Stability of Nonrotating Stellar Systems. I. Oblate ShellOrbit Models
Abstract
We investigate the dynamical stability of nonrotating oblate galaxy models constructed from thin shortaxis tube orbits ("shell" orbits). Models as flat or flatter than ~E6 (axis ratio of ~2:5) are axisymmetrically unstable and laminate into thin, curved cylinders on roughly an orbital time scale. All shellorbit models are unstable to a more global, nonaxisymmetric instability with an essentially dipole or "m = 1 " character, i.e., the perturbed density varies roughly as cos φ around the short axis. The strength of the m = 1 instability decreases with the roundness of the model, but models as round as E1 are still clearly unstable; the spherical model appears to be stable, in agreement with previous analytic and numerical work. The instability is apparent in integrations carried out with two very different Nbody codes: a harmonicexpansion code, in which the accuracy of the integration depends strongly on the choice of grid center at each time step, and a (much slower) "tree" code, which has no preferred center. Our results imply that oblate stellar systems require a minimum amount of radial kinetic energy to be dynamically stable, even in the absence of net rotation. In the case of models flatter than ~E5, the radial velocity dispersions required for stability appear to be quite large, of order 1/4 to 1/3 the circular velocity.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1990
 DOI:
 10.1086/168996
 Bibcode:
 1990ApJ...358..399M
 Keywords:

 Dynamic Stability;
 Galactic Rotation;
 Oblate Spheroids;
 Stellar Models;
 Stellar Motions;
 Stellar Systems;
 Galactic Structure;
 Stellar Rotation;
 Stellar Structure;
 Astrophysics;
 GALAXIES: INTERNAL MOTIONS;
 GALAXIES: STRUCTURE;
 INSTABILITIES;
 STARS: STELLAR DYNAMICS