Galaxy clusters are contrary to their name more than just a collection of galaxies. In the 1930s Fritz Zwicky (Zwicky 1937) discovered that it requires a large amount of unseen matter to bind the fast moving galaxies in the Coma galaxy cluster into a long lasting object. Today we have a clear cosmic scenario with galaxy clusters as an integral part of the large-scale structure of the Universe. They are the largest matter aggregates within the large-scale structure which have collapsed under their own gravity and are closely approaching a dynamical equilibrium. Much theoretical effort has been spent to understand and characterize this equilibrium structure. To the first order, galaxy clusters are now described as Dark Matter Halos with a characteristic universal shape of the Dark Matter potential (e.g. Navarro et al. 1995, Moore et al. 1999, Gao et al. 2008). Observations show indeed, that the cluster population can be described as constituting a nearly self-similar family with similar shapes of the matter distribution, where the small scatter is due to the different formation histories and differently close approaches to the equilibrium configuration.
Galaxy clusters are therefore very important giant astrophysical laboratories providing us with a well characterized physical environment in which we can study many interesting astrophysical phenomena and cosmic processes on giant scales (Sarazin 1986). They also allow us to study large coeval galaxy populations and enable us to investigate their evolution in connection with the chemical and thermal evolution of the embedding intracluster medium (ICM) (e.g. Dressler 1980, Dressler et al. 1997, Poggianti et al. 1999, Mei et al. 2006).
As tracers of the cosmic large-scale structure they are also important probes for cosmology. It is the growth of structure in the matter distribution of the Universe that has a strong dependence on the cosmological model parameters and in particular on the nature of Dark Matter and Dark Energy. Since galaxy clusters are very sensitive tracers of structure growth, a census of the cluster population as a function of redshift can be used to test cosmological models (e.g. Borgani et al. 2001, Schuecker et al. 2003a, Schuecker et al. 2003b, Henry 2004, Vikhlinin et al. 2003, Vikhlinin et al. 2009, Henry et al. 2009).
The current most important limitation in using galaxy cluster studies for cosmology is the calibration of the relation between various observables and cluster mass. Therefore a lot of effort is currently being spent to improve the cluster mass determination and the understanding of cluster structure (e.g. Arnaud et al. 2007, Vikhlinin et al. 2006, Pratt et al. 2006, Pratt et al. 2007). X-ray spectroscopy of the cluster emission plays a crucial technical role in this effort to characterize cluster structure precisely, to model the cluster population as a family of self-similar objects with explainable deviations, and to establish scaling relations of global cluster parameters that allow to draw comprehensive statistical conclusions on cluster properties from simple observables.
Most of the detailed knowledge on galaxy clusters has been obtained in recent years through X-ray astronomy. This is due to the fact that the intracluster medium (ICM) has been heated to temperatures of tens of Millions of degrees (several keV per particle) which causes the hot plasma to emit the bulk of the thermal energy in the regime of soft X-rays. Since this is also the photon energy range where the well developed X-ray telescopes come into play, galaxy clusters are among the most rewarding study objects for X-ray imaging and spectro-imaging observations. Fig. 1 shows a composite image of the Coma galaxy cluster, where an optical image from the Palomar Sky Survey showing the dense galaxy distribution of the Coma cluster is superposed in grey scale on top of an X-ray image from the ROSAT All-Sky Survey with X-ray brightness coded in red color. We clearly recognize that the X-ray image displays the cluster as one connected entity. This illustrates the fact that galaxy clusters are well defined, fundamental building blocks of our Universe.
Figure 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 in grey).
As largest cosmic objects they display several interesting astrophysical superlatives: (i) the ICM is the hottest thermal equilibrium plasma that we can study in detail, with temperatures up to two orders of magnitude larger than the temperature in the center of the sun, (ii) the gravitational potential of clusters gives rise to the largest effect of light deflection with deflection angles exceeding half an arcmin, producing the most spectacular gravitational lensing effects (e.g. Hattori et al. 1999), (iii) the hot plasma cloud of the ICM casts the darkest shadows onto the cosmic microwave background through the Sunyaev-Zeldovich effect (at wavelengths below about 1.4 mm they are seen as surface brightness enhancements) (e.g. Birkinshaw 1999), and (iv) the merger of galaxy clusters produces the largest energy release in the Universe after the big bang itself with energies up to orders of 1063 erg (e.g. Feretti et al. 2002).
X-ray observations and X-ray spectroscopy are the most important tools to obtain detailed information on cluster properties and the processes occuring in their ICM as will be illustrated in this article. In section 2 we will explain how observable X-ray spectra can be understood and modeled. In section 3 we show how this spectral modeling is applied to study the thermal structure of the ICM that also provides the tool for measuring cluster masses. Section 4 deals with the diagnostics of the central regions of clusters where massive cooling is prevented by AGN heating in those objects where the cooling time is short enough for effective cooling. In section 5 we illustrate how the observed spectral lines can be used for the chemical analysis of the ICM and what can be learned from these observations. In section 6 we take a look into the physics of plasma under non-equilibrium ionization conditions and in the last section, 7, we provide an outlook on the capabilities and potential of X-ray instruments planned for the future.