THE PREDICTION OF STELLAR EFFECTIVE TEMPERATURES FROM THE MIXING-LENGTH THEORY OF CONVECTION

A generalized version of the mixing-length theory (MLT) of convection, along with simplifications in the limits of high and low convective efficiency, is described. This forms the basis for a study of the effects of proposed modifications to the original (Böhm-Vitense) form of the MLT on the predicted effective temperatures of cool stars. These modifications include the parameters y and v that were introduced by Henyey, Vardya, and Bodenheimer, as well as Deupree's suggestion of opacity averaging, and Deupree and Varner's calibration of the mixing-length parameter, α, as a function of temperature. Somewhat surprisingly, it is found that none of the suggested refinements to the MLT affect the location and shape of an evolutionary track on the H-R diagram in ways that cannot be mimicked to high accuracy by a suitable choice of α alone. Thus, if α is calibrated by comparing stellar models with observed main-sequence stars with well-determined properties (e.g., the Sun, Groombridge 1830), then the subsequent evolutionary tracks and isochrones are uniquely defined, regardless of what version of the MLT is used in the calculations. A careful examination of the Revised Yale Isochrones suggests that the Teff scale of these isochrones is inconsistent with the assumed MLT, thereby resolving much of the known discrepancies between these calculations and those of VandenBerg and Bell. We also discuss some effects of variations in the MLT on other areas of stellar astrophysics (activity, tidal circularization) and implications for predicted effective temperatures of attaching model atmospheres onto interior structures at depth rather than at the photosphere.