Galaxy clusters

4.5 Galaxy clusters

Clusters of galaxies are the largest gravitationally bound systems known to be in quasi-equilibrium. This allows for reliable estimates to be made of their mass as well as their dynamical and thermal attributes. The richest clusters, arising from $3σ$ density fluctuations, can be as massive as $1014 –1015 M ⊙$ , and the environment in these structures is composed of shock heated gas with temperatures of order 10⁷ – 10⁸ K which emits thermal bremsstrahlung and line radiation at X-ray energies. Also, because of their spatial size of $−1 ∼ 1 h Mpc$ and separations of order $− 1 50h Mpc$ , they provide a measure of nonlinearity on scales close to the perturbation normalization scale $− 1 8h Mpc$ . Observations of the substructure, distribution, luminosity, and evolution of galaxy clusters are therefore likely to provide signatures of the underlying cosmology of our Universe, and can be used as cosmological probes in the observable redshift range $0 ≤ z ≤ 1$ .

4.5.1 Internal structure

Thomas et al. [155 ] investigated the internal structure of galaxy clusters formed in high resolution N-body simulations of four different cosmological models, including standard, open, and flat but low density Universes. They find that the structure of relaxed clusters is similar in the critical and low density Universes, although the critical density models contain relatively more disordered clusters due to the freeze-out of fluctuations in open Universes at late times. The profiles of relaxed clusters are very similar in the different simulations since most clusters are in a quasi-equilibrium state inside the virial radius and generally follow the universal density profile of Navarro et al. [125 ]. There does not appear to be a strong cosmological dependence in the profiles as suggested by previous studies of clusters formed from pure power law initial density fluctuations [65 ]. However, because more young and dynamically evolving clusters are found in critical density Universes, Thomas et al. suggest that it may be possible to discriminate among the density parameters by looking for multiple cores in the substructure of the dynamic cluster population. They note that a statistical population of 20 clusters could distinguish between open and critically closed Universes.

4.5.2 Number density evolution

The evolution of the number density of rich clusters of galaxies can be used to compute $Ω0$ and $σ8$ (the power spectrum normalization on scales of $8 h− 1 Mpc$ ) when numerical simulation results are combined with the constraint $0.5 σ8Ω0 ≈ 0.5$ , derived from observed present-day abundances of rich clusters. Bahcall et al. [24 ] computed the evolution of the cluster mass function in five different cosmological model simulations and find that the number of high mass (Coma-like) clusters in flat, low $σ8$ models (i.e., the standard CDM model with $σ8 ≈ 0.5$ ) decreases dramatically by a factor of approximately 10³ from $z = 0$ to $z ≈ 0.5$ . For low $Ω0$ , high $σ8$ models, the data result in a much slower decrease in the number density of clusters over the same redshift interval. Comparing these results to observations of rich clusters in the real Universe, which indicate only a slight evolution of cluster abundances to redshifts $z ≈ 0.5– 1$ , they conclude that critically closed standard CDM and Mixed Dark Matter (MDM) models are not consistent with the observed data. The models which best fit the data are the open models with low bias ( $Ω0 = 0.3 ± 0.1$ and $σ8 = 0.85 ± 0.5$ ), and flat low density models with a cosmological constant ( $Ω0 = 0.34 ± 0.13$ and $Ω0 + Λ = 1$ ).

4.5.3 X-ray luminosity function

The evolution of the X-ray luminosity function, as well as the number, size and temperature distribution of galaxy clusters are all potentially important discriminants of cosmological models and the underlying initial density power spectrum that gives rise to these structures. Because the X-ray luminosity (principally due to thermal bremsstrahlung emission from electron/ion interactions in the hot fully ionized cluster medium) is proportional to the square of the gas density, the contrast between cluster and background intensities is large enough to provide a window of observations that is especially sensitive to cluster structure. Comparisons of simulated and observed X-ray functions may be used to deduce the amplitude and shape of the fluctuation spectrum, the mean density of the Universe, the mass fraction of baryons, the structure formation model, and the background cosmological model.

Several groups [49 , 56 ] have examined the properties of X-ray clusters in high resolution numerical simulations of a standard CDM model normalized to COBE. Although the results are very sensitive to grid resolution (see [17 ] for a discussion of the effects from resolution constraints on the properties of rich clusters), their primary conclusion, that the standard CDM model predicts too many bright X-ray emitting clusters and too much integrated X-ray intensity, is robust since an increase in resolution will only exaggerate these problems. On the other hand, similar calculations with different cosmological models [56 , 52 ] suggest reasonable agreement of observed data with Cold Dark Matter + cosmological constant ( $Λ$ CDM), Cold + Hot Dark Matter (CHDM), and Open or low density CDM (OCDM) evolutions due to different universal expansions and density power spectra.

4.5.4 SZ effect

The Sunyaev–Zel’dovich (SZ) effect is the change in energy that CMB photons undergo when they scatter in hot gas typically found in cores of galaxy clusters. There are two main effects: thermal and kinetic. Thermal SZ is the dominant mechanism which arises from thermal motion of gas in the temperature range 10⁷ – 10⁸ K, and is described by the Compton $y$ parameter

where $σT = 6.65 × 10− 25 cm2$ is the Thomson cross-section, $me$ , $ne$ and $Te$ are the electron rest mass, density and temperature, $c$ is the speed of light, $k B$ is Boltzmann’s constant, and the integration is performed over the photon path. Photon temperature anisotropies are related to the $y$ parameter by $ΔT ∕T ≈ − 2y$ in the Rayleigh–Jeans limit. The kinetic SZ effect is a less influential Doppler shift resulting from the bulk motion of ionized gas relative to the rest frame of the CMB.

Springel et al. [150 ] used a Tree/SPH code to study the SZ effects in a CDM cosmology with a cosmological constant. They find a mean amplitude for thermal SZ ( $− 6 y = 3.8 × 10$ ) just below current observed upper limits, and a kinetic SZ about 30 times smaller in power. Da Silva et al. [66 ] compared thermal SZ maps in three different cosmologies (low density + $Λ$ , critical density, and low density open model). Their results are also below current limits: $y ≈ 4 × 10− 6$ for low density models with contributions from over a broad redshift range $z ≤ 5$ , and $y ≈ 1 × 10−6$ for the critical density model with contributions mostly from $z < 1$ . However, further simulations are needed to explore the dependence of the SZ effect on microphysics, i.e., cooling, star formation, supernovae feedback.