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Astron. Astrophys. 319, 637-647 (1997)

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3. The spectral analysis with the synthetic spectrum method

One of the most accurate methods to derive stellar abundances is based on the comparison of the observed spectrum with a synthetic spectrum. This approach requires the selection of an atmospheric model for the studied star. The main parameters of the model are the effective temperature [FORMULA], the surface gravity [FORMULA], the metallicity [FORMULA], and the microturbulent velocity [FORMULA].

We assumed as first estimate [FORMULA] according to previous determinations for the iron abundance (Adelman, 1973; Savanov & Malanushenko, 1990) and [FORMULA] from Faraggiana & Gerbaldi (1992). We assumed an "a priori" microturbulent velocity equal to 2 km s-1. Then, we derived the effective temperature from the comparison of observed and computed energy distributions. Observed energy distributions are the visual spectrophotometric observations from Pyper & Adelman (1985) and from the Breger (1976) catalog and the UV data from the TD1 S2/68 experiment (Jamar et al., 1976). Computed energy distributions were derived from Kurucz (1993a) models.

Fig. 2 shows the comparison of the observed energy distributions with those corresponding to models having effective temperatures equal to [FORMULA] K and [FORMULA] K respectively. The best agreement between the observed and computed visual and ultraviolet ([FORMULA] [FORMULA] 1650 Å) fluxes is yielded by the model with [FORMULA] = [FORMULA] K. The disagreement shortward [FORMULA] 1650 Å, where the Si I discontinuities at 1514.35 Å  and 1674.03 Å  occur, may partly be due to a Si abundance lower than 10 times the solar one, as it was assumed for the model. However, previous determinations (Adelman 1973, Savanov & Malanushenko, 1990) indicated solar abundance for Si. In this paper we found solar abundance as upper limit, because no Si lines were observed in the [FORMULA] 6693-6721 Å  range. On the other hand, comparison with few stars observed with TD1 S2/68 of about the same spectral type or earlier, indicates an ultraviolet excess of [FORMULA]  CrB (Table 2).

[FIGURE] Fig. 2. Observed and computed energy distributions. The crosses indicate the energy distribution obtained by assuming the presence of a [FORMULA] Boo companion with [FORMULA] = [FORMULA] K  and the squares indicate a [FORMULA] Boo companion with [FORMULA] = [FORMULA] K.

[TABLE]

Table 2. Ultraviolet magnitude differences for [FORMULA]  CrB compared with other stars of similar spectral type (data derived from fluxes observed with TD1-S2/68)


[FORMULA]  CrB is the primary member of a spectroscopic binary system with a companion which has about the same spectral type, since from visual observations [FORMULA] - [FORMULA] is about constant and equal to [FORMULA] (Kamper et al., 1990). No spectral lines of the companion have never been detected. Now, if we assume that the companion is a [FORMULA]  Boo star with high rotational velocity and [FORMULA] the UV excess could be explained. Table 3 gives the energy distribution obtained by summing up the flux [FORMULA] and [FORMULA]. [FORMULA] is obtained from the model for [FORMULA] divided by 5 and [FORMULA] from the model for [FORMULA] multiplied by 4/5, [FORMULA] corresponding to [FORMULA] - [FORMULA] = [FORMULA]. Assuming for [FORMULA]   [FORMULA] [FORMULA] = [FORMULA] K, the UV excess is still lower than the observed one, while assuming [FORMULA]  =  [FORMULA] K the UV excess is slightly larger than the observed one. A [FORMULA] Boo companion with parameters [FORMULA]   [FORMULA]   [FORMULA] K, [FORMULA] and [FORMULA] can explain the observed UV excess (Table 3).


[TABLE]

Table 3. Observed energy distribution and that computed assuming the presence of a [FORMULA] Boo companion


The Balmer discontinuity is the only feature in the energy distribution dependent on gravity. For [FORMULA] = [FORMULA] K, it is reproduced at best by the model with [FORMULA].

To analyse the high resolution spectrum in the range [FORMULA] 6693 - 6721 Å  we computed synthetic spectra with the SYNTHE code (Kurucz, 1993b) and compared them with the mean spectrum. As input data we used the ATLAS9 model with parameters [FORMULA] = [FORMULA] K, [FORMULA], [FORMULA], [FORMULA] = 2 km s-1, and the Kurucz (1993 b) line lists, with some modifications. For all the Fe I lines of the Li region we adopted wavelengths, energy levels, and [FORMULA] from Nave et al. (1994), when available. For Fe I 6712.676 Å , [FORMULA] from Kurucz (1993b) was replaced by [FORMULA], on the basis of the agreement between the observed and computed features both in [FORMULA]  CrB and Procyon. In fact , we used the Procyon atlas from Griffin & Griffin (1979) to check the wavelength scale of [FORMULA]  CrB and to estimate the reliability of the atomic data for the few lines common to the two stars. A model with parameters [FORMULA] = [FORMULA] K, [FORMULA], and [FORMULA] =2 km s-1   was used for Procyon. For Li at 6708 Å  we considered both the isotopes Li6 and Li7 and all the hyperfine structure components listed in Kurucz (1995).

As first iteration for the synthetic spectrum, we assumed abundances 10 times the solar ones for all the elements. The spectrum was broadened for a gaussian instrumental profile corresponding to a resolving power of 45000. To match the observed and computed wavelength scale, the observed spectrum was shifted toward the red by 3 km s-1, corresponding to a wavelength shift [FORMULA] [FORMULA] =0.07 Å . Then, as a second step, we decreased the abundances of C, Al, and Si, owing to the predicted presence of some lines which were not observed, and, at the same time, we increased the abundances of Li, La, Ce, Sm, and Gd owing to the presence in the spectrum of observed lines much stronger than the predicted ones.

After several trials with different values for the rotational velocity vsin i, we estimated that vsin i  = 11 km s-1   is the best suited value to reproduce the observed spectrum. Actually the rotational velocity, derived by the stellar radius and the rotational period of 18.5 days is about 3.5 km s-1, hence the broadening is mainly due to the magnetic field. Our choice agrees with the value vsin i [FORMULA]  11.2 km s-1  found by Mathys (1995).

The range [FORMULA] 6693 - 6721 Å  is too short and there are too few lines in it in order to determine a value for the microturbulent velocity [FORMULA]. The comparison of synthetic spectra computed with different values of [FORMULA] (0, 2, and 4 km s-1) has shown that the only lines affected by [FORMULA] in an appreciable way are Gd II at 6694.867 Å  and 6702.093 Å , the blend Gd II and Ce II at 6704.147 Å  and 6704.524 Å , Ce II at 6706.051 Å , the blend Ca I and Gd II at 6717.681 Å  and 6718.130 Å , and finally Ce II at [FORMULA]  6720.280 Å . Because there are no other lines of Gd , Ce and Ca weak enough to be independent from [FORMULA] we have been not able to estimate any value for the microturbulent velocity and we arbitrarily assumed it equal to 2 km s-1. Therefore, the abundances derived for Gd , Ce and Ca depend on this choice of [FORMULA].

After having fixed the wavelength scale, the rotational velocity, and the microturbulent velocity, we modified the abundances until we obtained the best agreement between the observed and computed spectra. The final abundances are listed in the last column of Table 4. Abundances from previous determinations are also given for comparison. In Fig. 3 the mean observed spectrum is compared with the final computed spectrum. The Li blend was computed with the terrestial ratio Li6 /Li7 =0.081 (Anders & Grevesse, 1989). The upper plot shows the computed spectrum not broadened for rotational velocity and magnetic field, the lower plot shows the computed spectrum broadened for vsin i =11 km s-1.


[TABLE]

Table 4. The abundances [FORMULA] of [FORMULA]  CrB relative to the solar ones from Anders & Grevesse (1989) are compared with previous determinations.


[FIGURE] Fig. 3. Comparison of the observed spectrum (thick line) in the Li region with the synthetic spectrum (thin line) computed for a model with [FORMULA] =8000 K, [FORMULA], [FORMULA], abundances listed in last column of Table 4, and microturbulent velocity [FORMULA] =2 km s-1. Upper plot: the computed spectrum is not broadened for the rotational velocity. Lower plot: the computed spectrum is broadened for a rotational velocity v sin i = 11 km s-1.

The upper plot of Fig. 3 shows that, owing to the lack of atomic data, several features are still unidentified, so that it is very hard to obtain a good agreement between the observed and the computed spectra. The lower plot shows that the agreement is not very good also when the lines are well identified. In fact for [FORMULA]  CrB, in addition to the usual problems occurring when observed and computed spectra are compared (difficulty in placing the continuum, uncertainty in the [FORMULA] values and line wavelengths, lack of atomic data), there are also problems due both to the spectrum variability, and to the effect of the magnetic field which was not considered in our computations. For instance, the comparison of two spectra taken at two different phases shows that several lines have different intensities, in particular the lines of Ce II and Gd II (see Fig. 1). The conclusion is that the final abundances of Table 4 have to be considered only estimates to be used as starting point for further analyses which will take into account also the magnetic field effects.

Landstreet (1996) discusses the several effects of magnetic field and surface inhomogeneities which lead to systematic errors when spectra are modeled using conventional spectrum synthesis codes. He concludes that the standard method treating "the abundances as constant over the visible disk should be able of getting reasonably useful abundances (accurate within a factor of two or three compared to the real abundances averaged over the central part of the visible hemisphere)". Hence, in the case of [FORMULA]  CrB, the abundances derived from a spectrum averaged over the whole rotational period should be accurate enough to show the abundance pattern of this magnetic peculiar star. A confirmation of this remark is given by the reasonably good agreement among determinations of abundances obtained at different epochs and in different spectral regions by different authors (Table 4).

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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