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

Gamma-Dor stars are ideal targets for studies of stellar innermost dynamical properties 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 gamma-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, contrast of the near-core Brunt-Väisälä frequency and rotation rate, as well as the core-to-near-core differential rotation. In the meantime, the effect of magnetism has been derived on envelope modes. We aim to revisit the inertial dip formation including core and envelope magnetism, and explore the probing power of this feature on dynamo-generated core fields. We consider a toroidal magnetic field with a bi-layer (core and envelope) Alfvén frequency. This configuration allows us to revisit the coupling problem using our knowledge on both core magneto-inertial modes and envelope magneto-gravito-inertial modes. We stay in an analytical framework to exhibit the magnetic effects on the inertial dip shape and location, setting up a laboratory towards the comprehension of magnetic effects on the dip structure. We show a shift of the inertial dip towards lower spin parameter values and a thinner dip with increasing core magnetic field, quite similar to the signature of differential rotation. The magnetic effects become sizeable when the ratio between the magnetic and the Coriolis effects is large enough. We explore the degeneracy of the magnetic effects with differential rotation. We study the detectability of core magnetism, considering observational constraints on the modes periods and potential gravito-inertial mode suppression.