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.

19 pages, 4 figures, Version accepted for publication on JCAP