On Secular Stability, Secular Instability, and Points of Bifurcation of Rotating Gaseous Masses
Abstract
The definitions of secular stability and secular instability of rotating gaseous masses are examined. They depend on the specification of some weak dissipative mechanism, and a mass may be secularly stable to one dissipative mechanism but secularly unstable to another. The effects of viscosity on uniformly rotating masses, and of gravitational radiation on generally rotating masses, are considered in detail. In both cases, secular instability sets in along a sequence of figures at a point of bifurcation when some appropriate operator ceases to be positive definite. This operator has been related to the total energy only for the viscous instability of uniformly rotating figures. Although both dissipative mechanisms cause secular instability to set in at the same stage of the sequence of Maclaurin spheroids, there is no reason for such a coincidence with other figures. Previous calculations by virial methods of the two points of bifurcation for other sequences of figures normally yield approximate, rather than exact, results, and overestimate the range of secular stability. An upper limit for the onset of both secular instabilities can be established rigorously, and is t (kinetic energy of mean motions/negative gravitational potential energy) = 0.170. Subject headings: hydrodynamics  instabilities  rotation
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1977
 DOI:
 10.1086/155181
 Bibcode:
 1977ApJ...213..497H