The Two-Point Correlation Function of Rich Clusters of Galaxies: Results from an Extended APM Cluster Redshift Survey

Abstract

We present new estimates of the spatial two-point correlation function of rich clusters of galaxies selected from the APM Galaxy Survey. We have measured redshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. The clusters have a mean space density of $\bar{n} = 3.4\times 10^{-5}\hmpccc$. The two-point correlation function, $\xi_{cc}$, for this sample is equal to unity at a pair-separation of $r_0 = 14.3\pm1.75\hmpc$ (2$\sigma$ errors), consistent with our earlier results from a smaller sample. The new observations provide an accurate determination of the shape of $\xi_{cc}$ to pair-separations of about $50\hmpc$. Our results show that $\xi_{cc}$ has a higher amplitude than expected according to the standard $\Omega=1$ cold dark matter (CDM) model on spatial scales $2\simlt s \simlt 50\hmpc$, but are in good agreement with scale-invariant fluctuations in either a low density CDM model or a critical density universe made up of a mixture of hot and cold dark matter. Our results provide strong constraints on so called `co-operative' models of galaxy formation in which the galaxy formation process introduces large-scale structure in the galaxy distribution.