ar X iv : a st ro - p h / 03 02 29 6 v 2 1 3 A ug 2 00 3 Chaotic Loss Cones , Black Hole Fueling and the M • − σ Relation

In classical loss cone theory, stars are supplied to a central black hole via gravitational scattering onto low angular momentum orbits. Higher feeding rates are possible if the gravitational potential near the black hole is non-axisymmetric and the orbits are chaotic. Motivated by recently published, self-consistent models, we evaluate rates of stellar capture and disruption in triaxial nuclei. Rates are found to substantially exceed those in collisionally-resupplied loss cones, as long as an appreciable fraction of the orbits are centrophilic. The mass captured by a black hole after a given time in a steep (ρ ∼ r) nucleus scales as σ with σ the stellar velocity dispersion, and the accumulated mass in 10 yr is of the correct order to reproduce the M• − σ relation. Triaxiality can solve the “final parsec problem” of decaying black hole binaries by increasing the flux of stars into the binary’s loss cone.