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Astron. Astrophys. 354, 193-215 (2000)

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3. Line blocking in plane-parallel models

In Paper I we found that the He I singlet and triplet lines of O stars hotter than 40 000 K indicated different stellar parameters when used for the determination of stellar temperatures. Following the results of Pauldrach et al. (1993), who stressed the importance of line blocking for the wind ionization structure and emergent flux, Herrero (1994) showed that this difference is considerably reduced when UV metal line opacity is included. The author attributed this to the different effect of the modified UV radiation field on the He I occupation numbers. However, no further proof was given there.

Here we want to discuss in a more detailed way the effect of this line blocking, as it is important for the analysis of the stars listed in Table 1.

We have included the line list of Pauldrach et al. (1993) between 228 and 912 Å. In this region the ionization of He I and H takes place. Thus, we can expect an effect on the occupation numbers of these two ionization stages. The line list comprises roughly 14 000 lines from 26 different elements and 137 ionization stages taken into account in the stellar wind NLTE calculations by Pauldrach et al. (1993). We calculate their occupation numbers in LTE. Although this is a rough approximation, we expect that its inclusion will already give us the major part of the effect.

We will use a model at [FORMULA] = 40 000 K, [FORMULA] = 3.40 and [FORMULA] = 0.09 to illustrate the effects of line blocking. In Fig. 1 we plot the emergent flux between 228 and 912 Å. As we can see, a considerable fraction of the flux has been blocked. This energy will appear at other wavelengths. However, as most of the flux escapes between 912 and 2 000 Å, this has no real influence redward of 912 Å. It has to be pointed out that Fig. 1 is only illustrative. It is not the emergent flux which is important here, but the mean intensity of the radiation field at the depths where the He I continuum becomes optically thin. The effect, however, is similar.

[FIGURE] Fig. 1. The Eddington flux in the region between 228 and 1200 Å, with and without approximate line blocking, for the model at [FORMULA] = 40 000 K, [FORMULA] = 3.40 and [FORMULA] = 0.09.

The most important effect is produced in the occupation numbers of the ground level of He I . As a consequence of the flux blocking, the ionization from this level (its ionization edge lies at 504 Å) is considerably reduced, and its population largely increases (see Fig. 2). This does not have any noticeable effect on other ionization stages, since He I is very scarcely populated. The lower level of the He I [FORMULA]4387, 4922 singlet lines, the 2p [FORMULA] level, is directly connected to the ground level (which also belongs to the singlet system) through a radiative transition at 584 Å, and thus partially follows their changes and also increases its population. On the contrary, the lower level of the He I [FORMULA]4471 triplet line (the 2p [FORMULA] level) is only weakly or indirectly coupled to the He I ground level. In addition, the ground level of the triplet system (to which 2p [FORMULA] is strongly coupled) is dominated by its ionization and recombination at around 2600 Å, and it is not affected by the line-blocking. As a result, the behaviour of 2p [FORMULA] follows that of the He I ground level to a much lesser extent than does the 2p [FORMULA] level (as do all triplet levels compared to their singlet counterparts). We can see this behaviour in Fig. 2, where we have additionally marked the formation depths of the center of the He I [FORMULA] 4387, 4922 and 4471 lines and the continuum. We can see that the populations of these levels increase over the whole region of formation, the changes being larger for the 2p [FORMULA] level. In addition, the formation region of the singlet lines is more extended than in the case without line-blocking (an effect that is not seen in the figure). The combination of larger changes over a larger line formation region produces the stronger variations of the singlet lines compared to the triplet one.

[FIGURE] Fig. 2. The changes in the occupation numbers of the ground level of He I (full line), the lower level of the singlet lines He I [FORMULA]4387, 4922 (2p [FORMULA], dashed line) and the ground level of the triplet line He I [FORMULA]4471 (2p[FORMULA], dashed-dotted), and the formation depths of the line centers and the continuum. Negative numbers mean that the atomic level populations calculated with line-blocking are larger. The peak near log m = -2.5 is a numerical artefact in the convergence of the model without line blocking and does not appear in other models. The model parameters are the same as in Fig. 1.

Figs. 3 and 4 show the variations in the line profiles of He I [FORMULA]4387, 4471. We see that the changes are much less in the second one, and thus this line should be preferred for analyses at high temperatures. At lower temperatures and gravities, however, and due to the so-called dilution effect in this line, the use of the singlet lines is preferable, even if the calculations are made without line-blocking. This effect refers to the fact that the fit of the He I  [FORMULA]4471 line becomes worse when going from dwarfs to supergiants, while the rest of the lines retain a good fit quality (see Voels et al. 1989). Although still not completely clarified, Smith & Howarth (1998) recently claimed that microturbulence could be the cause.

[FIGURE] Fig. 3. The helium line He I [FORMULA]4387 with and without line-blocking (solid and dashed lines, respectively) for the same model parameters as in Fig. 1. He I [FORMULA]4922 behaves the same way.

[FIGURE] Fig. 4. As Fig. 3, but for the He I [FORMULA]4471 line.

At lower temperatures or larger gravities, collisions play a stronger role, and the effects of line blocking are lower. This explains the behaviour of the corrections to the stellar parameters found by Herrero (1994, especially Fig. 3) when including line-blocking, and basically consist of obtaining lower temperatures when line-blocking is not taken into account. The amount of the correction will depend on the model temperature at a given gravity, being larger for higher temperatures. It has to be stressed, however, that the corrections are large only if we use the singlet lines for the temperature determination without line-blocking. Using the triplet line results in a smaller temperature than using the singlet ones (by 500-1 000 K at temperatures around 45 000 K). Gravity and helium abundance do not significantly vary, although sometimes variations of the parameters within our typical error boxes ([FORMULA]0.1 in [FORMULA] and [FORMULA]0.03 in helium abundance) have been adopted in the course of the parameter determinations.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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