Chaos and Mixing in Triaxial Stellar Systems

We investigate the timescales for stochasticity and chaotic mixing in afamily of triaxial potentials that mimic the distribution of light inelliptical galaxies. Some of the models include central point masses designedto represent nuclear black holes. Most of the boxlike orbits are found to bestochastic, with mean Liapunov times that are 3-6 times the period of thelong-axis orbit. In models with large cores or small black holes, thestochastic orbits mimic regular box orbits for hundreds of oscillations atleast. However a small core radius or significant black hole mass causes mostof the stochastic orbits to diffuse through phase space on the same timescale,visiting a significant fraction of the volume beneath the equipotentialsurface. We estimate timescales for chaotic mixing in the more stronglystochastic models by evolving ensembles of 10^4 points until their distributionreaches a nearly steady state. Mixing initially takes place rapidly, withcharacteristic times of 10-30 dynamical times, as the phase points fill aregion similar in shape to that of a box orbit. Subsequent mixing is slower,with characteristic times of hundreds of orbital times. Mixing rates were foundto be enhanced by the addition of modest force perturbations. The consequencesfor the structure and evolution of elliptical galaxies are discussed.Comment: 42 TEX pages, 12 PostScript figures, uses AASTEX, epsf.sty. To appear in The Astrophysical Journal, November 1996, Volume 47