8. Abundance results
Below we present a short description of the abundance results based on both applied approaches.
8.1. Standard approach
With atmospheric parameters specified by the usual way we calculated abundances for 26 elements (see Table 2), but in this section we will briefly mention only C and O abundances.
Table 2. Phased elemental abundances for Cep and averaged data (standard approach)
Table 2. (continued)
Table 2. (continued)
Our value of the relative carbon abundance obtained with standard approach [C/H]=-0.31 0.12 is exactly the same as that derived by Luck & Lambert (1992): [C/H]=-0.33. For oxygen, those authors found the relative abundance [O/H]=-0.18. Our analysis yielded similar value [O/H]=-0.10 0.04.
8.2. Non-standard approach
In Table 3 we give the abundances for seven phases and averaged values obtained using the non-standard approach. First of all, it should be noted that there are no noticeable differences between the results from the different spectra exposed at different phases. As has been already mentioned, the abundance based on lines is referred to W=0 mÅ (see Fig. 5). It was found using a formal extrapolation procedure and in this specific case the value represents the scattering with respect to the extrapolating line. The same procedure was adopted for determination of the nickel abundance based on lines, the number of which is sufficiently great (see the discussion below).
Table 3. Phased elemental abundances for Cep and averaged data (non-standard approach)
Table 3. (continued)
Table 3. (continued).
Carbon. This element is apparently deficient in Cep atmosphere. Such a deficiency implies that Cep has already passed the red supergiant phase.
In their pioneer work Luck & Lambert (1981) detected observed anomalies of the CNO abundances in galactic supergiants which are regarded as having passed the first dredge-up phase. All the subsequent spectroscopic studies confirmed these results, but they also brought to light the apparent discrepancy between the theory and observations. Theoretically expected carbon deficiency appeared to be less than that observed, while the remarkable oxygen deficiency observed in supergiants was not theoretically predicted at all.
With the new approach we have found that for Cep the relative carbon abundance  = -0.21. It agrees well with the theoretical prediction for the star suffered the first dredge-up (for example, Schaller et al. 1992give  = -0.17 after the first dredge-up for the star of 6 ; this theoretical value was interpolated between results for two models of 5 and 7 of the solar metallicity).
Nitrogen. While carbon appears to be deficient, nitrogen abundance has a tendency to be increased. This is in good agreement with the theoretical prediction concerning CN anomalies after the dredge-up phase. Our result is  = +0.43, while from the calculations of Schaller et al. (1992) one can obtain  = +0.42. As an independent confirmation, one can also mention the theoretical result for a star of 5-7 obtained by El Eid & Champagne (1995). They give  = 0.41-0.43.
Oxygen. The relative oxygen abundance derived by us is  = +0.06. Schaller et al. (1992) predict  = -0.03 after the first dredge-up. We can state that within the standard error of abundance analysis these values are in the close agreement.
8.3. Short conclusion on CNO abundances
The problem with a discrepancy between the theory and observations concerning CNO abundances is probably due to the wrong estimate of the gravity value, which is the result of parameter underestimation. The lines of , and available for the analysis are usually weak in the supergiant spectra (we do not consider the strong 7771 Å absorption). Therefore abundances derived from these lines are practically not sensitive to variation, but strongly depend upon changes. Artificially decreasing , we force these lines, with high excitation potentials of the lower level, to produce larger equivalent widths in the calculations. This is clearly demonstrated in Fig. 6, where dependences between the calculated equivalent widths of selected CNO lines and model atmosphere gravity are shown (for reference, we also show the behaviour of a gravity sensitive line of an ionized atom, in this case ). was 6000 K for all the models of the different gravities.
It is quite understandable, that after the comparison of the observed equivalent width of a certain CNO line with a theoretical one calculated from a model with artificially lowered gravity, the conclusion is that the considered element is relatively deficient.
8.4. Other elements
Surface abundance should also be altered after the first dredge-up phase (or even earlier - on the main sequence due to, e.g., turbulent diffusion), when processed material appears in the upper layers of the stellar atmosphere. Enhanced sodium is an ordinary feature of the atmospheres of supergiants. The theoretical ground of this phenomenon was discussed by Denissenkov (1988). Sasselov (1986) also explained the sodium overabundance in the supergiants as a result of cycle operation. Our result for Cep testifies about the modest sodium enrichment. We did not obtain a remarkable sodium overabundance, but this is exactly the same value that could be expected from the recent theoretical consideration (see, Table 2 from the work by El Eid & Champagne 1995).
The - elements do not show any significant anomalies in the atmosphere of Cep with one possible exception for sulfur, which seems to be slightly overabundant (but the value is rather big).
The iron-group elements show the solar-like ratios (M/Fe). Note, that using the traditional approach we were not able to keep ionization balances for /, /, / together with preserving the / equilibrium (see Table 2). With the new approach the situation seems to be much better (see averaged abundance values from Table 3).
It should be noted that Lyubimkov & Boyarchuk (1983) concluded that the NLTE effects are important not only for iron itself, but also for iron-peak elements. Really, the analysis of the great number of lines in Cep spectra has shown that their behaviour resembles that of lines. Therefore, for abundance determination we used the same method as for iron abundance determination based on lines (extrapolation of the "[/]-W" dependence for the sample of lines to value W=0 mÅ).
The number of available lines of other neutral species (, , , etc) is not large, therefore there is no sense applying such a procedure. In this case, one can recommend the use of only the weakest lines (having W less than 50 mÅ) for abundance determination that could minimize the influence of the NLTE effects on the resulting abundances.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999