Feasibility of structure inversions for gravity-mode pulsators

¹ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
e-mail: vincent.vanlaer@kuleuven.be
² Department of Astrophysics, IMAPP, Radboud University Nijmegen, PO Box 9010 6500 GL Nijmegen, The Netherlands
³ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
⁴ Guest Researcher, Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Ave, New York, NY, 10010 USA
⁵ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
⁶ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark

Received: 1 December 2022
Accepted: 2 May 2023

Abstract

Context. Gravity-mode asteroseismology has significantly improved our understanding of mixing in intermediate mass stars. However, theoretical pulsation periods of stellar models remain in tension with observations, and it is often unclear how the models of these stars should be further improved. Inversions provide a path forward by directly probing the internal structure of these stars from their pulsation periods, quantifying which parts of the model are in need of improvement. This method has been used with success in the case of solar-like pulsators, but has not yet been applied to main-sequence gravity-mode pulsators.

Aims. Our aim is to determine whether structure inversions for gravity-mode pulsators are feasible. We focus on the case of slowly rotating slowly pulsating B-type (SPB) stars.

Methods. We computed and analyzed dipole mode kernels for three variables pairs: (ρ, c), (N², c), and (N², ρ). We assessed the potential of these kernels by predicting the oscillation frequencies of a model after perturbing its structure. We then tested two inversion methods, regularized least squares (RLS) and subtractive optimally localized averages (SOLA), using a model grid computed with the MESA stellar evolution code and the GYRE pulsation code.

Results. We find that changing the stellar structure affects the oscillation frequencies in a nonlinear way. The oscillation modes for which this nonlinear dependency is the strongest are in resonance with the near-core peak in the buoyancy frequency. The near-core region of the star can be probed with SOLA, while RLS requires fine tuning to obtain accurate results. Both RLS and SOLA are strongly affected by the nonlinear dependencies on the structure differences, as these methods are based on a first-order approximation. These inversion methods need to be modified for meaningful applications of inversions to SPB stars.

Conclusions. Our results show that inversions of gravity-mode pulsators are possible in principle, but that the typical inversion methods developed for solar-like oscillators are not applicable. Future work should focus on developing nonlinear inversion methods.