During a galaxy merger, the supermassive black hole (SMBH) in each galaxy is thought to sink to the center of the potential and form a supermassive black hole binary; this binary can eject stars via 3-body scattering, bringing the SMBHs ever closer. In a static spherical galaxy model, the binary stalls at a separation of about a parsec after ejecting all the stars in its loss cone -- this is the well-known final parsec problem. Earlier work has shown that the centrophilic orbits in triaxial galaxy models are key in refilling the loss cone at a high enough rate to prevent the black holes from stalling. However, the evolution of binary SMBHs has never been explored in axisymmetric galaxies, so it is not clear if the final parsec problem persists in these systems. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in galaxy models with a range of ellipticity. For the first time, we show that mere axisymmetry can solve the final parsec problem; we find the the SMBH evolution is independent of N for an axis ratio of c/a=0.8, and that the SMBH binary separation reaches the gravitational radiation regime for c/a=0.75.
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