Convection in Stars I. Basic Boussinesq Convection

TLDR: In this paper, the authors take the optimistic view that present convective models are qualitatively reasonable, what can one expect of an improved theory? One desirable feature would be the prediction of convective transfer with, in addition, some reasonable estimate of the accuracy of the prediction.

Abstract: Convection occurs somewhere in most stars, yet our lack of understanding of convection has not seemed a major impediment to progress in stellar structure in recent years. In part this is true because convection often achieves the idealized adiabatic limit that is expected in convective cores of stars. I t has also been true that uncertainties in the other physical processes in stars have been reduced considerably, and this has permitted a better empirical determination of the arbitrary parameters used in stellar convec­ tion theory. Of course, there is always the possibility that things are not as satisfactory as one thinks. But if we take the optimistic view that present convective models are qualitatively reasonable, what can one expect of an improved theory? One desirable feature would be the prediction of convective transfer with, in addition, some reasonable estimate of the accuracy of the prediction. For this, a minimal but inadequate test is found in laboratory convection for which some quantitative data are available. Thus, a principal goal of stellar convection theory should be the development of a reasonable deductive theory whose reasonability can be minimally established by laboratory tests. Having obtained a theory at this level we would next be interested in finer details that characterize stellar convection. That is, we would like to be able to be quantitative about the time dependence and scales of the con­ vection motion and to compare these with solar observations; we would like to know how far convection may penetrate beyond the regions of in­ stability and by large-scale mixing remove chemical inhomogeneities; we would be interested in the precise temperature variations at the tops of convective envelopes to have better input for model atmospheres. And these are only a sample of some of the questions that one would hope to answer at this level of difficulty. There is, in addition, a series of dynamical questions which raise problems about the interaction of convection with other processes of stellar fluid dynamics. These bring in new instabilities and are probably the most in-