If dark matter is composed of massive bosons , a Bose-Einstein Condensation process must have occurred during the cosmological evolution .
Therefore galactic dark matter may be in a form of a condensate , characterized by a strong self-interaction .
We consider the effects of rotation on the Bose-Einstein Condensate dark matter halos , and we investigate how rotation might influence their astrophysical properties .
In order to describe the condensate we use the Gross-Pitaevskii equation , and the Thomas-Fermi approximation , which predicts a polytropic equation of state with polytropic index n = 1 .
By assuming a rigid body rotation for the halo , with the use of the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the basic equation describing the density distribution of the rotating condensate .
We obtain the general solutions for the condensed dark matter density , and we derive the general representations for the mass distribution , boundary ( radius ) , potential energy , velocity dispersion , tangential velocity and for the logarithmic density and velocity slopes , respectively .
Explicit expressions for the radius , mass , and tangential velocity are obtained in the first order of approximation , under the assumption of slow rotation .
In order to compare our results with the observations we fit the theoretical expressions of the tangential velocity of massive test particles moving in rotating Bose-Einstein Condensate dark halos with the data of 12 dwarf galaxies , and the Milky Way , respectively .