M = 1 instabilities in counterrotating stellar systems
Abstract
It is shown that in disks with equal numbers of stars in direct and retrograde nearcircular orbits, there is a purely growing m = 1 instability. This instability exists even when the system is stable to m = 0 axisymmetric modes. This result is first proved using a WKB analysis, and then criteria for the unstable mode to occur are found using a global analysis. It is proved that the instability exists when the Toomre parameter Q is greater than 1, but as Q increases further, the mode is stabilized. This analysis shows that highly flattened axisymmetric systems with little or no net rotation are unstable to these m = 1 modes. If the number of retrograde stars is reduced, the mode becomes overstable, and according to WKB analysis, in the absence of any retrograde stars, the mode ceases to occur for Q greater than 1.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 1990
 Bibcode:
 1990MNRAS.243..263P
 Keywords:

 Counter Rotation;
 Stellar Orbits;
 Stellar Systems;
 WentzelKramerBrillouin Method;
 Circular Orbits;
 Orbital Mechanics;
 Poisson Equation;
 Stellar Motions;
 Astrophysics