Issue |
A&A
Volume 687, July 2024
|
|
---|---|---|
Article Number | A265 | |
Number of page(s) | 26 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/202348369 | |
Published online | 30 July 2024 |
Non-linear three-mode coupling of gravity modes in rotating slowly pulsating B stars
Stationary solutions and modeling potential
1
Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
e-mail: jordan.vanbeeck@protonmail.com
2
TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
3
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
4
Royal Observatory of Belgium, Ringlaan 3, Brussels, Belgium
5
Dept. of Astrophysics, IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands
6
Max Planck Institute for Astronomy, Koenigstuhl 17, 69117 Heidelberg, Germany
7
Guest Researcher, Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Ave, New York, NY 10010, USA
Received:
23
October
2023
Accepted:
21
December
2023
Context. Slowly pulsating B (SPB) stars display multi-periodic variability in the gravito-inertial mode regime with indications of non-linear resonances between modes. Several have undergone asteroseismic modeling in the past few years to infer their internal properties, but only in a linear setting. These stars rotate fast, so that rotation is typically included in the modeling by means of the traditional approximation of rotation (TAR).
Aims. We aim to extend the set of tools available for asteroseismology, by describing time-independent (stationary) resonant non-linear coupling among three gravito-inertial modes within the TAR. Such coupling offers the opportunity to use mode amplitude ratios in the asteroseismic modeling process, instead of only relying on frequencies of linear eigenmodes, as has been done so far.
Methods. Following observational detections, we derive expressions for the resonant stationary non-linear coupling between three gravito-inertial modes in rotating stars. We assess selection rules and stability domains for stationary solutions. We also predict non-linear frequencies and amplitude ratio observables that can be compared with their observed counterparts.
Results. The non-linear frequency shifts of stationary couplings are negligible compared to typical frequency errors derived from observations. The theoretically predicted amplitude ratios of combination frequencies match with some of their observational counterparts in the SPB targets. Other, unexplained observed ratios could be linked to other saturation mechanisms, to interactions between different modes, or to different opacity gradients in the driving zone.
Conclusions. For the purpose of asteroseismic modeling, our non-linear mode coupling formalism can explain some of the stationary amplitude ratios of observed resonant mode couplings in single SPB stars monitored during 4 years by the Kepler space telescope.
Key words: asteroseismology / stars: evolution / stars: interiors / stars: oscillations / stars: rotation / stars: variables: general
© The Authors 2024
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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