Exploring the probing power of γ Dor's inertial dip for core magnetism: The case of a toroidal field

Context. γ Dor stars are ideal targets for studies of the innermost dynamical properties of stars, due to their rich asteroseismic spectrum of gravity modes. Integrating internal magnetism to the picture appears as the next milestone of detailed asteroseismic studies, for its prime importance on stellar evolution. The inertial dip in prograde dipole modes period-spacing pattern of γ Dors stands out as a unique window on the convective core structure and dynamics. Recent studies have highlighted the dependence of the dip structure on core density stratification, the contrast of the near-core Brunt-Väisälä frequency and rotation rate, as well as the core-to-near-core differential rotation. In addition, the effect of envelope magnetism has been derived on low-frequency magneto-gravito-inertial waves. Aims. We revisited the inertial dip formation including core and envelope magnetism, and explored the probing power of this feature on dynamo-generated core fields. Methods. We considered as a first step a toroidal magnetic field with a bi-layer (core and envelope) Alfvén frequency. This configuration allowed us to revisit the coupling problem using our knowledge on both core magneto-inertial modes and envelope magneto-gravito-inertial modes. Using this configuration, we were able to stay in an analytical framework to exhibit the magnetic effects on the inertial dip shape and location. This configuration allowed a laboratory to be set up that moves us towards the comprehension of magnetic effects on the dip structure. Results. We show a shift of the inertial dip towards lower spin parameter values and a thinner dip with increasing core magnetic field’s strength, quite similar to the signature of differential rotation. The magnetic effects become sizeable when the ratio of the magnetic to the Coriolis effects is high enough. We explored the potential degeneracy of the magnetic effects with differential rotation. We studied the detectability of core magnetism, considering both observational constraints on the periods of the modes and potential gravito-inertial mode suppression.