The Stability of Perfect Elliptic Disks. I. The Maximum Streaming Case
Abstract
Selfconsistent distribution functions are constructed for two dimensional perfect elliptic disks (for which the potential is exactly integrable) in the limit of maximum streaming; these are tested for stability by Nbody integration. To obtain a discrete representation for each model, simulated annealing is used to choose a set of orbits which sample the distribution function and reproduce the required density profile while carrying the greatest possible amount of angular momentum. A quiet start technique is developed to place particles on these orbits uniformly in actionangle space, making the initial conditions as smooth as possible. The roundest models exhibit spiral instabilities similar to those of cold axisymmetric disks; the most elongated models show bending instabilities like those seen in prolate systems. Between these extremes, there is a range of axial ratios 0.25 <~ b/a <~ 0.6 within which these models appear to be stable. All the methods developed in this investigation can easily be extended to integrable potentials in three dimensions.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1994
 DOI:
 10.1086/174262
 Bibcode:
 1994ApJ...428..493L
 Keywords:

 Distribution Functions;
 Elliptic Functions;
 Elliptical Orbits;
 Galactic Structure;
 Lenticular Bodies;
 Many Body Problem;
 Stability;
 Two Dimensional Bodies;
 Annealing;
 Computerized Simulation;
 Elongation;
 Numerical Analysis;
 Prolateness;
 Astronomy;
 GALAXIES: ELLIPTICAL AND LENTICULAR;
 CD;
 GALAXIES: KINEMATICS AND DYNAMICS;
 GALAXIES: STRUCTURE;
 METHODS: ANALYTICAL;
 METHODS: NUMERICAL