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Description
We analyze the rotation curves that correspond to a Bose--Einstein Condensate (BEC) type halo surrounding a Schwarzschild--type black hole to confront predictions of the model upon observations of galaxy rotation curves. We model the halo as a BEC in terms of a massive scalar field that satisfies a Klein--Gordon equation with a self--interaction term. We also assume that the bosonic cloud is not self--gravitating. To model the halo, we apply a simple form of the Thomas--Fermi approximation that allows us to extract relevant results with a simple and concise procedure. We find that in the centre of galaxies we must have a supermassive compact central object, i.e., supermassive black hole, in the range of $\log_{10} M/M_\odot = 11.08 \pm 0.43$ which condensate a boson cloud with average particle mass $M_\Phi = (3.47 \pm 1.43 )\times10^{-23}$ eV and a self--interaction coupling constant $\log_{10} (\lambda \; [{\rm pc}^{-1}]) = -91.09 \pm 0.74 $, i.e., the system behaves as a weakly interacting Bose--Einstein Condensate. We compare the Bose--Einstein Condensate model within the Thomas--Fermi approximation, with the Navarro--Frenk--White (NFW) model, concluding that in general the BEC model using the Thomas--Fermi approximation is strong enough compared with the NFW fittings. Moreover, we show that BECs still well--fit the galaxy rotation curves and, more importantly, could lead to an understanding of the dark matter nature from first principles.
