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Astron. Astrophys. 347, 348-354 (1999)

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4. Fe II lines and other indicators

4.1. Fe II lines

Results from Fe II lines (Holweger et al. 1990; Biémont et al. 1991; Hannaford et al. 1992) are in good agreement with the meteoritic value. However, other recent analyses (Pauls et al. 1990; Raassen & Uylings 1998a; Schnabel et al. 1999) cast some doubt on this agreement. The first two works conclude to "high" values for the iron abundance: [FORMULA] = 7.66 [FORMULA] 0.06 and [FORMULA] = 7.59 [FORMULA] 0.06 respectively, whereas the last authors derive a "low" solar iron abundance: [FORMULA] = 7.42 [FORMULA] 0.09, even lower than the meteoritic value! Are we going to face for Fe II lines, the same situation as for Fe I lines? The answer is no.

The work of Pauls et al. (1990) has been revised by Hannaford et al. (1992) and reasons given for the "high" result.

The analysis of Raassen & Uylings (1998a) is based on new theoretical semi-empirical transition probabilities calculated using the orthogonal operator approach. These authors show that their theoretical results agree well with recently measured oscillator strengths and lifetimes (see also Raassen & Uylings 1998b). But the tests only concern strong lines in the ultraviolet as well as lifetimes, which are essentially determined by the stronger lines in the branches. The solar lines of interest for abundance analyses are one to two orders of magnitude fainter than the lines tested. When the theoretical oscillator strengths of the solar lines, with low log gf- values around -3, are tested against the best gf-values obtained for Fe II lines using lifetimes and branching fraction measurements (see e.g. Hannaford et al. 1992; Schnabel et al. 1999), it appears that the mean differences, from 11 lines in common, is large: [FORMULA]log gf (experiment - theory) = +0.11 [FORMULA] 0.06. We thus suspect that, even if the theoretical gf-values for strong lines are correct, the relevant data for much fainter solar lines are too small by a rather large amount explaining the "high" abundance value found by Raassen & Uylings (1998a).

The same type of comments has also been made in the past concerning the results of Biémont et al. (1991) who also used solar Fe II lines with semi empirical theoretical gf-values of Kurucz (1988) to derive the solar abundance of iron (Hannaford et al. 1992; Grevesse & Noels 1993; Grevesse et al. 1995). Theoretical techniques have unfortunately not yet been able to achieve the accuracies of experimental techniques for faint lines of heavy elements.

Schnabel et al. (1999) rescaled the experimental gf-value of Heise & Kock (1990) with new very accurate lifetime data and also rescaled the solar abundance analysis of Holweger et al. (1990) to these new gf-values. The new [FORMULA], 7.42 [FORMULA] 0.09, is somewhat puzzling.

We made a new analysis of Fe II lines with the lines shown in Table 3. Actually the choice of solar Fe II lines is limited by the very few lines for which the oscillator strength is known with accuracy. We added two lines from Hannaford et al. (1992) at 722.2 and 722.4 nm because their gf-values perfectly agree with those of Schnabel et al. (1999) and deleted two lines difficult to measure in the solar spectrum from Schnabel et al.'s list (562.7 and 744.9 nm). For the 13 lines in Table 3, our equivalent widths agree with those of Holweger et al. (1990). With our new model atmosphere, constructed from the analysis of Fe I lines (Sect. 3), the solar abundance of iron derived from Fe II lines now leads to [FORMULA] = 7.50 [FORMULA] 0.095, in agreement with the result obtained from the Fe I lines and from the meteorites. However, the dispersion of the results (Fig. 7) is uncomfortably large .

[FIGURE] Fig. 7. The iron solar abundance values against the mean optical depth of line formation ([FORMULA]) for our 13 solar Fe II lines as derived with our new model (see text).


Table 3. Fe II lines in the solar spectrum .
1. log gf-values obtained by Schnabel et al. (1999); values for the lines 722.2 and 722.4 nm are from Hannaford et al. (1992)
2. Present work adopting the new photospheric model, [FORMULA] = 0.8 km s-1, and an enhancement factor of 2 for the collisional damping constant.

A few comments have to be made concerning the Fe II lines. The new theory for computing accurate cross-sections for the broadening of spectral lines by collisions with hydrogen atoms (Anstee & O'Mara 1995; Barklem & O'Mara 1997; Barklem et al. 1998a; Barklem et al. 1998b) is not applicable to ions. We therefore used the classical enhancement factor and used different values, 1.5, 2 and 2.5 respectively. Hopefully the lines of Table 3 are not very sensitive to this parameter: when E is enhanced from 1.5 to 2.5, the [FORMULA] decreases by 0.025 dex only. We adopted E = 2 in the results shown in Table 3.

The Fe II results of Table 3 also depend on the microturbulent velocity. When it is decreased from 1 km s-1 (Schnabel et al. 1999) to the value we adopted from the Fe I lines, 0.8 km s-1, [FORMULA] increases by 0.03 dex.

Actually, we have thus been able to increase the result of Schnabel et al., [FORMULA] = 7.42 up to 7.50, in agreement with the meteorites, just by making a slightly different choice of lines ([FORMULA] [FORMULA] +0.02; the line of Schnabel et al. at 744.9 nm leads to a very small value, 7.25), microturbulent velocity ([FORMULA] [FORMULA] +0.03), enhancement factor ([FORMULA] [FORMULA] +0.01), the new model atmosphere playing, as expected, a negligible role ([FORMULA] [FORMULA] +0.01).

The very large uncertainty of the Fe IIresults is certainly related to the mean uncertainty of the oscillator strengths . This is something which is not new. This is clearly shown by the Fe I and Fe II results when comparing the mean uncertainty of the log gf-values of the lines and the dispersion of the abundance results. In the case of Fe I , for the Oxford lines, [FORMULA]log gf = 0.02 dex and [FORMULA] = 0.037 dex whereas for the Kiel-Hannover lines, [FORMULA]log gf = 0.045 dex and [FORMULA] = 0.050 dex. For Fe II , the best oscillator strengths available are unfortunately less accurate with [FORMULA]log gf = 0.066 dex leading to [FORMULA] = 0.095! A detailed discussion of the oscillator strengths available for Fe I and Fe II lines has recently been made by Lambert et al. (1996).

4.2. Other indicators

The solar photospheric abundance of iron has also been derived from other indicators namely the forbidden lines of Fe II , very faint and difficult to measure with some accuracy in the solar spectrum (Grevesse & Swings 1969), the very high excitation lines of the 4f-5g, 4f-6g and 5g-6h transitions of Fe I in the far infrared (Johansson et al. 1994; Schoenfeld et al. 1995) and also coronal matter which, under certain circumstances, shows photospheric abundances (Feldman 1992).

The present result based on our new model agrees with the abundance results derived from these analyses which agree themselves, with rather large uncertainties in some cases, with the low abundance i.e. the meteoritic value. We emphasize that the forbidden Fe II lines already solved in 1969 the solar iron abundance problem existing at that time (see Sect. 1)!

When our new model is used with the wings of very strong Fe I lines as suggested by Anstee et al. (1997), the abundance result decreases somewhat below the meteoritic value. This is not surprising and probably related to the difficulties one has to reproduce line profiles with homogeneous models.

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Online publication: June 18, 1999