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Astron. Astrophys. 332, 928-938 (1998)

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3. Analysis

3.1. Atomic data

For the line identification we mainly used the line lists by Thévenin (1989, 1990), which are based on the lines identified in the solar spectrum by Moore et al. (1966). These lists are completed with the line lists of Van Winckel (1995) and Bakker (1995). We first performed a complete identification of the high S/N spectra (S/N [FORMULA] 250) of HR 1865 and HR 1017 which we used to identify and de-blend the lower quality spectra of the IRAS sources.

In recent years considerable efforts have been made in calculating improved model stellar atmospheres and oscillator strengths ([FORMULA]) for atomic transitions. Unfortunately, high precision gf-values are still unavailable for many elements. We have taken the excitation potential and the oscillator strengths mainly from the inverted solar abundance analysis of Thévenin (1989, 1990). The atomic data for O I, Mg I, Mg II, Si I, Si II, Ti I, Ti II, Cr I, Cr II, Fe II, Sr I, Sr II, Y I, Y II, Zr I and Zr II are obtained from the automatic data bank of Kurucz (http://cfa-www.harvard.edu/amp/data/kur23/sekur.html) and the mailserver of the `Vienna Atomic Line Data Base'. For the Fe I oscillator strengths we used the critical compilation of Lambert et al. (1996).

3.2. Determination of the atmospheric parameters

We used the CDROM grid of LTE model atmospheres of Kurucz (1993) in combination with his abundance calculation programme WIDTH9. A model atmosphere is uniquely determined by the metallicity, the effective temperature ([FORMULA]), the gravity ([FORMULA]) and the microturbulent velocity ([FORMULA]). We used input models with a solar metallicity Z for HR 1865 and HR 1017 and Z=-0.5 for the IRAS-sources with [FORMULA] =2 [FORMULA].

The determination of these atmospheric parameters were solely based on our high-resolution spectra. Quantitative photometric analysis is hampered by the uncertainty on the amount of circumstellar reddening, the possible anomalous circumstellar reddening law and by the inaccurate calibration of the photometric systems for supergiants in general. The photometry can therefore only be used as a first guess for the finer spectroscopic analysis.

3.2.1. The effective temperature

A spectroscopic estimate for [FORMULA] is found by forcing the abundances of an ion to be independent on the lower excitation potential of the transitions. For F-type supergiants, only Fe I lines are suitable for such an analysis since this method is only usable for ions with a large number of weak lines having a large spread in excitation potential. Moreover, for supergiants in the temperature range of our programme stars, non-LTE effects on the Fe I lines are small (Venn 1995b).

During our research it became clear that even a few unprecise oscillator strength values can limit the precision of this method considerably. When using the Fe I oscillator strengths of Thévenin we encountered the same problem for every star: the effective temperature determined on the base of the Fe I lines was some 500K higher than the temperature based on the Fe II lines. Moreover, the temperature estimates of the reference stars were higher than the temperatures found in the literature.

First we situated this discrepancy in the departure of local thermodynamic equilibrium (non-LTE effects). The LTE underabundance of iron due to overionisation of Fe I in F supergiants amounts from [FORMULA] 0.03 dex (F8 supergiants) to 0.2 dex (F0 supergiants) (Venn 1995b; Boyarchuk & Lyubimkov 1983; Boyarchuk et al. 1985, 1988). A shift of 0.2 dex in abundance corresponds to a temperature shift of [FORMULA] 200 K. It turned out, however, that for every star [FORMULA] (= [FORMULA] (Fe I)- [FORMULA] (Fe II)) was too large (e.g. 700 K for HR 1865 and 400 K for HR 1017) to be caused solely by non-LTE effects. Note that by limiting our abundance analysis to lines with an equivalent width smaller than 150 mÅ , we focus on lines formed in deeper layers where the non-LTE effects are known to be smaller.

We have then limited the Fe I lines to only those listed in the critical compilation of [FORMULA] -values by Lambert et al. (1996). They re-discussed the Fe I gf-values by comparing the gf-values of several authors (see Lambert for references). By using these oscillator strengths, all problems concerning discrepancy of [FORMULA], [FORMULA] or [FORMULA] (non-LTE effects) disappear! It is extremely important to limit the used Fe I lines to transitions with a precise oscillator strength. For Fe II we don't have any lines in common with Lambert. Therefore we have compared the [FORMULA] -values of Thévenin with these of Lambert: the [FORMULA] -values of Thévenin were systematically 0.19 [FORMULA] 0.08 smaller than these of Lambert, due to the fact that Lambert used 7.51 for the solar Fe abundance and Thévenin 7.67. We have thus increased the [FORMULA] -values of Fe II of Thévenin with 0.19. The solar abundances of the other chemical elements are from Grevesse (1989). For HR 1865, HR 1017 and IRAS 22223+4327 we derived a temperature of 7500 K, 6500 K and 6500 K respectively (e.g. see Fig. 1).

[FIGURE] Fig. 1a and b. The excitation potential-abundance diagram and the equivalent width-abundance diagram for IRAS 22223+4327.

For the faint object IRAS 04296+3429 it turned out to be impossible to determine the effective temperature with this method due to the lack of good quality Fe I lines. A rough estimate is found when comparing the spectra of the IRAS-stars with those of the two reference stars. Fig. 2 shows the spectra of the four programme stars in the wavelength coverage between 6110 Å and 6160 Å . This is an interesting spectral interval since besides the O I triplet and Ba II line, also Fe I and Fe II lines are present. The ratio of the Fe II line-strengths versus the Fe I lines gives an indicator of the effective temperature for these four stars of similar gravity.

[FIGURE] Fig. 2. Spectra of HR 1865, HR 1017, IRAS 22223+4327 and IRAS 04296+3429.

The resemblance between the spectra of HR 1017 and IRAS 22223+4327 is striking. This is confirmed by our spectroscopic temperature assessment of [FORMULA] =6500 K for HR 1017 and IRAS 22223+4327. For IRAS 04296+3429 the ratio of the Fe II to Fe I lines is higher than the ratio of HR 1017 and lower than this of HR 1865. We therefore estimate the temperature of IRAS 04296+3429 to be approximately 7000 K. To test the consistency of these [FORMULA], we have checked the excitation potential-abundance diagram of IRAS 04296+3429. The slope is small and positive, but it indicates that the temperature departure is still less than 300 K, within the bounds of the estimated accuracy.

Hrivnak (1995) has determined the spectral type of the IRAS sources on the basis of low resolution spectra and concluded that both IRAS 04296+3429 and IRAS 22223+4327 are G0Ia supergiants. This spectral classification was used by Kwok et al. (1995) and Bakker et al. (1996) to estimate the effective temperature of 5000-5500 K for both stars. This low temperature is, however, inconsistent with our high-resolution spectra! Not only because in the lower excitation potential-abundance plot, a significant upward trend shows up, but also because neutral lines of heavy elements should appear in the spectra at those temperatures. The strong Y I line at 6435 Å for instance, would have an equivalent width of 20 mÅ for the abundance computed from the Y II lines at a temperature of 5500 K and log g = 1.0.

We want to stress the fact that for reddened, chemically peculiar supergiants, high-resolution data are definitely needed for accurate fundamental parameter determinations. The line regions, used in the low resolution spectra to infer the spectral type, are influenced by strong resonance lines of s-process elements like Ba and Y. With strong s-process enhancements, like observed in IRAS 05341+0852 by Reddy et al. (1997), the optical spectrum is even completely dominated by lines of s-process isotopes. In our opinion, the chemical peculiarity and certainly the strong enhancements of s-process isotopes, make standard spectral classification difficult.

3.2.2. Gravity and the microturbulent velocity

We derived the model gravity by implying that different ions of the same element yield the same abundances to within 0.1 dex. For F supergiants, the only element useful for this purpose is again Fe by the lack of alternatives with enough lines of both ionisation stages. The observed hydrogen Balmer lines are affected by emission so we did not use them to constrain the gravity. A change in the [FORMULA] value by 0.5 makes the abundances derived for the two ionisation stages differ by in between 0.11 and 0.26 dex. The total uncertainty on the gravity of these objects is, however, more uncertain than the [FORMULA] 0.3 this method suggests, since it does not take into account other uncertainties on the abundances which are more difficult to quantify, like non-LTE effects, systematic [FORMULA] errors etc. Note that the main conclusions of this work (see discussion) are based on abundance ratios, which are much less influenced by uncertainties in effective temperature and gravity than absolute values.

The microturbulent velocity for each star has been determined by forcing the Fe I abundances to be independent on the equivalent width ([FORMULA]) (see Fig. 1 for IRAS 22223+4327).

IRAS 04296+3429 has not enough lines available with a good range in equivalent width for a reliable estimate. We assumed [FORMULA] =4.0 [FORMULA]. Nevertheless, the value of microturbulence is not critical in this analysis since only weak lines ([FORMULA] 150 mÅ) are included in the final average abundances. The use of weak lines also means that radiative damping terms will not be important.

A synopsis of the atmospheric parameters for the four stars is listed in Table 1.

3.3. Error analysis

3.3.1. Internal errors

The standard deviation [FORMULA] on the abundance of an element for which we observed more than five lines is a good indicator of the consistency of the chemical analysis (e.g. see Table 2). A typical value for [FORMULA] is between 0.10 and 0.25 dex.

For a good model in ionisation and excitation equilibrium, [FORMULA] is mainly determined by non-systematic errors on the equivalent width and especially on the oscillator strength. The equivalent widths were measured by fitting a Gaussian curve to the absorption lines.

To check our [FORMULA] -values for systematic errors, we compared our LTE abundance analysis of HR 1865 with a similar study of Venn (1995b). Venn mainly used the oscillator strengths of Führ et al. (1988); Wiese & Martin (1980); Führ et al. (1981); Wiese & Fuhr (1975) and O' Brian et al. (1991). No systematic differences occur, so we continued to use the [FORMULA] -values of Thévenin for most atomic species. Since we did not account for the hyperfine broadening of transitions of atoms with an odd atomic number, the abundances of these ions are slightly overestimated.

Other contributors to the scatter could be differential non-LTE effects and non-detected blends. The blends of the IRAS stars, which have broader lines, are detected by comparing the spectra with the narrow lined reference stars.

3.3.2. Inaccuracies on the model parameters

The model parameters ([FORMULA], [FORMULA] and [FORMULA]) are not independent: a change in one parameter generally induces a shift in another for the spectroscopic requirements (ionisation balance, independence of the abundance of an ion versus the excitation potential and equivalent width) to be fulfilled. A typical shift of 0.5 dex in the gravity induces a temperature shift of 300-400 K, so that the ionisation balance still would be maintained. We refer to Table 3 of Van Winckel (1997) for a quantitative estimation of the influence of the different uncertainties on the abundance determination. The temperature uncertainty has by far the biggest influence on the abundance accuracy, especially for ions with the smallest occupation level since they are most influenced by uncertainties on the ionisation balance induced by errors on the temperature and gravity.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998