A Large Convective-Core Overshoot in \textit{Kepler} Target KIC 11081729

Abstract

The frequency ratios $r_{01}$ and $r_{10}$ of KIC 11081729 decrease firstly and then increase with the increase in frequency. For different spectroscopic constraints, all models with overshooting parameter $\delta_{\mathrm{ov}}$ less than 1.7 can not reproduce the distributions of the ratios. However, the distributions of the ratios can be directly reproduced by models with $\delta_{\mathrm{ov}}$ in the range of about $1.7-1.8$. The estimations of mass and age of the star can be affected by spectroscopic results, but the determination of the $\delta_{\mathrm{ov}}$ is not dependent on the spectroscopic results. A large overshooting of convective core may exist in KIC 11081729. The characteristics of $r_{01}$ and $r_{10}$ of KIC 11081729 may result from the effects of the large overshooting of convective core. The distributions of $r_{01}$ and $r_{10}$ of different stars with a convective core can be reproduced by the function $B(\nu_{n,1})$. If the value of the critical frequency $\nu_{0}$ is larger than the value of frequency of maximum oscillation power $\nu_{max}$, a star may have a small convective core and $\delta_{\rm ov}$. But if the value of $\nu_{0}$ is less than that of $\nu_{max}$, the star may have a large convective core and $\delta_{\mathrm{ov}}$. The function aids in determining the presence of convective core and the size of the convective core including overshooting region from observed frequencies. The determination is not dependent on the calculation of stellar models.