Projection, spatial correlations, and anisotropies in a large and complete sample of Abell clusters

An analysis of R greater than or equal to 1 Abell clusters is presented for samples containing recent redshifts from the MX Northern Abell Cluster Survey. The newly obtained redshifts from the MX Survey as well as those from the ESO Nearby Abell Cluster Survey (ENACS) provide the necessary data for the largest magnitude-limited correlation analysis of rich clusters in the entire sky (excluding the galactic plane) to date. The MX Survey, undertaken primarily for large-scale structure studies, has provided a large compilation of galaxy redshifts in Abell cluster fields for the examination of projection effects within the Abell catalog. In addition, a large and complete set of cluster velocities (to m(10) = 16.8) is used to determine the two-point spatial correlation function and examine previously suggested line-of-sight cluster selection bias within the Abell catalog. The two-point spatial correlation function is determined for a complete magnitude-limited (m(10) less than or equal to 16.8) sample of northern Abell clusters (N-cl = 198), a complete whole-sky (excluding the galactic plane) magnitude-limited (m(10) less than or equal to 16.8) sample of Abell/ACO clusters (N-cl = 289), and a complete whole-sky magnitude and volume-limited (m(10) less than or equal to 16.8, z less than or equal to 0.1) sample of Abell/ACO clusters (N-cl = 238) In addition, we examined the largest sample of cD clusters (N-cl = 104) in the northern hemisphere. We find 19.4 less than or equal to r(o) less than or equal to 23.3 h(-1) Mpc - 1.92 less than or equal to gamma less than or equal to - 1.83 for the different cluster subsets examined (including the cD clusters). We have used the largest rich cluster data set available to date to look for line-of-sight anisotropies within the Abell/ACO catalogs. An examination of the correlation function separated into its line-of-sight and perpendicular-to-line-of-sight components show that the strong anisotropy present in previously studied Abell cluster data sets is not present in our samples. There are, however, indications of residual anisotropies which we show are the result of two elongated superclusters, Ursa Majoris and Corona Borealis, whose axes lie near the line of sight. After rotating these superclusters so that their semimajor axes are perpendicular to the line of sight, we find no indication of anisotropy in xi(sigma, pi). The amplitude and slope of the correlation function remain the same before and after these rotations. We also remove a subset of R=1 Abell/ACO clusters that show sizeable foreground/background galaxy contamination and again find no change in the amplitude or slope of the correlation function. We conclude that the correlation length of R greater than or equal to 1 Abell clusters is not artificially enhanced by line-of-sight anisotropies.