Cosmological Velocity Bias

Velocity bias is a reduction of the velocity dispersion of tracer galaxies in comparison to the velocity dispersion of the underlying mass field. There are two distinct forms of velocity bias. The single particle velocity reduction, $b_v(1)$, is the result of energy loss of a tracer population, and in virialized regions, such as galaxy clusters, is intimately associated with mass segregation which together lead to cluster mass underestimates. The pairwise velocity bias, $b_v(2)$, has an additional statistical reduction if the total mass per galaxy rises with velocity dispersion of the virialized cluster. Values of the velocity bias are estimated from n-body simulations, finding $b_v(1)\simeq 0.85\pm0.1$ and $b_v(2)\simeq 0.6\pm0.2$. The value of $b_v(1)$ is relatively secure and predicts that the virial radius of the cluster light is about 20\% of the cluster mass, which can be tested with observations of cluster mass profiles beyond the apparent virial radius. The value of $b_v(2)$ is sensitive to the formation efficiency of galaxies over environments ranging from voids to rich clusters, the latter of which are not yet well resolved in simulations. An $n=1$, $\Omega=1$, COBE normalized CDM spectrum requires $b_v(2)\simeq0.20(15\mu K/Q)(\sigma_{12}/317 \kms)$ which is well below the measured range of $b_v(2)$. The pairwise velocities at 1 \hmpc\ allow $\Omega=1$ for a galaxy clustering bias near unity if $b_v(2)\simeq0.6$.