Scaling Laws in the Stellar Mass Distribution and the Transition to Homogeneity

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 $r_0=5.8-7.0{\text{h}}^{-1}\text{Mpc}$ . 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 $10{\text{h}}^{-1}\text{Mpc}$ .