A Self-Consistent Study of Triaxial Black-Hole Nuclei

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, rho proportional to r(-gamma), with gamma=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 gamma: 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 gamma, 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.