The two-point correlation function of rich clusters of galaxies: results from an extended APM cluster redshift survey

We present new estimates of the spatial two-point correlation function ofrich clusters of galaxies selected from the APM Galaxy Survey. We have measuredredshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. Theclusters have a mean space density of $\bar{n} = 3.4\times 10^{-5}\hmpccc$. Thetwo-point correlation function, $\xi_{cc}$, for this sample is equal to unityat a pair-separation of $r_0 = 14.3\pm1.75\hmpc$ (2$\sigma$ errors), consistentwith our earlier results from a smaller sample. The new observations provide anaccurate determination of the shape of $\xi_{cc}$ to pair-separations of about$50\hmpc$. Our results show that $\xi_{cc}$ has a higher amplitude thanexpected according to the standard $\Omega=1$ cold dark matter (CDM) model onspatial scales $2\simlt s \simlt 50\hmpc$, but are in good agreement withscale-invariant fluctuations in either a low density CDM model or a criticaldensity universe made up of a mixture of hot and cold dark matter. Our resultsprovide strong constraints on so called `co-operative' models of galaxyformation in which the galaxy formation process introduces large-scalestructure in the galaxy distribution.Comment: 5 pages, uuencoded compressed postscript (4 figures), submitted to MNRA