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Astron. Astrophys. 335, 1003-1008 (1998)

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4. Results from representative test calculations

A number of models with different clump density enhancement D have been calculated. The results confirm the approximate scaling properties anticipated in Sect. 3. In this section we present models which are typical for different subclasses of Wolf-Rayet stars and study the influence of the clumping parameter.

The Galactic Wolf-Rayet stars of the nitrogen sequence (WN) have been analyzed in previous papers (Schmutz et al. 1989, Hamann et al. 1993, 1995a) with homogeneous models. In the recent upgrade (Hamann & Koesterke 1998), grids of helium-nitrogen models were compared to the observation. Now we select one example star from each spectral subclass and calculate appropriate models, setting the clump density enhancement to D=1 (i.e. no clumping), D=4 and D=16, respectively, while the transformed radius (Eq. 2) is kept constant. We compared the whole spectra and confirmed that the main features do not change by much. The only significant differences along a model series concerns the electron-scattering line wings, as expected. By comparison with observed spectra, a rough guess about the adequate value of D is obtained. The observations are taken from our atlas of WN spectra (Hamann et al. 1995b). The theoretical spectra are convolved with an appropriate gaussian for simulating the instrumental broadening.

For the early-type WN stars with strong lines (WNE-s), WR 6 (designation after van der Hucht et al. 1981; alias HD 50896) serves as our prototype. Taking the final parameters from Hamann & Koesterke (1998), we take the nearest grid model (which slightly differs from the best parameters) and re-calculate a series with different degree of clumping. The model atmosphere is assumed to consist of helium and nitrogen. The model parameters are compiled in Table 1, while in Fig. 1 the region around the He ii line at 4686 Å is displayed. This line is best-suited for our purpose, because the electron scattering wings are most pronounced at the red side of the strongest emissions. The comparison with the observation clearly reveals that the homogeneous model ([FORMULA]) gives too strong electron-scattering wings, especially at the red flank of the He ii 4686 line. The model with [FORMULA] fits much better, but higher values ([FORMULA]) can not be safely excluded. Note that at these parameters the N v feature at 4604-4620 Å reacts very sensitive on the slightly different ionization structure of the models, thus violating the scaling invariance at constant [FORMULA]. Schmutz (1997) has studied the same star and derived a clumping factor of [FORMULA], in full agreement with our result.


Table 1. Parameters of the test calculations

[FIGURE] Fig. 1. Spectral region around He ii 4686 for a series of models with different degree of clumping. Different drawing styles are applied for the model with density enhancement [FORMULA] (i.e. smooth), [FORMULA] and [FORMULA], respectively, as indicated in the inlet. The observed spectrum shown is from WR 6 (WN5-s). The model parameters for that early-subtype WN star with strong lines (WNE-s) are compiled in Table 1. Note that the mass-loss rate is changed such that the effect of clumping is compensated, while the other model parameters are kept constant.

[FIGURE] Fig. 2. Same as Fig. 1, but for an early-subtype WN star with weak lines (WNE-w). The observed spectrum shown is from WR 44 (WN4-w).The model parameters are compiled in Table 1.

[FIGURE] Fig. 3. Same as Fig. 1, but for a late-subtype WN star (WNL). The observed spectrum shown is from WR 123 (WN8). The model parameters are compiled in Table 1.

[FIGURE] Fig. 4. Same as Fig. 1, but for a WC4 star. The observed spectrum shown is from Br 43 in the LMC. The model parameters are compiled in Table 1.

Fig. 2 shows a model series together with the observation of WR 44, an early-type WN spectrum with weak lines (WNE-w). Although the electron-scattering wings are less pronounced than in the previous example, the homogeneous model ([FORMULA]) is definitely ruled out by the comparison, while again [FORMULA] seems to fit best.

As the prototype for late-type WN stars we select WR 123 (alias HD 177230). In this case we calculate models with the adequate terminal velocity, because the fixed value of the available grid is too different. Moreover, the detailed comparison with the observation reveals that the even members of the He ii Pickering series are systematically stronger than calculated, unless some hydrogen is put into the models. We find that a hydrogen mass fraction of 5% is adequate, which is quite usual for WNL stars, but in contrast to the zero hydrogen abundance given for that star in our earlier papers. Again, the comparison with the observed spectrum reveals that the [FORMULA] model fits best. However, models in this parameter range have an extremely sensitive ionization structure, and the scaling invariance is not accurately fulfilled. Only a marginal fine-tuning of the other parameters would suffice to restore consistent fits at different D values.

WC star analyses are still in their infancy, and their parameters are not well established yet. WC spectra are crowded with blending lines, which hinders the study of the line wings. Earlier WC subtypes have less complex spectra than later subtypes. Therefore we select for the present purpose the WC4 star Br 43 in the Large Magellanic Cloud, for which we have a fit model at hand. We prefer here somewhat different parameters than we have given in Gräfener et al. (1998) for that star. The model shown here is numerically improved and was selected for an optimum fit of the 4686 Å emission. The true parameters of WC stars are still rather uncertain.

An observation is available from Torres & Massey (1987), and we convolve our synthetic spectra according to its relatively poor spectral resolution (10 Å). The spectra are rectified by division through the theoretical continuum.

Fig. 4 shows the spectral region around the C iii/C iv/He ii blend 4650-4686 Å, displaying the model series for different values of D together with the observation of Br 43. As in the case of the WN stars, the smooth model ([FORMULA]) has too strong electron-scattering wings. But even the [FORMULA] model shows some scattered light at the flanks of the strong emission complex, filling the observed gaps to the neighboring lines. In contrast to the WN spectra, it is the [FORMULA] model which fits best. Although we should be careful when generalizing from one single object, this result might indicate that WC winds are even less homogeneous than the winds of WN stars.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998