A formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations. I - Application to the sun

Abstract

We have constructed a series of models of Alpha Centauri A and Alpha Centauri B for the purposes of testing the effects of convection modeling both by means of the mixing-length theory (MLT), and by means of parameterization of energy fluxes based upon numerical simulations of turbulent compressible convection. We demonstrate that while MLT, through its adjustable parameter alpha, can be used to match any given values of luminosities and radii, our treatment of convection, which lacks any adjustable parameters, makes specific predictions of stellar radii. Since the predicted radii of the Alpha Centauri system fall within the errors of the observed radii, our treatment of convection is applicable to other stars in the H-R diagram in addition to the sun. A second set of models is constructed using MLT, adjusting alpha to yield not the 'measured' radii but, instead, the radii predictions of our revised treatment of convection. We conclude by assessing the appropriateness of using a single value of alpha to model a wide variety of stars.