Differential Density Statistics of the Galaxy Distribution and the Luminosity Function

This paper uses data obtained from the galaxy luminosity function (LF) tocalculate two types of radial number densities statistics of the galaxydistribution as discussed in Ribeiro (2005), namely the differential density$\gamma$ and the integral differential density $\gamma^\ast$. By applying thetheory advanced by Ribeiro and Stoeger (2003), which connects the relativisticcosmology number counts with the astronomically derived LF, the differentialnumber counts $dN/dz$ are extracted from the LF and used to calculate both$\gamma$ and $\gamma^\ast$ with various cosmological distance definitions,namely the area distance, luminosity distance, galaxy area distance andredshift distance. LF data are taken from the CNOC2 galaxy redshift survey and$\gamma$ and $\gamma^\ast$ are calculated for two cosmological models:Einstein-de Sitter and an $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ standardcosmology. The results confirm the strong dependency of both statistics on thedistance definition, as predicted in Ribeiro (2005), as well as showing thatplots of $\gamma$ and $\gamma^\ast$ against the luminosity and redshiftdistances indicate that the CNOC2 galaxy distribution follows a power lawpattern for redshifts higher than 0.1. These findings bring support toRibeiro's (2005) theoretical proposition that using different cosmologicaldistance measures in statistical analyses of galaxy surveys can lead tosignificant ambiguity in drawing conclusions about the behavior of the observedlarge scale distribution of galaxies.Comment: LaTeX, 37 pages, 6 tables, 10 figures. Accepted for publication in "The Astrophysical Journal