Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and itsrichness-dependence from z = 0 to z = 3 using large-scale cosmologicalsimulations. A standard flat LCDM model with \Omega_m = 0.3 and, forcomparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionarypredictions are presented in a format suitable for direct comparisons withobservations. We find that the cluster correlation strength increases withredshift: high redshift clusters are clustered more strongly (in comovingscale) than low redshift clusters of the same mass. The increased correlationswith redshift, in spite of the decreasing mass correlation strength, is causedby the strong increase in cluster bias with redshift: clusters represent higherdensity peaks of the mass distribution as the redshift increases. Therichness-dependent cluster correlation function, presented as thecorrelation-scale versus cluster mean separation relation, R_0 - d, is found tobe, 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 fixedcomoving radius). The non-evolving R_0 - d relation implies that both thecomoving clustering scale and the cluster mean separation increase withredshift for the same mass clusters so that the R_0 - d relation remainsessentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~3 provides an important new tool in cosmology; it can be used to breakdegeneracies that exist at z ~ 0 and provide precise determination ofcosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200