[{"author":[{"first_name":"H.","last_name":"Dhouib","full_name":"Dhouib, H."},{"last_name":"Mathis","first_name":"S.","full_name":"Mathis, S."},{"first_name":"Lisa Annabelle","last_name":"Bugnet","orcid":"0000-0003-0142-4000","full_name":"Bugnet, Lisa Annabelle","id":"d9edb345-f866-11ec-9b37-d119b5234501"},{"first_name":"T.","last_name":"Van Reeth","full_name":"Van Reeth, T."},{"full_name":"Aerts, C.","first_name":"C.","last_name":"Aerts"}],"scopus_import":"1","_id":"11621","intvolume":"       661","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","date_created":"2022-07-19T08:04:15Z","article_processing_charge":"No","publication_status":"published","quality_controlled":"1","article_type":"original","publisher":"EDP Sciences","external_id":{"arxiv":["2202.10026"]},"year":"2022","citation":{"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>","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>","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.","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>.","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).","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."},"date_updated":"2022-08-22T07:58:54Z","abstract":[{"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.","lang":"eng"}],"day":"19","doi":"10.1051/0004-6361/202142956","arxiv":1,"extern":"1","volume":661,"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.","publication":"Astronomy & Astrophysics","article_number":"A133","month":"05","oa_version":"Preprint","keyword":["Space and Planetary Science","Astronomy and Astrophysics","magnetohydrodynamics (MHD) / waves / stars","rotation / stars: magnetic field / stars","oscillations / methods"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2022-05-19T00:00:00Z","oa":1,"publication_identifier":{"issn":["0004-6361"],"eissn":["1432-0746"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2202.10026","open_access":"1"}]},{"extern":"1","volume":647,"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.","external_id":{"arxiv":["2012.11050"]},"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.","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).","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."},"year":"2021","date_updated":"2022-08-19T10:11:52Z","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."}],"day":"18","doi":"10.1051/0004-6361/202039180","arxiv":1,"quality_controlled":"1","article_type":"original","publisher":"EDP Sciences","author":[{"full_name":"Mathis, S.","first_name":"S.","last_name":"Mathis"},{"id":"d9edb345-f866-11ec-9b37-d119b5234501","last_name":"Bugnet","first_name":"Lisa Annabelle","full_name":"Bugnet, Lisa Annabelle","orcid":"0000-0003-0142-4000"},{"first_name":"V.","last_name":"Prat","full_name":"Prat, V."},{"full_name":"Augustson, K.","last_name":"Augustson","first_name":"K."},{"full_name":"Mathur, S.","last_name":"Mathur","first_name":"S."},{"last_name":"Garcia","first_name":"R. A.","full_name":"Garcia, R. A."}],"scopus_import":"1","_id":"11606","intvolume":"       647","title":"Probing the internal magnetism of stars using asymptotic magneto-asteroseismology","date_created":"2022-07-18T12:15:27Z","article_processing_charge":"No","publication_status":"published","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/2012.11050","open_access":"1"}],"type":"journal_article","date_published":"2021-03-18T00:00:00Z","oa":1,"publication_identifier":{"issn":["0004-6361"],"eissn":["1432-0746"]},"keyword":["Space and Planetary Science","Astronomy and Astrophysics","asteroseismology / waves / stars","magnetic field / stars","oscillations / methods","analytical"],"language":[{"iso":"eng"}],"publication":"Astronomy & Astrophysics","article_number":"A122","month":"03","oa_version":"Preprint"}]