Investigation of clustering of galaxies, clusters and superclusters by the method of correlation Gamma-function

TL;DR

This study analyzes the spatial clustering of galaxies, clusters, and superclusters using the correlation Gamma-function, revealing scale-dependent clustering behavior and indications of a transition to homogeneity beyond 100 Mpc.

Contribution

It applies the correlation Gamma-function method to various samples, demonstrating scale-dependent clustering and complex large-scale structure beyond simple fractal models.

Findings

Clustering follows a power law with index 0.9-1.5 on small scales.

A break in the Gamma-function slope occurs around 30 Mpc, reducing to ~0.3.

Distribution tends to homogeneity beyond 100 Mpc.

Abstract

Using the apparatus of correlation Gamma-function (``conditional density''), we have analyzed spatial clustering of objects from several different samples of galaxies, clusters and superclusters. On small scales the distribution of objects obeys a power law drop of density with a power index of 0.9--1.5. On a scale of ~30 Mpc for independent samples of bright galaxies and clusters of galaxies we have detected a pronounced break in the slope of the Gamma-function with a power index decreasing to ~0.3. The clustering is much less pronounced in the region from 40 to 100 Mpc, and there is reason to suppose that the distribution of objects changes to homogeneous on scales larger than 100 Mpc. This is indicated by the slope of the Gamma-function close to 0 for a sample of rich clusters of galaxies up to 250 Mpc. The slope of the Gamma-function prior to the break, which characterizes the degree of clustering of matter, changes essentially and in a complex manner when passing to brighter (massive) objects. This suggests that the large-scale structure of the visible Universe even on small scales is considerably more complex than the fractal distribution described by one dimension (monofractal).