  We consider the steady-state regime describing the density profile of a dark
matter halo, if dark matter is treated as a Bose-Einstein condensate. We first
solve the fluid equation for "canonical" cold dark matter, obtaining a class of
density profiles which includes the Navarro-Frenk-White profile, and which
diverge at the halo core. We then solve numerically the equation obtained when
an additional "quantum pressure" term is included in the computation of the
density profile. The solution to this latter case is finite at the halo core,
possibly avoiding the "cuspy halo problem" present in some cold dark matter
theories. Within the model proposed, we predict the mass of the cold dark
matter particle to be of the order of M_chi c2 = 10^-24 eV, which is of the
same order of magnitude as that predicted in ultra-light scalar cold dark
matter models. Finally, we derive the differential equation describing
perturbations in the density and the pressure of the dark matter fluid.
