Cluster evolution as a diagnostic for Omega
Abstract
The population of rich galaxy clusters evolves much more rapidly in a universe with critical density than in a universe with low density. Thus, counts of clusters at intermediate redshift offer the possibility of determining the cosmological density parameter, {OMEGA}_0_ with a minimum of assumptions. We quantify this evolution using the PressSchechter formalism which we extend to flat cosmological models with a cosmological constant, {LAMBDA}_0_ = 1  {OMEGA}_0_. Using new large Nbody simulations, we verify that this formalism accurately predicts the abundance of rich clusters as a function of redshift in various cosmologies. We normalize the models by comparing them with the local abundance of clusters as a function of their Xray temperature which we rederive from data compiled by Henry & Arnaud. The resulting values of the rms density fluctuation in spheres of radius 8h^1^ Mpc are σ_8_ = (0.52 +/ 0.04){OMEGA}_0_^0.46+0.10{OMEGA}_0_^ if {LAMBDA}_0_ = and σ_8_ = (0.52+/0.04){OMEGA}_0_^ 0.52+0.13{OMEGA}_0_^ if {LAMBDA}_0_ = 1  {OMEGA}_0_. These values depend only weakly, and almost not at all if {OMEGA}_0_ = 1, on the shape of the power spectrum. We then examine how the distributions of mass, Xray temperature and SunyaevZel'dovich decrement evolve as a function of {OMEGA}_0_. We present the expected distributions at z = 0.33 and z = 0.5 and the predicted number counts of the largest clusters, both in space and in projection on the sky. We find that, even at z = 0.33, these distributions depend very strongly on {OMEGA}_0_ and only weakly on {LAMBDA}_0_. For example, at this redshift, we expect 15 times as many clusters per comoving volume with M > 3.5 x 10^14^h^1^ M_sun_ and 5 times as many clusters with kT > 5 keV if {OMEGA}_0_ = 0.3 than if {OMEGA}_0_ = 1. The splitting in the integrated counts is enhanced by the larger volume element in lowa models. There is therefore a real prospect of estimating {OMEGA}_0_ from forthcoming surveys of intermediate redshift clusters that will determine their masses, Xray temperatures or SunyaevZel'dovich decrements.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 1996
 DOI:
 10.1093/mnras/282.1.263
 arXiv:
 arXiv:astroph/9601088
 Bibcode:
 1996MNRAS.282..263E
 Keywords:

 Astrophysics
 EPrint:
 Compressed postscript also available at ftp://starftp.dur.ac.uk/pub/preprints/ecf.ps.gz