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⁻¹ Mpc). 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. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)