Multifractal analysis of cluster distribution in two dimensions

Statistics – Computation

Scientific paper

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Fractals, Galactic Clusters, Two Dimensional Models, Universe, Astronomical Catalogs, Computational Astrophysics

Scientific paper

Results are presented of a multifractal analysis on samples of galaxy clusters, obtained by cutting the Lick catalog at different values of the galaxy surface density as well as on the Lick galaxy distribution. The analysis is used to test the scaling behavior of the cluster distribution and how it changes when peaks of different height are selected. The highest selected peaks are found to possess well-defined scaling properties up to an angular scale of 6 to 7 deg, corresponding to about 20/h Mpc at the characteristic depth of the present samples, remarkably similar to the correlation length of rich galaxy systems. A correlation between scale-invariance of the cluster distribution and nonlinear clustering is suggested. The resulting spectrum of multifractal dimensions indicates that the rich cluster distribution is essentially space-filling in the underdense regions, while the overdense regions are characterized by a dimension of about 1.

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