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Astron. Astrophys. 363, 585-592 (2000)

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5. [FORMULA] Ori C

5.1. A polar spot model for [FORMULA] Ori C

[FORMULA] Ori C was first analysed in a similar way as [FORMULA] Ori E. We determined the rotational velocity using the Oiii[FORMULA]5592 line. With the high resolution of our data we are able to examine closely the line core, which is mostly unaffected by stellar wind effects. However, as can be seen in Fig. 5, the line profile shows significant deviations from a pure rotationally broadened photospheric profile. We find a value of [FORMULA] for [FORMULA] by fitting only the line core. This is much lower than earlier values derived using Hei and Balmer lines. Stahl et al. (1996) point out that this could be due to an unknown broadening mechanism in the Hei-lines. They found [FORMULA] as an upper limit.

[FIGURE] Fig. 5. Profile of the Oiii[FORMULA]5592 line of [FORMULA] Ori C. A computed profile with the fitted value of 32 km s-1 for [FORMULA] is overplotted. Note the strong wings in the observed profile which have not been taken into account in the fit since they do not show the shape of a rotational profile.

The stellar parameters of [FORMULA] Ori C are, except for the period, not well known. The period of [FORMULA]d found by Stahl et al. (1996) is confirmed by the new data. From [FORMULA] and the period, we can determine the stellar radius, if the inclination of the rotation axis is known and the period is assumed to be due to rotation. Donati & Wade (1999) discussed all available observations and found an inclination of [FORMULA]. This number has to be considered as quite uncertain.

Howarth & Prinja (1989) derived a radius of [FORMULA]. With their error estimate, the maximum radius is about [FORMULA]. Our value for [FORMULA], although small, favors larger radii. Assuming [FORMULA], which is about our lower limit for [FORMULA] and yields convenient values, and an inclination angle of [FORMULA], we obtain [FORMULA]. The minimum radius for an assumed [FORMULA] is [FORMULA].

As a compromise we assumed a radius of [FORMULA] which for the fixed period leads to [FORMULA]. In the following this set of parameters is called Model 1.

Alternatively, we investigated a model with [FORMULA] and [FORMULA]. This is the set of parameters for Model 2.

It was shown by Stahl et al. (1996) that He and metal equivalent width curves are in phase. The time series of Hei[FORMULA]4471 and Hei[FORMULA]4713 are shown in Fig. 6. Since we do not know the broadening mechanism of Balmer and Hei lines we concentrate on the metal lines.

[FIGURE] Fig. 6. Profiles of the Hei[FORMULA]4471 (left) and 4713 (right) lines of [FORMULA] Ori C versus phase. Phases are from -0.5 to 1.5 with a bin size of 0.06. A velocity range of [FORMULA] around the rest wavelength is shown. Tick marks on the right border show phases where data has been taken.

The assumption of local thermodynamic equilibrium in the model atmospheres used limits the applicability, especially in the case of the O6pe-star [FORMULA] Ori C. With the ATLAS9 model atmospheres which we used, it was not possible to calculate model atmospheres for the effective temperature of [FORMULA] Ori C of [FORMULA]K (Howarth & Prinja 1989). We used an effective temperaure of [FORMULA]K and log [FORMULA]. These are the parameters closest to [FORMULA] Ori C, where ATLAS9 models can still be computed.

Of course, we cannot expect to reproduce absolute values of the equivalent widths using these parameters. However, we believe that the qualitative behaviour of the line profiles and the relative strength of the equivalent widths due to abundance concentrations on the stellar surface can be reproduced reasonably well.

As described above, we synthesized series of spectral lines for the two models of [FORMULA] Ori C. Low abundance spots corresponding to a decentered dipole geometry turned out to be necessary - the spots do not lie exactly opposite each other. Thus we have four variables instead of two to parametrize the locations of the spots. Spectral lines of Civ, Oiii and Siiv have been synthesized. The parameters are summarized in Table 4.


[TABLE]

Table 4. Parameters of the geometry of the models. Positions and sizes of the spots are the same for all three ions; within error-limits there is no need for an offset between them. Metals are depleted in the spots. For the assumed decentered dipole, [FORMULA] and [FORMULA] are necessary for both spots independently. One rotational pole is at [FORMULA].


The equivalent width curve of Civ[FORMULA]5812 is shown in Fig. 7. In order to compare models and data, the equivalent widths are normalized to the same mean value in this figure. This was necessary as the model does not reproduce the absolute value of the equivalent widths. Data and model of the profiles of Civ[FORMULA]5812 and Oiii[FORMULA]5592 versus phase are shown in Fig. 8.

[FIGURE] Fig. 7. Normalized equivalent width of the Civ[FORMULA]5812 line of [FORMULA] Ori C versus phase. The full line shows the equivalent width of Model 1, the dashed line of Model 2.

[FIGURE] Fig. 8. Profiles of the Civ[FORMULA]5812 (top) and Oiii[FORMULA]5592 (bottom) lines of [FORMULA] Ori C versus phase (left column: data, center column: polar spots (Sect. 5.1), right column: equatorial spots (Sect. 5.2)). Phases are from -0.5 to 1.5 with a bin size of 0.06 (data) and 0.05 (model). A velocity range of [FORMULA] around the rest wavelength is shown. Tick marks on the right border show phases where data have been taken.

The models are able to qualitatively reproduce the line shapes at all phases of the series reasonably well. The normalized equivalent width curves show the same tendency as the data. The two models can hardly be distinguished in the time series, but there are differences in the models' equivalent width curves. The models are not good enough to distinguish between the parameters, but if we take the average model, we derive the following values:

[EQUATION]

5.2. An equatorial spot model for [FORMULA] Ori C

Given the uncertainties of the model presented above - especially in the model atmospheres - the agreement with the observations is reasonably good. Nevertheless, we also investigated an alternative model with high abundance spots at the equator. The element distribution for such a model is roughly similar to the polar spot model, but it shows a different behaviour in the time series.

With such a model, we find a reasonable fit with the data if the spots are placed at [FORMULA], [FORMULA] respectively [FORMULA], [FORMULA]. Radii are [FORMULA] and [FORMULA]. Abundances are [FORMULA] and [FORMULA]. A stellar radius of [FORMULA] was used for these calculations.

The normalized equivalent widths of this model are shown in Fig. 9. The agreement is remarkably good, but note that the equivalent widths are normalized to the same mean value.

[FIGURE] Fig. 9. Normalized equivalent width of the Civ[FORMULA]5812 line of [FORMULA] Ori C versus phase. The full line shows the equator spot model.

Data and model of the profiles of Civ[FORMULA]5812 and Oiii[FORMULA]5592 versus phase are shown in the right column of Fig. 8. It can be seen from this figure that the equatorial model produces line profile variations which fit the observations qualitatively better than the polar model. Both models fail to reproduce the line wings and the slight red-shift of the absorption feature crossing the lines.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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