Projection Contamination in Cluster Catalogs: Are the Abell Redshift Sample Correlations Significant?
We estimate the effect of projection contamination in the Abell catalog on the three-dimensional cluster autocorrelation function ξ_cc_(r) by constructing a new D <= 4, R >= 1 "uncontaminated" catalog. We use a model in which the galaxy number density field is a superposition of a uniform field and spherical halos centered on each cluster center, whose profiles are derived from observed cluster-galaxy correlation functions. This procedure eliminates 12-17 of the 102 clusters, six because of double counting within overlapping Abell circles and the rest mainly because of overlap <= 6h^-1^ Mpc in projection. Therefore the results do not depend critically on the details of our model. The correlation function is reduced in amplitude by about a factor of 2. While this analysis does not exclude a correlation function of high amplitude, we find that it does not necessarily fit a power law, no meaningful correlation length can be determined, the deviations from zero are less than 1.7 δ on any scale, and ξ_cc_(r) is not different from zero at the 1 δ level for r >~ 40h^-1^ Mpc. Thus the correlation function of this small sample cannot be regarded as a difficulty for any of the standard cosmological scenarios. The distribution of cluster pairs is much more isotropic in the uncontaminated catalog, leaving no significant evidence for larger peculiar velocities for clusters.