The Power Spectrum of Rich Clusters on Near-gigaparsec Scales

Recently, there have been numerous analyses of the redshift space power spectrum of rich clusters of galaxies. Some of these analyses indicate a “bump” in the Abell/ACO cluster power spectrum around k = 0.05hMpc. Such a feature in the power spectrum excludes most standard formation models and indicates possible periodicity in the distribution of large-scale structure. However, the data used in detecting this peak include clusters with estimated redshifts and/or clusters outside of Abell’s (1958) statistical sample, i.e. R = 0 clusters. Here, we present estimates of the redshift-space power spectrum for a newly expanded sample of 637 R ≥ 1 Abell/ACO clusters which has a constant number density to z = 0.10 in the Southern Hemisphere and a nearly constant number density to z = 0.14 in the Northern Hemisphere. The volume sampled, ∼ 10hMpc, is large enough to accurately calculate the power per mode to scales approaching 10hMpc. We find the shape of the power spectrum is a power-law on scales 0.02 ≤ k ≤ 0.10hMpc, with enhanced power over less rare clusters such as APM clusters. The power-law here follows n = −1.4. The power spectrum is essentially featureless, although we do see a dip near k = 0.04hMpc which cannot be considered statistically significant based on this data alone. We do not detect a narrow peak at k ∼ 0.05hMpc and there is no evidence for a turn-over in the power spectrum as has been previously reported. We compare the shape of the Abell/ACO rich cluster power spectrum to various linear models.