Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the black hole’s influence radius, with density ρ ∼ r−7/4; the mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentiallyanisotropic state induced by the binary. We show that density profiles similar to those observed at the center of the Milky Way and M32 can regenerate themselves in several Gyr following infall of a second black hole; the presence of a density cusp at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that ρ ∼ r−7/4 density cusps are ubiquitous in stellar spheroids fainter than MV ≈ −18.5 that contain supermassive black holes, but the cusps have not been detected outside of the Local Group since their angular sizes are less than ∼ 0.1′′. We show that the presence of a cusp implies a lower limit of ∼ 10−4 yr−1 on the rate of stellar tidal disruptions, and discuss the consequences of the cusps for gravitational lensing and the distribution of dark matter on sub-parsec scales.