Verification of Asymptotic Relation for Mixed Modes in Red Giant Stars

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.

10 pages, 11 figures, 4 tables

References in corpus (3)

• ADIPLS -- the Aarhus adiabatic oscillation package
• ASTEC -- the Aarhus STellar Evolution Code
• An Elementary Introduction to the JWKB Approximation

Cited by in corpus (9)

• Bayesian peak bagging analysis of 19 low-mass low-luminosity red giants observed with Kepler
• Probing the mid-layer structure of red giants I. Mixed-mode coupling factor as a seismic diagnosis
• Variations of the mixing character of dipolar mixed modes in red giant stars
• Asteroseismology of evolved stars with EGGMiMoSA I. Theoretical mixed-mode patterns from the subgiant to the RGB phase
• Evolution of Dipolar Mixed-mode Coupling Factor in Red Giant Stars: Impact of Buoyancy Spike
• Solar-like oscillations in $\gamma$ Cephei A as seen through SONG and TESS
• Pushing the boundaries of asteroseismic individual frequency modelling: unveiling two evolved very-low metallicity red giants
• Using the phase shift to asymptotically characterize the dipolar mixed modes in post-main-sequence stars
• Realising efficient computation of individual frequencies for red-giant models