Evolution of the Cluster Mass and Correlation Functions in a ΛCDM Cosmology

Abstract

The evolution of the cluster mass function and the cluster correlation function from z = 0 to 3 is determined using ~106 clusters obtained from high-resolution simulations of the current best-fit ΛCDM cosmology (Ωm = 0.27, σ8 = 0.84, h = 0.7). The results provide predictions for comparisons with future observations of high-redshift clusters. A comparison of the predicted mass function of low-redshift clusters with observations from early Sloan Digital Sky Survey data and the predicted abundance of massive distant clusters with observational results favor a slightly larger amplitude of mass fluctuations (σ8 ~ 0.9) and lower density parameter (Ωm ~ 0.2); these values are consistent within 1 σ with the current observational and model uncertainties. The cluster correlation function strength increases with redshift for a given mass limit; the clusters were more strongly correlated in the past because of their increasing bias with redshift—the bias reaches b ~ 100 at z = 2 for M > 5 × 1013 h-1 M☉ clusters. The richness-dependent cluster correlation function, represented by the correlation scale versus cluster mean separation relation, R0-d, is generally consistent with observations. This relation can be approximated as R0 = 1.7d0.6 h-1 Mpc for d ~ 20-60 h-1 Mpc. The R0-d relation exhibits surprisingly little evolution with redshift for z < 2; this finding can provide a new test of the current ΛCDM model when compared with future observations of high-redshift clusters.