Hydrodynamics 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. Modelling this halo as a spherically symmetric and static perfect fluid satisfying the field equations of general relativity, visible baryonic 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 eV < m < 60 eV and to a constraint between the central temperature and the particle mass. The allowed mass range includes popular supersymmetric particle candidates, such as the neutralino, axino and gravitino, as well as lighter particles (m approximate to keV) proposed by numerical n-body simulations associated with self-interactive CDM and WDM structure formation theories.