Equilibrium statistical mechanics for self-gravitating systems of two species

Abstract

In this work, we attempt to generalize the statistical mechanics of self-gravitating systems to systems consisting of two species gravitating particles. Under the nondegenerate condition, with the second-order approximation, and with virialization relationships as additional constraints, we obtain the entropy expression for the two species system. Then, by extremizing the constrained entropy with variational calculus, we obtain a series of equations to describe the equilibrium states of the system. Under the assumption that there is no difference of velocity distributions between the two species, from the series of equilibrium-state equations, we obtain the relative ratio of the spatial distributions for the two species. The two species may be mixed homogeneously in space, yet with different choices of the relevant parameters [Formula: see text] and [Formula: see text], two Lagrangian multipliers in the statistical equilibrium equations, their spatial distributions may also differ from each other. The deviation of the spatial distributions between the two species is usually explained as mass segregation, which is confirmed by recent observations in some Galactic stellar clusters. We emphasis, however, that the mass segregation here is not caused by kinetic-energy exchange between the two species, but a new feature of our statistical approach, which is different from Lynden-Bell’s statistics. We believe that these results may have general significance to the statistical mechanics for the general long-range interaction systems.