An effective Thermodynamic Description of Galactic Haloes

The observation of flat rotation curves in asymptotic region of galaxies implies that the dark matter density profile decreases exponentially with the gravitational potential in this region. It is curious that this behavior is identical to what one would have from a Boltzmann gas in thermal equilibrium. This suggests that an {\it effective} Boltzmann gas description of dark matter is possible for the halo, which follows even though no requirement of thermal equilibrium is assumed for the dark matter particles. We examine some qualitative and quantitative consequences of such an effective description. This is done by studying a simple model that takes into account gravitational self-interactions of dark matter and its gravitational interactions with the baryonic core. Solutions to the dynamics are determined by two parameters, one of which is the ratio of the dark matter mass to the effective temperature of the gas. Crude estimates can be made for these parameters based on observations.