%Edited by LCH%\NeedsTeXFormat{LaTeX2e}[1996/06/01]\def\aa{{A\&A}}\def\aas{{A\&AS}}\def\aj{{AJ}}\def\annrev{{ARA\&A}}\def\apj{{ApJ}}\def\apjs{{ApJS}}\def\baas{{BAAS}}\def\mnras{{MNRAS}}\def\nat{{Nature}}\def\pasp{{PASP}}\def\prl{{PRL}}\documentclass[cup5b]{caps}\usepackage{graphicx}\usepackage{amssymb}\usepackage{ociwsymp3}   \HeadText{R. F. Mushotzky}\def\plotone#1{\centering \leavevmode\includegraphics[width=.95\columnwidth]{#1}}\def\plottwo#1#2{\centering \leavevmode\includegraphics[width=.45\columnwidth]{#1} \hfil\includegraphics[width=.45\columnwidth]{#2}}\begin{document}\pagenumbering{arabic}\author[]{RICHARD F. MUSHOTZKY\\ NASA/Goddard Space Flight Center}\chapter{Clusters of Galaxies: An X-ray Perspective}\begin{abstract}There has been extensive recent progress in X-ray observations of clusters of galaxies with the analysis of the entire {\it ASCA} database and recent new results from {\it Beppo-SAX}, {\it Chandra}, and {\it XMM-Newton}.  The temperature profiles of most clusters are isothermal from 0.05--0.6 $R_{\rm viral}$,%XX 0.01 or 0.1?contrary to theoretical expectations and early results from{\it ASCA}. Similarly, the abundance profiles of Fe are roughly constantoutside the central regions. The luminosity-temperature relation fora very large sample of clusters show that $L_{\rm X}\propto T^3$ over thewhole observable luminosity range at low redshift, but the varianceincreases at low luminosity, explaining the previously claimedsteepening at low luminosity. Recent accurate cluster photometry inred and infrared passbands have resulted in much better correlations ofoptical and X-ray properties, but there is still larger scatterthan one might expect between total light and X-ray temperature andluminosity. The velocity dispersion and the X-ray temperature arestrongly correlated, but the slope of the relation is somewhat steeper thanexpected. The surface brightness profiles of clusters are very wellfit by the isothermal $\beta$ model out to large radii and showscaling relations, outside the central regions, consistent with a$\Lambda$-dominated Universe.At high masses the gas mass fraction of clusters is quite uniform andis consistent with the low WMAP value of $\Omega_{\rm m}$.  The recent analysis%XX Omaga_mof cluster mass-to-light ratio and the mass-to-light ratio of starsindicates that the ratio of gas to stellar mass is $\sim$10:1 inmassive clusters. There is an apparent decrease in gas mass fractionand increase in stellar mass fraction at lower mass scales, but thevery flat surface brightness of the X-ray emission makes extension ofthis result to large scale lengths uncertain. The normalization of the scaling of mass with temperature,derived from measurements of density and temperature profiles and assuming hydrostatic equilibrium, is lower thanpredicted from simulations that do not include gas cooling or heatingand has a slightly steeper slope.  Detailed {\it Chandra} and {\it XMM-Newton}imaging spectroscopy of several clusters show that the form of the potential is consistentwith the parameterization of Navarro, Frenk, \& White (1997) over a factor of 100 in length scale andthat there is no evidence for a dark matter core. {\it Chandra} X-ray imageshave revealed rather complex internal structures in the centralregions of some clusters, which are probably due to the effects ofmergers; however, their nature is still not completely clear.There are now more than 100 clusters with well-determined Fe abundance,several with accurate values at redshifts $z \approx 0.8$, with little orno evidence for evolution in the Fe abundance with redshift. There isreal variance in the Fe abundance from cluster to cluster, with a trendfor clusters with higher gas densities to have higher Feabundances. The Si, S, and Ni abundances do not follow patternsconsistent with simple sums of standard Type Ia and Type II supernova,%XX Ia, not Iindicating that the origin of the elements in clusters is differentfrom that in the Milky Way. The Si/Fe abundance rises with clustermass, but the S/Fe ratio does not. The high Ni/Fe ratio indicates theimportance of Type Ia supernovae. {\it XMM-Newton} grating spectra of the central regions of clusters have derived precise O, Ne, Mg, and Fe abundances. {\it XMM-Newton} CCD data are allowing O abundances to be measuredfor a large number of clusters.\end{abstract}\section{Introduction}Clusters of galaxies are the largest and most massive collapsedobjects in the Universe, and as such they are sensitive probes of thehistory of structure formation. While first discovered in the opticalband in the 1930's (for a review, see Bahcall 1977a), in same ways thename is a misnomer since most of the baryons and metals are in the hotX-ray emitting intracluster medium and thus they are basically ``X-rayobjects.''  Studies of their evolution can place strong constraints onall theories of large-scale structure and determine precise valuesfor many of the cosmological parameters. As opposed to galaxies,clusters probably retain all the enriched material created in them andbeing essentially closed boxes they provide an unbiased record ofnucleosynthesis in the Universe. Thus, measurement of the elementalabundances and their evolution provide fundamental data for the originof the elements. The distribution of the elements in clusters revealshow the metals were removed from stellar systems into the intergalactic medium(IGM). Clusters should be fair samples of the Universe, and studies oftheir mass and their baryon fraction reveal the gross properties of%XX quotes unnecessary fair, grossthe Universe as a whole. Since most of the baryons are in the gaseousphase and clusters are dark matter dominated, the detailed physics ofcooling and star formation are much less important than ingalaxies. This makes clusters much more amenable to detailedsimulations than galaxies or other systems in which star formation hasbeen an overriding process. Detailed measurements of their density andtemperature profiles allow an accurate determination of the darkmatter profile and total mass.  While gravity is clearly dominant inmassive systems, much of the entropy of the gas in low-mass systems maybe produced by nongravitational processes.%XX shocks makes no senseClusters are luminous, extended X-ray sources and are visible out tohigh redshifts with present-day technology. The virial temperature ofmost groups and clusters corresponds to $kT \approx (2-100) \times 10^6$ K(velocity dispersions of 180--1200 km s$^{-1}$), and while lowermass systems certainly exist, we usually call them galaxies. Most ofthe baryons in groups and clusters of galaxies lie in the hot X-rayemitting gas, which is in virial equilibrium with the dark matterpotential well [the ratio of gas to stellar mass is $\sim$(2--10):1;Ettori \& Fabian 1999]. This gas is enriched in heavy elements(Mushotzky et al. 1978) and is thus the reservoir of stellar evolutionin these systems. The presence of heavy elements is revealed by lineemission from H and He-like transitions, as well as L-shell transitionsof the abundant elements. Most clusters and groups are too hot to havesignificant line emission from C or N, but all abundant elements with $Z > 8$ (O) have strong lines from H and He-like states in the X-rayband, and their abundances can be well determined.Clusters of galaxies were discovered as X-ray sources in the late1960's (see Mushotzky 2002 for a historical review), and large sampleswere first obtained with the {\it Uhuru} satellite in the early 1970's(Jones \& Forman 1978). Large samples of X-ray spectra and imageswere first obtained in the late 1970's with the {\it HEAO} satellites (seeForman \& Jones 1982 for an early review). The early 1990's broughtlarge samples of high-quality images with the {\it ROSAT} satellite and goodquality spectra with {\it ASCA} and {\it Beppo-SAX}.  In the last three years there has been an enormous increase in the capabilities of X-ray instrumentation due to the launch and operation of {\it Chandra} and {\it XMM-Newton}. Both {\it Chandra} and {\it XMM-Newton} can find and identify clusters out to $z > 1.2$, and their morphologies can be clearly discerned to $z > 0.8$ (Fig. 1.1).  The cluster temperatures can be measured to $z \approx 1.2$, and {\it XMM-Newton} can determine their overall chemical abundances to $z \approx 1$ with sufficiently long exposures (very recently the temperature and abundance of a cluster at $z$ = 1.15 was measured accurately in a 1~Ms {\it XMM-Newton} exposure; Hasinger et al. 2003).  Temperature and abundance profiles to $z \approx 0.8$ can be well measured and large samples of X-ray selected clusters can be derived. {\it Chandra} can observe correlated radio/X-ray structure out to  $z > 0.1$ and has discovered internal structure in clusters. The {\it XMM-Newton} grating spectra can determine accurate abundances for the central regions of clusters, in a model independent fashion, for O, Ne, Mg, Fe, and Si.It is virtually impossible to give a balanced review of the presentobservational state of X-ray cluster research, with more than 100papers published each year. I will not say much about those issues forwhich we have had detailed talks at this meeting: cooling flows, high-redshiftclusters and evolution, X-ray data and the Sunyaev-Zel'dovich effect,radio source interaction, X-ray selected active galaxies in clusters,X-ray emission from groups, and detailed comparison of masses derivedfrom lensing and X-ray observations. Other areas, such as the presenceof nonthermal emission and the existence of very soft components, werenot discussed. Even limiting the talk this much results in an abundance of material. However, for the purposes of continuity, I have included some material that overlaps with the reviews on chemical abundance given by Renzini (2003) and on groups by Mulchaey (2003). This review does not consider work published after February 2003. %XX poor quality\begin{figure*}[t]\centering\includegraphics[width=1.00\columnwidth,angle=0,clip]{chandra_xmm_image_cl0838_bw.ps}\vskip 0pt \caption{{\it Chandra} (left panel) and {\it XMM-Newton} (right panel) images of the Lynx region (Stanford et al. 2001), which contains three high-redshift clusters. The {\it Chandra} image has $\sim$170 ks and the {\it XMM-Newton} image $\sim$20 ks exposure.}\end{figure*}\section{Temperature Structure of Clusters}As discussed in detail by Evrard (2003), we now have adetailed understanding of the formation of the dark matter structurefor clusters of galaxies. If gravity has completely controlled theformation of structure, one predicts that the gas should be inhydrostatic equilibrium with the vast majority of the pressure being dueto gas pressure.  If this is true, its density and temperature structureprovide a detailed measurement of the dark matter distribution in thecluster. Recent theoretical work has also taken into account otherprocess such as cooling and turbulence, which can be important. The fundamental formof the Navarro, Frenk, \& White (1997; hereafter NFW) dark matter potential and the assumption that the fraction of the total mass that is in gas isconstant with radius result in a prediction, both from analytic (Komatsu \& Seljak 2001) and numerical modeling (Loken et al.  2002), that the cluster gasshould have a declining temperature profile at a sufficiently largedistance from the center (in units of $R/R_{\rm virial}$).The size of the temperature drop in the outer regions ispredicted to be roughly a factor of 2 by $R/R_{\rm virial} \approx 0.5$, which is consistent with the {\it ASCA} results of Markevitch(1998). However, there is considerable controversy about the analysisand interpretation of temperature profiles before {\it XMM-Newton} and{\it Chandra}. Results from both {\it ASCA} (Kikiuchi et al. 1999; White \& Buote 2000) and {\it Beppo-SAX} (Irwin \& Bregman 2000; De~Grandi \& Molendi 2002), indicate either isothermal gas or a temperature gradient in the outerregions of some ``cooling flow'' clusters. {\it XMM-Newton} is perfect for resolving this controversy, having a much better point spread function than {\it ASCA} and much more collecting area than {\it Beppo-SAX} and {\it Chandra}, and having a larger field of view than {\it Chandra}. However, there is a selection effect due to the smaller {\it XMM-Newton} field of view than {\it ASCA}, and in order to go out to the virial radius in one pointing one must observe clusters at $z> 0.1$.There are several published temperature profiles from {\it XMM-Newton} (Tamura et al. 2001;Majerowicz, Neumann, \& Reiprich 2002; Pratt \& Arnaud 2002) and I have  analyzedseveral other moderate redshift clusters and others were presented at thisconference (Jones et al. 2003).  With the exception of oneobject (A1101S; Kaastra et al. 2001) all the published {\it XMM-Newton} profiles areconsistent with isothermal profiles out to $R/R_{\rm virial} \approx 0.5$ (Fig. 1.2), which is in strong disagreement with the numerical and analyticmodeling. This sample of $\sim$12 objects is highly biased to smooth,centrally condensed clusters (with the exception of Coma, which hasbeen known to be isothermal from the early work of Hughes etal. 1988). The data for A2163 are consistent with a temperature dropat even larger radii (Pratt, Arnaud, \& Aghanim 2002), but therelatively high {\it XMM-Newton} background makes the results somewhatuncertain. The origin of the difference between some of the {\it Beppo-SAX}, {\it ASCA},and {\it XMM-Newton} results is not clear. It is possible that there is adifference between the low-$z$ systems studied by {\it Beppo-SAX} and {\it ASCA} and thehigher-redshift systems studied by {\it XMM-Newton} and/or a selection effect inthe objects so far analyzed with {\it XMM-Newton}. While the {\it Chandra} data do not goout to very large length scales (Allen, Schmidt, \& Fabian 2002), analysis of 2 $z \approx 0.7$ clusters with {\it Chandra} (Ettori \& Lombardi2003) also show isothermal profiles. We must now take seriously the disagreement between theory andobservation in the temperature profiles in comparing clusterproperties with simulations. Another serious issue is the inability oftheoretical models to match the observed temperature drops in thecenters of the ``cooling flow'' clusters. The question is then, whatis the origin of the discrepancy? Several possibilities are that theform of the theoretical potential is incorrect, that the gasdistribution is not calculated correctly, or that physics other thangravity needs to be included. %XX poor quality\begin{figure*}[t]\centering\includegraphics[width=0.80\columnwidth,angle=0,clip]{cluster_kT_profile.ps}\vskip 0pt \caption{Normalized temperature profiles of three moderate redshift clusters derivedfrom {\it XMM-Newton} EPIC observations. The ratio of the temperature ina radial bin vs. the radius in units of $R_{500}$ is plotted.}\end{figure*}%\clearpage\noindentAs shown below (\S 1.8) the form ofthe potential from X-ray imaging spectroscopy agrees quite well withthe NFW potential, which is consistent with the analytic work. {\it ROSAT}and {\it XMM-Newton} analysis of X-ray surface brightness distributions (\S 1.5) shows that the $\beta$ model is a good description of the X-raysurface brightness at large radii. This leaves us with the possibilitythat additional physics is needed. Recent analysis of {\it Chandra} data(cf. Markevitch et al. 2003) strongly constrains the effects of conduction, which will tend to make isothermal spectra, while the inclusion ofcooling and heating in the theoretical models (Loken et al. 2002) doesnot seem to affect the temperature profile significantly. Thus, theorigin of this severe discrepancy is not currently known.%XX labels, what are other three lines?\begin{figure*}[t]%\centering\hspace*{-1.5cm}\includegraphics[width=0.85\columnwidth,angle=90,clip]{fig3.ps}\vskip 0pt \caption{X-ray luminosity vs. X-ray temperature, derived from {\it ASCA} observationsof $\sim$270 clusters (Horner 2001). The best-fit $L_{\rm X}\propto T^3.4$for the overall sample (solid line), while the best fit for clustersof luminosity less than $2/times 10^{44}$ ergs s$^{-1}$ is drawn as a dotted line}\end{figure*}\section{Luminosity-Temperature Relation for Clusters}As pointed out by Kaiser (1986), simple scaling relations predict thatthe cluster luminosity should scale as the temperature squared($T^2$).  To see this, note that the X-ray luminosityshould scale as the density squared times the volume times the gasemissivity, $L_{\rm X}  \propto \rho^2 V \Lambda$.  The mass of gas scaleslike $\sim \rho V$, and it is assumed that the total mass $M_{\rm T}$scales as $M_{\rm gas}$.  Since the emissivity for bremsstrahlung, theprime cooling mechanism in gas hotter than 2 keV, scales as $T^{0.5}$(Sutherland \& Dopita 1993), one has $L_{\rm X} \propto M \rho T^{0.5}$.Finally, since, theoretically, the total mass scales as $T^{1.5}$, onehas $L_{\rm X} \propto \rho T^2$.  The other free parameter, theaverage density, is related to the mass and collapse epoch of thecluster.It has been known for 20 years (Mushotzky 1984) that the actualrelationship between temperature and luminosity is steeper than the simplest theoretical prediction. Recently,Horner et al. (2003) have examined the $L_{\rm X}-T$ relation usingthe largest sample of clusters to date (270 clusters taken from the{\it ASCA} database).  In this sample one finds that, over a factor of $10^4$ inluminosity, the luminosity scales as $T^3$. As one goes to lowerluminosities there is a wider range of luminosity at a fixedtemperature (Fig. 1.3), but there is no need to change the scalinglaw. This increase in variance probably explains the steeper fit atlow luminosity found by Helsdon \& Ponman (2000). This continuity israther strange, since at $T<2$ keV the cooling function changes signand scales more like $T^{-1}$, and thus the theoretical relationbetween $L_{\rm X}$ and $T$ changes slope.There have been many papers written about the origin of thediscrepancy, but the main conclusion is that it is due to the breakingof scaling laws via the inclusion of physics other than gravity. Thesame physics that helps to explain the deviation of entropy in groups,such as heating and cooling, can also explain the slope andnormalization of the $L_{\rm X}-T$ relation (see the paper by Mulchaeyin this volume and Borgani et al. 2002).  Another indication of thisscale breaking is the relative low level of evolution in the $L_{\rm X}-T$ relation out to $z\approx 1$ (Borgani et al. 2002) which is notwhat is predicted in simple theories of cluster evolution, sinceobjects at $z\approx 1$ are predicted to be denser and have a highertemperature for a fixed mass.  Simple scaling predicts that $T \propto M^{1.5} (1+z)$, and thus one predicts $L \propto T^2 (1+z)^{0.5}$ at afixed mass, which is not seen (but see Vikhlinin et al. 2002 for adifferent opinion).It was pointed out by Fabian et al. (1994) that high central density,short cooling time clusters (alias ``cooling flow'' clusters) have aconsiderably higher luminosity for their temperature than non-cooling flowsystems. This result isconfirmed in the larger Horner et al. (2003) sample. Markevitch (1998)removed the high-central surface brightness central regions from theseclusters and found that the scatter in the $L_{\rm X}-T$ relationshipwas much reduced and the fit was flatter than $T^3$. If the scatter inthe $L_{\rm X}-T$ relationship was due to cool gas in the center ofthe cooling flow clusters, one should expect that the {\it ROSAT}luminosities, which are very sensitive to low-temperature gas, wouldbe systematically larger than the luminosities calculated fromisothermal fits to the {\it ASCA} data. However, Horner et al. (2003) findthat the bolometric luminosities obtained by {\it ASCA} are in very goodagreement with the {\it ROSAT} results. This indicates that thecentral luminosity ``excess'' is not due to cool gas, as was originallyshown in the {\it ASCA} data for the Centaurus cluster (Ikebe et al. 1999)and recently shown in detail by {\it XMM-Newton} spectroscopy of many cooling flowclusters (Peterson et al.  2003). Horner et al. (2003) find that themost reasonable explanation for the higher luminosity of the coolingflow clusters is due to their higher central density in the core. Thisresult is consistent with the detailed analysis of cluster surfacebrightness profiles by Neumann\& Arnaud (2001) (see \S 1.5). It thus seems that the scatter in the $L_{\rm X}-T$relation at high temperatures is due to differing cluster central gasdensities, while the scatter at low temperatures is due to different``amounts'' of additional, nongravitational physics.%XX poor quality\begin{figure*}[t]\centering\includegraphics[width=1.00\columnwidth,angle=0,clip]{fig4.ps}\vskip 0pt \caption{X-ray temperature vs. velocity dispersion, taken from Horner (2001).  Thetriangles represent points with fewer than 30 galaxies per cluster. Notethat these points contribute much of the variance in the fit.}\end{figure*}\section{Optical Light, Velocity Dispersion, and X-ray Properties}%XX wide range of what?  between makes no senseIt has been known since the early {\it Uhuru} results (Jones \& Forman 1978)that there is a great degree of scatter in the correlation between cataloged optical properties, suchas Abell richness, and X-ray properties, such as luminosity andtemperature. The best correlations between optical and x-ray propertiesseen in the early data were between central galaxy densityand X-ray luminosity (Bahcall 1977b), and between X-ray temperature and opticalvelocity dispersion (Edge \& Stewart 1991). The wide scatter isnicely illustrated in Figure 5 of Borgani \& Guzzo (2001)which shows that the Abell counts are only weakly related to total mass, while the x-ray luminosity is strong correlated.Bird, Mushotzky, \& Metzler (1995) showed that much of the scatter inthe temperature - velocity dispersion correlation was due toundersampled optical data and velocity substructure in theclusters. More recent optical and X-ray work (Girardi et al. 1998;Horner et al. 2003) shows that when the velocities of a sufficientnumber of galaxies in a cluster are measured (one needs more than 30galaxies) (Fig. 1.4) there is a tight relation between velocitydispersion and temperature of the form $\sigma\propto T^{0.59\pm0.03}$, consistent with the work of Bird etal. (1995) and close to the theoretical slope of 0.5. This has beenconfirmed in an infrared-selected sample by Kochanek etal. (2003). The normalization of this relation at high temperaturesagrees with theoretical work (Evrard 2003), and thus one has toconclude that low-velocity dispersion clusters are too hot for theirdispersion, or that low-temperature clusters have too low a dispersionfor their temperature.  The fact that clusters have very small radialvelocity dispersion gradients (Biviano \& Girardi 2003) or temperaturegradients (\S 1.2) makes comparison of the average temperature andvelocity dispersion meaningful. This variation with temperature of thevelocity dispersion to temperature ratio will also change theeffective X-ray vs. optically determined mass by a factor of 50\% overthe full mass range of clusters.Recent 2MASS work by Kochanek et al. (2003) shows that, if the ``optical'' data are handled carefully (e.g., accurate photometry, well-defined selection criteria, observing in a red passband, etc.), there is a strong relation between the total light in a cluster andthe X-ray temperature and luminosity (also see Yee \& Ellingson2003). However, while the correlations are much better than inprevious work, the scatter in the relation is large, almost a factorof 10 in light at a fixed X-ray temperature or luminosity, or,alternatively, a factor of $\sim$2 in temperature at a fixed opticalluminosity. Thus, one expects that optical and X-ray catalogs ofclusters might differ considerably depending on where the cuts aremade. There is no evidence for either optically or X-ray quietclusters, but there is evidence for relatively optically or X-raybright objects. The nature and origin of this variance is notunderstood at present, but, given the quality of modern data, this varianceseems tobe real, rather than due to measurement uncertainties. Assuming thatthe X-ray properties accurately trace mass, the $K$-band light is a mass indicator accurate to 50\% (Lin, Mohr, \& Stanford 2003). The converse test, estimating the mass from theoptical data and comparing it to the X-ray data, shows large scatter(Yee \& Ellingson 2003), where the temperature data are taken from theliterature. If it is indeed the case that there is a large variationin the ratio of optical light to X-ray temperature, this indicatesthat there is a considerable variance in cluster mass-to-light ratioat a fixed mass. This would be a major challenge to structureformation theories.\section{Surface Brightness Profiles}It has been known since the pioneering work of Jones \& Forman (1984)that the surface brightness profiles of most clusters can be well fit,at large  radii, by the ``isothermal'' $\beta$ model,$S(r)=S_0(1+(r/a)^2)^{(-3\beta + 0.5)}$, with a central excess above the $\beta$ model incooling flow clusters. As seen in {\it ROSAT} data for high-redshiftsystems (Vikhlinin, Forman, \& Jones 1999), the $\beta$ model fits amazingly well out to the largest radii measurable for massive clusters. The fittedvalues of $\beta$ are smaller for low-mass systems (Helsdon \& Ponman2000; Mulchaey et al. 2003), but there are two selection effects thatmake the interpretation of this result difficult. First of all, because of their low surface brightness, the group profile hits the background at relatively smalldistances from the center, and thus onedoes not detect low-mass systems out to large fractions of the virialradius. This can introduce a bias to the fitted values of $\beta$. Secondly,the effects of the central galaxy on the surface brightness is often not well determined from {\it ROSAT} PSPC data (Helsdon \& Ponman 2003)and thus, frequently, the structural parameters are not well constrained. This latter effect is not present in {\it XMM} or {\it Chandra} data. Neumann \& Arnaud (2001) have pointed out that the surface brightness profiles of high-temperature clusters remain self-similar as a function of mass and redshift, as expected from cold dark matter models (see also Vikhlinin et al. 1999). Since the conversion from angle todistance depends on the cosmology, they have been able to show thatthe change of profile with redshift is most consistent with a$\Lambda$ dominated cosmology. The homology of the profiles is only applicableoutside of the central 100 kpc, as inside this radius there are oftenlarge deviations from the scaling laws. However, in order to achievethe scaling they require that the relationship of gas mass totemperature be $M_{\rm gas} \propto T^2$, steeper than thetheoretical scaling between total mass and temperature (i.e., $M_{\rmtotal}\propto T^{1.5}$).  Since the surface brightness profiles scale according to the predicted evolution from the cold dark matter models, the lack of evolution in the luminosity-temperature law must be a cosmicconspiracy between the cosmological model and the change of densitywith redshift. The prediction is that the emission measure of the gas scales as $EM \propto \beta f^2_{\rm gas}\Delta^{1.5}(1+z)^{9/2}(kT)^{0.5} h^3$, where $\Delta$ is the overdensity of the cluster and $f_{\rm gas}$ is the fraction of mass that is in gas (Arnaud, Aghanim, \& Neumann 2002).There are ``single'' clusters that are not well fit by the $\beta$model.  The most obvious example is MS 1054$-$0321 at $z$ = 0.82(Jeltema et al.  2001), which is much more concentrated than a $\beta$model.  This is not a function of redshift, since many clusters at$z>0.6$ are well fit by the $\beta$ model.\section{Mass of  Baryons and Metals and How Are They Partitioned?}%XX shorten section title to fitThe two main baryonic components of clusters are theX-ray emitting gas and the stars, since the total contribution fromcold gas and dust is very small. The major uncertainty in the relativebaryonic contribution is due to the uncertainty in the transformationfrom light to mass for the stars.  Recent work from large opticalsurveys (Bell et al. 2003) shows that the mass-to-light ratio of starschanges as a function of galaxy type, %(presumably due to changes in the mass function) %XX remove, not true, agebut is $\sim$3.5 in the Sloan $g$ band for a bulge-dominated population. Using this value and the mean mass-to-lightratio of clusters $\sim$240 (Girardi et al. 2002), the stars have$\sim$0.015 of the total mass. The gas masses have been welldetermined from {\it ROSAT} data (Ettori \& Fabian 1999; Allen et al. 2002)and scatter around $f_{\rm gas} \approx 0.16 h_{70}^{-0.5}$.  Thus, thegas-to-stellar mass ratio is $\sim$10:1, and the total baryon fraction is%XXX reversed!almost exactly consistent with the recent {\it WMAP} results for theUniverse as a whole.  Since it is thought that clusters arerepresentative of the Universe as a whole, this suggests that the vastmajority of baryons in the Universe do not lie in stars. Turning thisaround, one can use the baryonic fraction in clusters as a bound on$\Omega_{\rm m}$ (White et al. 1993). The most recent analysis usingthis technique finds $\Omega_{\rm m} < 0.38 h_{70}^{-0.5}$ (Allen etal. 2002), in excellent agreement with the {\it WMAP} data. It is interestingto note that the high baryonic fraction in clusters has been known forover 10 years and was one of the first strong indications of a low $\Omega_{\rm m}$ Universe.  Since it is thought that the baryonicfraction in clusters should not evolve with redshift, derivation ofthe baryonic abundance in high-$z$ clusters, which depends on theluminosity distance, provides a strong constraint on cosmologicalparameters (Ettori \& Tozzi and Rosati 2003).The mean metallicity of the gas in clusters is $\sim$1/3 solar (see\S 1.10), while that of the stars may be somewhat larger. If we assume1/2 solar abundance for the stars, than $\sim$85\% of the metals arein the gas phase. Since all the metals are made in stars, which lieprimarily in galaxies, this implies that most of metals have eitherbeen ejected or removed from the galaxies.  Since the stellar mass isdominated by galaxies near $L^{\star}$, which have a mean escapevelocity, today, of $>$300 km s$^{-1}$, this implies very strong galacticwinds at high redshift. This scenario is consistent with the resultsof Adelberger et al. (2003) on the high-redshift, rapidly star-forming$U$ and $B$-band drop-out galaxies, which all have large-velocity winds.Analysis of the gas mass fraction in groups and clusters (Sanderson etal. 2003) indicates that the fraction apparently drops at lower massesby a factor of 2--3, with the reduction setting in at a mass scalecorresponding to 1--3 keV at 0.3 $R_{200}$. In addition, the stellar mass-to-light ratio decreases by 60\% over the same mass range (Marinoni \&Hudson 2002), and thus in groups the gas-to-stellar mass ratio is only(1--2):1 at 0.3 $R_{200}$, considerably smaller than in clusters. However,there is a serious problem for groups in evaluating both the gas andstellar masses at large radii (see Fig. 10 in Mulchaey et al. 2003), and this result should be taken with some caution. In particular, theX-ray surface brightness distribution of groups is often very flat, andextrapolating from 0.3 $R_{200}$ to $R_{200}$ is rather risky.However, if these trends are real,  this would indicate thatgroups are truly baryon poor, that the baryons have been pushedout of the group, or that the gas has been puffed up. If the gas has beenpuffed up, this is consistent with the somewhat high temperatures ofgroups compared to their optical galaxy velocity dispersions,indicative of extra heat deposited in the gas, which both heats it and``puffs'' it up (see discussion in the review by Mulchaey 2003).\section{Mass Scaling Laws}Detailed theoretical work has verified that clusters should satisfy the virial theorem, and thus their mass should scale as $M \propto T R$, with $R \propto T^{1/2}$, and thus $(1+z)M^{2/3} \propto T$ (e.g., Eke, Navarro, \& Frenk 1998), with the normalization being set by theory and the value ofthe cosmological parameters (Evrard 2003). The first test of this relation (Horner, Mushotzky, \& Scharf 1999) found a scaling that was somewhatsteeper, with $M \propto T^{1.7}$, and a normalization that was 40\% lower than predicted. Finoguenov, Reiprich, \& B\"{o}hringer (2001) and Reiprich \& B\"{o}hringer (2002) have confirmed these results with more uniform samples,and higher quality, spatially resolved spectra. Recent {\it Chandra} results(Allen, Schmidt, \& Fabian 2001) are also consistent with the Horner et al. (1999) finding. {\it XMM-Newton} data for A1413 (Pratt \& Arnaud 2002) show that the normalization scaling is not only violated by the sample, but byindividual objects.  The normalization in the Reiprich \&B\"{o}hringer (2002) sample agrees with theoretical expectations atthe high-mass end. This indicates that lower-temperature clusters areless massive than expected on the basis of their temperature, consistent with the trend seen in the velocity dispersion-temperature relation.  Recently, it has been pointed out (Shimizu etal. 2003) that the combination of the scaling of mass by $M \proptoT^{1.7}$ and the gas mass fraction scaling as $T^{1/3}$ (a reasonablefit to the Sanderson et al. 2003 data) can reproduce the observed $L_{\rmX} \propto T^3$ relationship. Theoretical calculations that includethe effects of cooling (Thomas et al. 2002) seem to be consistentwith the lower normalization, but so far the slope difference has notbeen explained.\section{Form of the Potential}As discussed extensively in this conference, the form of the potentialin clusters should be determined by the distribution of dark matter.Recent numerical work seems to validate the NFW potential, and muchhas been made of the fact that low-mass and low-surface brightnessgalaxies do not seem to follow this form in their centralregions. Recent {\it Chandra} and {\it XMM-Newton} observations (Allenet al. 2002; Arabadjis, Bautz, \& Garmire 2002; Pratt \& Arnaud 2002)have been able to determine extremely accurate mass profiles viaspatially resolved X-ray spectroscopy and the assumption ofhydrostatic equilibrium. Perhaps the best documented of these examplesare the {\it Chandra} data for Abell 2029 (Lewis, Buote, \& Stocke2003), in which the profile is determined over a factor of 100 inlength scale, from 0.001--0.1 characteristic lengths of the NFWprofile, with essentially no deviation from the NFW prediction. Thisstriking result is also seem in other {\it Chandra} results in thecores of clusters. The data show that the central regions of clusterstend to have rather steep density profiles in the innermost radii,indicating that whatever causes the deviation of the form of thepotential in dwarf galaxies does not occur in clusters. This resultsstrongly constrains interacting dark matter models (Bautz \& Arabadjis2003).  A survey of {\it Chandra} central mass profiles is madesomewhat difficult because of the possibly complex nature of the IGMin the central regions of many clusters, and the exact slope andnormalization of the mass depends on the details of the thermal modelused. However, if the data are of sufficiently high signal-to-noiseratio, the form of the mass profile can be determined precisely. Ianticipate quite a few exciting new results in this area; preliminaryresults, presented in several conferences, indicate a predominance ofsteep mass profiles with slopes close to the NFW level, but with somescatter.\begin{figure*}[t]\centering\includegraphics[width=1.00\columnwidth,angle=0,clip]{fig5.ps}\vskip 0pt \caption{The {\it Chandra} image of a cold front in Abell 2142 (courtesy of the{\it Chandra} Science Center). Note the very sharp boundary to the north,which is not an artifact of the image processing.}\end{figure*}%XX scale?\section{Merges, Structures, etc.}The early {\it Einstein} Observatory images of clusters (Henry et al. 1979)showed that a substantial fraction of the X-ray images were notsimple, round systems, but often complex in form and sometimes evendouble. This observation is consistent with the idea that clustersform in a hierarchical fashion via mergers, and that the complexsystems are in the process of merging. The fact that mergers areactually occurring, rather than the complex structures in the imagesbeing simply projection effects, was indicated by complexity in thetemperature structure of many of these systems shown by the {\it ROSAT}(Briel \& Henry 1994) and {\it ASCA} (Markevitch 1996) data. The details ofthe nature of this process have had to wait until the precise {\it Chandra}spectral images showed the full range of complexity. While``textbook'' examples of merger shocks have been seen (e.g., 1E~0657$-$56; Markevitch et al. 2002), many of the objects show only subtletemperature variations (e.g., Sun et al. 2002). These variations haveonly shown up in the most recent, very high-resolution numericalsimulations, indicating the non-intuitive nature of these data.The recent spectacular {\it XMM-Newton} temperature image of the Perseus cluster (Churazov et al. 2003) illustrates the wealth of detail that is nowpossible to obtain. It is interesting that these spectral images donot show the numerous ``cold spots'' that are predicted in clustersimulations that include cooling (Motl et al. 2003). Theability to obtain spectral images has also revealed ``hiddenmergers.'' Both the Coma and Ophiuchus clusters, the hottest nearbysystems, show smooth, regular X-ray images; however, X-ray temperaturemaps show strong spatial variations (Arnaud et al.  2001; Watanabe et al. 2001). So far the data on abundance variations in the mergers issparse, but the abundances seem uniform, within errors, in Coma and mayvary by less than a factor of $\sim$2 in Ophiuchus. It seems as if many of thelarge-scale length, non-cooling flow clusters are recent mergers.One of the surprises of the {\it Chandra} data was the discovery of surfacebrightness discontinuities in the surface brightness --- the so-calledcold fronts (Fig. 1.5; Vikhlinin \& Markevitch 2002). These cold fronts areapparently contact discontinuities, across which the pressure is smoothlyvarying but the density and temperature change discontinuously byfactors of $\sim$2. They can occur in ``pure hydro'' numerical simulations(Bialek, Evrard, \& Mohr 2002). Their relative frequency is a indication of themerger rate. However, the details (e.g., temperature drop, size ofregion, etc.) and their relation to merger dynamics are not certain(Fujita et al. 2002). The stability of the cold fronts, their sizes, and shapes are indications of the strength of the magnetic field,velocity vector of the merger, and the amount of turbulence (Mazzota,Fusco-Femiano, \& Vikhlinin 2002) in the cluster gas. It is clear that there is much to learnfrom further studies of these unexpected structures, but they alreadyconfirm that the gas is usually not strongly shocked, nor highly turbulent.\section{Abundances}As indicated above, most of the metals in the cluster lie in the hot,X-ray emitting gas. Thus, in order to understand the formation andevolution of the elements one must determine accurate abundances, theabundance distribution in the gas, and its evolution with cosmictime. Before giving the results it is important to remind the readerthat the measurement of abundances in the cluster gas via X-rayimaging spectroscopy is a robust process. Most of the baryons andmetals are in the hot gas, and the spectral signature of the heavyelements are relatively strong H and He-like lines (Fig. 1.6). This isa well-understood emission mechanism, with little or no radiativetransfer difficulties. Because of the high temperature and shortspallation times, dust is destroyed rapidly and thus is not a problem. The deep potential well capturesan integrated record of all the metals produced, and thus the derivedabundances are true averages of the metal production process. All theabundant elements from oxygen to nickel can have their abundancesdetermined.  Direct measurement of the electron temperature from theform of the continuum and from ratios of H to He-like lines ensures smallsystematic errors in the abundances. The strongest lines in thespectrum of hot clusters are due to Fe and Si, followed by O, S andNi. The emission from Ne and Mg is blended with Fe L-shell lines fromFe~XVII--XXIV at the resolution of X-ray CCDs, and the lines from Ca andAr are weak. With present-day technology, one can measure Fe to $z\approx 1$and Si to $z \approx 0.4$, and can thus obtain a true measure of themetal formation mechanism and its evolution. For much of the rationaleand background for cluster abundance measurements, see Renzini's (2003) reviewin this volume.\begin{figure*}[t]%\centering\hspace*{-0.5cm}\includegraphics[width=0.70\columnwidth,angle=-90,clip]{figure6.ps}\vskip 0pt \caption{Theoretical spectrum of an isothermal plasma with $kT \approx 3$ keV, withmany of the strong transitions labeled; however, many of the transitions fromthe same ion (e.g., multiple lines from Fe~XXIV) have been suppressed. Notethe strong lines from all the abundant elements. The data are plotted in theusual way for X-ray astronomers, photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$ vs. keV,which emphasizes the dynamic range of X-ray spectroscopy.}\end{figure*}%XXX labels!!, botoom right too, upper unnecessary\begin{figure*}[t]%\centering\hspace*{-1.0cm}\includegraphics[width=0.80\columnwidth,angle=90,clip]{fe_tx_bw.ps}\vskip 0pt \caption{Fe abundance vs. temperature for the {\it ASCA} cluster database (Horner2001). The dashed line shows the average for clusters with temperatures greater than 5 keV. Notice that there is little variation at high temperatures, butthere is a systematic rise in abundance and then fall at low temperatures.}\end{figure*}Recently (Baumgartner et al. 2003; Horner et al. 2003), a uniformanalysis of the {\it ASCA} cluster database of 270 clusters has beenperformed, which updates previous work (e.g., Mushotzky et al. 1996;Fukazawa et al. 2000) on cluster abundances. Horner et al. (2003) andBaumgartner et al. (2003) measure the average cluster Fe, Si, S, and Niabundances with no spatial information.  They find (Fig. 1.7) that the Feabundance is not the same for all clusters, but shows a small spread ofa factor of $\sim$2. In agreement with Fabian et al. (1994), the cooling flowclusters show, on average, a higher Fe abundance.  There is no evidencefor any evolution in the Fe abundance out to $z \approx 0.5$ on the basisof {\it ASCA} data.  Recent {\it XMM-Newton} and {\it Chandra} results (Jones et al.  2003; Mushotzky, private communication) show no evolution in the Fe abundance to $z \approx 0.8$. This lack of evolution indicates that themetals are created at $z > 1.3$ for a $\Lambda$ cosmology ( I haveadded in the lifetime of the A stars that would be visible forthe massive amount of star formation necessary to produce the observedmetals). Since the vast majority of the metals are in the gas, therate of specific star formation (e.g., the rate per unit visible stars)would have to be enormous to produce the elements if it were to occurat $z<2$. The Fe abundance is weakly correlated with the temperature,reaching a maximum at $kT \approx 2-3$ keV, but is more or less constantfor $kT>4.5$ keV clusters. Given the accuracy of recent plasma codes, the ``peak'' in abundance, which occurs at a temperature range whereboth Fe L and K lines contribute to the abundance determination, isalmost certainly a real effect. The physical origin of the variance inFe abundance and the trends are unknown. However, since there aretrends in the apparent ratio of starlight to gas (\S 1.6), thismay be the cause. Further progress in this area  requires an enhancement of the original work of Arnaudet al. (1992), which found a correlation between the light in ellipticalgalaxies and the total mass of Fe in the cluster.The distribution of the elements in a cluster determines the total amount of material and gives clues as to how the material was deposited in the IGM.  The previous generation of X-ray satellites ({\it ASCA}, {\it ROSAT}, and {\it Beppo-SAX}) derived abundance profiles of Fe in $>$20 clusters (Finoguenov, David, \& Ponman 2000; Irwin \& Bregman 2000; White \& Buote 2000; De~Grandi et al. 2003).  However, these results did not always agree(different analysis of the same data and comparison of data from the same objectfrom different  satellitesproduced different results). There was a tendency forcooling flow clusters to have high central Fe abundances and largertotal abundances, suggesting a different origin of IGM enrichment inthe central regions, the effects of mixing by mergers on the Feabundance profile, or a physical difference in the origin of the metalsin cooling flow clusters.{\it XMM-Newton} and {\it Chandra} data have much smaller systematic errors and much better signal-to-noise ratios than the data from the earlier observatories.  Early results are available for $\sim$15systems --- most are isochemical at large radii, with several having gradients in the central 100 kpc. The {\it Chandra} and {\it XMM-Newton} data are wellresolved and show that the abundance gradients are quite concentratedtoward the center (cf. David et al. 2001; Tamura et al. 2001).  For afew objects the profiles reach to near the virial radius (e.g.,Zw~3146, Cl~0016 (Mushotzky priv. comm.) , and A~1835; Majerowicz et al. 2002), two of which(Zw~3156 and A~1835) are  massivecooling flows  do not show abundance gradients outside~100 kpc. Numerical evaluation of the observed Fe abundance gradients(De~Grandi et al. 2003) shows that most of the variation in the average Feabundance between the cooling flow and non-cooling flow clusters isnot due to differences in the Fe gradients. The ``excess'' amount ofFe in the central regions seen in the cooling flow systems iscorrelated with the presence of a cD galaxy, and the mass of "excess"Fe is roughly consistent with its being produced in the stars in the central cDgalaxy. This is rather unexpected, since isolated elliptical galaxieshave only $\sim$1/5 of the Fe that should have been produced by thestars (Awaki et al. 1994). The fact that gradients do not dominate the average abundance allows a direct interpretation of the {\it ASCA} average abundances.  The {\it ASCA} database of $\sim$270 X-ray spectra allow determination ofaverage Fe, Si , S, and Ni in clusters of galaxies (Baumgartner et al.2003). However, the signal-to-noise  ratio for most of the individual clustersis not adequate to derive robust S or Ni abundances, and 20--40 objects in each temperature bin must be added together to derive averagevalues and their variation with temperature. Since cluster mass isdirectly related to the temperature and line strength is alsodirectly connected to temperature, this is the natural space foraveraging. As originally pointed out by Fukazawa et al. (2000), as $T$increases, Si/Fe increases. However, the new data show that S remainsroughly constant versus temperature. Baumgartner et al. (2003) also find that the Ni/Fe ratio is approximately 3 times solar.  While these are very surprising results, they are similar to previous analysis of smaller {\it ASCA} and {\it XMM-Newton} data sets.  The S/Fe, Si/Fe, and Ni/Fe ratios depend on the relative abundance of the types of supernovae (SNe). Type Ia SNe produce mostly Fe and Ni, while Type II SNe produce a wide range of elements but large ratios of the $\alpha$ elements (O, Ne, and Si) to Fe. Siand S are produced via very similar mechanisms, and at first sight itis hard to understand how they could have different abundancepatterns. In addition, in the Milky Way, S almost always directlytracks Si. The fact that both Si/Fe and S/Fe drop as Fe increasesshows that there is indeed a difference in the mechanisms producingthe metals as a function of mass scale. It seems rather unexpected that the ratio of Type II to Type Ia SNe in the stars that live in cluster galaxies should change with the mass scale of the cluster. However, the high Ni/Fe ratio indicates that Type Ia SNe are  important in the production of Fe, at least in the central regions of clusters (Dupke \& White%XXX important for what?  don't understand2000), and this high ratio does not allow a simple variation in SN type with clustermass to readily explain the abundances patterns seen in the ASCA data.{\it XMM-Newton} data allow the measurement of  O abundances for areasonable sample of objects for the first time. The best sample published to date isbased on the high-resolution RGS data (Peterson et al. 2003). They findthat the O/Fe ratio varies by a factor of $\sim$2 from cluster to cluster, with no apparent correlation with temperature. Analysis of {\it XMM-Newton} CCDdata taken over a larger scale (the RGS data sample only the central $1^{\prime}-2^{\prime}$ of the cluster) confirm this variance. As noted in Gibson, Loewenstein, \& Mushotzky  (1997), the elemental abundance ratios averaged over the cluster do not agree with any simple ratio of Type Ia to Type II SNe. However, it isclear that over 90\% of the O, Ne, and Mg must originate in Type II SNe.The new {\it XMM-Newton} O abundances further strengthen this conclusion. However, some of the difficulties may be caused by differentialabundance gradients of different elements. There are strongindications from {\it ASCA} data (Fukazawa et al. 2000; Finoguenov et al. 2001)that the Fe/Si ratio rises in the cluster centers, consistent with thecD galaxy being a source of Fe-rich material, probably due to Type Is SNe.However, the new {\it XMM-Newton} data show that O does not follow thispattern. It is clear that more work is necessary with larger samplesand abundance profiles before we can obtain a clear picture of the metalenrichment process in clusters.\section{Conclusion}The progress in this field in the last 10 years has beenamazing. The X-ray properties of objects at redshift $z \approx 0.8$ areroutinely measured, and clusters are now X-ray detectedat $z>1.15$. The use of clusters for cosmology, an area covered in the volume by Freedman (2003), is exploding. The physics of clusters and%XXX avoid negativegroups holds the key to understanding the origin and evolution ofstructure and the origin of the elements. It was the cluster data thatfirst showed that most of the baryons and metals in the Universe arein the hot phase, and that the baryonic Universe, as seen by our eyes,is only a shadow of the real Universe.  In the next few years we willcontinue to obtain vast amounts of new data from {\it Chandra} and{\it XMM-Newton}, and much of the present observations will be analyzed,interpreted, and new patterns found. There are over 400 {\it Chandra}and {\it XMM-Newton}observations of clusters and groups in the database so far, with many more to be observed over the lifetimes of these telescopes.I anticipate many major new discoveries based on these instruments.Furthermore, the launch of {\it Astro-E2} in 2005 will allowdetailed measurements of cluster turbulence, accurate abundances ofmany elements outside the cluster cores, and direct measures of thethermodynamic properties of the gas. The field has benefited enormously from the synergistic interactionof theory and observation. Most theorists and observers are now awareof the major issues and the current observational capabilities.Looking beyond the next few years, I anticipate that a major new X-raysurvey, perhaps 30 times better than {\it ROSAT}, will fly, producing an extremely large and uniform cluster catalog complete out to $z \approx 0.7$. In the more distant future, the {\it Constellation-X} mission will provide precision temperatures and abundances out to the highest redshifts that clusters exist.\vspace{0.3cm}{\bf Acknowledgements}.I would like to thank my long-time collaborators andstudents at Goddard for their major contribution to this work: KeithArnaud, Wayne Baumgartner, Don Horner, Mike Loewenstein, and JohnMulchaey. I would like to thank the {\it Chandra} and {\it XMM-Newton} projectsfor their major efforts in developing, launching, and operating theseamazing instruments. 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