Period spacings of $\gamma$ Doradus pulsators in the Kepler field: detection methods and application to 22 slow rotators

TL;DR

This paper introduces two automated methods for detecting period spacings in $b3$ Doradus stars using Kepler data, revealing a relation between period spacing slopes and rotational splittings, and identifying binary contamination.

Contribution

It presents new automated detection techniques for period spacings and their slopes, and applies them to 22 stars, uncovering the relation between rotation and period spacings and correcting for binary effects.

Findings

Cross-correlation method outperforms Fourier transform in detection accuracy.

Established the first observational relation between period spacing slopes and rotational splittings.

Identified binary stars misinterpreted as rotational splittings.

Abstract

In $\gamma$ Doradus stars, the g-mode period spacing shows an approximately linear relation with period. The slope is a new asteroseismic diagnostic, related to the rotation rate and the azimuthal order $m$. We report two automated methods, the `moving-window Fourier transform' and the `cross-correlation', to detect and measure the period spacings based on four-year light curves from the \textit{Kepler} satellite. The results show that the cross-correlation method performs better at detecting the period spacings and their slopes. In this paper, we apply our method to 22 $\gamma$ Dor stars with g-mode multiplets split by rotation. The rotation periods are similar to the g-mode period spacings, causing the multiplets to overlap. To clarify the overlapping patterns, we use the \'echelle diagram and introduce a `copy-shift' diagram to discern and measure the splittings. The first observational relation between slopes and splittings is shown. The slope deviates from zero when the splitting increases, as the theory predicts. We found that what appears to be rotational splittings in two stars is in fact caused by two nearly-identical overlapping patterns from binaries.