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

TL;DR

This paper introduces a new formula to estimate the convective core radius of main-sequence stars using observed oscillation frequencies, bypassing the need for detailed stellar modeling.

Contribution

A novel formula is proposed to directly estimate the convective core radius from observed frequencies, validated with real star data and evolutionary models.

Findings

Successfully estimated the convective core radius of four stars.

Estimated radius for KIC 9812850 is 0.140±0.028 R_sun.

Model-based radius for KIC 9812850 is 0.149 R_sun, in agreement with the estimate.

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 $\mathbf{0.140\pm0.028}$ $R_{\odot}$. 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.