Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials

We consider the effects of an uncorrelated random potential on the properties of Bose-Einstein Condensate (BEC) dark matter halos, which acts as a source of disorder, and which is added as a new term in the Gross-Pitaevskii equation, describing the properties of the halo. By using the hydrodynamic representation we derive the basic equation describing the density distribution of the galactic dark matter halo, by also taking into account the effects of the baryonic matter, and of the rotation. The density, mass and tangential velocity profiles are obtained exactly in spherical symmetry by considering a simple exponential density profile for the baryonic matter, and a Gaussian type disorder potential. To test the theoretical model we compare its predictions with a set of 39 galaxies from the Spitzer Photometry \& Accurate Rotation Curves (SPARC) database. We obtain estimates of the relevant astrophysical parameters of the dark matter dominated galaxies, including the baryonic matter properties, and the parameters of the random potential. The BEC model in the presence of baryonic matter and a random confining potential gives a good statistical description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core/cusp problem.