An equation of state for dark matter

Abstract

Dark matter, believed to be present in many galaxies, is interpreted as a hydrodynamical system in interaction with the gravitational field and nothing else. An equation of state determines the mass distribution and the associated gravitational field. Conversely, the gravitational field can be inferred from observation of orbital velocities of stars in the Milky Way, in a first approximation in which the field is mainly due to the distribution of dark matter. In this approximation, the equation of state is determined by the gravitational field via the equations of motion. The resulting equation of state is a simple expression that accounts for the main features of the galactic rotation curve over 6 orders of magnitude.