THE POWER SPECTRUM OF ABELL CLUSTER CORRELATIONS

We have carried out a power-spectrum analysis of the very large-scale spatial inhomogeneities in the distribution of Abell clusters. The data used consist of an all-sky sample volume-limited at redshift z < 0.08, containing a total of 427 clusters, for which the completeness of spectroscopic redshifts is 92 per cent for richness class R greater-than-or-equal-to 1 and 85 per cent for R = 0. Using this sample, we have re-examined the evidence for clustering anisotropies in redshift space, to see whether the cluster selection probability is uniform on the sky. For the R = 0 clusters, we find a very strong anisotropy signal: there appear to be many pairs of clusters which are close on the sky, but lie at very different redshifts. However, for R greater-than-or-equal-to 1 clusters this effect is absent: there is no evidence that the close pairs of clusters reflect anything other than true spatial correlations. For these richer clusters, the small-scale correlation function may be described by xi(r) = (r/r0)-gamma with r0 = 21.1 +/- 1.3 h-1 Mpc and gamma = 2.0 +/- 0.2. There is good evidence that the clustering strength is an increasing function of richness. On large scales, the power-spectrum analysis detects significant inhomogeneities in the cluster distribution with wavelengths > 100 h-1 Mpc. However, the cluster distribution is more uniform on these scales than would be predicted from an extrapolation of the small-scale power-law clustering. Converting the results to cell-count variances, the extrapolated rms fluctuation between cubes of side 100 h-1 Mpc is sigma = 0.48, whereas sigma = 0.32 +/- 0.03 is observed. Thus the distribution of Abell clusters adds further evidence to previous indications that the power spectrum of galaxy clustering has a break, with reduced power for wavelengths lambda greater than or similar to 100 h-1 Mpc.