The richness dependence of galaxy cluster correlations : Results from a redshift survey of rich APM clusters

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