Clusters of galaxies are next to quasars, the most luminous X-ray sources in the Universe with radiation powers of the order of 1043-1046ergs_1. The first detection of a cluster source was made with M87 in 1966 by Byram et al. , and 5 years later also the massive nearby clusters in the constellations Coma Berenices and Perseus were detected by Gursky et al.  and Fritz et al. . With the use of the Uhuru satellite, the extended nature of the cluster X-ray sources could be established . It turns out that the diffuse X-ray emission from clusters originates in a hot intracluster plasma with temperatures of several ten Million degrees, which radiates the bulk of its thermal radiation in the soft X-ray regime. As the hot plasma is tracing the shape of the cluster, the X-ray appearance provides us with information on the cluster structure. The soft X-ray band in which clusters radiate is fortunately also the wavelength regime for which X-ray telescopes with imaging optics provide us with a detailed picture of the X-ray sky. Therefore, galaxy clusters are among the most rewarding and informative objects for X-ray imaging studies.
With the very rapid evolution of X-ray observational techniques, the X-ray studies of galaxy clusters have also experienced a breathtaking evolution. X-ray observations have provided us with a wealth of detailed knowledge on the cluster structure, composition, and formation history as well as on the statistics of the galaxy cluster population. Most of our current systematic understanding of galaxy clusters, the cluster population, and the link to the formation of large scale structure and the underlaying cosmological model is based on X-ray observations. And the importance of X-ray astronomy for cluster research is still increasing. At this moment we can provide an overview on galaxy cluster research in X-rays where the advanced X-ray observatories Chandra and XMM-Newton have unfolded and demonstrated their full capabilities. This field of research is so rich, however, that such a contribution can only provide an illustrative tour through the field rather than a comprehensive review. In particular, the references give only examples of publications as a first starting point for a literature search and cannot be complete due to space limitations. The most detailed introduction to X-ray studies of galaxy clusters is given by the review of Sarazin , which is now outdated in its detailed description of observational results but still provides an excellent astrophysical background. More specialized recent reviews focus on X-ray cluster appearance by Forman and
Jones , cluster cooling flows by Fabian , X-ray properties of groups of galaxies by Mulchaey , galaxy cluster mergers by Feretti et al. , cluster evolution by Rosati et al.  and Voit , and the use of X-ray cluster for the test of cos-mological models by Schuecker .
In the structural hierarchy of our Universe we can recognize three fundamental building blocks, which are with increasing size: stars, galaxies, and clusters of galaxies. The study of their physical setup is at the base of astrophysics and the assessment of their population provides us with knowledge on the structure of the next larger unit in the hierarchy. In this sequence our knowledge decreases with the size and the distance of the objects. Thus, for the largest of these building blocks, the clusters, we are just starting to gain a systematic and detailed understanding of their make-up and their role in providing useful probes to cosmology.
In contrast to their name, which characterizes them only as collections of objects, clusters of galaxies are well defined, connected structural entities. This is revealed by X-rays where the diffuse X-ray emission from the hot intracluster medium traces the whole cluster structure in a contiguous way, as shown in Fig. 23.1, for the Coma cluster of galaxies with a distance of about 100 h— Mpc. As we shall see, galaxy clusters are defined by their own proper equilibrium structure. They are the largest objects in the Universe which have such a characteristic form, that can be well assessed by observations and well described by theoretical modeling. With these properties they also form the largest astrophysical laboratories, in which the physical environmental conditions can be well observed and described. They are therefore perfect laboratory sites for studies of a wide range of astrophysical processes at large scales, as for example the investigation of galaxy evolution within a well defined environment or the evolution of the dynamical and thermal structure as well as the chemical enrichment of the intergalactic medium.
Clusters of galaxies have been formed from the densest regions in the large-scale matter distribution of the Universe at scales of the order of 10 Mpc (in comoving units) and have collapsed to form matter aggregates that have reached an approximate dynamical equilibrium giving them their proper characteristic shape. They thus form an integral part of the cosmic large-scale structure, the seeds of which have been set in the early Universe. Therefore, the evolution of the galaxy cluster population is tightly connected to the evolution of the large-scale structure and the Universe as a whole. It is for this reason that observations of galaxy clusters can be used to trace the evolution of the Universe and to test cosmological models as we will illustrate later.
Another good didactical approach to contemplate galaxy clusters is to see them as large gravitational potentials holding mostly dark matter, hot thermal plasma, and galaxies together, roughly in proportions of 87,11, and 2%, respectively.1 The depth of this potential is characterized by the velocity dispersion of the visible test particles that probe the potential: the galaxies with typical velocity dispersions ranging from
1 Here and throughout the paper we adopt a Hubble constant of H0 = 70 km s-1 Mpc-1 and a concordance cosmological model with a normalized matter density parameter, Qm = 0.3, and a normalized cosmological constant parameter, Qa = 0.7, if not stated otherwise.
Fig. 23.1 The Coma cluster of galaxies as seen in X-rays in the ROSAT All-Sky Survey  (underlaying red color) and the optically visible galaxy distribution in the Palomar Sky Survey Image (galaxy and stellar images from the digitized POSS plate superposed). The sky area shown is 1.42 x 1.42 deg2
about 300 km s-1 for X-ray luminous galaxy groups up to about 1500 km s-1 for the most massive galaxy clusters. Similarly the hot X-ray luminous plasma is probing this potential in the form of an approximately hydrostatic atmosphere where the plasma temperature with values of kBT ~ 2-15 keV gives information about the potential depth. These facts are illustrated in Fig. 23.2, which shows how the gravitational potential depth is increasing with object mass from galaxies to galaxy clusters, whereas superclusters appear just as collections of cluster potentials because they are not fully formed virialized objects. This illustrates again the point that galaxy clusters are the largest objects in our Universe, which are characterized by their own proper equilibrium structure.
As mentioned earlier, X-ray observations play currently a prime role in the observational studies of the structure and astrophysics of clusters of galaxies. This is due to the gaseous intracluster medium (ICM), a hot, highly ionized thermal plasma with a temperature of ten to hundred Million degrees that fills the whole cluster vol-
field galaxy galaxy group massive cluster super cluster field galaxy galaxy group massive cluster super cluster
Fig. 23.2 Sketch of the gravitational potential of a part of the Universe, 0 and 0/, with galaxies, galaxy groups, clusters, and superclusters. (This particular potential is the potential of the matter density difference of the actual density and the mean density of the Universe and is negative for overdensities and positive in void regions.) We note the increasing depth of the potential with increasing mass of the objects, except for the last step where superclusters are not featuring as connect entities but merely as a collection of cluster potentials. The depth of the gravitational potential can be probed by the observable velocity dispersion of the stars or galaxies and the temperature of the interstellar or intracluster medium, respectively
Fig. 23.2 Sketch of the gravitational potential of a part of the Universe, 0 and 0/, with galaxies, galaxy groups, clusters, and superclusters. (This particular potential is the potential of the matter density difference of the actual density and the mean density of the Universe and is negative for overdensities and positive in void regions.) We note the increasing depth of the potential with increasing mass of the objects, except for the last step where superclusters are not featuring as connect entities but merely as a collection of cluster potentials. The depth of the gravitational potential can be probed by the observable velocity dispersion of the stars or galaxies and the temperature of the interstellar or intracluster medium, respectively ume and thus provides a contiguous picture of the cluster structure. The statistics of the structural information gained from X-rays thus depends on the number of photons collected, which is only limited by the observation time. This is to be compared to optical observations where the structure is traced by basically a limited number of galaxies. The X-ray imaging information is complemented by the contents of the X-ray spectra. Together they provide a wide range of insights into the galaxy cluster astrophysics as will be described in the following. In Sect. 23.2 I describe the measurements of cluster masses and the study of their composition from X-ray observations and discuss the self-similarity of the structural appearance in Sect. 23.3. In Sect. 23.4 I show observations of the Virgo cluster of galaxies and discuss the morphological variety of clusters. Sections 23.5 and 23.6 illustrate the information gained from X-ray spectroscopy on the cooling core structure in the cluster centers and the chemical composition of the ICM. The close relation of cluster masses and their X-ray luminosities make X-ray cluster surveys a good starting point for cosmological studies with clusters. These are described in Sect. 23.7 (surveys), 23.8 (measurements of the large scale structure), 23.9 (cluster evolution), and 23.10 (cosmological tests). Finally, Sect. 23.11 provides a conclusion and an outlook.
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