Can dark matter be a Bose–Einstein condensate?

Abstract

We consider the possibility that the dark matter which is required to explain the dynamicsof the neutral hydrogen clouds at large distances from the galactic centre could be in theform of a Bose–Einstein condensate. To study the condensate we use the non-relativisticGross–Pitaevskii equation. By introducing the Madelung representation of thewavefunction, we formulate the dynamics of the system in terms of the continuity equationand of the hydrodynamic Euler equations. Hence dark matter can be described as anon-relativistic, Newtonian Bose–Einstein gravitational condensate gas, whosedensity and pressure are related by a barotropic equation of state. In the case of acondensate with quartic non-linearity, the equation of state is polytropic with indexn = 1. In the framework of the Thomas–Fermi approximation the structure of the Newtoniangravitational condensate is described by the Lane–Emden equation, which can be exactlysolved. General relativistic configurations with quartic non-linearity are studied, bynumerically integrating the structure equations. The basic parameters (mass and radius) ofthe Bose–Einstein condensate dark matter halos sensitively depend on the mass of thecondensed particle and of the scattering length. To test the validity of the model we fit theNewtonian tangential velocity equation of the model with a sample of rotation curves oflow surface brightness and dwarf galaxies, respectively. We find a very good agreementbetween the theoretical rotation curves and the observational data for the low surfacebrightness galaxies. The deflection of photons passing through the dark matter halos isalso analysed, and the bending angle of light is computed. The bending angleobtained for the Bose–Einstein condensate is larger than that predicted by standardgeneral relativistic and dark matter models. The angular radii of the Einstein ringsare obtained in the small angle approximation. Therefore the study of the lightdeflection by galaxies and the gravitational lensing could discriminate between theBose–Einstein condensate dark matter model and other dark matter models.