A new generation of white dwarf envelope models and diffusion timescales (2020)

The atmosphere models, which provide the boundary conditions for the envelopes, use the latest code with a number of improvements (e.g. a more accurate treatment of molecule formation, more absorption processes), which are most important at the cool end of the sequence. The envelope code is a completely new development, described in more detail in Koester et al. (2020, A&A 635,103). The diffusion code has been completely rewritten. Major changes are the inclusion of nonideal effects in the diffusion equation after Beznogov & Yakovlev (2013, Phys. Rev. E, 111, 161101), new calculations for the collision integrals by Stanton & Murillo (2016, Phys.Rev. E, 93, 043203), and the Thomas-Fermi mean ionization model for the determination of average charges of all elements at higher densities. In the current version the average charges are calculated from the Saha equation (including nonideal effects) for log density < -3.0 and from the TF model for densities >-2.0 g/cm3. In the intermediate region a smooth transition is provided. The DA calculations use ML2/alpha=0.7 for the convection in atmosphere and envelope; the DB models use 1.25. The starting point for the envelope within the atmosphere is usually tau_ross=100. If there is no convection at this depth in the hotter models the boundary is shifted upwards in the atmosphere to the bottom of the cvz, but not above tau_ross ~1. The velocities and time scales are calculated at the bottom of the cvz, optionally including an overshoot. If there is no convection at the first envelope layer, the data are calculated there, but without applying an overshoot.
PLEASE NOTE: The (boundary) atmosphere models and the envelopes are pure H/He models. If the metal content is large enough to influence the atmosphere structure - which is most likely in low Teff helium-rich models - the boundary condition and therefore the depth of the convection zone and diffusion data may change. In those cases individually adjusted calculations should be used.


Diffusion timescales for DA and DB white dwarfs (2020)

Diffusion timescales for hydrogen-rich white dwarfs (DA, DAZ), no overshoot
Diffusion timescales for hydrogen-rich white dwarfs (DA, DAZ), overshoot 1.0Hp
Diffusion timescales for helium-rich white dwarfs (DB, DBZ, DC, DZ), no overshoot
Diffusion timescales for hydrogen-rich white dwarfs (DB, DBZ, DC, DZ), overshoot 1.0Hp

Diffusion timescales for DBAZ with atmospheric metals in the boundary conditions (2020)
(read the README first)

README DBAZ
log g = 7.50 overshoot 0.0Hp
log g = 7.50 overshoot 1.0Hp
log g = 7.75 overshoot 0.0Hp
log g = 7.75 overshoot 1.0Hp
log g = 8.00 overshoot 0.0Hp
log g = 8.00 overshoot 1.0Hp
log g = 8.25 overshoot 0.0Hp
log g = 8.25 overshoot 1.0Hp
log g = 8.50 overshoot 0.0Hp
log g = 8.50 overshoot 1.0Hp

A cautionary note on diffusion timescales for white dwarfs (2013)

Diffusion timescales have recently been calculated in Koester and Wilken (2006, A & A, 453,1051) and Koester (2009, A & A, 498, 517). In the course of changing the equations describing element diffusion from the version in Paquette et al. (1986, ApJS 61, 197, eq. 4) to the one in Pelletier et al. (1986, ApJ 307, 242, eq. 5), which is more accurate in the case of electron degeneracy, we (D.K.) discovered a typographical error in the former paper. A factor of rho^{1/3} is missing in the second alternative of eq. 21, which we had not noticed before. A rederivation of all our equations uncovered another error by us in the implementation of the contribution of thermal diffusion. These errors have only a very small effect in stars with relatively shallow convection zones, like the DAs. However, for cool DBs with very deep convection zones, the diffusion timescales can get larger by factors 2-3, with correspondingly lower diffusion fluxes. Fortunately, the relative timescales for different elements, which are important for the determination of the abundances in the accreted matter, change much less.
We also made several numerical experiments with the calculation of the outer envelopes, which determines the masses in the convection zones. In the helium-rich cool objects, the bottom of this zone reaches mass densities between 1 and 1000 g/cm^3. This range includes the regime of pressure ionization in helium. In the equation of state we use (Saumon et al. 1995, ApJS 99, 713) this regime is not treated explicitely but bridged by a smooth interpolation. The quantity most important for the convection zone calculation is the adiabatic gradient, since the structure is almost exactly adiabatic throughout the zone. Numerical experiments show that because of the cumulative effect of the inward integration a very small change in the adiabatic gradient can change the mass in the cvz by one or two orders of magnitude. As is demonstrated by Fig. 23 in Saumon et al. (1995) the adiabatic gradient is significantly different between various EOS calculations. It can also show irregular behaviour, which is probably not realistic but caused by the numerical calculation of the necessary second derivatives, if the EOS is determined by a Free Energy minimization method. As a consequence, absolute values of diffusion timescales and diffusion fluxes in cool DBs depend on the details of the EOS and may be quite uncertain. We are confident, however, that the relative timescales of different elements are probably correct to within a factor of two.
Updated tables (2013), which use the convection parameters ML2/0.8 in the case of DAs as recommended by the Montreal group, are available with the following links.

Diffusion timescales for hydrogen-rich white dwarfs (2013)(DA, DAZ)
Diffusion timescales for helium-rich white dwarfs (2013)(DB, DBZ, DC, DZ)