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

We report on the measurement of the two-point correlation function, and the pairwise peculiar velocity of galaxies in the IRAS PSCz survey. We compute these statistics first in redshift space, and then obtain the projected functions which 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, & B"orner (1998). We find that the real space two-point correlation function can be fitted to a power law $xi(r) = (r_0/r)^{gamma}$ with $gamma=1.69$ and $r_0=3.70 mpc$. The pairwise peculiar velocity dispersion $sigma_{12}(r_p)$ is close to $400 kms$ at $r_p=3mpc$ and decreases to about $150 kms$ at $r_p approx 0.2 mpc$. 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 ($Omega_0 = 0.3$, $lambda_0=0.7$, $Gamma=0.2$, $sigma_8=1$) using a set of high-resolution N-body simulations. Applying a stronger cluster-underweight biasing ($propto M^{-0.25}$) than for the LCRS ($propto M^{-0.08}$), 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 catalogues. 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.Comment: accepted for publication in ApJ; 24 pages with 9 figure