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

Research Center for Astronomy, Academy of Athens, Anagnostopoulou 10-14, Athens, Greece e-mail: cefthim@cc.uoa.gr; nvogl@cc.uoa.gr

Corresponding author: C. Efthymiopoulos, cefthim@cc.uoa.gr

Received: 18 April 2001
Accepted: 24 July 2001

Abstract

We present the results of a series of numerical simulations of gravitational collisionless N-body systems in equilibrium after a violent relaxation from cosmological initial conditions. The distribution function f of such systems 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 benefit 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 define thermodynamical quantities (e.g., temperatures) which, as we find, vary smoothly with the radius r of the shell. Using these quantities, we find a model that fits the number density function in each shell. For the greatest range of energies, this function tends to the form of 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 based on a spherical approximation, we show that it reproduces very accurately the global profiles of our triaxial N-body systems.