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We present numerical models for triaxial galaxies with central density cusps. The mass-density distribution is $\rho \propto m^{- \gamma}(1+m)^{-(4-\gamma)}$, $ m^{2} =\frac {x^{2}} {a^{2}} + \frac {y^{2}} {b^{2}}+ \frac {z^{2}} {c^{2}} $, which is an ellipsoidal generalization of the $\eta$-models of Tremaine et al. (1993). Such a distribution has the important properties that it resembles the de Vaucouleurs profile at large radii, while providing flexibility of the slope of the central cusp in accordance with recent data from HST.
Here we present results for triaxial models with $\gamma=2$ (``strong cusp''), similar to the observed luminosity density in $M32$, and for $\gamma = 1$ (``weak cusp''), similar to M87. We discuss the structure and stability of orbits in the potentials generated by the two mass-density distributions. A large fraction of the phase-space for both models is occupied by stochastic orbits. Self-consistent models were constructed using quadratic programming.
We constructed models in two ways. 1. Treating the stochastic orbits like regular ones; and 2. Assuming that the model is fully mixed, i.e. calculating the time-independent average density of stochastic orbits as the ensemble average. Quasi-equilibrium solutions, in which the stochastic orbits were treated like the regular orbits, exist for both mass models. However these models would evolve near the center due to the slow diffusion of the stochastic orbits through phase space. Fully mixed models exist for the weak-cusp model but not for the strong-cusp model. This result suggests that galaxies like M32 that have strong cusps must either be axisymmetric, or slowly evolving.
