Measuring internal magnetism in gamma-dor stars from dips in the gravity-mode period spacing pattern.

Asteroseismology probes deep dynamical processes including magnetism in the interior of stars. As such, it provides us unique constrains on the transport of angular momentum throughout stellar evolution. Its modelling is one of the major challenges for the theory of stellar evolution with major impact in different fields of Astrophysics. In this framework, the presence of dips in the gravity modes period spacing vs period diagram of gamma Doradus stars is now well established by recent asteroseismic studies from the Kepler mission. One key mechanism has been demonstrated to result in such dips formation with a well-defined period and shape: the interaction of gravito-inertial modes propagating in the radiative envelope of these stars with pure inertial modes propagating in their convective core. The analysis of these mixed modes brings unprecedented insights into the rotation of the convective core of such stars. A deep understanding of the dip formation has been described by Tokuno & Takata (2022), and the Lorentzian shape of the dip has been derived analytically for Kelvin modes in a star rotating as a solid-body. In this work, we aim to extend their formalism to the case of magnetic stars because magnetic fields are one of the main serious candidates to efficiently redistribute angular momentum throughout stellar evolution. For this, considering a toroidal magnetic topology corresponding to a uniform Alfvén frequency in each region, we study the waves behaviour both in the radiative envelope and in the convective core and we demonstrate that the MHD coupling problem shows similarities with the hydrodynamic case. We identify the three main influences of the magnetic field: a shift of the baseline, an additional slope of the period-spacing pattern and a shift of the location of the dip in the inertial frame. We extend the study to non-Kelvin modes previously detected in gamma-Dor stars. Our work thus demonstrates the remarkable potentiality of studying such dips to probe internal stellar magnetism and provides predictions for further detection in asteroseismic data.