M = 1 instabilities in counter-rotating stellar systems

Details M = 1 instabilities in counter-rotating stellar systems M = 1 instabilities in counter-rotating stellar systems

Mar 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.243..263p&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 243, March 15, 1990, p. 263-266.

Astronomy and Astrophysics

Astronomy

19

Counter Rotation, Stellar Orbits, Stellar Systems, Wentzel-Kramer-Brillouin Method, Circular Orbits, Orbital Mechanics, Poisson Equation, Stellar Motions

Scientific paper

It is shown that in disks with equal numbers of stars in direct and retrograde near-circular 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.

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