EDP Sciences
Free access
Volume 378, Number 2, November I 2001
Page(s) 679 - 699
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20011077

A&A 378, 679-699 (2001)
DOI: 10.1051/0004-6361:20011077

A "spherical shell number density" model for violently relaxed $\vec{N}$-body systems

C. Efthymiopoulos and N. Voglis

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

(Received 18 April 2001 / Accepted 24 July 2001 )

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 $\nu({\cal E},L^2,r)$ 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.

Key words: galaxies: formation -- galaxies: kinematics and dynamics -- stellar dynamics

Offprint request: C. Efthymiopoulos, cefthim@cc.uoa.gr

© ESO 2001