Abstract
With four years of nearly-continuous photometry from Kepler, we are finally
in a good position to apply asteroseismology to \$\gamma\$ 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 the present work, we define a new seismic diagnostic for
rotation in \$\gamma\$ Doradus stars that are too rapidly rotating to present
rotational splittings. Based on the non uniformity of their period spacings, we
define the observable \$\Sigma\$ as the slope of the period spacing when plotted
as a function of period. We provide a one-to-one relation between this
observable \$\Sigma\$ and the internal rotation, which applies widely in the
instability strip of \$\gamma\$ Doradus stars. We apply the diagnostic to a
handful of stars observed by Kepler. Thanks to g-modes in \$\gamma\$ 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.
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