The frequency separations of stellar p-modes

TL;DR

This paper introduces a new frequency separation for stellar p-modes, which is sensitive to the stellar core conditions and can help determine the central hydrogen abundance of stars.

Contribution

A novel frequency separation $\sigma_{l-1 l+1}(n)$ is derived from the asymptotic formula, providing a new tool to probe stellar core properties.

Findings

$\sigma_{l-1 l+1}(n)$ is similar to the scaled small separation.

It is mainly sensitive to the stellar core conditions.

Deviations increase as the central hydrogen decreases.

Abstract

Aims. The purpose of this work is to investigate a new frequency separation of stellar p-modes and its characteristics. Methods. Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical adiabatic frequencies of stellar model, we compute the frequency separations. Results. A new separation $\sigma_{l-1 l+1}(n)$, which is similar to the scaled small separation $d_{l l+2}(n)/(2l+3)$, is obtained from the asymptotic formula of stellar p-modes. The separations $\sigma_{l-1 l+1}(n)$ and $d_{l l+2}(n)/(2l+3)$ have the same order. And like the small separation, $\sigma_{l-1 l+1}(n)$ is mainly sensitive to the conditions in the stellar core. However, with the decrease of the central hydrogen abundance of stars, the $\sigma_{02}$ and $\sigma_{13}$ more and more deviate from the scaled small separation. This characteristic could be used to extract the information on the central hydrogen abundance of stars.