Estimate the radius of the convective core of main-sequence stars from observed oscillation frequencies

Abstract

The determination of the size of the convective core of main-sequence stars is usually dependent on the construction of models of stars. Here we introduce a method to estimate the radius of the convective core of main-sequence stars with masses between about 1.1 and 1.5 $M_{\odot }$ from observed frequencies of low-degree p-modes. A formula is proposed to achieve the estimation. The values of the radius of the convective core of four known stars are successfully estimated by the formula. The radius of the convective core of KIC 9812850 estimated by the formula is $0.140\pm 0.028$ $R_{\odot }$. In order to confirm this prediction, a grid of evolutionary models were computed. The value of the convective-core radius of the best-fit model of KIC 9812850 is $0.149$ $R_{\odot }$, which is in good agreement with that estimated by the formula from observed frequencies. The formula aids in understanding the interior structure of stars directly from observed frequencies. The understanding is not dependent on the construction of models.

arXiv commentAccepted for publication in ApJ. 13 pages, 5 figures

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