Nature of Clustering in the Las Campanas Redshift Survey

TL;DR

This study applies multi-fractal analysis to galaxy distributions in the Las Campanas Redshift Survey, revealing scale-dependent clustering behavior and a transition to homogeneity around 80-100 Mpc.

Contribution

It introduces a multi-fractal analysis method that accounts for survey geometry and selection effects, providing new insights into galaxy clustering and large-scale homogeneity.

Findings

Galaxy distribution shows multi-fractal scaling from 20 to 80 Mpc.

Distribution becomes homogeneous beyond 80 Mpc.

Transition to homogeneity occurs around 80-100 Mpc.

Abstract

We have carried out a multi-fractal analysis of the distribution of galaxies in the three Northern slices of the Las Campanas Redshift Survey. Our method takes into account the selection effects and the complicated geometry of the survey. In this analysis we have studied the scaling properties of the distribution of galaxies on length scales from $20 h^{-1} Mpc$ to $200 h^{-1} Mpc$. Our main results are: (1) The distribution of galaxies exhibits a multi-fractal scaling behaviour over the scales $20 h^{-1} Mpc$ to $80 h^{-1} Mpc$, and, (2) the distribution is homogeneous on the scales $80h^{-1} Mpc$ to $200 h^{-1} Mpc$. We conclude that the universe is homogeneous at large scales and the transition to homogeneity occurs somewhere in the range $80 h^{-1} Mpc$ to $100 h^{-1} Mpc$.