Interaction of Recoiling Supermassive Black Holes with Stars in Galactic
  Nuclei
  Supermassive black hole binaries (SMBHBs) are the products of frequent galaxy
mergers. The coalescence of the SMBHBs is a distinct source of gravitational
wave (GW) radiation. The detections of the strong GW radiation and their
possible electromagnetic counterparts are essential. Numerical relativity
suggests that the post-merger supermassive black hole (SMBH) gets a kick
velocity up to 4000 km/s due to the anisotropic GW radiations. Here we
investigate the dynamical co-evolution and interaction of the recoiling SMBHs
and their galactic stellar environments with one million direct N-body
simulations including the stellar tidal disruption by the recoiling SMBHs. Our
results show that the accretion of disrupted stars does not significantly
affect the SMBH dynamical evolution. We investigate the stellar tidal
disruption rates as a function of the dynamical evolution of oscillating SMBHs
in the galactic nuclei. Our simulations show that most of stellar tidal
disruptions are contributed by the unbound stars and occur when the oscillating
SMBHs pass through the galactic center. The averaged disruption rate is
~10^{-6} M_\odot yr^{-1}, which is about an order of magnitude lower than that
by a stationary SMBH at similar galactic nuclei. Our results also show that a
bound star cluster is around the oscillating SMBH of about ~ 0.7% the black
hole mass. In addition, we discover a massive cloud of unbound stars following
the oscillating SMBH. We also investigate the dependence of the results on the
SMBH masses and density slopes of the galactic nuclei.
