Outer boundary conditions for evolving cool white dwarfs

Abstract

Context. White dwarf evolution is essentially a gravothermal cooling process, which, for cool white dwarfs, depends on the treatment of the outer boundary conditions. Aims. We provide detailed outer boundary conditions that are appropriate to computing the evolution of cool white dwarfs by employing detailed nongray model atmospheres for pure hydrogen composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Methods. Detailed nongray model atmospheres were computed by considering nonideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman α quasi-molecular opacity. We explored the impact of outer boundary conditions provided by updated model atmospheres on the cooling times of 0.60 and 0.90 M white dwarf sequences. Results. Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 K for sequences with 0.60 M and 6100 K with 0.90 M . Detailed model atmospheres predict ages that are up to ≈10% shorter at log(L/L ) = −4 when compared with the ages derived using Eddington-like approximations at τ Ross = 2/3. We also analyze the effects of various assumptions and physical processes that are relevant in the calculation of outer boundary conditions. In particular, we find that the Lyα red wing absorption does not substantially affect the evolution of white dwarfs. Conclusions. White dwarf cooling timescales are sensitive to the surface boundary conditions for T eff < ∼ 6000 K. Interestingly enough, nongray effects have few consequences on these cooling times at observable luminosities. In fact, collision-induced absorption processes, which significantly affect the spectra and colors of old white dwarfs with hydrogen-rich atmospheres, have no noticeable effects on their cooling rates, except throughout the Rosseland mean opacity.

Comparison of theoretical white dwarf cooling timescales

“…At this stage, latent heat release upon crystallization was neglected. When the same OPAL radiative opacities and Cassisi et al (2007) electron conduction opacities, photospheric boundary conditions from the model atmospheres by Rohrmann et al (2012), neutrino energy loss rates (Itoh et al 1996;Haft et al 1994), and EOS (Magni & Mazzitelli 1979) are employed, cooling times obtained from the two codes agree within ∼2% at all luminosities, with the exclusion of models brighter than log(L/L ) ∼ −1.5, where differences up to ∼8% appear because of the different thermal structure of the first white dwarf structure converged at the beginning of the cooling sequence.…”

“…3. Calculations of both LPCODE and BaSTI models with the EOS of Magni & Mazzitelli (1979), electron conduction opacities by Cassisi et al (2007), employing now photospheric boundary conditions taken at an optical depth τ = 25 from the model atmospheres by Rohrmann et al (2012) when T eff < 10 000 K 2 . The same table of photospheric boundary conditions is used in both calculations.…”

“…There have been a few recent theoretical studies to assess the sensitivity of the predicted cooling times to uncertainties Article published by EDP Sciences A96, page 1 of 8 in the model core and envelope chemical stratification and electron conduction opacities, (Hansen 1999;Prada Moroni & Straniero 2007;Salaris 2009;Salaris et al 2010), and photospheric boundary conditions (Hansen 1999;Salaris et al 2000;Rohrmann et al 2012). However, there is no modern systematic study of the effect of employing different equations of state (EOS) and radiative opacities, especially the less established low-temperature opacities in cool white dwarfs.…”

New evolutionary sequences for extremely low-mass white dwarfs

“…In particular, the metal mass fraction Z in the envelope of our models is specified by scaling it to the local abundance of the CNO elements at each layer. For the white dwarf regime and for effective temperatures lower than 10 000 K, outer boundary conditions for the evolving models are derived from nongrey model atmospheres (Rohrmann et al 2012). Recently, LPCODE has been tested against other white dwarf code.…”

Pulsations powered by hydrogen shell burning in white dwarfs

“…In addition, abundance changes resulting from atomic element diffusion were considered during the white dwarf regime. -For the white-dwarf stage and for effective temperatures lower than 10,000 K, outer boundary conditions for the evolving models are derived from non-gray model atmospheres (Rohrmann et al 2012). Table 1 lists the initial masses of the sequences, the resulting white dwarf masses, the hydrogen mass fraction, log (M H /M ⊙ ), and the surface carbon to oxygen ratio, C/O, at the beginning of the white dwarf phase.…”