Beyond prewhitening: detection of gravity modes and their period spacings in slowly pulsating B stars using the multitaper F-test

TL;DR

This paper tackles the challenge of extracting gravity-mode frequencies in slowly pulsating B stars without relying on traditional, iterative prewhitening. It introduces the multitaper NUFFT periodogram (mtNUFFT) and its associated multitaper F-test to distinguish purely periodic g-modes from damped/quasi-periodic signals in Kepler time series, offering a fast, objective, and scalable alternative. Applying this method to 38 SPB stars, the authors demonstrate efficient recovery of known g-modes, identify new candidates, and uncover multiple period-spacing patterns, while enabling direct comparison with prior studies. The approach has the potential to expedite mode identification and constrain interior physics across large samples, including rotation, mixing, and excitation mechanisms, and lays groundwork for extending non-adiabatic asteroseismology to broader stellar populations.

Abstract

Gravity modes in main-sequence stars have traditionally been studied using a prewhitening approach, which iteratively identifies modes in the Fourier domain and subsequently tunes their frequencies, amplitudes, and phases through time-domain regression. While effective, this method becomes inefficient when analysing large volumes of long time-series data and often relies on subjective stopping criteria to determine the number of iterations. We aim to perform frequency extraction of gravity modes in slowly pulsating B (SPB) stars using a statistically robust, data-driven approach based on advanced power spectrum and harmonic analysis techniques. Our approach employs the multitaper non-uniform fast Fourier transform, mtNUFFT, a power spectrum estimator that addresses several statistical limitations of traditional methods such as the Lomb-Scargle periodogram. We apply its extension, the multitaper F-test, to extract coherent gravity modes from 4-year Kepler light curves of SPB stars and to search for period spacing patterns among the extracted modes. The multitaper F-test enables fast and accurate extraction of the properties of gravity modes with quasi-infinite lifetimes, preferentially selecting modes that exhibit purely periodic behaviour. Although the method typically extracts fewer frequencies than conventional prewhitening, it recovers most known modes and, in some cases, reveals new ones. We also find evidence for gravity modes with long but finite lifetimes, and detect more than one period spacing pattern in some of the studied SPB stars. Overall, the multitaper F-test offers a more objective and statistically sound alternative to prewhitening. It scales efficiently to large datasets containing thousands of pulsators, and has the potential to facilitate mode identification and to distinguish between the different excitation mechanisms operating in SPB stars.

Figures (32)

• Figure 1: Comparison of F-test detections for the SPB star KIC7760680 using two significance thresholds, $p < 1/N$ and $p < 10^{-3}$.The lower panel illustrates that adopting the more relaxed threshold of $p < 0.001$ rather than $p < 1/N$ increases sensitivity (yielding 14 additional detections in the figure), but some of these, particularly in the low-power region between 0.4 and 0.5 days, appear noise-like (see Section \ref{['subsec:multistep']}).
• Figure 2: Illustration of the multi-step procedure to detect g modes in KIC7760680 using the F-test. The five steps are described in Section \ref{['subsec:multistep']}.
• Figure 3: Frequencies extracted using the multi-step mtNUFFT/F-test and their comparison with estimates in van_beeck_2021 for the SPB KIC7760680. The comparison is made with frequencies extracted by each of the five prewhitening strategies, as well as those consistent across all strategies (dotted grey lines). Values of $NW=4$ and $K=7$ with a p-value $p < 0.01$ were used.
• Figure 4: Amplitude and phase comparison of g modes estimated using the F-test procedure described in this paper and those computed in van_beeck_2021 using Strategy 3 for KIC7760680. The comparison includes modes in our F-test catalogue that have a 3$\sigma$ (or 6$\sigma$) match with those reported by van_beeck_2021. To highlight relative shifts unambiguously, phase differences are shown as absolute values, mapped modulo $\pi/4$. The 68% and 98% confidence intervals are indicated by dark and light shaded regions, respectively, and are computed using the jackknife uncertainty estimates of amplitude and phase. The corresponding amplitude, phase, and uncertainty values are listed in Table \ref{['tab:KIC7760680_match']}. Note that although the amplitude plot includes the confidence intervals, they are too small to be visible.
• Figure 5: Effect of changing the time–bandwidth product $NW$ and number of tapers $K$ from $NW=4, K=7$ (orange) to $NW=3, K=5$ (blue) for KIC7760680. The top panel shows the mtNUFFT periodograms, while the middle and bottom panels display the corresponding F-statistics and p-values. The bottom panel also includes a $p < 10^{-12}$ threshold, highlighting that $NW=4$ yields three detections, whereas $NW=3$ produces none.