Chaos and chaotic phase mixing in cuspy triaxial potentials

Abstract

This paper investigates chaos and chaotic phase mixing in triaxial Dehnen potentials which have been proposed to describe realistic ellipticals. Earlier work is extended by exploring the effects of (1) variable axis ratios, (2) `graininess' associated with stars and bound substructures, idealised as friction and white noise, and (3) large-scale organised motions presumed to induce near-random forces idealised as coloured noise with finite autocorrelation time. Three important conclusions are: (1) not all the chaos can be attributed to the cusp; (2) significant chaos can persist even for axisymmetric systems; and (3) introducing a supermassive black hole can increase both the relative number of chaotic orbits and the size of the largest Lyapunov exponent. Sans perturbations, distribution functions associated with initially localised chaotic ensembles evolve exponentially towards a nearly time-independent form at a rate L that correlates with the finite time Lyapunov exponents associated with the evolving orbits. Perturbations accelerate phase space transport by increasing the rate of phase mixing in a given phase space region and by facilitating diffusion along the Arnold web that connects different phase space regions, thus facilitating an approach towards a true equilibrium. The details of the perturbation appear unimportant. All that matters are the amplitude and the autocorrelation time, upon which there is a weak logarithmic dependence. Even comparatively weak perturbations can increase L by a factor of three or more, a fact that has potentially significant implications for violent relaxation.