Evolution of the cluster correlation function

Neta A. Bahcall, H. A.O. Lei, Paul Bode, Feng Dong

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3 Scopus citations


We study the evolution of the cluster correlation function and its richness dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ωm = 0.3 and, for comparison, a tilted Ωm = 1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R0-d, is found to be, remarkably, independent of redshift to z ≲ 2 for LCDM and z ≲ 1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R0-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R0-d relation remains essentially unchanged. For LCDM, this relation is R0(Z) ≃ 2.6[d(z}]1/2 for z ≲ 2 in comoving h-1 Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at z ≳ 2 for LCDM and z ≳ 1 for TSCDM, where the amplitude of the relations declines. The evolution of the R0-d relation from z ∼ 0 to z ∼ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ∼ 0 and provide precise determination of cosmological parameters.

Original languageEnglish (US)
Pages (from-to)1-6
Number of pages6
JournalAstrophysical Journal
Issue number1 I
StatePublished - Mar 1 2004

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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