Clusters of Galaxies as Constraints on Structure Formation Scenarios:

Clusters of Galaxies

The number density of rich clusters, their baryonic mass fractions, the amount of substructure that they contain, the cluster-cluster correlation function and epoch of virialization of clusters are all probes of OMEGA and and structure formation scenarios.

In general, most of the structure formation models under consideration do not over-produce rich clusters and are consistent with the cluster-cluster correlation function.

However, there is some uncertainly in the cluster-cluster correlation length as it depends a bit on choice of clusters. Probably the best method is to use an X-ray flux limited sample of clusters and that produces a correlation length (see figure above) of 21 h^-1 Mpc.

Recently Mo \etal 1996 show how the proper determination of the cluster correlation length maps on to cosmological parameters. For a correlation length > 20 h^-1 Mpc, OMEGA < 0.3 is favored.

Baryonic Mass Fraction of Clusters of Galaxies

Cluster baryonic mass fractions have become a recent concern. Since most of the baryons in a cluster are not in the member galaxies, but rather in the hot intracluster medium (ICM), accurate cluster masses as inferred from X-ray observations are required.

Simon White and collaborators (White \etal 1993) have shown that the ratio

Omega_b/Omega_o

measured for a cluster should not be significantly different than the Universal value. The baryonic mass in clusters consists of two forms, a visible component (e.g. luminous galaxies and cluster X-ray emission), denoted by f_b and a dark component (\eg stellar remnants, low mass stars).

The total baryonic density Omega_b is inferred from primordial nucleosynthesis as previously discussed. Hence if f_b be determined for clusters then Omega_o can be inferred from the relation

Omega_o = Omega_b/f_b

Current observations indicate that f_b > 0.04 h^-3/2

When combined with the nucleosynthesis limits Omega_b ~ 0.015 h^-2 this leads to

Omega_o < 0.3 h^-1/2

To reconcile this with OMEGA = 1 requires H = 30 or that the total masses of clusters have been systematically underestimated. The latter possibility has been investigated by Evrard \etal (1996) and discounted.

Hence the measured values of f_b in clusters appears quite inconsistent with OMEGA = 1.

But a low value of OMEGA appears to be inconsistent with the substructure arguments that suggest the formation of clusters is still on going (or at least terminated rather recently). Late cluster formation requires high OMEGA since that prevents structure freeze-out at early times.

X-ray Luminosity Function of Clusters

Observations of the evolution of the X-ray luminosity function of clusters as a function of redshift may reveal the epoch of cluster core virialization. To date, the sensitivity of various X-ray satellites (\eg EINSTEIN, ROSAT, ASCA) has allowed the detection of X-ray emission in clusters of galaxies out to z ~ 1 ((Hattori \etal 1997).

To date, the most distant cluster detected in X-rays has z = 1.0 and was detected on the basis of an emission line at 3.35 keV which is thought to be the redshifted 6.7 keV iron line (Hattori \etal 1997). There is not yet enough data to see if their is a characteristic redshift at which most clusters "turn-on".

However, with future increases in X-ray satellite sensitivity (\eg AXAF) it may be possible to either detect or strongly constrain this "turn-on" epoch to redshifts less than some value. In fact, while the existence of some clustering at high redshift may not be too surprising, the detection of substantial x-ray emission originating from a virialized cluster core at redshifts z > 2 would seem to either strongly rule out the formation of these cores via gravitational instability or indicate a new population of significantly denser clusters than currently are known.

Velocity Dispersion Evolution in Rich Clusters

Zabludoff and Geller (1994) use kinematic observations of the densest clusters of galaxies to show that models which match the power on large scales do not match the observed distribution of velocity dispersions. Moreover, biased models predict too few high velocity dispersion clusters compared to the number of low velocity dispersion clusters.

In fact, they conclude that no model matches both the statistics of the galaxy distribution on large scales and the small scale velocity dispersion characteristics of clusters of galaxies.

Crone and Geller (1995) consider the effects of merging on the evolution of cluster velocity dispersions. Their models show that the abundance of clusters with dispersions of 1200 km/s or greater increases with time, while the number of groups decrease with time. The particular evolutionary rates depend upon choice of cosmogenic scenario.

The models which match the data best are either Omega_o =0.2 or strongly biased Omega_o = 1 (recall that strong bias on large scales is not favored by other data).

All models, however, predict fewer low velocity dispersion systems than is actually observed.

Lastly, Crone \etal 1994 show how cluster density profiles map into Cosmology. The find the general result that cluster density profiles, examples are shown below, are too steep to be consistent with OMEGA = 1.

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