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 h^-1Mpc). The main result is the discovery of a polytropic relationship I₁ ∝ ϱ^2-η between the velocity-dispersion kinetic energy density of the coarsening cells, I₁, and their mass density, ϱ. The exponent η, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction η_virial=0. This relationship supports the ``polytropic assumption'' which has been employed in theoretical models for the growth of cosmological structure by gravitational instability.