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 [Formula: see text] which condensate a boson cloud with average particle mass [Formula: see text] eV and a self-interaction coupling constant [Formula: see text], 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.