Period spacings of gravity modes in rapidly rotating magnetic stars

II. The case of an oblique dipolar fossil magnetic field

¹ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
e-mail: vincent.prat@cea.fr
² LESIA, Paris Observatory, PSL University, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195 Meudon, France
³ Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁴ Dept. of Astrophysics, IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands
⁵ Max Planck Institute for Astronomy, Koenigstuhl 17, 69117 Heidelberg, Germany

Received: 23 December 2019
Accepted: 12 March 2020

Abstract

Context. Stellar internal magnetic fields have recently been shown to leave a detectable signature on period spacing patterns of gravity modes.

Aims. We aim to investigate the effect of the obliquity of a mixed (poloidal and toroidal) dipolar internal fossil magnetic field with respect to the rotation axis on the frequency of gravity modes in rapidly rotating stars.

Methods. We used the traditional approximation of rotation to compute non-magnetic modes, and a perturbative treatment of the magnetic field to compute the corresponding frequency shifts. We applied the new formalism to HD 43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose field has an obliquity angle of about 80°.

Results. We find that frequency shifts induced by the magnetic field on high-radial-order gravity modes are larger with increasing obliquity angle, when the magnetic axis is closer to the equatorial region, where these modes are trapped. The maximum value is reached for an obliquity angle of 90°. This trend is observed for all mode geometries.

Conclusions. Our results predict that the signature of an internal oblique dipolar magnetic field is detectable using asteroseismology of gravity modes.