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Issue A&A
Volume 430, Number 3, February II 2005
Page(s) 771 - 778
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20041462



A&A 430, 771-778 (2005)
DOI: 10.1051/0004-6361:20041462

On the coarse-grained evolution of collisionless stellar systems

P. H. Chavanis1 and F. Bouchet2

1  Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
    e-mail: chavanis@irsamc.ups-tlse.fr
2  École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon, France
    e-mail: Freddy.Bouchet@ens-lyon.fr

(Received 14 June 2004 / Accepted 8 September 2004 )

Abstract
We describe the dynamical evolution of collisionless stellar systems on a coarse-grained scale. We first discuss the statistical theory of violent relaxation, following the seminal paper of Lynden-Bell (1967). Consistently with this statistical approach, we present kinetic equations for the coarse-grained distribution function $\overline{f}({\vec r},{\vec v},t)$ based on a Maximum Entropy Production Principle or on a quasi-linear theory of the Vlasov-Poisson system. Then, we develop a deterministic approach where the coarse-grained distribution function is defined as a convolution of the fine-grained distribution function $f({\vec r},{\vec v},t)$ by a Gaussian window. We derive the dynamical equation satisfied by $\overline{f}({\vec r},{\vec v},t)$ and show that its stationary states are different from those predicted by the statistical theory of violent relaxation. This implies that the notion of coarse-graining must be defined with care. We apply these results to the HMF (Hamiltonian Mean Field) model and find that the spatial density is similar to a Tsallis q-distribution where the q parameter is related to the resolution length.


Key words: Galaxy: kinematics and dynamics -- gravitation -- stellar dynamics




© ESO 2005


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