Void Statistics and Hierarchical Scaling in the Halo Model

Abstract

We study scaling behaviour of statistics of voids in the context of the halo model of nonlinear large-scale structure. The halo model allows us to understand why the observed galaxy void probability obeys hierarchical scaling, even though the premise from which the scaling is derived is not satisfied. We argue that the commonly observed negative binomial scaling is not fundamental, but merely the result of the specific values of bias and number density for typical galaxies. The model implies quantitative relations between void statistics measured for two populations of galaxies, such as SDSS red and blue galaxies, and their number density and bias.