The theoretical pulsation spectra of hot B subdwarfs

Static and evolutionary STELUM models

¹ Space Sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, 19C Allée du 6 Août, B-4000 Liège, Belgium
² Institut de Recherche en Astrophysique et Planétologie, CNRS, Université de Toulouse, CNES, 14 Avenue Edouard Belin, 31400 Toulouse, France
³ Département de Physique, Université de Montréal, Québec H3C 3J7, Canada

^⋆ Corresponding author; nathan.guyot@uliege.be

Received: 30 September 2024
Accepted: 17 February 2025

Abstract

Context. The Kepler and TESS space missions have revealed the rich gravity (g-)mode pulsation spectra of many hot subdwarf B (sdB) stars in detail. These spectra exhibit complex behaviors, with some stars exhibiting trapped modes interposing in the asymptotic period sequences of regular period spacing, while others do not.

Aims. We aim to thoroughly compute theoretical g-mode pulsation spectra, using our current sdB models, useful for future reference when comparing to observations. This also enables us to explore relationships with features of the internal structure of these stars. Such studies provide guidance in conducting future asteroseismic analyses of these pulsators and insights on how to interpret their outcomes.

Methods. We used our STELlar modeling from the Université de Montréal (STELUM) code to compute static (parametric) and evolutionary models of sdB stars, with different prescriptions for their chemical and thermal structures. We used our adiabatic PULSE code to compute the theoretical spectra of g-mode pulsations for degrees of ℓ = 1 to 4 and for periods between 1000 s and 15 000 s, amply covering the range of observed g-modes in these stars.

Results. We show that g-mode pulsation spectra and, in particular, the appearance of trapped modes are highly dependent on the chemical and thermal structures in the models as the star evolves, particularly in the region just above the He-burning core. Depending on the prescriptions and specific evolutionary stage, we observe mainly three types of spectra for mid to high radial-order g-modes (the ones observed in sdB stars): “flat” spectra of nearly constant period spacing; spectra with deep minima of the period spacing interposing between modes with more regular spacing (which correspond to trapped modes); and spectra showing a “wavy” pattern in period spacing. For the two latter cases, we have identified the region where the modes are trapped in the star.

Conclusions. Detailed comparisons with observed g-mode spectra ought to be carried out next to progress on this issue and constrain the internal structure of core-He burning stars via asteroseismology, in particular, for the region above the He-burning core.