  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.
