Research Note

Outer boundary conditions for evolving cool white dwarfs^⋆

¹ Instituto de Ciencias Astronómicas, de la Tierra y del Espacio (CONICET-UNSJ), Av. España 1512 (sur), 5400 San Juan, Argentina
e-mail: rohr@icate-conicet.gob.ar
² Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina
e-mail: althaus@fcaglp.unlp.edu.ar
³ Departament de Física Aplicada, Universitat Politècnica de Catalunya, c/Esteve Terrades 5, 08860 Castelldefels, Spain
e-mail: garcia@fa.upc.edu
⁴ Institute for Space Studies of Catalonia, c/Gran Capità 2–4, Edif. Nexus 104, 08034 Barcelona, Spain

Received: 27 March 2012
Accepted: 4 September 2012

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.