Dwarf spheroidal galaxies and Bose-Einstein condensate dark matter

Abstract: We constrain the parameters of a self-interacting massive dark matter scalar particle in a condensate using the kinematics of the eight brightest dwarf spheroidal satellites of the Milky Way. For the case of a repulsive self-interaction the condensate develops a mass density profile with a characteristic scale radius that is closely related to the fundamental parameters of the theory. We find that the velocity dispersion of dwarf spheroidal galaxies suggests a scale radius of the order of 1 kpc, in tension with previous results found using the rotational curve of low-surface-brightness and dwarf galaxies. The new value is however favored marginally by the constraints coming from the number of relativistic species at Big-Bang nucleosynthesis. We discuss the implications of our findings for the particle dark matter model and argue that while a single classical coherent state can correctly describe the dark matter in dwarf spheroidal galaxies, it cannot play, in general, a relevant role for the description of dark matter in bigger objects.