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Astron. Astrophys. 333, 644-646 (1998)

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3. Results and discussion

Fig. 1 shows the spectral region around the Li I line at the observed rotation phases. The wavelength scale has been first transformed to a heliocentric one, then corrected by the radial velocity [FORMULA]  km s-1 (Mathys et al. 1996) to put it in a rest frame. More details about the observations and reduction procedure were given by Hack et al. (1997).

[FIGURE] Fig. 1. Spectra of the star HD 83368 made in 1996 in residual intensity scale. The rotational phases are given on the right. At the left and right side of each spectrum, the position of the continuum is shown. The lines due to spot 1 and to spot 2 are indicated.

The strong variations of the profile and position of the Li blend at 6708 Å are evident (Fig. 1).

For our preliminary analysis of the variations of the profile of the Li blend, we have measured the line position ([FORMULA]), the equivalent width (EqW) and the central depth ([FORMULA]).

These measurements were carried out by approximating the line profile with a gaussian by the standard least-squares method. The results for the strongest line of the Li blend are presented in Table 1. Fig. 2 shows the variations of [FORMULA] for the strongest of the two lines, the wavelength " [FORMULA] " for the lines corresponding to the two spots, as well as the longitudinal magnetic field H [FORMULA] versus the rotational phase.


Table 1. Wavelength, residual intensity and equivalent width of the strongest of two lines at each rotation phase.

[FIGURE] Fig. 2. Variation of the central depth of the strongest of the two lines (top) and of the wavelengths of both components of the lithium blend (middle). The curves show the fit by a sinusoidal law (see text). Bottom: mean longitudinal magnetic field. Open circles :Thompson's (1983) measurements; filled triangles : Mathys' (1991) measurements. Vertical bars give the measurement errors.

We used the measurements of the magnetic field made by Thompson (1983) and Mathys (1991).

Fig. 2 shows clearly that the cause of the variations shown in Fig. 1 are due to two diametrically opposed spots. We have approximated the [FORMULA] variation by a sinusoidal law (Fig. 2 in the middle) and we have represented with a full line the part from phase 0.25 to phase 0.75, when spot 1 is visible, and the part from phase 0.75 to 1.25 when spot 2 is visible. The lines due to the two spots are actually visible at phases 0.678 and 0.679 in Fig. 1. We can see that all the [FORMULA] measurements fit this law very well.

The mean position of the line is [FORMULA]  Å, but the position varies from [FORMULA]  Å to [FORMULA]  Å, corresponding to a radial velocity variation from [FORMULA]  km s-1 to [FORMULA]  km s-1. The amplitude of this RV variation may be considered as a lower limit to the projected rotational velocity which, according to Mathys (1995), amounts to [FORMULA]  km s-1. Therefore, our result is in perfect agreement with that of Mathys.

HD 83368 has a good Hipparcos parallax of [FORMULA]  mas, which, combined with [FORMULA], [FORMULA] and V, yields an estimate of the radius R. Since it is a close binary ([FORMULA], [FORMULA] according to the Bright Star Catalogue), the [FORMULA] index of Geneva photometry has to be corrected from [FORMULA] to [FORMULA] (assuming a G2V companion), implying [FORMULA]  K (North & Hauck 1993); on the other hand the A component has [FORMULA], which translates into [FORMULA] and [FORMULA]  R [FORMULA] if the error on [FORMULA] is [FORMULA]  K. This radius implies [FORMULA]  km s-1 and [FORMULA] for Mathys' [FORMULA]. Now, if one assumes that the spots coincide with the magnetic poles, the amplitude of our [FORMULA] curves may be written as [FORMULA], where [FORMULA] is the angle between the magnetic and rotational axes, and one gets [FORMULA]. The constraint on the [FORMULA] angle does not depend on the estimated radius and is formally stronger than that on the inclination i. However, the spot's observed velocity can only be a lower limit to the true radial velocity of its center, because of perspective and limb-darkening effects, and the value given here for [FORMULA] must be considered as a lower limit to the true angle as well.

The value [FORMULA] roughly coincides with the position of the Li I resonance doublet (whose effective wavelength is 6707.804 for a solar isotopic ratio Li6 /Li7, see e.g. Hack et al. 1997), though the difference is slightly more than 3 [FORMULA] (even when the uncertainty on the wavelength calibration - 6.7 mÅ at most - is included). This suggests that either the Li6 /Li7 ratio may be strongly enhanced relative to the solar value, if the line is mainly due to Li I indeed, or the line may be due to some unidentified transition of another species (e.g. a rare earth).

We also fitted a sinusoid to the [FORMULA] measurements. As can be seen from Fig. 2 (upper part), a good agreement is evident. The value of [FORMULA] increases from phase 0.25 and reaches its maximum at phase 0.5, when [FORMULA], i.e. the spectral line is not shifted. Then this spot moves with a positive velocity relative to the central meridian and the line depth decreases until phase 0.75. Unfortunately, we have no good coverage of the rotational period, especially for the phases 0.5 to 1.0. For this reason we cannot discuss in detail the variations due to the second spot.

The comparison of our results with the measurements of the magnetic field by Mathys (1991) and Thompson (1983) shows a fairly good correlation between the position of the lithium spots and the position of the magnetic poles. However, the maximum of [FORMULA] occurs slightly earlier (by about 0.15 d) than the maximum of the magnetic field. Actually Kurtz et al. (1992) found that the variations of the magnetic field and pulsations are in phase, while the mean light variation, which is thought to be associated with the abundance spots, lag behind the magnetic field by [FORMULA]  d. We think that our observations give a too poor coverage of the rotation period (and especially the maximum of [FORMULA] in the upper part of Fig. 2 is extrapolated) to allow us to decide whether these differences are real.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998