Alternativa con un nivel de splitters

Galaxy clusters are the most recently formed gravitationally-relaxed objects. Due to the fact that density peaks have higher amplitudes at smaller scales, the first structures which deviated from the Hubble flow and started to collapse and virial- ize, under their own self-gravity, had sub-galactic sizes. These small objects then merged and created galaxies, which eventually were collected inside clusters. Hence, the formation and evolution of galaxy clusters directly trace structure growth in the universe. For this reason galaxy clusters yield valuable information about the under- lying cosmological model and can be used to conduct a number of critical tests both for the underlying cosmological parameters characterizing our universe and for the physics of structure formation in the primordial universe. Specifically, the most im- portant cosmological studies involving galaxy clusters can be summarized as follows: 1. the accurate determination of the clustermass function (Eq. 2.14) observed in the local universe and its evolution toward earlier cosmic epochs (see Fig. 2.4) can provide important constraints on the matter and dark energy con- tent of the universe. This effect is clearly shown in Fig. 2.11 via an N-body simulation result, which demonstrates how assessing the abundance of clusters beyond z = 0.6 can easily help to discriminate between models with and with- out a cosmological constant. The revelation of massive clusters at z > 0.6 at the end of the 90s (Donahue et al. 1998; Bahcall & Fan 1998) indeed started

22 Chapter 2. Cosmological context

Figure 2.11: Left: Evolution of the cluster number density with redshift n(> M, z) (normalized to the value at z = 0) for different cosmological models. Right: Visual- ization of the results reported in the left panel. The simulation shows the evolution of the cluster number density from z = 1.4 (bottom side) to z = 0 (top side) for a flat, low density universe with Ωm = 0.3, ΩΛ = 0.7 (left column) and for a flat,

matter dominated universe with Ωm = 1, ΩΛ = 0 (right column). Yellow circles mark

the position of clusters. Each snapshot is 250 h−1_{Mpc across and 75 h}−1_{Mpc thick.}

Section 2.5 The importance of galaxy clusters 23

Figure 2.12: Confidence regions of σ8 and Ωm constrained by means of the RDCS-

1 sample of 4 clusters at z > 0.9. The three panels refer to different values of the power-spectrum shape parameter Γ =hΩm. The dotted curves indicate the expected Ωm₋σ8 relations for different numbers of z >0.9 clusters (N = 0.1, 1, 10, 30 from

bottom to top); the solid line refers to the actual value of 4. Plot from Borgani et al. (2000).

to challenge the standard model (at that time with ΩΛ = 0 and Ωm =1) and

hence anticipated the ultimate discovery of a dark energy component currently accelerating the expansion of the universe, achieved via the Type Ia supernova surveys (Reiss et al. 1998; Perlmutter et al. 1999).

2. the characterization, from simple cluster counts, of the spatial distribution of the clusters at redshift zero and its evolution up to z > 1 contains a wealth of information on the statistical properties of the large scale structure of the un- derlying dark matter. This aspect is parametrized by using thepower spectrum, P(k), already defined in Eq. 2.9. The shape ofP(k) can be defined analytically, and is actually also constrained by the cluster mass function at z = 0, but its normalization can only be assessed empirically. This is obtained by introducing the parameter σ8, generically defined as the mass variance (Eq. 2.15) smoothed

within a sphere of radius 8h−1_{Mpc. Specifically,σ}

8 andP(k) are linked to one

other according to the relation σ2₈ =D_|δM/M_|2_8h−1Mpc E z=0 = 4π Z dk k2 (2π)3Pz=0(k)W 2 8h−1Mpc(k) (2.20)

24 Chapter 2. Cosmological context

i.e., σ8 is the rms of the dark matter density contrast linearly evolved to the

present epoch (δ(~x, t0)) and smoothed with a filter of 8 h−1Mpc. Currently,

the most accurate value for this parameter is provided by the WMAP7 mission (Komatsu et al. 2011): σ8 = 0.816 ± 0.024. There exists a strong degeneracy

between Ωm and σ8, as low matter density values can be compensated by

higher values of σ8, and vice versa. One way of breaking such a degeneracy

is to measure the evolution of the custer mass function, which is particularly sensitive to Ωm. An example of such an approach is shown in Fig. 2.12, where a sample of 4 distant clusters extracted from the ROSAT Distant Cluster Survey (RDCS, Rosati et al. 1998) has been used.

3. Already at the beginning of the 90s, the comparison of the baryon content in the local clusters (Fabian et al. 1991; Briel et al. 1992) with the primordial nucleosynthesis expectations, helped to rule out models of the universe with a critical matter density (White et al. 1993).

4. X-ray and SZ emissions coming from galaxy clusters are complementary as the former provides the integral along the line of sight ofρ2

gasand a gas temperature Tgas. By dividing the product ofTgas_×R

ρ2

gasd(l.o.s.) byy-Compton (Eq. 2.19) one can obtain the massdensity profile of the cluster ICM matter that can then be used to infer the physical thickness of the system. Under the assumption of spherical symmetry, the obtained physical size can be compared with the apparent angular size in order to get a constraint on cosmological parameters by means of the angular distance,dA(z). This is the method that was used for the first time by Birkinshaw et al. (1991).

As discussed for the aforementioned methods, a key ingredient for enabling the use of galaxy clusters as cosmological probes is the accurate measurement of theirmasses. However, cluster masses are not physical quantities that can be directly determined from observations, they have to be inferred from observables which correlate with mass. This aspect always motivated the need of understanding possible systematic effects associated with the use of different observables as mass proxies (e.g., Henry et al. 2009), some of which are discussed in the next session.