The spatial correlation function of rich clusters of galaxies

A series of objective statistical estimators is applied to directly study the three-dimensional distribution of rich clusters, using a recently completed redshift sample of 104 Abell clusters out to distance class four and galactic latitude of 30 deg or more. The sample and the relevant positional and redshift selection effects are discussed, and the two-point angular correlation function and nearest-neighbor distribution of clusters in the sample are determined, as well as in the larger D = 5+6 sample and in several subsamples of different richness classes and latitude zones. The redshift correlation function of clusters for various angular separations on the sky is examined as a test for the reality of the observed angular correlations. The two-point spatial correlation function of clusters in the sample is determined, and the consistency among the three observed correlation functions is tested. A model that describes all the observed correlations is presented.