On the coarse-grained evolution of collisionless stellar systems
Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France e-mail: email@example.com
2 École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon, France e-mail: Freddy.Bouchet@ens-lyon.fr
Accepted: 8 September 2004
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 ([CITE]). Consistently with this statistical approach, we present kinetic equations for the coarse-grained distribution function 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 by a Gaussian window. We derive the dynamical equation satisfied by 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