Convection theory and sub-photospheric stratification

As a preliminary step toward a complete theoretical integration of three-dimensional compressible hydrodynamic simulations into stellar evolution, convection at the surface and sub-surface layers of the Sun is re-examined, from a restricted point of view, in the language of mixing-length theory (MLT). Requiring that MLT use a hydrodynamically realistic dissipation length gives a new constraint on solar models. While the stellar structure which results is similar to that obtained by Yale Rotational Evolution Code (Guenther et al.; Bahcall & Pinsonneault) and Garching models (Schlattl et al.), the theoretical picture differs. A new quantitative connection is made between macro-turbulence, micro-turbulence, and the convective velocity scale at the photosphere, which has finite values. The "geometric parameter" in MLT is found to correspond more reasonably with the thickness of the superadiabatic region (SAR), as it must for consistency in MLT, and its integrated effect may correspond to that of the strong downward plumes which drive convection (Stein & Nordlund), and thus has a physical interpretation even in MLT. If we crudely require the thickness of the SAR to be consistent with the "geometric factor" used in MLT, there is no longer a free parameter, at least in principle. Use of three-dimensional simulations of both adiabatic convection and stellar atmospheres will allow the determination of the dissipation length and the geometric parameter (i.e., the entropy jump) more realistically, and with no astronomical calibration. A physically realistic treatment of convection in stellar evolution will require substantial additional modifications beyond MLT, including nonlocal effects of kinetic energy flux, entrainment (the most dramatic difference from MLT found by Meakin & Arnett), rotation, and magnetic fields.