Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..80..443k&link_type=abstract
Astrophysics and Space Science, Volume 80, Issue 2, pp.443-455
Astronomy and Astrophysics
Astrophysics
Scientific paper
In a simple approximation, the evolution of a stellar system can be described in terms of the solutions to a diffusion equation for motion in a harmonic potential. This paper presents a discussion and characterization of the normal modes for this equation. These solutions are of particular interest in that they provide a simple example of the interplay between dynamical and relaxation phenomena. For the case of a large system, in which the relaxation timet r is much greater than the dynamical timet d,there exists a well-defined sense in which the effects of relaxation may be viewed as a perturbation of motion in the fixed field: the dynamical effects give rise to a purely oscillatory behavior, whereas collisions among stars provide a dissipative mechanism that drives the system towards the unique isothermal equilibrium. Alternatively, the presence of the fixed potential serves to alter the ‘e-folding’ time for the various modes. In the limit thatt r ≫t d , all characteristic relaxation times are essentially doubled. This suggests a danger in the use of ‘velocity space’ equations to model the effects of evaporation.
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