Differential Density Statistics of 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 densities statistics of the galaxy distribution as discussed in Ribeiro (2005), namely the differential density $\gamma$ and the integral differential density ${\gamma }^{\ast }$. By applying the theory advanced by Ribeiro and Stoeger (2003), 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 $\gamma$ and ${\gamma }^{\ast }$ with various cosmological distance definitions, namely the area distance, luminosity distance, galaxy area distance and redshift 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 ${\Omega }_{m_0}=0.3$, ${\Omega }_{{\Lambda }_0}=0.7$ standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro (2005), as well as showing that plots of $\gamma$ and ${\gamma }^{\ast }$ 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 bring support to Ribeiro's (2005) 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.

LaTeX, 37 pages, 6 tables, 10 figures. Accepted for publication in "The Astrophysical Journal"

References in corpus (14)

• Cosmic homogeneity demonstrated with luminous red galaxies
• The CNOC2 Field Galaxy Luminosity Function I: A Description of Luminosity Function Evolution
• The growth of galaxies in cosmological simulations of structure formation
• Statistical Physics for Cosmic Structures
• The Merger Rate to Redshift One from Kinematic Pairs: Caltech Faint Galaxy Redshift Survey XI
• Fractals and the Distribution of Galaxies
• Statistical physics for complex cosmic structures
• Relativistic Cosmology Number Counts and the Luminosity Function
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. III. Numerical Results
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. II. Analysis of the Einstein-de Sitter Model
• Observations in the Einstein--de Sitter Cosmology: Dust Statistics and Limits of Apparent Homogeneity
• Cosmological Distances and Fractal Statistics of Galaxy Distribution
• The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies
• Scale Invariance in a Perturbed Einstein-de Sitter Cosmology

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