Correlation Properties of Cluster Distribution

Abstract

We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the correlation analysis by various authors. The statistical analysis of cluster correlations is performed without any assumptions on the nature of the distribution itself. The cluster samples show fractal correlations up to sample limits ($\approx 70 h^{-1} Mpc$) with fractal dimension $D \approx 2$, without any tendency towards homogenization. Our analysis shows that the standard correlation methods are incorrect, since they give a finite correlation length for a distribution that does not possess one. In particular, the so called correlation length $r_{0}$ is shown to be simply a fraction of the sample size. Moreover we conclude that galaxies and clusters are two different representations of the same self similar structure and that the correlations of clusters are the continuation of those of galaxies to larger scales.