Pulsations powered by hydrogen shell burning in white dwarfs

Context. In the absence of a third dredge-up episode during the asymptotic giant-branch phase, white dwarf models evolved from low-metallicity progenitors have a thick hydrogen envelope, which makes hydrogen shell burning be the most important energy source. Aims. We investigate the pulsational stability of white dwarf models with thick envelopes to see whether nonradial g-mode pulsations are triggered by hydrogen burning, with the aim of placing constraints on hydrogen shell burning in cool white dwarfs and on a third dredge-up during the asymptotic giant-branch evolution of their progenitor stars. Methods. We construct white-dwarf sequences from low-metallicity progenitors by means of full evolutionary calculations that take into account the entire history of progenitor stars, including the thermally pulsing and the post-asymptotic giant-branch phases, and analyze their pulsation stability by solving the linear, nonadiabatic, nonradial pulsation equations for the models in the range of effective temperatures T-eff similar to 15 000 8000 K. Results. We demonstrate that, for white dwarf models with masses M-star less than or similar to 0.71 M-circle dot and effective temperatures 8500 less than or similar to T-eff <= 11 600 K that evolved from low-metallicity progenitors (Z = 0.0001, 0.0005, and 0.001), the dipole (` = 1) and quadrupole (l = 2) g(1)-modes are excited mostly as a result of the hydrogen-burning shell through the epsilon-mechanism, in addition to other g-modes driven by either the kappa-gamma or the convective driving mechanism. However, the epsilon mechanism is insufficient to drive these modes in white dwarfs evolved from solar-metallicity progenitors. Conclusions. We suggest that efforts should be made to observe the dipole g(1)-mode in white dwarfs associated with low-metallicity environments, such as globular clusters and/or the galactic halo, to place constraints on hydrogen shell burning in cool white dwarfs and the third dredge-up episode during the preceding asymptotic giant-branch phase.