The richness dependence of galaxy cluster correlations: Results from a redshift survey of rich APM clusters

Abstract

We analyse the spatial clustering properties of a new catalogue of very rich galaxy clusters selected from the APM Galaxy Survey. These clusters are of comparable richness and space density to Abell Richness Class $\ge 1$ clusters, but selected using an objective algorithm from a catalogue demonstrably free of artificial inhomogeneities. Evaluation of the two-point correlation function ${\xi }_{cc}(r)$ for the full sample and for richer subsamples reveals that the correlation amplitude is consistent with that measured for lower richness APM clusters and X-ray selected clusters. We apply a maxmimum likelihood estimator to find the best fitting slope and amplitude of a power law fit to ${\xi }_{cc}(r)$, and to estimate the correlation length $r_0$ (the value of $r$ at which ${\xi }_{cc}(r)$ is equal to unity). For clusters with a mean space density of $1.6\times 10^{-6}\hmpccc$ (equivalent to the space density of Abell Richness $\ge 2$ clusters), we find $r_{0}=21.3^{+11.1}_{-9.3} \hmpc$ (95% confidence limits). This is consistent with the weak richness dependence of ${\xi }_{cc}(r)$ expected in Gaussian models of structure formation. In particular, the amplitude of ${\xi }_{cc}(r)$ at all richnesses matches that of ${\xi }_{cc}(r)$ for clusters selected in N-Body simulations of a low density Cold Dark Matter model.

MNRAS submitted, 9 pages, LaTeX (mn), 7 figures. Also available at http://www-astronomy.mps.ohio-state.edu/~racc/

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