The cluster-cluster correlation function

Abstract

The clustering properties of the Abell and Zwicky cluster catalogs are studied using the two-point angular and spatial correlation functions. The catalogs are divided into eight subsamples to determine the dependence of the correlation function on distance, richness, and the method of cluster identification. It is found that the Corona Borealis supercluster contributes significant power to the spatial correlation function to the Abell cluster sample with distance class of four or less. The distance-limited catalog of 152 Abell clusters, which is not greatly affected by a single system, has a spatial correlation function consistent with the power law Xi(r) = 300r exp -1.8. In both the distance class four or less and distance-limited samples the signal in the spatial correlation function is a power law detectable out to 60/h Mpc. The amplitude of Xi(r) for clusters of richness class two is about three times that for richness class one clusters. The two-point spatial correlation function is sensitive to the use of estimated redshifts.