noindent {\\bf Note} - As we finished the preparation of this\nmanuscript, we received a preprint by Foster et al. (1999) in which\nwater ice is independently identified in spectra from 1998. Foster et\nal. also report an unidentified absorption feature at 2.15 $\\micron$\nthat is not confirmed in our spectra.\n\n\\noindent {\\bf Acknowledgements}\n\n\\noindent The United Kingdom Infrared Telescope is operated by the\nJoint Astronomy Centre on behalf of the U.K. Particle Physics and\nAstronomy Research Council.\n\n\\noindent JXL thanks Ted Roush for his generosity in sharing his\nsoftware and database, Dale Cruikshank for constructive comments, and\nRonnie Hoogerwerf and Jan Kleyna for helpful discussions. This work\nwas partly supported by grants to JXL and DCJ from NASA.\n\n\\newpage\n\n\\begin{references}\n{\n\\reference{} Brown, M. E., and Koresko, C. D. (1998). 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Geo. Res. {\\bf 89},\nno. B7, 6341.\n\n\\reference{} Cruikshank, D., Roush, T. L., Bartholomew, M. J., Moroz,\nL. V., Geballe, T. R., White, S. M., Bell, J. F. III, Pendleton,\nY. J., Davies, J. K., Owen, T. C., deBergh, C., Tholen, D. J.,\nBernstein, M. P., Brown, R. H., and Tryka, K. A. (1998). Icarus {\\bf 135}, 389.\n\n\\reference{} Davies, J. K, Sykes, V. M., and Cruikshank, D. P. (1993a).\nIcarus {\\bf 102}, 166 - 169.\n\n\\reference{} Davies, J., Spencer, J., Sykes, M., Tholen, D., Green, S.\n(1993b). (5145) Pholus. IAUC 5698. \n\n\\reference{} Davies, J., McBride, N., Ellison, S., Green, S.F., and\nBallantyne, D. R. (1998). Icarus {\\bf 134}, 213 - 227.\n\n\\reference{} Fink, U., Hoffman, M., Grundy, W., Hicks, M., and Sears,\nW. (1992). Icarus {\\bf 97}, 145 - 149.\n\n\\reference{} Foster, M. J., Green, S. F., and McBride, N. (1999). \nDetection of Water Ice on 2060 Chiron. Submitted to Icarus.\n\n\\reference{} Gr\\\"un, E., Gebhard, J., Bar-Nun, A., Benkhoff, J., D\\\"uren,\nH., Eich, G., Hische, R., Huebner, W. F., Keller, H. U., Klees, G.,\nKochan, H., K\\\"olzer, G., Kroker, H., K\\\"uhrt, E., L\\\"ammerzahl, P.,\nLorenz, E., Markiewicz, W. J., M\\\"ohlmann, D., Oehler, A., Scholz, J.,\nSeidensticker, K. J., Roessler, K., Schwehm, G., Steiner, G., Thiel, K.,\nand Thomas, H. (1993). J. Geo. Res. {\\bf 98}, no. E8, 15,091 - 15,104.\n\n\\reference{} Hapke, B. (1993). {\\it Theory of Reflectance and Emittance\nSpectroscopy}. Cambridge University Press, Cambridge.\n\n\\reference{} Hartmann, W., Tholen, D., Meech, K., and Cruikshank,\nD. (1990). Icarus {\\bf 83}, 1-15.\n\n\\reference{} Jewitt, D. J., and Kalas, P. (1998). ApJ {\\bf 499}, L103.\n\n\\reference{} Jewitt, D., and Luu, J. (1998). AJ {\\bf 115}, 1667 - 1670.\n\n\\reference{} Johnson, R. E., Cooper, J. F., Lanzerotti, L. J., and \nStrazzulla, G. (1987). Astron. Astrophys. {\\bf 187}, 889.\n\n\\reference{} Lazzaro, D., Florczak, M. A., Angeli, C. A., Carvano, J. M.,\nBetzler, A. S., Casati, A. A., Barucci, M. A., Doressoundiram, A., and \nLazzarin, M. (1997). Planet. Space Sci. {\\bf 45}, 1607.\n\n\\reference{} Luu, J. X. (1993). Icarus {\\bf 104}, 138-148.\n\n\\reference{} Luu, J. X., and Jewitt, D. C. (1990). AJ {\\bf 100}, 913-932.\n\n\\reference{} Luu, J. X., Jewitt, D. C., and Cloutis, E. (1994).\nIcarus {\\bf 109}, 133-144.\n\n\\reference{} Luu, J. X., and Jewitt, D. C. (1996). AJ {\\bf 112}\n2310-2318.\n\n\\reference{} Luu, J. X., and Jewitt, D. C. (1998). ApJ {\\bf 494}, L117.\n\n\\reference{} Marcialis, R. L., and Buratti, B. (1993). Icarus {\\bf 104}, 234.\n\n\\reference{} Matthews, K., and Soifer, B. T. (1994). Experimental\nAstronomy {\\bf 3}, 77-84. \n\n\\reference{} McBride, N., Davies, J. K., Green, S. F., and Foster, M. J. (1999). MNRAS {\\bf 306}, 799 - 805.\n\n\\reference{} Mueller, B. E. A., Tholen, D. J., Hartmann,\nW. K., and Cruikshank, D. P. (1992). Icarus {\\bf 97}, 150 - 154. \n\n\\reference{} Roush, T. L. (1994). Icarus {\\bf 108}, 243 - 254.\n} \n\\end{references}\n\n\\newpage\n\n\\centerline{\\bf FIGURE CAPTIONS}\n\n\\noindent {\\bf Figure 1}. Infrared reflectance spectrum of 2060\nChiron, normalized at 2.2\\ $\\micron$. The date of each spectrum\nis indicated. The top panel shows the original spectra,\nwhile in the bottom panel the 1996 spectra have been smoothed by 3\npixels (the 1999 spectrum remains unsmoothed). There is a clear\nabsorption feature at 2\\ $\\micron$ in all three spectra, and a very\nweak absorption feature at 1.5 $\\micron$ in the 1999 spectra.\n\n\\noindent {\\bf Figure 2}. Infrared reflectance spectrum of Chiron\nfrom 1993 (from Luu et al. 1994) compared with the 1996 and 1999\nspectra. There was no apparent spectral feature in the 1993 spectra.\n\n\\noindent {\\bf Figure 3}. Chiron's 1996 spectra fitted with a model\nconsisting of a linear superposition of water ice and\nolivine spectra.\n\n\\newpage\n\n\\makeatletter\n\\def\\jnl@aj{AJ}\n\\ifx\\revtex@jnl\\jnl@aj\\let\\tablebreak=\\nl\\fi\n\\makeatother\n\n\\begin{deluxetable}{lllllcccc}\n\\footnotesize\n\\tablecaption{Observational Parameters of Spectra}\n\\tablewidth{0pc}\n\\tablehead{\n\\colhead{UT Date}&\\colhead{Instrument}& \n\\colhead{Wavelength}&\\colhead{Slit}& \n\\colhead{$\\lambda / \\Delta \\lambda$}&\n\\colhead{Int\\tablenotemark{a}}& R\\tablenotemark{b} & \n $\\Delta$\\tablenotemark{c} & $\\alpha$\\tablenotemark{d}\\\\[.2ex]\n\\colhead{}&\\colhead{}&\n\\colhead{[{$\\micron$}]}&\\colhead{[arcsec]}&\n\\colhead{}&\n\\colhead{[sec]}&\\colhead{[AU]}&\\colhead{[AU]}&\\colhead{[deg]}\n}\n\\startdata\n\n{\\it UKIRT} &&&&&&&&\\\\\n1996 Feb 7 & CGS4 K&1.3 - 2.0&1.2''$\\times$ 80\"&$\\sim$ 850&1080&\n8.45&7.86&5.6 \\\\\n1996 Feb 8 & CGS4 H&1.3 - 2.0&1.2''$\\times$ 80\"&$\\sim$ 850&400&\n8.45&7.85&5.5 \\\\\n1996 Feb 8 & CGS4 K&1.9 - 2.4&1.2''$\\times$ 80\"&$\\sim$ 850&1520&\n8.45&7.85&5.5 \\\\\n%&&&&&& \\\\\n{\\it Keck I} &&&&&&&&\\\\\n1999 Apr 3 & NIRC JH &1.00 - 1.55&0.68\" $\\times$ 38\"&$\\sim$ 100&600&\n9.39&8.72&4.7 \\\\\n1999 Apr 3 & NIRC HK &1.35 - 2.50&0.68\" $\\times$ 38\"&$\\sim$ 100&600&\n9.39&8.72&4.7 \\\\\n&&&&&& \\\\\n\\enddata\n\\tablenotetext{a}{Accumulated integration time on Chiron}\n\\tablenotetext{b}{Heliocentric distance}\n\\tablenotetext{c}{Geocentric distance}\n\\tablenotetext{d}{Phase angle}\n\\end{deluxetable}\n\n\\begin{deluxetable}{llcc}\n\\footnotesize\n\\tablecaption{Reflectivity Gradients of Chiron Spectra}\n\\tablewidth{0pc}\n\\tablehead{\n\\colhead{UT Date}&\\colhead{Instrument}&\\colhead{Wavelength Range}&\n\\colhead{S'}\\\\[.2ex]\n\\colhead{}&\\colhead{}&\\colhead{[$\\micron$]}&\n\\colhead{[\\%/1000\\AA]}\n}\n\\startdata\n1996 Feb 7 & CGS4 K&2.0 -- 2.4&$0.7 \\pm 0.2$\\\\\n1996 Feb 8 & CGS4 H&1.4 -- 2.0&$-0.3 \\pm 0.2$\\\\\n1996 Feb 8 & CGS4 K&2.0 -- 2.4&$-2.1 \\pm 0.3$\\\\\n\n1999 Apr 3 & NIRC JH &1.0 -- 1.5&$0.9 \\pm 0.2$\\\\\n1999 Apr 3 & NIRC HK &1.5 -- 2.5&$-0.8 \\pm 0.1$\\\\\n\\enddata\n\\end{deluxetable}\n\n\n\\begin{deluxetable}{llccc}\n\\footnotesize\n\\tablecaption{Spectral Properties of Centaurs and Kuiper Belt Objects}\n\\tablewidth{0pc}\n\\tablehead{\n\\colhead{Object}&\\colhead{Type}&\\colhead{$p_V$\\tablenotemark{a}}&\\colhead{V-J}&\n\\colhead{$D_{2 \\micron}$\\tablenotemark{b}}\\\\[.2ex]\n\\colhead{}&\\colhead{}&\\colhead{[\\%]}&\\colhead{}&\n\\colhead{[\\%]}\n}\n\\startdata\n2060 Chiron & Centaur &$\\le 0.14^{+0.06}_{-0.03}$&\n$1.24 \\pm 0.02$&10\\\\\n&&(1)&(2)& This work\\\\\n5145 Pholus & Centaur &$0.04 \\pm 0.13 $&$2.59 \\pm 0.02$&18\\\\\n&&(3)&(4)&(4)\\\\\n1997 CU$_{26}$ & Centaur &$0.04 \\pm 0.01$&$1.74 \\pm 0.02$&10\\\\\n&&(5)&(6)&(7)\\\\\n1996 TL$_{66}$& KBO &?&$1.15 \\pm 0.08$&$<20$\\\\\n&&&(8)&(9)\\\\\n1996 TO$_{66}$ & KBO &?&$0.72 \\pm 0.09$&50\\\\\n&&&(8)&(10)\\\\\n1993 SC & KBO &?&$1.97 \\pm 0.0.08$&$<20$\\\\\n&&&(8)&(11)\\\\\n\\enddata\n\\tablenotetext{a}{Geometric albedo}\n\\tablenotetext{b}{Depth of $2\\micron$ feature}\n\\tablecomments{References are given in parentheses beneath each quantity:\n(1) Campins et al. 1994, Altenhoff et al. \n1995, Bus et al. 1996; (2) Hartmann et al. 1990, Davies et al. 1998; \n(3) Davies et al. 1993; (4) Cruikshank et al. 1998;\n(5) Jewitt and Kalas 1998; (6) McBride et al. 1999; (7) Brown and\nKoresko 1998; (8) Jewitt and Luu 1998; (9) Luu and Jewitt 1998;\n(10) Brown et al. 1999; (11) Brown et al. 1997.}\n\\end{deluxetable}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002095
|
The CDS information hub
|
[
{
"author": "Fran\\c{c}oise Genova"
},
{
"author": "Daniel Egret"
},
{
"author": "Olivier Bienaym\\'e"
},
{
"author": "Fran\\c{c}ois Bonnarel"
},
{
"author": "Pascal Dubois"
},
{
"author": "Pierre Fernique"
},
{
"author": "G\\'erard Jasniewicz\\thanks{Groupe de Recherche en Astronomie et Astrophysique du Languedoc (GRAAL), Montpellier}"
},
{
"author": "Soizick Lesteven"
},
{
"author": "Richard Monier"
},
{
"author": "Fran\\c{c}ois Ochsenbein"
},
{
"author": "Marc Wenger"
}
] |
The {Centre de Donn\'ees astronomiques de Strasbourg} (CDS) provides homogeneous access to heterogeneous information of various origins: information about astronomical objects in {\sc Simbad}; catalogs and observation logs in {\sc VizieR} and in the catalogue service; reference images and overlays in {\sc Aladin}; nomenclature in the {Dictionary of Nomenclature}; Yellow Page services; the AstroGLU resource discovery tool; mirror copies of other reference services; and documentation. With the implementation of links between the CDS services, and with other on--line reference information, CDS has become a major hub in the rapidly evolving world of information retrieval in astronomy, developing efficient tools to help astronomers to navigate in the world-wide `Virtual Observatory' under construction, from data in the observatory archives to results published in journals. The WWW interface to the CDS services is available at: http://cdsweb.u-strasbg.fr/ \keywords{Astronomical data bases: miscellaneous -- Catalogs -- Publications, bibliography -- Surveys -- Standards}
|
[
{
"name": "cdsaa99.tex",
"string": "%\\documentclass[referee]{aa}\n\\documentclass{aa}\n\\usepackage{graphics}\n%\\usepackage{times}\n\\hyphenation{data-base}\n\\begin{document}\n\n\\thesaurus{?? (04.01.1; 04.03.1; 01.16.1; 04.19.1; 01.19.2)}\n\n\\title{The CDS information hub}\n\n\\subtitle{On--line services and links at the Centre de Donn\\'ees \nastronomiques de Strasbourg}\n\n\\author{Fran\\c{c}oise Genova, Daniel Egret, Olivier Bienaym\\'e, Fran\\c{c}ois \nBonnarel, \nPascal Dubois, Pierre Fernique, \nG\\'erard Jasniewicz\\thanks{Groupe de Recherche en\nAstronomie et Astrophysique du Languedoc (GRAAL), Montpellier}, \nSoizick Lesteven, \nRichard Monier, Fran\\c{c}ois Ochsenbein, Marc Wenger}\n\n\\institute{CDS, Observatoire astronomique de Strasbourg, UMR 7550, 11\nrue de l'Universit\\'e, F--67000 Strasbourg, France \\\\\nemail: [email protected]}\n\n\\date{Received \\today/ Accepted}\n\n\\authorrunning{Fran\\c{c}oise Genova et al.}\n\n\\offprints{Fran\\c{c}oise Genova}\n\n\\maketitle\n\n\\begin{abstract}\n\nThe {\\it Centre de Donn\\'ees astronomiques de Strasbourg} (CDS)\nprovides homogeneous access to heterogeneous \ninformation of various origins: information about \nastronomical objects in {\\sc Simbad};\ncatalogs and observation logs in {\\sc VizieR} and in the\ncatalogue service; reference images and overlays \nin {\\sc Aladin}; nomenclature in the {\\it\nDictionary of Nomenclature}; Yellow Page services; the AstroGLU resource\ndiscovery tool; mirror copies of other reference services; and\ndocumentation. With the implementation of links between\nthe CDS services, and with other on--line reference information, CDS\nhas become a major hub in the rapidly evolving world of information\nretrieval in astronomy, developing efficient tools to help astronomers\nto navigate in the world-wide `Virtual\nObservatory' under construction, from\ndata in the observatory archives to results published in journals.\n\nThe WWW interface to the CDS services is available at:\n\nhttp://cdsweb.u-strasbg.fr/\n\n\\keywords{Astronomical data bases: miscellaneous -- Catalogs\n-- Publications, bibliography -- Surveys -- Standards}\n\\end{abstract} \n\n\\section{Introduction}\n\nThe {\\it Centre de Donn\\'ees astronomiques de Strasbourg} (CDS) was\nfounded in 1972 as the {\\it Centre de Donn\\'ees Stellaires}, and\ninstalled in Strasbourg as the result of an agreement\nbetween the INAG ({\\it Institut National d'Astronomie et de\nG\\'eophysique}), now INSU ({\\it Institut National des Sciences de\nl'Univers}), and {\\it Universit\\'e Louis Pasteur}. This was\nthe outcome from the\nvery prospective vision of Jean Delhaye, then Director of INAG, who \nanticipated the importance of computer-readable\ndata. It was decided to found CDS as a part of the French research system,\nas a Data Center serving the international astronomical scientific\ncommunity.\n\nThe objectives of CDS at its creation could be summarized as follows :\n\n\\begin{itemize}\n\\item\ncollect `useful' data about astronomical sources, in electronic form;\n\\item\nimprove them by critical evaluation and combination;\n\\item\ndistribute the results to the international community;\n\\item\nconduct research programs using the data collected.\n\\end{itemize}\n\nInsertion of CDS into a research institution, \nthe {\\it Observatoire astronomique de Strasbourg}, \nhelps to maintain direct\ncontacts with the evolution of astronomy, and with researchers' actual needs.\n\nAt the beginning, CDS was dealing with stellar data, \naiming at the study of the galactic structure. In 1983, \nit was decided that {\\sc Simbad}, one of the two important\nCDS services at that time, would also deal with other galactic and\nextragalactic objets -- i.e., with all astronomical objects outside the\nSolar System. The CDS's name was changed to {\\it Centre\nde Donn\\'ees astronomiques de Strasbourg}, thus preserving the acronym\nwhich was already well known.\n\nIn recent years, research activities in astronomy have \nevolved significantly, with the very rapid development \nof on-line information at all levels, from\nobservatory archives to results published in journals.\nThe challenge is now to deal with {\\it information} more than \nwith {\\it\ndata}, which includes data, but also know-how about data,\ntechnical information about instruments, published results,\ncompilations, etc.\n \nThe CDS goals can now be summarized \nas {\\bf collect, homogenize, distribute, and preserve astronomical\ninformation for the scientific use of the whole astronomical \ncommunity}. This `mission\nstatement' still\ncontains all the drivers from the early CDS charter: \ndealing with electronic data,\ntaking up an international role, developing expertise on astronomical\ndata, having research as a goal. \n\nAll on-line CDS services can be accessed from the CDS home page\non the World-Wide Web\\footnote{http://cdsweb.u-strasbg.fr/}.\n\n\n\\section{The present context of CDS activities}\n\nThe ground- and space-based observatories, the sky surveys,\nand the deep field observations, produce \nlarge amounts of data, obtained at different wavelengths with different\ntechniques. To understand the physical phenomena at work in objects,\nastronomers need to access this wealth of data, to understand\ntheir meaning (error bars, etc.), and to combine the use of data from different\norigins, especially with the\ndevelopment of {\\it panchromatic} astronomy. At all steps of an\nastronomer's work, it is thus more and more necessary to\nre-use data obtained by others and to take into account\nprevious results, often from other fields of astronomy. \n\nAstronomers and funding Agencies are now well aware of\nthe necessity of preserving and diffusing data and results. This leads to\nseveral types of developments:\n\n\\begin{itemize}\n\n\\item the data producing teams, which have the knowledge of instruments\nand observation techniques, have to preserve all or part of their data,\nin a form usable by all astronomers -- in the majority of\nrecent large projects, \nthe building of the {\\it observatory archive} is now considered as one of\nthe project missions;\n\n\\item in some domains, a {\\it specialized center} provides access to and\ninformation about data in a given subfield of astronomy -- this is the\ncase in particular of the\ndisciplinary NASA Centers, HEASARC\\footnote{http://heasarc.gsfc.nasa.gov/}\n for High Energy astrophysics, IRSA\\footnote{http://irsa.ipac.caltech.edu/}\nat \nIPAC\\footnote{http://www.ipac.caltech.edu/} for Infrared data, \nand MAST\\footnote{http://archive.stsci.edu/mast.html}\nat the Space Telescope Science Institute\\footnote{http://www.stsci.edu/},\nfor optical and UV data;\n\n\\item as a Data Center, the role of CDS \nis to bridge the gap between the specialized approach of the\nscientific teams, and the general approach of the community of\nresearchers. In the present context, with the very rapidly growing\nnumber of on-line services of interest to astronomers, this\nmeans in practical terms the definition, development, and\ndistribution of tools for retrieving useful information among\nthe vast array of possible sources (Sections 3, 5).\n\n\\end{itemize}\n\nIn addition, journals are recent, but very active actors in\nthe on-line distribution of information in astronomy. Electronic\npublication has made rapid progress\nand many journals now have on-line\nversions, which often display external links. Moreover, NASA {\\it\nAstrophysics Data System}\\footnote{http://ads.harvard.edu/, with several\nmirror sites, including one at CDS at http://cdsads.u-strasbg.fr/}\n(ADS, Kurtz et al. \\cite{ads}) has become a major reference tool for\nastronomers. Several aspects of the ADS are described in a set of\ncompanion papers.\nThe bibliographic astronomy network, and the CDS role in this\nnetworking, are described in more detail in Section 5.2.\n\nOn the other hand, computers and\nnetworks evolve very rapidly: the high rate of increase in the volume \nof data and results,\nthe irruption of the Internet and World Wide Web,\nthe widespread usage of graphical interfaces, the lower and lower cost of\ninformation storage, completely changed the technical context of the CDS\nactivities in the last few years.\n\n\\section{The CDS activities}\n\nCDS activity has different aspects. Some are directly visible to\nthe users, whereas others, though fundamental for maintaining the CDS\nexpertise and role, may be less conspicuous.\n\nThe most perceptible activity of CDS is certainly the development,\nmaintenance and on-line diffusion of reference, value-added\ndatabases and services, such as\n{\\sc Simbad}, {\\sc VizieR}, {\\sc Aladin},\nthe {\\it Dictionary of Nomenclature of\nastronomical objects outside the solar system} (Lortet et al.\n\\cite{dic}), the AstroGLU discovery tools (Egret et al. \n\\cite{astroglu}), etc. \nThe CDS services are described in more detail in Section 4,\nand in the set of companion papers by Wenger et al. (\\cite{simbad}),\nOchsenbein et al. (\\cite{vizier}), and Bonnarel et al. (\\cite{aladin}).\n\nFrom the point of view of contents, CDS deals with\nselected information: raw observational data are generally not available\nat CDS, but rather upper level data such as observation logs,\ncatalogues, results, etc.\nThis `reference' information is then documented, organized, and made\naccessible in the CDS services.\n\nIn addition, in order to cope with the congestion of\ninter-continental connections, CDS has developed an active\npolicy of mirror copy implementation. \nThe redundant availability of data on several sites is also\nimportant to ensure data security.\nMirror copies of {\\sc Simbad} and ADS are installed in CfA and CDS\nrespectively (Eichhorn et al. \\cite{mirror}). \nMirror copies of {\\sc VizieR} are installed \nat NASA ADC\\footnote{http://adc.gsfc.nasa.gov/} \nand NAOJ ADAC\\footnote{http://adac.mtk.nao.ac.jp/}\n(which also hosts a copy of the {\\it Dictionary of\nNomenclature}), another one is foreseen at the Indian Data Center \n(IUCAA\\footnote{http://www.iucaa.ernet.in/}, Pune). \nCDS hosts mirror copies of several electronic journals\nand of CFHT documentation.\n\nLess visible from the users, but an important field for\nnetworking international partnership, \nCDS develops generic tools and distributes them to other information\nproviders: for example,\nthe GLU ({\\it G\\'en\\'erateur\nde Liens Uniformes}), for maintaining links to\ndistributed heterogeneous databases (Fernique et al.\n\\cite{glu}, Section 5.1), or\nthe {\\sc Simbad} client/server package, which allows archive services and the\nADS to use {\\sc Simbad} as a name resolver.\n\nCDS is also active in the development of exchange standards, \nsuch as the {\\it bibcode}, first defined by\nNED\\footnote{http://nedwww.ipac.caltech.edu/}\nand the CDS (Schmitz et al. \\cite{bibcode}), \nand now widely used by the ADS and the on-line\njournals, or the standard description of tables, defined by CDS and\nshared with the other data centers and the journals (Ochsenbein et al.\n\\cite{vizier}).\nCDS collaboration with journals is described in Section~5.2.\n\nCDS expertise in the domain of astronomical data is also useful for\nprojects. Strasbourg Observatory has been deeply involved in\nconstruction of the input and result catalogues of Hipparcos and\nTycho (\\cite{hip}),\nand {\\sc Simbad} has been used as a basis for ROSAT identification tools.\nAt present, the XMM Survey Science\nCenter\\footnote{http://xmmssc-www.star.le.ac.uk/}\nrelies on the CDS services to build a\ncross-identification database for the X-ray sources observed by\nthe satellite. The CDS participation to the DENIS and\nTERAPIX/MEGAPRIME surveys is described in Section 5.4.\n\nFinally, to keep up with the pace of technical\nevolution, CDS has to develop a resolute activity in the domain of\ntechnological and methodological watch, and to undertake\nResearch and Technology (R\\&T) actions to assess new techniques.\nThe GLU development (Fernique et al. \\cite{glu}, \nSection 5.1.), and the {\\sc Aladin} Java\ninterface (Fernique \\& Bonnarel, \\cite{java}),\nare examples of R\\&T actions which came out as operational\nservices. More recently, one can cite the {\\it ESO/CDS Data Mining Project}\n(Ortiz et al. \\cite{datamining}), \nor the assessment of commercial object oriented\ndatabase systems (Wenger et al. \\cite{oodb}) (Section 5.4).\n\nIn practice, the main challenge in the CDS activity is to\nconstantly tune the contents and the services to the rapid scientific\nand technical evolution, to be able to deal with ever increasing volumes\nof information, and to be ready to respond to the new projects and\nto the evolution of the policy of the national and international\nAgencies. The guidelines in prioritizing the tasks are several:\noffer the best service to the users, ensure the quality of\ncontents, and make the best of technological innovation. This\nimplies that new developments are begun neither too early, to rely on\ntechniques which are as secure as possible, nor too late, to offer the\nbest possible services and improve the functionalities -- hence\nthe importance of technical watch. A balance has constantly to\nbe kept, between very long term activities, on time scales of\nseveral ten years, to build up the contents; the development\nand maintenance of database systems and user interfaces, on\ntime scales of a few months to a few years; R\\&T activities, on\nsimilar times scales ; and operational constraints\non a day-to-day basis. Hence the\nimportance of careful strategy definition and activity\nscheduling. \n\n\\section{The main CDS services}\n\n% one column figure\n% first citation beginning of Sect. 4\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{CDSorg2.ps}}\n\\caption{The main CDS on-line services.}\n\\label{cdsorg}\n\\end{figure}\n\n%\tone column figure\n% first citation beginning on Sect. 4\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{cdshome.ps}}\n\\caption{CDS home page on the World-Wide Web.}\n\\label{cdshome}\n\\end{figure}\n\nA diagram of the main CDS services is shown in\nFig.~\\ref{cdsorg}, and their list is given in the CDS Home\nPage (Figure~\\ref{cdshome}).\n\nThe first two main products of CDS have been\nthe collection of information about astronomical objects from published\npapers and reference catalogues in {\\sc Simbad}, and the collection,\ndocumentation, long term storage \nand distribution of catalogues in the catalogue service, with\nthe recent addition of the catalogue browser functionality of\nthe {\\sc VizieR} service. \nMore recently, the {\\sc Aladin} project has permitted us\nto construct an image server, and a comprehensive tool to overlay the\ninformation from {\\sc Simbad}, {\\sc VizieR}, and from other sources such\nas NED or data archives, on digitized images of the sky. These services\nare described in companion papers\n(Wenger et al. \\cite{simbad}, Ochsenbein et al. \\cite{vizier}, Bonnarel et\nal. \\cite{aladin}).\n\nThe CDS also has the\nresponsibility of the {\\it Dictionary of Nomenclature} (Lortet et al.\n\\cite{dic}),\nhosts bibliographical information, with\nmirror copies of the ADS and of the {\\it Astrophysical Journal}, the {\\it\nAstronomical Journal}, and the {\\it Publications of the Astronomical Society\nof the Pacific}, and develops\nbibliographic information retrieval tools (Poin\\c{c}ot et al.\n\\cite{kohonen}). It maintains the AstroGLU information discovery tool\n(Egret et al. \\cite{astroglu}), and hosts two Yellow Page services: \nAstroWeb (Jackson et al. \\cite{astroweb}), and\nthe {\\it Star*s Family of Astronomy and Related Resources}\n(Heck \\cite{starpages}). CDS is the French IUE National host,\nthe host of a copy of the\nCFHT user documentation and \nof the unpublished data on variable stars of IAU Commission 27.\n\nThe main evolution of the CDS in recent years, is the rapid\ndevelopment of the {\\it World Wide Web} access to the \nservices\\footnote{http://cdsweb.u-strasbg.fr/}. Before\n1996, the only CDS service available on the Web, besides documentation,\nwas the access to the catalogues and tables (via ftp) and to the \non-line abstracts of\nthe journal {\\it Astronomy and Astrophysics}. {\\sc VizieR} was released in\nFebruary 1996, the first Web version of {\\sc Simbad} in November 1996, and the\nWeb access to {\\sc Aladin} in November 1998 (Previewer) and February 1999\n({\\sc Aladin} Java). Now all the services are accessible from the CDS Home\nPage (Figure 2).\n\nThe usage of the CDS services has been continuously\nincreasing, with over 6,000 queries submitted to the CDS\nservices and their mirror copies every day,\nand over 25,000 hits per day on the Web pages (November 1999).\n\n\n\\section {Major evolution trends}\n\nWith the development of the World Wide Web, building links \nbetween heterogeneous, distributed information,\nhas been an important evolution trend recently, and it is also an\nimportant \ntopic for international partnership among service providers. \n\n\\subsection{Building links between heterogeneous services}\n\nHistorically, the CDS services had developed separately, with different\ncontents, functionalities, database management systems and user\ninterfaces. The World Wide Web opened the possibility to increase the\nsynergy between the services, by building links allowing the users to\nnavigate in a transparent way.\nMaintenance is a major challenge however, as soon as\none tries to build links between distributed, heterogeneous services:\nany change in the service address, or in the query syntax, breaks links.\nThis is particularly difficult when `anchors' (links in HTML syntax) are\nhard-coded in the HTML pages. CDS\nhas solved this problem by developing\nthe {\\it G\\'en\\'erateur de Liens Uniformes} (GLU), a\nsoftware package which manages a distributed dictionary of resources\n(Fernique et al. \\cite{glu}).\nEach resource is described by its address, the query syntax, \ntest information, links to\ndescription and help files, etc. The {\\it GLU Dictionary} descriptions are\nmaintained up-to-date by each service provider \nand shared among all participants. The {\\it GLU\nResolver} allows the service manager to use symbolic names, \ninstead of physical names, for the links; these names\nare then translated on the fly using the information contained in the\n{\\it GLU Dictionary}. \n\nThe GLU development has allowed CDS to build reliable links between its own\nservices, to manage mirror copies,\nand to implement a common presentation of the\nCDS pages, with homogenized headers. \n\nMoreover, the GLU is being shared with\nall the partners of the AstroBrowse NASA initiative:\ninformation retrieval tools are being\ndeveloped for providing a homogeneous access to a large list of\nresources maintained in a common GLU Dictionary (Heikkila et al.\n\\cite{astrobrowse}). One of these tools, AstroGLU (Egret et al.\n\\cite{astroglu}), is developed by CDS. It permits us to search on-line\nservices such as observatory archives, databases, etc., by coordinates,\nastronomical object names, astronomer names, keywords, etc. In\nfact, AstroGLU is a Web interface to the GLU Dictionary.\n\nGLU is also used by the French\n{\\it Centre de Donn\\'ees de la Physique des Plasmas}\n(CDPP)\\footnote{http://cdpp.cesr.fr/}.\n\n\\subsection{The CDS role in the bibliographic network}\n\nStarting with the {\\it Bibliographical Star Index} (BSI, Ochsenbein \n\\cite{bsi}) as early as\n1975, CDS has always been dealing with bibliographic data: references and\nobjects citations in published papers are stored in {\\sc Simbad}, \nand published tables in the\ncatalogue service. The last few years have seen a revolution\nin this domain, with the extremely rapid development of electronic\npublication, which has led to major conceptual evolutions in the work\nof journal \neditors and publishers, and in the usage of published information by\nscientists. \n\nThe collaboration with the journal {\\it Astronomy and\nAstrophysics}, for which CDS implements on-line abstracts and tables\nin close cooperation with the editors,\nwas settled in 1993, very early in the history of electronic publication\n(Ochsenbein \\& Lequeux \\cite{aa}).\nAs explained in the companion paper by Ochsenbein et al. (\\cite{vizier}), the\nstandard description of tabular catalogues proposed by CDS in 1994 has\nsince then been accepted by other reference journals and by the\ncollaborating data centers. It is now one of the important exchange\nstandards for astronomy, allowing for data exchange, transformation and\nchecks, complementary to FITS which is widely used for\nbinary and image data. A new standard in XML is presently being\nimplemented for formatting tables (Ochsenbein et al. \\cite{xml}),\nand to facilitate interoperability between services. In particular,\nthis standard has been implemented in {\\sc VizieR}, and is already used for\ndata ingestion by {\\sc Aladin}.\n\nThe CDS role in the world-wide astronomy bibliographical\nnetwork, sometimes called \n{\\it Urania} (Boyce \\cite{urania}), has several aspects (Lesteven\net al. \\cite{lisa}):\n\n\\begin{itemize}\n\n\\item provision of selected and homogenized\nbibliographic information in {\\sc Simbad} and {\\sc VizieR};\n\n\\item publication of `long' tables on behalf of some of the major\nastronomy journals;\n\n\\item implementation of mirror copies of the {\\it Astrophysical\nJournal}, {\\it Astronomical Journal}, and {\\it Publications of the\nAstronomical Society of the Pacific}, in collaboration in particular\nwith the\n{\\it University of Chicago Press}, and of NASA {\\it Astrophysics Data\nSystem} abstracts and scanned images of articles;\n\n\\item active participation to the definition of exchange standards;\n\n\\item R\\&T efforts to handle `textual' information, which have\nled to the development of {\\it Document maps}, using the technique of\n`Self-Organizing maps' (Kohonen, \\cite{origk}) for displaying\nreferences classified on the basis of the semantic proximity of their\ncontents (Poin\\c{c}ot et al. \\cite{kohonen}).\n\n\\end{itemize}\n\nThe definition of exchange standards such as the bibcode and the\nstandard description of tables, the close collaboration with the\njournals and the ADS, have permitted an excellent synergy among\nthe on-line bibliographic services. For instance, data exchange,\nlinks, exchange and installation of mirror copies, have been\nimplemented between CDS and ADS, which also uses {\\sc Simbad} as a name\nresolver. The on-line versions of {\\it Astronomy and\nAstrophysics} and the {\\it Supplement Series} contain links to\nthe CDS catalogue service, as part\nof the publication, and to the list of {\\sc Simbad} objects for each paper.\n\nThe Data Center has also brought new\nmethods to validate the journal contents, complementary to the referees'\nwork: tools have been developed to check the consistency of data in\nelectronic tables, and detected errors are reported directly to the author\nby CDS before publication, and corrected. \n\nIn addition, the development of semi-automatic methods for\nrecognition of astronomical object names in texts is being\nstudied (Lesteven at al.\n\\cite{lisa}). This is \nrendered difficult by the extreme complexity of astronomical\nnomenclature, but there are potentially innovative applications,\nsuch as building links between object names in journal articles and\nthe information contained in {\\sc Simbad}. A prototype implementation is\noperational at CDS in a simple case (object names in abstract\nkeywords). {\\it New Astronomy} also provides links from object names in\narticles to {\\sc Simbad} and NED, with manual tagging and verification. But many\nfundamental questions remain to be solved, e.g. the management of links\nbetween object names in journals that remain unchanged, and object\nnames contained in databases which may change. \n\n\\subsection{The CDS role for the access to observation archives}\n\nThe objective is to use the CDS as a `hub' to observatory archives: each\nCDS service, with its own functionalities, allows the user to select the\nobservation he or she would like to check, and to access these\nobservations through an http link to the archive service.\n\n{\\sc VizieR} is potentially a major tool to access observatory databases: the\narchive holdings are normally listed in a `log', i.e. in a table which\ncontains the list of available observations with some additional\ninformation, such as the instrument mode, time and duration of\nobservation, target position, target name, PI name, etc. Data in tabular\nform are very easy to include in {\\sc VizieR} -- one just has to build their\ndescription in standard format. A data archive log included in {\\sc VizieR}\ncan be searched by querying any of its fields, thus allowing the user to\nselect the information of interest. The next step is to build links\nbetween the log entries in {\\sc VizieR}, and the data in the archive:\nthis is already operational for several archives, in collaboration with\nthe data providers, and using the GLU to implement the links. \nOne also has to update evolving\nlogs, for implementing links to on-going space missions or \nground-based programs. \nThis has been developed in recent years, and is now\nfully operational. In November 1999, {\\sc VizieR} \nwas able to access the FIRST/VLA survey data, and the IUE and \nHST archives. Discussions are under way with several\nother projects.\n\nImplementation of links from {\\sc Simbad} to data archives is less\nstraightforward, since the logs are usually not easy to\ncross-identify with the database. This is done on a\ncase-by-case basis. Links to IUE and HEASARC are available at\npresent time: the IUE log has been cross-identified with {\\sc\nSimbad}, taking advantage of the fact that CDS had homogenized\nthe mission target nomenclature on behalf of ESA (Jasniewicz et\nal. {\\cite{iue}); for the links to HEASARC, the high energy\nobjects are recognized by checking the list of identifiers for names\ncoming\nfrom a high-energy mission (e.g., RX or 1RXS, among others, for\nROSAT). More will be done in the future through the implementation \nin {\\sc Simbad} of\nlinks pointing to {\\sc VizieR}.\n\n{\\sc Aladin} gives access to data archives through their logs in {\\sc VizieR}, and is also\nable to display archive images. This is a major evolution towards a\ncomprehensive tool permitting comparison of images at different resolutions or\nwavelengths, with active links to the original data.\n\n\n\\subsection{Dealing with large surveys}\n\nThe large surveys underway or planned at different wavelengths, such as\nDENIS and 2MASS in the infrared, SLOAN at optical wavelengths, the large\nSchmidt telescope plate catalogues (GSC I and II, USNO, APM, \netc.), play an important role, \nboth for multi-wavelength studies, and by providing reference\nobjects. Astronomers thus need\neasy access to the data of each survey, and also tools\nto use the data from one survey, together with information from other\norigins. These needs have recently been summarized in the concept of\n`Virtual Observatory'(see e.g.\\ Szalay \\& Brunner \\cite{terabyte}).\n\nCDS has been involved in active discussions with the major survey \nprojects in the\nlast few years. As explained in Ochsenbein et al. (\\cite{vizier}), an\nefficient method to query very large tables by position \nhas been implemented in the\nCDS catalogue service, with the same user interface as {\\sc VizieR},\nfor tables larger than the few million\nobjects manageable in relational systems. The USNO\ncatalogue (520 million objects), the public data of DENIS and 2MASS, have\nbeen made rapidly\navailable in this service. The APM catalogue will also be installed\nsoon, as well as GSC II as soon as it will be publicly available.\n{\\sc Aladin} gives access to the surveys implemented in {\\sc VizieR}, and is very\nuseful for data validation and for the assessment of criteria for\nstatistical cross-identification.\n\nMoreover, CDS has been contributing to the DENIS project, by \ndeveloping an\non-line service to distribute public and private information\n(Derriere et al. \\cite{deniscds}), and data comparison with the\ninformation in the other CDS services has already served for data\nvalidation. CDS also participates in TERAPIX (data pipeline of the CFHT\nMEGAPRIME project): it will distribute the result catalogue and probably\nalso summary images.\n\nIn addition to the present access to very large catalogues by coordinate\nqueries, evaluation of the usage of commercial Object Oriented database\nsystems for multicriteria access to very large catalogues \nis under way (Wenger et al. \\cite{oodb}). Moreover, the {\\it ESO/CDS\nData Mining project} aims at accessing and combining information stored at ESO\nor CDS, and to perform cross-correlations in all the\nparameter space provided by the data catalogues -- not restricting the\ncorrelations to positional ones (Ortiz et al. \\cite{datamining}).\n\n\n\\section{Conclusion}\n\nThe usage of the CDS services has undergone a revolution in the last\nfew years, with the outcome of the World Wide Web, allowing easy access to\non-line information, the integration of data and documentation,\nand navigation between distributed information. This means an\nexplosion in the usage of the services, new\nfunctionalities, new concepts in the partnership of\ndata centers and journals, since published information can now be\nconsidered as data (e.g., published tables are now usable like reference\ncatalogues), and an increase in international partnership, to build up\nlinks and to define exchange standards. In parallel, the construction\nof the\ndatabase contents remains a long-term activity, with increasing\nvolume of information to deal with, \nand high standards of scientific and technical expertise\nneeded in the value-added data center activities.\n\nNavigation and links will certainly remain important keywords for the\nfuture, and the topic of interoperability is clearly emerging. One\naspect is the construction of links between distributed services.\nAnother one is the building of comprehensive information retrieval tools,\nas stressed in the AstroBrowse NASA initiative. To go further, one needs\nto be able to integrate the result of queries to heterogeneous services\n(ISAIA project, Hanisch \\cite{isaia}).\nIn this context, the elaboration of exchange standards and\nmetadata descriptions common to all service providers are fundamental\nkeys to success. On a technical point of view,\nXML may be one important tool for data integration.\n{\\sc Aladin} is an example of a comprehensive tool, allowing integration of\nreference images, with information from catalogues, databases and data\narchives.\n\nThe rapid development of the world-wide `bibliographic network' \nhas been particularly\nimpressive, and the `data archive network' seems well under way. The CDS\nis a major hub in the on-line `Virtual Observatory' presently\nunder construction: its services allow astronomers to select\nthe information of interest for their research, and to access\noriginal data, observatory archives and results published in\njournals. \n\n\n\\begin{acknowledgements}\nCDS acknowledges the support of INSU-CNRS, the Centre National\nd'Etudes Spatiales (CNES), and Universit\\'e Louis Pasteur. Many\nof the current developments have been made possible by\nlong-term support from NASA, ESA and ESO,\nand {\\it Astronomy \\& Astrophysics}.\nMany other partners are involved in building up the\ninternational astronomy network, among which are the\nAAS, ADS, HEASARC, IPAC and NED, STScI, \nADC, CADC, INASAN, NOAJ, and many others which cannot\nall be cited here.\n\nDeveloping and maintaining the data-bases is a collective\nundertaking. The expertise and dedicated work of the\ndocumentalists, engineers and astronomers who work for CDS in\nStrasbourg and elsewhere are the foundations of the quality of the\nservices. All of them are associated with this paper.\nLong term support from Institut d'Astrophysique de Paris, Observatoire\nde Paris (DASGAL), Observatoire de Bordeaux, GRAAL (Montpellier) \nand Observatoire Midi-Pyr\\'en\\'ees (Toulouse), is gratefully\nacknowledged.\n\nWe thank Jean Delhaye, Jean Jung, Carlos Jaschek, and Michel\nCr\\'ez\\'e, for their vision and leadership in the different phases of\nthe CDS project.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem[2000]{aladin}\nBonnarel, F., Fernique, P., Bienaym\\'e, O., et al., 2000,\nA\\&AS, this issue\n\n\\bibitem[1998]{urania}\nBoyce, P.B., 1998, in {\\it LISA III}, eds.\\ U. Grothkopf,, H. Andernach, \nS. Stevens-Rayburn, M. Gomez, ASP Conf. Ser. 153, p.107\n\n\\bibitem[2000]{deniscds}\nDerriere, S., Ochsenbein, F., Egret, D., 2000, in {\\it ADASS IX}, ASP Conf.\nSer. in press\n\n\\bibitem[1998]{astroglu}\nEgret, D., Fernique, P., Genova, F., 1998, in {\\it ADASS VII}, \neds.\\ R. Albrecht, R. N. Hook, H. A. Bushouse, ASP Conf.\nSer. 145, p.416\n\n\\bibitem[1996]{mirror}\nEichhorn, G., Accomazzi, A., Grant, C. S., et al., 1996, BAAS 189,\n\\#06.01\n\n\\bibitem[1999]{denis}\nEpchtein, N., Deul, E., Derriere, S., et al., 1999, A\\&A 349, 236\n\n\\bibitem[1997]{hip}\nESA, 1997, {\\it The Hipparcos and Tycho catalogue}, ESA--SP 1200\n\n\\bibitem[2000]{java}\nFernique, P., Bonnarel, F., 2000, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1998]{glu} \nFernique, P., Ochsenbein, F., Wenger, M., 1998,\nin {\\it ADASS VII}, eds.\\ R. Albrecht, R. N. Hook, H. A. Bushouse,\nASP Conf. Ser. 145, p. 466\n\n\\bibitem[2000]{isaia}\nHanisch, R.A., 2000, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1997]{starpages}\nHeck, A., 1997, in {\\it Electronic Publishing for Physics and Astronomy},\ned.\\ A. Heck, Kluwer, p. 211\n\n\\bibitem[1999]{astrobrowse2}\nHeikkila, C.W, McGlynn, T.A., White, N.E, 1999, in {\\it ADASS VIII},\neds.\\ D. M. Mehringer, R. L. Plante, D.\nA. Roberts, ASP Conf. Ser. 172, p. 221\n\n\\bibitem[1995]{astroweb}\nJackson, R.E., Wells, D., Adorf, H.-M., et al., 1994, A\\&AS\n108, 235\n\n\\bibitem[1990]{iue}\nJasniewicz, G., Egret, D., Barylak, M., Wamsteker, W., 1990, in {\\it\nEvolution in Astrophysics: IUE Astronomy in the Era of New Space\nMissions}, ESA Report, p. 601\n\n\\bibitem[2000]{ads}\nKurtz, M.J., Eichhorn, G., Accomazzi, A., et al., 2000, this issue\n\n\\bibitem[1982]{origk}\nKohonen, T., 1982, Biological Cybernetics 43, 59\n\n\\bibitem[1998]{lisa}\nLesteven, S., Bonnarel, F., Dubois, P., et al.,\n1998, in {\\it LISA III}, op. cit.\np.61\n\n\\bibitem[1994]{dic}\nLortet, M.C., Borde, S., Ochsenbein, F., 1994, A\\&AS 107, 193\n\n\\bibitem[1997]{astrobrowse}\nMcGlynn, T.A., White, N.E., Fernique, P., Wenger, M, Ochsenbein, F.,\n1997, BAAS 191, \\#17.04\n\n\\bibitem[1982]{bsi}\nOchsenbein, F., 1982, in {\\it Automated Data Retrieval in Astronomy}, eds.\\\nC. Jaschek \\& W.D. Heintz, IAU Coll. 64, Dordrecht, D. Reidel\nPublishing Company, p.171\n\n\\bibitem[1995]{aa}\nOchsenbein, F., Lequeux, J., 1995, Vistas in Astron. 39, 227\n\n\\bibitem[2000]{vizier}\nOchsenbein, F., Bauer, P., Marcout, J., 2000, A\\&AS this issue\n\n\\bibitem[2000]{xml}\nOchsenbein, F., Albrecht, M., Brighton, A., et al., 2000, \nin {\\it ADASS IX}, in press\n\n\\bibitem[1999]{datamining} \nOrtiz, P.F., Ochsenbein, F., Wicenec, A., \nAlbrecht, M., 1999,\nin {\\it ADASS VIII}, eds.\\ D. M. Mehringer, R. L. Plante, D.\nA. Roberts, ASP Conf. Ser. 172, p. 379\n\n\\bibitem[1998]{kohonen}\nPoin\\c{c}ot, P., Lesteven, S., Murtagh, F., 1998, A\\&AS 130, 183\n\n\\bibitem[1995]{bibcode}\nSchmitz, M., Helou, G., Dubois, P., et al.,\n1995, in {\\it Information \\& On-line Data in\nAstronomy}, eds.\\ D. Egret \\& M. Albrecht, Kluwer Acad. Publ., p.259\n\n\\bibitem[1998]{terabyte}\nSzalay, A.S., Brunner, R.J., 1998, in {\\it New Horizons from\nMulti-Wavelength Sky Surveys}, IAU Symp. 179, eds.\\\nMcLean, B.J., Golombek, D.A., Hayes, J.J.E., Payne, H.E.,\nKluwer Acad. Publ., p.455\n\n\\bibitem[2000a]{simbad}\nWenger, M., Ochsenbein, F., Egret, D., et al., \n2000a, A\\&AS this issue\n\n\\bibitem[2000b]{oodb}\nWenger, M., Kinnar, F., Jocqueau, R., 2000b, in {\\it ADASS IX}, ASP Conf.\nSer. in press\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n\n"
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{
"name": "astro-ph0002095.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[2000]{aladin}\nBonnarel, F., Fernique, P., Bienaym\\'e, O., et al., 2000,\nA\\&AS, this issue\n\n\\bibitem[1998]{urania}\nBoyce, P.B., 1998, in {\\it LISA III}, eds.\\ U. Grothkopf,, H. Andernach, \nS. Stevens-Rayburn, M. Gomez, ASP Conf. Ser. 153, p.107\n\n\\bibitem[2000]{deniscds}\nDerriere, S., Ochsenbein, F., Egret, D., 2000, in {\\it ADASS IX}, ASP Conf.\nSer. in press\n\n\\bibitem[1998]{astroglu}\nEgret, D., Fernique, P., Genova, F., 1998, in {\\it ADASS VII}, \neds.\\ R. Albrecht, R. N. Hook, H. A. Bushouse, ASP Conf.\nSer. 145, p.416\n\n\\bibitem[1996]{mirror}\nEichhorn, G., Accomazzi, A., Grant, C. S., et al., 1996, BAAS 189,\n\\#06.01\n\n\\bibitem[1999]{denis}\nEpchtein, N., Deul, E., Derriere, S., et al., 1999, A\\&A 349, 236\n\n\\bibitem[1997]{hip}\nESA, 1997, {\\it The Hipparcos and Tycho catalogue}, ESA--SP 1200\n\n\\bibitem[2000]{java}\nFernique, P., Bonnarel, F., 2000, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1998]{glu} \nFernique, P., Ochsenbein, F., Wenger, M., 1998,\nin {\\it ADASS VII}, eds.\\ R. Albrecht, R. N. Hook, H. A. Bushouse,\nASP Conf. Ser. 145, p. 466\n\n\\bibitem[2000]{isaia}\nHanisch, R.A., 2000, in {\\it ADASS IX}, ASP Conf. Ser. in press\n\n\\bibitem[1997]{starpages}\nHeck, A., 1997, in {\\it Electronic Publishing for Physics and Astronomy},\ned.\\ A. Heck, Kluwer, p. 211\n\n\\bibitem[1999]{astrobrowse2}\nHeikkila, C.W, McGlynn, T.A., White, N.E, 1999, in {\\it ADASS VIII},\neds.\\ D. M. Mehringer, R. L. Plante, D.\nA. Roberts, ASP Conf. Ser. 172, p. 221\n\n\\bibitem[1995]{astroweb}\nJackson, R.E., Wells, D., Adorf, H.-M., et al., 1994, A\\&AS\n108, 235\n\n\\bibitem[1990]{iue}\nJasniewicz, G., Egret, D., Barylak, M., Wamsteker, W., 1990, in {\\it\nEvolution in Astrophysics: IUE Astronomy in the Era of New Space\nMissions}, ESA Report, p. 601\n\n\\bibitem[2000]{ads}\nKurtz, M.J., Eichhorn, G., Accomazzi, A., et al., 2000, this issue\n\n\\bibitem[1982]{origk}\nKohonen, T., 1982, Biological Cybernetics 43, 59\n\n\\bibitem[1998]{lisa}\nLesteven, S., Bonnarel, F., Dubois, P., et al.,\n1998, in {\\it LISA III}, op. cit.\np.61\n\n\\bibitem[1994]{dic}\nLortet, M.C., Borde, S., Ochsenbein, F., 1994, A\\&AS 107, 193\n\n\\bibitem[1997]{astrobrowse}\nMcGlynn, T.A., White, N.E., Fernique, P., Wenger, M, Ochsenbein, F.,\n1997, BAAS 191, \\#17.04\n\n\\bibitem[1982]{bsi}\nOchsenbein, F., 1982, in {\\it Automated Data Retrieval in Astronomy}, eds.\\\nC. Jaschek \\& W.D. Heintz, IAU Coll. 64, Dordrecht, D. Reidel\nPublishing Company, p.171\n\n\\bibitem[1995]{aa}\nOchsenbein, F., Lequeux, J., 1995, Vistas in Astron. 39, 227\n\n\\bibitem[2000]{vizier}\nOchsenbein, F., Bauer, P., Marcout, J., 2000, A\\&AS this issue\n\n\\bibitem[2000]{xml}\nOchsenbein, F., Albrecht, M., Brighton, A., et al., 2000, \nin {\\it ADASS IX}, in press\n\n\\bibitem[1999]{datamining} \nOrtiz, P.F., Ochsenbein, F., Wicenec, A., \nAlbrecht, M., 1999,\nin {\\it ADASS VIII}, eds.\\ D. M. Mehringer, R. L. Plante, D.\nA. Roberts, ASP Conf. Ser. 172, p. 379\n\n\\bibitem[1998]{kohonen}\nPoin\\c{c}ot, P., Lesteven, S., Murtagh, F., 1998, A\\&AS 130, 183\n\n\\bibitem[1995]{bibcode}\nSchmitz, M., Helou, G., Dubois, P., et al.,\n1995, in {\\it Information \\& On-line Data in\nAstronomy}, eds.\\ D. Egret \\& M. Albrecht, Kluwer Acad. Publ., p.259\n\n\\bibitem[1998]{terabyte}\nSzalay, A.S., Brunner, R.J., 1998, in {\\it New Horizons from\nMulti-Wavelength Sky Surveys}, IAU Symp. 179, eds.\\\nMcLean, B.J., Golombek, D.A., Hayes, J.J.E., Payne, H.E.,\nKluwer Acad. Publ., p.455\n\n\\bibitem[2000a]{simbad}\nWenger, M., Ochsenbein, F., Egret, D., et al., \n2000a, A\\&AS this issue\n\n\\bibitem[2000b]{oodb}\nWenger, M., Kinnar, F., Jocqueau, R., 2000b, in {\\it ADASS IX}, ASP Conf.\nSer. in press\n\n\\end{thebibliography}"
}
] |
astro-ph0002096
|
The Broad Line Region in Active Galactic Nuclei
|
[
{
"author": "D. Dultzin-Hacyan\\altaffilmark{1}"
},
{
"author": "P. Marziani\\altaffilmark{2}"
},
{
"author": "J.W. Sulentic\\altaffilmark{3}"
}
] |
We review constraints on models of the broad line region that are imposed by observations of the emission lines in Active Galactic Nuclei. Comparison of high and low ionization lines in sources with FWHM H$\beta\leq$4000 km s$^{-1}$ points toward low ionization line emission produced in a flattened geometry (the accretion disk?) with an associated high ionization wind. It remains unclear whether these results can be extended to all radio quiet AGN and particularly to radio loud AGN.
|
[
{
"name": "dd_submitted.tex",
"string": "%%% Sample proceedings article for rmaa.cls\n%%%\n%%% Converted to RMAA(SC) style and annotated by Will Henney\n%%% (04 Oct1999)\n%% This file contains examples of many of the commands in the LaTeX\n%% document class rmaa.cls, such as the commands for specifying data\n%% for the title page and the commands for including postscript\n%% figures. For more details, you should consult the accompanying\n%% Author Guide (`rmuser.tex'). A further sample document\n%% (`rmtest.tex') contains examples of some commands not used in this\n%% file, eg. for marking up tables. You may also want to use this file\n%% as a template for your own article.\n%% Note: This article was originally published in `IAU Symposium 182:\n%% Herbig-Haro Objects and the Birth of Low-mass Stars',\n%% ed. B. Reipurth & C. Bertout (Dordrecht: Kluwer). Hopefully, I've\n%% changed it enough to avoid copyright violation!\n%% All proceedings articles must begin with the following line\n\\documentclass[proceedings,onecolumn]{rmaa}\n%%\n%% The file `rmaa.cls' should be somewhere in your TeX search path\n%% (e.g, in the current directory, or in a personal or system-wide\n%% directory of LaTeX packages.\n%%\n%% This will not work with old versions of LaTeX: any version\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\n%% complains that it doesn't recognise the command `\\documentclass'\n%% then your LaTeX installation needs updating!\n%% The following package allows one to do the citations\n%% semi-automatically. It defines the commands \\cite{KEY},\n%% \\scite{KEY}, and \\pcite{KEY} which respectively produce citations\n%% in the following styles:\n%% (AUTHOR YEAR)\n%% AUTHOR (YEAR)\n%% AUTHOR YEAR\n%% For this to work, you need to pay attention to the formatting of\n%% the `\\bibitem's in your `thebibliography ' environment, qv.\n\\usepackage{rmaacite}\n%% If you would rather do your citations by hand, then comment out the\n%% above line\n\n%% Here, you can put the definitions of your own personal macros.\n%% All the special commands defined in AASTEX 4.0 (e.g. \\ion{}{},\n%% \\gtrsim, \\arcsec, \\apj, etc) are already defined. I haven't checked\n%% if there are any new ones in AASTEX 5.0 yet.\n\\newcommand{\\thOr}{$\\theta^1\\,$C~Ori}\n\\newcommand{\\zero}{_0}\n\\newcommand{\\kms}{\\,\\mbox{km s$^{-1}$}}\n\\newcommand{\\Othree}{[\\ion{O}{3}]~5007\\AA}\n\\renewcommand{\\P}[1]{%\n\\ifnum#1=1\\hbox{OW~168--326E}\\fi \\ifnum#1=2\\hbox{OW~167--317}\\fi\n\\ifnum#1=3\\hbox{OW~163--317}\\fi \\ifnum#1=5\\hbox{OW~158--323}\\fi\n\\ifnum#1=0\\hbox{OW~171--334}\\fi}\n\n%%\n%% The following commands specify the title, authors etc\n%%\n\\title{The Broad Line Region in Active Galactic Nuclei}\n\\author{D. Dultzin-Hacyan\\altaffilmark{1},\nP. Marziani\\altaffilmark{2}, J.W. Sulentic\\altaffilmark{3}} \\altaffiltext{1}{Instituto\nde Astronom\\'{\\i}a, UNAM, M\\'exico} \\altaffiltext{2}{Osservatorio Astronomico, Padova,\nItalia} \\altaffiltext{3}{Dept. Physics and Astronomy, University of Alabama,\nTuscaloosa, USA}\n\n\n%%\\altaffiltext{1}{Just to see that the affiliation subscripts work OK}\n%% Note that the \\affil{} command is inside the argument of the\n%% \\author{} command and that a short version of the address should go\n%% here. More complicated author/address examples are discussed in the\n%% Author Guide (`rmuser.tex') and illustrated in the example document\n%% `rmtest.tex'\n%% The full postal addresses are specified here - they will be typeset\n%% at the end of the article. Here is also the place to put email\n%% addresses.\n%\\fulladdresses{\\item}\n%\\item D. Dultzin-Hacyan: Instituto de Astronom\\'\\i a,\n% UNAM, Ap.do Postal 70-264, M\\'exico D. F. 04510, M\\'exico ([email protected])\n%\\item P. Marziani: Osservatorio Astronomico di Padova,\n%Vicolo dell' Osservatorio 5, I--35122 Padova, Italia ([email protected])\n% \\item J.W. Sulentic: Dept of Physics And Atronomy, Univesity of Alabama,\n%Tuscaloosa, AL 35487 ([email protected]) }\n%% Note that the `\\fulladdresses' command defines a list-like\n%% environment, so each separate address must be preceded by the\n%% `\\item' command (here there is only one, since the authors share the\n%% same address).\n\n%% Title/author for running headers\n\\shortauthor{Dultzin-Hacyan et al.} \\shorttitle{BLR in AGN}\n%% These will automatically be converted to upper case in the current\n%% style.\n\n%% No more than 5 keywords, chosen from the standard list\n\\keywords{galaxies: active --- lines: profiles --- quasars: emission lines}\n\n\\abstract{We review constraints on models of the broad line region that are imposed by\nobservations of the emission lines in Active Galactic Nuclei. Comparison of high and\nlow ionization lines in sources with FWHM H$\\beta\\leq$4000 km s$^{-1}$ points toward low\nionization line emission produced in a flattened geometry (the accretion disk?) with an\nassociated high ionization wind. It remains unclear whether these results can be\nextended to all radio quiet AGN and particularly to radio loud AGN.}\n\n\\resumen{Revisamos las limitaciones que se pueden imponer a partir de las\nobservaciones, sobre los modelos de la estructura de las regiones que emiten las lineas\nanchas en los N\\'ucleos Activos de Galaxias. La comparaci\\'on entre las lineas de\nbaja- y alta ionizaci\\'on, sugiere que la emisi\\'on proviene, en parte, de una\ngeometr\\'{\\i}a fuertemente aplanada (el disco de acreci\\'on?) y, en parte, de un viento\nasociado, para una fracci\\'on importante de objetos radio callados que incluye a los\nnucleos Seyfert 1 de lineas angostas (NLSy1). Sin embargo, es incierto si estos\nresultados pueden extenderse a todos los Nucleos Activos radio callados y, sobre todo,\na los radio fuertes.}\n\n\n%% This command is so LaTeX won't stop on errors. I've put it in so\n%% you will still be able to compile the file even if you have lost\n%% the associated PS files of the figures.\n\\nonstopmode\n\\def\\habc{{\\sc{H}}$\\alpha_{\\rm BC}$\\/}\n\\def\\hbnc{{\\sc{H}}$\\beta_{\\rm NC}$\\/}\n\\def\\lya{{\\sc L}{\\rm y}$\\alpha$\\/}\n\\def\\fevii{{\\sc{Fe vii}}$\\lambda$6087\\/}\n\\def\\ovi{{\\sc{Ovi}}$\\lambda$1034\\/}\n\\def\\mgii{{\\rm Mg\\sc{ii}}$\\lambda$2800\\/}\n\\def\\niv{{\\sc{Niv]}}$\\lambda$1486\\/}\n\\def\\ciii{{\\sc{Ciii}]}$\\lambda$1909\\/}\n\\def\\oiiiopt{{\\sc{[Oiii]}}$\\lambda$4959,5007\\/}\n\\def\\o4363{{\\sc{[Oiii]}}$\\lambda$4363\\/}\n\\def\\oiiiuv{{\\sc{Oiii]}}$\\lambda$1663\\/}\n\\def\\heiiuv{{\\rm He\\sc{ii}}$\\lambda$1640}\n\\def\\heiiuvnc{He{\\sc{ii}}$\\lambda$1640$_{\\rm NC}$\\/}\n\\def\\feiiuv{\\rm Fe{\\sc ii}$_{\\rm UV}$\\/}\n\\def\\fei{\\rm Fe{\\sc i}}\n\\def\\feii{\\rm Fe{\\sc ii}}\n\\def\\feiii{\\rm Fe{\\sc iii}}\n\\def\\feiiopt{\\rm Fe{\\sc ii}$_{\\rm opt}$\\/}\n\\def\\feiiq{\\rm Fe{\\sc ii }$\\lambda$4570\\/}\n\\def\\heiiopt{\\rm He{\\sc{ii}$\\lambda$4686}\\/}\n\\def\\heii{He{\\sc{ii}}$\\lambda$4686\\/}\n\\def\\oiii{{\\sc [Oiii]}$\\lambda\\lambda$4959,5007}\n\\def\\oii{{\\sc [Oii]}$\\lambda$3727}\n\\def\\oiir{{\\sc Oi}$\\lambda$8442}\n\\def\\aliii{Al{\\sc iii}$\\lambda$1860}\n\\def\\siiii{Si{\\sc iii]}$\\lambda$1892}\n\\def\\iron{{[Fe/H]\\/}}\n\\def\\ironsol{{ [Fe/H]}$_{\\odot}$\\/}\n\\def\\feka{Fe~{\\sc K$\\alpha$\\/}}\n\\def\\apj{{\\it Ap. J.}}\n\\def\\aap{{\\it Astr. Astroph.}}\n\\def\\apjs{{\\em Ap. J. Suppl.}}\n\\def\\nat{{\\it Nature}}\n\\def\\b{$\\beta$}\n\\def\\kms{km~s$^{-1}$}\n\\def\\l{$\\lambda$}\n\\def\\araa{{\\it Annu. Rev. Astron. Astrophys. }}\n\\def\\aj{{\\it Astron. J. }}\n\\def\\mnras{{\\it MNRAS}}\n\\def\\aap{{\\it Astron. Astrophys.}}\n\\def\\apjl{{\\it Ap. J. Lett. }}\n\\def\\aaps{{\\it Astron. Astrophys. Suppl. }}\n\\def\\REF{\\par\\noindent\\hangindent 20pt}\n\\def\\ab{{\\sc Z}}\n\\def\\absol{{\\sc Z$_{\\odot}$\\/}}\n\\def\\msol{$\\rm M_\\odot$}\n\\def\\msoly{$ M_\\odot~yr^{-1}$}\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\simlt{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\rfe{R$_{\\rm FeII}$}\n\\def\\ai{A.I.($\\frac{1}{4}$)\\/}\n\\def\\aox{$\\alpha_{ox}$\\/}\n\\def\\gs{$\\Gamma_{\\rm soft}$}\n\\def\\gh{$\\Gamma_{\\rm hard}$}\n\\def\\G{$\\Gamma$}\n\\def\\ne{n$_{\\rm e}$\\/}\n\\def\\ergss{ergs s$^{-1}$}\n\\def\\simgt{\\lower.5ex\\hbox{\\gtsima}} % > over MMM\n\\def\\bv{{\\bf $\\bigvee$}\\/}\n\\def\\qu{{$\\lambda$ 1400}}\n\\def\\h{$h^{-1}$}\n\\def\\hii{{\\sc Hii\\/}}\n\\def\\hi{{\\sc Hi\\/}}\n\\def\\a{$\\alpha$}\n\\def\\ha{{\\sc H}$\\alpha$}\n\\def\\nv{{\\sc Nv}$\\lambda$1240}\n\\def\\civ{{\\sc{Civ}}$\\lambda$1549\\/}\n\\def\\civnc{{\\sc{Civ}}$\\lambda$1549$_{\\rm NC}$\\/}\n\\def\\civbc{{\\sc{Civ}}$\\lambda$1549$_{\\rm BC}$\\/}\n\\def\\cmsq{cm$^{-2}$\\/}\n\\def\\cm3{cm$^{-3}$\\/}\n\\def\\md{$\\dot{\\rm M}$}\n\\def\\rg{$\\rm R_{\\rm g}$}\n\\def\\hb{{\\sc{H}}$\\beta$\\/}\n\\def\\hg{{\\sc{H}}$\\gamma$\\/}\n\\def\\hbbc{{\\sc{H}}$\\beta_{\\rm BC}$\\/}\n\\begin{document}\n\\maketitle\n\\section{Introduction \\label{sec:intro}}\n\nThe Broad Line Region (BLR) in Active Galactic Nuclei (AGN) is unresolved with present\nday imaging detectors and it will remain so for the foreseeable future. This is why\n``one quasar spectrum is really worth a thousand images'' as stressed by Gary Ferland\nat this meeting. In response we would add that {\\em a thousand spectra are better than\none average spectrum}. Understanding the diversity in optical spectroscopic properties\nof AGN is the key to any realistic AGN modeling \\cite{bg92,smd}. The ideal to\nreconstruct the BLR velocity field from a single profile is not realistic \\cite{pen90}.\n\nDetermination of BLR structure and kinematics can be approached in two ways. It has\nbeen recognized for a long time that strong broad and narrow emission lines coming from\nboth high and low ionization species are present in Seyfert galaxies and quasars. This\nis considered a defining spectroscopic property of AGN. Restricting attention to broad\nlines: a) typical (i.e., strongest and most frequently observed) high ionization lines\n(HIL: ionization potential $\\simgt$ 50 eV) are \\civ\\ \\heii\\ and \\heiiuv\\ lines; while\nb) observed low ionization lines (LIL: ionization potential $\\simlt $ 20 eV) include\n\\hi\\ Balmer lines, \\feii\\ multiplets, \\mgii, and the Ca{\\sc ii}\\ IR triplet.\n\nThe first approach involves the study of line variability in response to continuum\nchanges. This approach has been pursued through a number of successful monitoring\ncampaigns using Reverberation Mapping (RM) techniques. RM requires a large amount of\ntelescope time and, consequently, has been achieved only for a handful of sources. RM\nconfirms that photoionization is the main heating process in the BLR and that a large\npart of the BLR is optically thick to the ionizing continuum (e. g. \\pcite{baldwin97}).\nRM studies have quantified a main difference between HIL and LIL; HIL respond to\ncontinuum changes with a time delay of a few days while the LIL respond with a delay of\ntens of days. This implies that the LIL are emitted at larger distance from the\ncontinuum source (\\pcite{ulr,kor95}. An exhaustive list of reference can be found in\n\\pcite{smd}). RM applied to line profiles suffers from uncertainty in our knowledge\nabout the physics of continuum and broad line formation, so that conflicting models can\nstill describe the same lag times \\cite{pen91,wanpet96}.\n\nThe second approach involves statistical analysis of large samples of line profiles\nwhich differ because of properties that may affect the BLR structure, for example\nsamples of radio quiet (RQ) and radio loud (RL) AGN. Statistical studies can be done\nfor a single line or by comparing lines sensible to different physical parameters (e.g.,\nstrongest LIL and HIL). The statistical approach, on which we will focus here, is more\nempirical and therefore requires a conceptual framework for interpretation. This\napproach is often criticized as relying on several assumptions including that the\nprofile variability does not influence profile shapes and that the non-simultaneity of\nthe observations of LIL and HIL are unimportant. Actually as the size of high quality\ndata samples grow these effects become less and less important.\n\n\\section{Baring the Broad Profiles \\label{bare}}\n\nThe collection of moderate resolution (\\l/$\\Delta$\\l $\\sim 10^3$) optical and UV\nspectra of good quality (S/N $\\simgt$ 20 in the continuum) has become possible only in\nrecent years thanks to the widespread use of CCD detectors and the unprecedented\nsensitivity and resolution of the UV spectrographs on board HST. For practical\npurposes, \\hi\\ \\hb\\ and \\civ can be considered representative of HIL and LIL\nrespectively. They are also the best lines for statistical studies because they permit\ncomparison in the same sources out to z=1.0. The linearity of response of the\ncurrently employed detectors has made possible a reliable correction for emission\nfeatures contaminating \\hb\\ and \\civ, which are: (1) \\feii\\ emission; significant\n\\feiiuv\\ emission contaminates the red wing of \\civ, and has been identified in I Zw 1\nby \\pcite{m96} and later confirmed by \\pcite{lao97}; (2) \\heii\\ emission for \\hb, and\n\\heiiuv\\ + \\oiiiuv\\ for \\civ; (3) \\oiii\\ for \\hb; (4) narrow component, present in\nseveral cases in both \\hb\\ and \\civ.\n\n\n\\civ\\ often shows a narrow core with FWHM $\\sim$ 1000-2000 \\kms, which is\nsystematically broader than the narrow component of \\hb\\ (\\hbnc). The separation\nbetween the broad component \\civbc\\ and the core component is often ambiguous. This\ncore however shows no shift with respect to the AGN rest frame \\cite{brot94}, no\nvariations \\cite{turla}, and correlates with \\oiii\\ prominence \\cite{franc92}. It can\ntherefore be ascribed to the NLR and considered as the narrow line component of \\civ\\\n(\\civnc). The different width between \\civnc\\ and \\hbbc\\ can be understood in terms of\ndensity stratification \\cite{sm99} without invoking an additional emitting region such\nas the so-called ``intermediate line region''. Even if \\civnc\\ fractional intensity is\nsmall ($\\sim$ 10\\%), and in some cases obviously absent, failure to account for \\civnc\\\nhas led to the erroneous conclusions that FWHM \\civbc\\ $>$ FWHM \\hbbc\\ and that the\n\\civ\\ peak shows no shift with respect to \\hb\\ \\cite{cb96}.\n\n\\section{A DIFFERENT BLR STRUCTURE IN RADIO LOUD AND RADIO QUIET AGN? \\label{struct}}\n\n\\scite{m96} made a comparison between \\civbc\\ and \\hbbc\\ for a sample of 52 AGN (31\nRL). They presented measures of radial velocity for the blue and red sides of \\hbbc\\\nand \\civbc\\ at 5 different values of fractional intensity which provide a quantitative\ndescription of the profiles. The reference frame was set by the measured velocity of\n\\oiii$\\lambda$5007$\\rm{\\AA}$ (IZw1 was the only exception). Standard profile parameters\nlike peak shift, FWHM, asymmetry index and curtosis can be extracted from these\nmeasures. Representative profiles constructed from the {\\em median values} of \\civbc\\\nand \\hbbc\\ $v_r$\\ are reproduced in the left panels of Fig. \\ref{fig:rq} and\n\\ref{fig:rl} for the radio quiet (RQ) and radio loud (RL) samples respectively.\n\\begin{figure}\n %\\begin{center}\n \\leavevmode\n \\includegraphics[width=\\columnwidth, height=8cm]{fig01.eps}\n% \\includegraphics[width=\\textwidth, height=10cm]{Fig01dd.eps}\n\\caption[]{Profiles of \\civbc\\ (solid lines) and \\hbbc\\ normalized to the same peak\nintensity and constructed from median values of the radial velocities measured on the\nblue and red sides of the profiles for the 21 RQ AGN of \\scite{m96} (left panel).\nEmission line profiles of \\civ\\ (middle panel) and \\hb\\ (right panel) of the prototype\nNLSy1 galaxy I Zw 1, adapted from \\scite{m96}. The thick and the dotted lines trace \\hb\\\nand \\oiii\\ after \\feiiopt\\ (dashed line) subtraction. \\label{fig:rq}}\n %\\end{center}\n\\end{figure}\n\n\\civbc\\ is broader than \\hbbc in both RQ and RL samples and it is {\\em almost always}\nblueshifted relative to \\hbbc. However Fig. \\ref{fig:rq} and Fig. \\ref{fig:rl} show\nsignificant differences between RQ and RL AGN. In RQ AGN, \\civbc\\ is significantly\nblueshifted with respect to the source rest frame while \\hbbc\\ is symmetric and\nunshifted. Contrarily in RL AGN \\civbc\\ is more symmetric, while \\hbbc\\ is shifted to\nthe red at peak intensity and redward asymmetric as well (the median profile\ncorresponds to the type AR,R according to \\pcite{sul89}). There are two important\nresults which are not displayed in the Figures: (i) in RQ AGN, \\civbc\\ blueshifts are\napparently uncorrelated with respect to any \\hbbc\\ line profile parameter and the\nlargest \\civ\\ blueshifts are associated with the lowest W(\\civ); (ii) in RL AGN, on the\ncontrary, \\civbc\\ and \\hbbc\\ line profile parameters (FWHM and peak shift) appear to be\ncorrelated. Asymmetry index of \\civbc\\ and \\hbbc, even if not correlated, shows a clear\ntrend toward asymmetries of the same kind (symmetric or redward asymmetric). These\nfindings on \\civbc\\ have been confirmed by other authors (\\pcite{wills95}, save the\ndifference in terminology and line profile decomposition) and especially by an analysis\nof archival HST/FOS observations which have become publicly available after 1995\n\\cite{sul20}.\n\nThe LIL and HIL emitting regions are apparently de-coupled in at least some RQ\nsources. The ``de-coupling'' is well seen in I Zw 1, the prototype Narrow Line Seyfert\n1 Galaxy (NLSy1; see Fig. \\ref{fig:rq}). The \\hb\\ profile is very narrow, slightly\nblueward asymmetric and unshifted with respect to the rest frame defined by 21 cm\nobservations, while the \\civ\\ profile is almost totally blueshifted. At least in the\ncase of I Zw 1 the distinction between LIL and HIL emitting regions appears to be\nobservationally established (it was actually suggested because of the difficulty to\nexplain the relative strengths of LIL and HIL emission using a photoionized ``single\ncloud;'' \\pcite{cs88}). There is a very important zeroth-order result here: since I Zw\n1 is a strong \\feiiuv\\ emitter, we have HIL \\civ\\ and LIL \\feiiuv\\ in the same\nrest-frame wavelength range. We see that \\feiiuv\\ is obviously unshifted (this can be\nvery well seen by shifting an \\feiiuv\\ template to the peak radial velocity of \\civ).\nThis result disproves models that see an (unknown) wavelength dependent mechanism\naccounting for the quasar broad line shifts relative to the quasar rest frame.\n\nRL AGN apparently mirror RQ AGN in a curious way: \\civbc\\ is more symmetric, while\n\\hbbc\\ shows preferentially redshifted profiles and increasingly redward asymmetries.\nLarge peak redshifts ($v_r \\simgt 1000$ \\kms, as in the case of OQ 208, Fig.\n\\ref{fig:rl}) are rarely observed; \\hbbc\\ peak shifts are usually small ($\\Delta\nv_r$/FWHM $\\ll$ 1, median profile of Fig. \\ref{fig:rl}). RL \\civbc\\ and \\hbbc\\ data\nleave open the possibility that both lines are emitted in the same region. \\civbc\\\nshows a red-wing (very evident in the latest, higher S/N spectra analyzed by\n\\scite{sul20}), which cannot be entirely accounted for by \\feiiuv emission. It is\ninteresting to note that superluminal sources with apparent radial velocity $\\beta_{\\rm\napp} \\sim 5-10$~ (whose radio axis is probably oriented close to the line of sight in\nthe sample of \\scite{m96} show very strong \\civ\\ redward asymmetries, low W(\\civ) and\nW(\\hbbc). This result suggests that redshifts are maximized in RL objects at\n``face-on'' orientation (we assume that any disk is perpendicular to the radio axis).\n\n\\section{NLSy1 NUCLEI ARE NOT A DISJOINT RQ POPULATION}\n\nNLSy1 are neither peculiar nor rare. The 8$^{th}$\\ edition of the \\scite{veron98}\ncatalogue includes 119 NLSy1 satisfying the defining criterion FWHM Balmer $\\simlt$\n2000 \\kms. They account for $\\approx 10$\\%\\ of all AGN in the same redshift and\nabsolute magnitude range. Attention toward NLSy1 remained dormant after their\nidentification as a particular class \\cite{op85} until it was discovered that they may\nrepresent $\\approx$1/3--1/2 of all soft X-ray selected Seyfert 1 sources (e. g.,\n\\pcite{grupe98}). NLSy1 are also apparently favored in AGN samples selected on the\nbasis of color. They account for 27\\%\\ of the RQ \\scite{bg92} sample, probably because\nof an optical continuum that is steeply rising toward the near UV. NLSy1 do not occupy\na disjoint region in parameter space. They are at an extremum in the FWHM(\\hb) vs.\n\\rfe\\ (=I(\\feii \\l 4570/I(\\hbbc)) and in the ``Eigenvector 1'' parameter spaces\n\\cite{bg92,bf99,smd}. Also, the soft X-ray spectral index \\gs\\ shows a continuous\ndistribution which includes NLSy1 at the high end \\cite{wang96,smd,sul20}.\n\n\\begin{figure}\n %\\begin{center}\n \\leavevmode\n \\includegraphics[width=\\columnwidth, height=8cm]{fig02.eps}\n% \\includegraphics[width=\\textwidth, height=10cm]{Fig01dd.eps}\n \\caption[]{Left panel: Profiles of \\civbc\\ (solid lines) and \\hbbc\\ normalized to the same\n peak intensity and constructed from median values of the radial velocities measured on\n the blue and red sides of the profiles for the 31 RL AGN of \\scite{m96}.\n Middle panel: \\hb\\ spectrum of OQ 208, showing a single, widely displaced \\hbbc\\ peak (adapted from \\pcite{m93}).\n Right panel: \\ha\\ profile of the prototype of ``wide-separation double peakers'' Arp 102B.\n Unpublished spectrum obtained at the 1.82 m telescope of the Asiago observatory on March 25, 1989.\n The thick solid line traces \\hbbc.}\n \\label{fig:rl}\n %\\end{center}\n\\end{figure}\n\nOrientation can easily explain much of the RQ phenomenology observed by \\scite{m96}. I\nZw 1 can be considered as an extremum with an accretion disk seen face-on\n(i$=0^\\circ$), and an outflowing wind observed along the disk axis. We can infer that\nthe opening angle of any \\civ\\ outflow is probably large (i. e., the wind is quasi\nspherical) because \\civ\\ profiles like I Zw 1 are rare. Other NLSy1 show low W(\\civ),\nand strong \\feiiopt, but do not always show large \\civ\\ blueshifts \\cite{rp97}.\nNonetheless, it is still possible that NLSy1 may be structurally different from other\nRQ AGN. If the soft X-ray excess of NLSy1 is due to high accretion rate, then a slim\naccretion disk is expected to form \\cite{abram88}. Line correlations presented in\n\\cite{sul20} appear to hold until FWHM(\\hb)$\\simlt$ 4000 \\kms. For FWHM$\\simgt$ 4000\n\\kms line parameters appear to be uncorrelated however it is still unclear it is at\npresent unclear because of the difficulty in measuring weak and broad \\feiiopt sources\nand/or because of a BLR structural difference. This limit may be related to the\npossibility of sustaining a particular disk structure and an HIL outflow. A second\nparameter, independent from orientation is needed to account for the FWHM(\\hbbc) vs\n\\rfe\\ vs \\gs\\ sequences (see \\pcite{smd,sul20} for a detailed discussion).\n\n\n\\section{Inferences on BLR Models for RQ AGN}\n\nModels developed almost independently of the data through the 80's and early 90's.\nThe situation has now changed because of three main developments: (1) the ``Eigenvector\n1'' correlations allow a systematic view of the change in optical emission line\nproperties for different classes of AGN \\cite{bg92,bf99,smd}; (2) the \\civ\\ - \\hb\\\ncomparison has yielded direct clues about the structure of the BLR \\cite{m96,sul20} and\n(3) data collected for RM projects provide a high-sampling description of line\nvariations. For instance, binary black hole scenarios \\cite{gask96} were recently\nchallenged by the failure to detect the radial velocity variations expected from\nprevious observations and model predictions \\cite{eracl97}.\n\nA model in which \\civ\\ is emitted by outflowing gas (e.g. a spherical wind) while\n\\hbbc\\ is emitted in a flattened distribution of gas (observed in a direction that\nminimizes velocity dispersion) such as an optically thick disk (obscuring the receding\nhalf of the \\civ\\ flow, \\pcite{liv97}) or at the wind base is immediately consistent\nwith the I Zw 1 data. The big question is whether the results for I Zw 1 can be\nstraightforwardly extended to other RQ AGN.\n\nAn accretion disk (AD) provides a high density and high column density medium for\n\\feii\\ production (e. g. \\pcite{dj92}), and possibly other low ionization lines such as\nCaII (e. g. \\pcite{dd99}). AD avoid conflict with the stringent restrictions on line\nprofile smoothness imposed by the first extremely high s/n Balmer line observations\n(\\pcite{arav97,arav98}) of -incidentally- two NLSy1. They place a lower limit of\n(10$^{7-8}$) on the number of discrete emitters needed to explain the observed profiles.\n\nWinds arise as a natural component of an AD model when the effects of radiative\nacceleration are properly taken into account \\cite{murray95,mc98} or when a\nhydromagnetic or hydrodynamic treatment is performed \\cite{bottorff97,williams99}. A\nsignature of radiative acceleration is provided by observations of ``double troughs'' in\n$\\approx \\frac{1}{5}$ of BAL QSOs i. e., of a hump in the absorption profiles of \\nv\\\nand \\civ\\ at the radial velocity difference between \\lya\\ and \\nv, 5900 \\kms. Such a\nfeature indicates that \\lya\\ photons are accelerating the BAL clouds (\\pcite{arav94},\nand references therein). Additional evidence is provided by the radial velocity\nseparation in the narrow absortion components of \\lya\\ and \\nv\\ which show the same\n$\\Delta v_r$\\ of the two doublet components of \\civ\\ (e. g. \\pcite{wampler91}).\n\n\\section{The Trouble With Bare Accretion Disks and Bipolar Flows}\n\nRelativistic Keplerian disks \\cite{ch89,sb93} may explain unusual profile shapes (e.g.\ndouble-peaked profiles of Balmer emission lines; \\pcite{eh94,sul95}). Uniform\naxisymmetric disk models produce double-peaked line profiles with the blue peak\nstronger than the red peak because of Doppler boosting, a feature that is not always\nobserved in these already rare profiles. To solve this problem, \\scite{sb95} and\n\\scite{eracl95}, proposed that the lines can originate in an eccentric (i.e.\nelliptical) disk. Simple disk illumination models can also produce single peaked LIL,\nprovided they are produced at large radii ($\\simgt 10^3$\\ gravitational radii) or that\nthe disk is observed at small inclination \\cite{dc90,rokaki92,sul98}. The first of these\nconditions may be met in all NLSy1 galaxies; both of them seem to be met in I Zw 1.\n\nAside from NLSy1 sources, there is general disagreement between observations and model\npredictions for externally illuminated Keplerian disks in a line shift-- asymmetry\nparameter space \\cite{sul90}. Only a minority ($\\simlt$ 10 \\%) of RL and a handful of\nRQ AGN show double peaked Balmer lines suggestive of a Keplerian velocity field\n\\cite{eh94,sul99}. Double-peakers (e. g. Arp 102B in Fig. \\ref{fig:rl},\nFWHM(\\hbbc)$\\simgt$10000 \\kms) cannot be like the classical cases because the line\nwidths are much smaller. The peaks often vary out of phase (Arp 102B: \\pcite{mp90}, 3C\n390.3: \\pcite{zheng91}). Double peaks (NGC 1097) \\cite{sb93,sb95} or one of the peaks\n(Pictor A) \\cite{sul95} sometimes appear quite suddenly. Profile variability studies of\nBalmer lines force us to introduce second order modifications to the basic scheme, such\nas: eccentric rings and precession \\cite{eracl95,sb97}, inhomogeneities such as\norbiting hot spots \\cite{zheng91}, and warps \\cite{bachev99}. Not even these {\\em\nepicycles} are always capable of explaining the observed variability patterns. Even if\nelliptical AD models do well in explaining the integrated profiles, they face important\ndifficulties in explaining variability patterns.\n\nA serious problem for AD models of emission lines is emerging from spectropolarimetric\nobservations. If profile broad line shapes are orientation dependent then, in\nprinciple, the profile shape in polarized light will depend on the distribution of the\nscatterers relative to the principal axis and to our line of sight. Early\nspectropolarimetric results showed a discrepancy with the simple disk +\nelectron-scattering-dominated atmosphere models, which predicted polarization\nperpendicular to the radio axis. The observed polarization is low, parallel to the disk\naxis, and shows no statistically significant wavelength dependence \\cite{anton88}.\nRecently \\scite{anton96} and \\scite{corbett98} included double-peakers in their\nsamples, and obtained troublesome results for disk emission models because the\npolarized \\ha\\ profiles are centrally peaked \\cite{corbett98}. They investigated the\ncase of disk emission where the scattering particles are located above and below an\nobscuring torus, along its poles. This ``polar scattering model'' is successful in\nexplaining the polarized profiles {\\em but not the position angle of the polarization\nvector}.\n\nThe same polarization studies indicate that the {\\em only} scenario that can account\nfor both the shapes of the scattered line profiles and the alignment of the optical\npolarization with the radio jet in wide separation double peakers like Arp 102B (Fig.\n\\ref{fig:rl}) involves a {\\em biconical} BLR within an obscuring torus. \\ha\\ photons\nemitted by clouds participating in a biconical flow are scattered towards the observer\nby dust or electrons in the inner wall of the surrounding torus. The particular case of\nbiconical outflow was first developed to reproduce observed profiles by\n\\scite{zheng90}. This model has been successfully applied to fit observed profiles in\ndouble-peaked objects \\cite{zheng91,sul95}.\n\nDouble peaked or single blueshifted peak LIL profiles fitted with bi-cone outflow\nmodels require that the receding part of the flow is also seen. Self-gravity may be\nimportant beyond $\\sim 1$ pc, and the disk may be advection-dominated and optically\nthin \\cite{liv96}. Recent work by \\scite{sh99} models the vertical structure of AD and\nthe origin of thermal winds above AD. They not only find that a wind powered by a\nthermal instability develops in all disks with certain opacity laws but also that in\ndisks dominated by bremsstrahlung radiation, a time-dependent inner hole develops below\na critical accretion rate. This scenario provides a natural explanation for transient\ndouble-peakers, such as NGC1097 \\cite{sb95,sb97}, but low accretion rate is a\nrequirement for {\\em both} advection dominated disks and hole formation.\n\n\\scite{sul95} explored the idea that the double-peaked emitters represent a\ngeometrical extremum where an outflow is viewed close to pole-on. However,\ndouble-peakers are associated with double-lobe radio-sources suggesting that the line\nof sight has a considerable inclination to the axis of the jets. The problem arises\n{\\em only} if the core (pc scale) jets is related to the much larger (100 kpc scale)\njets. There is both theoretical (e. g. \\pcite{valtonen99}) and observational evidence\nagainst this assumption.\n\n\\section{Emission from Clouds Illuminated by an Anisotropic Continuum}\n\nModels based on radiative acceleration of optically thick clouds with small volume\nfilling factor gained wide acceptance in the Eighties (\\pcite{om86} and references\ntherein; see also \\pcite{binette96}). However, problems with cloud confinements and\nstability \\cite{mathews90} have made them increasingly less frequently invoked to\nexplain observations.\n\nFirst RM studies on Balmer lines excluded radial, and favored orbital or chaotic\nmotions (e.g. \\pcite{kg91,kor95}). \\scite{goadw96} applied RM techniques to one of the\nmost extensively monitored objects: NGC 5548. They ruled out radial motions, and found\nthat the \\civ\\ line variations are broadly consistent with a spherical BLR geometry, in\nwhich clouds following randomly inclined circularly Keplerian orbits are illuminated by\nan anisotropic source of ionizing continuum. A RM result favoring Keplerian motion may\nbe approximately correct also for models in which the emitting gas is not bound, such\nas a wind, since most of the emission occurs near the base of the flow, when the\nvelocity is still close to the escape velocity which is similar to the Keplerian\nvelocity \\cite{mc98}.\n\n\\section{Is the disk + wind model applicable to all AGN?}\n\nEmission from a terminal flow can explain the recent observations of Goad et al. 1999\nwho reported that LIL (\\mgii + \\feiiuv) in NGC 3516 do not respond to continuum\nvariations which did induce detectable variability in the HIL (\\lya\\ and \\civ) lines.\nHydromagnetic wind models such as those developed by \\scite{emmering92} and\n\\scite{bottorff97} exhibit these basic properties. A two-zone wind provides another\nscenario for the different origins of LIL and HIL.\n\nTurning to the general population of RL AGN, the predominance of redshifts and redward\nasymmetric profiles is difficult to explain. Several lines of evidence suggest a\nsignificant role of gravitational redshift in RL AGN \\cite{corbin97} possibly related\nto a lower distance (in units of gravitational radii) between BLR and central black\nhole, which may be systematically more massive in RL than in RQ AGN. If this is the\ncase, then a double zone wind may be present also in RL AGN, since \\civbc\\ is still\nsystematically blueshifted with respect to \\hbbc. The ``correlation'' between \\civbc\\\nand \\hbbc\\ parameters could be due to the impossibility of maintaining a radial flow\nalong the disk axis, where a relativistic jet is instead propagating. This will make\nany HIL outflow possible only at lower latitudes over the disk plane, and therefore\nwill produce more similar \\hbbc\\ and \\civbc\\ profiles.\n\n\n\\section{CONCLUSION}\n\nWhile observations support emission from an accretion disk and an associated spherical\nwind in RQ AGN with FWHM(\\hbbc) $\\simlt$ 4000 \\kms, there is not enough observational\nsupport to warrant the same conclusion for RL AGN (and possibly RQ with FWHM$>$4000\n\\kms), although a disk + wind model is a viable possibility also in this case. Wide\nseparation double peakers (mostly RL) do not provide conclusive evidence in favor of\nLIL disk emission; rather, there is evidence against disk emission as well as against\nevery other reasonably simple scenario.\n\n\\acknowledgements DD-H acknowledges support through grant IN109698 from PAPIIT-UNAM. PM\nacknowledges financial support from MURST through grant Cofin 98-02-32, as well as\nhospitality and support from IA-UNAM. We also acknowledge consistent (cycles5-9 AR and\nGO) rejection of proposals to continue this work.\n\n%There are conflicting lines of evidences. It is unclear whether\n%wide separation double-peaks in Balmer lines are due to rotation\n%or to outflow. Their rarity and abnormal line width suggest that\n%they may be a peculiar class in a short-lived phase of their\n%evolution.\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format:\n%%\n%% \\bibitem[AUTHOR<YEAR>]{KEY}\n%%\n%% so that the \\cite{KEY}, etc. commands will work properly.\n%%\n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%%\n\\begin{thebibliography}{}\n%\\bibitem[Aretxaga et al.<1999>]{arex} Aretxaga, I., Joguet, B., Kunth, D., Melnick, J. \\& Terlevich, R. 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}
] |
[
{
"name": "astro-ph0002096.extracted_bib",
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}
] |
astro-ph0002097
|
A phase-reference study of the quasar pair 1038+528A,B
|
[
{
"author": "Mar\\'{\\i}a J. Rioja \\inst{1} \\inst{2}"
},
{
"author": "Richard W. Porcas\\inst{3} % \\fnmsep\\thanks{Just to show the usage % of the elements in the author field}"
}
] |
We present results from $\lambda$ 3.6~cm observations of the quasar pair \object{1038+528} A and B, made in 1995 using the VLBA together with the Effelsberg 100m telescope. We describe the use of a phase-referencing technique to measure the astrometric separation between the quasars. We also introduce a new data analysis method - "hybrid double mapping" - which preserves the relative astrometric information in a single VLBI hybrid map for close source pairs. We combine our measurements with those from three previous epochs, the earliest in 1981. Our new observations confirm the evolution within the structure of quasar B, previously proposed to explain the measured change in the relative separation of the pair. Our upper bound for any systematic proper motion between the mass centres of quasars A and B is 10~$\mu$as~yr$^{-1}$. This is set by the limited precision in defining the reference points in the quasars at different epochs and by possible instabilities of the source "core" locations. A separate analysis enables us to put more stringent upper limits to any core motions along the two source axes. \keywords{Instrumentation: interferometers -- Techniques: interferometric -- Astrometry -- Radio continuum: general }
|
[
{
"name": "rioja_17jan2000.tex",
"string": "% aa.dem\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% demonstration file\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n%\n\\usepackage{psfig}\n\n\\begin{document}\n\n \\thesaurus{03 % A&A Section 3: Extragalactic astronomy\n (03.09.2; % Instrumentation: interferometers,\n 03.20.2; % Techniques: interferometric, \n 05.01.1; % Astrometry,\n 13.18.2)} % Radio continuum: general.\n%\n \\title{A phase-reference study of the quasar pair 1038+528A,B }\n% \\title{A phase-reference study of the}\n% \\subtitle{quasar pair 1038+528A,B }\n\n% \\subtitle{I. Overviewing the $\\kappa$-mechanism}\n\n \\author{Mar\\'{\\i}a J. Rioja \n \\inst{1}\n \\inst{2}\n \\and\n Richard W. Porcas\\inst{3}\n% \\fnmsep\\thanks{Just to show the usage\n% of the elements in the author field}\n }\n\n \\offprints{Mar\\'{\\i}a J. Rioja}\n\n \\institute{Observatorio Astron\\'omico Nacional (OAN), Apdo. 1143, \n E-28800 Alcal\\'a de Henares, Spain \\\\\n email: [email protected]\n \\and\n Joint Institute for VLBI in Europe (JIVE), \n NL-7990 AA Dwingeloo, The Netherlands \\\\\n \\and\n Max-Planck Institut f\\\"ur Radioastronomie, Auf dem H\\\"ugel 69,\n D-53121 Bonn, Germany \\\\\n email: [email protected] \n% \\thanks{The university of heaven temporarily does not\n% accept e-mails}\n }\n\n \\date{Received 5 October, 1999; accepted XX }\n\n \\titlerunning{Relative Astrometry of 1038+528AB}\n \\authorrunning{Rioja \\& Porcas}\n\n \\maketitle\n \n \\begin{abstract}\n\nWe present results from $\\lambda$ 3.6~cm observations of the quasar pair \n\\object{1038+528} A and B, made in 1995 using the VLBA together with the \nEffelsberg 100m telescope. We describe the use of a phase-referencing \ntechnique to measure the astrometric separation between the quasars.\nWe also introduce a new data analysis method - \"hybrid double mapping\" - \nwhich preserves the relative astrometric information in a single VLBI \nhybrid map for close source pairs. We combine our measurements with those \nfrom three previous epochs, the earliest in 1981. \nOur new observations confirm the evolution within the structure of quasar B, \npreviously proposed to explain the measured change in the relative separation \nof the pair. Our upper bound for any systematic proper motion between the \nmass centres of quasars A and B is 10~$\\mu$as~yr$^{-1}$. This is set by the \nlimited precision in defining the reference points in the quasars at \ndifferent epochs and by possible instabilities of the source \"core\" locations.\nA separate analysis enables us to put more stringent upper limits to any \ncore motions along the two source axes.\n\n \\keywords{Instrumentation: interferometers --\n Techniques: interferometric --\n Astrometry --\n Radio continuum: general\n }\n \\end{abstract}\n\n%\n%________________________________________________________________\n\n\\section{Introduction}\n\nThe quasar pair 1038+528~A,B (Owen et al. \\cite{owen78}) \nconsists of two\nflat-spectrum radio sources, with redshifts 0.678 and 2.296 (Owen et\nal. \\cite{owen80}), separated on the sky by only 33\\arcsec. \nThis system provides a unique opportunity to carry out high precision, relative\nastrometric studies using the full\nprecision of VLBI relative phase measurements, \nsince most sources of phase errors are common for the 2 sources\n(Marcaide \\& Shapiro \\cite{marca83}).\n\n VLBI studies of the mas-scale structure of flat-spectrum quasars\nshow that they typically have ``core-jet'' morphologies, consisting of a highly\ncompact feature (the ``core'') located at the base of an extended linear feature \nor line of lower brightness components (the ``jet'').\nBoth 1038+528 A and B exhibit such structures.\nIn standard models of extragalactic radio sources, these radio-emitting \nfeatures\narise from a collimated beam of plasma which is ejected with a highly \nrelativistic bulk velocity from a region close to a central massive object \nsuch as a black hole (see eg. Blandford \\& K\\\"onigl \\cite{blandford86}).\nWhilst jet features may correspond to shocks in the moving plasma, and \ncan give rise to the observed ``superluminal'' component motions in some \nsources (Porcas \\cite{porcas87}),\nthe ``core'' emission is thought to arise from a more-or-less permanent location close to\nthe origin of the beam, where the ambient conditions correspond to a transition\nfrom optically thick to optically thin emission at the observed frequency.\nAlthough the ``core'' position may thus be frequency-dependent, for a fixed\nobserving frequency\nthe core should provide a stable marker, anchored to the central mass of\nthe quasar, whose location can be used to define a precise position for\nthe object as a whole.\nAlthough short time-scale variations in physical conditions may cause\nsmall changes in the ``core'' location, over long time-scales it may be\nused to track any systematic proper motion of the quasar.\n\nThe results from a near decade-long VLBI monitoring program on 1038+52A,B at\n$\\lambda$ 3.6 and 13~cm (from 1981.2 to 1990.5) \nare reported by Rioja et al. (\\cite{rioja97}), whose main conclusions \ncan be summarized as follows:\n\n\\begin{enumerate}\n\n\\item There is no evidence of any relative proper motion between the \n quasars A and B. The uncertainties in the astrometric parameters \n result in an upper bound to any systematic relative \n motion between the cores of 10~$\\mu$as~yr$^{-1}$, consistent\n with zero.\n\n\\item A compact feature within the jet of quasar B, chosen as the \n reference point for the structure, expands away from the core at \n a steady, slow rate of $\\sim~18~\\pm~5~\\mu$as~yr$^{-1}$, corresponding \n to v=$(0.8~\\pm~0.2)~h^{-1}$~c for a Hubble constant,\n H$_0$ = 100~h~km~s$^{-1}$~Mpc$^{-1}$; q$_0=0.5$. These values are used \n here throughout.\n\n\\item The accuracy of the relative separation measurement is limited by \n noise and source structure, with estimated precisions of about \n $50~\\mu$as at $\\lambda$ 3.6~cm at any epoch.\n\n\\item Confirmation of the consistently large offset (about 0.7 mas) between\n the positions of the peak of brightness (``core'') at $\\lambda$ 3.6 \n and 13~cm in quasar A.\n\n\\end{enumerate}\n\nNew VLBI observations of this pair were made in November 1995 (1995.9) \nat $\\lambda$ 2, 3.6 and 13~cm. In this paper we report on results from \nour analysis of the 3.6~cm observations and investigate the temporal \nevolution of the source structures and relative separation from all \nfour epochs spanning $\\sim 15$ years. \nInvestigations of frequency-dependent source structure have also been made \nfrom a comparison of the astrometric measurements\nof the separations between A and B at all 3 wavelengths observed in 1995;\nthese will be presented elsewhere (Rioja \\& Porcas in preparation).\n\nOur new observations are described in Sect. 2. In Sect. 3 we describe\nthe data reduction and mapping techniques used, and in Sect. 4 an analysis\nof the measurements in the maps.\nIn Sect. 5 we compare the astrometric results from these observations\nwith those from previous epochs and analyse the changes in \nseparation. Conclusions are presented in Sect. 6.\n\n%__________________________________________________________________\n\n\\section{Observations}\n\nThe pair of radio sources 1038+528 A and B was observed with the\nNRAO Very Long Baseline Array (VLBA) on November 10, 1995,\nfor a total of 13 hours, alternating every 13 minutes between\nobservations in dual 3.6/13~cm mode and observations at 2~cm. The\n100m telescope at Effelsberg was also included in the array for the\n3.6/13~cm scans. The primary beamwidths of all the antennas were\nsufficiently large that both sources could be observed simultaneously\nat all wavelengths. Each 10 minute observation of 1038+52A,B was\npreceded by a 3 minute observation of the compact calibration source\n\\object{0917+624}, to monitor the behaviour of the array.\n\nAll stations used VLBA terminals to record an aggregate \nof 64 MHz bandwidth for each scan, using 1-bit sampling, subdivided into\n8 channels (mode 128-8-1). For the dual 3.6/13~cm scans, four 8-MHz channels\nwere recorded for each band (2254.5--2286.5 MHz; 8404.5--8436.5 MHz), \nusing \nRHC polarisation. At 2~cm, eight 8-MHz channels (15\\,331.5--15\\,395.5 MHz)\nwere recorded in LHC polarisation.\n\nThe correlation was made at the VLBA correlator in Socorro (New Mexico).\nAs for previous epochs, two separate ``passes'' were needed, using different \nfield centres for the two sources, to recover data\nfor both the A and B quasars from the single observation. \nOutput data sets were generated for the two sources, consisting of the\nvisibility functions averaged to 2 s, with samples every 1 MHz in frequency\nacross the bands. \n\n\\section{Data reduction} \n\nWe used the NRAO AIPS package for the data reduction. \nWe applied standard fringe-fitting, amplitude and phase (self-) calibration \ntechniques and produced hybrid maps of each quasar. \nThe astrometric analysis was done using two different mapping methods: \na ``standard'' phase-referencing approach, transferring phase solutions\nfrom one quasar to the other\n(see e.g. Alef \\cite{alef88}; Beasley \\& Conway \\cite{beasley95}) and a \nnovel mapping method for astrometry of close pairs\nof sources, hybrid double mapping (HDM) (Porcas \\& Rioja \\cite{porcas96}). \nBoth routes preserve the signature of the relative separation of the source \npair present in the calibrated phases. These analysis paths are described \nin Sects. 3.1 to 3.3 below. \n\n\\subsection{Hybrid mapping in AIPS} \n\nWe applied standard VLBI hybrid mapping\ntechniques in AIPS for the analysis of the observations of both\nquasars A and B. We used the\ninformation on system temperature, gain curves and telescope gains measured at\nthe individual array elements, to calibrate the raw correlation\ncoefficients. \nWe used the AIPS task FRING to estimate residual antenna-based phases\nand phase derivatives (delay and rate) at intervals of a few minutes.\nIt is important to realise that FRING is a global self-calibration\nalgorithm, and performs an initial phase self-calibration also. We ran\nFRING on the A quasar data set, with a point-source input model.\n\nAnticipating our phase-referencing scheme (Sect. 3.2) we applied the antenna\nphase, delay and rate solutions from A to both the A and B data sets, and\naveraged them in time to 60 s, and over the total observed bandwidth of 32 MHz.\nAfter suitable editing of the data, we made hybrid maps of both quasars,\nusing a number of iterations of a cycle including the mapping task MX and\nfurther phase self-calibration with CALIB.\n\nFig.~\\ref{fig1}a and b show the hybrid maps for both sources at 3.6~cm \nin 1995.9. \nThe maps are made using uniform weighting of the visibilities, a map\ncell size of 0.15 mas and a circular CLEAN restoring beam of 0.5 mas\n(these same mapping parameters are used throughout this work).\nThe ``dirty'' beam has a central peak of 0.57 x 0.47 mas in PA -29\\degr\n(PA = position angle, defined starting at North, increasing through East).\nThe root-mean-square (rms) levels in the A and B maps, in regions away \nfrom the source structures (estimated using AIPS task IMSTAT) are 1.0 and \n0.12 mJy/beam respectively, an indication that dynamic range considerations \ndominate over thermal noise in determining the map noise levels. \n\n%%% FIGURE 1\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig1a.ps,width=6.cm}}\n\\put (-150,150) {\\bf {a)}}\n{\\psfig{figure=fig1b.ps,width=6.cm}}\n\\put (-150,150) {\\bf {b)}}\n}\n\\caption{VLBI hybrid maps of 1038+528 at 3.6~cm. Uniform weighting, \nCLEAN beam 0.5 x 0.5 mas, pixel size 0.15 mas, tick interval 1 mas.\n{\\bf a} Quasar A. Contours at 3,6,12,24... mJy/beam.\n{\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy/beam.\n\\label{fig1}} \n\\end{figure*}\n\n\\subsection{Phase referencing in AIPS}\n\nIn order to make an astrometric estimate of the separation between\nquasars A and B at this 4th epoch, we first used a \"conventional\" \nphase-reference\ntechnique to make maps of the quasars which preserve the relative phase\ninformation.\nIn practice this consists of using the antenna-based residual terms \nderived from the analysis of the data of one ``reference'' source (A), \nto calibrate the data from simultaneous observations of the other \"target\" \nsource (B).\nThe reference quasar source structure must first \nbe estimated from a hybrid map, and then fed back into\nthe phase self-calibration process to produce estimates of the antenna-based \nresiduals, free from contamination by source structure. \n\nPhase referencing techniques work under the assumption that the\nangular separation between the reference and target sources is smaller\nthan the isoplanatic patch size (i.e. the effects of unmodelled perturbations,\nintroduced by the propagation medium,\non the observed phases of both sources are not very different) and that \nany instrumental terms are common. Geometric errors in the correlator model\nmust also be negligible.\n\nAssuming that the antenna residuals have been ``cleanly'' estimated using the\nreference source data, the calibrated phases of the target \nsource should be free from the errors mentioned above, but still retain the\ndesired signature of the source structure and relative position\ncontributions. The Fourier Transformation of the calibrated visibility\nfunction of the target source produces a ``phase referenced'' map. The\noffset of the brightness distribution from the centre of this map reflects\nany error in the assumed relative separation in the correlator model.\nIf the reference source has a true ``point'' structure and is at the\ncentre of its hybrid map, this offset will be equal to the error;\nmore generally, one should also measure the offset of a\nreference point in the reference source map, and estimate the\nerror in the source separation used in the correlator model from the difference\nbetween the target and reference source offsets.\n\nIn general, the success of the phase-referencing technique is critically\ndependent on the angular separation of the target and reference sources.\nSimultaneous observation of the sources, as was possible here, significantly \nsimplifies the procedure, eliminates the need for temporal interpolation,\nand reduces the propagation of errors introduced in the\nanalysis. While random errors increase the noise level in the phase\nreferenced map, systematic errors may bias the estimated angular\nseparation.\n\nFor our implementation of phase-referencing using AIPS, we chose\nto re-FRING the (calibrated) A data set, using our hybrid map of quasar \nA as an input model, and applied the adjustments to the antenna phase, \ndelay and rate solutions to both the A and B data sets before re-averaging. \nWe then made maps of both A and B using MX, performing no further phase \nself-calibration. These are our ``phase-reference astrometry'' (PRA) \nmaps (shown in Fig.~\\ref{fig2}a and b) on which we performed\nastrometric measurements (see Sect. 4.2). Although the rms noise levels \nin the PRA maps are slightly higher than in the corresponding hybrid maps \n(2.0~mJy~beam$^{-1}$ for A and 0.24~mJy~beam$^{-1}$ for B),\nour procedure ensures that the A and B\nvisibility functions from which they are derived have been calibrated \nidentically. \n\n%%% FIGURE 2\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig2a.ps,width=6.cm}}\n\\put (-150,150) {\\bf {a)}}\n\\put (-84.5,88.5) {\\bf {+}}\n{\\psfig{figure=fig2b.ps,width=6.cm}}\n\\put (-150,150) {\\bf {b)}}\n\\put (-85,88) {\\bf {+}}\n}\n\\caption{VLBI phase-reference astrometry maps. Map parameters as in Fig. 1.\nAstrometry reference points are indicated with a cross.\n{\\bf a} Quasar A. Contours at 3.5,7,14,28... mJy~beam$^{-1}$.\n{\\bf b} Quasar B. Contours at 1.5,3,6,12... mJy~beam$^{-1}$.\n\\label{fig2}} \n\\end{figure*}\n\n\n\\subsection{New mapping method for astrometry of close source pairs} \n\nWhile the conventional phase-referencing approach worked well for our\nNovember 1995 observations of 1038+52A and B, the method relies on\nmaking a good estimate of the antenna residuals from just one of the \nsources - the reference. We have devised an alternative method which\nextends the standard VLBI self-calibration procedure to work on both\nsources together, for cases where they have been observed simultaneously,\nand when either could be used as the reference (see Appendix A).\n\nThe basis of the new method is to recognise that, since the visibility \nfunctions for both sources are corrupted by the same (antenna-based) \nphase and phase derivative errors, the sum of the two visibilities also \nsuffers the same errors. We form the point-by-point sum of the two data \nsets, creating a new one which represents the visibility function of a \n``compound source'' consisting of a superposition of the two structures, \ncorrupted by the common antenna phase errors.\nIf the source separation is close enough, the (summed) data as\na function of the (averaged) uv-coordinates can be\nFourier Transformed to form a map of the\ncompound source structure, and (iterative) self-calibration in FRING or CALIB\nyields the antenna-based residuals. The advantage of this approach is that\nthe antenna-based residuals are determined using both source structures\nsimultaneously, and may thus reduce the chance that reference source structural\nphase terms contaminate the residuals. We term this process ``Hybrid Double\nMapping'' (HDM); a detailed description is given in Porcas \\& Rioja \n(\\cite{porcas96}).\n\nIt is convenient to shift the source position in one of the data\nsets (by introducing artificial phase corrections)\nprior to the combination into a compound-source data set, to avoid \nsuperposition of the images in the map. The phase self-calibration \nsteps which are then applied to the combined data set are \nidentical to the case of a single source. In HDM the information\non the angular separation between the sources is preserved in the \nprocess of self-calibration of the combined visibilities, and can be measured\ndirectly from the compound-image map;\nthe relative positions between the individual source images in the \ncompound map, taken together with any artificial position shift introduced,\ngive the error in the assumed angular separation in the correlator model. \nIn this approach one must be careful to use the same number of visibility\nmeasurements in each time interval from the two data sets, in order to avoid\nthe predominance of data from a particular source. \n\nFig.~\\ref{fig3} shows the HDM map of quasars A and B in 1995.9 at \n$\\lambda$ 3.6~cm; \nthe B source is artificially offset by -4 mas in declination.\nThe rms noise in the map is 0.82~mJy~beam$^{-1}$ - higher than that in \nthe hybrid map of B but lower than in that of A.\n\n\n%%%FIGURE 3\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig3.ps,width=6.cm}}\n}\n\\caption{HDM map of 1038+52 (A+B). Map parameters as in Fig. 1. \nQuasar B has been offset by -4.0 mas in\ndeclination. Contours at 3,6,12,24... mJy~beam$^{-1}$. \n\\label{fig3}} \n\\end{figure}\n\n\n\n\\section{Analysis of the maps} \n\n\\subsection{Source structures} \n\nThe 1995.9 hybrid maps of quasars A and B at $\\lambda$ 3.6~cm \n(Fig.~\\ref{fig1}) show the core-jet structures typical of quasars at \nmas scales. They may be compared with maps from previous epochs given \nin Rioja et al. (\\cite{rioja97}). \nThe structure of A in the new map shows no major changes with respect \nto previous epochs. There is a prominent peak at the SW end of the\nstructure (the ``core'') and a jet extending in PA 15--25\\degr\n~containing at least two ``knot'' components (k1 and k2).\n\nThe new map of B at 3.6~cm is qualitatively similar to\nthose from previous epochs. It shows 2 point-like components separated\nby just under 2 mas in PA 127\\degr.\nSpectral arguments support the identification of\nthe NW component as a ``core'' (Marcaide \\& Shapiro \\cite{marca84}); \nthe SE component, corresponding to a knot in the jet, has been used as \na reference component in previous astrometric studies.\nThe separation between these 2 components in 1995.9 has increased, \ncontinuing the expansion along the axis of the source, as discovered \nfrom previous epochs of observations at this wavelength (Rioja et al. \n\\cite{rioja97}).\nThere is no trace of the third, extreme SE component, seen in maps\nof this source at 13~cm. This feature is evidently of lower surface\nbrightness at 3.6~cm and is resolved out at the resolution of these \nobservations.\n\nWe used AIPS task IMSTAT to estimate total flux densities for quasars A and\nB (within windows surrounding the sources in the hybrid maps). The values \nare given in Table~\\ref{tab1}.\nTable~\\ref{tab1} also lists the fluxes and relative positions of the \nmost prominent features in the maps of A and B, obtained using task JMFIT to\nfind parameters of elliptical Gaussian functions which best\nfit the various source sub-components. The formal errors from the fits,\nhowever, do not give realisitic values for the parameter uncertainties.\nThe distribution of flux between the core and k1 in quasar A, and their\nrelative separation, are quite uncertain, for example. \n\n%%%TABLE 1\n\\begin{table*}\n\\caption {Parameters derived from the Hybrid Maps of 1038+528 A and B.} \n\n\\vspace*{0.25cm}\n\n\\begin{center}\n\\begin{tabular} {|c|c|c|c|c|c|c|c|c|c|} \\hline\n & S-tot & & S-pk & S-int & maj.& min. & PA & sep. & PA \\\\\n & (mJy) & &(mJy/b) & (mJy) & (mas) & (mas) & (deg) & (mas) & (deg) \\\\\n\\hline\n1038+528 A & 603.0 & core & 301.6 & 355.3 & 0.28 & 0.12 & 3 & - & - \\\\\n & & k1 & 171.8 & 235.5 & 0.42 & 0.16 & 13 & 0.639 & 15.1 \\\\\n & & k2 & 9.3 & 14.0 & - & - & - & 1.796 & 24.8 \\\\\n&&&&&&&&& \\\\\n1038+528 B & 86.5 & core & 33.5 & 40.9 & 0.32 & 0.11 & 132 & - & - \\\\\n & & ref & 24.6 & 34.4 & 0.39 & 0.24 & 123 & 1.869 & 127.1 \\\\ \n\\hline \\hline\n\\end{tabular}\n\\end {center}\n\\label{tab1}\n\\end{table*}\n\n\n\\subsection{Estimating positions of reference features} \n\nThe astrometric measurement of a separation between two non-point sources\nmust always refer to the measured positions of reference points within \nmaps (or other representations) of the source structures. \nThe selection of suitable reference points is crucial in monitoring\nprograms, where the results from the analysis of a multi-epoch \nseries of observations are compared. \nIdeally, a reference point should correspond to the peak of\na strong, unresolved component, which is well separated from\nother radio emission within the source structure.\n\nFor the 1995.9 epoch observations of 1038+528 A,B we selected the same \nreference features as those used for the analyses of previous observing \nepochs. These are the ''core'' component for quasar A, and the prominent \nSE component for quasar B.\nThese features are labelled with a cross in Fig.~\\ref{fig2}a and b.\nThe core of A is indeed strong and compact, but has the disadvantage\nthat it merges with knot k1.\nAlthough the SE component of B is no longer the strongest feature at 3.6~cm,\nit has always been strong at both 3.6 and 13~cm wavelengths,\nis reasonably compact and is easily distinguishable\nin maps made at longer wavelengths, thus facilitating spectral studies.\nOur astrometric analysis refers to the measured positions of the peaks\nof these components in A and B. We used the AIPS task MAXFIT to measure \nthe position of these peaks in the PRA and HDM maps.\nMAXFIT defines the location of a peak in a given map region by fitting \na quadratic function to the peak pixel value and those of the adjacent pixels.\nA comparison of this method of defining the peak position with that used\nfor earlier epochs is described in the next section. \n\n\\subsection{Position error analysis} \n\nAn analysis of errors presented in Rioja et al. (\\cite{rioja97}) shows \nthat the dominant uncertainty in the astrometric measurements of the \nseparation between this close pair of quasars comes from the limited \nreproducibility of the reference point positions in the VLBI maps, \nfrom epoch to epoch. The magnitude of this effect\nis hard to quantify, however, since it depends on the nature of the\nsource brightness distribution surrounding the reference point, and\nthe method used to define the position of the peak, in addition\nto the resolution of the array and the signal-to-noise\nratio of the peak in the map.\n\nA rough estimate of the error due solely to finite signal-to-noise in\nthe maps is given by dividing the beam size by the ratio of the\ncomponent peak to the rms noise level in the maps (see e.g. \nThompson et al. \\cite{thompson86}). \nThis yields values of 3.3, 3.5 and 1.4~$\\mu$as for the A and B PRA \nmaps and the HDM map. These may be taken to represent lower limits to \nthe reference point position errors; realistic errors will be larger,\nand will depend on the nature of the reference features \nand the manner in which the position is estimated.\n\nIt is important to choose a definition of the reference point position \nsuch that it can be reproduced reliably from epoch to epoch, and is as \nindependent as possible from the parameters used in making the map \n(e.g. cell size and beam width).\nThe AIPS task JMFIT can be used to fit an elliptical Gaussian to a component\nin a CLEAN map, for example. However, the position of the peak of the \nGaussian depends on how asymmetric the component brightness distribution \nis, and the area of the map to which the fit is restricted. MAXFIT fits \njust to the local maximum around the peak map value, and is thus less \nsensitive to the rest of the distribution.\n\nWe have attempted to quantify some limits to reproducibility arising from \nthe use of MAXFIT for defining the peak position in CLEAN maps.\nWe investigated the effect of changing the true position of a point-like\nsource with respect to the pixel sampling (here 3.3 pixels per beam) \nby offsetting the source position in 10 increments of 1/10 of a pixel \nin the visibility domain, mapping and CLEANing the new data sets, and \nestimating the new positions in the CLEAN maps using MAXFIT. The\nmaximum discrepancy found between the values of the artificial offset\nand the shift derived by MAXFIT was 1/20 of a pixel.\nThis corresponds to 8~$\\mu$as in our 3.6~cm maps.\n\nFor the analysis of previous observing epochs, the reference points\nwere defined to be the centroid of the most prominent delta functions \nfrom which the CLEAN source map was derived (Rioja et al. \\cite{rioja97}).\nWe examined possible systematic differences resulting from these\ndifferent definitions of reference points.\nOne might expect the largest discrepancies to arise when the underlying\nsource structure near the reference point is asymmetric, as in quasar A.\nWe investigated such differences by determining ``centroid'' positions for\nboth A and B reference components, using various criteria for excluding\nclean components from the calculation; this included the ``25 percent\nof the value at the peak'' threshold used for earlier epochs.\nFor A the difference between this centroid position and the MAXFIT\nvalue was 0.12 pixel (18~$\\mu$as). For B the difference was less\nthan 0.1 pixel.\nThese are probably the largest potential sources of error arising from using\ndifferent methodologies at different epochs.\n\nOur use of two different mapping procedures - phase-reference mapping\nand HDM - also gives some insight into the size of position errors resulting\nfrom standard CLEAN + phase self-cal mapping algorithms.\nThe differences between the separation estimates from the PRA maps and the\nHDM map are 27 and 28~$\\mu$as in RA and Dec respectively.\nThis would suggest that differences in the positions of peaks in \nmaps reconstructed in different ways may vary at the 14~$\\mu$as level.\n\nAfter considering the various possible effects which can limit the\naccuracy of postion estimates, we adopt a ``conservative'' value for \nthe error in estimating the peak position in our $\\lambda$ 3.6~cm maps,\nembracing all the effects detailed above, of $18~\\mu$as\n(this corresponds to a thirtieth of the CLEAN beam).\nThe associated estimated error for a separation measurement between\nthe two sources is $25~\\mu$as.\n\n\n\\subsection{Astrometry results} \n\nTable~\\ref{tab2} lists the results of our astrometric measurements of \nreference point positions in the maps.\nThey are presented as changes in measured separation between the \nreference points in A and B in 1995.9, with respect to their separation \nin 1981.3. \nThe values given from the phase-reference technique correspond to the \ndifference between the A and B reference feature position offsets in \ntheir respective PRA map. The values derived from HDM have been corrected \nfor the artificial offset introduced before adding the A and B source \nvisibilities.\n\n%%%TABLE 2\n\n\\begin{table}\n\\caption{Change in the separation between quasars A and B in 1995.9\nwith respect to 1981.2, estimated using standard phase referencing \n(PRA) and hybrid double mapping (HDM) techniques.}\n\\begin{center}\n\n\\vspace*{0.25cm}\n\n\\begin{tabular} {|c| c| c|} \\hline \n$\\Delta(\\Delta \\alpha)$ $\\cos \\delta_A$ & $\\Delta(\\Delta \\delta)$ & Method \\\\ \n$[\\mu$as$]$ & $[\\mu$as$]$ & \\\\ \\hline \\hline\n% (%) = Without Correlator position offset: RA -159muas; DEC 74 muas\n% 11 & 175 & Phase Referencing \\\\\n -148 & 249 & PRA \\\\\n% -16 & 203 & HDM$^1$ \\\\\n% -175 & 277 & HDM$^1$ \\\\ \\hline \\hline\n -175 & 277 & HDM \\\\ \\hline \\hline\n% -7.5 & 204 & HDM$^2$ \\\\\n% -167 & 278 & HDM$^2$ \\\\\n% -9 & 180 & HDM$^3$ \\\\ \\hline\n% -168 & 254 & HDM$^3$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab2}\n\\end{table}\n\n\nAll these values have been corrected for a small error in the AIPS calculation\nof the u,v coordinates in the frequency-averaged data set.\n(Distances measured within the maps must be adjusted\nby a small correction factor of\n$1 - \\Delta \\nu \\ast (2~\\nu)^{-1} = 0.998$.) \n \\\\\n\nTable~\\ref{tab3} lists the coordinates of the reference source (A) adopted in\nthe analysis and the measured coordinate separation between quasars A\nand B in 1995.9.\n\n%%%TABLE 3\n\n\\begin{table*}\n\\caption{{\\it Fixed} source coordinates used for quasar A\nin the astrometric analysis (these coordinates correspond to GSFC global\nsolution GLB831 (Chopo Ma, priv. comm.)), and\nseparation between quasars A and B measured in 1995.9.}\n\n\\begin{center}\n\n\\vspace*{0.25cm}\n\n\\begin{tabular} { |l| r| r|} \\hline\n{\\bf Coordinates} & {\\bf RA} (J2000) \\hspace*{0.5cm} & {\\bf DEC} (J2000) \\hspace*{0.5cm}\n \\\\ \\hline \\hline\n{\\it Reference Source {\\bf (A)}} & 10$^h$ 41$^m$ 46\\fs781613 \n\\hspace*{0.05cm} & 52$^0$ 33\\arcmin 28\\farcs23373 \\hspace*{0.05cm} \\\\ \\hline \n{\\it Relative Sep. {\\bf (B-A)}} & $2\\fs1160588 $ \n& $27\\farcs376325$ \\\\\n{\\it Estimated error {\\bf (B-A)}} & $\\pm 0\\fs0000027$ & $ \\pm 0\\farcs000025$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\label{tab3}\n\\end{table*}\n\n\n\\section{Comparison of astrometry at all 4 epochs} \n\nIn this section we make a comparison of the astrometric\nmeasurements from the series of 4 epochs of observations.\nAny increase of the temporal baseline in the program of monitoring the \nseparation between A and B should result in a more precise \nidentification of any systematic trends,\nwith an improved elimination of random contributions.\nIn Sect. 5.1 we justify comparing\nthe astrometric values measured at the various epochs, even\nthough non-identical observing, post-processing and analysis\nprocedures were involved.\nIn Sect. 5.2 we present the astrometric results from the 4 epochs.\nIn Sects. 5.3, 5.4, 5.5 and 5.6 we present various analyses of these\nresults, and attempt to quantify, or put upper-limits to,\nproper motions within and between the A and B quasars.\n\n\n\\subsection{Comparison between the techniques used at different epochs}\n\nBefore attempting a comparison of the astrometric results from \nthe 4 observing epochs, we need to\nshow that any bias in the astrometric estimates introduced by the\nuse of different procedures is small compared with other errors in\nthe measurements for the individual epochs.\nThe consistency between the results from previous epochs of observations \nhas been exhaustively tested (Marcaide et al. \\cite{marca94}; \nRioja et al. \\cite{rioja97}).\nWe outline here the largest changes involved in the fourth epoch, 1995.9,\nwith respect to previous ones:\n\n\\begin{enumerate}\n\n\\item The observing array and frequency set-up used in the fourth epoch\nwas different from previous epochs of observations \n(frequency range 8404.5 to 8436.5 MHz instead of 8402.99 to 8430.99 MHz\nat first 3 epochs). This results in a different coverage of the {\\it UV} \nplane, leading to changes in the reconstruction of the source images. \nInvestigations of such effects by Marcaide et al. (\\cite{marca94}) show that\nthe effect on the astrometric anaylsis is only a few $\\mu$as. \nIt is important to note that the observations at all 4 epochs have\ncomparable resolutions and sample the same range of structural scales\nin the sources.\n\n\\item The processing of the fourth epoch was done using the VLBA correlator,\nwhich uses a theoretical model derived from CALC 8.2; we used AIPS to\nanalyse the data with visibility phases residual to that model.\nFor previous epochs the correlation was done at the MPIfR (Bonn) MK3\ncorrelator, and an analysis of the data using total phases was made\nwith VLBI3 (Robertson \\cite{robertson75}).\nThe differences between CALC 8.2 and the one implemented in VLBI3 \npropagate into changes of only 1-2~$\\mu$as in the astrometric analysis\nof the 1038+528 A-B separation (Rioja \\cite{rioja93}, Rioja et al. \n\\cite{rioja97}). \nThis is because any such differences are ``diluted'' by the source \nseparation expressed in radians - \n$10^{-4}$ in the case of this very close source pair.\n\n\\item The values used in the analysis of previous epochs for\nEarth Orientation Parameters (EOP), stations and reference source coordinates\nwere consistently derived from a single global solution provided by Goddard \nSpace Flight Center (GSFC). \nFor the correlation of the fourth epoch, the values used for \nEOP were derived from IERS solutions, and the station coordinates from \nUSNO catalogs.\nWe have made a comparison of the values derived for all the parameters at\nthe 4 epochs from a single global solution from IERS (namely IERS eopc04),\nwith the actual values\nused in the individual epoch analysis. The difference between the corresponding\nEOP values is always less than 4 mas. Such discrepancies propagate into \nerrors in the relative position estimates at each epoch of only a few \n$\\mu$as.\n\n\\item Our astrometric analysis in AIPS using a phase-referencing approach and\nHDM differs from the phase difference method used in VLBI3 analysis.\nComparisons show that these procedures are equivalent \n(Porcas \\& Rioja \\cite{porcas96}; Thompson et al. \\cite{thompson86}).\nBoth involve the definition of reference points in source maps;\nuncertainties in the reference point positions \n(as described in Sect. 4.3) arise in the same way.\n\n\\item Finally, a minor VLBA correlator error (Romney priv. comm.) caused\nincorrect time labels to be attached to the visibility records, resulting in\nincorrect ({\\it u,v}) values. \nThe effect on the relative visibility phases for our source pair is small\n($\\sim 0.004$\\degr) and can be neglected.\n\n\\end{enumerate}\n\n The magnitudes of all of the effects reported in this section are\nmuch smaller than our estimate in Sect. 4.3 of the uncertainity in reproducing\nthe reference point in the source, from epoch to epoch, and we are thus\njustified in comparing the astrometric results from all 4 epochs.\n\n\n\\subsection{Astrometric separations at the 4 epochs} \n\nThe astrometric measurements of the separations between the reference \npoints in A and B at $\\lambda$ 3.6~cm from 4 epochs are presented in \nFig.~\\ref{fig4}.\nIt includes our new 1995.9 measurement and those from three earlier epochs, \nin 1981.3, 1983.4 and 1990.5, reported in Marcaide \\& Shapiro \n(\\cite{marca84}), Marcaide et al. (1994) and Rioja et al. (\\cite{rioja97}), \nrespectively. The origin of the plot represents the separation at epoch 1.\n\n%%% FIGURE 4\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig4.ps,width=6.cm}}\n}\n\\caption{Measured separations between the A and B reference points at epochs\n2 (1983.4), 3 (1990.5) and 4 (1995.9), with respect to epoch 1 (1981.2).\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig4}} \n\\end{figure}\n\n\nChanges with time in Fig.~\\ref{fig4} represent the vector difference between\nany motions of the reference points in quasars A and B.\nThe near-orthogonal nature of the source axes in 1038+52 A,B (along\nwhich one might expect any motion to occur) simplifies the\ninterpretation of any trends seen. The new 1995.9 value follows the\nsame steady trend towards the NW shown by the three previous epochs.\nRioja et al. (\\cite{rioja97}) interpreted this as an outward expansion of the\nreference component in quasar B at a rate of $18~\\pm~5~\\mu$as~yr$^{-1}$, \nand quoted an upper bound on any proper motion of quasar A of \n$10~\\mu$as~yr$^{-1}$.\n\n\\subsection{Vector decomposition} \n\nIn this section we attempt to separate the individual contributions from \nthe 2 quasars in the astrometric separation measurements presented in \nFig.~\\ref{fig4}. We make no assumption about the stability of either \ncomponent, but\nassume that any displacements of the A or B reference points from their \npositions at epoch 1 are along the corresponding source axis directions.\nThis is a plausible assumption if the reference point coincides \nwith a non-stationary component moving along a ballistic trajectory, \nor with the location of the peak of brightness within an active core \nor near the base of jet, where changes during episodes of activity are \nlikely to occur along the jet direction.\nThis approach is closely related to that used previously \nby Rioja et al. (\\cite{rioja97}). For fixed assumed source axes for A and B,\nit results in a unique decomposition of the changes in the A-B separation\ninto separate A and B displacements, from 1981 to 1995.\n\nIt is clear that the dominant contribution to the separation changes\nseen in Fig.~\\ref{fig4} comes from quasar B, \nin which the source axis is well defined by the 127\\degr PA of\nthe separation between core and reference components.\nFor quasar A the source axis bends, from the inner ``core'' region \n(PA = 15\\degr) to the outer jet components, and it is not so clear which \ndirection should be chosen.\n\nIn our analysis we tried a range of values for fixing the A source axis \n(0 to 45\\degr ~in steps of 5\\degr).\nFor each, we calculated A and B reference-point displacements at epochs 2, \n3 and 4 with respect to epoch 1.\nThen we performed a least-squares fit to the B displacements with time to\nestimate a linear expansion rate for the B reference feature along \nPA 127\\degr. In Fig.~\\ref{fig5} we plot the deconvolved B reference point \ndisplacements from the analysis with the A source axis fixed at \nPA 25\\degr (the value adopted by Rioja et al. \\cite{rioja97}).\nThe fitted expansion rate is $16.9~\\pm~0.6~\\mu$as~yr$^{-1}$;\nthe error and associated rms values take account of the small number \nof points and 2 degrees of freedom. This rate agrees well with the value\nof $18~\\pm~5~\\mu$as~yr$^{-1}$ deduced by Rioja et al. (\\cite{rioja97}).\nThe rms residual from the fit (7~$\\mu$as) is low, and vindicates\nour use of measurements derived from differing techniques for\ninvestigating the relative proper motion between A and B. \n\n%%% FIGURE 5\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig5.ps,width=6.cm}}\n}\n\\caption{Changes in position of reference component in B along PA 127\\degr,\ndeduced from deconvolution of the A-B separation measurements. Assumed source\naxis for A is 25\\degr.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig5}} \n\\end{figure}\n\n\n\\subsection{Structural evolution within 1038+528 B} \n\nOur deconvolution analysis of the changes in separation measured between \nall 4 epochs supports the finding, previously proposed, that the B reference\ncomponent moves along the source axis, away from the B core.\nIn this section we make an independent determination of the separation \nrate between the core and reference component in B from measurements \nwithin the maps at the 4 epochs.\n\nFig.~\\ref{fig6} shows the separation between the core and reference \ncomponent in B at the four epochs plotted against time. For epochs 1--3 \nwe used the values given in Rioja et al. (\\cite{rioja97}). For 1995.9 we \nused AIPS task UVFIT to estimate a separation from the B visibility data \ndirectly, in order to follow the methodology used for the other epochs as \nclosely as possible; the value obtained was 1.895 mas.\nThe slope from a least-squares fit corresponds to an expansion rate \nof $13.0~\\pm~0.7~\\mu$as~yr$^{-1}$.\nIn the standard picture of extragalactic radio sources, the ``core'' is\nstationary, so this corresponds to an outward expansion of the\nreference component along PA 127\\degr.\n\n%%% FIGURE 6\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig6.ps,width=6.cm}}\n}\n\\caption{Changes in the position of the reference component in B \nalong PA 127\\degr, from measurements of its separation from the core\nin hybrid maps of B.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig6}} \n\\end{figure}\n\n\nThe rms of the fit (8~$\\mu$as) is again surprisingly low, implying\ntypical errors in the separation measurements at each epoch \n(both within the B structure and between the reference points)\nof only about 10--12$~\\mu$as along the direction of the B source axis.\nThis is considerably less than the estimate of position separation \nerrors given in Sect. 4.3. \n\n\\subsection{Relative proper motion }\n\nThe analysis presented in the previous sections demonstrate\nclearly that the chosen reference component within quasar B is\nunsuitable for use as a marker for tracing any relative proper motion\nbetween quasars A and B. The value of its expansion velocity derived \nin Sect. 5.4 appears to differ significantly from that deduced by \nvector-decomposition in Sect. 5.3. Although the difference between \nthese estimates, if real, could be interpreted as motion of the core of B \nat a rate of $\\sim 4~\\mu$as~yr$^{-1}$, this is not a conclusive result\nsince differences of this order arise from choosing different values of \nPA for the motion in A in the vector decomposition method.\n\nA more suitable tracer of relative proper motion between the quasars is \nthe variation of the separation between the cores of A and B.\nWe have used the separations between the core and reference component\nmeasured in the B map at each epoch, and the astrometric\nseparations between A and B, to calculate the separations between the\nA and B cores at each epoch; these are plotted in Fig.~\\ref{fig7}.\nThe area occupied by the points defines an upper limit of \n$\\sim 10~\\mu$as~yr$^{-1}$ for any relative proper motion between \nthe A and B cores, and hence between the quasars themselves, during\nthe period of nearly 15 years for which the separation has been\nmonitored with VLBI.\nThe limit seems to be set by the relatively large deviation of the\n1995.9 epoch point in the direction of the A source axis, presumably\narising from the difficulty in defining the reference point at the\nA ``core'' from epoch to epoch. \n\n%%% FIGURE 7\n\n\\begin{figure}[h]\n\\centerline{\n{\\psfig{figure=fig7.ps,width=6.cm}}\n}\n\\caption{Separation between the cores of A and B (with respect to epoch 1),\nderived by correcting the A-B reference point separation measurements with the\ncore-reference separations measured in the B hybrid maps.\nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig7}} \n\\end{figure}\n\n\n\\subsection{Possible ``core'' motions ? } \n\nFinally, we investigate any possible residual motions of the ``cores'' \nin A and B. The most likely causes of any such apparent motions are \nchanges in the relative brightness or positions of features in the \nsource structures at a resolution below that of the maps.\nOne might expect that these, too, would produce effects predominantly\nalong the source axis directions.\nWe therefore used the vector deconvolution method on the plot of\ncore-core separation with time to study displacements of the cores\nalong their source axis directions.\nFig.~\\ref{fig8}a and b show plots of the separated contributions from \nB and A, for an assumed A source axis PA 25\\degr.\nThe displacements for the B core seem to increase systematically.\nThe fitted rate is $3.8~\\pm~0.3~\\mu$as~yr$^{-1}$, indicating a possible \nslow outward motion. The displacements for the A core do not seem to \nvary systematically - the fitted slope is $5.5~\\pm~3.6~\\mu$as~yr$^{-1}$.\nHere the scatter is considerably larger, reflecting both the difficulties of\ndefining the reference point along the A core-jet axis, and\nalso, perhaps, real ``jitter'' of the position of the peak due to variations \nin the ``core'' substructure. These plots indicate the level of stability \nof the individual core positions; the fits represent realistic upper limits \nto any possible systematic core motion in the A and B quasars along their \nsource axis directions.\n\n%%% FIGURE 8\n\n\\begin{figure*}\n\\centerline{\n{\\psfig{figure=fig8a.ps,width=6.cm}}\n\\put (-140,140) {\\bf {a)}}\n{\\psfig{figure=fig8b.ps,width=6.cm}}\n\\put (-130,140) {\\bf {b)}}\n}\n\\caption{Residual motions of the cores using the deconvolution approach.\n {\\bf a} Displacements of B core along PA 127\\degr; \n{\\bf b} Displacements of A core along PA 25\\degr. \nPlotted error bars correspond to $25~\\mu$as.\n\\label{fig8}} \n\\end{figure*}\n\n\n\\section{Conclusions} \n\nThe series of astrometric VLBI measurements of the separation between \nthe quasar pair 1038+528 A and B, spanning\nnearly 15 years, provides excellent material for investigating \nthe relative proper motion of two extragalactic radio sources and\nthe positional stability of their cores.\nThe changes measured in the separations between quasars A and B \nat 3.6~cm are dominated by the motion of the reference feature in quasar B. \nThese astrometric results, and measurements in the hybrid maps of B are\ncompatible with an expansion rate for the B reference component of \n13--17$~\\mu$as~yr$^{-1}$.\nAt a redshift of 2.296 this translates to an apparent\ntransverse velocity of 0.55--0.70~c~h$^{-1}$.\nWe note that this is an order of magnitude smaller than the more\ntypical superluminal velocities seen in many quasars; it is a \nrare example of a subluminal velocity measured for a knot in a quasar jet.\n\nAfter correcting for the motion of the reference component in B,\nwe can put a conservative upper bound to any relative proper\nmotion between the quasars of $10~\\mu$as~yr$^{-1}$.\nDespite the increase in temporal baseline, this upper bound is no\nbetter than that given by Rioja et al. (\\cite{rioja97}).\nIts value is related to the difficulty in reproducing a stable reference\nposition along the A source axis near its ``core''.\n\nTheories in which the redshifts of quasars do not indicate cosmological\ndistances, and in which quasars are ``local'' and have high Doppler\nredshifts (e.g. Narlikar \\& Subramanian \\cite{narlikar83}) are incompatible \nwith our measured upper-limit to relative proper motion. Quasars at \n100 Mpc distance moving at relativistic speeds would have proper motions \nof the order of $600~\\mu$as~yr$^{-1}$, nearly 2 orders of magnitude \ngreater than our limit. Assuming cosmological distances,\nour limit corresponds to apparent transverse velocities of \n0.43~c~h$^{-1}$ and 0.22~c~h$^{-1}$ at the redshifts of the B and A\nquasars, respectively.\n\nWe have investigated the way in which the definition of \nreference points in a map may be only loosely ``fixed'' to the radio\nsource structure, especially when the latter is strongly asymmetric.\nWe have also developed an alternative analysis route - Hybrid Double\nMapping - for imaging both sources of a close pair simultaneously, and\nat the same time preserving their relative astrometric information\nin a single map.\n\nThe surprisingly low rms from the fits of linear expansion in quasar B,\nand the discrepancy between the two estimates \n($16.9~\\pm~0.6~\\mu$as~yr$^{-1}$ from the astrometric measurements and\n $ 13.0~\\pm~0.7~\\mu$as~yr$^{-1}$ from the hybrid maps)\nare suggestive of (but do not prove) a residual motion of the core \nin quasar B; our decomposition along the source axis direction gives a fit\nof $3.8~\\pm~0.3~\\mu$as~yr$^{-1}$, corresponding to an apparent transverse \nvelocity of 0.17~c~h$^{-1}$. If real, this might indicate a steady change \nin physical conditions at the base of the jet, or perhaps the emergence \nof a new knot component moving outwards with a velocity similar to the \nreference component, but as yet unresolved by our 0.5 mas beam.\nIn this regard, it is interesting to note the slight extension of\nthe core of quasar B in PA 132\\degr given by the Gaussian model fit.\n\nThe low rms derived from fits to the expansion of the B reference component \nindicate that we have been overly conservative in our estimate of \n$18~\\mu$as for the error in reference point positions. Errors at least \n2 times smaller are implied, corresponding to a sixtieth of the beamwidth. \nIt is interesting to note that such small errors are also implied in the \nwork of Owsianik \\& Conway (\\cite{owsianik98}), where the low scatter in \nthe plot of expansion of the CSO source \\object{0710+439} allows an \nexpansion rate of $14.1~\\pm~1.6~\\mu$as~yr$^{-1}$ to be determined.\n\nThere are no obvious systematic motions within quasar A, but the ``noise'' \nin the estimates of position along its axis are much larger.\nThis noise, along with any associated underlying changes in source\nsubstructure, provides a fundamental limit to estimates of\nany systematic core motion in A. Improvements on the estimates of (or upper\nbounds to) the relative motion between the quasars, or of the\nindividual motion of the A core, will require a considerable\nincrease in the temporal baseline of VLBI monitoring.\n\n\\newpage\n\n\\appendix \n\n\\section {Hybrid Double Mappping (HDM)}\n\n\n{\\bf A.1 Principle of Hybrid Double Mapping} \\\\\n\n\\noindent\nThe visibility function, $V$, measured at time $t$, on a baseline between\nantennas $i$ and $j$, is represented by a complex function with amplitude $A$, \nphase $P$:\n\n\\[ V(i,j) = A * e^{i[\\phi]}(t) \\]\n\n\\noindent\nFor this analysis it is convenient to indentify 3 contributions to\nthe visibility phase:\n\n\\[ \\phi(i,j) = \\phi_{s}(u,v) + \\phi_{p}(u,v) + \\phi_{m}(t) \\]\n\n\\noindent\nwhere \n\n\\begin{description} \n\\item [$\\phi_s$] is due to source structure, evaluated w.r.t. a reference\nposition for the source. \\\\\n\n \\item [$\\phi_p$] is due to any offset of the \ntrue source position from the reference position. \\\\\n\nBoth $\\phi_s$ and \n$\\phi_p$ are functions of the resolution coordinates, $u$ and $v$, at time \n$t$. \\\\\n\n\\item [$\\phi_m$] is due to inaccuracies in the correlator model calculation of\n the interferometer geometry and the signal propagation delays\n in the ionosphere, troposphere and receiving system; it is an \n unknown function of time. \\\\\n This term can be represented by the difference of two\n ''antenna-based'' phases, $\\theta_i$ and $\\theta_j$, since it can \n be related to the \n difference in signal arrival times at the two sites.\n (This analysis is a simplification which ignores possible\n ''non-closing'' instrumental baseline phase terms arising from\n e.g. un-matched bandpasses and polarisation impurities.) \n\\end{description}\n\n\\[ \\phi(i,j) = \\phi_s(u,v) + \\phi_p(u,v) + \\theta_i(t) - \\theta_j(t) \\]\n\n\\noindent\nIn conventional hybrid mapping, an iterative procedure is used\nto separate out the antenna-based phase terms from the ''source'' terms;\nthe latter must produce a consistent and physically plausible source\nstructure after Fourier transformation of the corrected visibility:\n\n\\[ \\underbrace {A * e^{i[\\phi_s+\\phi_p]}(u,v)}_{corrected \\: visibility} = \nV(i,j) * \\underbrace {e^{-i[\\theta_i(t)-\\theta_j(t)]}}_{antenna \\: phase \\: terms} \\] \n\n\\noindent\nHowever, the position offset term, $\\phi_p$, can also be expressed as a difference \nin wavefront arrival times at the 2 antennas and so it is also\n''absorbed'' in antenna phase terms $\\theta_i'$, $\\theta_j'$; \nthe ''absolute'' position information is lost:\n\n\\[ \\underbrace {A * e^{i[\\phi_s]}(u,v)}_{corrected \\: visibility} = \nV(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\: phase\n\\: terms} \\]\n\n\\noindent\nIn Hybrid Double Mapping (HDM), the visibility functions of two \nsources observed simultaneously are added. For a close source pair, we \nmake the same assumption as for conventional phase-referencing - that the \nmodel error phase terms are essentially the same for both sources. We make \na further assumption that the $u,v$ coordinates are also essentially the same\nfor both sources, for each baseline and time. The visibility sum, $V^1 + V^2$,\ncan then be re-written: \\\\\n\n\n\\[ \\underbrace {(A^1 * e^{i[\\phi^1_{s}]} + A^2 * e^{i[\\phi^2_{s}+(\\phi^2_{p}\n-\\phi^1_{p})]})(u,v)}_{corrected \\: visibility \\: sum} = \\]\n\\[ \\;\\;\\; \\vspace*{2cm} = V^{sum}(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\:\n phase \\: terms} \\] \n\n\n%\\begin{eqnarray*}\n%\\lefteqn{ \\[ \\underbrace {(A_1e^{i[\\phi_{1s}]}+A_2e^{i[\\phi_{2s}+(\\phi_{2p}-\\phi_{1p})]})(u,v)}_{corrected \\: visibility \\: sum} = } \\\\\n%& & V^{sum}(i,j) * \\underbrace {e^{-i[\\theta_i'(t)-\\theta_j'(t)]}}_{antenna \\:\n%phase \\: terms} \\] \n%\\end{eqnarray*}\n\n\\noindent\nThis may be recognised as the visibility function of a ''composite''\nsource consisting of the sum of the brightness distributions of sources\n1 and 2, with antenna-based phase error terms $\\theta_i'$, $\\theta_j'$, \nas before.\nThe HDM method consists of performing the normal hybrid mapping\nprocedure with the visibility sum, resulting in the separation of the\nantenna-based errors, and a physically plausible map of the sum of\nthe two source brightness distrubutions. An important point is that,\nwhereas the {\\it origin} of the map of the composite source is arbitrary (as\nit depends on the position of the starting model), the {\\it separation} of\nthe two source brightness distributions within the composite map\n(determined by $\\phi^2_{p}-\\phi^1_{p}$) is fixed during the phase \nseparation procedure,\nand is equal to the {\\it difference} of the errors in the two source\npositions used for correlation. We call this the ''residual separation''. \\\\\n\n\\noindent\n{\\bf A.2 Practical aspects} \\\\\n\n\\noindent\nThere are some practical aspects to be considered. If the source\ncoordinates used in the correlator model are very precise, then the\nresidual separation may be less than the interferometer beamwidth, and\nthe two source distributions will lie on top of each other. \nIn this case it is desireable to\nintroduce an artificial position offset into one of the\nsource visibility functions before forming the visibility sum, to\nensure that the two source reference features are well separated in the\nHDM map. One should also arrange that the peak of one source\ndoes not lie on the sidelobe response of the other in the \"dirty\" map,\nas this may degrade the CLEAN deconvolution process in the mapping step.\\\\\n\n\\noindent\n Another important consideration is that the time-averaged samples\nof the summed visibility function contain equal contributions from both\nsource visibility functions. When both sources are observed\nsimultaneously this will normally be the case, except when different\namounts of data are lost in the two separate correlator passes needed\nfor the two source positions. It is important to edit the data sets\ncarefully to fulfil this condition. \\\\\n\n\\noindent\n The range of validity of the assumption that the $(u,v)$\ncoordinates for the two sources are the same depends on the ''dilution\nfactor'', i.e. the reciprocal of the source separation, measured in\nradians. The $(u,v)$ value assigned to the summed visibility will be\nincorrect for either source by roughly 1 part in the dilution factor\n(roughly 1 in 6000 for 1038+528A,B). \nThis is equivalent to having source visibility phase errors of this\norder, and thus limits the size of an HDM map to be less than the\nbeamwidth times the dilution factor; the residual separation should be\nmuch smaller than this value.\\\\\n\n\\noindent\nIn the actual analysis used in this work, we first made a rough \ncorrection to the phase of the summed visibility of 1038+528 A + B, using\nthe antenna phase and phase derivative errors from fringe-fitting\n1038+528A using a point source model. However, there is no reason why\none should not fringe-fit the summed visibility function directly. \\\\\n\n\\noindent\n{\\bf A.3 Applications} \\\\\n\n\\noindent\nThe HDM method can in principle be applied\nwhenever two (or more !) radio sources are observed simultaneously,\nbut are correlated at separate field centres; however, \nthey must be close enough so that the conditions of same $(u,v)$\ncoverage and same correlator model errors apply.\nThe method uses the structures of BOTH sources simultaneously to\nseparate out the antenna phase errors, as opposed to a single source in \nsimple hybrid mapping.\nIf both sources are strong (as with 1038+528 A and B),\nconstraining the (single) antenna phase solutions with two structures\nshould lead to a more rigorous and robust separation between the\nsource and antenna phase terms.\nOne field of application is in high resolution VLBI imaging of\ngravitational lens systems with wide image separations (e.g. \nimages A and B of QSO 0957+561 with 6.1 arcsec separation)\nwhere preserving the necessary wide field-of-view from a single \ncorrelation may result in inconveniently large data sets.\nWhen one source is very weak, however,\nthere is probably little to be gained over normal hybrid mapping. \\\\\n\n\\noindent\nFor relative astrometry studies (as described in this paper),\nthe HDM method has some advantages over conventional phase-reference \nmapping and explicit phase-differencing methods.\nIn phase-differencing astrometry, separate hybrid maps must be made of\nboth sources to correct for source structural phase terms and \nthe antenna phase errors are NOT constrained to be the same. Imperfect \nseparation between source and antenna phase terms can increase the noise \non the differenced phase, as well as lead to possible systematic errors.\nIn phase-reference astrometry, only one of the sources is used to solve\nfor the antenna phase terms; imperfect separation can lead to extra\nphase noise in the phase-referenced visibility of the ''target'' source.\nIn HDM we use both source\nstructures simultaneously to separate the (common) antenna error\nphases from that of a single \"structure\" in which the \nreference points of the two sources are spaced by the residual separation.\\\\\n\n\\noindent\nWhen the separation between the two sources of a pair exceeds\nthe telescope primary beamwidths, astrometric and phase-reference \nobservations \nmust involve switching between the sources, and the visibility phase of at \nleast one of the sources must normally be interpolated in the observing gap. \nThe condition that must be fulfilled for HDM to work in\nthis case is that an equal number of observations of both sources must\nbe added to form an average visibility function for the length of the\n''solution interval'' in the phase self-calibration step of HDM.\nThis length is generally limited by the coherence time of the\natmosphere, and would imply a very fast switching cycle in most cases.\nAnother application for HDM could be in the the analysis of\n''cluster-cluster'' VLBI (see e.g. Rioja et al. \\cite{rioja97b}), \nin which two or more sources are observed simultaneously on VLBI baselines \nby using more than one telescope at each site.\n\n\n\\begin{acknowledgements}\n\nWe thank Dave Graham for help with the observations in Effelsberg,\nTony Beasley for asistance at the VLBA, and Mark Reid for useful comments\non the text. M.J.R. wishes to acknowledge support for this research by the\nEuropean Union under contract CHGECT920011.\nThe National Radio Astronomy Observatory is a facility\nof the National Science Foundation operated under cooperative\nagreement by Associated Universities, Inc.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \ned. Reid M., Moran J., Kluwer, p. \\ 523 \n\n\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \nVery Long Baseline Interferometry and the VLBA, eds. Zensus J.A., \nDiamond P.J., Napier P.J., ASP Conference Series, Vol. 82, p. \\ 327.\n\n\\bibitem[1986]{blandford86} Blandford R.D., K\\\"onigl A., 1986, \nApJ 308, 83\n\n\\bibitem[1983]{marca83} Marcaide J.M., Shapiro I.I., 1983, AJ 88, 1133 \n\\bibitem[1984]{marca84} Marcaide J.M., Shapiro I.I., 1984, ApJ 276, 56\n\\bibitem[1994]{marca94} Marcaide J.M., El\\'{o}segui P., Shapiro I.I., 1994, \n AJ 108, 368 \n\\bibitem[1983]{narlikar83} Narlikar J.V., Subramanian K., 1983, \nApJ 273, 44\n\\bibitem[1978]{owen78} Owen F.N., Porcas R.W., Neff S.G., 1978, \nAJ 83, 1009\n\\bibitem[1980]{owen80} Owen F.N., Wills B.J., Wills D., 1980, ApJ 235, L57\n\\bibitem[1998]{owsianik98} Owsianik I., Conway J.E., 1998, A\\&A 337, 69\n\\bibitem[1986]{porcas87} Porcas R.W., 1987, Superluminal Radio Sources, ed.\n Zensus A., Pearson A., Cambridge University Press, p. \\ 12\n\\bibitem[1996]{porcas96} Porcas R.W., Rioja M.J., 1996, Proc. of the 11th \nWorking Meeting on European VLBI for Geodesy and Astrometry, Ed. Elgered\nG., p. \\ 209\n\\bibitem[1993]{rioja93} Rioja M.J., 1993, PhD. Thesis, Universidad de Granada\n\\bibitem[1997]{rioja97} Rioja M.J., Marcaide J.M., El\\'osegui P., \nShapiro I.I., 1997, A\\&A 325, 383 \n\\bibitem[1997]{rioja97b} Rioja M.J., Stevens E.,\nGurvits L., et al., 1997, {\\it Vistas in Astronomy} 41 (2), 213 \n%\\bibitem[2000]{rioja00} Rioja, M.J., Porcas, R.W., 2000, {\\it in preparation}\n\\bibitem[1975]{robertson75} Robertson D.S., 1975, PhD Thesis, MIT\n%\\bibitem[1996]{romney96} Romney, J.D., 1996, (VLBA email memorandum \n%of 14 March) \n\\bibitem[1986]{thompson86} Thompson A.R., Moran J.M., Swenson G.W., 1986, \nInterferometry and Synthesis in Radio Astronomy. Wiley-Interscience, \nNew York, p. 400\n\n\\end{thebibliography}{}\n\n\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002097.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1988]{alef88} Alef W.A., 1988, in Proc. IAU Symp. 129, \ned. Reid M., Moran J., Kluwer, p. \\ 523 \n\n\\bibitem[1995]{beasley95} Beasley A.J., Conway J.E., 1995, \nVery Long Baseline Interferometry and the VLBA, eds. Zensus J.A., \nDiamond P.J., Napier P.J., ASP Conference Series, Vol. 82, p. \\ 327.\n\n\\bibitem[1986]{blandford86} Blandford R.D., K\\\"onigl A., 1986, \nApJ 308, 83\n\n\\bibitem[1983]{marca83} Marcaide J.M., Shapiro I.I., 1983, AJ 88, 1133 \n\\bibitem[1984]{marca84} Marcaide J.M., Shapiro I.I., 1984, ApJ 276, 56\n\\bibitem[1994]{marca94} Marcaide J.M., El\\'{o}segui P., Shapiro I.I., 1994, \n AJ 108, 368 \n\\bibitem[1983]{narlikar83} Narlikar J.V., Subramanian K., 1983, \nApJ 273, 44\n\\bibitem[1978]{owen78} Owen F.N., Porcas R.W., Neff S.G., 1978, \nAJ 83, 1009\n\\bibitem[1980]{owen80} Owen F.N., Wills B.J., Wills D., 1980, ApJ 235, L57\n\\bibitem[1998]{owsianik98} Owsianik I., Conway J.E., 1998, A\\&A 337, 69\n\\bibitem[1986]{porcas87} Porcas R.W., 1987, Superluminal Radio Sources, ed.\n Zensus A., Pearson A., Cambridge University Press, p. \\ 12\n\\bibitem[1996]{porcas96} Porcas R.W., Rioja M.J., 1996, Proc. of the 11th \nWorking Meeting on European VLBI for Geodesy and Astrometry, Ed. Elgered\nG., p. \\ 209\n\\bibitem[1993]{rioja93} Rioja M.J., 1993, PhD. Thesis, Universidad de Granada\n\\bibitem[1997]{rioja97} Rioja M.J., Marcaide J.M., El\\'osegui P., \nShapiro I.I., 1997, A\\&A 325, 383 \n\\bibitem[1997]{rioja97b} Rioja M.J., Stevens E.,\nGurvits L., et al., 1997, {\\it Vistas in Astronomy} 41 (2), 213 \n%\\bibitem[2000]{rioja00} Rioja, M.J., Porcas, R.W., 2000, {\\it in preparation}\n\\bibitem[1975]{robertson75} Robertson D.S., 1975, PhD Thesis, MIT\n%\\bibitem[1996]{romney96} Romney, J.D., 1996, (VLBA email memorandum \n%of 14 March) \n\\bibitem[1986]{thompson86} Thompson A.R., Moran J.M., Swenson G.W., 1986, \nInterferometry and Synthesis in Radio Astronomy. Wiley-Interscience, \nNew York, p. 400\n\n\\end{thebibliography}"
}
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astro-ph0002098
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Chemistry in the Envelopes around Massive Young Stars
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[
{
"author": "Ewine F.\\ van Dishoeck and Floris F.S.\\ van der Tak"
}
] |
Recent observational studies of intermediate- and high-mass star-forming regions at submillimeter and infrared wavelengths are reviewed, and chemical diagnostics of the different physical components associated with young stellar objects are summarized. Procedures for determining the temperature, density and abundance profiles in the envelopes are outlined. A detailed study of a set of infrared-bright massive young stars reveals systematic increases in the gas/solid ratios, the abundances of evaporated molecules, and the fraction of heated ices with increasing temperature. Since these diverse phenomena involve a range of temperatures from $<100\,$K to 1000~K, the enhanced temperatures must be communicated to both the inner and outer parts of the envelopes. This `global heating' plausibly results from the gradual dispersion of the envelopes with time. Similarities and differences with low-mass YSOs are discussed. The availability of accurate physical models will allow chemical models of ice evaporation followed by `hot core' chemistry to be tested in detail.
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[
{
"name": "dishoeck.tex",
"string": "% SAMPLE1.TEX -- WGAS sample paper with minimal markup.\n\n% Lines starting with \"%\" are comments; they will be ignored by LaTeX.\n\n\\documentstyle[11pt,newpasp,psfig,epsf,twoside]{article}\n\\def\\gtsim{{_>\\atop{^\\sim}}}\n\\def\\ltsim{{_<\\atop{^\\sim}}}\n\n\\begin{document}\n\n\\title{Chemistry in the Envelopes around Massive Young Stars}\n\\author{Ewine F.\\ van Dishoeck and Floris F.S.\\ van der Tak}\n\\affil{Leiden Observatory, P.O.\\ Box 9513, 2300 RA Leiden,\nThe Netherlands}\n\n\\begin{abstract}\nRecent observational studies of intermediate- and high-mass\n star-forming regions at submillimeter and infrared wavelengths are\n reviewed, and chemical diagnostics of the different physical\n components associated with young stellar objects are summarized.\n Procedures for determining the temperature, density and abundance\n profiles in the envelopes are outlined. A detailed study of a set of\n infrared-bright massive young stars reveals systematic increases in\n the gas/solid ratios, the abundances of evaporated molecules, and the\n fraction of heated ices with increasing temperature. Since these\n diverse phenomena involve a range of temperatures from $<100\\,$K to\n 1000~K, the enhanced temperatures must be communicated to both the\n inner and outer parts of the envelopes. This `global heating'\n plausibly results from the gradual dispersion of the envelopes with\n time. Similarities and differences with low-mass YSOs are discussed.\n The availability of accurate physical models will allow chemical\n models of ice evaporation followed by `hot core' chemistry to be\n tested in detail.\n\n\n\\end{abstract}\n\n\n%% Keywords: High-mass star formation, ices, hot cores, envelopes\n%% \n%% Objects: Orion-KL, Orion-IRc2, SGrB2, W~3 IRS5, W~3(H$_2$O), AFGL 2591,\n%% AFGL 2136, NGC 7538 IRS9, W~33A, G34.3, S 140, W~3 IRS4\n%% Molecules: CO, C$^{17}$O, CS, H$_2$CO, HC$_5$N, H$_2$O, CO$_2$,\n%% CH$_3$OH, CH$_3$OCH$_3$, CH$_3$CN, C$_2$H$_2$, S~I, PAHs\n%% OH, SiO, SO$_2$, CN, HCN, C~II, CO$^+$\n\n\\section{Introduction}\n\nMassive star-forming regions have traditionally been prime targets for\nastrochemistry owing to their bright molecular lines (e.g., Johansson\net al.\\ 1984, Cummins et al.\\ 1986, Irvine et al.\\ 1987, Ohishi 1997).\nMassive young stellar objects (YSOs) have luminosities of $\\sim 10^4 -\n10^6$ L$_\\odot$ and involve young O- and B-type stars. Because their\nformation proceeds more rapidly than that of low-mass stars and\ninvolves ionizing radiation, substantial chemical differences may be\nexpected. The formation of high mass stars is much less well\nunderstood than that of low-mass stars. For\nexample, observational phenomena such as ultracompact H II regions,\nhot cores, masers and outflows have not yet been linked into a single\nevolutionary picture. Chemistry may well be an important diagnostic\ntool in establishing such a sequence.\n \nMost of the early work on massive star-forming regions has centered on\ntwo sources, Orion--KL and SgrB2. Numerous line surveys at millimeter\n(e.g., Blake et al.\\ 1987, Turner 1991) and submillimeter (Jewell et\nal.\\ 1989, Sutton et al.\\ 1991, 1995, Schilke et al.\\ 1997)\nwavelengths have led to an extensive inventory of molecules through\nidentification of thousands of lines. In addition, the surveys have\nshown strong chemical variations between different sources.\n\nIn recent years, new observational tools have allowed a more detailed and\nsystematic study of the envelopes of massive YSOs. Submillimeter observations\nroutinely sample smaller beams (typically 15$''$ vs.\\ 30$''$--1$'$ ) and\nhigher critical densities ($\\geq 10^6$ vs.\\ $10^4$ cm$^{-3}$) than the earlier\nwork. Moreover, interferometers at 3 and 1 millimeter provide maps with\nresolutions of $0.5''$--5$''$. Finally, ground- and space-based infrared\nobservations allow both the gas and the ices to be sampled (e.g., Evans et\nal.\\ 1991, van Dishoeck et al.\\ 1999). These observational developments have\nled to a revival of the study of massive star formation within the last few\nyears. Recent overviews of the physical aspects of high-mass star formation\nare found in Churchwell (1999) and Garay \\& Lizano (1999).\n\n\nIn this brief review, we will first summarize available observational\ndiagnostics to study the different phases and physical components\nassociated with massive star formation. Subsequently, an overview of\nrecent results on intermediate mass YSOs is given, which are often\nbetter characterized than their high-mass counterparts because of\ntheir closer distance. Subsequently, we will discuss a specific sample\nof embedded massive YSOs which have been studied through a combination\nof infrared and submillimeter data. After illustrating\nthe modeling techniques, we address the question how the\nobserved chemical variations are related to evolutionary effects,\ndifferent conditions in the envelope (e.g., $T$, mass) or different\nluminosities of the YSOs. More extensive overviews of the chemical\nevolution of star-forming regions are given by van Dishoeck \\& Blake\n(1998), Hartquist et al.\\ (1998), van Dishoeck \\& Hogerheijde (1999)\nand Langer et al.\\ (2000). Schilke et al.\\ (this volume) present high\nspatial resolution interferometer studies, whereas Macdonald \\&\nThompson (this volume) focus on submillimeter data of hot\ncore/ultracompact H~II regions. Ices are discussed by Ehrenfreund \\&\nSchutte (this volume).\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig1.ps}{11.0cm}{0}{50}{50}{-150}{-30}\n\\caption{Overview of the SEST 230 GHz line survey of SgrB2 at the N, M and\nNW positions, illustrating the chemical differentiation in high-mass\nstar-forming regions (from:\nNummelin et al.\\ 1998).}\n\\label{fig-1}\n\\vspace{-0.3cm}\n\\end{figure}\n\n\n\\section{Submillimeter and Infrared Diagnostics}\n\nThe majority of molecules are detected at (sub-)millimeter\nwavelengths, and line surveys highlight the large variations in\nchemical composition between different YSOs, both within the same\nparent molecular cloud and between different clouds. The recent 1--3\nmm surveys of Sgr~B2 (Nummelin et al.\\ 1998, Ohishi \\& Kaifu 1999)\ndramatically illustrate the strong variations between various\npositions (see Figure~1). The North position is typical of\n`hot core'-type spectra, which are rich in lines of saturated\norganic molecules. This position has also been named \nthe `large molecule heimat'\n(e.g., Kuan \\& Snyder 1994, Liu \\& Snyder 1999). The Middle position\nhas strong SO and SO$_2$ lines, whereas the Northwest position has a\nless-crowded spectrum with lines of ions and long carbon chains. A\nsimilar differentiation has been observed for three positions in the\nW~3 giant molecular cloud by Helmich \\& van Dishoeck (1997), who\nsuggested an evolutionary sequence based on the chemistry.\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig2.ps}{10cm}{0}{55}{55}{-150}{-115}\n\\caption{ISO-SWS spectra of two massive YSOs at different evolutionary stages.\nCep A ($L \\approx 2.4\\times 10^4$ L$_{\\odot}$) is in the embedded\nstage, whereas S~106 ($L \\approx 4.2\\times 10^4$ L$_{\\odot}$) is\nin a more evolved stage (from:\nvan den Ancker et al.\\ 2000a).}\n\\label{fig-2}\n\\end{figure}\n\n\nThe availability of complete infrared spectra from 2.4--200 $\\mu$m\nwith the {\\it Infrared Space Observatory }(ISO) allows complementary\nvariations in infrared features to be studied. Figure~2 shows an\nexample of ISO--SWS and LWS spectra of two objects: Cep A ($L \\approx\n2.4\\times 10^4$ L$_{\\odot}$) and S~106 ($L \\approx 4.2\\times 10^4$\nL$_{\\odot}$). The Cep A spectrum is characteristic of the deeply\nembedded phase, in which the silicates and ices in the cold envelope\nare seen in absorption. The S~106 spectrum is typical of a more\nevolved massive YSO, with strong atomic and ionic lines in emission\nand prominent PAH features. A similar sequence has been shown by\nEhrenfreund et al.\\ (1998) for a set of southern massive young stars\nwith luminosities up to $4\\times 10^5$ L$_{\\odot}$.\n\nThe most successful models for explaining these different chemical\ncharacteristics involve accretion of species in an icy mantle during the\n(pre-)collapse phase, followed by grain-surface chemistry and evaporation of\nices once the YSO has started to heat its surroundings (e.g., Millar 1997). \nThe evaporated molecules subsequently drive a rapid high-temperature gas-phase\nchemistry for a period of $\\sim 10^4 - 10^5$ yr, resulting in complex,\nsaturated organic molecules (e.g., Charnley et al.\\ 1992, 1995; Charnley 1997;\nCaselli et al.\\ 1993, Viti \\& Williams 1999). The abundance ratios of species\nsuch as CH$_3$OCH$_3$/CH$_3$OH and SO$_2$/H$_2$S show strong variations with\ntime, and may be used as `chemical clocks' for a period of 5000--30,000 yr\nsince evaporation. Once most of the envelope has cleared, the ultraviolet\nradiation can escape and forms a photon-dominated region (PDR) at the\nsurrounding cloud material, in which molecules are dissociated into radicals\n(e.g., HCN $\\to$ CN) and PAH molecules excited to produce infrared emission.\nThe (ultra-)compact H~II region gives rise to strong ionic lines due to\nphotoionization.\n\n\\begin{table}[t]\n\\caption{Chemical characteristics of massive star-forming regions}\n\\begin{center}\\scriptsize\n\\begin{tabular}{lllll}\n\\hline\n\\noalign{\\smallskip}\nComponent & Chemical & Submillimeter & Infrared & Examples \\\\\n & characteristics & diagnostics & diagnostics \\\\\n\\tableline\n\\noalign{\\smallskip}\nDense cloud & Low-T chemistry &Ions, long-chains &Simple ices & SgrB2 (NW) \\\\\n & & (HC$_5$N, ...) & (H$_2$O, CO$_2$) \\\\\n\\noalign{\\smallskip}\nCold envelope & Low-T chemistry, & Simple species & Ices & N7538 IRS9, \\\\\n & Heavy depletions & (CS, H$_2$CO) & (H$_2$O, CO$_2$, CH$_3$OH)\n & W~33A \\\\\n\\noalign{\\smallskip}\nInner warm & Evaporation & High T$_{\\rm ex}$ & High gas/solid, High\n & GL 2591, \\\\\nenvelope & & (CH$_3$OH) & T$_{\\rm ex}$, Heated ices \n & GL 2136 \\\\\n & & & (C$_2$H$_2$, H$_2$O, CO$_2$) \\\\\n\\noalign{\\smallskip}\nHot core & High-T chemistry & Complex organics & Hydrides & Orion hot core, \\\\\n & & (CH$_3$OCH$_3$, CH$_3$CN, & (OH, H$_2$O) \n& SgrB2(N),G34.3 \\\\\n&&vib.\\ excited mol.) && W~3(H$_2$O) \\\\\n\\noalign{\\smallskip}\nOutflow: & Shock chemistry, & Si- and S-species & \n Atomic lines, Hydrides & W~3 IRS5, \\\\\nDirect impact &Sputtering & (SiO, SO$_2$) &([S I], H$_2$O) & SgrB2(M) \\\\\n\\noalign{\\smallskip}\nPDR, Compact & Photodissociation,& Ions, radicals & Ionic lines, PAHs\n& S~140, \\\\\nH~II regions & Photoionization & (CN/HCN, CO$^+$) &([NeII], [CII])\n& W~3 IRS4 \\\\\n \n%\\noalign{\\vspace{-0.8cm}}\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\nTable~1 summarizes the chemical characteristics of the\nvarious physical components, together with the observational\ndiagnostics at submillimeter and infrared wavelengths. \nWithin the single-dish submillimeter and ISO beams,\nmany of these components are blended together and interferometer\nobservations will be essential to disentangle them. Nevertheless, the\nsingle-dish data are useful because they encompass the entire envelope\nand highlight the dominant component in the beam. Combined\nwith the above chemical scenario, one may then attempt to establish an\nevolutionary sequence of the sources.\n\nThe physical distinction between the `hot core' and the warm\ninner envelope listed in Table~1 is currently not clear: does the `hot\ncore' represent a separate physical component or is it simply the\ninner warm envelope at a different stage of chemical evolution? Even\nfrom an observational point of view, there appear to be different\ntypes of `hot cores': some of them are internally heated by the young\nstar (e.g., W~3(H$_2$O)), whereas others may just be dense clumps of\ngas heated externally (e.g., the Orion compact ridge). This point\nwill be further discussed in \\S\\S 4 and 5. Disks are not included in\nTable~1, because little is known about their chemical characteristics,\nor even their existence, around high-mass YSOs (see Norris, this\nvolume).\n\n\n\\section{Intermediate-Mass YSOs}\n\nIntermediate-mass pre-main sequence stars, in particular the so-called\nHerbig Ae/Be stars, have received increased observational attention in\nrecent years (see Waters \\& Waelkens 1998 for a review). These stars\nhave spectral type A or B and show infrared excesses due to \ncircumstellar dust. Typical luminosities are in the range $10^2 -\n10^4$ L$_{\\odot}$, and several objects have been located within 1 kpc\ndistance. Systematic mapping of CO and the submillimeter continuum of\na sample of objects has been performed by Fuente et al.\\ (1998) and\nHenning et al.\\ (1998). The data show the dispersion of the envelope\nwith time starting from the deeply embedded phase (e.g.,\nLkH$\\alpha$234) to the intermediate stage of a PDR (e.g., HD 200775\nilluminating the reflection nebula NGC 7023) to the more evolved stage\nwhere the molecular gas has disappeared completely (e.g., HD 52721).\nThe increasing importance of photodissociation in the chemistry is\nprobed by the increase in the CN/HCN abundance ratio. This ratio has\nbeen shown in other high-mass sources to be an excellent tracer of\nPDRs (e.g., Simon et al. 1997, Jansen et al.\\ 1995). Line surveys of\nthese objects in selected frequency ranges would be useful to\ninvestigate their chemical complexity, especially in the embedded\nphase.\n\nISO-SWS observations of a large sample of Herbig Ae/Be stars have been\nperformed by van den Ancker et al.\\ (2000b,c). In the embedded phase,\nshock indicators such as [S I] 25.2 $\\mu$m are strong, whereas in the\nlater phases PDR indicators such as PAHs are prominent. An excellent\nexample of this evolutionary sequence is provided by three Herbig Ae\nstars in the BD+40$^o$4124 region ($d\\approx 1$ kpc). The data\nsuggest that in the early phases, the heating of the envelope is\ndominated by shocks, whereas in later phases it is controlled by\nultraviolet photons.\n\n\n\\begin{figure}[t]\n\\vspace{-3.8cm}\n\\plottwo{dishoeck_fig3a.ps}{dishoeck_fig3b.ps}\n\\vspace{-0.3cm}\n\\caption{Left: ISO-LWS spectra of the intermediate mass YSO \nLkH$\\alpha$234, showing strong atomic fine-structure lines of\n[C II] 158 $\\mu$m and [O~I] 63 $\\mu$m, but weak molecular CO and\nOH lines. Right: CO excitation diagram, indicating the presence\nof a warm ($T\\approx 200-900$~K), dense ($n>10^5$ cm$^{-3}$) \nregion (from:\nGiannini et al.\\ 2000).}\n\\label{fig-3}\n\\vspace{-0.5cm}\n\\end{figure}\n\n\nISO-LWS data have been obtained for a similar sample of Herbig Ae/Be\nstars by Lorenzetti et al.\\ (1999) and Giannini et al.\\ (2000), and\nare summarized by Saraceno et al.\\ (1999). The [C II] 158 $\\mu$m and\n[O I] 63 and 145 $\\mu$m lines are prominent in many objects and are\ndue primarily to the PDR component in the large LWS beam ($\\sim\n80''$). High-$J$ CO and OH far-infrared lines have been detected in\nsome objects and indicate the presence of a compact, high temperature\nand density region of $\\sim$1000 AU in size, presumably tracing the\ninner warm envelope (see Figure~3).\nFar-infrared lines of H$_2$O are seen in low-mass YSO spectra, but are\nweak or absent in those of intermediate- and high-mass YSOs, with the\nexception of Orion-KL and SgrB2 (e.g., Harwit et al.\\ 1998, Cernicharo\net al.\\ 1997, Wright et al.\\ 2000). The absence of H$_2$O lines in\nhigher-mass objects may be partly due to the larger distance of these\nobjects, resulting in substantial dilution in the LWS beam. However,\nphotodissociation of H$_2$O to OH and O by the enhanced ultraviolet radiation\nmay also play a role.\n\nIn summary, both the submillimeter and infrared diagnostics reveal an\nevolutionary sequence from the youngest `Group I' objects to `Group\nIII' objects (cf.\\ classification by Fuente et al.\\ 1998), in which\nthe envelope is gradually dispersed. Such a sequence is analogous to\nthe transition from embedded Class 0/I objects to more evolved Class\nII/III objects in the case of low-mass stars (Adams et al.\\ 1987). The\nISO data provide insight into the relative importance of the heating\nand removal mechanisms of the envelope. At the early stages of\nintermediate-mass star formation, shocks due to outflows appear to\ndominate whereas at later stages radiation is more important.\n\n\\section{Embedded, Infrared-Bright Massive YSOs}\n\n\\subsection{Sample}\n\nThe availability of complete, high quality ISO spectra for a\nsignificant sample of massive young stars provides a unique\nopportunity to study these sources through a combination of infrared\nand submillimeter spectroscopy, and further develop these diagnostics.\nVan der Tak et al.\\ (2000a) have selected a set of $\\sim$10 deeply\nembedded massive YSOs which are bright at mid-infrared wavelengths (12\n$\\mu$m flux $>$ 100 Jy), have luminosities of $10^3 - 2\\times 10^5$\nL$_{\\odot}$ and distances $d\\leq$4 kpc. The sources are all in an\nearly evolutionary state (comparable to the `Class 0/I' or `Group I'\nstages of low- and intermediate-mass stars), as indicated by their\nweak radio continuum emission and absence of ionic lines and PAH\nfeatures. In addition to ISO spectra, JCMT submillimeter data and\nOVRO interferometer observations have been obtained. For most of the\nobjects high spectral resolution ground-based infrared data of CO,\n$^{13}$CO and H$_3^+$ are available (Mitchell et al.\\ 1990, Geballe \\&\nOka 1996, McCall et al.\\ 1999), and occasionally H$_2$ (Lacy et\nal.\\ 1994, Kulesa et al.\\ 1999). For comparison, 5 infrared-weak\nsources with similar luminosities are studied at submillimeter\nwavelengths only. This latter set includes hot cores and ultracompact\nH~II regions such as W~3(H$_2$O), IRAS 20126+4104 (Cesaroni et al.\\ \n1997, 1999), and NGC~6334 IRS1.\n\n\\subsection{Physical structure of the envelope}\n\nIn order to derive molecular abundances from the observations, a good\nphysical model of the envelope is a prerequisite. Van der Tak et al.\\ \n(1999, 2000a) outline the techniques used to constrain the temperature\nand density structure (Figure~4). The total mass within the\nbeam is derived from submillimeter photometry, whereas the size scale\nof the envelope is constrained from line and continuum maps. The dust\nopacity has been taken from Ossenkopf \\& Henning (1994) and yields\nvalues for the mass which are consistent with those derived from\nC$^{17}$O for warm sources where CO is not depleted\nonto grains.\n\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig4.ps}{7.7cm}{0}{45}{45}{-120}{-60}\n\\caption{Overview of method used for constraining the temperature and density\nstructure of envelopes. A power-law density structure with trial values\nfor the exponent\n$\\alpha_i$ and molecular abundances $X_j$ is adopted\n(based on: van der Tak et al.~2000a).}\n\\label{fig-4}\n\\end{figure}\n\n\nThe temperature structure of the dust is calculated taking the\nobserved luminosity of the source, given a power-law density structure\n(see below). At large distances from the star, the temperature follows\nthe optically thin relation $\\propto r^{-0.4}$, whereas at smaller\ndistances the dust becomes optically thick at infrared wavelengths and\nthe temperature increases more steeply (see Figure~5). It is assumed\nthat $T_{\\rm gas}=T_{\\rm dust}$, consistent with explicit calculations\nof the gas and dust temperatures by, e.g., Doty \\& Neufeld (1997)\nfor these high densities.\n\nThe continuum data are sensitive to temperature and column density,\nbut not to density. Observations of a molecule with a large dipole\nmoment are needed to subsequently constrain the density structure. One\nof the best choices is CS and its isotope C$^{34}$S, for which lines\nranging from $J$=2--1 to 10--9 have been observed. Assuming a\npower-law density profile $n(r)= n_o (r/r_o)^{-\\alpha}$, values of\n$\\alpha$ can be determined from minimizing $\\chi^2$ between the CS\nline data and excitation models. The radiative transfer in the lines\nis treated through a Monte-Carlo method. The best fit to the data on\nthe infrared-bright sources is obtained for $\\alpha = 1.0 - 1.5$,\nwhereas the hot core/compact H~II region sample requires higher\nvalues, $\\alpha \\approx 2$. This derivation assumes that the CS\nabundance is constant through the envelope; if it increases with\nhigher temperatures, such as may be the case for hot cores, the values\nof $\\alpha$ are lowered. Note that the derived values of\n$\\alpha=1.0-1.5$ are lower than those found for deeply embedded\nlow-mass objects, where $\\alpha\\approx 2$ (e.g., Motte et al.\\ 1998,\nHogerheijde et al.\\ 1999).\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig5.ps}{7.0cm}{-90}{45}{45}{-170}{260}\n\\vspace{-0.3cm}\n\\caption{Derived temperature and density structure for the envelope\naround the massive YSO\nGL 2591 (L=$2\\times 10^4$ L$_{\\odot}$, $d$=1 kpc). \nThe critical densities of the CS 2--1 and 10--9 lines are\nindicated, as are the typical beam sizes of the JCMT \nat 345 GHz and OVRO at 100 GHz (based on: van der Tak et \nal.\\ 1999).}\n\\label{fig-5}\n\\vspace{-0.5cm}\n\\end{figure}\n\n\nFigure 5 displays the derived temperature and density structure\nfor the source GL 2591, together with the sizes of the JCMT and\nOVRO beams. While the submillimeter data are weighted toward the\ncolder, outer envelope, the infrared absorption line observations sample\na pencil-beam line of sight toward the YSO and are more sensitive to\nthe inner warm ($\\sim 1000$~K) region. On these small scales, the\nenvelope structure deviates from a radial power law, which decreases\nthe optical depth at near-infrared wavelengths by a factor of \n$\\sim 3$ (van der Tak et al.\\\n1999).\n\n\nFor sources for which interferometer data are available, unresolved\ncompact continuum emission is detected on scales of a few thousand AU\nor less. This emission is clearly enhanced compared with that\nexpected from the inner ``tip'' of the power-law envelope, and its\nspectral index indicates optically thick warm dust, most likely in a\ndense circumstellar shell or disk. The presence of this shell or disk\nis also indicated by the prevalence of blue-shifted outflowing dense\ngas without a red-shifted counterpart on $< 10''$ scales.\n\n\n\\subsection{Chemical structure: infrared absorption lines}\n\nThe ISO-SWS spectra of the infrared-bright sources show absorption by\nvarious gas-phase molecules, in addition to strong features by ices.\nMolecules such as CO$_2$ (van Dishoeck et al.\\ 1996,\nBoonman et al.\\ 1999, 2000a), H$_2$O (van Dishoeck \\& Helmich 1996, Boonman\net al.\\ 2000b), CH$_4$ (Boogert et al.\\ 1998), HCN and C$_2$H$_2$\n(Lahuis \\& van Dishoeck 2000) have been detected (see also van\nDishoeck 1998, Dartois et al.\\ 1998).\n\nIn the infrared, absorption out of all $J$-levels is observed in a\nsingle spectrum. The excitation temperatures $T_{\\rm ex}$ of the\nvarious molecules, calculated assuming LTE, range from $\\ltsim 100$ to\n$\\sim 1000$~K between sources, giving direct information on \nthe physical component in which the molecules reside. While CO \nis well-mixed throughout the envelopes, H$_2$O, HCN and C$_2$H$_2$ are\nenhanced at high temperatures. In contrast, CO$_2$ seems to avoid the\nhottest gas. High spectral resolution ground-based data of HCN and\nC$_2$H$_2$ by Carr et al.\\ (1995) and Lacy et al.\\ (1989) for a few\nobjects suggest line widths of at most a few km s$^{-1}$, excluding an\norigin in outflowing gas.\n\nThe abundances of H$_2$O, HCN and C$_2$H$_2$ increase by factors of\n$\\gtsim 10$ with increasing $T_{\\rm ex}$ (see Figure~7). The warm\nH$_2$O must be limited to a $\\ltsim 1000$~AU region, since the pure\nrotational lines are generally not detected in the $80''$ ISO-LWS beam\n(Wright et al.\\ 1997). For CO$_2$, the abundance variation between\nsources is less than a factor of 10, and no clear trend with $T_{\\rm\n ex}$ is found. For the same sources, the H$_2$O and CO$_2$ ice\nabundances show a decrease by an order of magnitude, consistent with\nevaporation of the ices. However, the gas-phase H$_2$O and CO$_2$\nabundances are factors of $\\sim 10$ lower than expected if all\nevaporated molecules stayed in the gas phase, indicating that\nsignificant chemical processing occurs after evaporation. More\ndetailed modeling using the source structures derived from\nsubmillimeter data is in progress.\n\n\\begin{figure}[t]\n\\plotfiddle{dishoeck_fig6.ps}{6.8cm}{-90}{50}{50}{-210}{260}\n\\caption{{\\it Left:}~Abundance of HCN,\n$N$(HCN)/$N_{\\rm tot}$(H$_2$), as a function of the\n$^{13}$CO excitation temperature measured by\nMitchell et al.\\ (1990). {\\it Middle:} Abundance of H$_2$O in the warm gas\n$N$(H$_2$O)/$N_{\\rm warm}$(H$_2$) as a function of $^{13}$CO excitation\ntemperature;\n{\\it Right:}~Abundance of H$_2$O ice as a function of\n$^{13}$CO excitation temperature. The same trend\nis found if the dust temperature, as derived from the 45/100 $\\mu$m\nflux, is used (based on: Lahuis \\& van Dishoeck 2000; van Dishoeck 1998).}\n\\label{fig-6}\n\\end{figure}\n\n\n\\subsection{Chemical structure: submillimeter emission}\n\nThe JCMT data of the infrared-bright objects show strong lines, but\nlack the typical crowded `hot core' spectra observed for objects such\nas W~3(H$_2$O) and NGC 6334 IRS1. Complex organics such as\nCH$_3$OCH$_3$ and CH$_3$OCHO are detected in some sources (e.g., GL\n2591, NGC 7538 IRS1), but are not as prominent as in the comparison\nsources. Yet warm gas is clearly present in these objects.\nIs the `hot core' still too small to be picked up by the\nsingle dish beams, or are the abundances of these molecules not (yet)\nenhanced?\n\nTo investigate this question, \nvan der Tak et al.\\ (2000b) consider the analysis of\ntwo species, H$_2$CO and CH$_3$OH. Both\nspecies have many lines throughout the submillimeter originating from\nlow- and high-lying energy levels. Given the physical structure\ndetermined in \\S 4.2, abundance {\\it profiles} can be constrained. Two\nextreme, but chemically plausible models are considered: (i) a model\nwith a constant abundance throughout the envelope. This model is\nmotivated by the fact that pure gas-phase reaction schemes do not show\nlarge variations in calculated abundances between 20 and 100~K; (ii) a\nmodel in which the abundance `jumps' to a higher value at the ice\nevaporation temperature, $T_d\\approx 90$~K. In this model, the\nabundances in the outer envelope are set at those observed in cold\nclouds, so that the only free parameter is the amount of abundance\nincrease.\n\nIt is found that the H$_2$CO data can be well fit with a constant\nabundance of a few $\\times 10^{-9}$ throughout the envelope. However,\nthe high $J,K$ data for CH$_3$OH require a jump in its abundance from\n$\\sim 10^{-9}$ to $\\sim 10^{-7}$ for the warmer sources. This is\nconsistent with the derived excitation temperatures: H$_2$CO has a\nrather narrow range of $T_{\\rm ex}$=50--90~K, whereas CH$_3$OH shows\n$T_{\\rm ex}$=30--200~K. Moreover, the interferometer maps of CH$_3$OH\nrule out constant abundance models. The jump observed for CH$_3$OH is\nchemically plausible since this molecule is known to be present in icy\ngrain mantles with abundances of 5--40\\% with respect to H$_2$O ice,\ni.e., $\\sim 10^{-7}-10^{-6}$ w.r.t.\\ H$_2$. Similar increases in the\nabundances of organic molecules (e.g., CH$_3$OH, C$_2$H$_3$CN, ....)\nare found with increasing $T_{\\rm dust}$ for a set of `hot--core'\nobjects by Ikeda \\& Ohishi (1999).\n\n\n\\subsection{Comparison with chemical models}\n\nBoth the infrared and submillimeter data show increases in the\nabundances of various molecules with increasing temperature. Four\ntypes of species can be distinguished: (i) `passive' molecules which\nare formed in the gas phase, freeze out onto grains during the cold\n(pre-)collapse phase and are released during warm-up without chemical\nmodification (e.g., CO, C$_2$H$_2$); (ii) molecules which are formed\non the grains during the cold phase by surface reactions and are\nsubsequently released into the warm gas (e.g., CH$_3$OH); (iii)\nmolecules which are formed in the warm gas by gas-phase reactions with\nevaporated molecules (e.g., CH$_3$OCH$_3$); (iv) molecules which are\nformed in the hot gas by high temperature reactions (e.g., HCN). These\ntypes of molecules\nare associated with characteristic temperatures of (a) $T_{\\rm\n dust}<20$~K, where CO is frozen out; the presence of CO ice is\nthought to be essential for the formation of CH$_3$OH; (b) $T_{\\rm\n dust} \\approx 90$~K, where all ices evaporate on a time scale of\n$<10^5$ yr; and (c) $T_{\\rm gas}>230$~K, where gas-phase reactions\ndrive the available atomic oxygen into water through the reactions O +\nH$_2$ $\\to$ OH $\\to$ H$_2$O (Ceccarelli et al.\\ 1996, Charnley 1997).\nAtomic oxygen is one of the main destroyers of radicals and carbon\nchains, so that its absence leads to enhanced abundances of species\nlike HCN and HC$_3$N in hot gas.\n\nWater is abundantly formed on the grains, but the fact that the\nH$_2$O abundance in the hot gas is not as large as that of the ices\nsuggests that H$_2$O is broken down to O and OH after evaporation by\nreactions with H$_3^+$. H$_2$O can subsequently be reformed in warm\ngas at temperatures above $\\sim$230~K, but Figure~7 indicates that not\nall available gas-phase oxygen is driven into H$_2$O, as the models\nsuggest. The low abundance of CO$_2$ in the warm gas is still a\npuzzle, since evaporation of abundant CO$_2$ ice is observed. The\nmolecule must be broken down rapidly in the warm gas, with no\nreformation through the CO + OH $\\to$ CO$_2$ reaction (see question by\nMinh).\n\n\\subsection{Evolution?}\n\nThe objects studied by van der Tak et al.\\ (2000a) are all in an early\nstage of evolution, when the young stars are still deeply embedded in\ntheir collapsing envelope. Nevertheless, even within this narrow\nevolutionary range, there is ample evidence for physical and chemical\ndifferentiation of the sources. This is clearly traced by the\nincrease in the gas/solid ratios, the increase in abundances of several\nmolecules, the decrease in the ice abundances, and the increase\nof the amount of crystalline ice with increasing temperature\n(Boogert et al.\\ 2000a).\n\nThe fact that the various indicators involve different\ncharacteristic temperatures ranging from $<$50 K (evaporation of\napolar ices) to 1000 K ($T_{\\rm ex}$ of gas-phase molecules)\nindicates that the heating is not a local effect, but that `global\nwarming' occurs throughout the envelope. Moreover, it cannot be a\ngeometrical line-of-sight effect in the mid-infrared data, since the\nfar--infrared continuum (45/100 $\\mu$m) and submillimeter line data\n(CH$_3$OH) show the same trend. Shocks with different filling factors\nare excluded for the same reason.\n\nCan we relate this `global warming' of the envelope to an evolutionary\neffect, or is it determined by other factors? The absence of a\ncorrelation of the above indicators with luminosity or mass of the\nsource argues against them being the sole controlling factor. The\nonly significant trend is found with the ratio of envelope mass over\nstellar mass. The physical interpretation of such a relation would be\nthat with time, the envelope is dispersed by the star, resulting in a\nhigher temperature throughout the envelope.\n\n\\section{Outstanding questions and future directions}\n\nThe results discussed here suggest that the observed chemical abundance and\ntemperature variations can indeed be used to trace the evolution of\nthe sources, and that, as in the case of low- and intermediate-mass\nstars, the dispersion of the envelope plays a crucial role. \nThe combination of infrared and submillimeter diagnostics\nis very important in the analysis. An\nimportant next step would be to use these diagnostics to probe a much\nwider range of evolutionary stages for high-mass stars, especially in\nthe hot core and (ultra-)compact H II region stages, to develop a more\ncomplete scenario of high-mass star formation. The relation between\nthe inner warm envelope and the `hot core' is still uncertain: several\nobjects have been observed which clearly have hot gas and evaporated\nices (including CH$_3$OH) in their inner regions, but which do not\nshow the typical crowded `hot core' submillimeter spectra. Are these\nobjects just on their way to the `hot core' chemical phase? Or is the\n`hot core' a separate physical component, e.g., a dense shell at the\nedge of the expanding hyper-compact H~II region due to the pressure\nfrom the ionized gas, which is still too small to be\npicked up by the single-dish beams? In either case, time or evolution\nplays a role and would constrain the ages of the infrared-bright\nsources to less than a few $\\times 10^4$ yr since evaporation.\nInterferometer data provide evidence for the presence of a separate\nphysical component in the inner 1000 AU, but lack the spatial\nresolution to distinguish a shell from any remnant disk, for example\non kinematic grounds. \n\nAn important difference between high- and low-mass objects may be the\nmechanism for the heating and dispersion of their envelopes. For\nlow-mass YSOs, entrainment of material in outflows is the\ndominant process (Lada 1999). For intermediate-mass stars, outflows\nare important in the early phase, but ultraviolet radiation\nbecomes dominant in the later stages (see \\S~3). The situation for\nhigh-mass stars is still unclear. The systematic increase in\ngas/solid ratios and gas-phase abundances point to global heating of\nthe gas and dust, consistent with a radiative mechanism. However, a\nclear chemical signature of ultraviolet radiation on gas-phase species\nand ices in the embedded phase has not yet been identified, making it\ndifficult to calibrate its effect. On the other hand, high-mass stars\nare known to have powerful outflows and winds, but a quantitative\ncomparison between their effectiveness in heating an extended part\nof the envelope and removing material is still\nlacking. Geometrical effects are more important in less embedded\nsystems, as is the case for low-mass stars, where the circumstellar\ndisk may shield part of the envelope from heating (Boogert et al.\\ \n2000b).\n\n\nTo what extent does the chemical evolution picture also apply to\nlow-mass stars? Many of the chemical processes and characteristics\nlisted in Table~1 are also known to occur for low-mass YSOs, but\nseveral important diagnostic tools are still lacking. In particular,\nsensitive mid-infrared spectroscopy is urgently needed to trace the evolution\nof the ices for low-mass YSOs and determine gas/solid ratios. Also,\nmolecules as complex as CH$_3$OCH$_3$ and C$_2$H$_5$CN have not yet\nbeen detected toward low-mass YSOs, although the limits are not very\nstringent (e.g., van Dishoeck et al.\\ 1995). Evaporation of ices\nclearly occurs in low-mass environments as evidenced by enhanced\nabundances of grain-surface molecules in shocks (e.g., Bachiller \\&\nP\\'erez-Guti\\'errez 1997), but whether a similar `hot core' chemistry\nensues is not yet known. Differences in the \nH/H$_2$ ratio and temperature structure in the (pre-)collapse\nphase may affect the\ngrain-surface chemistry and the ice composition,\nleading to different abundances of solid CH$_3$OH, which \nis an essential ingredient\nfor building complex molecules.\n\nFuture instrumentation with high spatial resolution ($< 1''$) and\nhigh sensitivity will be essential to make progress in our\nunderstanding of the earliest phase of massive star formation, in\nparticular the SMA and ALMA at submillimeter wavelengths, and SIRTF,\nSOFIA, FIRST and ultimately NGST at mid- and far-infrared wavelengths.\n\n\n\n\\acknowledgments\n\nThe authors are grateful to G.A. Blake, A.C.A.\\ Boogert, A.M.S.\\ Boonman, P.\\ \nEhrenfreund, N.J.\\ Evans, T.\\ Giannini, F.\\ Lahuis, L.G.\\ Mundy, A.\\ \nNummelin, W.A.\\ Schutte, A.G.G.M.\\ Tielens, and M.E.\\ van den Ancker\nfor discussions, collaborations and figures. 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E. 1999, \\apj, 523, 683 \n\n\n\\reference\nLorenzetti, D. et al.\\ 1999, A\\&A, 346, 604\n\n\\reference\nMcCall, B.J., Geballe, T.R., Hinkle, K.H. \\& Oka, T. 1999, ApJ, 522, 338\n\n\\reference\nMillar, T.J.\\ 1997, in \nMolecules in Astrophysics: Probes and Processes,\nIAU Symposium 178, ed.\\ E.F.\\ van Dishoeck (Dodrecht: Kluwer), p.\\ 75\n\n\\reference\nMitchell, G.F., Maillard, J.--P., Allen, M., Beer, R., \\& Belcourt, K. 1990,\nApJ, 363, 554\n\n\\reference\nMotte, F., Andr\\'e, \nP. \\& Neri, R. 1998, \\aap, 336, 150 \n\n\\reference Nummelin, A., Bergman, \nP., Hjalmarson, \\AA., Friberg, P., Irvine, W. M., Millar, T. J., Ohishi, M. \n\\& Saito, S. 1998, \\apjs, 117, 427 \n\n\n\\reference\nOhishi, M.\\ 1997, in Molecules in Astrophysics: Probes and Processes,\nIAU Symposium 178, ed.\\ E.F.\\ van Dishoeck (Dordrecht: Kluwer), p.\\ 61\n\n\\reference\nOhishi, M. \\& Kaifu, N.\\ 1999, in IAU Symposium 197 Abstract Book,\nAstrochemistry: from molecular clouds to planetary systems, \np.\\ 143\n\n\n\\reference\nOssenkopf, V.\\ \\& Henning, Th.\\ 1994, A\\&A, 291, 943\n\n\n\\reference\nSaraceno, P., Benedettini, M., Di Giorgio, A.M., et al.\\ 1999,\nin Physics and Chemistry of the Interstellar Medium III, eds.\\\nV.\\ Ossenkopf et al. (Berlin: Springer), p.\\ 279\n\n\\reference\nSchilke, P., Groesbeck, T.D., Blake, G.A., \\& Phillips, T.G.\\ 1997,\nApJS, 108, 301\n\n\n\\reference\nSimon, R., Stutzki, J., Sternberg, A., \\& Winnewisser, G.\\ 1997,\nA\\&A, 327, L9\n\n\\reference\nSutton, E.C., Jaminet, P.A., Danchi, W.C., \\& Blake, G.A.\\ 1991,\nApJS, 77, 255\n\n\\reference\nSutton, E.C., Peng, R., Danchi, W.C., et al.\\ 1995, ApJS, 97, 455\n\n\\reference\nTurner, B.E.\\ 1991, ApJS, 76, 617\n\n\\reference\nvan den Ancker, M. et al.\\ 2000a, A\\&A, submitted\n\n\\reference\nvan den Ancker, M. et al.\\ 2000b, A\\&A, in press\n\n\\reference\nvan den Ancker, M. et al.\\ 2000c, A\\&A, submitted\n\n\\reference\nvan der Tak, F.F.S., van Dishoeck, E.F., Evans, N.J., Bakker, E.J., \\&\nBlake, G.A.\\ 1999, ApJ, 522, 991\n\n\\reference\nvan der Tak, F.F.S., van Dishoeck, E.F., Evans, N.J., \\& Blake, G.A.\\ 2000a,\nApJ, in press\n\n\\reference\nvan der Tak, F.F.S.\\ \\& van Dishoeck, E.F.\\ 2000b,\nA\\&A, to be submitted\n\n\\reference\nvan Dishoeck, E.F.\\ 1998, Far.\\ Disc., 109, 31\n\n\\reference\nvan Dishoeck, E.F. \\& Blake, G.A.\\ 1998, ARAA, 36, 317\n\n\n\\reference\nvan Dishoeck, E. F., Blake, G. A., Jansen, D. J. \\& Groesbeck, T. D. 1995, \n\\apj, 447, 760 \n\n\\reference\nvan Dishoeck, E.F. \\& Helmich, F.P. 1996, A\\&A, 315, L177\n\n\\reference\nvan Dishoeck, E.F., Helmich, F.P., de Graauw, Th. et al. 1996,\nA\\&A, 315, L349\n\n\\reference\nvan Dishoeck, E.F. \\& Hogerheijde, M.R. 1999, in Origin of Stars and Planetary\nSystems,\neds.\\ C.J.\\ Lada and N.\\ Kylafis (Dordrecht:\nKluwer), p.\\ 97\n\n\\reference\nvan Dishoeck, E.F. et al.\\ 1999, in The Universe as seen by ISO,\neds.\\ P.\\ Cox and M.F.\\ Kessler (Noordwijk: ESTEC), ESA SP-427, p.\\ 437\n\n\n\\reference\nWaters, L.B.F.M.\\ \\& Waelkens, C.\\ 1998, ARAA, 36, 233\n\n\n\\reference\nWright, C.M., van Dishoeck, E.F., Helmich, F.P., Lahuis, F., Boogert, A.C.A.,\n\\& de Graauw, Th. 1997, \nin First ISO Workshop on Analytical Spectroscopy,\nESA SP-419, p. 37\n\n\\reference\nWright, C.M., van Dishoeck, E.F., Black, J.H., Feuchtgruber, H.,\nCernicharo, J., Gonz\\'alez-Alfonso, E., \\& de Graauw,\nTh.\\ 2000, A\\&A, in press \n\n\\end{references}\n\n\n\\begin{question}{M.\\ Ohishi}\nI agree with the point you mentioned, that the chemical differences among\nhot cores is due to a difference of evolutionary stage. Now we have\nseveral well-known hot cores such as Orion KL/S, W~3 IRS5/H$_2$O/IRS4,\nSgrB2 N/M/NW etc. Can you give us your personal view on the evolutionary\ndifferences of these sources?\n\\end{question} \n\n\\begin{answer}{E.F.\\ van Dishoeck}\nVan der Tak et al.\\ (2000a) argue that the infrared-bright objects such as W~3\nIRS5 represent an earlier evolutionary phase than the hot cores, on the basis\nof an anti-correlation with the radio continuum. The physical picture is that\nthe ionizing UV radiation and stellar winds push the hottest dust in the inner\nregions further out, decreasing the temperature of the dust and thus the\nnear-infrared continuum. At the same time, the size of the region which can be\nionized is increased. The `erosion' of the envelopes thus occurs from the\ninside out. For other sources, infrared diagnostics are lacking, so that the\nsituation is less clear. It would be great if chemistry could help to tie down\nthe time scales of the various phases.\n\\end{answer}\n\n\\begin{question}{W.\\ Irvine}\nHow do you interpret the behavior of the PAH features as a function of\nevolutionary stage in the sources that you discussed?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nThe absence of PAH features in the early embedded stage can be due either\nto a lack of ultraviolet radiation to excite the features or to an absence\nof the carriers. Manske \\& Henning (1999, A\\&A 349, 907) have argued \nfor the case of Herbig Ae/Be stars that\nthere should be sufficient radiation to excite PAHs in the envelope/disk\nsystem,\nso that the lack is likely due to the absence of the PAHs\nthemselves. Perhaps the PAHs have accreted into the icy mantles at the\nhigh densities in the inner envelope and do not evaporate\nand/or are chemically transformed into\nother more refractory species on grains. Alternatively, the region producing\nultraviolet radiation (H~II region) may be very small \nin these massive objects, and the photons may not reach the PAH-rich\nmaterial or have a very small beam filling factor.\nOnce the envelope breaks up and\nultraviolet radiation can escape to the less dense\nouter envelope, the PAH features from those\nregions will appear in spectra taken with large beams.\n\\end{answer}\n\n\\begin{question}{T.\\ Geballe}\nYou said that there is little evidence of the effect of ultraviolet radiation\non solid-state chemistry. Isn't the 4.6 $\\mu$m XCN feature a good example\nof that influence?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nThe `XCN' feature is indeed the best candidate for tracing the \nultraviolet processing\nof ices. If ascribed to OCN$^-$, it likely involves HNCO as\na precursor. In the laboratory, HNCO is produced by photochemical\nreactions of CO and NH$_3$, but in the interstellar medium grain surface\nchemistry is an alternative possibility which does not necessarily\ninvolve ultraviolet radiation (see Ehrenfreund \\& Schutte,\nthis volume). \n\\end{answer}\n\n\\begin{question}{Y.C.\\ Minh}\nDo you have an explanation of the low and constant abundances of CO$_2$\nin the gas phase?\n\\end{question}\n\n\\begin{answer}{E.F.\\ van Dishoeck}\nCharnley \\& Kaufman (2000, ApJ, 529, L111) argue that the evaporated CO$_2$ is\ndestroyed by reactions with atomic hydrogen at high temperatures in shocks.\nThis is an interesting suggestion, but needs to be tested against other\nspecies such as H$_2$O and H$_2$S which can be destroyed by\nreactions with atomic hydrogen as well. Also, the amount of material \nin the envelope that can be affected by shocks is not clear.\n\\end{answer}\n\n\\end{document}\n\n\n\n"
}
] |
[] |
astro-ph0002099
|
Geodetic Precession and the Binary Pulsar B1913+16
|
[
{
"author": "A. Karastergiou"
},
{
"author": "M. Kramer"
},
{
"author": "N. Wex"
},
{
"author": "A. von Hoensbroech"
}
] |
A change of the component separation in the profiles of the binary pulsar PSR B1913+16 has been observed for the first time (Kramer 1998) as expected by geodetic precession. In this work we extend the previous work by accounting for recent data from the Effelsberg 100-m telescope and Arecibo Observatory and testing model predictions. We demonstrate how the new information will provide additional information on the solutions of the system geometry.
|
[
{
"name": "contrib1.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Karastergiou, Kramer, Wex \\& von Hoensbroech}\n{Geodetic Precession and the Binary Pulsar B1913+16}\n\\pagestyle{myheadings}\n\\nofiles\n\n\\begin{document}\n\\title{Geodetic Precession and the Binary Pulsar B1913+16}\n\\author{A. Karastergiou, M. Kramer, N. Wex, A. von Hoensbroech}\n\\affil{\nMax Planck Institut f\\\"ur Radioastronomie, Auf dem H\\\"ugel 69, 53121 Bonn, Germany\n}\n\\begin{abstract}\nA change of the component separation in the profiles of the binary pulsar PSR B1913+16\nhas been observed for the first time (Kramer 1998) as\nexpected by geodetic precession.\nIn this work we extend the previous work by accounting\nfor recent data from the Effelsberg 100-m telescope and Arecibo Observatory\nand testing model predictions. We demonstrate how the new information will provide additional\ninformation on the solutions of the system geometry.\n\\end{abstract}\n\n\\vspace{-3ex}\n\n\\section{Introduction}\n\nThe binary pulsar PSR B1913+16 exhibits\na measurable amount of geodetic precession due to a misalignment of its\nspin axis and orbital angular momentum (relativistic spin orbit coupling) by an angle $\\delta$\n(see also Stairs et al., for geodetic precession in PSR B1534+12).\nThe angle between the line of sight and the spin axis, $\\zeta$, changes according to:\n\\begin{displaymath}\n\\cos\\zeta(t) = -\\cos\\delta\\cos i\n +\\sin\\delta\\sin i \\cos \\Omega_{{\\rm prec}} (t-T_0) \\;,\n\\end{displaymath}\nwhere $i$ is the orbital inclination of the binary system.\nGeneral Relativity (GR) predicts a rate of precession $\\Omega_{{\\rm prec}}=1.21$ deg yr$^{-1}$,\nleading to a change in the pulse profile and polarization characteristics with time.\n\\\\\nPrevious observations by Weisberg, Romani and Taylor (1989) detected\na change in the relative amplitude of the trailing and leading component, but no\nchange in the component separation. Also, there were no\nchanges in the position angle swing of the linear polarization noted (Cordes, Wasserman \\&\nBlaskiewicz 1990).\n\n\\section{Recent Observations Cast Some Light}\n\nThe evolution of the observed radio pulse profile of PSR B1913+16 would be\ndetermined when the four parameters\n$\\alpha, \\delta, \\rho, T_{0}$ were specified for a given $i$, where\n%\\begin{description}\n$\\alpha$ is the angle between the magnetic pole and the spin axis,\n$\\delta$ is as mentioned above,\n$\\rho$ is the angular radius of the emission cone and\n$T_{0}$ the epoch of precession.\n%\\end{description}\n\\nopagebreak\nBased on recent data from the Effelsberg 100-m telescope, Kramer (1998) first noticed a\nchange in the component separation $W$. This allows a solution region in parametric space\nthat respects GR and the\n{\\bf{\\underline{hollow cone model} (HCM)}}.\n\\begin{displaymath}\n W(t) = 2\\arccos\\left[\\frac{\\cos\\rho - \\cos\\alpha \\cos\\zeta(t)}\n {\\sin\\alpha \\sin\\zeta(t)}\\right] \n\\end{displaymath}\nEffelsberg polarization data has been used\nin respect with the \\underline{\\bf rotating vector} \\\\ \\underline{\\bf model} {\\bf(RVM)},\nto further narrow down the solution region.\n\\begin{displaymath}\n \\psi(t) = \\arctan\\left[\\frac{\\sin\\alpha\\sin(\\phi-\\phi_0)}\n {\\cos\\alpha \\sin\\zeta(t) - \\sin\\alpha\\cos\\zeta(t)}\\right] \\quad + const. \n\\end{displaymath}\n\nThe inclination of the binary orbit with respect to the line-of-sight, $i$,\nis known from timing observations modulo the ambiguity\n$i\\longrightarrow 180^\\circ - i$. The possibilities are:\nCase A: $i= 47.2^\\circ$, Case B: $i= 132.8^\\circ$ \n\n\\vspace{-2ex}\n\n\\section{The Solution Today}\n\n%\\parbox[t]{6cm}{\n\\begin{figure}[h]\n\\centerline{\n%\\hspace*{-1cm}\n\\epsfxsize=7cm\n\\epsfysize=7cm\n\\epsffile{fig.eps}\n%\\caption{The solutions for $\\alpha$ and $\\delta$ are found in the unshaded regions\n%within the areas confined by the black curves and the bounding box}\n\\hspace{0.25cm}\n\\parbox[b]{6cm}{\\sloppy\nFigure 1. {\\small The pulse component separation data (Effelsberg + Arecibo) in conjunction with the HCM\nwas used to produce a $\\chi^{2}$ area plot indicating the $3\\sigma$ confidence level\nsolutions for $\\alpha$ and $\\delta$, areas inside the surfaces traced by the black lines.\nAll possible solutions were then fed into the RVM to produce\nposition angle curves, which were compared to Effelsberg polarization data,\nonly allowing for solutions in the unshaded areas. So, the solution must be located on\na black surface\ninside an unshaded region (for detailed explanation of this figure check out \n{\\it http://www.mpifr-bonn.mpg.de/staff/akara/psr1913})\n}}}\n\\end{figure}\n\nThe set of plausible solutions has been well limited, as shown in Fig 1.\nThe inclination of the binary orbit is most likely to be Case B rather than Case A (Wex, Kalogera, Kramer\n2000). More precise use of the polarization data plus a molding of the\ntwo models (HCM \\& RVM) to specifically suit PSR B1913+16\n(see also Weisberg \\& Taylor in these proceedings)\ncould further limit the solutions and\nenable a prediction on the future of this system.\n\n\\vspace{-2ex}\n\n\\begin{references}\n\\vspace{-2ex}\n\\reference\nCordes,~J.M., Wasserman,~I., \\& Blaskiewicz,~M. 1990, \\apj, 349, 546\n\n\\reference\nDamour,~T., \\& Ruffini,~R. 1974, Acad. Sci. Paris, 279, s\\'erie A, 971\n\n\\reference\nDamour,~T., \\& Taylor,~J.H. 1992, Phys. Rev. D, 45, 1840\n\n\\reference\nHulse,~R.A., \\& Taylor,~J.H. 1975, \\apj, 195, L51\n\n\\reference\nKramer,~M. 1998, \\apj, 509, 856\n\n\\reference\nTaylor,~J.H. 1999, Proceedings of the XXXIV'th Rencontres de Moriond, to be published\n\n\\reference\nWeisberg,~J.M., Romani,~R., \\& Taylor,~J.H. 1989, \\apj, 347, 1029\n\n\\reference\nWex,~N., Kalogera,~V., Kramer,~M. 2000, \\apj, 528, 401\n\n\\end{references}\n\n\\end{document}\n\n\n"
}
] |
[] |
astro-ph0002100
|
Reionization of the Universe and the Photoevaporation of Cosmological Minihalos
|
[
{
"author": "Alejandro C. Raga \\affil{Instituto de Astronom\\'{\\i}a, Universidad Nacional Aut\\'onoma de M\\'exico}"
}
] |
The first sources of ionizing radiation to condense out of the dark and neutral IGM sent ionization fronts sweeping outward through their surroundings, overtaking other condensed objects and photoevaporating them. This feedback effect of universal reionization on cosmic structure formation is demonstrated here for the case of a cosmological minihalo of dark matter and baryons exposed to an external source of ionizing radiation with a quasar-like spectrum, just after the passage of the global ionization front created by the source. We model the pre-ionization minihalo as a truncated, nonsingular isothermal sphere in hydrostatic equilibrium following its collapse out of the expanding background universe and virialization. Results are presented of the first gas dynamical simulations of this process, including radiative transfer. A sample of observational diagnostics is also presented, including the spatially-varying ionization levels of C, N, and O in the flow if a trace of heavy elements is present and the integrated column densities of H~I, He~I and II, and C~IV thru the photoevaporating gas at different velocities which would be measured in absorption against a background source like that responsible for the ionization.
|
[
{
"name": "shapiro.tex",
"string": "\\documentclass[proceedings]{rmaa}\n%%\n%% The file `rmaa.cls' should be somewhere in your TeX search path\n%% (e.g, in the current directory, or in a personal or system-wide\n%% directory of LaTeX packages. \n%%\n%% This will not work with old versions of LaTeX: any version\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\n%% complains that it doesn't recognise the command `\\documentclass'\n%% then your LaTeX installation needs updating!\n\n%% The following package allows one to do the citations\n%% semi-automatically. It defines the commands \\cite{KEY},\n%% \\scite{KEY}, and \\pcite{KEY} which respectively produce citations\n%% in the following styles: \n%% (AUTHOR YEAR)\n%% AUTHOR (YEAR)\n%% AUTHOR YEAR\n%% For this to work, you need to pay attention to the formatting of\n%% the `\\bibitem's in your `thebibliography ' environment, qv.\n\\usepackage{rmaacite}\n%% If you would rather do your citations by hand, then comment out the \n%% above line\n\n%% Here, you can put the definitions of your own personal macros.\n%% All the special commands defined in AASTEX 4.0 (e.g. \\ion{}{},\n%% \\gtrsim, \\arcsec, \\apj, etc) are already defined. I haven't checked \n%% if there are any new ones in AASTEX 5.0 yet. \n\\newcommand{\\thOr}{$\\theta^1\\,$C~Ori}\n\\newcommand{\\zero}{_0}\n\\newcommand{\\kms}{\\,\\mbox{km s$^{-1}$}}\n\\newcommand{\\Othree}{[\\ion{O}{3}]~5007\\AA}\n\\renewcommand{\\P}[1]{%\n\\ifnum#1=1\\hbox{OW~168--326E}\\fi\n\\ifnum#1=2\\hbox{OW~167--317}\\fi\n\\ifnum#1=3\\hbox{OW~163--317}\\fi\n\\ifnum#1=5\\hbox{OW~158--323}\\fi\n\\ifnum#1=0\\hbox{OW~171--334}\\fi}\n\n%%\n%% The following commands specify the title, authors etc\n%%\n\\title{Reionization of the Universe and the Photoevaporation of Cosmological\nMinihalos}\n\\author{Paul R. Shapiro \\affil{Department of Astronomy, The University of Texas at Austin, USA} \\and Alejandro C. Raga \\affil{Instituto de Astronom\\'{\\i}a, Universidad Nacional Aut\\'onoma de M\\'exico}}\n%\\author{Paul R. Shapiro \\altaffilmark{1} and Alejandro C. Raga \\altaffilmark{2}}\n%% \\affil{Instituto de Astronom\\'{\\i}a, UNAM, Morelia} }\n%\\altaffiltext{1}{Department of Astronomy, The University of Texas at Austin,\n%Austin, TX 78712 USA}\n%\\altaffiltext{2}{Instituto de Astronom\\'{\\i}a, UNAM, Mexico D.F., Mexico}\n%% Note that the \\affil{} command is inside the argument of the\n%% \\author{} command and that a short version of the address should go \n%% here. More complicated author/address examples are discussed in the \n%% Author Guide (`rmuser.tex') and illustrated in the example document\n%% `rmtest.tex' \n\n%% The full postal addresses are specified here - they will be typeset \n%% at the end of the article. Here is also the place to put email\n%% addresses. \n\\fulladdresses{\n\\item P. R. Shapiro: Department of Astronomy, University of Texas, Austin,\nTX 78712, USA ([email protected])\n\\item A. C. Raga: Instituto de Astronom\\'\\i a,\n UNAM, Apartado Postal 70-264, 04510 M\\'exico D. F.,\nM\\'exico ([email protected])\n}\n%% Note that the `\\fulladdresses' command defines a list-like\n%% environment, so each separate address must be preceded by the\n%% `\\item' command (here there is only one, since the authors share the \n%% same address). \n\n%% Title/author for running headers\n\\shortauthor{Shapiro \\& Raga}\n\\shorttitle{Reionization and photoevaporation}\n%% These will automatically be converted to upper case in the current\n%% style. \n\n%% No more than 5 keywords, chosen from the standard list\n\\keywords{cosmology: theory --- galaxies: formation --- hydrodynamics ---\nintergalactic medium}\n\n%% The abstract:\n\n\\resumen{Las primeras fuentes de radiaci\\'on ionizante que se\n condensaron del IGM generaron frentes de ionizaci\\'on en sus\n alrededores, que iluminaron a otros objetos condensados y los\n fotoevaporaron. Mostramos la retroalimentaci\\'on causada por la\n reionizaci\\'on del Universo en la formaci\\'on de estructuras\n c\\'osmicas para el caso de un mini halo de materia oscura y bariones,\n ionizado por una fuente externa con un espectro similar al de los\n cu\\'asares, justo despu\\'es del paso del frente de ionizaci\\'on\n generado por la fuente. El mini halo es modelado, siguiendo su\n condensaci\\'on del gas en expansi\\'on as\\'{\\i} como su\n virializaci\\'on, como una esfera isot\\'ermica en equilibrio\n hidrost\\'atico. Se presentan los resultados de la primera simulaci\\'on\n hidrodin\\'amica del proceso incluyendo transferencia radiativa.\n Tambi\\'en se dan ejemplos de diagn\\'osticos observacionales,\n incluyendo la distribuci\\'on espacial del grado de ionizaci\\'on en\n el flujo de C, N y O si existen trazas de estos elementos en la\n densidad columnar integrada de H~I, He~I y II, as\\'{\\i} como el C~IV\n a diferentes velocidades en el gas fotoevaporado, que podr\\'{\\i}a\n ser observado en absorci\\'on en contra de la fuente de\n ionizaci\\'on.}\n\n\\abstract{ \nThe first sources of ionizing radiation to condense out of the dark and\nneutral IGM sent ionization fronts sweeping outward through their\nsurroundings, overtaking other condensed objects and photoevaporating them.\nThis feedback effect of universal reionization on cosmic structure \nformation is demonstrated here for the case of a cosmological minihalo of\ndark matter and baryons exposed to an external source of ionizing radiation\nwith a quasar-like spectrum, just after the passage of the global \nionization front created by the source. We model the pre-ionization\nminihalo as a truncated, nonsingular isothermal sphere in hydrostatic\nequilibrium following its collapse out of the expanding background universe\nand virialization. Results are presented of the first gas dynamical\nsimulations of this process,\nincluding radiative transfer. A sample of observational diagnostics is\nalso presented, including the spatially-varying ionization levels\nof C, N, and O in the flow if a trace of heavy elements is present and the \nintegrated column densities of H~I, He~I and II, and C~IV thru the \nphotoevaporating gas at different velocities which would be measured in\nabsorption against a background source like that responsible for the\nionization. }\n%% If your spanish is up to it, you may want to supply the resumen by\n%% uncommenting the following line:\n%\\resumen{Versi\\'on espa\\~nol del ``abstract''}\n%% Alternatively, you can leave the translation to the editors. \n\n\n%% This command is so LaTeX won't stop on errors. I've put it in so\n%% you will still be able to compile the file even if you have lost\n%% the associated PS files of the figures. \n\\nonstopmode\n\n%% The following command is necessary before beginning the text of\n%% your article. There should be a matching \\end{document} at the end\n%% of the file. \n\\begin{document}\n\n%% This command is necessary to typeset the title, abstract, etc. \n\\maketitle\n\n%%\n%% And here starts the text....\n%%\n\\section{Introduction}\n\\label{sec:intro}\nObservations of quasar absorption spectra indicate that the universe\nwas reionized prior to redshift $z=5$. Recent detections of H Lyman alpha\nemission lines from sources at even higher redshift ($z\\leq5.6$) strengthen\nthis conclusion \\cite{Hu98,Wey98}. As new discoveries push the observable\n horizon back in time ever-closer to the epoch of reionization at redshift \n$z>5$, increased awareness of its importance as a missing link in the \ntheory of galaxy formation has caused a great renewal of interest in\nuniversal reionization. If reionization took place early enough, then\nThompson scattering of cosmic microwave background (CMB) photons by free\nelectrons in an ionized intergalactic medium (IGM) would \nalso have left a detectable imprint on\nthe CMB observed today. Recent data on the first Doppler peak in\nthe angular spectrum of CMB anisotropy set limits which imply a \nreionization redshift $z\\lesssim40$ (model-dependent) \\cite{Gri98}.\n(For a review and references on reionization work prior to 1996,\nthe reader is referred to Shapiro 1995, while more recent developments are\nsummarized in Haiman \\& Knox 1999.)\n\nA review of the theory of reionization is outside the scope of this\nbrief report. In keeping with the focus of this meeting, I will\nconfine myself to a description of some recent progress on the\ncalculational side of the problem. To solve the full reionization\nproblem we must also solve the problem of how density fluctuations\nled to galaxy formation and this, in turn, led to secondary energy\nrelease in the form of ionizing and dissociating radiation by the\nstars and quasars formed inside early galaxies, as well as other forms of \nenergy release like supernova explosions, jets and winds, which in turn \ninfluenced the future course of galaxy formation. The modern context for\nthis description is the Cold Dark Matter (CDM) model, in which\na cold, pressure-free,\ncollisionless gas of dark matter dominates the\nmatter density and structure arises from the gravitational amplification of\na scale-free power-spectrum of\ninitially small-amplitude, Gaussian-random-noise primordial density\nfluctuations, in a hierarchical fashion, with small mass objects collapsing\nout first and merging together to form larger-mass objects which\nform later. The calculation of these effects poses an enormous multi-scale \ncomputational challenge, involving numerical gas dynamics coupled to \ngravitational N-body dynamics, which raises the bar of cosmological \nsimulation considerably by adding the requirement that radiative transfer\neffects be included, as well. To simplify matters,\nI will henceforth focus on just one of the central challenges of\nreionization theory, the effect of cosmological ionization fronts.\n\n\\section{Ionization Fronts in the IGM} \n\\label{sec:constraints}\n\nThe neutral, opaque IGM\nout of which the first bound objects condensed was dramatically reheated\nand reionized at some time between a redshift $z\\approx50$ and $z\\approx5$\nby the radiation released by some of these objects.\nAn early analysis of the inhomogeneous nature of reionization for the case\nof short-lived quasars occurring at random positions in a uniform\nIGM was described by Arons \\& Wingert (1972). In that treatment it was\nassumed that each quasar was instantaneously surrounded by an isolated \nH~II region, a ``relict H~II region'' undergoing recombination only, each\nsuch region filling\na volume containing just as many initially neutral H atoms as there were\nionizing photons emitted by the QSO during its lifetime. The effect\nof successive generations of QSO's was accounted for on a \nstatistically-averaged basis by allowing new generations of QSO's to turn \non at random positions, including those inside pre-existing relict H~II\nregions before their H atoms had fully recombined, leading eventually to \nthe complete overlap of these discrete ionized zones.\n\nWhen the first sources\nturned on, they actually\nionized their surroundings, not instantaneously, but\nrather by propagating weak, R-type\nionization fronts which moved outward supersonically with respect to both\nthe neutral gas ahead of and the ionized gas behind the front, racing ahead\nof the hydrodynamical response of the IGM, as first described by \nShapiro (1986) and Shapiro \\& Giroux (1987). These authors solved the\nproblem of the time-varying radius of a spherical I-front which surrounds \nisolated sources in a cosmologically-expanding IGM analytically, taking\nproper account of the I-front jump condition generalized to cosmological\nconditions. They applied these solutions to determine when the I-fronts\nsurrounding isolated sources would grow to overlap and, thereby,\ncomplete the reionization of the universe\n(Donahue \\& Shull 1987 and Meiksen \\& Madau 1993\nsubsequently adopted a similar approach to answer that question).\nThe effect of density inhomogeneity on the rate of I-front propagation\nwas described by a mean ``clumping factor'' $c_l>1$, which\nslowed the I-fronts by increasing the average recombination rate per H atom\ninside clumps. This suffices to describe the rate of I-front propagation\nas long as the\nclumps are either not self-shielding or, if so, only\nabsorb a fraction of the ionizing photons emitted by the central source. \nNumerical radiative transfer methods are currently under\ndevelopment to solve this problem in 3D for the inhomogeneous density \ndistribution which arises as cosmic structure forms, so far limited to a \nfixed density field without gas dynamics (e.g.\\ Abel, Norman, \\& Madau 1999;\nRazoumov \\& Scott 1999). The question of what\ndynamical effect the I-front had on the density inhomogeneity it\nencountered, however, requires further analysis. \n\n\nThe answer depends on the size and density of the clumps overtaken by\nthe I-front. The fate of linear density fluctuations depends upon\ntheir Jeans number, $L_J\\equiv\\lambda/\\lambda_J$, the wavelength in\nunits of the baryon Jeans length in the IGM at temperatures of order\n$10^4\\rm K$. Fluctuations with $L_J<1$ find their growth halted and\nreversed (cf.\\ Shapiro, Giroux, \\& Babul 1994). For nonlinear density\nfluctuations, however, the answer is more complicated, depending upon\nat least three dimensionless parameters, their internal Jeans number,\n$L_J\\equiv R_c/\\lambda_J$, the ratio of the cloud radius $R_c$ to the\nJeans length $\\lambda_J$ inside the cloud at about $10^4{\\rm K}$,\ntheir ``Str\\\"omgren number'' $L_s\\equiv 2 R_c/\\ell_s$, the ratio of\nthe cloud diameter $2R_c$ to the Str\\\"omgren length $\\ell_s$ inside\nthe cloud (the length of a column of gas within which the unshielded\narrival rate of ionizing photons just balances the total recombination\nrate), and their optical depth to H ionizing photons at 13.6 eV,\n$\\tau_{\\rm H}$, before ionization. If $\\tau_{\\rm H}<1$, the I-front\nsweeps across the cloud, leaving an ionized gas at higher pressure\nthan its surroundings, and exits before any mass motion occurs in\nresponse, causing the cloud to blow apart. If $\\tau_{\\rm H}>1$ and\n$L_s>1$, however, the cloud shields itself against ionizing photons,\ntrapping the I-front which enters the cloud, causing it to decelerate\ninside the cloud to the sound speed of the ionized gas before it can\nexit the other side, thereby transforming itself into a weak, D-type\nfront preceded by a shock. Typically, the side facing the source\nexpels a supersonic wind backwards towards the source, which shocks\nthe IGM outside the cloud, while the remaining neutral cloud material\nis accelerated away from the source by the so-called ``rocket effect''\nas the cloud photoevaporates (cf.\\ Spitzer 1978). As long as $L_J<1$\n(the case for gas bound to dark halos with virial velocity less than\n$\\rm 10\\,km\\,s^{-1}$), this photoevaporation proceeds unimpeded by\ngravity. For halos with higher virial velocity, however, $L_J>1$, and\ngravity competes with pressure forces. For a uniform gas of H density\n$n_{\\rm H,c}$, located a distance $r_{\\rm Mpc}$ (in Mpc) from a UV\nsource emitting $N_{\\rm ph,56}$ ionizing photons (in units of\n$\\rm10^{56}s^{-1}$), the Str\\\"omgren length is only\n$\\ell_s\\cong(100\\,{\\rm pc}) (N_{\\rm ph,56}/r_{\\rm Mpc}^2)(n_{\\rm\n H,c}/0.1\\,\\rm cm^{-3})^{-2}$. We focus in what follows on the\nself-shielded case which traps the I-front.\n \n\\section{The Photoevaporation of Dwarf Galaxy Minihalos\nOvertaken by a Cosmological Ionization Front}\n\\label{sec:anal}\n\n\n\n\n\nThe importance of this photoevaporation process has long been\nrecognized in the study of interstellar clouds exposed to ionizing\nstarlight (e.g. Oort \\& Spitzer 1955;\nSpitzer 1978; Bertoldi 1989; Bertoldi \\& McKee 1990;\nLefloch \\& Lazareff 1994; Lizano et al.\\ 1996). Radiation-hydrodynamical \nsimulations were performed in 2D in the early 1980's of\na stellar I-front overtaking a clump inside a molecular\ncloud (Sandford, Whitaker, \\& Klein 1982; Klein, Sandford, \\& Whitaker 1983).\nMore recently, 2D simulations for the case of circumstellar clouds\nionized by a single nearby star have also been performed\n(Mellema et al.\\ 1998). In the cosmological context, however,\nthe importance of this process has only recently been fully appreciated. \nIn proposing the expanding minihalo model to explain Lyman alpha\nforest (``LF'') quasar absorption lines, Bond, Szalay, \\& Silk (1988)\ndiscussed how gas originally confined by the gravity of dark\nminihalos in the CDM model would be expelled by pressure forces\nif photoionization by ionizing background radiation suddently\nheated all the gas to an isothermal condition at $T\\approx10^4\\rm K$.\nThe first radiation-hydrodynamical \nsimulations of the photoevaporation of a primordial density\ninhomogeneity overtaken by a cosmological I-front, however,\nwere described in Shapiro, Raga, \\& Mellema (1997, 1998).\nBarkana \\& Loeb (1999) subsequently considered the relative\nimportance of this process for dwarf galaxy minihalos of different masses\nin the CDM model, using static models of uniformly-illuminated spherical\nclouds in thermal and ionization equilibrium, taking H atom self-shielding\ninto account, and assuming that gas which is heated above the minihalo\nvirial temperature must be evaporated. They concluded that 50\\%--90\\% of \nthe gas in gravitationally bound objects when reionization\noccurred should have been evaporated.\n\\begin{figure}[h]\n\\parbox{0.5\\textwidth}{\n \\includegraphics[height=6.8cm]{shapiro_fig1.ps}}\n \\label{fig1}\n\\begin{minipage}{0.45\\textwidth}\n \\caption{MINIHALO INITIAL CONDITIONS BEFORE REIONIZATION:\nTruncated, nonsingular isothermal sphere (TIS) of gas and dark matter in\nhydrostatic equilibrium (Shapiro, Iliev, \\& Raga 1999) surrounded by the\ncorresponding self-similar spherical infall for an Einstein-de Sitter\nbackground universe (cf.\\ Bertschinger 1985). (a) (Top) gas density and (b)\n(Bottom) gas velocity versus distance from minihalo center.}\n\\end{minipage}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\parbox{0.5\\textwidth}{%\n \\includegraphics[height=7cm]{shapiro_fig2.ps}}\n \\label{fig2}\n\\begin{minipage}{0.45\\textwidth}\n \\caption{IONIZATION FRONT PHOTOEVAPORATES MINIHALO:\n(a) (Top) I-front position along $x$-axis versus time; (b) (Bottom) Mass\nfraction of the initial mass $M_{\\rm I}$ of minihalo hydrostatic \n core which remains neutral (H~I) versus time. }\n\\end{minipage}\n\\end{figure}\n\n\\begin{figure}[h]\n \\begin{center}\n \\leavevmode\n \\includegraphics[width=\\textwidth]{shapiro_fig3.ps}\n \\caption{PHOTOEVAPORATING MINIHALO.\n50 Myr after turn-on of quasar 1 Mpc to the left of computational box along\nthe $x$-axis. \n(a) (Upper Panel) isocontours of atomic density, logarithmically spaced, \nin $(r,x)-$plane of cylindrical coordinates; (b) (Lower Panel)\nvelocity arrows are plotted with length proportional to gas velocity.\nAn arrow of length equal to the spacing between arrows has velocity\n$30 \\kms$. Solid line shows current extent of gas originally in\nhydrostatic core. Dashed line is I-front (50\\% H-ionization contour).}\n \\label{fig3}\n \\end{center}\n\\end{figure}\n\n\\begin{figure}[p]\n \\begin{center}\n \\leavevmode\n \\includegraphics[height=0.7\\textheight]{shapiro_fig4.ps}\n \\caption{\n PHOTOEVAPORATING MINIHALO. One time-slice 50 Myr after turn-on\n of quasar located 1 Mpc away from cloud to the left of\n computational box along the $x$-axis. From top to bottom: (a)\n isocontours of pressure, logarithmically spaced, in\n $(r,x)-$plane of cylindrical coordinates; (b) pressure along the\n $r=0$ symmetry axis; (c) temperature; (d) H~I fraction; (e) He~I\n (solid) and He~II (dashed) fractions; (f) bound-free optical\n depth along $r=0$ axis at the threshold ionization energies for\n H~I (solid), He~I (dashed), He~II (dotted). Key features of the\n flow are indicated by the numbers which label them on the\n temperature plot: 1 = IGM shock; 2 = contact discontinuity\n between shocked cloud wind and swept up IGM; 3 = wind shock;\n between 3 and 4 = supersonic wind; 4 = I-front; 5 = boundary of\n gas originally in hydrostatic core; 6 = shock in shadow region\n caused by compression of shadow gas by shock-heated gas outside\n shadow.}\n \\label{fig4}\n \\end{center}\n\\end{figure}\n\n\\begin{figure}\n%\\parbox{0.55\\textwidth}\n\\begin{center}\n\\leavevmode\n{\\includegraphics[height=9.0cm]{shapiro_fig5.ps}}%\n%\\begin{minipage}{0.45\\textwidth}\n \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n MINIHALO I: IONIZATION STRUCTURE OF METALS.\n Carbon, nitrogen, and oxygen ionic fractions along symmetry\n axis at $t = 50\\rm\\,Myr$.}\n \\label{fig5}\n\\end{center}\n%\\end{minipage}\n% \\begin{center}\n% \\leavevmode\n% \\includegraphics[totalheight=4in]{shapiro_fig5.ps}\n% \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n% MINIHALO I: IONIZATION STRUCTURE OF METALS.\n% Carbon, nitrogen, and oxygen ionic fractions along symmetry\n% axis at $t = 50\\rm\\,Myr$.}\n% \\label{fig5}\n% \\end{center}\n\\end{figure}\n\nAs a first study of these important effects, \nShapiro, Raga, \\& Mellema (1997, 1998) simulated the\nphotoevaporation of a uniform, spherical, neutral, intergalactic cloud of \ngas mass $1.5\\times10^6M_\\odot$, radius $R_c=0.5\\,\\rm kpc$, \ndensity $n_{\\rm H,c}=0.1\\,{\\rm cm^{-3}}$ and $T=100\\,\\rm K$, located \n$1\\,\\rm Mpc$ from a quasar with emission spectrum $F_\\nu\\propto\\nu^{-1.8}$\n($\\nu>\\nu_{\\rm H}$) and $N_{\\rm ph}=10^{56}{\\rm s}^{-1}$, initially\nin pressure balance with\nan ambient IGM of density $0.001\\,\\rm cm^{-3}$ which\nat time $t=0$ had\njust been photoionized by the passage of\nthe intergalactic R-type I-front generated when the quasar turned on\n[i.e. $(L_J,L_s,\\tau_H)\\approx (0.1,10,10^3)$].\n [A standard top-hat \nperturbation which collapses and virializes at $z_{\\rm coll}=9$,\nfor example, with total mass $\\cong10^7M_\\odot$, has circular velocity\n$v_c\\cong7\\,\\rm km\\,s^{-1}$, $R_c\\cong560\\rm\\,pc$, and\n$n_{\\rm H,c}=0.1\\,\\rm cm^{-3}$, if $\\Omega_{\\rm bary}h^2=0.03$ and $h=0.5$.]\nThe cloud contained H, He, and heavy elements at $10^{-3}$\ntimes the solar abundance. Our simulations in 2D, axisymmetry used an\nEulerian hydro code with Adaptive Mesh Refinement and\nthe Van~Leer flux-splitting algorithm, which\nsolved nonequilibrium ionization rate equations (for H, He, C, N, O, Ne,\nand S) and included an explicit treatment of radiative transfer\nby taking into account the bound-free opacity of H and He \n(Raga et al.\\ 1995; Mellema et al.\\ 1997; Raga, Mellema, \\& Lundquist 1997).\nThe reader is referred to Shapiro et al.\\ (1997, 1998) for further details.\n\\begin{figure}\n%\\parbox{0.6\\textwidth}\n\\begin{center}\n\\leavevmode\n{\\includegraphics[height=8cm]{shapiro_fig6.ps}}%\n%\\begin{minipage}{0.4\\textwidth}\n \\caption{OBSERVATIONAL DIAGNOSTICS OF PHOTOEVAPORATING\n MINIHALO II. ABSORPTION LINES: \n Cloud column densities ($\\rm cm^{-2}$) along symmetry axis at\n different velocities. (Top) H~I; (Middle) He~I (solid) and\n He~II (dotted); (Bottom) C~IV. Each box labelled with time \n (in Myrs) since QSO turn-on.}\n \\label{fig6}\n%\\end{minipage}\n\\end{center}\n\\end{figure}\n\nHere we shall present for the first time the results of simulations\nof a more realistic, cosmological minihalo, in which the uniform cloud \ndescribed above is replaced by a self-gravitating,\ncentrally condensed object.\nOur initial condition before ionization, shown in Figure 1, is\nthat of a $10^7M_\\odot$ minihalo in an Einstein-de~Sitter\nuniverse ($\\Omega_{\\rm CDM}=1-\\Omega_{\\rm bary}$; $\\Omega_{\\rm\nbary}h^2=0.02$;\n$h=0.7$) which collapses out and virializes at $z_{\\rm coll}=9$,\nyielding a truncated, nonsingular isothermal sphere of radius \n$R_c=0.5\\,\\rm kpc$ in hydrostatic equilibrium\nwith virial temperature $T_{\\rm vir}=5900\\,\\rm K$\nand dark matter velocity dispersion $\\sigma=6.3\\,\\rm km\\,s^{-1}$,\naccording to the solution of Shapiro, Iliev, \\& Raga (1999),\nfor which the finite central density inside a radius about 1/30 of the\ntotal size of the sphere \nis 514 times the surface density. This\nhydrostatic core of radius $R_c$ is embedded in a self-similar,\nspherical, cosmological infall according to Bertschinger (1985).\nThe results of our simulation on an $(r,x)$-grid with $256\\times512$ cells\n(fully refined)\nare summarized in Figures~2--6.\nThe background IGM and infalling gas outside the minihalo are quickly\nionized, and the resulting pressure gradient in the infall region\nconverts the infall into an outflow.\nThe I-front is trapped, however, inside the hydrostatic core\nof the minihalo. Figure~2(a) shows the position of the I-front inside\nthe minihalo as it slows from weak, R-type to weak D-type as it advances\nacross the original hydrostatic core. Figure~2(b) shows the mass of the\nneutral zone within the original hydrostatic core shrinking as\nthe minihalo photoevaporates within about 70~Myrs. \nThis photoevaporation time is significantly less than that found previously for a similar-mass object with\nthe same external source in the uniform cloud case.\nFigures~3 and 4\nshow the structure of the photoevaporative flow 50~Myrs after the\nglobal I-front first overtakes the minihalo, with key features of\nthe flow indicated by the labels on the temperature plot in Figure~4.\nFigure~5 shows the spatial variation of the relative ionic abundances of\nC, N, O ions along the symmetry axis after 50~Myrs.\nAs in the case of the uniform cloud,\nFigure~5 shows the presence at 50~Myrs\nof low as well as high\nionization stages of the metals.\nCompared to the uniform cloud case at the same time-slice, however,\nFigure~5 shows a somewhat higher degree of ionization on the\nside facing the source than in those previous results.\nThe column densities of H~I, He~I and II, and C~IV for minihalo gas of\ndifferent velocities as seen along the symmetry axis at different times\nare shown in Figure~6. \nAt early times, the cloud gas resembles a weak\nDamped Lyman Alpha (``DLA'') absorber with small velocity width \n($\\sim10\\rm\\,km\\,s^{-1}$) and $N_{\\rm H\\,I}\\sim10^{20}\\rm cm^{-2}$,\nwith a \nLF-like red wing ($\\hbox{velocity width}\\,\\sim10\\,\\rm km\\,s^{-1}$)\nwith $N_{\\rm H\\,I}\\sim10^{16}\\rm cm^{-2}$ on the side moving toward\nthe quasar, with a C~IV feature with\n$N_{\\rm C\\,IV}\\sim10^{12}\\rm cm^{-2}$ displaced in\nthis same asymmetric way from the velocity of peak H~I column\ndensity. After 160~Myr,\nhowever, only a narrow H~I feature with LF-like column density\n$N_{\\rm H\\,I}\\sim10^{14}\\rm cm^{-2}$ remains, with \n$N_{\\rm He\\,II}/N_{\\rm H\\,I}\\sim10^2$ and\n$N_{\\rm C\\,IV}/N_{\\rm H\\,I}\\sim\\rm[C]/[C]_\\odot$. \nA comparison with the\nresults of the uniform cloud case in Shapiro et al.\\ (1997, 1998)\nshows that, despite their differences,\nthere is a surprising degree of similarity between the qualitative \nfeatures presented there and those found here for a highly \ncentrally-concentrated minihalo. Future work will extend this study to \nminihalos\nof higher virial temperatures, for which gravity competes more effectively\nwith photoevaporation.\n\n\n\\acknowledgements \nThis work was supported by NASA Grants NAG5-2785, NAG5-7363, and\nNAG5-7821, and NSF Grant ASC-9504046,\nand was made possible by a UT Dean's Fellowship and a National\nChair of Excellence, UNAM, M\\'exico awarded by CONACyT in 1997 to Shapiro.\nThis material is based in part upon work supported by the\nTexas Advanced Research Program under Grant No. 3658-0624-1999.\n\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format: \n%%\n%% \\bibitem[AUTHOR<YEAR>]{KEY} \n%%\n%% so that the \\cite{KEY}, etc. commands will work properly. \n%% \n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%% \n\\enlargethispage{4ex}\n\\begin{thebibliography}\n\n%\\bibitem[Bally et al.{}<1995>]{p:Bal95} \n% Bally, J., Devine, D. \\& Sutherland, R. 1995, In: S. Lizano \\&\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\n\n\\bibitem[{}<>]{}\nAbel, T., Norman, M. L., \\& Madau, P. 1999, ApJ, {523}, 66\n\n\\bibitem[{Arons} \\& {Wingert}<1972>]{Aro72}\n{Arons}, J., \\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\n\n\\bibitem[{}<>]{} Barkana, R., \\& Loeb, A. 1999, ApJ, {523}, 54\n\n\\bibitem[{}<>]{} \nBertoldi, F. 1989, ApJ, {346}, 735\n\n\\bibitem[{}<>]{} \nBertoldi, F., \\& McKee, C. 1990, ApJ, {354}, 529\n\n\\bibitem[{}<>]{}\nBertschinger, E. 1985, ApJS, {58}, 39\n\n\\bibitem[{}<>]{} \nBond, J. R., Szalay, A. S., \\& Silk, J. 1988, \nApJ, 324, 627\n\n\\bibitem[{}<>]{}\nDonahue, M., \\& Shull, J. M. 1987, ApJ, {323}, L13\n\n\\bibitem[{Griffiths}, {Barbosa}, \\& {Liddle}<1998>]{Gri98}\n{Griffiths}, L.~M., {Barbosa}, D., \\& {Liddle}, A.~R. 1998,\nMNRAS, {308}, 854\n\n\\bibitem[{Haiman} \\& {Knox}<1999>]{Hai99}\n{Haiman}, Z., \\& {Knox}, L. 1999, in ASP Conf.\\ Ser.\\ Vol.\\ 181, Sloan Summit on Microwave Foreground, ed.\\ A.~de~Oliveira \\& M. Tegmark (San Francisco: Astronomical Society of the Pacific), 227 (astro-ph/9902311)\n\n\\bibitem[{Hu}, {Cowie}, \\& {McMahon}<1998>]{Hu98}\n {Hu}, E.~M., {Cowie}, L.~L., \\& {McMahon}, R.~G. 1998, ApJ, {502}, 99\n\n\\bibitem[{}<>]{} \nKlein, R. I., Sandford, M. T., \\& Whitaker, R. W. 1983, \nApJ, {271}, L69\n\n\\bibitem[{}<>]{}\nLefloch, B., \\& Lazareff, B. 1994, \nA\\&A, {289}, 559\n\n\\bibitem[{}<>]{} \nLizano, S., Cant\\'o, J., Garay, G., \\& Hollenbach, D. 1996, \nApJ, {468}, 739\n\n\\bibitem[{}<>]{}\nMeiksen, A., \\& Madau, P. 1993,\nApJ, {412}, 34\n\n\\bibitem[{}<>]{} \nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\n Steffen, W., \\& Noriega-Crespo, A. 1998, \nA\\&A, {331}, 335\n\n\\bibitem[{}<>]{}\n Oort, J. H., \\& Spitzer, L. 1955, ApJ, {121}, 6\n\n\\bibitem[{}<>]{} \nRaga, A. C., Taylor, S. D., Cabrit, S., \\& Biro, S. 1995, \n A.Ap., {296}, 833\n\n\\bibitem[{}<>]{} \nRaga, A. C., Mellema, G., \\& Lundquist, P. 1997, ApJS, {109}, 517\n\n\\bibitem[{}<>]{}\nRazoumov, A., \\& Scott, D. 1999, MNRAS, {309}, 287 \n\n\\bibitem[{}<>]{}\nSandford, M. T., Whitaker, R. W., \\& Klein, R. I. 1982, ApJ, {260}, 183\n\n\\bibitem[{Shapiro}<1995>]{Sha95}\n{Shapiro}, P.~R. 1995, in ASP Conf.\\ Ser.\\ Vol.\\ 80, The Physics of the Interstellar Medium and\nThe Intergalactic Medium, ed. A.~Ferrara, C.~F.~McKee,\nC.~Heiles, \\& P.~R.~Shapiro (San Francisco: Astronomical Society of the Pacific), 55\n \n\\bibitem[{}<>]{} \nShapiro, P. R. 1986, PASP, {98}, 1014\n\n\\bibitem[{}<>]{} \nShapiro, P. R., \\& Giroux, M. L. 1987, ApJ, {321}, L107\n\n\\bibitem[{}<>]{}\n Shapiro, P. 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"string": "\\begin{thebibliography}\n\n%\\bibitem[Bally et al.{}<1995>]{p:Bal95} \n% Bally, J., Devine, D. \\& Sutherland, R. 1995, In: S. Lizano \\&\n% J.~M. Torrelles (eds.): {Circumstellar Disks, Outflows and Star\n% Formation}, RMAA (Serie de Conferencias) {1}, 19\n\n\\bibitem[{}<>]{}\nAbel, T., Norman, M. L., \\& Madau, P. 1999, ApJ, {523}, 66\n\n\\bibitem[{Arons} \\& {Wingert}<1972>]{Aro72}\n{Arons}, J., \\& {Wingert}, D.~W. 1972, ApJ, {177}, 1\n\n\\bibitem[{}<>]{} Barkana, R., \\& Loeb, A. 1999, ApJ, {523}, 54\n\n\\bibitem[{}<>]{} \nBertoldi, F. 1989, ApJ, {346}, 735\n\n\\bibitem[{}<>]{} \nBertoldi, F., \\& McKee, C. 1990, ApJ, {354}, 529\n\n\\bibitem[{}<>]{}\nBertschinger, E. 1985, ApJS, {58}, 39\n\n\\bibitem[{}<>]{} \nBond, J. R., Szalay, A. S., \\& Silk, J. 1988, \nApJ, 324, 627\n\n\\bibitem[{}<>]{}\nDonahue, M., \\& Shull, J. M. 1987, ApJ, {323}, L13\n\n\\bibitem[{Griffiths}, {Barbosa}, \\& {Liddle}<1998>]{Gri98}\n{Griffiths}, L.~M., {Barbosa}, D., \\& {Liddle}, A.~R. 1998,\nMNRAS, {308}, 854\n\n\\bibitem[{Haiman} \\& {Knox}<1999>]{Hai99}\n{Haiman}, Z., \\& {Knox}, L. 1999, in ASP Conf.\\ Ser.\\ Vol.\\ 181, Sloan Summit on Microwave Foreground, ed.\\ A.~de~Oliveira \\& M. Tegmark (San Francisco: Astronomical Society of the Pacific), 227 (astro-ph/9902311)\n\n\\bibitem[{Hu}, {Cowie}, \\& {McMahon}<1998>]{Hu98}\n {Hu}, E.~M., {Cowie}, L.~L., \\& {McMahon}, R.~G. 1998, ApJ, {502}, 99\n\n\\bibitem[{}<>]{} \nKlein, R. I., Sandford, M. T., \\& Whitaker, R. W. 1983, \nApJ, {271}, L69\n\n\\bibitem[{}<>]{}\nLefloch, B., \\& Lazareff, B. 1994, \nA\\&A, {289}, 559\n\n\\bibitem[{}<>]{} \nLizano, S., Cant\\'o, J., Garay, G., \\& Hollenbach, D. 1996, \nApJ, {468}, 739\n\n\\bibitem[{}<>]{}\nMeiksen, A., \\& Madau, P. 1993,\nApJ, {412}, 34\n\n\\bibitem[{}<>]{} \nMellema, G., Raga, A. C., Canto, J., Lundqvist, P., Balick, B.,\n Steffen, W., \\& Noriega-Crespo, A. 1998, \nA\\&A, {331}, 335\n\n\\bibitem[{}<>]{}\n Oort, J. H., \\& Spitzer, L. 1955, ApJ, {121}, 6\n\n\\bibitem[{}<>]{} \nRaga, A. C., Taylor, S. D., Cabrit, S., \\& Biro, S. 1995, \n A.Ap., {296}, 833\n\n\\bibitem[{}<>]{} \nRaga, A. C., Mellema, G., \\& Lundquist, P. 1997, ApJS, {109}, 517\n\n\\bibitem[{}<>]{}\nRazoumov, A., \\& Scott, D. 1999, MNRAS, {309}, 287 \n\n\\bibitem[{}<>]{}\nSandford, M. T., Whitaker, R. W., \\& Klein, R. I. 1982, ApJ, {260}, 183\n\n\\bibitem[{Shapiro}<1995>]{Sha95}\n{Shapiro}, P.~R. 1995, in ASP Conf.\\ Ser.\\ Vol.\\ 80, The Physics of the Interstellar Medium and\nThe Intergalactic Medium, ed. A.~Ferrara, C.~F.~McKee,\nC.~Heiles, \\& P.~R.~Shapiro (San Francisco: Astronomical Society of the Pacific), 55\n \n\\bibitem[{}<>]{} \nShapiro, P. R. 1986, PASP, {98}, 1014\n\n\\bibitem[{}<>]{} \nShapiro, P. R., \\& Giroux, M. L. 1987, ApJ, {321}, L107\n\n\\bibitem[{}<>]{}\n Shapiro, P. R., Giroux, M. L., \\& Babul, A. 1994, ApJ, {427}, 25\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Iliev, I. T., \\& Raga, A. C. 1999, MNRAS, {307}, 203\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1997, in {Structure and Evolution of the Intergalactic Medium From QSO \n Absorption Line Systems}, ed. P.~Petitjean \\& S.~Charlot (Gif-sur-Yvette: Editions Fronti\\'eres), 41\n\n\\bibitem[{}<>]{}\nShapiro, P. R., Raga, A. C., \\& Mellema, G. 1998, \nin Mem.\\ Soc.\\ Astron.\\ Italiana\\ Vol.\\ 69, {H$_2$ in the Early Universe}, ed. E.~Corbelli, D.~Galli, \\& F.~Palla, 463 (astro-ph/9804117)\n\n\\bibitem[{}<>]{} \nSpitzer, L. 1978, {Physical Processes in the Interstellar Medium} (New York: Wiley Interscience)\n\n\\bibitem[{Weymann} et al.{}<1998>]{Wey98}\n {Weymann}, R.~J., {Stern}, D., {Bunker}, A., {Spinrad}, H.,\n{Chaffee}, F.~H., {Thompson}, R.~I., \\& {Storrie-Lombardi}, L.~J. 1998\n ApJ, {505}, L95\n\n\\end{thebibliography}"
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