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

Details A ``spherical shell number density'' model for violently relaxed N-body systems A ``spherical shell number density'' model for violently relaxed N-body systems

Nov 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001a%26a...378..679e&link_type=abstract

Astronomy and Astrophysics, v.378, p.679-699 (2001)

Astronomy and Astrophysics

Astrophysics

4

Galaxies: Formation, Galaxies: Kinematics And Dynamics, Stellar Dynamics

Scientific paper

% 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 (E,L2,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.

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