3D non-LTE abundance analyses of late-type stars

The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundances ratios, and our interpretations of them, strongly depend on the physical assumptions that dictate the generation of synthetic stellar spectra. Three-dimensional radiation-hydrodynamic (3D RHD) ``box-in-a-star'' simulations of stellar atmospheres offer a more realistic representation of surface convection occurring in late-type stars compared to traditional one-dimensional (1D) hydrostatic models. As evident from a multitude of observational tests, the coupling of 3D RHD models with line-formation in non-local thermodynamic equilibrium (non-LTE) today provides a solid foundation for abundance analysis for many elements. This review describes the ongoing and transformational work to advance the state-of-the-art and replace 1D LTE spectrum synthesis with its 3D non-LTE counterpart. In summary: 1) 3D and non-LTE effects are intricately coupled and consistent modelling thereof is necessary for high-precision abundances, which is currently feasible for individual elements in large surveys. Mean 3D (<3D>) models are not adequate as substitutes. 2) The solar abundance debate is presently dominated by choices and systematic uncertainties that are not specific to 3D non-LTE modelling. 3) 3D non-LTE abundance corrections have a profound impact on our understanding of FGK-type stars, exoplanets, and the nucleosynthetic origins of the elements.