Using the phase shift to asymptotically characterize the dipolar mixed modes in post-main-sequence stars

TL;DR

This paper explores the use of phase shifts in eigenvalue conditions to better characterize dipolar mixed modes in post-main-sequence stars, offering a new approach that complements existing methods like the coupling strength.

Contribution

It introduces phase shifts as a novel tool for analyzing mixed modes, providing improved insights into mode properties and stellar structure in post-main-sequence stars.

Findings

Phase shifts vary significantly across modes, unlike coupling strength.

The method improves understanding of pressure and gravity mode radial orders.

Application to Kepler star KIC 3744043 shows promising results.

Abstract

Mixed modes have been extensively observed in post-main-sequence stars by the Kepler and CoRoT space missions. The mixture of the p and g modes can be measured by the dimensionless coefficient $q$, the so-called coupling strength factor. In this paper we discuss the utility of the phase shifts $\theta$ from the eigenvalue condition for mixed modes as a tool to characterize dipolar mixed modes from the theoretical as well as the practical point of view. Unlike the coupling strength, whose variation in a given star is very small over the relevant frequency range, the phase shifts vary significantly for different modes. The analysis in terms of $\theta$ can also provide a better understanding of the pressure and gravity radial order for a given mixed mode. Observed frequencies of the Kepler red-giant star KIC 3744043 are used to test the method. The results are very promising.