Period spacings of γ Doradus pulsators in theKeplerfield: detection methods and application to 22 slow rotators

Abstract

In γ 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 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 γ 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 theéchelle 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.

Gravity-mode period spacings and near-core rotation rates of 611 γ Doradus stars with Kepler

“…Rossby modes are the third most common modes (11.5%). Apart from these three modes, we also see l = 1, m = 0 and l = 1, m = −1 modes with percentages of 3.0% and 2.3%, respectively, which were mainly found in the slow rotators reported by Li et al (2019a). 11 fast rota-tors with splittings are detected in this work, which will be described in Section 6.…”

“…The distribution increases rapidly after 0.4 d −1 and drops slowly after ∼ 1 d −1 . The most rapid rotators are KIC 8458690A and KIC 8458690B with f rot ∼ 3.01 d −1 , whose two identical period-spacing patterns form 'splittings' reported by Li et al (2019a). However, many stars rotate less quickly than expected, which forms an excess at f rot 0.4 d −1 in Fig.…”

“…• l = 1, m = 0 and l = 1, m = −1 g modes: they are marked by the yellow circles and the red rectangles. These two modes are rare (for m = 0) or absent (for m = −1) in rapid rotators but are seen in the slow rotators reported by Li et al (2019a). Due to the slow rotation rate, the rotational effect is not strong so the period spacings in those modes remain nearly identical.…”

“…with the assumption that the period spacing changes linearly with period. Here, P i is the i th pulsation period, P 0 is the first pulsation period, ∆P 0 is the first period spacing, Σ is the slope in the linear assumption, n ≡ (1+Σ) i −1 Σ is the normalised index, and is the ratio P 0 /∆P 0 (Li et al 2019a). The x-axis of the sidewayséchelle diagram is the observed period and the y-axis is the difference between the observed and fitted periods from Eq.…”

“…1.00(2) -0.055(5) -0.0148 (8) 7701947 0.32(1) -0.0281(1) -0.0165(5) 7778114 0.50(2) -0.0355(5) -0.0202(2) 8523871 0.32(5) -0.075(5) -0.067(7) 9595743 0.42(1) -0.044(4) -0.027(7) 12102187 0.291(6) -0.017 (7) -0.019(9) 12401800 0.43(1) -0.0308(8) -0.021(1) Li et al (2019a) reported 22 γ Dor stars in which rotational splittings were seen. The rotation rates of those stars are generally slow (with splitting smaller than 0.2 d −1 ), hence their period-spacing patterns with different azimuthal orders m overlap each other.…”