Asteroseismology and Buoyancy Glitch Inversion with Fourier Spectra of Gravity Mode Period Spacings

TL;DR

This paper introduces a Fourier-based method to analyze buoyancy glitches in gravity-mode period spacings, enabling detailed internal structure inferences and stellar age estimations in pulsating stars.

Contribution

The paper presents a novel Fourier transform technique to invert buoyancy glitches from g-mode period spacings, improving internal stellar structure diagnostics.

Findings

Fourier transform of period spacings reveals glitch locations and sharpness.

The dominant frequency correlates with stellar age and hydrogen abundance.

Typical glitch amplitudes are around 1%, concentrated at chemical gradients.

Abstract

We investigate the small, quasi-periodic modulations seen in the gravity-mode period spacings of pulsating stars. These ``wiggles'' are produced by buoyancy glitches -- sharp features in the buoyancy frequency ($N$) caused by composition transitions and the convective-radiative interface. Our method takes the Fourier transform of the period-spacing series, $FT(\Delta P_k)$ as a function of radial order $k$. We show that $FT(\Delta P_k)$ traces the radial derivative of the normalized glitch profile $\delta N/N$ with respect to the normalized buoyancy radius; peaks in $FT(\Delta P_k)$ therefore pinpoint jump/drop locations in $N$ and measure their sharpness. We also note that the Fourier transform of relative period perturbations (deviations from asymptotic values), $FT(\delta P/P)$, directly recovers the absolute value of the glitch profile $|\delta N/N|$, enabling a straightforward inversion for the internal structure. The dominant $FT(\Delta P_k)$ frequency correlates tightly with central hydrogen abundance ($X_c$) and thus with stellar age for slowly pulsating B-stars, with only weak mass dependence. Applying the technique to MESA stellar models and to observed slowly pulsating B-stars and $\gamma$ Dor pulsators, we find typical glitch amplitudes $\delta N/N \lesssim 0.01$ and derivative magnitudes $\lesssim 0.1$, concentrated at chemical gradients and the convective boundary. This approach enables fast, ensemble asteroseismology of g-mode pulsators, constrains internal mixing and ages, and can be extended to other classes of pulsators, with potential links to tidal interactions in binaries.