Statistical analysis of catalogs of extragalactic objects. VIII. Cross-correlation of the Abell and the 10''' Shane-Wirtanen catalogs.
Results are presented for an analysis of the cross correlation between the angular positions of Abell (1958) rich compact clusters of galaxies and the galaxy counts of Shane and Wirtanen (SW, 1967), performed on the basis of a recent reduction of the SW data in the original 10 by 10 arcmin cells. A total of 1339 clusters in the galactic polar caps, covering 27% of the sky, are examined. A cross-correlation function is determined for each cluster distance and richness class; it is shown that the cross-correlation data do not fit a simple power law. A semiempirical model is considered in which each Abell cluster is assigned a spherical power-law halo extending to a certain radius. This highly simplified model takes account of irregularities in each cluster only insofar as they add to the effective mean power-law halos assigned, but does give a fairly good fit to the data. The mean space density of galaxies around a cluster is investigated, the Abell luminosity function is found to give the best fit to the observed amplitude ratios, and a richness-magnitude relation is evaluated for the Abell-cluster members.