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 ≥ 1| and 85 per cent for R = 0. Using this sample, we have re-examined the evidence for clustering anisotropics 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 ≥ 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 |ξ(r)=(r/r₀)-γ| with |r₀=21.1±1.3 h⁻¹| Mpc and |γ = 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 |σ=0.48|⁠, whereas |σ=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 |λ 100 h⁻¹| Mpc.