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
Abstract
Context. Asteroseismology has revealed small coretosurface rotation contrasts in stars in the whole HertzsprungRussell 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 socalled 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 intermediatemass 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 magnetogravitoinertial (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 nonperturbative 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 10^{5} G leads to signatures that are detectable in period spacings for highradialorder 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 nonperturbative 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.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 May 2022
 DOI:
 10.1051/00046361/202142956
 arXiv:
 arXiv:2202.10026
 Bibcode:
 2022A&A...661A.133D
 Keywords:

 magnetohydrodynamics (MHD);
 waves;
 stars: rotation;
 stars: magnetic field;
 stars: oscillations;
 methods: analytical;
 Astrophysics  Solar and Stellar Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Fluid Dynamics
 EPrint:
 21 pages, 15 figures, 1 table, abstract shortened for arXiv. Published in A&