Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's (1993) spherical mass models are presented, which have densities that vary as r −γ near the center and r −4 at large radii. We computed libraries of ∼ 7000 orbits in each of two triaxial models with γ = 1 (" weak cusp ") and γ = 2 (" strong cusp "); these two models have density profiles similar to those of the " core " and " power-law " galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. The major orbit families and their associated periodic orbits were mapped as a function of energy. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong-cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 10 2 − 10 3 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 10 3 dynamical times or longer. Attempts to construct self-consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochas-tic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These " fully mixed " solutions were found to exist only for the weak-cusp potential; as much as ∼ 1/3 of the mass near the center of these models could be placed on stochastic orbits without destroying the self-consistency. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density. Our results suggest that chaos is a generic feature of the motion in realistic triaxial potentials, but that the presence of chaos is not necessarily inconsistent with the existence of stationary triaxial configurations.