Probing the internal magnetism of stars using asymptotic magneto-asteroseismology

Context. Our knowledge of the dynamics of stars has undergone a revolution through the simultaneous large amount of high-quality photometric observations collected by space-based asteroseismology and ground-based high-precision spectropolarimetry. They allowed us to probe the internal rotation of stars and their surface magnetism in the whole Hertzsprung-Russell diagram. However, new methods should still be developed to probe the deep magnetic fields in these stars.Aims. Our goal is to provide seismic diagnoses that allow us to probe the internal magnetism of stars.Methods. We focused on asymptotic low-frequency gravity modes and high-frequency acoustic modes. Using a first-order perturbative theory, we derived magnetic splittings of their frequencies as explicit functions of stellar parameters.Results. As in the case of rotation, we show that asymptotic gravity and acoustic modes can allow us to probe the different components of the magnetic field in the cavities in which they propagate. This again demonstrates the high potential of using mixed-modes when this is possible.