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Astron. Astrophys. 322, 256-265 (1997)

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2. Model calculations

Hydrogen and helium composed models are calculated with the NLTE code developed by Werner (1986), which is based on the ALI method mentioned above. Plane parallel geometry as well as hydrostatic and radiative equilibrium are assumed. For a detailed description and recent updates see Werner & Dreizler (1996).

The aim of this article is a comparison of NLTE and LTE models to detect the influence of NLTE effects on important spectroscopic features. Comparisons of results of the NLTE program with LTE models is usually hampered by different physical input data and numerical algorithms used in both programs. To overcome this problem LTE models are calculated with the NLTE code by drastically enhancing the collisional rates ([FORMULA]) between the atomic levels. An a posteriori check guarantees that the Saha and Boltzmann equations are fulfilled in every atmospheric layer. The result are LTE models which are completely consistent with the corresponding NLTE atmospheres. Any difference is due to deviations from LTE!

In our calculations the the influence of heavy elements is neglected. Metal line blanketed NLTE model calculations published during the last years generally showed only minor influence on hydrogen and helium lines; see, e.g., the computations of Werner & Dreizler (1993) for atmospheres of hot central stars, and Haas et al. (1996) for hot sdO stars, which includes line blanketing by C, N, O, and Fe. However, Werner (1996a) has demonstrated recently that the inclusion of Stark broadening for C, N, and O lines can have a strong influence on the atmospheric structure of very hot hydrogen-rich stars. It is likely that the effect on the emergent spectrum is pronounced enough to solve the Balmer line problem reported in Napiwotzki (1992) and Napiwotzki & Rauch (1994). Previous calculations generally took into account only Doppler broadening and thus failed to reproduce this effect.

However, the computional effort for including metal line blanketing in a proper way is large and the exploration of a reasonable large parameter space, as necessary for our investigation, would need an unrealistic amount of computer time. Thus we decided to restrict ourselves to model atmospheres without metals, which nevertheless should be sufficient to check the importance of NLTE effects.

Detailed hydrogen and helium model atoms are used for the model calculations (cf. Napiwotzki & Rauch 1994). In view of the high densities in white dwarf atmospheres which yield very broad lines, we consider the Stark broadening of the first two series of hydrogen and the first four series of ionized helium. For further sources of atomic data cf. Dreizler et al. (1990). Let us only note that the collisional ionization of H I and He II is calculated according to Mihalas (1967) and Mihalas & Stone (1968). However, the authors gave fit polynoms of the atom and level dependent function [FORMULA] based on the data of Kieffer & Dunn (1965) and Percival (1966), which are only valid for [FORMULA] K and yield in some cases negative rates for higher temperatures. Therefore we calculated new fits, which are now valid up to [FORMULA] K (Napiwotzki 1993a).

The collisional rates (bound-bound and bound-free) are the major drawback of today's NLTE calculations because they are much less accurately known than the radiative data. More recent calculations for hydrogen cross sections were published by Giovanardi et al. (1987) and Giovanardi & Palla (1989). However, Chang et al. (1991) have shown that these data contain major inconsistencies. Thus they are not used for our calculations. Changes of the collisional rates within reasonable limits may moderately modify some NLTE results. However, it will hardly change the regions in which NLTE is important.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998