Fractal large-scale structure from a stochastic scaling law model

TL;DR

This paper presents a stochastic model explaining the fractal distribution of galaxies on large scales, linking their hierarchical structure to a power-law density profile and resulting in a correlation function consistent with observations.

Contribution

It introduces a novel stochastic scaling law model that connects galaxy parameters to their granular components, explaining the fractal large-scale structure.

Findings

Galaxy distribution follows a fractal pattern with dimension ~2.

The model predicts a two-point correlation function inversely proportional to distance.

Results align with observed transition to homogeneity at large scales.

Abstract

A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the density profile of galaxies on a given scale is described by a power law then the stochastic model leads naturally to a mass function that is proportional to the square of the distance from an occupied point, which corresponds to a two-point correlation function that is inversely proportional to the distance. This result is consistent with observations indicating that galaxies are, on the largest scales, characterized by a fractal distribution with a dimension of order 2 and well-fit with transition to homogeneity at cosmological scales.