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

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4. Hydrogen-rich white dwarfs

4.1. Balmer lines of hot DA/DAO white dwarfs

Due to the lack of other temperature indicators the Balmer lines of hot hydrogen-rich DA and DAO white dwarfs are used for the simultaneous determination of [FORMULA] and [FORMULA]. In a recent paper Bergeron et al. (1994) reported a strong influence of small traces of helium ([FORMULA]) on the Balmer line profiles and thus on the temperature determination of hot DA white dwarfs. Since such small traces are invisible in optical spectra this would introduce an uncomfortably large ambiguity for the parameter determination of these stars. The reason for this behavior is the strong He II absorption edge at 228 Å. Due to the lack of other opacity sources the EUV flux in the pure hydrogen atmosphere of a DA is very strong. In the presence of helium traces flux shortward of 228 Å is absorbed and heats the atmosphere. The resulting higher temperatures weaken the Balmer lines.

This effect is displayed in Fig. 1: the Balmer lines of LTE models ([FORMULA] K, [FORMULA]) with pure hydrogen and traces of helium ([FORMULA] and [FORMULA]) are compared. A strong dependence of the Balmer lines on the helium content is visible, indeed. However, this sensitivity almost vanishes for the corresponding NLTE models and can be neglected for practical purposes.

[FIGURE] Fig. 1. Influence of different amounts of helium on the Balmer lines of LTE and NLTE model atmospheres with [FORMULA] K and [FORMULA]

The reason for this different behavior is the dramatic overionization of helium in NLTE. Due to the strong flux in the He II Lyman continuum most He II is ionized to He III. Fig. 2 displays the ionization structure of helium in NLTE and LTE atmospheres with [FORMULA]. In the Balmer line forming region He II is less abundant in the NLTE calculations by more than one order of magnitude compared to LTE. Thus it is obvious that the temperature structure in the relevant region and thus the Balmer lines are much less affected by traces of helium than predicted by LTE calculations.

[FIGURE] Fig. 2. Ionization structure of helium in the atmosphere of a DA star with [FORMULA] K, [FORMULA], and [FORMULA] for a NLTE model (solid lines) and a LTE model (dashed lines). The formation region of the Balmer lines is marked

A general overview of the NLTE deviations of the hydrogen lines of DA/DAO white dwarfs and their temperature dependence is given in Fig. 3 for [FORMULA], a typical gravity for hot white dwarfs. The relative deviation [FORMULA] is plotted for the Balmer lines H [FORMULA], H [FORMULA], and H [FORMULA] and Lyman- [FORMULA]. Positive/negative values of [FORMULA] correspond to LTE profiles stronger/weaker than the NLTE profiles. It is well known that H [FORMULA] is the Balmer line most sensitive to NLTE effects and thus this line is seldom used for LTE analyses. However, the two Balmer lines H [FORMULA] and H [FORMULA] are frequently used. Ly [FORMULA] is the only line of the Lyman series accessible by the IUE and HST space observatories and is of special importance for the analysis of white dwarfs in binary systems (e.g. Barstow et al. 1994). Calculations were carried out for pure hydrogen and [FORMULA] ranging from [FORMULA] up to [FORMULA]. While helium traces of [FORMULA] and [FORMULA] are undetectable in the optical and FUV range and the stars would therefore be classified DA, the models with [FORMULA] and [FORMULA] correspond to DAO/DAB white dwarfs with visible He II or He I lines.

[FIGURE] Fig. 3. NLTE effects on Balmer and the Lyman- [FORMULA] lines of DA/DAO white dwarfs with various helium contents as function of [FORMULA] for [FORMULA]. The deviation of equivalent width [FORMULA] in percent is plotted. The symbols are explained in the plot

The results for [FORMULA] are displayed in Fig. 3. The NLTE deviations can be explained by two basic patterns. As can be seen for the pure hydrogen models individual departures of the hydrogen levels from LTE start to become significant at [FORMULA] K and are very important for the hottest models with [FORMULA] K. As was discussed above the influence of helium on the temperature structure is overestimated in the LTE atmospheres due to overionization in NLTE. This effect becomes important at different [FORMULA] ranges for different helium content. Generally, the structure is not significantly different below a certain temperature and after the maximum is reached more and more helium is ionized to He III. Therefore finally even in the LTE atmospheres virtually no He II is left to heat the atmosphere in the line forming regions. This is reflected in the very similar deviations of the pure hydrogen and the [FORMULA] models at the hottest temperatures.

The [FORMULA] of maximum NLTE deviations and the amplitude increase with increasing helium abundance. Bergeron et al. (1994) reported that the influence of helium traces on the Balmer lines vanishes for [FORMULA] K. This corresponds to the lower temperature limits for NLTE effects on the Balmer lines. From Fig. 1 it can be concluded that the differences of hydrogen lines calculated from more realistic NLTE models with [FORMULA] and pure hydrogen models don't exceed a few percent in the relevant [FORMULA] range. Thus we recommend the following recipe: for LTE analyses of hot DA white dwarfs it is better not to include trace helium abundances in the model atmospheres. Otherwise the neglect of NLTE overionization of helium leads to unrealistic temperature stratifications.

Since the collisional coupling of the occupation numbers to the local temperature is more effective for higher densities and hence gravities, it is expected that NLTE deviations increase with decreasing gravity. The effect of varying g is shown in Fig. 4 for models with [FORMULA] K. The expected trend is indeed present: high gravity models of [FORMULA] show only relatively small NLTE deviations, while the effects become quite strong for [FORMULA]. However, note that the [FORMULA] model with [FORMULA] still shows 15% difference between LTE and NLTE! The remaining H [FORMULA] deviation of the [FORMULA], [FORMULA] model is due to the NLTE emission core (see Fig. 1).

[FIGURE] Fig. 4. NLTE effects on Balmer and the Lyman- [FORMULA] lines in dependence of [FORMULA] for [FORMULA] K. The deviation of equivalent width [FORMULA] in percent is plotted

Since the surface gravity of DAO white dwarfs is generally lower than that of DA stars being typically in the range [FORMULA] (Napiwotzki 1993a, 1993b, 1995a; Bergeron et al. 1994), we calculated a sequence of models with [FORMULA] and a helium abundance [FORMULA], typical for these stars. The deviations are quite strong even for relatively low temperatures. A comparison of line profiles is shown in Fig. 5. It is evident that the complete profiles of the Balmer lines are affected, though the differences in the cores are strongest. We conclude that the results of LTE analysis of hot DAO white dwarfs are therefore unreliable. Additionally, one should be aware of moderate NLTE effects also in cool DAO white dwarfs, still. However, we should add that even the NLTE model atmospheres presented here are not able to fit the observed spectra of the very hot DAO central stars consistently (Napiwotzki 1992; Napiwotzki & Rauch 1994). The inclusion of C, N, O with Stark broadened lines in the atmospheric calculations is necessary to achieve a satisfactory fit (Werner 1996a). However, while the agreement for the calculated H [FORMULA] profiles used by Napiwotzki (1995a) for the temperature determination, is reasonable for NLTE calculations with and without this treatment of metal lines, the LTE results deviate from both.

[FIGURE] Fig. 5. Synthetic spectra for DAO stars with [FORMULA] and [FORMULA]. The profiles are convolved with a Gaussian of 2 Å FWHM. NLTE is drawn with solid lines, LTE with dashed lines

4.2. The helium lines of DAO/DAB white dwarfs

Since no other helium lines are strong enough in the optical range, the helium abundance of DAO white dwarfs is commonly determined from the He II 4686 Å line. Another strong line available in the FUV is He II 1640 Å. In cooler stars of this class He I lines may become detectable and provide a potentially accurate temperature indicator via the He I /He II ionization equilibrium. Still cooler hydrogen-rich white dwarfs display only the He I lines and are called DAB.

A NLTE/LTE comparison for DAO/DAB models with [FORMULA] and [FORMULA] is shown in Fig. 6. It is evident that the important He II line at 4686 Å is always smaller in NLTE than in LTE by about [FORMULA] %. This causes the helium abundance to be overestimated by a LTE analysis of DAO white dwarfs. As expected, the differences become larger for smaller gravities. Changing the gravity from [FORMULA] to 6.5 increases [FORMULA] by approximately a factor of two to three. This also holds for the other helium lines discussed in this section. The NLTE emission core of He II 4686 Å causes the large fluctuations of the equivalent width ratio for [FORMULA] K (cf. Figs. 5 and  6). The deviations for He II 1640 Å are smaller and can certainly be ignored for most stars with FUV spectra of IUE quality. The He I lines deviate moderately from LTE as well. The effect is stronger for the 5876 Å line, which remains detectable for higher temperatures than the 4471 Å line does.

[FIGURE] Fig. 6. NLTE effects on the helium lines of DAO models with [FORMULA] and [FORMULA]
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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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