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

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6. Subdwarf B stars

Subdwarf B (sdB) stars have somewhat lower gravities ([FORMULA]) than white dwarfs. Their temperatures are in the range [FORMULA] K [FORMULA] K. The photospheric helium of a typical sdB star is moderately depleted with respect to the solar value. Yet, a wide spread of abundances is observed. The hotter stars of this class ([FORMULA] K), which display He II lines in addition to the Balmer and He I lines are often classified sdOB (see Heber 1992 for a review).

There exist two different strategies for the analysis of sdB stars in the literature. Saffer et al. (1994) determine [FORMULA] and g by a simultaneous fit of the Balmer lines, similar to the method commonly adopted for the analysis of DA white dwarfs. Since the sdB stars are cooler than the hot white dwarfs discussed in the previous sections, a temperature determination from the FUV or optical continuum is also possible. Gravity is then derived from one or more Balmer lines with [FORMULA] fixed. This approach was used, e.g., by Heber (1986) with temperature determination from IUE UV spectrophotometry, and by Moehler et al. (1990) with temperatures derived from optical Strömgren photometry. Unfortunately, the results of the two different approaches are not in good agreement. An extensive discussion of this problem is given in Saffer et al. (1994) arguing that the most important reason for the discrepancy lies in the use of inappropriate color-temperature calibrations for the analysis of the photometric data. However, this issue is not yet settled.

Since the sdB gravities are lower than white dwarf gravities, one expects stronger NLTE effects in the atmospheres of sdB stars. We calculated a set of models along the sdB sequence (see e.g. Heber 1986 or Saffer et al. 1994) for this purpose. A typical helium abundance of [FORMULA] was chosen. Model parameters are given in Table 1.


[TABLE]

Table 1. Parameters of the sdB model atmospheres


The results are shown in Fig. 9. For the Balmer lines and the He I 4471 Å line the LTE and NTLE calculations agree very well for [FORMULA] K if we exclude the notorious He I 5876 Å and other red He I lines. Moderate differences are still present the cores of the Balmer lines at [FORMULA] K, but only a small influence on the analysis is expected. However, the NLTE deviations rapidly increase above 30000 K. The Balmer lines for the representative 35000 K model atmosphere are plotted in Fig. 10 together with a metal line blanketed LTE model (see discussion below). It is obvious that these effects modify the whole line profiles of the Balmer lines and not only the cores. Now, the He I 4471 Å line is deviating from LTE, too, and the He II 4686 Å line is virtually never in agreement with LTE models.

[FIGURE] Fig. 9. NLTE effects on important hydrogen and helium lines of sdB stars. The deviation of equivalent width [FORMULA] in percent is plotted. Note that both [FORMULA] and g are varied simultaneously to match the observed sdB sequence
[FIGURE] Fig. 10. Comparison of synthetic Balmer line profiles computed for NLTE (solid lines) LTE (dotted lines) hydrogen and helium composed model atmospheres with a LTE model atmosphere including metal line blanketing (dashed line). Model parameters are [FORMULA] K, [FORMULA], [FORMULA]

The implications of the NLTE deviations on the results are different for both analysis strategies discussed above. Since Saffer et al. (1994) derived both temperature and gravity from the line fits, it is obvious that both can be influenced. Since H [FORMULA], which is predominantly temperature sensitive (Saffer et al.), shows the strongest NLTE deviations of the lines used by Saffer et al., the primary effect would be an underestimate of temperature. This would change the derived gravity, too. Heber (1986) and Moehler et al. (1990) used the Balmer lines only for the determination of gravity. Thus only the gravity determination is influenced by NLTE effects on the lines. NLTE deviations of the continuum are unimportant in the sdB regime (Wesemael et al. 1980). In their Fig. 8 Saffer et al. show the result of a comparison of photometric temperature determinations with the [FORMULA] from their line fits. The general agreement is good, but for [FORMULA] K a trend of higher [FORMULA] from the photometric determinations is present. This is in line with our prediction of the impact of the NLTE effects on the analysis method applied by Saffer et al.

However, the overall disagreement of the results derived with the different analysis methods can certainly not be explained by the influence of NLTE. Thus we will shortly discuss the different LTE model calculations performed by the different groups. While, e.g., Heber (1986) and Moehler et al. (1990) applied fully metal line blanketed model atmospheres, Saffer et al. (1994) based their analysis on relatively simple LTE atmospheres considering only hydrogen and helium. The latter calculations are similar to the LTE models presented in this article. The impact of metal line blanketing on the Balmer lines is demonstrated in Fig. 10 and compared to the NLTE deviations. The metal line blanketed LTE atmosphere is calculated with the LTE program of Heber et al. (1984) using the opacity distribution functions of Kurucz (1979) with a solar mixture.

It is obvious that both metal line blanketing as well as NLTE cause pronounced effects on the line profiles. Since we are interested in the impact on fit results we performed a fitting of the Balmer line profiles (H [FORMULA], H [FORMULA], H [FORMULA]) of the hydrogen and helium composed model spectra with a grid of metal blanketed LTE model atmospheres. A simultaneous determination of [FORMULA] and g was done according to the procedure described in Saffer et al. (1994). Our "fit" result of the H and He LTE model spectrum is [FORMULA] K and [FORMULA] corresponding to a shift of [FORMULA] K and [FORMULA] caused by the neglect of heavy elements. Analogous we found [FORMULA] K and [FORMULA] for the NTLE/LTE differences. This proves that both effects are important for the chosen parameter set. While NLTE becomes less and less important for cooler temperatures the influence of metal line blanketing is not very temperature sensitive and thus remains important. A proper way to include both effects, NLTE and metal line blanketing, might be the NLTE line formation on a LTE atmosphere as discussed in the next section.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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