SPATIAL CORRELATIONS IN A REDSHIFT SURVEY OF APM GALAXY CLUSTERS

We have constructed a new catalog of rich clusters of galaxies by applying an objective selection algorithm to the APM Galaxy Survey. We have measured redshifts for 173 clusters from this catalog leading to a redshift survey of over 200 rich APM clusters with z less-than-or-similar-to 0.1 when we include published redshifts. The mean space density for this subsample is nBAR = 2.4 x 10(-5) h3 Mpc-3,2 i.e., about four times the mean space density of R greater-than-or-equal-to 1 A bell clusters. The spatial correlation function for our redshift sample can be approximated by xi(cc)(s) = (r0/s)2 with r0 = 12.9 +/- 1.4 h-1 Mpc. The correlation length for the 93 richest clusters in our sample is r0 = 14 +/- 4 h-1 Mpc. These results are consistent with the amplitude for xi(cc) expected in the standard cold dark matter model on scales less-than-or-similar-to 10 h-1 Mpc and are lower than the amplitude (r0 approximately 25 h-1 Mpc) found by Bahcall & Soneira from the Abell catalog. However, our results indicate more clustering than expected in the standard cold dark matter model on scales greater-than-or-similar-to 10 h-1 Mpc. We argue that the APM cluster catalog is more homogeneous than the Abell sample, and we demonstrate that our redshift-space correlation function is free from spurious large-scale anisotropies and is compatible with small (less-than-or-similar-to 500 km s-1) cluster peculiar velocities.