---
_id: '11621'
abstract:
- lang: eng
  text: "Context. Asteroseismology has revealed small core-to-surface rotation contrasts
    in stars in the whole Hertzsprung–Russell diagram. This is the signature of strong
    transport of angular momentum (AM) in stellar interiors. One of the plausible
    candidates to efficiently carry AM is magnetic fields with various topologies
    that could be present in stellar radiative zones. Among them, strong axisymmetric
    azimuthal (toroidal) magnetic fields have received a lot of interest. Indeed,
    if they are subject to the so-called Tayler instability, the accompanying triggered
    Maxwell stresses can transport AM efficiently. In addition, the electromotive
    force induced by the fluctuations of magnetic and velocity fields could potentially
    sustain a dynamo action that leads to the regeneration of the initial strong axisymmetric
    azimuthal magnetic field.\r\n\r\nAims. The key question we aim to answer is whether
    we can detect signatures of these deep strong azimuthal magnetic fields. The only
    way to answer this question is asteroseismology, and the best laboratories of
    study are intermediate-mass and massive stars with external radiative envelopes.
    Most of these are rapid rotators during their main sequence. Therefore, we have
    to study stellar pulsations propagating in stably stratified, rotating, and potentially
    strongly magnetised radiative zones, namely magneto-gravito-inertial (MGI) waves.\r\n\r\nMethods.
    We generalise the traditional approximation of rotation (TAR) by simultaneously
    taking general axisymmetric differential rotation and azimuthal magnetic fields
    into account. Both the Coriolis acceleration and the Lorentz force are therefore
    treated in a non-perturbative way. Using this new formalism, we derive the asymptotic
    properties of MGI waves and their period spacings.\r\n\r\nResults. We find that
    toroidal magnetic fields induce a shift in the period spacings of gravity (g)
    and Rossby (r) modes. An equatorial azimuthal magnetic field with an amplitude
    of the order of 105 G leads to signatures that are detectable in period spacings
    for high-radial-order g and r modes in γ Doradus (γ Dor) and slowly pulsating
    B (SPB) stars. More complex hemispheric configurations are more difficult to observe,
    particularly when they are localised out of the propagation region of MGI modes,
    which can be localised in an equatorial belt.\r\n\r\nConclusions. The magnetic
    TAR, which takes into account toroidal magnetic fields in a non-perturbative way,
    is derived. This new formalism allows us to assess the effects of the magnetic
    field in γ Dor and SPB stars on g and r modes. We find that these effects should
    be detectable for equatorial fields thanks to modern space photometry using observations
    from Kepler, TESS CVZ, and PLATO."
acknowledgement: 'We thank the referee for her/his positive and constructive report,
  which has allowed us to improve the quality of our article. H.D. and S.M. acknowledge
  support from the CNES PLATO grant at CEA/DAp. T.V.R. gratefully acknowledges support
  from the Research Foundation Flanders (FWO) under grant agreement No. 12ZB620N and
  V414021N. This research was supported in part by the National Science Foundation
  under Grant No. NSF PHY-1748958. C.A. is supported by the KU Leuven Research Council
  (grant C16/18/005: PARADISE) as well as from the BELgian federal Science Policy
  Office (BELSPO) through a PLATO PRODEX grant.'
article_number: A133
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: H.
  full_name: Dhouib, H.
  last_name: Dhouib
- 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
- first_name: T.
  full_name: Van Reeth, T.
  last_name: Van Reeth
- first_name: C.
  full_name: Aerts, C.
  last_name: Aerts
citation:
  ama: 'Dhouib H, Mathis S, Bugnet LA, Van Reeth T, Aerts C. Detecting deep axisymmetric
    toroidal magnetic fields in stars: The traditional approximation of rotation for
    differentially rotating deep spherical shells with a general azimuthal magnetic
    field. <i>Astronomy &#38; Astrophysics</i>. 2022;661. doi:<a href="https://doi.org/10.1051/0004-6361/202142956">10.1051/0004-6361/202142956</a>'
  apa: 'Dhouib, H., Mathis, S., Bugnet, L. A., Van Reeth, T., &#38; Aerts, C. (2022).
    Detecting deep axisymmetric toroidal magnetic fields in stars: The traditional
    approximation of rotation for differentially rotating deep spherical shells with
    a general azimuthal magnetic field. <i>Astronomy &#38; Astrophysics</i>. EDP Sciences.
    <a href="https://doi.org/10.1051/0004-6361/202142956">https://doi.org/10.1051/0004-6361/202142956</a>'
  chicago: 'Dhouib, H., S. Mathis, Lisa Annabelle Bugnet, T. Van Reeth, and C. Aerts.
    “Detecting Deep Axisymmetric Toroidal Magnetic Fields in Stars: The Traditional
    Approximation of Rotation for Differentially Rotating Deep Spherical Shells with
    a General Azimuthal Magnetic Field.” <i>Astronomy &#38; Astrophysics</i>. EDP
    Sciences, 2022. <a href="https://doi.org/10.1051/0004-6361/202142956">https://doi.org/10.1051/0004-6361/202142956</a>.'
  ieee: 'H. Dhouib, S. Mathis, L. A. Bugnet, T. Van Reeth, and C. Aerts, “Detecting
    deep axisymmetric toroidal magnetic fields in stars: The traditional approximation
    of rotation for differentially rotating deep spherical shells with a general azimuthal
    magnetic field,” <i>Astronomy &#38; Astrophysics</i>, vol. 661. EDP Sciences,
    2022.'
  ista: 'Dhouib H, Mathis S, Bugnet LA, Van Reeth T, Aerts C. 2022. Detecting deep
    axisymmetric toroidal magnetic fields in stars: The traditional approximation
    of rotation for differentially rotating deep spherical shells with a general azimuthal
    magnetic field. Astronomy &#38; Astrophysics. 661, A133.'
  mla: 'Dhouib, H., et al. “Detecting Deep Axisymmetric Toroidal Magnetic Fields in
    Stars: The Traditional Approximation of Rotation for Differentially Rotating Deep
    Spherical Shells with a General Azimuthal Magnetic Field.” <i>Astronomy &#38;
    Astrophysics</i>, vol. 661, A133, EDP Sciences, 2022, doi:<a href="https://doi.org/10.1051/0004-6361/202142956">10.1051/0004-6361/202142956</a>.'
  short: H. Dhouib, S. Mathis, L.A. Bugnet, T. Van Reeth, C. Aerts, Astronomy &#38;
    Astrophysics 661 (2022).
date_created: 2022-07-19T08:04:15Z
date_published: 2022-05-19T00:00:00Z
date_updated: 2022-08-22T07:58:54Z
day: '19'
doi: 10.1051/0004-6361/202142956
extern: '1'
external_id:
  arxiv:
  - '2202.10026'
intvolume: '       661'
keyword:
- Space and Planetary Science
- Astronomy and Astrophysics
- magnetohydrodynamics (MHD) / waves / stars
- 'rotation / stars: magnetic field / stars'
- oscillations / methods
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2202.10026
month: '05'
oa: 1
oa_version: Preprint
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: 'Detecting deep axisymmetric toroidal magnetic fields in stars: The traditional
  approximation of rotation for differentially rotating deep spherical shells with
  a general azimuthal magnetic field'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 661
year: '2022'
...