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Astron. Astrophys. 357, 920-930 (2000)

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4. Analysis of the spectra

Spectral observations were performed at ESO with the 1.4m Coudé Auxiliary Telescope (CAT) and the Coudé Échelle Spectrometer (CES). The detector was ESO CCD #34 with 2048 pixels along the direction of dispersion (the pixels are [FORMULA] wide). Table 1 details the observations, i.e. time, phase and wavelength coverage. The resolving power for all spectra was [FORMULA] (resolution at 6705 Å: 67.1 mÅ) and signal-to-noise ratio was S/N = 100 to 120.

Fig. 3 shows the variability of the Li I feature; it shows the spectra, as well as the equivalent width and radial velocity of each of the two components of this feature. The quantitative analysis of the spectrum of this star in the regions 6675-6735 Å, 6120-6180 Å and 6615-6675 Å, to our knowledge, is carried out for the first time. In Fig. 4 the normalized spectrum in the region of the lithium blend 6708 Å for the rotational phases 0.055 and 0.419 is shown. The variability of the spectral lines, which change both their position (shift of the line as a whole) and the profile appearance, is evident. These changes are the largest and impressive for the lithium blend 6708 Å. The other lines, in particular 6690.9 Å, 6706.7 Å, 6727.7 Å also reveal some variability. Apparently we observe surface abundance variability not only of lithium, but of other elements too, connected with different geometry and probably physical conditions in the spots and in the non-spotted photosphere.

[FIGURE] Fig. 3. Spectra of the star HD 83368 made in 1996 in residual intensity scale (North et al., 1998). The rotational phases are given on the right. At the left side of each spectrum, the position of the continuum is shown. The lines due to spot 1 and spot 2 are indicated. Below: lithium line equivalent width and radial velocity variation for the two spots: dark circles - spot N 1, open circles - spot N 2.

[FIGURE] Fig. 4. The comparison of two spectra of HD 83368 at the phases 0.419 and 0.055 nearest to the maximum and minimum respectively of the longitudinal magnetic field. Continuous line: the spectrum for phase 0.419; dashed line: for phase 0.055. In the last spectrum the lines of Nd III and Pr III are remarkably enhanced.

The quantitative analysis of the spectra of HD 83368 was carried out by the method of synthetic spectra with the help of Tsymbal's code STARSP (Tsymbal, 1994) and Kurucz's atmospheric models (Kurucz, 1993). We used the Kurucz line lists (Kurucz, 1995, CDROM 23) and the VALD list (Piskunov et al., 1995, Kupka et al., 1999), accessible on INTERNET (URL http://cefa-www.harvard.edu/amdata/ampdata/kurucz23/sekur.html and http://www.astro.univie.ac.at/ vald , respectively). The data for the doubly ionized rare earth element (REE) were taken from the list of Reader & Corliss (1980). For Nd III , Pr III , Ce II and Ce III we used the level energy data and gf data provided to us by Cowley (1998), Bord (1998) from Michigan University and by Sugar (1998) from NIST (National Institute of Standards and Technologies). For identification purpose we have also calculated the positions of the lines of the ionized rare elements using the energy level data of NIST (URL http://www.aeldata.nist.gov ) and, for Dy III , the energy levels from the paper of Spector et al. (1997). Due to the small observed spectral region and the insufficient covering of rotation phases we carried out only a preliminary analysis. We have tried to determine the mean chemical composition (in the photosphere and spots) for each observed rotational phase, using one atmospheric model with [FORMULA] and metal abundance [M/H]=0.0. The calculated spectra were convolved with the rotation profile with the value of [FORMULA]. This and other parameters for the calculations of the synthetic spectrum were chosen in accordance with the data of North et al. (1998). We also tried to calculate the synthetic spectra with other model atmospheres, changing [FORMULA] on [FORMULA] and [FORMULA] on [FORMULA]. The best agreement in the abundances computed from Fe I and Fe II lines was achieved for the model [FORMULA]. By fitting the calculated synthetic spectra with the observed ones we have found line intensity changes for several elements, depending on the rotational phase.

The values of [FORMULA] relative to hydrogen for the different phases are given in Table 2 (Columns 2 to 10). The number of lines used for abundance estimate and the errors for each element are given in Columns 11 and 12 of Table 2. Let us note that the estimated errors on the abundances depend mainly on the line intensities, numbers of lines, blending with other lines, accuracy of gf-values and inhomogeneous surface distribution of the element (and of other elements, due to blending), and therefore depend on the rotation phase too. Because of these difficulties we give only one estimated value of the error for all phases. The procedure of fitting observed and calculated spectra was carried out until the discrepancy for all the analysed lines of each element reached its minimum. The last three columns of Table 2 give, for comparison, the solar abundances (Kurucz, 1993) and the abundances for a similar roAp star, HD 24712, by Ryabchikova et al. (1997). HD 24712 also shows variability of chemical composition versus the rotational phase, but has no measurable Li 6708 Å line. We notice that the abundances and their behaviour for the majority of the elements (Fe, Ca, REE, light elements) are essentially similar to the case of HD 83368. The data for the light elements (C,N,O) in HD 24712 were taken from the paper of Roby & Lambert (1990).


Table 2. The element abundances for each rotation phase from the spectral range 6675-6735 Å.
a: from spectral range 6120-6180 Å;
b: these phases corespond to the maximum (minimum) of stellar magnetic field;
c: this estimate was obtained from line 6645.06 Å in the phase 0.768, nearest to 0.760.

  • For neutral iron, which shows small abundance variations with phase ([FORMULA] to [FORMULA]), such errors were estimated as 0.1 dex. For Fe II ([FORMULA] = -4.3 to -4.7), it was estimated to 0.2 dex. A more reliable value of the abundance of Fe II , taking into account the Zeeman line splitting, was obtained only for the phase 0.320 ([FORMULA] 6120-6178 Å) from the lines 6147 Å and 6149 Å, giving [FORMULA]. Some variability of abundance with rotational phases was also shown by other elements of the iron group: Ti II (-6.8 to -7.3), Cr I (-4.1 to -5.0) and Co I (-5.5 to -6.3).

  • The noticeable excesses of abundances in the atmosphere of this CrSrEu star relative to the solar ones were shown by Cr I (1.4 to 2.3 dex), Y I (2.8 to 3.4 dex), Ba II (0.9 dex) and by rare earths (2.0 dex on the average, see Table 2). Y and Ba are s-process elements like Sr, but no Sr lines are present in the spectral regions studied here.

  • We made an attempt to determine ourselves the value of the magnetic field from the line profiles of Fe II 6147 Å and 6149 Å (Fig. 5). We have computed the profiles of these lines taking into account the magnetic splitting for two values of the magnetic field: 2 kG, calculated by us as described in Sect. 2, and 11 kG (taking into account the Paschen-Back effect, see Mathys, 1995; Mathys & Hubrig, 1997). The calculated Fe II line profiles in Fig. 5a correspond to the flux from whole visible stellar surface with a homogeneous abundance. For a magnetic field strength of 2 kG, we can get a much better fit to the observe spectra when we assume that the surface of the star is covered with Fe II spots at [FORMULA] and [FORMULA] and Pr II spot at [FORMULA] (where l is longitude in spherical coordinates relative to the observer) - see Fig. 5b. For a field strength of 11 kG, we did have to exclude the Fe II spot at [FORMULA] and Pr II spot in order to get reasonable agreement (we used only one main spot of Fe II with [FORMULA], the nearest to the centre of visible hemisphere of star for this phase 0.320, i.e. [FORMULA]). However, the fit for a 2 kG field is still much better suggesting that the field strength is indeed closer to 2 kG than to 11 kG.

  • Abundance variability with the rotational phase was found also for the light elements: C I (-3.8 to -4.5), N I (-3.0 to -4.0), O I (-3.4 to -4.4). The more reliable value for O I is probably [FORMULA], obtained in the region 6120-6180 Å from some O I lines near 6156-6158 Å for the phase 0.320. The analysis of two weak O I lines in the lithium region (6726.28 Å and 6726.54 Å) is difficult due to the blending with the Ca II line 6726.06 Å, the intensity of which also changes with the phase. The Ca I abundance change is (-5.1 to -5.6) with an error of 0.1 dex.

  • For the phase 0.055, corresponding to the passage of one of the lithium spots through the central meridian (in this phase the spot is near the centre of the visible hemisphere), we have found the maximum abundances of N I (-3.1), Cr I (-4.1), Fe I (-4.6) and most of the rare earth elements (see Tables 2).

    The phase 0.419, nearest to the central position of the other lithium spot, does not show strengthening of some rare earth elements lines (see Fig. 4 for Nd III and Pr III lines and Tables 2).

[FIGURE] Fig. 5. a  The calculated profiles of Fe II 6147.74 Å and 6149.26 Å lines with the magnetic splitting. Continuous thick line: observed spectrum for the phase 0.320, dashed line: the calculated one for the field of 2 kG (Zeeman splitting), and thin line: for the field of 11 kG (Paschen-Back effect). Both spectra were calculated assuming a homogeneous surface abundance. b  The comparison of the observed and calculated spectra for Fe II with taking into account surface spot structure of star (see Sect. 6.1). Also, dashed line - for 2 kG and thin continuous line - for 11 kG.

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Online publication: June 5, 2000