7. Summary and conclusions
This paper presents the set of equations which define a LTE model atmosphere in radiative equilibrium with account of Compton scattering. Scattering is described in the diffusion approximation. Full contribution of Compton scattering to the equation of radiative transfer clearly splits into the coherent (Thomson) scattering part and the small noncoherent scattering term.
The corresponding computer code solves the equation of transfer which includes explicitly temperature corrections. Iterations of a model atmosphere are performed following the Rybicki numerical scheme, in which coherent scattering terms alone are directly taken into account in the linearized radiative transfer equation. Noncoherent terms are included here as inhomogeneities. Iterations of a model atmosphere converge very quickly, particularly in the uppermost layers in which continuum scattering exceeds absorption by many orders of magnitude. This occurs because the equation of radiative equilibrium was linearized with respect both to absorption and Compton scattering terms. Numerical tests showed also, that inclusion of Compton scattering in the model equations causes an only very small increase of the computer cpu time, as compared with the cpu time necessary to run the Thomson scattering code.
In other words, the presence of strong Compton scattering helps to restore the radiative equilibrium and fix the right run of temperature with the doubly linearized code. This can occur since Compton scattering causes a nonzero effect on the local temperature, and it is explicitly included in the radiative transfer and the radiative equilibrium equations. On the other hand, coherent Thomson scattering represents a perfect decoupling between radiation and matter, which is the reason of very serious convergence problems. This topic was extensively discussed e.g. by Mihalas (1978).
The new computer code has been used to calculate sample model atmospheres and continuum spectra of hot, hydrogen dominated white dwarf atmospheres. In case of pure H atmospheres of K and various gravities , effects of Compton scattering appear distinctly in two ways. First, they cause a rise of electron temperature in the uppermost layers, due to Compton heating of electron gas by hard radiation from below the photosphere. The effect is still rather marginal at , roughly corresponding to the real white dwarfs, and increases at lower . Second, Comptonized spectra exhibit a deficiency of X-ray flux and a subsequent cutoff below . This effect occurs at all investigated .
In the case of pure H or H dominated atmospheres of HZ 43 and PG 0824+289, no significant heating effect was found there. However, both white dwarfs are predicted to exhibit a deficiency of X-ray flux below and the cutoff at 40 and , respectively, which is in the range of the ROSAT PSPC and HRI instruments. The presence and exact position of the X-ray cutoff in both stars is the intrisic property of a hydrogen dominated stellar atmosphere, and it vanishes when He number abundance, , rises above . Compton scattering of X-rays is therefore equivalent to some additional opacity in that spectral region, which appears only in DA white dwarfs with very little or no amounts of heavier elements in their atmospheres.
Additional model computations showed also, that the effects of Compton scattering vanish in mixed H/He or pure He model atmospheres, at least at below 150 000 K. In all the models tested up to now, including pure H atmospheres, these effects do not influence neither IUE, ROSAT WFC, nor EUVE detectors. Therefore Compton scattering cannot account for any "missing" opacity which is sometimes observed in spectra of DA white dwarf stars in the X-ray spectral window.
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998