Seismic Cartography of White-Dwarf Interiors From the Toulouse-Montréal Optimal-Design Approach

Abstract

Probing internal properties of white-dwarf stars has been amongst the earliest objectives of asteroseismology, following the first discovery in the late 1960s of non-radial pulsations in these evolved compact stars. It was swiftly recognized that white-dwarf pulsators could offer new opportunities to unravel their inner structure and dynamics from the observed low-degree, low-order gravity (g-)modes. From these early days on, many approaches have been attempted to fully exploit this potential, with various levels of success. Here, we review the most recent efforts from our group to perform a complete seismic cartography of white-dwarf interiors. Our approach involves new models incorporating flexible internal profiles for the main chemical constituents (H, He, C, and O) that are optimized, along with other fundamental parameters (Teff and log g), to determine the stellar structure that best reproduces the observed period spectrum of a given star. The method is meant to reduce as much as possible solution dependency relative to stellar evolution uncertainties. The outcome is a full seismic model of the pulsating white-dwarf star under consideration, including its internal core and envelope chemical stratification. Searching for seismic solutions that do not depend on stellar evolution calculations is a key requirement of this strategy. Late stages of evolution that ultimately shape the inner structure of white dwarf stars are known to rely on still uncertain processes. One of our hopes is to be able to test these processes, therefore requiring that seismic models do not incorporate strong preconceived expectations from evolutionary models. We present and discuss results obtained so far from the application of this method to a handful of DB and DA pulsators. In all cases, significant qualitative improvements of the seismic solutions is obtained, providing as an outcome strong quantitative constraints on the core chemical structure of these stars. In particular, we consistently find that the homogeneous C/O mixed core, inherited from the core helium-burning phase, is ∼40% larger (in mass) and ∼15% richer in oxygen (in mass fraction) than expected from standard evolution calculations. Such results constitute precious guidelines for modeling late stages of stellar evolution and better understanding their constitutive physics. As an illustration of this, we show that the central oxygen mass fraction measured by seismology can indeed be reproduced when helium-burning cores experience the so-called breathing pulses. The latter are usually suppressed in standard evolution calculations, as the result of an old debate whether such events are real or numerical artefacts. In other words, our seismic determination of the central amount of oxygen in white dwarfs provides evidence that breathing pulses occurred in the core of their progenitors and should not be dismissed in models after all.

Current challenges in the physics of white dwarf stars

“…As such, white dwarf asteroseismology is a promising tool to answer current questions in other subfields of stellar astrophysics. In particular, the C-O abundance profiles of white dwarfs contain critical information on the difficult-to-model convective mixing at the boundary of the He-fusing cores of red giant stars [72,73,74], as well as on the poorly constrained 12 C(α, γ) 16 O reaction rate, dubbed "the holy grail of nuclear astrophysics" [75,76,77,78,79,80]. Furthermore, the internal structure of high-mass white dwarfs that descend from double white dwarf mergers (including hot DQs) [81] may provide valuable constraints for numerical simulations of such mergers.…”

“…Because of this phenomenon, asteroseismology provides a powerful method to constrain the internal stratification of white dwarfs and to determine the thicknesses of their He and H layers [56]. In contrast, the degenerate interior of a white dwarf is difficult (but not impossible [73,74]) to survey using pulsations since the eigenfunctions have very low amplitudes in those regions.…”

On Trapped Modes in Variable White Dwarfs as Probes of the 12C(α, γ)16O Reaction Rate

“…The root-mean-square residuals to the 150−400 s low-order g-mode periods are typically in the range σ rms 0.3 s (e.g., Bischoff-Kim et al 2014), for a fit precision of σ rms /P 0.3%. Lower root-mean-square residuals using ab initio WD models are possible (Charpinet et al 2019;Giammichele et al 2022), although see De Gerónimo et al (2019).…”

Carbon–Oxygen Phase Separation in Modules for Experiments in Stellar Astrophysics (MESA) White Dwarf Models

“…It has been suggested that WD asteroseismology could be used to constrain interior structure and composition of WD models, and ultimately may even yield constraints on the 12 C (α, γ) 16 O reaction rate as a result (Metcalfe et al 2001(Metcalfe et al , 2002Fontaine & Brassard 2002;Metcalfe 2003). Indeed, some recent studies have attempted to use seismology to constrain WD interior compositions (Giammichele et al 2018;Charpinet et al 2019;Giammichele et al 2022), yielding central O mass fractions as high as 0.86, which would be difficult to produce with reasonable assumptions in 1D stellar evolution models (De Gerónimo et al 2019). However, Timmes et al (2018) and Chidester et al (2021) have pointed out some additional pieces of physics that are not accounted for in the parameterized models used for the Giammichele et al (2018) fitting procedure, and including these extra effects on the structure can shift the mode frequencies beyond the quoted uncertainties of the models.…”