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

¹ Max-Planck-Institut für Metallforschung, Heisenbergstr. 3, 70569 Stuttgart, Germany
² Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstr. 37, 80333 München, Germany
³ Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA

Corresponding author: A. Domínguez, alvaro@fluids.mpi-stuttgart.mpg.de

Received: 23 October 2003
Accepted: 5 February 2004

Abstract

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, . The exponent η measures the deviations from the virial prediction,  . For self-similar models, η 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, with a time and coarsening length dependent η. The dependence  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.