Regular and Chaotic Dynamics of Triaxial Stellar Systems
Abstract
We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of ~10^{4} orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of greatest importance in structuring phase space are found to be the threedimensional resonant tori, regions where the fundamental frequencies satisfy a relation of the form 0 = lω_{1} + mω_{2} + nω_{3} with integer (l, m, n). When stable, resonant tori generate phasespace regions in which the motion is regular; these regions are not necessarily associated with a stable periodic orbit as in systems with only 2 degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stochastic as well. The spectrum of diffusion rates for boxlike orbits at a given energy is well approximated as a power law over at least 6 decades. Models with high central concentrationssteep central cusps or massive black holesexhibit the most stochasticity. Even a modest black hole, with a mass of ~0.5% the mass of the galaxy, is as effective as the steepest central density cusp at inducing stochastic diffusion. There is a transition to global stochasticity in boxlike phase space when the mass of the central black hole exceeds ~2% of the galaxy mass. We estimate the dependence of orbital evolution rates on galaxy structural parameters. We predict a greater average degree of dynamical evolution in faint elliptical galaxies because of their high central densities and short crossing times. The evolution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about 19 or 20, consistent with the observed change in many elliptical galaxy properties at this luminosity.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1998
 DOI:
 10.1086/306269
 arXiv:
 arXiv:astroph/9801041
 Bibcode:
 1998ApJ...506..686V
 Keywords:

 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 GALAXIES: KINEMATICS AND DYNAMICS;
 GALAXIES: STRUCTURE;
 Celestial Mechanics;
 Stellar Dynamics;
 Galaxies: Kinematics and Dynamics;
 Galaxies: Structure;
 Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 Revised version to appear in the Astrophysical Journal, vol 498, Oct 20 1998. Minor changes to text. References and 1 new figure added. 28 Latex pages, 22 Postscript figures, style file included