Measuring core rotation in γ Doradus stars from dips in the gravity-mode period spacing pattern

Asteroseismology provides unique tools to constrain the transport of angular momentum throughout stellar evolution, a major caveat in stellar modeling. Dips in the gravity-mode period spacing vs period diagram of γ Doradus stars, already proven to form from the chemical discontinuities in the radiative zone, were also shown to arise from the interaction of gravito-inertial modes in the radiative zone with pure inertial modes in the convective interior of these stars. The analysis of these mixed modes brings unprecedented insight into the convective interior. The inertial dip formation has been described by Tokuno & Takata (2022) and the Lorentzian shape of the dip is derived analytically for Kelvin modes with a solid body rotation. We aim to extend the formalism developed in this pioneering work to the case of a two-zone rotation profile, and investigate the detectability of such differential rotation inside γ Doradus stars. We solve the coupling equation numerically, which was further compared to an analytical derivation of the Lorentzian profile. We investigate the detectability of radial differential rotation in Kepler data. We show that, with an increasing differential rotation rate from the envelope to the core, the dip gets shifted to shorter periods, and gets deeper and narrower. Studying the dip structure and location in asteroseismic data might allow accessing radial differential rotation and better understand the transport of angular momentum in main-sequence stars.