A Semianalytic Model of the Pairwise Velocity Distribution between Dark Matter Halos

Abstract

Abstract We study the probability distribution function (PDF) of relative velocity between two different dark matter halos (i.e., pairwise velocity) with high-resolution cosmological N-body simulations. We revisit a non-Gaussian framework to predict pairwise velocity statistics developed in Tinker. We investigate the pairwise velocity PDFs over a wide range of halo masses of 1012.5 ≲ M [h −1 M ⊙] ≲ 1015 and redshifts of 0 < z < 1. At a given set of masses, redshift, and separation length between two halos, our model requires three parameters to set the pairwise velocity PDF, whereas previous non-Gaussian models in the literature assumed four or more free parameters. At length scales of 5 < r [h −1 Mpc] < 40, our model predicts the mean and dispersion of the pairwise velocity for dark matter halos with masses of 1012.5 ≲ M [h −1 M ⊙] ≲ 1013.5 at 0.3 < z < 1 with a 5%-level precision. We demonstrate that our model of the pairwise velocity PDF provides an accurate mapping of the two-point clustering of massive-galaxy-sized halos at scales of O(10)h −1 Mpc between redshift and real space for a given real-space correlation function. For a mass-limited halo sample with masses greater than 1013.5 h −1 M ⊙ at z = 0.55, our model can explain the monopole and quadrupole moments of the redshift-space two-point correlations with a precision better than 5% at the scales of 5−40 and 10–30 h −1 Mpc, respectively. Our model of the pairwise velocity PDF will give a detailed explanation of the statistics of massive galaxies at intermediate scales in redshift surveys.