Constraining core-to-envelope differential rotation in gamma-Doradus stars from inertial dips properties

The presence of dips in the gravito-inertial modes period-spacing pattern of γ-Dor stars is now well established by recent asteroseismic studies. Such Lorentzian-shaped inertial dips arise from the interaction of gravito-inertial modes propagating in the radiative envelope of intermediate-mass main sequence stars with pure inertial modes that propagate in their convective core. We aim to investigate the signature of a differential rotation between the convective core and the near-core region inside γ-Dor stars from the inertial dip properties. We first describe the bi-layer rotation profile we use and the approximations we adopt to maintain the analyticity of our study. We then describe our results on the inertial dip formation, location, and shape. We derive a modified Lorentzian profile and we compare it to the previously obtained results in the solid-body rotation case. This work highlights the inertial dips' probing power of the convective core rotation, an important observable in the context of the understanding of the angular momentum transport and chemicals mixing inside stars.