On the distribution of dark matter in galaxies: quantum treatments
  The problem of modeling the distribution of dark matter in galaxies in terms
of equilibrium configurations of collisionless self-gravitating quantum
particles is considered. We first summarize the pioneering model of a Newtonian
self-gravitating Fermi gas in thermodynamic equilibrium developed by Ruffini
and Stella (1983), which is shown to be the generalization of the King model
for fermions. We further review the extension of the former model developed by
Gao, Merafina and Ruffini (1990), done for any degree of fermion degeneracy at
the center ($\theta_0$), within general relativity. Finally, we present here
for the first time the solutions of the density profiles and rotation curves
corresponding to the Gao et. al. model, which have a definite mass $M_h$ and
circular velocity $v_h$, at the halo radius $r_h$ of the configurations,
typical of spiral galaxies. This treatment allow us to determine a novel
core-halo morphology for the dark matter profiles, as well as a novel particle
mass bound associated with them.
