Models of dark matter halos based on statistical mechanics: The fermionic King model

We discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into account the escape of high-energy particles and has a finite mass. On the other hand, the Pauli exclusion principle puts an upper bound on the phase-space density of the system and stabilizes it against gravitational collapse. We consider stable and metastable states and emphasize the importance of the latter for systems with long-range interactions. Phase transitions can take place between a "gaseous" phase unaffected by quantum mechanics and a "condensed" phase dominated by quantum mechanics. The phase diagram exhibits two critical points, one in each ensemble, beyond which the phase transitions disappear. We relate the existence of black holes to the microcanonical critical point and determine the minimum halo mass above which black holes can form. We also compare fermionic and bosonic models of dark matter and discuss the value of the mass of the dark matter particle in each case.