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Stothers, R.B., 1974: Violation of the Vogt-Russell theorem for homogeneous nondegenerate stars. Astrophys. J., 194, 699-708.
A systematic study is made of the number and types of solutions of the equilibrium equations of stellar structure, in the case of homogeneous stars of Population I over the mass range 2-1000 M☉, with four different opacity representations. A variant of the usual "fitting" method permits the simultaneous investigation of convergence and tendency toward multiplicity of the solutions. Quadratic interpolation and extrapolation of Carson's new opacity tables produces a very large opacity at low temperatures that greatly affects the loose outer layers of massive stars, while leaving the cores practically unaffected. As a result, over a small mass range, well above 100 M☉, triple solutions exist, always near an effective temperature of log Te ≈ 4.73. In such a situation, a "cool" sequence of low masses overlaps a "hot" sequence of high masses, with a short "middle" sequence of intermediate masses connecting them. Multiplicity is found to be favored by a high helium abundance, a high metals abundance, and fast uniform rotation. Secular stability of the models is discussed. The close resemblance between the kinds of multiplicity found in homogeneous stars and in composite stars is pointed out. A simple classification of the known exceptions to the Vogt-Russell theorem on the uniqueness of stellar structure is given.
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