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Abstract:

We apply a new statistics, the factorial moment correlators, to density maps obtained from the APM survey The resulting correlators are all proportional to the two-point correlation function, substantially amplified with an amplification nearly exponential with the total rank of the correlators. This confirms the validity of the hierarchical clustering assumption on the dynamic range examined, corresponding to 0.5-50 h^-1 Mpc in three-dimensional space. The Kirkwood superposition with loop terms is strongly rejected. The structure coefficients of the hierarchy are also fitted. The high quality of the APM catalog enabled us to disentangle the various contributions from the power spectrum, small-scale nonlinear clustering, and combinatorial effects, all of which affect the amplification of the correlators. These effects should appear in correlations of clusters in a similar fashion.

Abstract:

The APM Cluster Survey was based on a modification of Abell's original classification scheme for galaxy clusters. Here we discuss the results of an investigation of the stability of the statistical properties of the cluster catalogue to changes in the selection parameters. For a poor choice of selection parameters we find clear indications of line-of-sight clusters, but there is a wide range of input parameters for which the statistical properties of the catalogue are stable. We conclude that clusters selected in this way are indeed useful as tracers of large-scale structure.