Stellar orbits in triaxial clusters around black holes in galactic nuclei

We investigate the orbital structure of a model triaxial star cluster, centered around a supermassive black hole (BH), appropriate to galactic nuclei. Sridhar & Touma proved in 1999 that the presence of the BH enforces some regularity in the dynamics within the radius of influence of the BH. We employ their averaging method to reduce the degrees of freedom from 3 to 2. Numerical orbit integrations, together with Poincare surfaces of section, allow us to draw a global portrait of the orbital structure; in our calculations we employ a model cluster potential that is triaxial and harmonic. The averaged dynamics of the axisymmetric case is integrable, and we present a detailed comparison of orbits in oblate and prolate axisymmetric potentials. Both cases support resonant orbits with fixed values of eccentricity, inclination, and periapsis, whose lines of nodes rotate steadily. We then systematically explore significantly triaxial potentials possessing small oblateness or prolateness. Resonant orbits and their families are studied both numerically and through secular perturbation theory. Chaos appears to be suppressed for all the cases we studied, and we obtain effective third integrals. Some of the orbits appear to reinforce the shape of the potential; we provide phase-space as well as real-space portraits of these orbits. A particularly promising resonant orbit exists in highly prolate, triaxial potentials.