The Keplerian three-body encounter II. Comparisons with isolated
  encounters and impact on gravitational wave merger timescales
  We investigate the role of the Keplerian tidal field generated by a
supermassive black hole (SMBH) on the three-body dynamics of stellar mass black
holes. We consider two scenarios occurring close to the SMBH: the breakup of
unstable triples and three-body encounters between a binary and a single. These
two cases correspond to the hard and soft binary cases, respectively. The tidal
field affects the breakup of triples by tidally limiting the system, so that
the triples break earlier with lower breakup velocity, leaving behind slightly
larger binaries (relative to the isolated case). The breakup direction becomes
anisotropic and tends to follow the shape of the Hill region of the triple,
favouring breakups in the radial direction. Furthermore, the tidal field can
torque the system, leading to angular momentum exchanges between the triple and
its orbit about the SMBH. This process changes the properties of the final
binary, depending on the initial angular momentum of the triple. Finally, the
tidal field also affects binary-single encounters: binaries tend to become both
harder and more eccentric with respect to encounters that occur in isolation.
Consequently, single-binary scattering in a deep Keplerian potential produces
binaries with shorter gravitational wave merger timescales.
