Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richnessdependence 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 (in comoving scale) than low redshift clusters of the same mass. The increased correlations 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 correlationscale versus cluster mean separation relation, R0 d, is found to be, remarkably, independent of redshift to z . 2 for LCDM and z . 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving 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) for z . 2 (in comoving h Mpc scales). TSCDM 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. Subject headings: cosmology:observations–cosmology:theory–cosmological parameters– dark matter–galaxies:clusters: general–large-scale structure of universe Princeton University Observatory, Princeton, NJ 08544