---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '21658'
abstract:
- lang: eng
text: Dipolar (ℓ = 1) mixed modes have revealed a surprisingly weak differential
rotation between the core and the envelope of evolved solar-like stars. Quadrupolar
(ℓ = 2) mixed modes also contain information regarding internal dynamics but are
very rarely characterised due to their low amplitude and the challenging identification
of adjacent or overlapping rotationally split multiplets affected by near-degeneracy
effects. We aim to extend the broadly used asymptotic seismic diagnostics beyond
ℓ = 1 mixed modes by developing an analogue asymptotic description of ℓ = 2 mixed
modes while explicitly accounting for near-degeneracy effects that distort their
rotational multiplets. We have derived a new asymptotic formulation of near-degenerate
mixed ℓ = 2 modes that describes off-diagonal terms representing the interaction
between modes of adjacent radial orders. This formalism, expressed directly in
the mixed-mode basis, provides analytical expressions for the near-degeneracy
effects. We implemented the formalism within a global Bayesian mode-fitting framework
for a direct fit of all ℓ = 0, 1, 2 modes in the power spectrum density. We were
able to asymptotically model the asymmetric rotational splitting present in various
radial orders of ℓ = 2 modes observed in young red giant stars without the need
for any numerical stellar modelling. We applied our formalism to the Kepler target
KIC 7341231, and it yielded core and envelope rotation rates consistent with previous
numerical modelling while providing improved constraints from the global and model-independent
approach. We also characterised the new target, KIC 8179973, measuring its rotation
rate and mixed-mode parameters for the first time. As our framework relies on
a direct global fit, it allows for much better precision on the asteroseismic
parameters and rotation rate estimates than standard methods, yielding better
constraints for rotation inversions. We have placed the first observational constraints
on the asymptotic ℓ = 2 mixed-mode parameters (ΔΠ2, q2, and εg, 2), thus paving
the way towards the use of asymptotic seismology beyond ℓ = 1 mixed modes.
acknowledgement: 'We thank the referee for their careful and constructive report,
which has substantially enhanced both the quality and clarity of the manuscript.
L. Bugnet and L. Einramhof gratefully acknowledge support from the European Research
Council (ERC) under the Horizon Europe programme (Calcifer; Starting Grant agreement
N°101165631). While partially funded by the European Union, views and opinions expressed
are, however, those of the authors only and do not necessarily reflect those of
the European Union or the European Research Council. Neither the European Union
nor the granting authority can be held responsible for them. The authors acknowledge
the great support and feedback provided during the redaction of this article by
Pr. Rafael García and Pr. Savita Mathur. We would also like to thank Dr. Emily Hatt
for her insights on uncertainty estimates. The authors also thank the members of
the Asteroseismology and Stellar Dynamics group of the Institute of Science and
Technology Austria (ISTA) for very useful discussions: L. Barrault, S.B. Das, K.
Smith. This paper includes data collected by the Kepler mission and obtained from
the MAST data archive at the Space Telescope Science Institute (STScI). Funding
for the Kepler mission is provided by the NASA Science Mission Directorate. STScI
is operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5–26555. Software: AstroPy (Astropy Collaboration 2013,
2018), Matplotlib (Hunter 2007), NumPy (Harris et al. 2020), SciPy (Virtanen et
al. 2020), emcee (Foreman-Mackey et al. 2013), celerite (Foreman-Mackey et al. 2017),
slepc4py (Dalcin et al. 2011; Hernandez et al. 2005), KADACS (García et al. 2011),
sloscillations (Kuszlewicz et al. 2019, 2023).'
article_number: A321
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Bastien Raymond Bernard
full_name: Liagre, Bastien Raymond Bernard
id: 662f1873-cab4-11f0-a719-8087d302868d
last_name: Liagre
- first_name: Aayush A
full_name: Desai, Aayush A
id: 502cfd30-32c1-11ee-a9a4-d8dad5c6739e
last_name: Desai
- first_name: Lukas
full_name: Einramhof, Lukas
id: f1497a1a-72ef-11ef-b75a-fd877bbf6e8c
last_name: Einramhof
- first_name: Lisa Annabelle
full_name: Bugnet, Lisa Annabelle
id: d9edb345-f866-11ec-9b37-d119b5234501
last_name: Bugnet
orcid: 0000-0003-0142-4000
citation:
ama: 'Liagre BRB, Desai AA, Einramhof L, Bugnet LA. Near-degeneracy effects in quadrupolar
mixed modes: From an asymptotic description to data fitting. Astronomy and
Astrophysics. 2026;707. doi:10.1051/0004-6361/202558023'
apa: 'Liagre, B. R. B., Desai, A. A., Einramhof, L., & Bugnet, L. A. (2026).
Near-degeneracy effects in quadrupolar mixed modes: From an asymptotic description
to data fitting. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/202558023'
chicago: 'Liagre, Bastien Raymond Bernard, Aayush A Desai, Lukas Einramhof, and
Lisa Annabelle Bugnet. “Near-Degeneracy Effects in Quadrupolar Mixed Modes: From
an Asymptotic Description to Data Fitting.” Astronomy and Astrophysics.
EDP Sciences, 2026. https://doi.org/10.1051/0004-6361/202558023.'
ieee: 'B. R. B. Liagre, A. A. Desai, L. Einramhof, and L. A. Bugnet, “Near-degeneracy
effects in quadrupolar mixed modes: From an asymptotic description to data fitting,”
Astronomy and Astrophysics, vol. 707. EDP Sciences, 2026.'
ista: 'Liagre BRB, Desai AA, Einramhof L, Bugnet LA. 2026. Near-degeneracy effects
in quadrupolar mixed modes: From an asymptotic description to data fitting. Astronomy
and Astrophysics. 707, A321.'
mla: 'Liagre, Bastien Raymond Bernard, et al. “Near-Degeneracy Effects in Quadrupolar
Mixed Modes: From an Asymptotic Description to Data Fitting.” Astronomy and
Astrophysics, vol. 707, A321, EDP Sciences, 2026, doi:10.1051/0004-6361/202558023.'
short: B.R.B. Liagre, A.A. Desai, L. Einramhof, L.A. Bugnet, Astronomy and Astrophysics
707 (2026).
corr_author: '1'
date_created: 2026-04-05T22:01:32Z
date_published: 2026-03-01T00:00:00Z
date_updated: 2026-04-07T09:01:44Z
day: '01'
ddc:
- '520'
department:
- _id: LiBu
- _id: IlCa
- _id: GradSch
doi: 10.1051/0004-6361/202558023
external_id:
arxiv:
- '2511.05314 '
file:
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intvolume: ' 707'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
publication: Astronomy and Astrophysics
publication_identifier:
eissn:
- 1432-0746
issn:
- 0004-6361
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Near-degeneracy effects in quadrupolar mixed modes: From an asymptotic description
to data fitting'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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...