Evolution of the cluster mass and correlation functions in a ACDM cosmology

Joshua D. Younger, Neta A. Bahcall, Paul Bode

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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 ACDM 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 ACDM model when compared with future observations of high-redshift clusters.

Original languageEnglish (US)
Pages (from-to)1-6
Number of pages6
JournalAstrophysical Journal
Issue number1 I
StatePublished - Mar 20 2005

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmological parameters
  • Cosmology: observations
  • Cosmology: theory
  • Dark matter galaxies: clusters: general
  • Large-scale structure of universe


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