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If dark matter is composed of massive bosons, a Bose-Einstein Condensationprocess must have occurred during the cosmological evolution. Thereforegalactic dark matter may be in a form of a condensate, characterized by astrong self-interaction. We consider the effects of rotation on theBose-Einstein Condensate dark matter halos, and we investigate how rotationmight influence their astrophysical properties. In order to describe thecondensate we use the Gross-Pitaevskii equation, and the Thomas-Fermiapproximation, which predicts a polytropic equation of state with polytropicindex $n=1$. By assuming a rigid body rotation for the halo, with the use ofthe hydrodynamic representation of the Gross-Pitaevskii equation we obtain thebasic equation describing the density distribution of the rotating condensate.We obtain the general solutions for the condensed dark matter density, and wederive the general representations for the mass distribution, boundary(radius), potential energy, velocity dispersion, tangential velocity and forthe logarithmic density and velocity slopes, respectively. Explicit expressionsfor the radius, mass, and tangential velocity are obtained in the first orderof approximation, under the assumption of slow rotation. In order to compareour results with the observations we fit the theoretical expressions of thetangential velocity of massive test particles moving in rotating Bose-EinsteinCondensate dark halos with the data of 12 dwarf galaxies, and the Milky Way,respectively.

Slowly rotating Bose Einstein Condensate galactic dark matter halos, and their rotation curves