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

We derive the pairwise peculiar velocity distribution function of dark matter particles applying the dark matter halo approach. Unlike the previous work, we do not assume a Gaussian velocity distribution function of dark matter in a single halo, but compute it self-consistently with the assumed density profile for dark matter halo. The resulting distribution function is well approximated by an exponential distribution which is consistent with the previous observational, numerical and theoretical results. We also compute the pairwise peculiar velocity dispersion for different density profiles, and provide a practical fitting formula. We apply an empirical biasing scheme into our model and present prediction for pairwise peculiar velocity dispersion of {\it galaxies}, and reproduce the previous results of simulations using our semi-analytical method.