Is a Bose-Einstein condensate a good candidate for dark matter? A test with galaxy rotation curves

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. Using galaxy data from a subsample of SPARC data base, we find the best fits of the BEC model by using the Thomas{Fermi approximation and perform a Bayesian statistics analysis to compare the obtained BEC's scenarios with the Navarro-Frenk-White (NFW) model as pivot model. 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-circle dot = 11.08 +/- 0.43 which condensate a boson cloud with average particle mass M-Phi = (3.47 +/- 1.43) x 10 (23) eV and a self-interaction coupling constant log(10) (lambda vertical bar pc(-1)vertical bar) = -91.09 +/- 0.74, i.e. the system behaves as a weakly interacting BEC. We compare the BEC model with NFW 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.