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

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.

💡 Research Summary

This paper introduces a statistically robust, data‑driven method for extracting gravity‑mode frequencies and period‑spacing patterns in slowly pulsating B (SPB) stars, based on the multitaper non‑uniform fast Fourier transform (mtNUFFT) and its extension, the multitaper F‑test. Traditional analyses of SPB stars rely on Lomb‑Scargle periodograms combined with iterative pre‑whitening, which become inefficient for long, high‑quality Kepler light curves and depend on subjective stopping criteria. The mtNUFFT computes a power spectrum by averaging several tapered spectra obtained with discrete prolate spheroidal sequences (DPSS) and a non‑uniform FFT, thereby reducing spectral leakage and improving detection of low‑SNR signals. The multitaper F‑test then evaluates each candidate frequency against an F‑distribution to distinguish truly coherent (quasi‑infinite lifetime) modes from those with finite lifetimes, using a strict significance threshold (e.g., α = 0.01).

Applying this pipeline to 38 SPB stars with four‑year Kepler data, the authors recover >95 % of previously identified modes while extracting roughly 20 % fewer frequencies, demonstrating higher specificity. Importantly, the method uncovers new gravity modes, identifies multiple period‑spacing sequences in several stars, and detects signatures of long‑lived but damped modes that appear as broadened peaks in traditional spectra. These findings provide tighter constraints on internal rotation, mixing, and possible magnetic effects.

From a computational standpoint, mtNUFFT scales as O(N log N) and its multitaper averaging is trivially parallelizable, yielding a 2–3× speed‑up over conventional pre‑whitening pipelines. Consequently, the approach is well‑suited for large‑scale asteroseismic surveys containing thousands of pulsators. The authors conclude that the multitaper F‑test offers an objective, statistically sound alternative to pre‑whitening, facilitating reliable mode identification and opening new avenues for probing angular momentum transport and excitation mechanisms in SPB stars. Future work will focus on quantifying mode lifetimes and incorporating the detected damped modes into forward asteroseismic modelling.