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Astron. Astrophys. 323, 909-922 (1997)

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3. Model atmospheres and line formation

3.1. Model atmospheres

In the context of standard theoretical LTE model atmospheres considerable improvements have been obtained by Kurucz (1995b, and references therein). His new opacity line lists are enormously extended compared to the ones of Kurucz (1979), which have been the standard for more than a decade. Certainly many working groups benefit very much from this work. The model atmosphere program we use (Gehren 1977, Fuhrmann et al. 1993) also rests upon the opacity distribution functions (ODF) issued by Kurucz. In this respect it is interesting to investigate how much the new ODFs influence the temperature structure of the standard solar model.

There is, however, one aspect we have to mention in advance, namely the discussion of the solar iron abundance. Holweger et al. (1990) found log [FORMULA] (Fe)= 7.48, a value considerably lower than log [FORMULA] (Fe)= 7.67, the one proposed by Blackwell et al. (1984) and recommended in Anders & Grevesse (1989). Since then the literature saw a lot of pros and cons (e.g. Holweger et al. 1991, Grevesse 1991, Hannaford et al. 1992, Grevesse & Noels 1993, Milford et al. 1994, Anstee & O'Mara 1995, Blackwell et al. 1995, and references therein), "final" words (Biémont et al. 1991) and arguments against this (Kostik et al. 1996). But in spite of the continued discussion, there is currently a preference to assume the meteoritic value log [FORMULA] (Fe)= 7.51 to be the most probable one and this is also adopted in our analysis. Kurucz (1992b), however, took log [FORMULA] (Fe)= 7.67 for his opacity calculations, because he referred to the compilation of Anders & Grevesse (1989). Thus, compared to the meteoritic value, the iron opacities enter his tabulated ODF files with a systematic offset of [FORMULA]  dex. Were it not this element which is the dominant line blanketing contributor to our stellar model atmospheres, this would not cause doubt about the tabulated opacity calculations. Even more, the recent investigation of Bell et al. (1994) has shown that the Kurucz line lists obviously produce more absorption lines than are actually observed in the solar spectrum. Of course, those lines which are only predicted, can be shifted in wavelength position, but Bell et al. particularly criticize the absence of a balance of observed versus predicted lines that is anyhow required.

In this situation we decided not to use the original Kurucz ODFs, but instead to generate interpolated ODFs scaled by -0.16 dex, although this scaling inevitably treats all elements in the same way. In view of a much faster hardware and with respect to metal-poor stars with their intrinsically non-solar abundance patterns, there can be no doubt that drawbacks of this kind can only be solved by opacity sampling (OS) methods instead of using pretabulated ODFs. Therefore our model atmosphere program is currently revised and tested to allow for this option. For the time being and in what follows we rely however on the ODF approximation and the scaling described above. Note, that this choice does not affect differential analyses to first order.

The models recently generated this way either assume relative solar abundances (but scaled by -0.16 dex) or an abundance pattern with [FORMULA] -elements (O, Ne, Mg, Si, S, Ar, Ca and Ti) increased by +0.4 dex. Except for a small grid around Procyon, whose microturbulence parameter is close to [FORMULA] km s-1, all calculations were done with [FORMULA] km s-1 (in the case of Procyon this difference in microturbulence changes the temperature structure by some 30 K).

In Fig. 4 we show the comparison of our old ("GRS88") and new solar model. As is obvious from inspection the model with the new ODFs (labeled "high Fe") results in a slightly steeper temperature gradient, i.e. a model atmosphere that is also somewhat hotter in the deeper layers. Scaling of these opacities by -0.16 dex however reduces the differences to about [FORMULA] K. This is by no means an unexpected result, and since iron produces much of the line blanketing, it addresses the necessity to know its abundance to a very high precision. Although Fig. 4 reveals significant changes as a result of new opacities, a good deal of it is due to the increased solar iron abundance value log [FORMULA] (Fe)= 7.67, compared to log [FORMULA] (Fe)= 7.54 Kurucz used in 1979. Note, however, that this result is claimed only on the grounds of Fig. 4, i.e. for the solar model. A completely different picture can be expected from molecular opacities of cooler stars, where much progress has occurred in recent years.

[FIGURE] Fig. 4. Atmospheric temperature stratifications vs. optical depth for models with solar parameters [FORMULA] K and [FORMULA]. Bottom: "GRS88" refers to the old model (cf. Fuhrmann et al. 1993) which employed Kurucz (1979) opacities. The new ODF data result in the model labeled "high Fe". The dot-dashed curve is obtained from ODF-scaling by -0.16 dex (see text). Top: differences in temperature in the sense GRS88 - high Fe and GRS88 - this work (dot-dashed). All models have been calculated with a mixing-length parameter [FORMULA]

Very recently Castelli, Gratton & Kurucz (1997) recalculated the solar ATLAS9 model by means of an ODF, where the high iron abundance is replaced by the meteoritic value. There are considerable changes between both models, albeit a second test, in which Castelli et al. scale all line opacities by -0.2 dex, also reveals that the integral effect of other elements is obviously more important. The model with the -0.2 dex reduced opacities decreases a gap in the H [FORMULA] region of observed and computed fluxes, but conversely introduces discrepancies longward of 5800 Å. These calculations again remind us that line blanketing is a dominant contributor to the atmospheric structure and now as before a source of uncertainties (for recent progress reports in line identifications and calculations see e.g. Nave & Johansson1993a, 1993b and Kurucz 1995c).

3.2. Line formation

One consequence of the changed structure of the new solar model atmosphere is a slight decrease in the effective temperature value derived from Balmer lines. Whereas our previous models (Fuhrmann et al. 1993) more or less reproduced the observations with 5780 K, the new calculations provide [FORMULA] K (cf. Fig. 5 and 6). A similar effect is present in the tracings of Procyon as discussed in the next section, but decreases in the models of metal-poor stars.

[FIGURE] Fig. 5. Balmer line profiles of H [FORMULA] for two solar models [FORMULA] K, [FORMULA] =4.44 (top) and [FORMULA] K, [FORMULA] =4.44 (below) compared to the Moon (=reflected sunlight) spectrum. The calculated wings for [FORMULA] K are slightly too deep, a [FORMULA] K lower effective temperature value is indicated. Bottom: spectrum synthesis of [FORMULA] 800 unadjusted, but convolved (rotation, macroturbulence + instrumental profile) metal lines. In spite of existing discrepancies between theory and observation (e.g. Kurucz 1995cfor a recent reference) it is most obvious that there is enough information to trace the Balmer line wings of H [FORMULA] from the "high points" in panel b

[FIGURE] Fig. 6. Same as Fig. 5, but for H [FORMULA], which is superposed by strong line-blanketing. Bottom panel: spectrum synthesis of [FORMULA] 3100 unadjusted, but convolved atomic + molecular lines. As in Fig. 5, the comparison of panels b and c shows that tracing the Balmer line wings from the "high points" in panel b is feasible at the resolution of the FOCES spectrograph

In view of the fact that the F OCES spectrograph produces spectra that cover a large part of the visual region, and as a result of our new grid of model atmospheres, a completely revised Fe I and Fe II line list of astrophysical oscillator strengths and damping parameters had to be established. All calculations were done in LTE and applied to the Kitt Peak Solar Flux Atlas (Kurucz et al. 1984). For this sample of iron lines ([FORMULA]) we derive a (depth-independent) microturbulence value of [FORMULA] km s-1. Rotational broadening is assumed to be [FORMULA] km s-1 and broadening by macroturbulence is taken into account by a radial-tangential profile of [FORMULA] km s-1 for stronger lines, and up to [FORMULA] km s-1 for weak lines (cf. Gray 1977).

Fig. 7 compares our astrophysical gf -values to those of Kurucz (1992a). As could have been expected there is considerable scatter in the oscillator strengths, but the a verage scale is practically the same. This is, of course, no striking argument in favour or against a particular value of the solar iron abundance (cf. Sect. 3.1). Our gf -values result from a prespecified temperature structure, turbulence parameters and an adopted solar iron abundance. But, on the other hand, it is interesting to see that our gf -values on average compare to the one of Kurucz if we adopt the solar iron abundance to be the meteoritic value.

[FIGURE] Fig. 7. Comparison of astrophysical versus theoretical (Kurucz 1992a) iron oscillator strengths. Top: Fe I, bottom: Fe II. There is no systematic difference [FORMULA] (Kurucz - this work) if we discard the few mavericks indicated by open symbols. The solar abundance assumed in deriving the astrophysical gf -values is the meteoritic value log [FORMULA] (Fe)= 7.51

To apply the method proposed in the next section, we also had to analyse the profiles of the few magnesium lines available in the visible. Most of them possess fairly well-known gf -values, especially the Mg Ib lines, where we directly adopt the absolute oscillator strengths from the literature. Radiation damping constants [FORMULA] are taken from Wiese et al. (1969) and Chang (1990), whereas the damping parameters from van der Waals ([FORMULA]) broadening are part of our differential analysis of the Kitt Peak Solar Flux Atlas. Stark effect damping ([FORMULA]) has a small influence on the strong lines and is only considered for [FORMULA] and 5528 (cf. Gray 1992); isotopic wavelength shifts, however, are small and not taken into account. Table 2 summarizes the atomic data of the Mg I lines employed in the analyses.


Table 2. Line data of Mg I lines

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Online publication: May 26, 1998