A non-LTE study of neutral and singly-ionized iron line spectra in 1D models of the Sun and selected late-type stars

Aims. We evaluate non-local thermodynamical equilibrium (non-LTE) line formation for the two ions of iron and check the ionization equilibrium between Fe I and Fe II in model atmospheres of the cool reference stars based on the best available complete model atom for neutral and singly-ionized iron. Methods. We present a comprehensive model atom for Fe with more than 3000 measured and predicted energy levels. As a test and first application of the improved model atom, iron abundances are determined for the Sun and five stars with well determined stellar parameters and high-quality observed spectra. The efficiency of inelastic collisions with hydrogen atoms in the statistical equilibrium of iron is empirically estimated from inspection of their different influence on the Fe I and Fe II lines in the selected stars. Results. Non-LTE leads to systematically depleted total absorption in the Fe I lines and to positive abundance corrections in agreement with the previous studies, however, the magnitude of such corrections is smaller compared to the earlier results. These non-LTE corrections do not exceed 0.1 dex for the solar metallicity and mildly metal-deficient stars, and they vary within 0.21 dex and 0.35 dex in the very metal-poor stars HD 84937 and HD 122563, respectively, depending on the assumed efficiency of collisions with hydrogen atoms. Based on the analysis of the Fe I/Fe II ionization equilibrium in these two stars, we recommend to apply the Drawin formalism in non-LTE studies of Fe with a scaling factor of 0.1. For the Fe II lines non-LTE corrections do not exceed 0.01 dex in absolute value over the whole range of stellar parameters that are considered. This study reveals two problems. The first one is that gf-values available for the Fe I and Fe II lines are not accurate enough to pursue high-accuracy absolute stellar abundance determinations. For the Sun, the mean non-LTE abundance obtained from 54 Fe I lines is 7.56 +/- 0.09 and the mean abundance from 18 Fe II lines varies between 7.41 +/- 0.11 and 7.56 +/- 0.05 depending on the source of the gf-values. The second problem is that lines of Fe I give, on average, a 0.1 dex lower abundance compared with those of Fe II lines for HD61421 and HD102870, even when applying a differential line-by-line analysis with regard to the Sun. A disparity between neutral atoms and first ions points to problems of stellar atmosphere modelling or/and effective temperature determination.