Discussion

The differences we find here between emergent spectra computed using Thomson and Compton scattering are essentially negligible for practical purposes. Such differences are in fact much smaller than the predicted spectral uncertainties resulting from uncertainties in the current knowledge of the fundamental parameters of DA white dwarfs--even the best known examples such as HZ 43 and Sirius B. The spectrum in this Wien tail region is especially sensitive to uncertainties in the effective temperature.

Comparison of the calculations presented here using both Methods 1 and 2 with the earlier work of Madej (1998) do, however, reveal some significant differences. For HZ 43, Fig. 3 of Madej (1998) suggests a large X-ray flux deficit due to Compton scattering of photons to longer wavelengths, with a precipitous decline in emergent flux at $\sim 40$ Å. However, our Figs. 2 and 3 illustrate much smaller effects.

A careful examination of the Madej (1998) computer code performed by one of us (JM) has shown that the earlier code (which used Kompaneets scattering terms) could strongly exaggerate effects of Compton scattering in cases when they were of only marginal significance. This is the case for the X-ray spectrum of HZ43. The effect was caused by an approximation adopted in the solution of the transfer equation that was quite valid for the study of X-ray burst sources, for which the code was primarily developed, but which became marginally inaccurate for the case of hot DA white dwarf atmospheres. This problem has been solved by the very stable algorithm of the new code (see Method 2), described in Madej & Rózanska (2000).

One should note that the differences between this work and that of Madej (1998) are not related to the numerical approaches adopted for Compton scattering. Both the Kompaneets diffusion approximation (Method 1) and the Compton scattering terms of the integral form (Method 2) satisfactorily describe effects of Compton scattering in X-ray spectra of hot white dwarf stars. The results of the work presented here using both methods supersede those of Madej (1998).

At the higher effective temperatures represented by the $T_{\rm eff} = 100 000$ K models, the emergent spectra for Thomson and Compton scattering begin to diverge at $\sim 50$ Å for the $\log g=6$ model, and the effects are much larger toward shorter wavelengths than for the higher gravity $\log g=8$ case. It is of course questionable as to whether any white dwarfs with pure H atmospheres exist with such high effective temperatures, since in hotter stars radiative levitation tends to enrich the atmosphere with metals. In atmospheres with significant metal abundances the electron scattering opacity is insignificant compared with that due to metals, and Compton redistribution effects are rendered irrelevant.

Our calculations show that even in the hottest pure H atmospheres it is highly unlikely that future X-ray observations will be sufficiently sensitive to discern the Compton redistribution effects. Again, uncertainties in model parameters such as effective temperature and surface gravity, and abundances of He and trace elements, together with uncertainties in parameters entering into the modelling calculations themselves will dominate. Even for models normalised to the same flux at UV wavelengths a 1% error in $T_{\rm eff}$ will induces a 20% flux error at 75Å.