Calibration of mixing length parameters with 3D simulation models

Observation by space missions such as CoRoT and Kepler have provided with a wealth of high-quality data of stellar oscillations. Particularly, rich spectra of solar-like oscillations should allow us to perform precise determination of stellar global parameters such as age, mass and radius, and interior structure. To make the best of such data, we need theoretical stellar models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. Mixing length parameters of the convection models are a key factor to determine the near-surface structure. However, we have not yet a definitive recipe for giving its value.

We aim at calibrating values of these parameters across the Heltzsprung-Russell (HR) diagram based on 3D hydrodynamical models, provided by the CO5BOLD code. Although previous calibration with 3D models have limited to the classical mixing length theory (MLT), we analyze also the full spectrum turbulence (FST) models proposed by Canuto & Mazzitelli (1991) and Canuto, Goldman & Mazzitelli (1996). We perform calibration by matching entropy profiles of 1D envelope models with those of the 3D models. For atmosphere of the 1D models, we compare the Eddington grey T-tau relation and the one with the solar calibrated Hopf function based on Vernazza et al. (1981).

For both the MLT and FST models with a mixing length l=alpha*H_p, calibrated alpha values increase with increasing surface gravity or decreasing effective temperature. For the solar model, the calibrated alpha values for the MLT and FST models with the Eddington T-tau relation are found to be in good agreement with previous works which performed alpha calibration with the Eddington T-tau by matching with the observables of the Sun. It is found that the solar Hopf T-tau relation generally gives photospheric minimum entropy closer to a 3D model than the Eddington T-tau in a wide range of the HR diagram. Since the alpha values substantially vary with effective temperature and surface gravity, 1D computation of stellar evolution should not be performed with the alpha value fixed, but the calibrated alpha values should be implemented into such computation.