  It is known that two supermassive black holes (SMBHs) cannot merge in a
spherical galaxy within a Hubble time; an emerging picture is that galaxy
geometry, rotation, and large potential perturbations may usher the SMBH binary
through the critical three-body scattering phase and ultimately drive the SMBH
to coalesce. We explore the orbital content within an N-body model of a mildly-
flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the
foundation for a study on the SMBH binary coalescence, the black holes bypassed
the binary stalling often seen within spherical galaxies and merged on Gyr
timescales (Khan et al. 2013). Using both frequency-mapping and angular
momentum criteria, we identify a wealth of resonant orbits in the axisymmetric
model, including saucers, that are absent from an otherwise identical spherical
system and that can potentially interact with the binary. We quantified the set
of orbits that could be scattered by the SMBH binary, and found that the
axisymmetric model contained nearly seven times the number of these potential
loss cone orbits compared to our equivalent spherical model. In this flattened
model, the mass of these orbits is roughly 3 times of that of the SMBH, which
is consistent with what the SMBH binary needs to scatter to transition into the
gravitational wave regime.
