Abstract
We use the standard method of Schwarzschild to construct self-consistent solutions for the triaxial de Zeeuw & Carollo (1996) models with central density cusps. ZC96 models are triaxial generalizations of spherical γ-models of Dehnen whose densities vary as r <sup>-γ</sup> near the center and r <sup>-4</sup> at large radii and hence, possess a central density core for γ = 0 and cusps for γ > 0. We consider four triaxial models from ZC96, two prolate triaxials: (p, q) = (0.65,0.60) with γ = 1.0 and 1.5, and two oblate triaxials: (p, q) = (0.95, 0.60) with γ = 1.0 and 1.5. We compute 4500 orbits in each model for time periods of 10 <sup>5</sup> T <sub>D</sub> . We find that a large fraction of the orbits in each model are stochastic by means of their nonzero Liapunov exponents. The stochastic orbits in each model can sustain regular shapes for ∼10 <sup>3</sup> T <sub>D</sub> or longer, which suggests that they diffuse slowly through their allowed phase-space. With the exception of the oblate triaxial models with γ = 1.0, our attempts to construct self-consistent solutions employing only the regular orbits fail for the remaining three models. However, the self-consistent solutions are found to exist for all models when the stochastic and regular orbits are treated in the same way because the mixing-time, ∼10 <sup>4</sup> T <sub>D</sub> , is shorter than the integration time, 10 <sup>5</sup> T <sub>D</sub> . Moreover, the "fully-mixed" solutions can also be constructed for all models when the stochastic orbits are fully mixed at 15 lowest energy shells. Thus, we conclude that the self-consistent solutions exist for our selected prolate and oblate triaxial models with γ = 1.0 and 1.5. © ESO 2007.