Voids and constraints on nonlinear clustering of galaxies
Michael S. Vogeley, Margaret J. Geller, Changbom Park, J. P. Huchra · The Astronomical Journal · 1994
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 2 depend only on pairwise products of the two-point function ξ(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 ρ L^*^) in the "voids." Underdensities are ~> 2σ 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}=1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model ({OMEGA} = 0.4, h = 0.6 λ_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.