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.