Differential Density Statistics of the Galaxy Distribution and the Luminosity Function

Abstract

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number density statistics of the galaxy distribution as discussed in Ribeiro, namely, the differential density γ and the integral differential density γ*. By applying the theory advanced by Ribeiro & Stoeger, which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts dN/dz are extracted from the LF and used to calculate both γ and γ* with various cosmological distance definitions, namely, area distance, luminosity distance, galaxy area distance, and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey, and γ and γ* are calculated for two cosmological models: Einstein-de Sitter and an Ω = 0.3, Ω = 0.7 standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro, as well as showing that plots of γ and γ* against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power-law pattern for redshifts higher than 0.1. These findings support Ribeiro's theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large-scale distribution of galaxies.