Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar densitycusp can regrow at the center of a galaxy via energy exchange between starsmoving in the gravitational field of the single, coalesced hole. We illustratethis process via high-accuracy N-body simulations. Regeneration requiresroughly one relaxation time and the new cusp extends to a distance of roughlyone-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; themass in the cusp is of order 10% the mass of the black hole. Growth of the cuspis preceded by a stage in which the stellar velocity dispersion evolves towardisotropy and away from the tangentially-anisotropic state induced by thebinary. We show that density profiles similar to those observed at the centerof the Milky Way and M32 can regenerate themselves in several Gyr followinginfall of a second black hole; the presence of density cusps at the centers ofthese galaxies can therefore not be used to infer that no merger has occurred.We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainterthan M_V ~ -18.5 that contain supermassive black holes, but the cusps have notbeen detected outside of the Local Group since their angular sizes are lessthan 0.1". We show that the presence of a cusp implies a lower limit of\~10^{-4} per year on the rate of stellar tidal disruptions, and discuss theconsequences of the cusps for gravitational lensing and the distribution ofdark matter on sub-parsec scales.Comment: Accepted for publication in The Astrophysical Journa