Verification of Asymptotic Relation for Mixed Modes in Red Giant Stars

TL;DR

This paper investigates the asymptotic relation for mixed modes in red giant stars using theoretical models and observational data, revealing the behavior of mode inertia, coupling strength, and period spacing, and highlighting limitations of existing asymptotic equations.

Contribution

It provides a detailed analysis of mixed mode properties in red giants, comparing theoretical asymptotic descriptions with observations, and identifies issues with current asymptotic equations in the evanescent region.

Findings

Good estimates of period spacing and coupling strength are obtained for evolved models.

Mode inertia varies dramatically with strong coupling.

Theoretical asymptotic equations face issues in the evanescent region.

Abstract

High-precision space observations, such as made by the \kepler\ and \corot\ missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 M$_{\sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense. By comparing the theoretical coupling strength from the integral expression with the ones from fitting methods, we confirmed that the theoretical asymptotic equation is problematic in the evanescent region due to the potential singularities as well as the use of the Cowling approximation.