Supermassive black hole binary coalescence and orbital structure of the host galaxy
When two galaxies coalesce, the supermassive black holes (SMBHs) at each galaxy center will also coalesce. In spherical galaxies, there are not enough stars with centrophilic orbits to interact with the black hole binary (BHB) to shrink the orbit enough to merge, and the binary stalls at roughly 1 parsec. This is called the final parsec problem". Previous investigations show that there is no final parsec problem in triaxial galaxies, since there are many centrophilic orbits in triaxial galaxies that can easily interact with the BHB. However the question of whether black holes can merge in an axisymmetric galaxy is still a matter of debate. Using N-body simulations, we classify stellar orbits in an SMBH-embedded axisymmetric galaxy to probe the orbital types that could interact with a BHB. We find a rich variety of resonant orbits in the axisymmetric galaxy, which do not exist in the spherical galaxy. The stellar mass in the loss cone is roughly 3 times of that of the SMBH, which is sufficient to make the SMBH binary merge. We also find saucer and pyramid orbits in our axisymmetric model, which are previously predicted in analytical potentials. Finally, we find that the shape of the nucleus is slightly triaxial.