Other
Scientific paper
May 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...245..829d&link_type=abstract
Astrophysical Journal, Part 1, vol. 245, May 1, 1981, p. 829-839.
Other
4
Astronomical Models, Dynamic Stability, Ellipsoids, Halos, Harmonic Oscillation, Incompressible Fluids, Angular Momentum, Disk Galaxies, Gravitational Waves, Hydrodynamics, Internal Energy, Protoplanets, Secular Variations, Stellar Mass Accretion, Virial Theorem
Scientific paper
The stability of the third-harmonic modes for Maclaurin spheroids embedded in gravitating halos is determined by the tensor virial equation method. These spheroid-halo systems can be considered crude analogs of disk galaxies, accretion disks around stars, and proto-planetary nebulae. By combining results with earlier work on the second harmonics and with results from the thin-disk approximation valid for higher-order axisymmetric and nonaxisymmetric modes, a complete characterization of self-gravitating instabilities, both secular and dynamic, is obtained. This characterization spans the range from global to local analyses.
We find that halos always have a stabilizing effect. For dynamic instabilities, successively higher order modes become the most unstable as halo mass increases, while low-order modes become completely stabilized. This agrees with expectations from local analyses. An analog of the Toomre Q-parameter proves a useful stability discriminant even for low-order global modes. Secular instabilities of the low-order modes, as evidenced by neutral points, occur for all halo masses. For fixed halo mass and geometry, the secular instabilities always set in for substantially lower values of the spheroid angular momentum (i.e., for "hotter" spheroids) than the dynamic instabilities. The secular instability of the second harmonic bar modes sets in first.
We estimate the time scales for growth of the secular instabilities due to dissipative mechanisms like viscosity and gravitational radiation. Results indicate that secular instabilities are likely to be important only for systems with a halo-to-disk mass ratio less than about 10, as in disk galaxies and some solar nebula models. For systems with very much larger halo-to-disk mass ratios, such as accretion disks and Saturn's rings, the growth times are so long that other global changes are likely to occur long before the nonaxisymmetric modes can grow by secular instability.
Bacon B. A.
Durisen Richard H.
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