Exact solution for core-collapsed isothermal star clusters

Star clusters in isothermal spheres are studied from a thermodynamic point of view. New density profiles are presented, that describe the collapsed phase at low temperatures. At the transition a set of binaries is formed that carries 13 % of the gravitational energy, while also a huge latent heat is generated. The total energy of the binaries is fixed by thermodynamics. In the canonical ensemble all specific heats are positive, while previously discussed negative specific heat solutions are metastable. In a microcanonical ensemble the latter remain partly dominant.