Void Statistics of the CfA Redshift Survey
Abstract
We study clustering properties of two samples from the CfA redshift survey each containing ~ 2500 galaxies. Comparison of the velocity distributions using a KS test reveals structure on scales comparable with the extent of the survey. We use the void probability function (VPF) for these samples to examine the structure and to test for scaling relations in the galaxy distribution. Using moments of galaxy counts we calculate the galaxy correlation function and find that ζ(R) = <(δp/p)^2^> = 1 on a scale R = 7h^1^ Mpc. The shape and amplitude of the correlation function roughly agree with previous determinations. The VPFs for distancelimited samples of the CfA survey do not match the scaling relation predicted by hierarchical clustering models. On scales <~ 10h^1^ Mpc, the VPFs for these samples roughly follow the hierarchical pattern. However, on scales >~ 10h^1^ Mpc we find large variations between the VPFs for distancelimited subsamples of each survey region. Variations in the VPF for different samples depend on the different largescale features and sampling density in these samples. We introduce a variant of the VPF which uses nearly all the data in magnitudelimited samples. This statistic, P_0_(N), accounts for the variation of the sampling density with velocity in a magnitudelimited survey. For samples with a range of limiting apparent magnitude, P_0_(N) behaves like P_0_ is proportional to exp ( N/N_cluster_) where N_cluster_ ~ 78. Agreement of P_0_ for N <~ 15 indicates that the Northern and Southern galactic regions of the survey are similarly clustered on scales <~10h^1^ Mpc. The similar behavior of P_0_ for the two survey regions, which include qualitatively different largescale features, suggests that this statistic is robust with respect to variations in individual structures within the survey and may provide a useful discriminant among nbody models.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1991
 DOI:
 10.1086/170691
 Bibcode:
 1991ApJ...382...44V
 Keywords:

 Computational Astrophysics;
 Galactic Clusters;
 Red Shift;
 Astronomical Models;
 Galactic Structure;
 Many Body Problem;
 Probability Distribution Functions;
 Velocity Distribution;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING