Influence of inelastic collisions with hydrogen atoms on the non-local thermodynamic equilibrium line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars

Context. Iron plays a crucial role in studies of late-type stars. In their atmospheres, neutral iron is the minority species, and lines of Fe I are subject to the departures from local thermodynamic equilibrium (LTE). In contrast, one believes that LTE is a realistic approximation for Fe II lines. The main source of the uncertainties in the non-LTE (NLTE) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms. Aims. Our aim is to investigate the effect of Fe I + H I and Fe II + H I collisions and their different treatments on the Fe I/Fe II ionisation equilibrium and iron abundance determinations for three Galactic halo benchmark stars (HD 84937, HD 122563, and HD 140283) and a sample of 38 very metal-poor giants in the dwarf galaxies with well known distances. Methods. We performed the NLTE calculations for Fe I-Fe II by applying quantum-mechanical rate coefficients for collisions with H I from recent papers. Results. We find that collisions with H I serve as efficient thermalisation processes for Fe II, to an extent that the NLTE abundance corrections for Fe II lines do not exceed 0.02 dex, in absolute value, for [Fe/H] greater than or similar to -3, and reach +0.06 dex at [Fe/H] similar to -4. For a given star, different treatments of Fe I + H I collisions lead to similar average NLTE abundances from the Fe I lines, although discrepancies in the NLTE abundance corrections exist for individual lines. By using quantum-mechanical collisional data and the Gaia-based surface gravity, we obtain consistent abundances from the two ionisation stages, Fe I and Fe II, for red giant HD 122563. For turn-off star HD 84937, and subgiant HD 140283, we analyse the iron lines in the visible and the ultra-violet (UV, 1968-2990 angstrom) ranges. For either Fe I or Fe II, abundances from the visible and UV lines are found to be consistent in each star. The NLTE abundances from the two ionisation stages agree within 0.10 dex and 0.13 dex for two different treatments of Fe I + H I collisions. The Fe I/Fe II ionisation equilibrium is achieved for each star of our stellar sample in the dwarf galaxies, with the exception of stars at [Fe/H] less than or similar to -3.7.