Velocity dispersion in N-body simulations of CDM models

This work reports on a study of the spatially coarse-grained velocity dispersion in cosmological N-body simulations (OCDM and ΛCDM models) as a function of time (redshifts z = 0–4) and of the coarsening length (0.6–20 hMpc). The main result is the discovery of a polytropic relationship I1 ∝ ̺ between the velocity-dispersion kinetic energy density of the coarsening cells, I1, and their mass density, ̺. The exponent η, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction ηvirial = 0. This relationship supports the “polytropic assumption” which has been employed in theoretical models for the growth of cosmological structure by gravitational instability.