{γ} Doradus stars as test of angular momentum transport models

Helioseismology and asteroseismology of red giant stars have shown that the distribution of angular momentum in stellar interiors, and its evolution with time remains an open issue in stellar physics. Owing to the unprecedented quality of Kepler photometry, we are able to seismically infer internal rotation rates in \gamma Doradus stars, which provide the MS counterpart to the red-giants puzzle. We confront these internal rotation rates to stellar evolution models with rotationally induced transport of angular momentum, in order to test angular momentum transport mechanisms. We used a stellar model-independent method developed by Christophe et al. in order to obtain seismically inferred, buoyancy radii and near-core rotation for 37 \gamma Doradus stars observed by Kepler. We show that the buoyancy radius can be used as a reliable evolution indicator for field stars on the MS. We computed rotating evolutionary models including transport of angular momentum in radiative zones, following Zahn and Maeder, with the CESTAM code. This code calculates the rotational history of stars from the birth line to the tip of the RGB. The initial angular momentum content has to be set initially, which is done by fitting rotation periods in young stellar clusters. We show a clear disagreement between the near-core rotation rates measured in the sample and the rotation rates obtained from evolutionary models including rotationally induced transport following Zahn (1992). These results show a disagreement similar to that of the Sun and red giant stars. This suggests the existence of missing mechanisms responsible for the braking of the core before and along the MS. The efficiency of the missing mechanisms is investigated. The transport of angular momentum as formalized by Zahn and Maeder cannot explain the measurements of near-core rotation in main-sequence intermediate-mass stars we have at hand.