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.