Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998mnras.300..981c&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Volume 300, Issue 4, pp. 981-991.
Astronomy and Astrophysics
Astronomy
31
Diffusion, Methods: Analytical, Methods: Miscellaneous, Stars: Evolution, Stars: Kinematics
Scientific paper
We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f, the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker-Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of `violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie-King model to the case of (possibly degenerate) collisionless stellar systems.
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