Is a 1D perturbative method sufficient for asteroseismic modelling of β Cephei pulsators?

Implications for measurements of rotation and internal magnetic fields

¹ Université Paris-Saclay, Université de Paris, Sorbonne Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
² Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
³ Institute of Science and Technology Austria (ISTA), Am Campus 1, Klosterneuburg, Austria
⁴ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
⁵ IRAP, Université de Toulouse, CNRS, UPS, CNES, 14 avenue Édouard Belin, F-31400 Toulouse, France
⁶ Department of Astrophysics, IMAPP, Radboud University Nijmegen, PO Box 9010 6500 GL Nijmegen, The Netherlands
⁷ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
⁸ LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS, 92190 Meudon, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 15 September 2025
Accepted: 10 November 2025

Abstract

Context. Asymmetries in the observed rotational splittings of a multiplet contain information about the star’s rotation profile and internal magnetic field. Moreover, the frequency regularities of multiplets can be used for mode identification. However, to exploit this information, highly accurate theoretical predictions are needed.

Aims. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then place these differences between 1D and 2D methods in the context of asteroseismic measurements of internal magnetic fields. We only focus on the asymmetries and not on possible additional frequency peaks that can arise when the magnetic and rotation axis are misaligned.

Methods. We coupled the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compared the oscillation predictions with the results from the 2D TOP pulsation code. We focused on zero-age main-sequence models representative of rotating β Cephei pulsators spinning at up to 20 per cent of the critical Keplerian rotation rate. Specifically, we investigated low-radial-order gravity and pressure modes.

Results. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. We report differences in predicted mode multiplet asymmetries of mostly below 0.06 d⁻¹. Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging.

Conclusions. Differences in the predicted mode asymmetries of a rotating star between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with n_pg ≥ 2 modes if the internal rotation is roughly below 10 per cent of the Keplerian critical rotation frequency for (aligned) magnetic fields of the order of a few hundred kilogauss. While the differences between the 1D and 2D frequency predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars with identified low-order modes.