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 −2 ) nucleus scales as σ 5 with σ the stellar velocity dispersion, and the accumulated mass in 10 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.

Orbital motion in triaxial nuclei with central point masses, representing supermassive black holes, is investigated. The stellar density is assumed to follow a power law, ρ ∝ r −γ , with γ = 1 or γ = 2. At low energies the motion is essentially regular; the major families of orbits are the tubes and the pyramids. Pyramid orbits are similar to box orbits but have their major elongation parallel to the short axis of the figure. A number of regular orbit families associated with resonances also exist, most prominently the banana orbits, which are also elongated parallel to the short axis. At a radius where the enclosed stellar mass is a few times the black hole mass, the pyramid orbits become stochastic. The energy of transition to this "zone of chaos" is computed as a function of γ and of the shape of the stellar figure; it occurs at lower energies in more elongated potentials. Our results suggest that supermassive black holes may place tight constraints on departures from axisymmetry in galactic nuclei, both by limiting the allowed shapes of regular orbits and by inducing chaos.

We demonstrate that the nuclei of galaxies containing supermassive black holes can be triaxial in shape. Schwarzschild's method was first used to construct self-consistent orbital superpositions representing nuclei with axis ratios of 1 : 0.79 : 0.5 and containing a central point mass representing a black hole. Two different density laws were considered, ρ ∝ r −γ , γ = {1, 2}. We constructed two solutions for each γ: one containing only regular orbits and the other containing both regular and chaotic orbits. Monte-Carlo realizations of the models were then advanced in time using an N -body code to verify their stability. All four models were found to retain their triaxial shapes for many crossing times. The possibility that galactic nuclei may be triaxial complicates the interpretation of stellar-kinematical data from the centers of galaxies and may alter the inferred interaction rates between stars and supermassive black holes.

We construct models of triaxial galactic nuclei containing central black holes using the method of orbital superposition and then verify their stability by advancing N-body realizations of the models forward in time. We assume a power-law form for the stellar density, / r À , with ¼ 1 and 2; these values correspond approximately to the nuclear density profiles of bright and faint galaxies, respectively. Equidensity surfaces are ellipsoids with fixed axis ratios. The central black hole is represented by a Newtonian point mass. We consider three triaxial shapes for each value of : almost prolate, almost oblate, and maximally triaxial. Two kinds of orbital solution are attempted for each mass model: the first including only regular orbits, the second including chaotic orbits as well. We find that stable configurations exist, for both values of , in the maximally triaxial and nearly oblate cases; however, steady state solutions in the nearly prolate geometry could not be found. A large fraction of the mass, of order 50% or more, could be assigned to the chaotic orbits without inducing evolution. Our results demonstrate that triaxiality may persist even within the sphere of influence of the central black hole and that chaotic orbits may constitute an important building block of galactic nuclei.