Improving spectroscopic lithium abundances. Fitting functions for 3D non-LTE corrections in FGK stars of different metallicity

Context.Accurate spectroscopic lithium abundances are essential in addressing a variety of open questions, such as the origin of a uniform lithium content in the atmospheres of metal-poor stars (Spite plateau) or the existence of a correlation between the properties of extrasolar planetary systems and the lithium abundance in the atmosphere of their host stars. Aims.We have developed a tool that allows the user to improve the accuracy of standard lithium abundance determinations based on 1D model atmospheres and the assumption of local thermodynamic equilibrium (LTE) by applying corrections that account for hydrodynamic (3D) and non-LTE (NLTE) effects in FGK stars of different metallicity. Methods.Based on a grid of CO5BOLD 3D models and associated 1D hydrostatic atmospheres, we computed three libraries of synthetic spectra of the lithium lambda 670.8 nm line for a wide range of lithium abundances, accounting for detailed line formation in 3D NLTE, 1D NLTE, and 1D LTE, respectively. The resulting curves-of-growth were then used to derive 3D NLTE and 1D NLTE lithium abundance corrections. Results.For all metallicities, the largest corrections are found at the coolest effective temperature,T-eff= 5000 K. They are mostly positive, up to + 0.2 dex, for the weakest lines (lithium abundance A(Li)(1DLTE)= 1.0), whereas they become more negative towards lower metallicities, where they can reach - 0.4 dex for the strongest lines (A(Li)(1DLTE)= 3.0) at [Fe/H] = - 2.0. We demonstrate that 3D and NLTE effects are small for metal-poor stars on the Spite plateau, leading to errors of at most +/- 0.05 dex if ignored. We present analytical functions evaluating the 3D NLTE and 1D NLTE corrections as a function ofT(eff)[5000 horizontal ellipsis 6500 K], logg[3.5 horizontal ellipsis 4.5], and LTE lithium abundanceA(Li) [1.0 horizontal ellipsis 3.0] for a fixed grid of metallicities [Fe/H] [ - 3.0 horizontal ellipsis 0.0]. In addition, we also provide analytical fitting functions for directly converting a given lithium abundance into an equivalent width, or vice versa, a given equivalent width (EW) into a lithium abundance. For convenience, a Python script is made available that evaluates all fitting functions for givenT(eff), logg, [Fe/H], andA(Li) or EW. Conclusions.By means of the fitting functions developed in this work, the results of complex 3D and NLTE calculations are made readily accessible and quickly applicable to large samples of stars across a wide range of metallicities. Improving the accuracy of spectroscopic lithium abundance determinations will contribute to a better understanding of the open questions related to the lithium content in metal-poor and solar-like stellar atmospheres.