Gravity-mode period spacings and near-core rotation rates of 611 $\gamma$ Doradus stars with \textit{Kepler}

TL;DR

This study analyzes 611 b df3r stars observed by Kepler, revealing their internal rotation rates and period-spacing patterns, which provide insights into stellar interior physics and challenge existing theoretical predictions.

Contribution

It is the first large-scale survey of b df3r stars using Kepler data, identifying period-spacing patterns and measuring near-core rotation rates for a significant sample.

Findings

Most stars have near-core rotation rates around 1 c/d.

Many stars show longer period spacings than theoretical predictions.

Interiors generally rotate faster than the surface, but by less than 5%.

Abstract

We report our survey of $\gamma$\,Doradus stars from the 4-yr \textit{Kepler} mission. These stars pulsate mainly in g modes and r modes, showing period-spacing patterns in the amplitude spectra. The period-spacing patterns are sensitive to the chemical composition gradients and the near-core rotation, hence they are essential for understanding the stellar interior. We identified period-spacing patterns in 611 $\gamma$\,Dor stars. Almost every star pulsates in dipole g modes, while about 30\% of stars also show clear patterns for quadrupole g modes and 16\% of stars present r mode patterns. We measure periods, period spacings, and the gradient of the period spacings. These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the Traditional Approximation of Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes. Most stars have a near-core rotation rate around $1$\,$\mathrm{c/d}$ and an asymptotic spacing around 4000\,s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. 11 stars show rotational splittings with fast rotation rates. We compared the observed slope--rotation relation with the theory and find a large spread. We detected rotational modulations in 58 stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5\%.