Astron. Astrophys. 324, 281-288 (1997)

6. Discussion

Our computations were carried out for 2-D models of solar thermal convection. In the frame of our procedure, the radiative transfer was treated more explicitly than in an earlier paper (Atroshchenko & Gadun 1994). This is important for the realistic modeling of the upper atmospheric layers. However, these 2-D models were obtained with the old ODF tables of Kurucz (1979). One may expect that a multidimensional simulation of the solar granulation with a larger list of atomic and molecular lines will give higher temperatures in the outer part of the atmosphere and higher values of iron and lithium abundances obtained from Fe I and Li I lines.

We have synthesized spectral lines without taking into account possible effects of horizontal radiative transfer. We expect that effects of multidimensional radiative transfer do not change our main conclusions (at least qualitatively), because a) we used weak lines, b) our main conclusions were based on the analysis.

Our abundances were computed within the frame of LTE. The question arises whether NLTE may change our results. For lithium the answer is simple. Results of Steenbock & Holweger (1984), Pavlenko (1994), and Carlsson et al. (1994) show that NLTE effects for lithium lines are rather small in the solar atmosphere. NLTE lithium abundance corrections are less than 0.05 dex. Moreover, lithium resonance lines are photoinization controlled (Thomas 1957). Indeed, NLTE lithium lines are less sensitive to the temperature structure of the outer atmospheric layers in comparison with LTE (Pavlenko 1995; Pavlenko et al. 1995). For iron lines the picture is more complicated. Solanki & Steenbock (1988) predicted, for a cool HSRA-like model (Gingerich et al. 1971), differences of about 0.1 dex between LTE and NLTE iron abundances determined for Fe I lines with low excitation potentials.

For weak iron lines we found that the influence of the multidimensional convection on the abundance determination is about 0.1 dex. A slightly larger value (up to 0.16 dex for ) was obtained for the Li I line. Furthermore, we do not confirm the suggestion of Kurucz (1995) that the convection should weaken the lithium lines. Our computations show that the 2-D models produce even stronger Li lines than 1-D homogeneous ones. Note, however, that this result depends upon the spectrum of inhomogeneities in 2-D time-dependent models.

Kurucz (1995) suggested that the multidimensional convection in metal-deficient dwarfs of solar  may affect the observed lithium abundances (  = 2.1; Spite & Spite 1982). Many investigators trust that the Spite plateau halo stars have conserved their primordial lithium (Rebolo 1991). So Kurucz's conclusion seems critical for many branches of modern astrophysics. However a few suggestions made by Kurucz should be reconsidered. For example, he used the model granule extended over the whole atmosphere. Due to a higher temperature inside that granule, the ratio in the region of Li I lines formation region increases. As a result, the lithium abundances, obtained from the Li I line modeling should increase also. From multidimensional computations it is well known that the temperature over a granule region may be cooler as well as hotter than the surrounding matter (at different geometric heights in the atmosphere, see Atroshchenko & Gadun 1994). We note, however, that overshooting convection in halo dwarfs may change their nature with respect to the Sun. Indeed, in halo dwarf atmospheres we can see deeper layers that may have a larger contrast. On the other hand, the radiative cooling of granules in metal-poor atmospheres is more efficient due to the same reason, namely the opacity decrease. To obtain more reliable conclusions the numerical simulation of 2-D and 3-D convection is needed. That work is in progress.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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