Scaling laws in the stellar mass distribution and the transition to homogeneity

TL;DR

This study analyzes the large-scale distribution of stellar mass in SDSS data, revealing a multifractal structure with a transition to homogeneity around 10 Mpc/h, consistent with power-law clustering.

Contribution

It provides a new statistical analysis of stellar mass distribution, extending the scaling range and confirming multifractal behavior with a transition to homogeneity.

Findings

Two-point correlation function follows a power-law with exponent ~1.8

Clustering length estimated between 5.8 and 7.0 Mpc/h

Evidence of multifractal scaling and transition to homogeneity at 10 Mpc/h

Abstract

We present a new statistical analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey (data release 7). A set of volume-limited samples shows that the stellar mass of galaxies is concentrated in a range of galaxy luminosities that is very different from the range selected by the usual analysis of galaxy positions. Nevertheless, the two-point correlation function is a power-law with the usual exponent $\gamma=1.71$--$1.82$, which varies with luminosity. The mass concentration property allows us to make a meaningful analysis of the angular distribution of the full flux-limited sample. With this analysis, after suppressing the shot noise, we extend further the scaling range and thus obtain $\gamma=1.83$ and a clustering length \redc{$r_0= 5.8$--$7.0\,h^{-1}$Mpc.} Fractional statistical moments of the coarse-grained stellar mass density exhibit multifractal scaling. Our results support a multifractal model with a transition to homogeneity at about $10\,h^{-1}$Mpc.