VOID STATISTICS OF THE CFA REDSHIFT SURVEY

We study clustering properties of two samples from the CfA redshift survey each containing approximately 2500 galaxies. Comparison of the velocity distributions using a K-S 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 xiBAR(R) = <(delta-rho/rho)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 distance-limited samples of the CfA survey do not match the scaling relation predicted by hierarchical clustering models. On scales less-than-or-similar-to 10h-1 Mpc, the VPFs for these samples roughly follow the hierarchical pattern. However, on scales greater-than-or-similar-to 10h-1 Mpc we find large variations between the VPFs for distance-limited subsamples of each survey region. Variations in the VPF for different samples depend on the different large-scale features and sampling density in these samples. We introduce a variant of the VPF which uses nearly all the data in magnitude-limited samples. This statistic, P0(NBAR), accounts for the variation of the sampling density with velocity in a magnitude-limited survey. For samples with a range of limiting apparent magnitude, P0(NBAR) behaves like P0 is-proportional-to exp (- NBAR/N(cluster) where N(cluster) almost-equal-to 7-8. Agreement of P0 for NBAR less-than-or-similar-to 15 indicates that the Northern and Southern galactic regions of the survey are similarly clustered on scales less-than-or-similar-to 10h-1 Mpc. The similar behavior of P0 for the two survey regions, which include qualitatively different large-scale features, suggests that this statistic is robust with respect to variations in individual structures within the survey and may provide a useful discriminant among n-body models.