Collisionless loss-cone refilling: there is no final parsec problem

Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low-frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with N ∼ 10⁶ stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N, a signature of spurious two-body relaxation. We present a novel approach for studying loss-cone repopulation in galactic nuclei. Since loss-cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1:0.9:0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no `final parsec problem'.