In addition to being interesting astrophysical objectsper se, galaxy clusters are also non-linear tracers of the large-scale structure, making them powerful tools to con- strain the cosmological parameters Ωm,σ8 and to a lesser degree, ΩΛ.
Several methodologies based on X-ray observations of clusters are available to constrain cosmological parameters, the most robust being:
• The mass function of local clusters, n(M), can constrain the amplitude of the power spectrum, σ8, and the matter density, Ωm, at the cluster scale,
through the comparison of the theoretical mass function (Jenkins et al. (2001)) with the observed X-ray luminosity function (XLF) (see for e.g., B¨ohringer et al. (2002)).
• Considering that thebaryon mass fraction fb of clusters is representative
of the relative matter content of the Universe, and since the baryon density of the Universe Ωb is known from the Big Bang Nucleosynthesis calculations
or the CMB, the matter density can be constrained assuming Ωm=Ωb/fb (e.g.
White & Frenk (1991), see Vikhlinin et al. (2003) for more recent results)
• The gas mass fraction in clusters,fgas, should be constant and a mea-
sure of the Universe’s value. Therefore measurements of its apparent evolution (fgas(z)∝d1.5) can used to probe the acceleration of the Universe, hence con-
straining ΩΛ (Allen et al. (2008)).
• Theevolution of the cluster mass function reflects the growth of density perturbations and can be used to constrain ΩΛ, in addition to Ωmandσ8. This
test requires a sample of clusters covering a large redshift range, for which the survey volume is well known. The application of the scaling relations to derive the X-ray temperature function (XTF) or the XLF (Mullis et al. (2004)) offer proxies to estimate the total mass, which are then compared to then(M, z).
• Theclustering properties of clustersdescribed by means of the power spec- trumP(k), can be used as a measure of the large scale-structure of the Universe, allowing us to constrain the cosmological parameters Ωm,σ8 (Schuecker et al.
(2001, 2003a,b)) .
In this era of precision cosmology it is essential to obtain Ωm andσ8 with different
methodologies in order to break degeneracies between these parameters. In this respect, clusters offer a valuable means to test cosmological models, complementary
2.4 Clusters in a cosmological framework
to other observational probes such as the CMB (Spergel et al. (2007)) and SN Ia (Riess et al. (2004), Astier et al. (2006)), and are more competitive than weak lensing studies. However, cosmological parameters derived with clusters still have error bars larger than desired. This situation arises because clusters are not perfect standard candles as deviations have been observed in the scaling laws that provide the link with the total cluster mass. The nature of the scatter is under intense investigation, in order to decrease the uncertainties in the measurements of cosmological parameters derived with clusters. The future looks bright though, with eROSITA coming online in the next three years, the statistics of clusters will dramatically increase, improving the measurements of Ωm and σ8, in addition to constrain ΩΛ.
3
Galaxy evolution in clusters
Abstract
This Chapter introduces the two main galaxy formation scenarios, the monolithic and the hierarchical models. A final consensus has not yet been reached between these contradictory hypotheses, thus motivating studies on the evolution of massive galaxies.
The properties of early-type galaxies are described with several methodologies: (i) via a morphological characterization; (ii) through the analysis of the color-magnitude relation, (iii) and by modelling the galaxies’ spectral energy distributions or spectra. To end this section we summarize the most recent results obtained with studies of galaxies in clusters at redshift∼> 1.
3.1 Galaxy formation scenarios
Two conflicting scenarios of galaxy formation and evolution have been proposed over 30 years ago: the monolithic collapse model (Eggen et al. (1962); Larson (1974), Arimoto & Yoshii (1987)), in which massive galaxies result from a single burst of star formation at high redshift; and the hierarchical merging model (Toomre (1977), White & Rees (1978)), in which galaxies are formed by accretion of smaller proto- galaxies.
Early-type galaxies (ETGs) form a homogeneous class of massive, red and pas- sively evolving galaxies, characterized by absorption-line spectra and negligible (if
any) emission lines. ETGs also contribute to most of the total stellar mass in clus- ters (∼60%), therefore the study of their evolution is essential to investigate galaxy formation and evolution.
In the current paradigm of the ΛCDM cosmology, large galaxies assembled over time through the accretion of smaller low-mass progenitors, thus favoring thehier- archical scenario. However, this picture apparently is at odds with the observation that (i) early-type galaxies are found to be the most massive and oldest systems, and (ii) their star formation histories indicate that the bulk of the stars in massive ellipticals formed at redshift z>2 (van Dokkum (2005), Tran et al. (2005)), which is in contradiction with the predictions from the the ΛCDM model.
The physical processes involved in galaxy formation and evolution are numerous and complex, such as radiative cooling, AGN and supernova feedback, and star forma- tion. Figure 3.1 taken from De Lucia et al. (2004), illustrates the complex interplay of processes affecting the state of the baryons in clusters. It is reasonable to say that we have not yet reached a full understanding of these intricate mechanisms in spite of major observational work and a large effort in developing semi-analytical models (SAM), which, when coupled to N-body simulations, provide a means to tackle these phenomena. Although simulations have for a long time overestimated the fraction of blue galaxies, the introduction of a heating mechanism in the form of AGN feedback has prevented the overproduction of stars. In this way, simulations have succeeded in predicting a large amount of massive old galaxies, thus providing a good match to the observations (De Lucia et al. (2004), Bower et al. (1992), Menci et al. (2006)).
Observations of metal abundances in the intracluster medium are one of the best means to place constraints on the star formation history in clusters - a measure of the efficiency with which gas was converted into stars, in addition to providing information on the processes responsible for the circulation of metals.