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

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3. New photospheric model

We thus face a problem. Using the best data we could adopt for the equivalent widths, thegf-values, the damping constants, the microturbulent velocity and the model atmosphere, the iron abundance, derived from Fe Ilines of different excitation energies (0 to 4.55 eV), strongly depends on the excitation energy (see Fig. 2). This dependence cannot be explained by possible small non-LTE effects (Steenbock 1985; Holweger 1988, 1996).

We know that the low excitation lines are generally formed higher in the photosphere than high excitation lines. Fig. 3 is the same plot as Fig. 2 but as a function of the mean optical depth of formation of the line ([FORMULA]) defined in a way suggested by Magain (1986). We see that most of the Oxford low excitation lines are formed higher in the photosphere than the Kiel-Hannover high excitation lines. As we know that low excitation lines are much more sensitive to the temperature than high excitation lines, it is tempting to solve the dependence of [FORMULA] on excitation and on log [FORMULA] by slightly decreasing the temperature of the Holweger & Müller (1974) model in the layers of concern in order to bring the results obtained with the low excitation lines down to the level of the high excitation lines without changing the result obtained from these lines. Note that we already suggested such a solution to the so-called solar iron problem (Grevesse et al. 1995; Grevesse & Sauval 1998).

[FIGURE] Fig. 3. The iron solar abundance values against the mean optical depth of line formation (log [FORMULA]) for our 65 solar Fe I lines as derived with the Holweger & Müller model (1974) using [FORMULA] = 0.85 km s-1. Representative points are indicated `o' for the Oxford set of lines and `h' for the Kiel-Hannover set.

We finally came up with the new model illustrated in Fig. 4 and listed in Table 2 (the full table is available at the CDS, but part of the table is included in the paper). Our new model started from the original Holweger & Müller (1974) for layers deeper than log [FORMULA] [FORMULA] -1.0. For higher layers we had to decrease the temperature gradually to reach a uniform [FORMULA]T = -200 K for layers higher than log [FORMULA] [FORMULA] -2.0. With this new model, the solar iron abundance derived from the Fe Ilines of Table 1 does not depend any more neither on the mean optical depth of formation nor on the excitation energy as illustrated by Figs 5 and 6. We also see, when comparing Fig. 6 and Fig. 2, that the results from high excitation lines, hardly depend on the temperature modification.

[FIGURE] Fig. 4. Temperature distribution against log [FORMULA] for the Holweger & Müller model (1974) (dotted line) and the new photospheric model (solid line).

[FIGURE] Fig. 5. The iron solar abundance values against the mean optical depth of line formation ([FORMULA]) for our 65 solar Fe I lines as derived with our new model (see text). Representative points are indicated `o' for the Oxford set of lines and `h' for the Kiel-Hannover set.

[FIGURE] Fig. 6. The iron solar abundance values against the excitation potential for our 65 solar Fe I lines as derived with our new model (see text). Representative points are indicated `o' for the Oxford set of lines and `h' for the Kiel-Hannover set.


[TABLE]

Table 2. New photospheric model


We derived the best microturbulent velocity in a way suggested by Blackwell et al. (1984): the best value being chosen as the value which leads to the smallest dispersion of the abundance results. We found [FORMULA] = 0.8 km s-1, very slightly smaller than Blackwell et al. (1984). With this microturbulent velocity and our new photospheric model, we find a solar abundance of iron of [FORMULA] = 7.497 [FORMULA] 0.048. We also note that the abundance anomaly for the 2.2 eV lines, found by Blackwell et al. (1984), has disappeared.

The result from the 33 Oxford lines, [FORMULA] = 7.514 [FORMULA] 0.036, is 0.035 dex larger than the result from the 32 Kiel-Hannover lines, [FORMULA] = 7.479 [FORMULA] 0.050. This small difference might possibly be related to the 0.026 ([FORMULA] 0.044) dex differences in the absolute scales of the oscillator strengths between the two groups (Sect. 2).

As we mention hereabove, our new model results from small modifications of the Holweger & Müller (1974) model; moreover this slight temperature decrease occurs in rather high photospheric layers. This new model will not lead to appreciable modifications in the absolute intensities predicted at the center of the solar disk. It will also not change appreciably the center to limb predictions. In other words, as the Holweger & Müller model satisfies these two criteria, i.e. agreement between predicted and observed absolute intensities and center to limb variations respectively, our new model also does.

We have to note that our new model, slightly cooler than the Holweger & Müller model, agrees, at least qualitatively, with a new semiempirical solar photospheric model constructed by Allende Prieto et al. (1998) from the direct inversion of observed line profiles.

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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