  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.
