The γ Dor stars as revealed by Kepler: A key to reveal deep-layer rotation in A and F stars

The γ Dor pulsating stars present high-order gravity modes, which make them important targets in the intermediate-and low-mass main-sequence region of the Hertzsprung-Russell diagram. Whilst we have only access to rotation in the envelope of the Sun, the g modes of γ Dor stars can in principle deliver us constraints on the inner layers. With the puzzling discovery of unexpectedly low rotation rates in the core of red giants, the γ Dor stars appear now as unique targets to explore internal angular momentum transport in the progenitors of red giants. Yet, the γ Dor pulsations remain hard to detect from the ground for their periods are close to 1 day. While the CoRoT space mission first revealed intriguing frequency spectra, the almost uninterrupted 4-year photometry from the Kepler mission eventually shed a new light on them. It revealed regularities in the spectra, expected to bear signature of physical processes, including rotation, in the shear layers close to the convective core. We present here the first results of our effort to derive exploitable seismic diagnosis for mid- to fast rotators among γ Dor stars. We confirm their potential to explore the rotation history of this early phase of stellar evolution.