Asteroseismology and buoyancy glitch inversion with Fourier spectra of gravity mode period spacings

Aims. We investigated the small, quasi-periodic modulations seen in the gravity-mode period spacings (ΔPk) 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. Methods. We computed the Fourier transform of the period-spacing series, FT(ΔPk), as a function of radial order k. We show that FT(ΔPk) traces the radial derivative of the normalized glitch profile δN/N with respect to the normalized buoyancy radius; peaks in FT(ΔPk) 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(δP/P), directly recovers the absolute value of the glitch profile |δN/N|, enabling a straightforward inversion for the internal structure. Results. The dominant FT(ΔPk) frequency correlates tightly with the central hydrogen abundance (Xc), and thus with stellar age, for slowly pulsating B-stars, with only weak mass dependence. Applying the technique to Modules for Experiments in Stellar Astrophysics (MESA) stellar models and to observed slowly pulsating B-stars and γ Dor pulsators, we find typical glitch amplitudes δN/N ≲ 0.01 and derivative magnitudes ≲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.