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 ~ 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 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
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 Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter
than M_V ~ -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} per year 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.Comment: Accepted for publication in The Astrophysical Journa