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

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4. [FORMULA] Ori E

A crucial parameter needed to model the line profile variations is the rotational velocity. For determination of [FORMULA], the line Cii[FORMULA]4267 was used. This line is a close blend, but this does not affect the determination of [FORMULA]. To take care of the intrinsic variations in the line profile, the maximum flux spectrum of the series was used instead of an individual spectrum. A rotational profile was fitted to the spectrum. We derive [FORMULA], which is in good agreement with previous works.

With the period of [FORMULA]d and a stellar radius of [FORMULA] (Groote & Hunger 1982) this leads to [FORMULA] and [FORMULA].

In order to extract the equivalent width of the lines we fitted a Lorentzian profile of the shape


to the data. The local continuum is fitted with a straight line. The equivalent width then is derived from an integration of the fitted profile. In this way, the scatter in the equivalent width measurements is smaller than by direct integration. In Fig. 1 and Fig. 2 the equivalent widths of Hei[FORMULA]4173 and Cii[FORMULA]4267 are shown versus phase.

[FIGURE] Fig. 1. Equivalent width of the Hei[FORMULA]4713 line of [FORMULA] Ori E versus phase (for a period of 1.19084 d and an epoch of [FORMULA]). The curve shows the equivalent width computed from of the model.

[FIGURE] Fig. 2. Same as Fig. 1 but for the Cii[FORMULA]4267 line.

The long time basis of our equivalent width curves of Hei[FORMULA]4471, combined with the data from other authors (Groote & Hunger 1997, 1977; Hunger et al. 1989), made it possible to improve the period of [FORMULA] d found by Hesser et al. (1977). We found the slightly different value of [FORMULA] d.

If we assume that this period difference is due to a period change, we derive [FORMULA]yr-1 or [FORMULA]yr. (Note that the longer period is a mean over 22 years.) The rotational braking time due to angular-momentum loss in the wind can be estimated according to Brandt (1970, p.84). With a mass-loss rate of [FORMULA][FORMULA]yr-1 (Groote & Hunger 1997) a spin-down time of [FORMULA]yr is derived, using [FORMULA] ([FORMULA], c.f. Mihalas & Conti 1980) and [FORMULA][FORMULA].

The results differ by one order of magnitude. Thus it seems indeed possible that the period difference might be due to spin-down. It should be noted, however, that the period given by Hesser et al. (1977) was derived from a time basis of 793 d only. Our period is based on data covering 22 yr. Both studies quote the same error for the period. We think that the error given by Hesser et al. (1977) is a bit optimistic and that the period difference might be an artefact.

In this paper we work with data covering only a span of 41 days and the influence on our work of such a small period-correction is negligible.

With the present set of parameters we have a complete stellar model of [FORMULA] Ori E. For the Kurucz stellar atmospheres we adopted a polar temperature of [FORMULA] K, [FORMULA] and [FORMULA]. The only free parameter left is the abundance distribution of the elements.

The phase dependence of the equivalent widths shows two absorption maxima which are separated by approximately [FORMULA]. For simplicity we assumed a centered magnetic dipole with circular abundance spots at the poles. The spot sizes can be varied individually in the model. The poles are located at a angular distance [FORMULA] from the rotational poles. The element-abundances are assumed to be constant inside and outside the spots. It was not our aim to determine locations of abundance variations of orders of a few percent. The priority was to reproduce qualitatively the behaviour of the spectral lines versus phase. Therefore, we only varied the size and chemical abundance of the spots and the surrounding stellar surface, until a reasonable match in the observed and modeled time series was achieved.

We are mainly interested in the behaviour of He- and metal-lines. The lines Hei[FORMULA]4471, 4713, 4921, Cii[FORMULA]4267 and Siiii[FORMULA]4552, 4567 were modeled. Four of them are shown in Fig. 3 and Fig. 4. The parameters used to model the profile variations are shown in Table 3. [FORMULA] and [FORMULA] are the radii of the two spots, [FORMULA] and [FORMULA] are the abundances inside and outside of the spots, respectively. The absolute abundances of the carbon line Cii[FORMULA]4267 are known to be given incorrectly by BHT (Kaufer et al. 1994). Their value is about 0.7 dex too low.

[FIGURE] Fig. 3. Gray-scale representation of the profiles of Hei[FORMULA]4471 (top) and 4713 (bottom) of [FORMULA] Ori E versus phase (left frames: observed data, right frames: model). Phases are from -0.5 to 1.5 with a bin size of 0.06 (data) and 0.05 (model), respectively. A velocity range of [FORMULA] around the rest wavelength is shown. Tick marks on the right border show phases where data have been taken.

[FIGURE] Fig. 4. Same as Fig. 3 but for Cii[FORMULA]4267 (top) and Siiii[FORMULA]4567 (bottom).


Table 3. Ion-abundances inside ([FORMULA]) and outside ([FORMULA]) of the spots in our model. The parameters of obliquity, [FORMULA] (angle between the rotational and magnetic axes) and the sizes of the spots at the magnetic poles ([FORMULA] and [FORMULA]) are the same for all elements. There is an offset of [FORMULA] between them. In the spots, He is overabundant and the metals are depleted. The absolute abundances of the carbon line Cii[FORMULA]4267 are known to be determined incorrectly by BHT (Kaufer et al. 1994). Their value is about 0.7 dex too low.

Our model nicely reproduces the phase variations of the observed line profiles versus phase. The polar spots for all ions are of the same size on the stellar surface. In the caps, He is overabundant and the metals are depleted. There is an offset of [FORMULA] between He- and metal-caps within error limits. This corresponds to a distance of the centres of the spots on the stellar surface of [FORMULA]. Also the different behaviour of the different Hei-lines is reproduced. The shape and velocity pattern of the modeled time-series spectra strongly depend on size and position of the spots. It is not very sensitive to the absolute abundance in the spots and in the vicinity.

After comparison of the time-series, the equivalent widths have been calculated as described above. The modeled equivalent widths variation of Hei[FORMULA]4713 and Cii[FORMULA]4267 are shown as full drawn lines in Fig. 1 and Fig. 2. The model reproduces the tendency of the equivalent widths. For the carbon line it delivers an adequate fit to the data. Hei[FORMULA]4713 is not properly fitted. Fine-tuning has not been tried. Obviously, a slightly off-centered dipole could produce an even better fit. NLTE-effects may also play a role in the differences between model and data, especially for the Hei-lines but also for Cii[FORMULA]4267.

Reproduction of the line-profiles means that the wings and core of the spectral lines at all phases are fitted correctly. The velocity distribution on the stellar surface at different times matches the model, i.e. no large scale motions other than rotation are present. Correspondence between the synthetic profile and the data is better than three percent of the continuum at all phases. No other simple model geometry was found to be able to reproduce the data equally well.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000