Perturbative analysis of the effect of a magnetic field on gravito-inertial modes

Context. Magnetic fields have been measured recently in the cores of red giant stars thanks to their effects on stellar oscillation frequencies. The search for magnetic signatures in pulsating stars, such as γ Doradus (γ Dor) or slowly pulsating B stars, requires us to adapt the formalism developed for slowly rotating red giants to rapidly rotating stars. Aims. We perform a theoretical analysis of the effects of an arbitrary magnetic field on high radial order gravity and Rossby modes in a rapidly rotating star. Methods. The magnetic effects were treated as a perturbation. For high radial order modes, the contribution of the radial component of the magnetic field is likely to dominate over the azimuthal and latitudinal components. The rotation is taken into account through the traditional approximation of rotation. Results. General expressions of the frequency shift induced by an arbitrary radial magnetic field are derived. Approximate analytical forms are obtained in the high-order, high-spin-parameter limits for the modes most frequently observed in γ Dor stars. We propose simple methods to detect seismic magnetic signatures and measure possible magnetic fields in such stars. Conclusions. These methods offer new possibilities to look for internal magnetic fields in future observations, such as those of the PLATO mission, or of revisiting existing Kepler or TESS data. © 2024 Oxford University Press. All rights reserved.