Modeling peculiar velocities of dark matter halos

We present a simple model that accurately describes various statistical properties of peculiar velocities of dark matter halos. We pay particular attention to the following two effects; first, the evolution of the halo peculiar velocity depends on the local matter density, instead of the global density. Second, dark matter halos are biased tracers of the underlying mass distribution, thus halos tend to be located preferentially at high density regions. For the former, we develop an empirical model calibrated with N-body simulations, while for the latter, we use a conventional halo bias models based on the extended Press-Schechter model combined with an empirical log-normal probability distribution function of the mass density distribution. We find that compared with linear theory, the present model significantly improves the accuracy of predictions of statistical properties of the halo peculiar velocity field including the velocity dispersion, the probability distribution function, and the pairwise velocity dispersion at large separations. Thus our model predictions may be useful in analyzing future observations of the peculiar velocities of galaxy clusters.