Toward a realistic description of dark matter overdensities around black holes

Dark matter overdensities around black holes can be searched for by looking at the characteristic imprint they leave on the gravitational waveform of binary black hole mergers. Current theoretical predictions of the density profile of dark matter overdensities are based on highly idealized formation scenarios, in which black holes are assumed to grow adiabatically from an infinitesimal seed to their final mass, compressing dark matter cusps at the center of galactic halos into very dense spikes. These scenarios were suitable for dark matter indirect detection studies, since annihilating dark matter cannot reach very high densities, but they fail to capture the dark matter distribution in the innermost regions where the gravitational wave signal is produced. We present here a more realistic formation scenario where black holes form from the collapse of supermassive stars, and follow the evolution of the dark matter density as the supermassive star grows and collapses to a black hole. We show that in this case dark matter forms shallower mounds, instead of spikes, on scales comparable with the size of the supermassive stars originating them. We discuss the implications for the detectability of these systems.