Constraining differential rotation in γ Doradus stars from the properties of inertial dips

Context. The presence of dips in the gravity mode period spacing versus period diagram of γ Doradus stars is now well established thanks to recent asteroseismic studies. Such Lorentzian-shaped inertial dips arise from the interaction of gravito-inertial modes in the radiative envelope of intermediate-mass main sequence stars with pure inertial modes in their convective core, and allow us to study stellar internal properties. This window onto stellar internal dynamics is extremely valuable in the context of the understanding of angular-momentum transport inside stars, as it allows us to probe rotation in their core. Aims. We investigate the signature and the detectability of a differential rotation between the convective core and the near-core region inside γ Doradus stars from the properties of inertial dips. Methods. We studied the coupling between gravito-inertial modes in the radiative zone and pure inertial modes in the convective core in the sub-inertial regime, allowing for a two-zone differential rotation from the two sides of the core-to-envelope boundary. We solved the coupling equation numerically and matched the result to an analytical derivation of the Lorentzian dip properties. We then used typical values of measured near-core rotation and buoyancy travel time to infer ranges of parameters for which differential core to near-core rotation would be detectable in current Kepler data. Results. We show that increasing the convective core rotation with respect to the near-core rotation leads to a shift of the period of the observed dip to lower periods. In addition, the dip gets deeper and thinner as the convective core rotation increases. We demonstrate that such a signature is detectable in Kepler data, given appropriate dip-parameter ranges and near-core structural properties. Conclusions. Studying the dip properties in asteroseismic data thus allows us to access core to near-core radial differential rotation and to better understand the transport of angular momentum at convective–radiative interfaces in intermediate-mass main sequence stars.