Orbital Structure of Triaxial Black Hole Nuclei

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 rho proportional to r(-gamma), with gamma = 1 or gamma = 2. At low energies the motion is essentially regular; the major families of orbits are tubes and 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 gamma 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 by both limiting the allowed shapes of regular orbits and inducing chaos.