Inferring main-sequence stage and buoyancy-glitch amplitudes from Fourier spectra of gravity-mode period spacings: Ensemble Analysis of 26 Slowly Pulsating B Stars

TL;DR

The paper demonstrates that the Fourier spectra of gravity-mode period spacings $FT(\Delta P)$ and their perturbations $FT(\delta P)$ in 26 SPB stars encode the near-core buoyancy structure and the star’s main-sequence age. By transforming to the co-rotating frame and applying a calibrated relation between the dominant variation frequency $u$ and the central hydrogen mass fraction $X_c$, the authors obtain $X_c$ values largely consistent with detailed forward modelling, while also constraining buoyancy-glitch amplitudes via $|\delta N/N|$ to be typically below $2\%$. The approach yields a fast, ensemble-capable route to gravito-inertial seismology, enabling efficient characterization of rotation, mixing, and evolutionary state for large samples in current and future space missions. The results support the use of $FT(\Delta P)$ as a robust diagnostic for SPB interiors, with caveats for very fast rotators and potential magnetic effects, and point to future improvements by incorporating variable chemical compositions and envelope mixing.

Abstract

Gravito-inertial-mode asteroseismology of intermediate-mass main-sequence stars took off with the 5-month uninterrupted light curves of the CoRoT space mission. It was developed in detail from the 4-year-long Kepler light curves, which provided a practical means to measure the rotation frequency in the transition layer between the convective core and the radiative envelope, where the local buoyancy frequency reaches a maximum. Recently, a new buoyancy glitch inversion method based on the Fourier spectra of gravity-mode period spacings was developed to probe that region further (Guo 2025). We aim to exploit the information contained in the variability of gravity-mode period spacings ($ΔP$) in Slowly Pulsating B (SPB) stars with rotation. We investigate how well the main-sequence evolutionary stage can be inferred from this variability. We extract the frequency and amplitude of the variability in $ΔP$ from the Fourier spectrum (FT). Both the period spacing $ΔP$ and its periodic perturbations $δP$ (deviations from their asymptotic values) are used. The measured dominant frequency of $ΔP$ allows us to infer the central hydrogen mass fraction, $X_c$, which is a main-sequence age indicator. The inferred $X_c$ values from $FT(ΔP)$ mostly agree with previous results reported in the literature based on forward modelling of individual identified mode frequencies. We find that the buoyancy glitches $δN/N$ in SPB stars are generally less than $2\%$ in amplitude. Ensemble asteroseismic modeling of gravity-mode pulsators can now be carried out efficiently with our novel $FT(ΔP)$ method once the internal rotation rate of the pulsators is known. Our methodology offers a fast method for gravito-inertial asteroseismic applications in the era of ongoing and future space-based observations.

Figures (5)

• Figure 1: Left: Observed gravity-mode period spacings of 26 SPB stars in Ped21. Right: Period spacings transformed to the co-rotating frame.
• Figure 2: Fourier spectra of g-mode relative period spacings $\Delta P/P$ (blue) and period perturbations $\delta P/P$ (orange) for 24 SPB pulsators. The adopted peaks, which indicate the chemical transition points, are marked by circles.
• Figure 3: Lower: Amplitudes of relative period spacings $FT(\Delta P/P)$ for 26 SPB stars. Upper: Amplitudes of relative period perturbations $FT(\delta P/P)$, which are equal to the amplitudes of buoyancy glitches $\delta N/N$. The right panels show the corresponding histograms.
• Figure 4: Central hydrogen mass fraction $X_c$ of 26 SPB stars obtained by Pedersen et al. (2021) and (2022) (black and gray squares, respectively) and those inferred from Fourier spectra of period spacings (circles). Red symbols lie within $2\sigma$ of the Pedersen et al. results, while purple symbols do not.
• Figure 5: Upper: Observed g-mode period spacings in HD 50230. Lower: Fourier spectra of relative period spacings $\Delta P/P$ and relative pulsation-period perturbations $\delta P/P$. The dominant peak is at $u=0.375$, indicating $X_c \approx 0.28$.