Hydrodynamical description of Galactic Dark Matter

We consider simple hydrodynamical models of galactic dark matter in which the galactic halo is a self-gravitating and self-interacting gas that dominates the dynamics of the galaxy. Modeling this halo as a sphericaly symmetric and static perfect fluid satisfying the field equations of General Relativity, visible barionic matter can be treated as ``test particles'' in the geometry of this field. We show that the assumption of an empirical ``universal rotation curve'' that fits a wide variety of galaxies is compatible, under suitable approximations, with state variables characteristic of a non-relativistic Maxwell-Boltzmann gas that becomes an isothermal sphere in the Newtonian limit. Consistency criteria lead to a minimal bound for particle masses in the range $30 \hbox{eV} \alt m \alt 60 \hbox{eV}$ and to a constraint between the central temperature and the particles mass. The allowed mass range includes popular supersymmetric particle candidates, such as the neutralino, axino and gravitino, as well as lighter particles ($m\sim$ keV) proposed by numerical N-body simulations associated with self-interactive ``cold'' and ``warm'' dark matter structure formation theories.