A "spherical shell number density" model for violently relaxed N-body systems

We present the results of a series of numerical simulations of gravitationa l collisionless N-body systems in equilibrium after a violent relaxation fr om cosmological initial conditions. The distribution function f of such sys tems has a complicated form due to the complex structure of the phase space of stellar orbits. This complexity makes hardly tractable the old problem of writing a simple model for f. However, we show that it is possible to be nefit from various statistical regularities of the phase space in order to compose a heuristic approximation for f. Such regularities are revealed if we decompose a system in a number of spherical shells. For each shell we de fine thermodynamical quantities (e.g., temperatures) which, as we find, var y smoothly with the radius r of the shell. Using these quantities, we find a model that fits the number density function nu(epsilon, L-2, r) in each s hell. For the greatest range of energies, this function tends to the form o f the Stiavelli-Bertin (1987) model. By adding the contributions of all the spherical shells, we then find a global model for f. While our method is b ased on a spherical approximation, we show that it reproduces very accurate ly the global profiles of our triaxial N-body systems.