Numerical study of the cosmological velocity field as a function of density

We report on a new study of the velocity distribution in N-body simulations. We investigate the center-of-mass and internal kinetic energies of coarsening cells as a function of time, cell size and cell mass. By using self-similar cosmological models, we are able to derive theoretical predictions for comparison and to assess the influence of finite-size and resolution effects. The most interesting result is the discovery of a polytropic-like relationship between the average velocity dispersion (internal kinetic energy) and the mass density in an intermediate range of densities, K ~ rho^{2-eta}. The exponent eta measures the deviations from the virial prediction, eta_virial=0. For self-similar models, eta depends only on the spectral index of the initial power spectrum. We also study CDM models and confirm a previous result that the same polytropic-like dependence exists (astro-ph/0103313), with a time and coarsening length dependent eta. The dependence K(rho) is an important input for a recently proposed theoretical model of cosmological structure formation which improves over the standard dust model (pressureless fluid) by regularizing the density singularities.