The role of stellar envelope convection in gravity-darkening and its relation to observational data

Abstract

We study the role of convection in the surface heat flow of low mass stellar envelopes with the aid of Paczynski’s public domain program program GOB. This role is important, for example, for the analysis of light curves of close binary stars. We have considered atmospheric models for a range of masses similar to the components of contact or near-contact binaries between 0.4 and 1.1 M ⊙ and examined the effects of changing luminosity, surface temperature and mixing length for stars of given mass. Our presentation includes checks of the modeling against published standard stellar envelopes. A slight program modification allowed gravity darkening coefficients for selected models to be calculated directly. If the procedure proposed by Lucy is followed, similar values of the index β (∼0.06–0.1) are obtained for a fairly wide range of masses, luminosities and effective temperatures of cool stars. There also appears no strong dependence on the mixing-length parameter α. There are, however, physical differences between the conditions that apply to this derivation of the index and those of a photosphere distorted by rotation and tides, but having net dynamical stability. Thus, the dependency of T e on g was argued to come from the ratio of partial derivatives of the adiabatic constant K for the layer where convection starts; but a subconvective equipotential surface, where K would be constant, cannot coincide with such a layer. The adopted procedure is therefore inappropriate, and would involve different heat transfer regimes in different radial directions (say, polar or equatorial). A corresponding evaluation for the layer in which the convective flux becomes maximal shows less sensitivity to T e. The corresponding index is then much closer to, or even greater than, the von Zeipel value. Other arguments are also considered, including those of Anderson and Shu [Anderson, L., Shu, F.H., 1977. ApJ 214, 798] about the independence of the convective flux to local gravity, as well as the role of superphotospheric circulation effects, which could reduce the gravity darkening index to less than its subphotospheric value. Observational evaluations of gravity darkening for close binary systems, in general, are still inconclusive, due to the strong correlation between β and other parameters characterizing the light curve shape, particularly in the scale photometric ‘ellipticity’ effects. It is possible that very precise light curves that may be obtained in the future will allow this situation to be improved. The general surface distribution of emergent flux in the far infra-red of Jupiter may be a pointer in the direction of future studies of the subject.