Gravitational, lensing, and stability properties of Bose-Einstein
  condensate dark matter halos
  The possibility that dark matter, whose existence is inferred from the study
of the galactic rotation curves, and from the mass deficit in galaxy clusters,
can be in a form of a Bose-Einstein Condensate, has been extensively
investigated lately. In the present work, we consider a detailed analysis of
the astrophysical properties of the Bose-Einstein Condensate dark matter halos
that could provide clear observational signatures that help discriminate
between different dark matter models. In the Bose-Einstein condensation model
dark matter can be described as a non-relativistic, gravitationally confined
Newtonian gas, whose density and pressure are related by a polytropic equation
of state with index $n=1$. The mass and gravitational properties of the
condensate halos are obtained in a systematic form, including the mean
logarithmic slopes of the density and of the tangential velocity. The lensing
properties of the condensate dark matter are investigated in detail. In
particular, a general analytical formula for the surface density, an important
quantity that defines the lensing properties of a dark matter halos, is
obtained in the form of series expansions. This enables arbitrary-precision
calculations of the surface mass density, deflection angle, deflection
potential, and of the magnification factor, thus giving the possibility of the
comparison of the predicted lensing properties of the condensate dark matter
halos with observations. The stability properties of the condensate halos are
also investigated by using the scalar and the tensor virial theorems,
respectively, and the virial perturbation equation for condensate dark matter
halos is derived.
