Richness Dependence of Galaxy Cluster Correlations: Results from a Redshift Survey of Rich APM Clusters

摘要

We analyze the spatial clustering properties of a new catalog of very rich galaxy clusters selected from the APM Galaxy Survey. These clusters are of comparable richness and space density to Abell Richness Class greater than or equal to 1 clusters, but selected using an objective algorithm from a catalog demonstrably free of artificial inhomogeneities. Evaluation of the two-point correlation function xi(sub cc)(r) for the full sample and for richer subsamples revelas that the correlation amplitude is consistent with that measured for lower richness APM clusters and X-ray selected clusters. We apply a maximum likelihood estimator to find the best fitting slope and amplitude of a power law fite to x(sub cc)(r), and to estimate the correlation length r(sub 0) (the value of r at which xi(sub cc)(r) is equal to unity). For clusters with a mean space density of 1.6 x 10(exp -6)h(exp 3) MpC(exp -3) (equivalent to the space density of Abell Richness greater than or equal to 2 clusters), we find r(sub o)=21.3(+11.1/-9.3)h(exp-1) Mpc (95% confidence limits). This is consistent with the weak richness dependence of xi(sub cc)(r) expected in Gaussian models of structure formation. In particular, the amplitude of xi(sub cc) (r) at all richnesses matches that of xi(sub cc)(r) for clusters selected in N-Body simulations of a low density Cold Dark Matter model.