Section: New Results

Models of dark matter halos based on statistical mechanics: I. The classical King model

In [48] we consider the possibility that dark matter halos are described by the Fermi-Dirac distribution at finite temperature. This is the case if dark matter is a self-gravitating quantum gas made of massive neutrinos at statistical equilibrium. This is also the case if dark matter can be treated as a self-gravitating collisionless gas experiencing Lynden-Bell?s type of violent relaxation. In order to avoid the infinite mass problem and carry out a rigorous stability analysis, we consider the fermionic King model. In this paper, we study the non-degenerate limit leading to the classical King model. This model was initially introduced to describe globular clusters and we propose to apply it also to large dark matter halos where quantum effects are negligible. We study the thermodynamical stability of the different configurations and compare the prediction of the classical King model to the observations of large dark matter halos. Because of collisions and evaporation, the central density increases while the slope of the halo density profile decreases until an instability takes place. We show that large dark matter halos are relatively well-described by the King model at, or close to, the point of marginal microcanonical stability. At that point, the King model generates a density profile that can be approximated by the modified Hubble profile. This profile has a flat core and decreases as r?3 at large distances, like the observational Burkert profile. For large halos, the flat core is due to finite temperature effects, not to quantum mechanics. We argue that statistical mechanics may provide a good description of dark matter halos and interpret the discrepancies as a result of incomplete relaxation like in the case of stellar systems.