VOIDS AND CONSTRAINTS ON NONLINEAR CLUSTERING OF GALAXIES

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R less than or similar to 10h(-1) Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales less than or similar to 10h(-1) Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling [such scaling implies that the N-point correlation functions for N>2 depend only on pairwise products of the two-point function xi(r)] However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of ''voids'' with density p<0.2p. This statistic reveals a paucity of very bright galaxies (L>L*) in the ''voids.'' Underdensities are greater than or similar to 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and CDM-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (Omega=0.4, h=0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the ''standard'' CDM model (Omega=0.1, b=1.5; see below for definitions) and nonzero cosmological constant CDM model (Omega=0.4, h=0.6 lambda(0)=0.6, b=1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M<M*=-19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.