On the 'coarse-grained' evolution of collisionless stellar systems |
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| Authors: | Pierre-Henri Chavanis |
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| Institution: | Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon, France,;Istituto di Cosmogeofisica, Corso Fiume 4, 10133 Torino, Italy |
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| Abstract: | 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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| Keywords: | diffusion methods: analytical methods: miscellaneous stars: evolution stars: kinematics |
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