Abstract
Numerical computations on the evolution of realistically stratified, asymmetric, self-gravitating masses reveal the onset of an instability that is suggestive of, but not decisive for, the formation of a binary star. On the other hand, analysis of the evolution and stability of idealized models consisting of uniform-density ellipsoids has been qualitatively accurate in predicting certain features of the behavior of the more realistically stratified figures. This idealized theory is, therefore, reconsidered in an attempt to isolate additional qualitative features that may be common both to the idealized and to realistic figures, and therefore, serve not only as a guide in formulating issues to be addressed in numerical computations but also as a means of interpreting the outcomes of such calculations. Several such features are isolated in this paper, the most striking of which is the existence and importance of resonance bands of instability encountered by the evolutionary trajectories.
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