Calibration of the mixing-length parameter $\hat{I}\pm$ for the MLT and FST models by matching with CO${}^5$BOLD models

Abstract

The CoRoT and Kepler missions provided a wealth of high-quality data for solar-like oscillations. To make the best of such data for seismic inferences, we need theoretical models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. The mixing-length parameter, $\hat{I}\pm$, is a key factor for the near-surface structure. In the convection formulations used in evolution codes, the $\hat{I}\pm$ is a free parameter that needs to be properly specified. We calibrated $\hat{I}\pm$ values by matching entropy profiles of 1D envelope models with those of 3D CO${}^5$BOLD models. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. For the atmosphere part in the 1D models, we use the Eddington grey $T(\ddot{I}„)$ relation and the one with the solar-calibrated Hopf-like function. For both the MLT and FST models with a mixing length $l=\hat{I}\pm H_p$, calibrated $\hat{I}\pm$ values increase with increasing $g$ or decreasing $T_{\mathrm{eff}}$. For the FST models, we also calibrated values of $\hat{I}{\pm }^{\ast }$ defined as $l=r_{\mathrm{top}}-r+\hat{I}{\pm }^{\ast }{H}_{p,\mathrm{top}}$. $\hat{I}{\pm }^{\ast }$ is found to increase with $T_{\mathrm{eff}}$ and $g$. As for the correspondence to the 3D models, the solar Hopf-like function gives a photospheric-minimum entropy closer to a 3D model than the Eddington $T(\ddot{I}„)$. The structure below the photosphere depends on the convection model. However, not a single convection model gives the best correspondence since the averaged 3D quantities are not necessarily related via an EOS. Although the FST models with $l=r_{\mathrm{top}}-r+\hat{I}{\pm }^{\ast }{H}_{p,\mathrm{top}}$ are found to give the frequencies closest to the solar observed ones, a more appropriate treatment of the top part of the 1D convective envelope is necessary.

14 pages, 18 figures, accepted to Astronomy and Astrophysics