Phase transitions in gravitating systems and the formation of condensed objects

The thermal equilibrium of a self-gravitating classical fluid with local equation of state corresponding to a system of hard spheres is studied numerically. When the volume effectively occupied by the particles is much smaller than the accessible volume, a phase transition occurs at which the system can shuttle between a quasi-uniform state and one in which a highly condensed nucleus is immersed in a dilute atmosphere. Under isothermal contact conditions, the two states have different energies; under isoenergetic conditions, they have different temperatures. The isothermal transition bridges a region of negative specific heat in the family of isoenergetic systems. The phase transitions mark nonlinear fluid stability thresholds. These can differ by orders of magnitude from the traditional linear ones, i.e. the gravothermal catastrophe and Jeans instability, which only mark the stability limits of thermally metastable regions. It is discussed how phase transitions may give the proper onset criteria for the formation of condensed objects from the size of planetoids up to stars.