We construct models of triaxial galactic nuclei containing central black holes using the method of orbital superposition , 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 \propto r ^ { - \gamma } , with \gamma = 1 and \gamma = 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 .