@article{11621,
  abstract     = {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.

Aims. 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.

Methods. 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.

Results. 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.

Conclusions. 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.},
  author       = {Dhouib, H. and Mathis, S. and Bugnet, Lisa Annabelle and Van Reeth, T. and Aerts, C.},
  issn         = {1432-0746},
  journal      = {Astronomy & Astrophysics},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, magnetohydrodynamics (MHD) / waves / stars, rotation / stars: magnetic field / stars, oscillations / methods},
  publisher    = {EDP Sciences},
  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}},
  doi          = {10.1051/0004-6361/202142956},
  volume       = {661},
  year         = {2022},
}

@article{11605,
  abstract     = {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.

Aims. 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.

Methods. 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.

Conclusions. 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.},
  author       = {Bugnet, Lisa Annabelle and Prat, V. and Mathis, S. and Astoul, A. and Augustson, K. and García, R. A. and Mathur, S. and Amard, L. and Neiner, C.},
  issn         = {1432-0746},
  journal      = {Astronomy & Astrophysics},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, stars, oscillations / stars, magnetic field / stars, interiors / stars, evolution / stars, rotation},
  publisher    = {EDP Sciences},
  title        = {{Magnetic signatures on mixed-mode frequencies: I. An axisymmetric fossil field inside the core of red giants}},
  doi          = {10.1051/0004-6361/202039159},
  volume       = {650},
  year         = {2021},
}

@article{11606,
  abstract     = {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.

Aims. Our goal is to provide seismic diagnoses that allow us to probe the internal magnetism of stars.

Methods. 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.

Results. 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.},
  author       = {Mathis, S. and Bugnet, Lisa Annabelle and Prat, V. and Augustson, K. and Mathur, S. and Garcia, R. A.},
  issn         = {1432-0746},
  journal      = {Astronomy & Astrophysics},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, asteroseismology / waves / stars, magnetic field / stars, oscillations / methods, analytical},
  publisher    = {EDP Sciences},
  title        = {{Probing the internal magnetism of stars using asymptotic magneto-asteroseismology}},
  doi          = {10.1051/0004-6361/202039180},
  volume       = {647},
  year         = {2021},
}