Abstract
Baker's one-zone model of a radiative stellar envelope is generalized here to include additional forces that can be represented as a function of only the stellar radius. The criteria for dynamical, secular, and pulsational stability against radial perturbations are derived and expressed in simple, general analytic forms. Applications are made to the outer envelopes of luminous blue variables (LBVs). The acceleration of stellar-wind mass loss has no effect on the stability criteria, but axial rotation and slowly adapting convective turbulence produce more complicated effects, depending on whether the envelope is dynamically stable or not. On the other hand, rotation and turbulence are probably very weak in most LBV outer envelopes.
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