Violation of the Vogt-Russell theorem for homogeneous nondegenerate stars

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 solar masses, 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 solar masses, triple solutions exist, always near an effective temperature of log Te = 4.73. A simple classification of the known exceptions to the Vogt-Russell theorem on the uniqueness of stellar structure is given.