Gravitational phase transition of heavy neutrino matter

In the framework of the Thomas-Fermi model at finite temperature, we show that a cooling nondegenerate gas of massive neutrinos will undergo a phase transition in which quasi-degenerate supermassive neutrino stars are formed through gravitational collapse. For neutrinos in the mass range of 10 to 25 keV these compact dark objects could mimic the role of supermassive black holes that are usually assumed to exist at the centres galaxies. Astrophysical implications and constraints on the neutrino mass are discussed for this scenario.