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Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain : II. Inertial models
Pierre-Henri Chavanis and Clément Sire
par - 11 avril 2006
We propose a general kinetic and hydrodynamic description of
self-gravitating Brownian particles in 
dimensions. We go beyond
usual approximations by considering inertial effects and finite 
effects while previous works use a mean-field approximation valid in a
proper thermodynamic limit (
) and consider an
overdamped regime (
). We recover known models
in some particular cases of our general description. We derive the
expression of the Virial theorem for self-gravitating Brownian
particles and study the linear dynamical stability of isolated
clusters of particles and uniform systems by using technics introduced
in astrophysics. We investigate the influence of the equation of
state, of the dimension of space and of the friction coefficient on
the dynamical stability of the system. We obtain the exact expression
of the critical temperature 
for a multi-components
self-gravitating Brownian gas in 
. We also consider the limit of
weak frictions 
and derive the
orbit-averaged-Kramers equation.