Modeling a Pairwise Peculiar Velocity Distribution Function of Dark Matter from Halo Density Profiles

We derive the pairwise peculiar velocity distribution function of dark matterparticles applying the dark matter halo approach. Unlike the previous work, wedo not assume a Gaussian velocity distribution function of dark matter in asingle halo, but compute it self-consistently with the assumed density profilefor dark matter halo. The resulting distribution function is well approximatedby an exponential distribution which is consistent with the previousobservational, numerical and theoretical results. We also compute the pairwisepeculiar velocity dispersion for different density profiles, and provide apractical fitting formula. We apply an empirical biasing scheme into our modeland present prediction for pairwise peculiar velocity dispersion of {\itgalaxies}, and reproduce the previous results of simulations using oursemi-analytical method.Comment: 16 pages, 9 figures, accepted for publication in PASJ (2002