Computational Methods

In both our numerical approaches, outlined below, we computed model atmospheres of hot white dwarfs subject to the constraints of hydrostatic and radiative equilibrium assuming planar geometry using standard methods (e.g. Mihalas, 1978). The equation of state of an ideal gas used assumes local thermodynamic equilibrium (LTE), and therefore did not include terms describing the local radiation field.

The model atmosphere structure for a hot WD is described by the hydrostatic equilibrium equation,

$$\frac {d P_{\rm g}}{dm} = \frac{GM_{\rm wd}}{R^2_{\rm wd}} ... ...nt_0^{\infty} H_{\nu} \, \frac{k_{\nu}+\sigma_\nu}{c} \, d\nu,$$ (1)

where $k_{\nu}$ is opacity per unit mass due to free-free, bound-free and bound-bound transitions, $\sigma_\nu$ is the electron (Compton) opacity, $H_{\nu}$ is Eddington flux, $P_{\rm g}$ is a gas pressure, and $m$ is column density

$$dm = -\rho \, dz \, .$$ (2)

Variable $\rho$ denotes the gas density and $z$ is the vertical distance. As is obvious from Eqn. 1, the structure of the atmosphere is coupled to the radiation field and the structure and radiative transfer equations need to be solved simultaneously under the constraint of radiative equilibrium.

In the Thomson approximation, in which no energy or momentum between photons and electrons is exchanged, $\sigma_\nu=\sigma_{\rm e}$, where $\sigma_{\rm e}$ is the classical Thomson opacity.