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Optical and X-Ray Clusters as Tracers of the Supercluster-Void Network. II. The Spatial Correlation Function

We study the spatial distribution of Abell and X-ray–selected clusters of galaxies from the ROSAT Bright Source Catalog and determine correlation functions for both cluster samples. We find that on small scales the correlation functions depend on the cluster environment: clusters in rich superclusters have a larger correlation length and amplitude than clusters of the whole sample. On large scales the correlation functions depend on the distribution of superclusters, but for both X-ray and Abell clusters they are oscillating with a period of ∼115 h-1 Mpc, indicating the presence of a local peak in the power spectrum at an effective wavenumber k = 0.055 h Mpc-1.