General relations are derived among the so-called critical luminosity L it, and the actual radiative and convective luminosities, L d and L , within a star in hydrostatic and local thermodynamic equilibrium. Convection sets in before L &d reaches L it, and the total luminosity can exceed L it at points well below the surface without mass-outflow being a necessary consequence. A density inversion develops at a value of L d which is less than , and a gas-pressure inversion appears whenever L a exceeds L 1 however, if convection is efficient, neither type of inversion will occur. A general boundary condition for an outer layer of small fractional mass is derived which expresses the surface luminosity in terms of temperature, density, and opacity at the base of the layer and a parameter a. This parameter is of order unity as long as the boundary layer is stable against convection; in some cases, it is possible to make an a priori determination of convective stability. Explicit expressions are obtained for a perfect gas plus blackbody radiation and Kramers opacity plus electron scattering. Subject headings: convection - instabilities - interiors, stellar - luminous stars - mass loss
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Joss et al. (1973) studied this question.