[{"article_number":"A133","doi":"10.1051/0004-6361/202142956","publication_identifier":{"eissn":["1432-0746"],"issn":["0004-6361"]},"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.","language":[{"iso":"eng"}],"external_id":{"arxiv":["2202.10026"]},"month":"05","scopus_import":"1","oa_version":"Preprint","date_published":"2022-05-19T00:00:00Z","author":[{"first_name":"H.","full_name":"Dhouib, H.","last_name":"Dhouib"},{"first_name":"S.","last_name":"Mathis","full_name":"Mathis, S."},{"id":"d9edb345-f866-11ec-9b37-d119b5234501","full_name":"Bugnet, Lisa Annabelle","last_name":"Bugnet","first_name":"Lisa Annabelle","orcid":"0000-0003-0142-4000"},{"first_name":"T.","last_name":"Van Reeth","full_name":"Van Reeth, T."},{"first_name":"C.","last_name":"Aerts","full_name":"Aerts, C."}],"date_updated":"2022-08-22T07:58:54Z","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","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-07-19T08:04:15Z","year":"2022","quality_controlled":"1","article_type":"original","oa":1,"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>","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.","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>.","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>.","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.","short":"H. Dhouib, S. Mathis, L.A. Bugnet, T. Van Reeth, C. Aerts, Astronomy &#38; Astrophysics 661 (2022)."},"publication":"Astronomy & Astrophysics","extern":"1","publisher":"EDP Sciences","article_processing_charge":"No","type":"journal_article","volume":661,"day":"19","keyword":["Space and Planetary Science","Astronomy and Astrophysics","magnetohydrodynamics (MHD) / waves / stars","rotation / stars: magnetic field / stars","oscillations / methods"],"arxiv":1,"publication_status":"published","_id":"11621","intvolume":"       661","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"}],"status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2202.10026"}]},{"article_processing_charge":"No","publisher":"EDP Sciences","extern":"1","publication":"Astronomy & Astrophysics","day":"08","keyword":["Space and Planetary Science","Astronomy and Astrophysics","hydrodynamics / turbulence / stars","rotation / stars","evolution"],"volume":646,"type":"journal_article","publication_status":"published","arxiv":1,"main_file_link":[{"url":"https://arxiv.org/abs/2006.10660","open_access":"1"}],"status":"public","abstract":[{"text":"Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars.\r\n\r\nAims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f.\r\n\r\nMethods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids.\r\n\r\nResults. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ <  180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.","lang":"eng"}],"_id":"11609","intvolume":"       646","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration","article_type":"original","quality_controlled":"1","year":"2021","date_created":"2022-07-18T13:24:32Z","citation":{"ieee":"J. Park, V. Prat, S. Mathis, and L. A. Bugnet, “Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration,” <i>Astronomy &#38; Astrophysics</i>, vol. 646. EDP Sciences, 2021.","short":"J. Park, V. Prat, S. Mathis, L.A. Bugnet, Astronomy &#38; Astrophysics 646 (2021).","mla":"Park, J., et al. “Horizontal Shear Instabilities in Rotating Stellar Radiation Zones: II. Effects of the Full Coriolis Acceleration.” <i>Astronomy &#38; Astrophysics</i>, vol. 646, A64, EDP Sciences, 2021, doi:<a href=\"https://doi.org/10.1051/0004-6361/202038654\">10.1051/0004-6361/202038654</a>.","ama":"Park J, Prat V, Mathis S, Bugnet LA. Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration. <i>Astronomy &#38; Astrophysics</i>. 2021;646. doi:<a href=\"https://doi.org/10.1051/0004-6361/202038654\">10.1051/0004-6361/202038654</a>","ista":"Park J, Prat V, Mathis S, Bugnet LA. 2021. Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration. Astronomy &#38; Astrophysics. 646, A64.","apa":"Park, J., Prat, V., Mathis, S., &#38; Bugnet, L. A. (2021). Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration. <i>Astronomy &#38; Astrophysics</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/0004-6361/202038654\">https://doi.org/10.1051/0004-6361/202038654</a>","chicago":"Park, J., V. Prat, S. Mathis, and Lisa Annabelle Bugnet. “Horizontal Shear Instabilities in Rotating Stellar Radiation Zones: II. Effects of the Full Coriolis Acceleration.” <i>Astronomy &#38; Astrophysics</i>. EDP Sciences, 2021. <a href=\"https://doi.org/10.1051/0004-6361/202038654\">https://doi.org/10.1051/0004-6361/202038654</a>."},"oa":1,"external_id":{"arxiv":["2006.10660"]},"language":[{"iso":"eng"}],"oa_version":"Preprint","scopus_import":"1","month":"02","author":[{"last_name":"Park","full_name":"Park, J.","first_name":"J."},{"full_name":"Prat, V.","last_name":"Prat","first_name":"V."},{"first_name":"S.","full_name":"Mathis, S.","last_name":"Mathis"},{"first_name":"Lisa Annabelle","orcid":"0000-0003-0142-4000","id":"d9edb345-f866-11ec-9b37-d119b5234501","last_name":"Bugnet","full_name":"Bugnet, Lisa Annabelle"}],"date_published":"2021-02-08T00:00:00Z","date_updated":"2022-08-19T10:18:03Z","article_number":"A64","doi":"10.1051/0004-6361/202038654","acknowledgement":"The authors acknowledge support from the European Research Council through ERC grant SPIRE 647383 and from GOLF and PLATO CNES grants at the Department of Astrophysics at CEA Paris-Saclay. We thank the referee, Prof. A. J. Barker, for his constructive comments that allow us to improve the article.","publication_identifier":{"issn":["0004-6361"],"eissn":["1432-0746"]}}]