Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of-classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical. entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse "transition" is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters ("double stars"). We analyze the thermodynamics of the system and the stability of the different equilibrium, configurations against rotational symmetry breaking, and provide the global phase diagram.