Self-interacting superfluid dark matter droplets

We assume dark matter to be a cosmological self-gravitating Bose-Einstein condensate of non-relativistic ultralight scalar particles with competing gravitational and repulsive contact interactions and investigate the observational implications of such model. The system is unstable to the formation of stationary self-bound structures that minimize the energy functional. These cosmological superfluid droplets, which are the smallest possible gravitationally bound dark matter structures, exhibit a universal mass profile and a corresponding universal rotation curve. Assuming a hierarchical structure formation scenario where granular dark matter haloes grow around these primordial stationary droplets, the model predicts cored haloes with rotation curves that obey a single universal equation in the inner region (r less than or similar to 1 kpc). A simultaneous fit to a selection of galaxies from the SPARC data base chosen with the sole criterion of being strongly dark matter dominated even within the innermost region, indicates that the observational data are consistent with the presence of a Bose-Einstein condensate of ultralight scalar particles of mass m similar or equal to 2.2 x 10(-22)eVc(-2) and repulsive self-interactions characterized by a scattering length a(s) similar or equal to 7.8 x 10(-77)m. Such small self-interactions have profound consequences on cosmological scales. They induce a natural minimum scale length for the size of dark matter structures that makes all cores similar in length (similar to 1kpc) and contributes to lower their central densities.