A new asteroseismic diagnostic for internal rotation in γ Doradus stars

With four years of nearly continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to γ Doradus stars. In particular, several analyses have demonstrated the possibility to detect non-uniform period spacings, which have been predicted to be directly related to rotation. In this paper, we define a new seismic diagnostic for rotation in γ Doradus stars which are too rapidly rotating to present rotational splittings. Based on the non-uniformity of their period spacings, we define the observable Σ as the slope of the period spacing when plotted as a function of period. We provide a one-to-one relation between this observable Σ and the internal rotation, which applies widely in the instability strip of γ Doradus stars. We apply the diagnostic to a handful of stars observed by Kepler. Thanks to g modes in γ Doradus stars, we are now able to determine the internal rotation of stars on the lower main sequence, which is still not possible for Sun-like stars.