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 rho similar to r(-7/4); the mass in the cusp is of the order of 10% of the mass of the black hole. The growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentially anisotropic 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 the infall of a second black hole; the presence of density cusps at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that rho similar to r(-7/4) density cusps are ubiquitous in stellar spheroids fainter than M-V approximate to -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 similar to 0.1. We show that the presence of a cusp implies a lower limit of similar to 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 subparsec scales.