Statistical analysis of catalogs of extragalactic objects. VIII. Crosscorrelation of the Abell and the 10''' ShaneWirtanen catalogs.
Abstract
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 crosscorrelation function is determined for each cluster distance and richness class; it is shown that the crosscorrelation data do not fit a simple power law. A semiempirical model is considered in which each Abell cluster is assigned a spherical powerlaw 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 powerlaw 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 richnessmagnitude relation is evaluated for the Abellcluster members.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1977
 DOI:
 10.1086/155404
 Bibcode:
 1977ApJ...215..703S
 Keywords:

 Astronomical Catalogs;
 Cross Correlation;
 Galactic Clusters;
 Statistical Analysis;
 Correlation Coefficients;
 Graphs (Charts);
 Luminous Intensity;
 Astrophysics