On the "critical Luminosity" in Stellar Interiors and Stellar Surface Boundary Conditions . .

Abstract

General relations are derived among the so-called critical luminosity Lit, 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 {\amp}d reaches L it, and the totalluminosity can exceed L it at points well below the surface withoutmass-outflow being a necessary consequence. A density inversion developsat a value of L d which is less than , and a gas-pressure inversionappears whenever L a exceeds L 1 however, if convection is efficient,neither type of inversion will occur. A general boundary condition foran outer layer of small fractional mass is derived which expresses thesurface luminosity in terms of temperature, density, and opacity at thebase of the layer and a parameter a. This parameter is of order unity aslong as the boundary layer is stable against convection; in some cases,it is possible to make an a priori determination of convectivestability. Explicit expressions are obtained for a perfect gas plusblackbody radiation and Kramers opacity plus electron scattering.Subject headings: convection - instabilities - interiors, stellar -luminous stars - mass loss