---
_id: '14256'
abstract:
- lang: eng
  text: "Context. Space asteroseismology is revolutionizing our knowledge of the internal
    structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries
    of signatures of strong magnetic fields in the core of red giant stars. The key
    signature for such a detection is the asymmetry these fields induce in the frequency
    splittings of observed dipolar mixed gravito-acoustic modes.\r\nAims. We investigate
    the ability of the observed asymmetries of the frequency splittings of dipolar
    mixed modes to constrain the geometrical properties of deep magnetic fields.\r\nMethods.
    We used the powerful analytical Racah-Wigner algebra used in quantum mechanics
    to characterize the geometrical couplings of dipolar mixed oscillation modes with
    various realistically plausible topologies of fossil magnetic fields. We also
    computed the induced perturbation of their frequencies.\r\nResults. First, in
    the case of an oblique magnetic dipole, we provide the exact analytical expression
    of the asymmetry as a function of the angle between the rotation and magnetic
    axes. Its value provides a direct measure of this angle. Second, considering a
    combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry
    is blind to the unraveling of the relative strength and sign of each component.
    Finally, in the case of a given multipole, we show that a negative asymmetry is
    a signature of non-axisymmetric topologies.\r\nConclusions. Asymmetries of dipolar
    mixed modes provide a key bit of information on the geometrical topology of deep
    fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints
    should therefore be combined with spectropolarimetric observations and numerical
    simulations, which aim to predict the more probable stable large-scale geometries."
acknowledgement: The authors are grateful to the referee for her/his detailed and
  constructive report, which has allowed us to improve our article. S. M. acknowledges
  support from the CNES GOLF-SOHO and PLATO grants at CEA/DAp and PNPS (CNRS/INSU).
  We thank R. A. Garcia for fruitful discussions and suggestions.
article_number: L9
article_processing_charge: Yes (in subscription journal)
article_type: letter_note
arxiv: 1
author:
- first_name: S.
  full_name: Mathis, S.
  last_name: Mathis
- 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: 'Mathis S, Bugnet LA. Asymmetries of frequency splittings of dipolar mixed
    modes: A window on the topology of deep magnetic fields. <i>Astronomy &#38; Astrophysics</i>.
    2023;676. doi:<a href="https://doi.org/10.1051/0004-6361/202346832">10.1051/0004-6361/202346832</a>'
  apa: 'Mathis, S., &#38; Bugnet, L. A. (2023). Asymmetries of frequency splittings
    of dipolar mixed modes: A window on the topology of deep magnetic fields. <i>Astronomy
    &#38; Astrophysics</i>. EDP Sciences. <a href="https://doi.org/10.1051/0004-6361/202346832">https://doi.org/10.1051/0004-6361/202346832</a>'
  chicago: 'Mathis, S., and Lisa Annabelle Bugnet. “Asymmetries of Frequency Splittings
    of Dipolar Mixed Modes: A Window on the Topology of Deep Magnetic Fields.” <i>Astronomy
    &#38; Astrophysics</i>. EDP Sciences, 2023. <a href="https://doi.org/10.1051/0004-6361/202346832">https://doi.org/10.1051/0004-6361/202346832</a>.'
  ieee: 'S. Mathis and L. A. Bugnet, “Asymmetries of frequency splittings of dipolar
    mixed modes: A window on the topology of deep magnetic fields,” <i>Astronomy &#38;
    Astrophysics</i>, vol. 676. EDP Sciences, 2023.'
  ista: 'Mathis S, Bugnet LA. 2023. Asymmetries of frequency splittings of dipolar
    mixed modes: A window on the topology of deep magnetic fields. Astronomy &#38;
    Astrophysics. 676, L9.'
  mla: 'Mathis, S., and Lisa Annabelle Bugnet. “Asymmetries of Frequency Splittings
    of Dipolar Mixed Modes: A Window on the Topology of Deep Magnetic Fields.” <i>Astronomy
    &#38; Astrophysics</i>, vol. 676, L9, EDP Sciences, 2023, doi:<a href="https://doi.org/10.1051/0004-6361/202346832">10.1051/0004-6361/202346832</a>.'
  short: S. Mathis, L.A. Bugnet, Astronomy &#38; Astrophysics 676 (2023).
das_tickbox: '1'
date_created: 2023-09-03T22:01:15Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2026-07-08T06:45:55Z
day: '01'
ddc:
- '520'
department:
- _id: LiBu
doi: 10.1051/0004-6361/202346832
external_id:
  arxiv:
  - '2306.11587'
  isi:
  - '001046037700007'
file:
- access_level: open_access
  checksum: 7b30d26fb2b7bcb5b5be1414950615f9
  content_type: application/pdf
  creator: dernst
  date_created: 2023-09-06T07:13:19Z
  date_updated: 2023-09-06T07:13:19Z
  file_id: '14271'
  file_name: 2023_AstronomyAstrophysics_Mathis.pdf
  file_size: 458120
  relation: main_file
  success: 1
file_date_updated: 2023-09-06T07:13:19Z
has_accepted_license: '1'
intvolume: '       676'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Astronomy & Astrophysics
publication_identifier:
  eissn:
  - 1432-0746
  issn:
  - 0004-6361
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Asymmetries of frequency splittings of dipolar mixed modes: A window on the
  topology of deep magnetic fields'
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)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 676
year: '2023'
...