DYNAMIC BIASES IN GRAVITATIONAL CLUSTERING

The centers of dark matter halos, where galaxies form, have spatial distributions and pairwise random velocities that misrepresent those in the general density field. The origin and evolution of these biases are studied with the aid of dissipationless n-body models. Velocity bias originates when the galaxies, along with their extended dark matter halos, fall into virialized regions and become subject to dynamical friction. As a consequence, galaxy random velocities are always less than those in the density field. A first-order model that includes the dynamical friction experienced by two gravitationally bound galaxies with their correlated dark halos reproduces the general features of the velocity-acceleration relation measured in n-body experiments roughly to the accuracy to which the Coulomb integral, In-LAMBDA, is known. The model predicts that the ratio of the mean pairwise peculiar velocity of galaxies to the dark matter dispersion tends to 3(pi)1/2/[2(2)1/2-In-LAMBDA] almost-equal-to 0.7 in regions of high acceleration. To emphasize the distinction between dark halos and the locations of galaxies the relative correlation amplitudes of halos, xi-hh, and the general dark matter distribution, xi-pp, are compared as a function of epoch, finding that the two-point correlations of the halos have little dependence on epoch. Moreover xi-hh of galaxy mass halos is always less than xi-gg, the observed correlation of galaxies. To match the n-body data to the amplitude of xi-gg requires that galaxies be identified with the z = 0 locations of the centers of halos that are formed in the redshift range z congruent-to 1-3. By redshift zero these halos have undergone considerable dynamical evolution, including clustering, merging, and tidal stripping, but overall have become considerably more clustered than halos of the same mass and overdensity identified at z = 0. The correlation function of these "galaxies" is not too sensitive to the particular redshift choice, at separations where xi-gg-greater-than-or-similar-to-10, although there are interesting enhancements at xi-gg-less-than-or-similar-to-1 with increasing redshift of selection. The mean cosmological density estimated with the cosmic virial theorem can be corrected to OMEGA-true = b-xi(2)-b-nu(-2)-OMEGA-CVT, where the biases are estimated using a simple galaxy identification algorithm within the context of this particular OMEGA = 1 CDM model to be b-xi = 1.08 +/- 0.20 and b-nu = 0.6 +/- 0.2. Overall, these models and a variety of other observations suggest that standard luminous galaxies have a modest b-xi congruent-to 1.4, and a velocity bias b-nu congruent-to 0.7, which together imply that apparent OMEGA-CVT should be corrected upward by a factor of congruent-to-4.