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 the orbital analysis of a static supermassive black hole (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 an 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 L-z distribution, where L-z is the z component of a stellar particle's angular momentum. Of minor note: because of the larger mass, the binary SMBH has a larger radius of influence 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 f(x):f(y) = 1:1 orbits and 10% have other resonant orbits.