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| - Numerical study of the cosmological velocity field as a function of density
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| - 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, ${\kappa}_{\rm int}\propto \varrho^{2-eta}$. The exponent η measures the deviations from the virial prediction, $eta_{\rm virial}=0$. 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 ${\kappa}_{\rm int}(\varrho)$ 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.
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