Statistical analysis of catalogs of extragalactic objects. IV. Cross-correlation of the Abell and Shane--Wirtanen catalogs

The cross-correlation between the galaxy counts compiled by Shane and Wirtanen and the angnlar positions of the rich clusters listed by Abell gives a powerful statistical measure on how galaxies are distributed around the rich clusters, and on how the galaxies counted by Shane and Wirtanen are distributed in distance from us. The correlation between clusters and galaxy counts is detected for clusters as distant as those in Abell's distance class S, and over angnlar separations as large as 5. The observations can be fitted by a cloud (supercluster) model, with 2 rich clusters per cloud, and 25 percent of all bright galaxies members of clouds. The clusters in Abell's richness class 1? > 3 are distingnished mainly by the fact that the long-range correlation with the galaxy counts is weaker than the correlation found for the clusters in richness classes 1 and 2. Subject headings: galaxies, clusters of