The Fission Theory of Binary Stars. II. Stability to Third-Harmonics Disturbances
Abstract
The stability of the compressible Riemann ellipsoids to modes of disturbance associated with the third ellipsoidal harmonics is worked out, and the implications of the stability theory for the evolution of a contracting, ellipsoidal mass are discussed. The principal qualitative difference from the classical, incompressible theory is the occurrence of extremely narrow bands of instability in the plane of the parameters. The presence of these bands makes the evolution of an ellipsoidal mass very sensitive to the initial state of the ellipsoid. All contracting, ellipsoidal masses of large enough angular momentum and small enough initial departure from axial symmetry become unstable, at some stage in their evolution, to third-harmonics disturbances. However, a certain fraction of contracting masses, which have initial departures from axial symmetry above a certain critical value, may escape the third-harmonics instability and become unstable first to harmonics of fourth or higher order. Subject headings: binaries - rotation
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 1974
- DOI:
- 10.1086/152855
- Bibcode:
- 1974ApJ...190..121L