Spatial Correlation Functions and the Pairwise Peculiar Velocity Dispersion of Galaxies in the Point Source Catalog Redshift Survey: Implications for the Galaxy Biasing in Cold Dark Matter Models

Abstract

We report on the measurement of the two-point correlation function and the pairwise peculiar velocity of galaxies in the IRAS Point Source Catalog Redshift (PSCz) Survey. We compute these statistics first in redshift space and then obtain the projected functions that have simple relations to the real-space correlation functions on the basis of the method developed earlier in analyzing the Las Campanas Redshift Survey (LCRS) by Jing, Mo, & Borner. We find that the real space two-point correlation function can be fitted to a power law xi(r) = (r(o)/r)(gamma) with gamma = 1.69 and r(o) = 3.70 h(-1) Mpc. The pairwise peculiar velocity dispersion (PVD) sigma(12)(r(p)) is close to 400 km s(-1) at r(p) = 3 h(-1) Mpc and decreases to about 150 km s(-1) at r(p) approximate to 0.2 h(-1) Mpc. These values are significantly lower than those obtained from the LCRS. In order to understand the implications of those measurements on the galaxy biasing, we construct mock samples for a low-density spatially flat cold dark matter model (Omega(o) = 0.3, lambda(o) = 0.7, Gamma = 0.2, sigma(8) = 1), using a set of high-resolution N-body simulations in a box size of 100, 300, and 800 h(-1) Mpc. Applying a stronger cluster underweight biasing (proportional toM(-0.25)) than for the LCRS (proportional toM(-0.08)), we are able to reproduce these observational data, except for the strong decrease of the pairwise peculiar velocity at small separations. This is qualitatively ascribed to the different morphological mixture of galaxies in the two catalogs. Disk-dominated galaxy samples drawn from the theoretically constructed GIF catalog yield results rather similar to our mock samples with the simple cluster underweight biasing. We further apply the phenomenological biasing model in our N-body mock samples, which takes account of the density-morphology relation of galaxies in clusters. The model does not reduce the velocity dispersions of galaxies to the level measured in the PSCz data either. Thus, we conclude that the PVDs of the PSCz galaxies require a biasing model that substantially reduces the PVD on small scales relative to their spatial clustering.