Is a Bose-Einstein Condensate a good candidate for Dark Matter? A test with Galaxy Rotation Curves

Abstract

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 Bose--Einstein condensate 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 ${\log }_{10}M/M_{\odot }=11.08\pm 0.43$ which condensate a boson cloud with average particle mass $M_{\Phi }=(3.47\pm 1.43)\times 10^{-23}$ eV and a self--interaction coupling constant ${\log }_{10}(\lambda [{\mathrm{pc}}^{-1}])=-91.09\pm 0.74$, 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.

21 pages, 17 figures