A new asteroseismic diagnostic for internal rotation in $\gamma$ Doradus stars

TL;DR

This paper introduces a new asteroseismic diagnostic called Sigma, which uses period spacing slopes to measure internal rotation in rapidly rotating gamma Doradus stars, expanding the ability to probe stellar interiors.

Contribution

The study defines a novel seismic diagnostic based on period spacing non-uniformity that relates directly to internal rotation in gamma Doradus stars, especially those too rapid to show rotational splittings.

Findings

Established a one-to-one relation between Sigma and internal rotation.

Applied the diagnostic to Kepler stars, successfully measuring their internal rotation.

Enabled internal rotation measurements for lower main sequence stars.

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.