The final-parsec problem in the collisionless limit

A binary supermassive black hole loses energy via ejection of stars in a galactic nucleus, until emission of gravitational waves becomes strong enough to induce rapid coalescence. Evolution via the gravitational slingshot requires that stars be continuously supplied to the binary, and it is known that in spherical galaxies the reservoir of such stars is quickly depleted, leading to stalling of the binary at parsec-scale separations. Recent N-body simulations of galaxy mergers and isolated nonspherical galaxies suggest that this stalling may not occur in less idealized systems. However, it remains unclear to what degree these conclusions are affected by collisional relaxation, which is much stronger in the numerical simulations than in real galaxies. In this study, we present a novel Monte Carlo method that can efficiently deal with both collisional and collisionless dynamics, and with galaxy models having arbitrary shapes. We show that without relaxation, the final-parsec problem may be overcome only in triaxial galaxies. Axisymmetry is not enough, but even a moderate departure from axisymmetry is sufficient to keep the binary shrinking. We find that the binary hardening rate is always substantially lower than the maximum possible, "full-loss-cone" rate, and that it decreases with time, but that stellar-dynamical interactions are nevertheless able to drive the binary to coalescence on a timescale <=1 Gyr in any triaxial galaxy.