FURTHER IMPROVEMENTS OF A NEW MODEL FOR TURBULENT CONVECTION IN STARS

In this paper we analyze the effect of several improvements of the input physics of a recent model for stellar turbulent convection. We first study the effect of (1) the inclusion of a variable molecular weight (Cox & Giuli's variable Q) and (2) the use of the newest opacities of Rogers & Iglesias. On the basis of the evolutionary tracks for the Sun (Fig. 2, curves 1 and 2), we conclude that the original model for turbulence with the mixing length LAMBDA = z, together with Q not-equal 1 and the new opacities, yields a fit to the solar T(eff) within 0.5%. The model has no adjustable parameters. Second, we propose a formulation of the mixing length LAMBDA that extends the purely nonlocal LAMBDA = z expression used in our previous work so as to include local effects. We derive the expression LAMBDA = alpha(S, a)z, where S = 160A2(NABLA - NABLA(ad)) and where 1 - a represents the weight of local effects. The new expression generalizes both the mixing-length theory (MLT) phenomenological expression LAMBDA = alpha-H(p), as well as our model LAMBDA = z. By adjusting the parameter a we can achieve an even better fit to the solar T(eff). However, we also conclude that as long as one is interested in evolutionary studies only, the new version of the mixing length is not quite necessary since the previous model has no free parameters and yet yields a fit to T(eff) within 0.5%. We point out, however, that this new model for LAMBDA may become instrumental in helioseismology where one needs to fit the solar radius considerably more accurately than in evolutionary studies. Finally, in section 7 we use qualitative and quantitative arguments to discuss the new model versus the standard MLT and give reasons why we believe that the MLT should be abandoned.