Semi-analytic Expressions for the Isolation and Coupling of Mixed Modes

Abstract

In the oscillation spectra of giant stars, nonradial modes may be seen to undergo avoided crossings, which produce a characteristic "mode bumping" of the otherwise uniform asymptotic p- and g-mode patterns in their respective echelle diagrams. Avoided crossings evolve very quickly relative to typical observational errors, and are therefore extremely useful in determining precise ages of stars, particularly in subgiants. This phenomenon is caused by coupling between modes in the p- and g-mode cavities that are near resonance with each other. Most theoretical analyses of the coupling between these mode cavities rely on the JWKB approach, which is strictly speaking inapplicable for the low-order g-modes observed in subgiants, or the low-order p-modes seen in very evolved red giants. We present both a nonasymptotic prescription for isolating the two mode cavities, as well as a perturbative (and also nonasymptotic) description of the coupling between them, which we show to hold good for the low-order g- and p-modes in these physical situations. Finally, we discuss how these results may be applied to modelling subgiant stars and determining their global properties from oscillation frequencies. We also make our code for all of these computations publicly available.

21 pages, 16 figures. Accepted to ApJ

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• Unveiling the Structure and Dynamics of Red Giants with Asteroseismology
• Mode Mixing and Rotational Splittings: I. Near-Degeneracy Effects Revisited
• Revisiting the Red-giant Branch Hosts KOI-3886 and $\iota$ Draconis. Detailed Asteroseismic Modeling and Consolidated Stellar Parameters
• Near-Core Acoustic Glitches are Not Oscillatory: Consequences for Asteroseismic Probes of Convective Boundary Mixing
• Acoustic modes in M67 cluster stars trace deepening convective envelopes
• TESS Asteroseismic Analysis of HD 76920: The Giant Star Hosting An Extremely Eccentric Exoplanet
• In search of gravity mode signatures in main sequence solar-type stars observed by Kepler
• Asteroseismology with PBjam 2.0: measuring dipole mode frequencies in coupling regimes from main sequence to low-luminosity red giant stars
• Evolutionary and Observational Properties of Red Giant Acoustic Glitch Signatures
• Reggae: A Parametric Tuner for PBJam, and a Visualization Tool for Red Giant Oscillation Spectra
• From core to envelope: revealing the deep dynamics of stars with two convective zones
• Impact of near-degeneracy effects on linear rotational inversions for red-giant stars