The Stellar Orbital Structure in Axisymmetric Galaxy Models with
  Supermassive Black Hole Binaries
  It has been well-established that particular centrophilic orbital families in
non-spherical galaxies can, in principle, drive a black hole binary to shrink
its orbit through three-body scattering until the black holes are close enough
to strongly emit gravitational waves. Most of these studies rely on orbital
analysis of a static SMBH-embedded galaxy potential to support this view; it is
not clear, however, how these orbits transform as the second SMBH enters the
center, so our understanding of which orbits actually interact with a SMBH
binary is not ironclad. Here, we analyze two flattened galaxy models, one with
a single SMBH and one with a binary, to determine which orbits actually do
interact with the SMBH binary and how they compare with the set predicted in
single SMBH-embedded models. We find close correspondence between the
centrophilic orbits predicted to interact with the binary and those that are
actually scattered by the binary, in terms of energy and Lz distribution, where
Lz is the z component of a stellar particle's angular momentum. Of minor note:
because of the larger mass, the binary SMBH has a radius of influence about 4
times larger than in the single SMBH model, which allows the binary to draw
from a larger reservoir of orbits to scatter. Of the prediction particles and
scattered particles, nearly half have chaotic orbits, 40% have fx:fy=1:1
orbits, 10% have other resonant orbits.
