---
_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'
...
---
_id: '11605'
abstract:
- lang: eng
  text: "Context. The discovery of moderate differential rotation between the core
    and the envelope of evolved solar-like stars could be the signature of a strong
    magnetic field trapped inside the radiative interior. The population of intermediate-mass
    red giants presenting surprisingly low-amplitude mixed modes (i.e. oscillation
    modes that behave as acoustic modes in their external envelope and as gravity
    modes in their core) could also arise from the effect of an internal magnetic
    field. Indeed, stars more massive than about 1.1 solar masses are known to develop
    a convective core during their main sequence. The field generated by the dynamo
    triggered by this convection could be the progenitor of a strong fossil magnetic
    field trapped inside the core of the star for the remainder of its evolution.\r\n\r\nAims.
    Observations of mixed modes can constitute an excellent probe of the deepest layers
    of evolved solar-like stars, and magnetic fields in those regions can impact their
    propagation. The magnetic perturbation on mixed modes may therefore be visible
    in asteroseismic data. To unravel which constraints can be obtained from observations,
    we theoretically investigate the effects of a plausible mixed axisymmetric magnetic
    field with various amplitudes on the mixed-mode frequencies of evolved solar-like
    stars.\r\n\r\nMethods. First-order frequency perturbations due to an axisymmetric
    magnetic field were computed for dipolar and quadrupolar mixed modes. These computations
    were carried out for a range of stellar ages, masses, and metallicities.\r\n\r\nConclusions.
    We show that typical fossil-field strengths of 0.1 − 1 MG, consistent with the
    presence of a dynamo in the convective core during the main sequence, provoke
    significant asymmetries on mixed-mode frequency multiplets during the red giant
    branch. We provide constraints and methods for the detectability of such magnetic
    signatures. We show that these signatures may be detectable in asteroseismic data
    for field amplitudes small enough for the amplitude of the modes not to be affected
    by the conversion of gravity into Alfvén waves inside the magnetised interior.
    Finally, we infer an upper limit for the strength of the field and the associated
    lower limit for the timescale of its action in order to redistribute angular momentum
    in stellar interiors."
article_number: A53
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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: V.
  full_name: Prat, V.
  last_name: Prat
- first_name: S.
  full_name: Mathis, S.
  last_name: Mathis
- first_name: A.
  full_name: Astoul, A.
  last_name: Astoul
- first_name: K.
  full_name: Augustson, K.
  last_name: Augustson
- first_name: R. A.
  full_name: García, R. A.
  last_name: García
- first_name: S.
  full_name: Mathur, S.
  last_name: Mathur
- first_name: L.
  full_name: Amard, L.
  last_name: Amard
- first_name: C.
  full_name: Neiner, C.
  last_name: Neiner
citation:
  ama: 'Bugnet LA, Prat V, Mathis S, et al. Magnetic signatures on mixed-mode frequencies:
    I. An axisymmetric fossil field inside the core of red giants. <i>Astronomy &#38;
    Astrophysics</i>. 2021;650. doi:<a href="https://doi.org/10.1051/0004-6361/202039159">10.1051/0004-6361/202039159</a>'
  apa: 'Bugnet, L. A., Prat, V., Mathis, S., Astoul, A., Augustson, K., García, R.
    A., … Neiner, C. (2021). Magnetic signatures on mixed-mode frequencies: I. An
    axisymmetric fossil field inside the core of red giants. <i>Astronomy &#38; Astrophysics</i>.
    EDP Sciences. <a href="https://doi.org/10.1051/0004-6361/202039159">https://doi.org/10.1051/0004-6361/202039159</a>'
  chicago: 'Bugnet, Lisa Annabelle, V. Prat, S. Mathis, A. Astoul, K. Augustson, R.
    A. García, S. Mathur, L. Amard, and C. Neiner. “Magnetic Signatures on Mixed-Mode
    Frequencies: I. An Axisymmetric Fossil Field inside the Core of Red Giants.” <i>Astronomy
    &#38; Astrophysics</i>. EDP Sciences, 2021. <a href="https://doi.org/10.1051/0004-6361/202039159">https://doi.org/10.1051/0004-6361/202039159</a>.'
  ieee: 'L. A. Bugnet <i>et al.</i>, “Magnetic signatures on mixed-mode frequencies:
    I. An axisymmetric fossil field inside the core of red giants,” <i>Astronomy &#38;
    Astrophysics</i>, vol. 650. EDP Sciences, 2021.'
  ista: 'Bugnet LA, Prat V, Mathis S, Astoul A, Augustson K, García RA, Mathur S,
    Amard L, Neiner C. 2021. Magnetic signatures on mixed-mode frequencies: I. An
    axisymmetric fossil field inside the core of red giants. Astronomy &#38; Astrophysics.
    650, A53.'
  mla: 'Bugnet, Lisa Annabelle, et al. “Magnetic Signatures on Mixed-Mode Frequencies:
    I. An Axisymmetric Fossil Field inside the Core of Red Giants.” <i>Astronomy &#38;
    Astrophysics</i>, vol. 650, A53, EDP Sciences, 2021, doi:<a href="https://doi.org/10.1051/0004-6361/202039159">10.1051/0004-6361/202039159</a>.'
  short: L.A. Bugnet, V. Prat, S. Mathis, A. Astoul, K. Augustson, R.A. García, S.
    Mathur, L. Amard, C. Neiner, Astronomy &#38; Astrophysics 650 (2021).
date_created: 2022-07-18T12:10:59Z
date_published: 2021-06-07T00:00:00Z
date_updated: 2022-08-19T10:06:33Z
day: '07'
doi: 10.1051/0004-6361/202039159
extern: '1'
external_id:
  arxiv:
  - '2102.01216'
intvolume: '       650'
keyword:
- Space and Planetary Science
- Astronomy and Astrophysics
- stars
- oscillations / stars
- magnetic field / stars
- interiors / stars
- evolution / stars
- rotation
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2102.01216
month: '06'
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: 'Magnetic signatures on mixed-mode frequencies: I. An axisymmetric fossil field
  inside the core of red giants'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 650
year: '2021'
...
---
_id: '11606'
abstract:
- lang: eng
  text: "Context. Our knowledge of the dynamics of stars has undergone a revolution
    through the simultaneous large amount of high-quality photometric observations
    collected by space-based asteroseismology and ground-based high-precision spectropolarimetry.
    They allowed us to probe the internal rotation of stars and their surface magnetism
    in the whole Hertzsprung-Russell diagram. However, new methods should still be
    developed to probe the deep magnetic fields in these stars.\r\n\r\nAims. Our goal
    is to provide seismic diagnoses that allow us to probe the internal magnetism
    of stars.\r\n\r\nMethods. We focused on asymptotic low-frequency gravity modes
    and high-frequency acoustic modes. Using a first-order perturbative theory, we
    derived magnetic splittings of their frequencies as explicit functions of stellar
    parameters.\r\n\r\nResults. As in the case of rotation, we show that asymptotic
    gravity and acoustic modes can allow us to probe the different components of the
    magnetic field in the cavities in which they propagate. This again demonstrates
    the high potential of using mixed-modes when this is possible."
acknowledgement: The authors thank the referee and Pr. J. Christensen-Dalsgaard for
  their very constructive comments and remarks that allowed us to improve the article.
  St. M., L. B., V. P., and K. A. acknowledge support from the European Research Council
  through ERC grant SPIRE 647383. All the members from CEA acknowledge support from
  GOLF and PLATO CNES grants of the Astrophysics Division at CEA. S. Mathur acknowledges
  support by the Ramon y Cajal fellowship number RYC-2015-17697. We made great use
  of the megyr python package for interfacing MESA and GYRE codes.
article_number: A122
article_processing_charge: No
article_type: original
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
- first_name: V.
  full_name: Prat, V.
  last_name: Prat
- first_name: K.
  full_name: Augustson, K.
  last_name: Augustson
- first_name: S.
  full_name: Mathur, S.
  last_name: Mathur
- first_name: R. A.
  full_name: Garcia, R. A.
  last_name: Garcia
citation:
  ama: Mathis S, Bugnet LA, Prat V, Augustson K, Mathur S, Garcia RA. Probing the
    internal magnetism of stars using asymptotic magneto-asteroseismology. <i>Astronomy
    &#38; Astrophysics</i>. 2021;647. doi:<a href="https://doi.org/10.1051/0004-6361/202039180">10.1051/0004-6361/202039180</a>
  apa: Mathis, S., Bugnet, L. A., Prat, V., Augustson, K., Mathur, S., &#38; Garcia,
    R. A. (2021). Probing the internal magnetism of stars using asymptotic magneto-asteroseismology.
    <i>Astronomy &#38; Astrophysics</i>. EDP Sciences. <a href="https://doi.org/10.1051/0004-6361/202039180">https://doi.org/10.1051/0004-6361/202039180</a>
  chicago: Mathis, S., Lisa Annabelle Bugnet, V. Prat, K. Augustson, S. Mathur, and
    R. A. Garcia. “Probing the Internal Magnetism of Stars Using Asymptotic Magneto-Asteroseismology.”
    <i>Astronomy &#38; Astrophysics</i>. EDP Sciences, 2021. <a href="https://doi.org/10.1051/0004-6361/202039180">https://doi.org/10.1051/0004-6361/202039180</a>.
  ieee: S. Mathis, L. A. Bugnet, V. Prat, K. Augustson, S. Mathur, and R. A. Garcia,
    “Probing the internal magnetism of stars using asymptotic magneto-asteroseismology,”
    <i>Astronomy &#38; Astrophysics</i>, vol. 647. EDP Sciences, 2021.
  ista: Mathis S, Bugnet LA, Prat V, Augustson K, Mathur S, Garcia RA. 2021. Probing
    the internal magnetism of stars using asymptotic magneto-asteroseismology. Astronomy
    &#38; Astrophysics. 647, A122.
  mla: Mathis, S., et al. “Probing the Internal Magnetism of Stars Using Asymptotic
    Magneto-Asteroseismology.” <i>Astronomy &#38; Astrophysics</i>, vol. 647, A122,
    EDP Sciences, 2021, doi:<a href="https://doi.org/10.1051/0004-6361/202039180">10.1051/0004-6361/202039180</a>.
  short: S. Mathis, L.A. Bugnet, V. Prat, K. Augustson, S. Mathur, R.A. Garcia, Astronomy
    &#38; Astrophysics 647 (2021).
date_created: 2022-07-18T12:15:27Z
date_published: 2021-03-18T00:00:00Z
date_updated: 2022-08-19T10:11:52Z
day: '18'
doi: 10.1051/0004-6361/202039180
extern: '1'
external_id:
  arxiv:
  - '2012.11050'
intvolume: '       647'
keyword:
- Space and Planetary Science
- Astronomy and Astrophysics
- asteroseismology / waves / stars
- magnetic field / stars
- oscillations / methods
- analytical
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2012.11050
month: '03'
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: Probing the internal magnetism of stars using asymptotic magneto-asteroseismology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 647
year: '2021'
...