THE RICHNESS DEPENDENCE OF GALAXY CLUSTER CORRELATIONS - RESULTS FROMA REDSHIFT SURVEY OF RICH APM CLUSTERS

We analyse the spatial clustering properties of a new catalogue of ver y rich galaxy clusters with newly measured redshifts selected from the APM Galaxy Survey. These clusters are of comparable richness and spac e density to Abell richness class greater than or equal to 1 clusters, but selected using an objective algorithm from a catalogue demonstrab ly free of artificial inhomogeneities. Evaluation of the two-point cor relation function xi(cc)(r) for the full sample and for richer subsamp les reveals that the correlation amplitude is consistent with that mea sured for lower richness APM clusters and X-ray selected clusters. We apply a maximum likelihood estimator to find the best-fitting slope an d amplitude of a power-law fit to xi(cc)(r), and to estimate the corre lation length r(0) [the value of r at which xi(cc)(r) is equal to unit y]. For clusters with a mean space density of 1.6 x 10(-6) h(3) Mpc(-3 ) (equivalent to the space density of Abell richness greater than or e qual to 2 clusters), we find r(0) = 21.3(-9.3)(+11.1) h(-1) Mpc (95 pe r cent confidence limits). This is consistent with the weak richness d ependence of xi(cc)(r) expected in Gaussian models of structure format ion. In particular, the amplitude of xi(cc)(r) at all richnesses match es that of xi(cc)(r) for clusters selected in N-body simulations of a low-density cold dark matter model.